diff --git a/.travis.yml b/.travis.yml index 4fa4e5430..d84b2bcc6 100644 --- a/.travis.yml +++ b/.travis.yml @@ -2,7 +2,7 @@ language: python python: - 2.7 - - 3.3 + - 3.5 notifications: email: false @@ -14,7 +14,7 @@ branches: before_install: - wget http://repo.continuum.io/miniconda/Miniconda-latest-Linux-x86_64.sh -O miniconda.sh - chmod +x miniconda.sh - - ./miniconda.sh -b + - ./miniconda.sh -b -p /home/travis/miniconda - export PATH=/home/travis/miniconda/bin:$PATH - conda update --yes conda - sudo rm -rf /dev/shm @@ -28,7 +28,7 @@ install: - cp quantecon/tests/matplotlibrc . script: - - nosetests --with-coverage --cover-package=quantecon + - nosetests --with-coverage --cover-package=quantecon --exclude=models #quantecon.models excluded from tests to prevent triggering the ImportWarning after_success: - coveralls diff --git a/MANIFEST b/MANIFEST index c398408bc..7adf65608 100644 --- a/MANIFEST +++ b/MANIFEST @@ -26,6 +26,8 @@ quantecon/quadsums.py quantecon/rank_nullspace.py quantecon/robustlq.py quantecon/version.py +quantecon/game_theory/__init__.py +quantecon/game_theory/normal_form_game.py quantecon/markov/__init__.py quantecon/markov/approximation.py quantecon/markov/core.py @@ -33,20 +35,6 @@ quantecon/markov/ddp.py quantecon/markov/gth_solve.py quantecon/markov/random.py quantecon/models/__init__.py -quantecon/models/arellano_vfi.py -quantecon/models/asset_pricing.py -quantecon/models/career.py -quantecon/models/ifp.py -quantecon/models/jv.py -quantecon/models/lucastree.py -quantecon/models/odu.py -quantecon/models/optgrowth.py -quantecon/models/uncertainty_traps.py -quantecon/models/solow/__init__.py -quantecon/models/solow/ces.py -quantecon/models/solow/cobb_douglas.py -quantecon/models/solow/impulse_response.py -quantecon/models/solow/model.py quantecon/random/__init__.py quantecon/random/utilities.py quantecon/tests/__init__.py @@ -75,5 +63,6 @@ quantecon/util/__init__.py quantecon/util/array.py quantecon/util/common_messages.py quantecon/util/external.py +quantecon/util/notebooks.py quantecon/util/random.py quantecon/util/timing.py diff --git a/README.md b/README.md index be6e2b2ca..cb6489b7e 100644 --- a/README.md +++ b/README.md @@ -67,3 +67,16 @@ modification, are permitted provided that the following conditions are met: LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +## Major Changes + +#### Ver. 0.3.1 (22-January-2016) + +1. Adds the ``quantecon/game_theory/`` sub package +2. Updates api for using ``distributions`` as a module ``qe.distributions`` + +#### Ver. 0.3 + +1. Removes ``quantecon/models`` subpackage and the collection of code examples. Code has been migrated to the [QuantEcon.applications](https://github.com/QuantEcon/QuantEcon.applications) repository. +2. Adds a utility for fetching notebook dependencies from [QuantEcon.applications](https://github.com/QuantEcon/QuantEcon.applications) to support community contributed notebooks. + diff --git a/docs/qe_apidoc.py b/docs/qe_apidoc.py index 197eb935f..4923ce60a 100644 --- a/docs/qe_apidoc.py +++ b/docs/qe_apidoc.py @@ -20,7 +20,7 @@ Examples -------- $ python qe_apidoc.py # generates the two separate directories -$ python qe_apidoc.py foo_bar # generates the two separate directories +$ python qe_apidoc.py foo_bar # generates the two separate directories $ python qe_apidoc.py single # generates the single directory @@ -49,28 +49,19 @@ :show-inheritance: """ -markov_module_template = """{mod_name} -{equals} - -.. automodule:: quantecon.markov.{mod_name} - :members: - :undoc-members: - :show-inheritance: -""" - -model_module_template = """{mod_name} +game_theory_module_template = """{mod_name} {equals} -.. automodule:: quantecon.models.{mod_name} +.. automodule:: quantecon.game_theory.{mod_name} :members: :undoc-members: :show-inheritance: """ -solow_model_module_template = """{mod_name} +markov_module_template = """{mod_name} {equals} -.. automodule:: quantecon.models.solow.{mod_name} +.. automodule:: quantecon.markov.{mod_name} :members: :undoc-members: :show-inheritance: @@ -119,10 +110,10 @@ ======================= The `quantecon` python library consists of a number of modules which -includes economic models (models), markov chains (markov), random -generation utilities (random), a collection of tools (tools), -and other utilities (util) which are -mainly used by developers internal to the package. +includes economic models (models), markov chains (markov), random +generation utilities (random), a collection of tools (tools), +and other utilities (util) which are +mainly used by developers internal to the package. The models section, for example, contains implementations of standard models, many of which are discussed in lectures on the website `quant- @@ -131,8 +122,8 @@ .. toctree:: :maxdepth: 2 + game_theory markov - models random tools util @@ -170,7 +161,7 @@ def source_join(f_name): def all_auto(): # Get list of module names mod_names = glob("../quantecon/[a-z0-9]*.py") - mod_names = map(lambda x: x.split('/')[-1], mod_names) + mod_names = list(map(lambda x: x.split('/')[-1], mod_names)) # Ensure source/modules directory exists if not os.path.exists(source_join("modules")): @@ -185,54 +176,55 @@ def all_auto(): # write index.rst file to include these autogenerated files with open(source_join("index.rst"), "w") as index: - generated = "\n ".join(map(lambda x: "modules/" + x.split(".")[0], - mod_names)) + generated = "\n ".join(list(map(lambda x: "modules/" + x.split(".")[0], + mod_names))) temp = all_index_template.format(generated=generated) index.write(temp) def model_tool(): + # list file names with game_theory + game_theory_files = glob("../quantecon/game_theory/[a-z0-9]*.py") + game_theory = list(map(lambda x: x.split('/')[-1][:-3], game_theory_files)) + # Alphabetize + game_theory.sort() + # list file names with markov markov_files = glob("../quantecon/markov/[a-z0-9]*.py") - markov = map(lambda x: x.split('/')[-1][:-3], markov_files) + markov = list(map(lambda x: x.split('/')[-1][:-3], markov_files)) # Alphabetize markov.sort() - # list file names with models - mod_files = glob("../quantecon/models/[a-z0-9]*.py") - models = map(lambda x: x.split('/')[-1][:-3], mod_files) - # Alphabetize - models.sort() - - # list file names with models.solow - solow_files = glob("../quantecon/models/solow/[a-z0-9]*.py") - solow = map(lambda x: x.split('/')[-1][:-3], solow_files) - # Alphabetize - solow.sort() - # list file names with random random_files = glob("../quantecon/random/[a-z0-9]*.py") - random = map(lambda x: x.split('/')[-1][:-3], random_files) + random = list(map(lambda x: x.split('/')[-1][:-3], random_files)) # Alphabetize random.sort() # list file names of tools (base level modules) tool_files = glob("../quantecon/[a-z0-9]*.py") - tools = map(lambda x: x.split('/')[-1][:-3], tool_files) + tools = list(map(lambda x: x.split('/')[-1][:-3], tool_files)) # Alphabetize tools.remove("version") tools.sort() - + # list file names of utilities util_files = glob("../quantecon/util/[a-z0-9]*.py") - util = map(lambda x: x.split('/')[-1][:-3], util_files) + util = list(map(lambda x: x.split('/')[-1][:-3], util_files)) # Alphabetize util.sort() - for folder in ["markov","models","models/solow","random","tools","util"]: + for folder in ["game_theory", "markov", "random", "tools", "util"]: if not os.path.exists(source_join(folder)): os.makedirs(source_join(folder)) + # Write file for each game_theory file + for mod in game_theory: + new_path = os.path.join("source", "game_theory", mod + ".rst") + with open(new_path, "w") as f: + equals = "=" * len(mod) + f.write(game_theory_module_template.format(mod_name=mod, equals=equals)) + # Write file for each markov file for mod in markov: new_path = os.path.join("source", "markov", mod + ".rst") @@ -240,20 +232,6 @@ def model_tool(): equals = "=" * len(mod) f.write(markov_module_template.format(mod_name=mod, equals=equals)) - # Write file for each model - for mod in models: - new_path = os.path.join("source", "models", mod + ".rst") - with open(new_path, "w") as f: - equals = "=" * len(mod) - f.write(model_module_template.format(mod_name=mod, equals=equals)) - - # Write file for each model.solow - for mod in solow: - new_path = os.path.join("source", "models", "solow", mod + ".rst") - with open(new_path, "w") as f: - equals = "=" * len(mod) - f.write(solow_model_module_template.format(mod_name=mod, equals=equals)) - # Write file for each random file for mod in random: new_path = os.path.join("source", "random", mod + ".rst") @@ -279,21 +257,20 @@ def model_tool(): with open(source_join("index.rst"), "w") as index: index.write(split_index_template) + gt = "game_theory/" + "\n game_theory/".join(game_theory) mark = "markov/" + "\n markov/".join(markov) - mods = "models/" + "\n models/".join(models) - mods = mods + "\n solow/" #Add solow sub directory to models rand = "random/" + "\n random/".join(random) tlz = "tools/" + "\n tools/".join(tools) utls = "util/" + "\n util/".join(util) #-TocTree-# - toc_tree_list = {"markov":mark, - "models": mods, + toc_tree_list = {"game_theory": gt, + "markov": mark, "tools": tlz, - "random":rand, - "util":utls, + "random": rand, + "util": utls, } - for f_name in ("markov","models","random","tools","util"): + for f_name in ("game_theory", "markov", "random", "tools", "util"): with open(source_join(f_name + ".rst"), "w") as f: temp = split_file_template.format(name=f_name.capitalize(), equals="="*len(f_name), diff --git a/docs/source/game_theory.rst b/docs/source/game_theory.rst new file mode 100644 index 000000000..dbd3f2541 --- /dev/null +++ b/docs/source/game_theory.rst @@ -0,0 +1,7 @@ +Game_theory +=========== + +.. toctree:: + :maxdepth: 2 + + game_theory/normal_form_game diff --git a/docs/source/game_theory/normal_form_game.rst b/docs/source/game_theory/normal_form_game.rst new file mode 100644 index 000000000..6f8d426f3 --- /dev/null +++ b/docs/source/game_theory/normal_form_game.rst @@ -0,0 +1,7 @@ +normal_form_game +================ + +.. automodule:: quantecon.game_theory.normal_form_game + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/source/index.rst b/docs/source/index.rst index 5d5c87bc1..6a9e03446 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -3,10 +3,10 @@ QuantEcon documentation ======================= The `quantecon` python library consists of a number of modules which -includes economic models (models), markov chains (markov), random -generation utilities (random), a collection of tools (tools), -and other utilities (util) which are -mainly used by developers internal to the package. +includes economic models (models), markov chains (markov), random +generation utilities (random), a collection of tools (tools), +and other utilities (util) which are +mainly used by developers internal to the package. The models section, for example, contains implementations of standard models, many of which are discussed in lectures on the website `quant- @@ -15,8 +15,8 @@ econ.net `_. .. toctree:: :maxdepth: 2 + game_theory markov - models random tools util diff --git a/docs/source/util.rst b/docs/source/util.rst index 0d08cd3f2..b4a08b104 100644 --- a/docs/source/util.rst +++ b/docs/source/util.rst @@ -7,5 +7,6 @@ Util util/array util/common_messages util/external + util/notebooks util/random util/timing diff --git a/docs/source/util/notebooks.rst b/docs/source/util/notebooks.rst new file mode 100644 index 000000000..fb1c378d9 --- /dev/null +++ b/docs/source/util/notebooks.rst @@ -0,0 +1,7 @@ +notebooks +========= + +.. automodule:: quantecon.util.notebooks + :members: + :undoc-members: + :show-inheritance: diff --git a/examples/3dplot.py b/examples/3dplot.py deleted file mode 100644 index 753f721d0..000000000 --- a/examples/3dplot.py +++ /dev/null @@ -1,24 +0,0 @@ -import matplotlib.pyplot as plt -from mpl_toolkits.mplot3d.axes3d import Axes3D -import numpy as np -from matplotlib import cm - - -def f(x, y): - return np.cos(x**2 + y**2) / (1 + x**2 + y**2) - -xgrid = np.linspace(-3, 3, 50) -ygrid = xgrid -x, y = np.meshgrid(xgrid, ygrid) - -fig = plt.figure(figsize=(8, 6)) -ax = fig.add_subplot(111, projection='3d') -ax.plot_surface(x, - y, - f(x, y), - rstride=2, cstride=2, - cmap=cm.jet, - alpha=0.7, - linewidth=0.25) -ax.set_zlim(-0.5, 1.0) -plt.show() diff --git a/examples/3dvec.py b/examples/3dvec.py deleted file mode 100644 index af9d7cfe7..000000000 --- a/examples/3dvec.py +++ /dev/null @@ -1,63 +0,0 @@ -""" -QE by Tom Sargent and John Stachurski. -Illustrates the span of two vectors in R^3. -""" -import numpy as np -import matplotlib.pyplot as plt -from matplotlib import cm -from mpl_toolkits.mplot3d import Axes3D -from scipy.interpolate import interp2d - -fig = plt.figure() -ax = fig.gca(projection='3d') - -x_min, x_max = -5, 5 -y_min, y_max = -5, 5 - -alpha, beta = 0.2, 0.1 - -ax.set_xlim((x_min, x_max)) -ax.set_ylim((x_min, x_max)) -ax.set_zlim((x_min, x_max)) - -# Axes -ax.set_xticks((0,)) -ax.set_yticks((0,)) -ax.set_zticks((0,)) -gs = 3 -z = np.linspace(x_min, x_max, gs) -x = np.zeros(gs) -y = np.zeros(gs) -ax.plot(x, y, z, 'k-', lw=2, alpha=0.5) -ax.plot(z, x, y, 'k-', lw=2, alpha=0.5) -ax.plot(y, z, x, 'k-', lw=2, alpha=0.5) - - -# Fixed linear function, to generate a plane -def f(x, y): - return alpha * x + beta * y - -# Vector locations, by coordinate -x_coords = np.array((3, 3)) -y_coords = np.array((4, -4)) -z = f(x_coords, y_coords) -for i in (0, 1): - ax.text(x_coords[i], y_coords[i], z[i], r'$a_{}$'.format(i+1), fontsize=14) - -# Lines to vectors -for i in (0, 1): - x = (0, x_coords[i]) - y = (0, y_coords[i]) - z = (0, f(x_coords[i], y_coords[i])) - ax.plot(x, y, z, 'b-', lw=1.5, alpha=0.6) - - -# Draw the plane -grid_size = 20 -xr2 = np.linspace(x_min, x_max, grid_size) -yr2 = np.linspace(y_min, y_max, grid_size) -x2, y2 = np.meshgrid(xr2, yr2) -z2 = f(x2, y2) -ax.plot_surface(x2, y2, z2, rstride=1, cstride=1, cmap=cm.jet, - linewidth=0, antialiased=True, alpha=0.2) -plt.show() diff --git a/examples/amss.py b/examples/amss.py deleted file mode 100644 index cd94ac8f2..000000000 --- a/examples/amss.py +++ /dev/null @@ -1,295 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Created on Sun Feb 22 10:26:11 2015 - -@author: dgevans -""" -import numpy as np -from scipy.optimize import root -from scipy.optimize import fmin_slsqp -import utilities -import lucas_stokey as LS -from utilities import simulate_markov - -class Planners_Allocation_Bellman(object): - ''' - Compute the planner's allocation by solving Bellman - equation. - ''' - def __init__(self,Para,mugrid): - ''' - Initializes the class from the calibration Para - ''' - self.beta = Para.beta - self.Pi = Para.Pi - self.G = Para.G - self.S = len(Para.Pi) # number of states - self.Theta = Para.Theta - self.Para = Para - self.mugrid = mugrid - - #now find the first best allocation - self.solve_time1_bellman() - self.T.time_0 = True #Bellman equation now solves time 0 problem - - def solve_time1_bellman(self): - ''' - Solve the time 1 Bellman equation for calibration Para and initial grid mugrid0 - ''' - Para,mugrid0 = self.Para,self.mugrid - Pi = Para.Pi - S = len(Para.Pi) - - #First get initial fit from lucas stockey solution. - #Need to change things to be ex_ante - PP = LS.Planners_Allocation_Sequential(Para) - interp = utilities.interpolator_factory(2,None) - - def incomplete_allocation(mu_,s_): - c,n,x,V = PP.time1_value(mu_) - return c,n,Pi[s_].dot(x),Pi[s_].dot(V) - cf,nf,xgrid,Vf,xprimef = [],[],[],[],[] - for s_ in range(S): - c,n,x,V = zip(*map(lambda mu: incomplete_allocation(mu,s_),mugrid0)) - c,n = np.vstack(c).T,np.vstack(n).T - x,V = np.hstack(x),np.hstack(V) - xprimes = np.vstack([x]*S) - cf.append(interp(x,c)) - nf.append(interp(x,n)) - Vf.append(interp(x,V)) - xgrid.append(x) - xprimef.append(interp(x,xprimes)) - cf,nf,xprimef = utilities.fun_vstack(cf), utilities.fun_vstack(nf),utilities.fun_vstack(xprimef) - Vf = utilities.fun_hstack(Vf) - policies = [cf,nf,xprimef] - - - #create xgrid - x = np.vstack(xgrid).T - xbar = [x.min(0).max(),x.max(0).min()] - xgrid = np.linspace(xbar[0],xbar[1],len(mugrid0)) - self.xgrid = xgrid - - #Now iterate on Bellman equation - T = BellmanEquation(Para,xgrid,policies) - diff = 1. - while diff > 1e-6: - PF = T(Vf) - - Vfnew,policies = self.fit_policy_function(PF) - diff = np.abs((Vf(xgrid)-Vfnew(xgrid))/Vf(xgrid)).max() - - print(diff) - Vf = Vfnew - - #store value function policies and Bellman Equations - self.Vf = Vf - self.policies = policies - self.T = T - - def fit_policy_function(self,PF): - ''' - Fits the policy functions - ''' - S,xgrid = len(self.Pi),self.xgrid - interp = utilities.interpolator_factory(3,0) - cf,nf,xprimef,Tf,Vf = [],[],[],[],[] - for s_ in range(S): - PFvec = np.vstack([PF(x,s_) for x in self.xgrid]).T - Vf.append(interp(xgrid,PFvec[0,:])) - cf.append(interp(xgrid,PFvec[1:1+S])) - nf.append(interp(xgrid,PFvec[1+S:1+2*S])) - xprimef.append(interp(xgrid,PFvec[1+2*S:1+3*S])) - Tf.append(interp(xgrid,PFvec[1+3*S:])) - policies = utilities.fun_vstack(cf), utilities.fun_vstack(nf),utilities.fun_vstack(xprimef),utilities.fun_vstack(Tf) - Vf = utilities.fun_hstack(Vf) - return Vf,policies - - def Tau(self,c,n): - ''' - Computes Tau given c,n - ''' - Para = self.Para - Uc,Un = Para.Uc(c,n),Para.Un(c,n) - - return 1+Un/(self.Theta * Uc) - - def time0_allocation(self,B_,s0): - ''' - Finds the optimal allocation given initial government debt B_ and state s_0 - ''' - PF = self.T(self.Vf) - - z0 = PF(B_,s0) - c0,n0,xprime0,T0 = z0[1:] - return c0,n0,xprime0,T0 - - def simulate(self,B_,s_0,T,sHist=None): - ''' - Simulates planners policies for T periods - ''' - Para,Pi = self.Para,self.Pi - Uc = Para.Uc - cf,nf,xprimef,Tf = self.policies - - if sHist == None: - sHist = simulate_markov(Pi,s_0,T) - - cHist,nHist,Bhist,xHist,TauHist,THist,muHist = np.zeros((7,T)) - #time0 - cHist[0],nHist[0],xHist[0],THist[0] = self.time0_allocation(B_,s_0) - TauHist[0] = self.Tau(cHist[0],nHist[0])[s_0] - Bhist[0] = B_ - muHist[0] = self.Vf[s_0](xHist[0]) - - #time 1 onward - for t in range(1,T): - s_,x,s = sHist[t-1],xHist[t-1],sHist[t] - c,n,xprime,T = cf[s_,:](x),nf[s_,:](x),xprimef[s_,:](x),Tf[s_,:](x) - - Tau = self.Tau(c,n)[s] - u_c = Uc(c,n) - Eu_c = Pi[s_,:].dot(u_c) - - muHist[t] = self.Vf[s](xprime[s]) - - cHist[t],nHist[t],Bhist[t],TauHist[t] = c[s],n[s],x/Eu_c,Tau - xHist[t],THist[t] = xprime[s],T[s] - return cHist,nHist,Bhist,xHist,TauHist,THist,muHist,sHist - - -class BellmanEquation(object): - ''' - Bellman equation for the continuation of the Lucas-Stokey Problem - ''' - def __init__(self,Para,xgrid,policies0): - ''' - Initializes the class from the calibration Para - ''' - self.beta = Para.beta - self.Pi = Para.Pi - self.G = Para.G - self.S = len(Para.Pi) # number of states - self.Theta = Para.Theta - self.Para = Para - - self.xbar = [min(xgrid),max(xgrid)] - self.time_0 = False - - self.z0 = {} - cf,nf,xprimef = policies0 - - for s_ in range(self.S): - for x in xgrid: - self.z0[x,s_] = np.hstack([cf[s_,:](x),nf[s_,:](x),xprimef[s_,:](x),np.zeros(self.S)]) - - self.find_first_best() - - def find_first_best(self): - ''' - Find the first best allocation - ''' - Para = self.Para - S,Theta,Uc,Un,G = self.S,self.Theta,Para.Uc,Para.Un,self.G - - def res(z): - c = z[:S] - n = z[S:] - return np.hstack( - [Theta*Uc(c,n)+Un(c,n), Theta*n - c - G] - ) - res = root(res,0.5*np.ones(2*S)) - if not res.success: - raise Exception('Could not find first best') - - self.cFB = res.x[:S] - self.nFB = res.x[S:] - IFB = Uc(self.cFB,self.nFB)*self.cFB + Un(self.cFB,self.nFB)*self.nFB - - self.xFB = np.linalg.solve(np.eye(S) - self.beta*self.Pi, IFB) - - self.zFB = {} - for s in range(S): - self.zFB[s] = np.hstack([self.cFB[s],self.nFB[s],self.Pi[s].dot(self.xFB),0.]) - - - - def __call__(self,Vf): - ''' - Given continuation value function next period return value function this - period return T(V) and optimal policies - ''' - if not self.time_0: - PF = lambda x,s: self.get_policies_time1(x,s,Vf) - else: - PF = lambda B_,s0: self.get_policies_time0(B_,s0,Vf) - return PF - - def get_policies_time1(self,x,s_,Vf): - ''' - Finds the optimal policies - ''' - Para,beta,Theta,G,S,Pi = self.Para,self.beta,self.Theta,self.G,self.S,self.Pi - U,Uc,Un = Para.U,Para.Uc,Para.Un - - def objf(z): - c,n,xprime = z[:S],z[S:2*S],z[2*S:3*S] - - Vprime = np.empty(S) - for s in range(S): - Vprime[s] = Vf[s](xprime[s]) - - return -Pi[s_].dot(U(c,n)+beta*Vprime) - - def cons(z): - c,n,xprime,T = z[:S],z[S:2*S],z[2*S:3*S],z[3*S:] - u_c = Uc(c,n) - Eu_c = Pi[s_].dot(u_c) - return np.hstack([ - x*u_c/Eu_c - u_c*(c-T)-Un(c,n)*n - beta*xprime, - Theta*n - c - G - ]) - - if Para.transfers: - bounds = [(0.,100)]*S+[(0.,100)]*S+[self.xbar]*S+[(0.,100.)]*S - else: - bounds = [(0.,100)]*S+[(0.,100)]*S+[self.xbar]*S+[(0.,0.)]*S - out,fx,_,imode,smode = fmin_slsqp(objf,self.z0[x,s_],f_eqcons=cons, - bounds=bounds,full_output=True,iprint=0) - - if imode >0: - raise Exception(smode) - - self.z0[x,s_] = out - return np.hstack([-fx,out]) - - def get_policies_time0(self,B_,s0,Vf): - ''' - Finds the optimal policies - ''' - Para,beta,Theta,G = self.Para,self.beta,self.Theta,self.G - U,Uc,Un = Para.U,Para.Uc,Para.Un - - def objf(z): - c,n,xprime = z[:-1] - - return -(U(c,n)+beta*Vf[s0](xprime)) - - def cons(z): - c,n,xprime,T = z - return np.hstack([ - -Uc(c,n)*(c-B_-T)-Un(c,n)*n - beta*xprime, - (Theta*n - c - G)[s0] - ]) - - if Para.transfers: - bounds=[(0.,100),(0.,100),self.xbar,(0.,100.)] - else: - bounds=[(0.,100),(0.,100),self.xbar,(0.,0.)] - out,fx,_,imode,smode = fmin_slsqp(objf,self.zFB[s0],f_eqcons=cons, - bounds=bounds,full_output=True,iprint=0) - - if imode >0: - raise Exception(smode) - - return np.hstack([-fx,out]) diff --git a/examples/amss_figures.py b/examples/amss_figures.py deleted file mode 100644 index 1aa42a821..000000000 --- a/examples/amss_figures.py +++ /dev/null @@ -1,210 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Created on Fri Feb 20 14:07:56 2015 - -@author: dgevans -""" -import matplotlib.pyplot as plt -import numpy as np -import lucas_stokey as LS -import amss -from calibrations.BGP import M1 -from calibrations.CES import M1 as M_convergence -from calibrations.CES import M_time_example -import utilities - -#initialize mugrid for value function iteration -muvec = np.linspace(-0.7,0.01,200) - - -''' -Time Varying Example -''' - -M_time_example.transfers = True #Government can use transfers -PP_seq_time = LS.Planners_Allocation_Sequential(M_time_example) #solve sequential problem -PP_im_time = amss.Planners_Allocation_Bellman(M_time_example,muvec) - -sHist_h = np.array([0,1,2,3,5,5,5]) -sHist_l = np.array([0,1,2,4,5,5,5]) - -sim_seq_h = PP_seq_time.simulate(1.,0,7,sHist_h) -sim_im_h = PP_im_time.simulate(1.,0,7,sHist_h) -sim_seq_l = PP_seq_time.simulate(1.,0,7,sHist_l) -sim_im_l = PP_im_time.simulate(1.,0,7,sHist_l) - -plt.figure(figsize=[14,10]) -plt.subplot(3,2,1) -plt.title('Consumption') -plt.plot(sim_seq_l[0],'-ok') -plt.plot(sim_im_l[0],'-or') -plt.plot(sim_seq_h[0],'-^k') -plt.plot(sim_im_h[0],'-^r') -plt.subplot(3,2,2) -plt.title('Labor') -plt.plot(sim_seq_l[1],'-ok') -plt.plot(sim_im_l[1],'-or') -plt.plot(sim_seq_h[1],'-^k') -plt.plot(sim_im_h[1],'-^r') -plt.legend(('Complete Markets','Incomplete Markets'),loc='best') -plt.subplot(3,2,3) -plt.title('Government Debt') -plt.plot(sim_seq_l[2],'-ok') -plt.plot(sim_im_l[2],'-or') -plt.plot(sim_seq_h[2],'-^k') -plt.plot(sim_im_h[2],'-^r') -plt.subplot(3,2,4) -plt.title('Tax Rate') -plt.plot(sim_seq_l[3],'-ok') -plt.plot(sim_im_l[4],'-or') -plt.plot(sim_seq_h[3],'-^k') -plt.plot(sim_im_h[4],'-^r') -plt.subplot(3,2,5) -plt.title('Government Spending') -plt.plot(M_time_example.G[sHist_l],'-ok') -plt.plot(M_time_example.G[sHist_l],'-or') -plt.plot(M_time_example.G[sHist_h],'-^k') -plt.plot(M_time_example.G[sHist_h],'-^r') -plt.ylim([0.05,0.25]) -plt.subplot(3,2,6) -plt.title('Output') -plt.plot(M_time_example.Theta[sHist_l]*sim_seq_l[1],'-ok') -plt.plot(M_time_example.Theta[sHist_l]*sim_im_l[1],'-or') -plt.plot(M_time_example.Theta[sHist_h]*sim_seq_h[1],'-^k') -plt.plot(M_time_example.Theta[sHist_h]*sim_im_h[1],'-^r') -plt.tight_layout() -plt.savefig('TaxSequence_time_varying_AMSS.png') - - - - -''' -BGP Example -''' - -M1.transfers = False #Government can use transfers -PP_seq = LS.Planners_Allocation_Sequential(M1) #solve sequential problem -PP_bel = LS.Planners_Allocation_Bellman(M1,muvec) #solve recursive problem -PP_im = amss.Planners_Allocation_Bellman(M1,muvec) - -T = 20 -#sHist = utilities.simulate_markov(M1.Pi,0,T) -sHist = np.array([0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0],dtype=int) - -#simulate -sim_seq = PP_seq.simulate(0.5,0,T,sHist) -#sim_bel = PP_bel.simulate(0.5,0,T,sHist) -sim_im = PP_im.simulate(0.5,0,T,sHist) - -#plot policies -plt.figure(figsize=[14,10]) -plt.subplot(3,2,1) -plt.title('Consumption') -plt.plot(sim_seq[0],'-ok') -#plt.plot(sim_bel[0],'-xk') -plt.plot(sim_im[0],'-^k') -plt.legend(('Complete Markets','Incomplete Markets'),loc='best') -plt.subplot(3,2,2) -plt.title('Labor') -plt.plot(sim_seq[1],'-ok') -#plt.plot(sim_bel[1],'-xk') -plt.plot(sim_im[1],'-^k') -plt.subplot(3,2,3) -plt.title('Government Debt') -plt.plot(sim_seq[2],'-ok') -#plt.plot(sim_bel[2],'-xk') -plt.plot(sim_im[2],'-^k') -plt.subplot(3,2,4) -plt.title('Tax Rate') -plt.plot(sim_seq[3],'-ok') -#plt.plot(sim_bel[3],'-xk') -plt.plot(sim_im[4],'-^k') -plt.subplot(3,2,5) -plt.title('Government Spending') -plt.plot(M1.G[sHist],'-ok') -#plt.plot(M1.G[sHist],'-^k') -plt.ylim([0.05,0.25]) -plt.subplot(3,2,6) -plt.title('Output') -plt.plot(M1.Theta[sHist]*sim_seq[1],'-ok') -#plt.plot(M1.Theta[sHist]*sim_bel[1],'-xk') -plt.plot(M1.Theta[sHist]*sim_im[1],'-^k') -plt.savefig('TaxSequence_AMSS.png') -plt.tight_layout() - - -#Now long simulations -T_long = 200 -sim_seq_long = PP_seq.simulate(0.5,0.,T_long) -sHist_long = sim_seq_long[-3] -sim_im_long = PP_im.simulate(0.5,0.,T_long,sHist_long) - -plt.figure(figsize=[14,10]) -plt.subplot(3,2,1) -plt.title('Consumption') -plt.plot(sim_seq_long[0],'-k') -plt.plot(sim_im_long[0],'-.k') -plt.legend(('Complete Markets','Incomplete Markets'),loc='best') -plt.subplot(3,2,2) -plt.title('Labor') -plt.plot(sim_seq_long[1],'-k') -plt.plot(sim_im_long[1],'-.k') -plt.subplot(3,2,3) -plt.title('Government Debt') -plt.plot(sim_seq_long[2],'-k') -plt.plot(sim_im_long[2],'-.k') -plt.subplot(3,2,4) -plt.title('Tax Rate') -plt.plot(sim_seq_long[3],'-k') -plt.plot(sim_im_long[4],'-.k') -plt.subplot(3,2,5) -plt.title('Government Spending') -plt.plot(M1.G[sHist_long],'-k') -plt.plot(M1.G[sHist_long],'-.k') -plt.ylim([0.05,0.25]) -plt.subplot(3,2,6) -plt.title('Output') -plt.plot(M1.Theta[sHist_long]*sim_seq_long[1],'-k') -plt.plot(M1.Theta[sHist_long]*sim_im_long[1],'-.k') -plt.tight_layout() -plt.savefig('Long_SimulationAMSS.png') - -''' -Show Convergence example -''' -muvec = np.linspace(-0.15,0.0,100) #change -PP_C = amss.Planners_Allocation_Bellman(M_convergence,muvec) -xgrid = PP_C.xgrid -xf = PP_C.policies[-2] #get x policies -plt.figure() -for s in range(2): - plt.plot(xgrid,xf[0,s](xgrid)-xgrid) - -sim_seq_convergence = PP_C.simulate(0.5,0.,2000) -sHist_long = sim_seq_convergence[-1] - -plt.figure(figsize=[14,10]) -plt.subplot(3,2,1) -plt.title('Consumption') -plt.plot(sim_seq_convergence[0],'-k') -plt.legend(('Complete Markets','Incomplete Markets'),loc='best') -plt.subplot(3,2,2) -plt.title('Labor') -plt.plot(sim_seq_convergence[1],'-k') -plt.subplot(3,2,3) -plt.title('Government Debt') -plt.plot(sim_seq_convergence[2],'-k') -plt.subplot(3,2,4) -plt.title('Tax Rate') -plt.plot(sim_seq_convergence[3],'-k') -plt.subplot(3,2,5) -plt.title('Government Spending') -plt.plot(M_convergence.G[sHist_long],'-k') -plt.ylim([0.05,0.25]) -plt.subplot(3,2,6) -plt.title('Output') -plt.plot(M_convergence.Theta[sHist_long]*sim_seq_convergence[1],'-k') -plt.tight_layout() -plt.savefig('Convergence_SimulationAMSS.png') - - diff --git a/examples/ar1_acov.py b/examples/ar1_acov.py deleted file mode 100644 index 7aa1370f6..000000000 --- a/examples/ar1_acov.py +++ /dev/null @@ -1,22 +0,0 @@ -""" -Plots autocovariance function for AR(1) X' = phi X + epsilon -""" -import numpy as np -import matplotlib.pyplot as plt - -num_rows, num_cols = 2, 1 -fig, axes = plt.subplots(num_rows, num_cols, figsize=(10, 8)) -plt.subplots_adjust(hspace=0.4) - -# Autocovariance when phi = 0.8 -temp = r'autocovariance, $\phi = {0:.2}$' -for i, phi in enumerate((0.8, -0.8)): - ax = axes[i] - times = list(range(16)) - acov = [phi**k / (1 - phi**2) for k in times] - ax.plot(times, acov, 'bo-', alpha=0.6, label=temp.format(phi)) - ax.legend(loc='upper right') - ax.set_xlabel('time') - ax.set_xlim((0, 15)) - ax.hlines(0, 0, 15, linestyle='--', alpha=0.5) -plt.show() diff --git a/examples/ar1_cycles.py b/examples/ar1_cycles.py deleted file mode 100644 index 83dd1941b..000000000 --- a/examples/ar1_cycles.py +++ /dev/null @@ -1,42 +0,0 @@ -""" -Helps to illustrate the spectral density for AR(1) X' = phi X + epsilon -""" -import numpy as np -import matplotlib.pyplot as plt - -phi = -0.8 -times = list(range(16)) -y1 = [phi**k / (1 - phi**2) for k in times] -y2 = [np.cos(np.pi * k) for k in times] -y3 = [a * b for a, b in zip(y1, y2)] - -num_rows, num_cols = 3, 1 -fig, axes = plt.subplots(num_rows, num_cols, figsize=(10, 8)) -plt.subplots_adjust(hspace=0.25) - -# Autocovariance when phi = -0.8 -ax = axes[0] -ax.plot(times, y1, 'bo-', alpha=0.6, label=r'$\gamma(k)$') -ax.legend(loc='upper right') -ax.set_xlim(0, 15) -ax.set_yticks((-2, 0, 2)) -ax.hlines(0, 0, 15, linestyle='--', alpha=0.5) - -# Cycles at frequence pi -ax = axes[1] -ax.plot(times, y2, 'bo-', alpha=0.6, label=r'$\cos(\pi k)$') -ax.legend(loc='upper right') -ax.set_xlim(0, 15) -ax.set_yticks((-1, 0, 1)) -ax.hlines(0, 0, 15, linestyle='--', alpha=0.5) - -# Product -ax = axes[2] -ax.stem(times, y3, label=r'$\gamma(k) \cos(\pi k)$') -ax.legend(loc='upper right') -ax.set_xlim((0, 15)) -ax.set_ylim(-3, 3) -ax.set_yticks((-1, 0, 1, 2, 3)) -ax.hlines(0, 0, 15, linestyle='--', alpha=0.5) - -plt.show() diff --git a/examples/ar1_sd.py b/examples/ar1_sd.py deleted file mode 100644 index 2f5e49c9c..000000000 --- a/examples/ar1_sd.py +++ /dev/null @@ -1,25 +0,0 @@ -""" -Plots spectral density for AR(1) X' = phi X + epsilon -""" -import numpy as np -import matplotlib.pyplot as plt - - -def ar1_sd(phi, omega): - return 1 / (1 - 2 * phi * np.cos(omega) + phi**2) - -omegas = np.linspace(0, np.pi, 180) -num_rows, num_cols = 2, 1 -fig, axes = plt.subplots(num_rows, num_cols, figsize=(10, 8)) -plt.subplots_adjust(hspace=0.4) - -# Autocovariance when phi = 0.8 -temp = r'spectral density, $\phi = {0:.2}$' -for i, phi in enumerate((0.8, -0.8)): - ax = axes[i] - sd = ar1_sd(phi, omegas) - ax.plot(omegas, sd, 'b-', alpha=0.6, lw=2, label=temp.format(phi)) - ax.legend(loc='upper center') - ax.set_xlabel('frequency') - ax.set_xlim((0, np.pi)) -plt.show() diff --git a/examples/beta-binomial.py b/examples/beta-binomial.py deleted file mode 100644 index 09c9bdc59..000000000 --- a/examples/beta-binomial.py +++ /dev/null @@ -1,25 +0,0 @@ -""" -Filename: beta-binomial.py -Authors: John Stachurski, Thomas J. Sargent - -""" -from scipy.special import binom, beta -import matplotlib.pyplot as plt -import numpy as np - - -def gen_probs(n, a, b): - probs = np.zeros(n+1) - for k in range(n+1): - probs[k] = binom(n, k) * beta(k + a, n - k + b) / beta(a, b) - return probs - -n = 50 -a_vals = [0.5, 1, 100] -b_vals = [0.5, 1, 100] -fig, ax = plt.subplots() -for a, b in zip(a_vals, b_vals): - ab_label = r'$a = %.1f$, $b = %.1f$' % (a, b) - ax.plot(list(range(0, n+1)), gen_probs(n, a, b), '-o', label=ab_label) -ax.legend() -plt.show() diff --git a/examples/bifurcation_diagram.py b/examples/bifurcation_diagram.py deleted file mode 100644 index ccb5c0fa6..000000000 --- a/examples/bifurcation_diagram.py +++ /dev/null @@ -1,18 +0,0 @@ -""" -Filename: bifurcation_diagram.py -Reference: http://quant-econ.net/py/python_oop.html -""" -from chaos_class import Chaos -import matplotlib.pyplot as plt - -fig, ax = plt.subplots() -ch = Chaos(0.1, 4) -r = 2.5 -while r < 4: - ch.r = r - t = ch.generate_sequence(1000)[950:] - ax.plot([r] * len(t), t, 'b.', ms=0.6) - r = r + 0.005 - -ax.set_xlabel(r'$r$', fontsize=16) -plt.show() diff --git a/examples/binom_df.py b/examples/binom_df.py deleted file mode 100644 index c41e48ea9..000000000 --- a/examples/binom_df.py +++ /dev/null @@ -1,19 +0,0 @@ -import matplotlib.pyplot as plt -from scipy.stats import binom - -fig, axes = plt.subplots(2, 2) -plt.subplots_adjust(hspace=0.4) -axes = axes.flatten() -ns = [1, 2, 4, 8] -dom = list(range(9)) - -for ax, n in zip(axes, ns): - b = binom(n, 0.5) - ax.bar(dom, b.pmf(dom), alpha=0.6, align='center') - ax.set_xlim(-0.5, 8.5) - ax.set_ylim(0, 0.55) - ax.set_xticks(list(range(9))) - ax.set_yticks((0, 0.2, 0.4)) - ax.set_title(r'$n = {}$'.format(n)) - -fig.show() diff --git a/examples/bisection.py b/examples/bisection.py deleted file mode 100644 index dd7a688a9..000000000 --- a/examples/bisection.py +++ /dev/null @@ -1,20 +0,0 @@ - -def bisect(f, a, b, tol=10e-5): - """ - Implements the bisection root finding algorithm, assuming that f is a - real-valued function on [a, b] satisfying f(a) < 0 < f(b). - """ - lower, upper = a, b - - while upper - lower > tol: - middle = 0.5 * (upper + lower) - # === if root is between lower and middle === # - if f(middle) > 0: - lower, upper = lower, middle - # === if root is between middle and upper === # - else: - lower, upper = middle, upper - - return 0.5 * (upper + lower) - - diff --git a/examples/boxplot_example.py b/examples/boxplot_example.py deleted file mode 100644 index d3c797986..000000000 --- a/examples/boxplot_example.py +++ /dev/null @@ -1,15 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt - -n = 500 -x = np.random.randn(n) # N(0, 1) -x = np.exp(x) # Map x to lognormal -y = np.random.randn(n) + 2.0 # N(2, 1) -z = np.random.randn(n) + 4.0 # N(4, 1) - -fig, ax = plt.subplots(figsize=(10, 6.6)) -ax.boxplot([x, y, z]) -ax.set_xticks((1, 2, 3)) -ax.set_ylim(-2, 14) -ax.set_xticklabels((r'$X$', r'$Y$', r'$Z$'), fontsize=16) -plt.show() diff --git a/examples/calibrations/BGP.py b/examples/calibrations/BGP.py deleted file mode 100644 index 44c30cdac..000000000 --- a/examples/calibrations/BGP.py +++ /dev/null @@ -1,60 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Created on Wed Feb 18 15:32:07 2015 - -@author: dgevans -""" -import numpy as np - -class baseline(object): - beta = 0.9 - psi = 0.69 - - Pi = 0.5 *np.ones((2,2)) - - G = np.array([0.1,0.2]) - - Theta = np.ones(2) - - transfers = False - - #derivatives of utiltiy function - def U(self,c,n): - return np.log(c) + self.psi*np.log(1-n) - - def Uc(self,c,n): - return 1./c - - def Ucc(self,c,n): - return -c**(-2) - - def Un(self,c,n): - return -self.psi/(1-n) - - def Unn(self,c,n): - return -self.psi/(1-n)**2 - - -#Model 1 -M1 = baseline() - -#Model 2 - -M2 = baseline() -M2.G = np.array([0.15]) -M2.Pi = np.ones((1,1)) -M2.Theta = np.ones(1) - -#Model 3 with time varying - -M_time_example = baseline() - -M_time_example.Pi = np.array([[0., 1., 0., 0., 0., 0.], - [0., 0., 1., 0., 0., 0.], - [0., 0., 0., 0.5, 0.5, 0.], - [0., 0., 0., 0., 0., 1.], - [0., 0., 0., 0., 0., 1.], - [0., 0., 0., 0., 0., 1.]]) - -M_time_example.G = np.array([0.1, 0.1, 0.1, 0.2, 0.1, 0.1]) -M_time_example.Theta = np.ones(6) # Theta can in principle be random \ No newline at end of file diff --git a/examples/calibrations/CES.py b/examples/calibrations/CES.py deleted file mode 100644 index 6c8144ef8..000000000 --- a/examples/calibrations/CES.py +++ /dev/null @@ -1,68 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Created on Tue Mar 10 08:55:03 2015 - -@author: dgevans -""" - -import numpy as np - -class baseline(object): - beta = 0.9 - - sigma = 2. - - gamma = 2. - - Pi = 0.5 *np.ones((2,2)) - - G = np.array([0.1,0.2]) - - Theta = np.ones(2) - - transfers = False - - #derivatives of utiltiy function - def U(self,c,n): - sigma = self.sigma - if sigma == 1.: - U = np.log(c) - else: - U = (c**(1-sigma)-1)/(1-sigma) - return U - n**(1+self.gamma)/(1+self.gamma) - - def Uc(self,c,n): - return c**(-self.sigma) - - def Ucc(self,c,n): - return -self.sigma*c**(-self.sigma-1.) - - def Un(self,c,n): - return -n**self.gamma - - def Unn(self,c,n): - return -self.gamma * n**(self.gamma-1.) - -#Model 1 -M1 = baseline() - -#Model 2 - -M2 = baseline() -M2.G = np.array([0.15]) -M2.Pi = np.ones((1,1)) -M2.Theta = np.ones(1) - -#Model 3 with time varying - -M_time_example = baseline() - -M_time_example.Pi = np.array([[0., 1., 0., 0., 0., 0.], - [0., 0., 1., 0., 0., 0.], - [0., 0., 0., 0.5, 0.5, 0.], - [0., 0., 0., 0., 0., 1.], - [0., 0., 0., 0., 0., 1.], - [0., 0., 0., 0., 0., 1.]]) - -M_time_example.G = np.array([0.1, 0.1, 0.1, 0.2, 0.1, 0.1]) -M_time_example.Theta = np.ones(6) # Theta can in principle be random \ No newline at end of file diff --git a/examples/calibrations/__init__.py b/examples/calibrations/__init__.py deleted file mode 100644 index a0a54464b..000000000 --- a/examples/calibrations/__init__.py +++ /dev/null @@ -1,7 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Created on Wed Feb 18 16:13:07 2015 - -@author: dgevans -""" - diff --git a/examples/career_vf_plot.py b/examples/career_vf_plot.py deleted file mode 100644 index 31c96b60b..000000000 --- a/examples/career_vf_plot.py +++ /dev/null @@ -1,35 +0,0 @@ -""" -Origin: QE by John Stachurski and Thomas J. Sargent -Filename: career_vf_plot.py -Authors: John Stachurski and Thomas Sargent -LastModified: 11/08/2013 - -""" - -import matplotlib.pyplot as plt -from mpl_toolkits.mplot3d.axes3d import Axes3D -import numpy as np -from matplotlib import cm -import quantecon as qe -from quantecon.models import CareerWorkerProblem - -# === solve for the value function === # -wp = CareerWorkerProblem() -v_init = np.ones((wp.N, wp.N))*100 -v = qe.compute_fixed_point(wp.bellman_operator, v_init) - -# === plot value function === # -fig = plt.figure(figsize=(8, 6)) -ax = fig.add_subplot(111, projection='3d') -tg, eg = np.meshgrid(wp.theta, wp.epsilon) -ax.plot_surface(tg, - eg, - v.T, - rstride=2, cstride=2, - cmap=cm.jet, - alpha=0.5, - linewidth=0.25) -ax.set_zlim(150, 200) -ax.set_xlabel('theta', fontsize=14) -ax.set_ylabel('epsilon', fontsize=14) -plt.show() diff --git a/examples/cauchy_samples.py b/examples/cauchy_samples.py deleted file mode 100644 index c0a3e0d94..000000000 --- a/examples/cauchy_samples.py +++ /dev/null @@ -1,29 +0,0 @@ - -import numpy as np -from scipy.stats import cauchy -import matplotlib.pyplot as plt - -n = 1000 -distribution = cauchy() - -fig, ax = plt.subplots() -data = distribution.rvs(n) - -if 0: - ax.plot(list(range(n)), data, 'bo', alpha=0.5) - ax.vlines(list(range(n)), 0, data, lw=0.2) - ax.set_title("{} observations from the Cauchy distribution".format(n)) - -if 1: - # == Compute sample mean at each n == # - sample_mean = np.empty(n) - for i in range(n): - sample_mean[i] = np.mean(data[:i]) - - # == Plot == # - ax.plot(list(range(n)), sample_mean, 'r-', lw=3, alpha=0.6, - label=r'$\bar X_n$') - ax.plot(list(range(n)), [0] * n, 'k--', lw=0.5) - ax.legend() - -fig.show() diff --git a/examples/chaos_class.py b/examples/chaos_class.py deleted file mode 100644 index e29da6de4..000000000 --- a/examples/chaos_class.py +++ /dev/null @@ -1,25 +0,0 @@ -""" -Filename: chaos_class.py -Reference: http://quant-econ.net/py/python_oop.html -""" -class Chaos: - """ - Models the dynamical system with :math:`x_{t+1} = r x_t (1 - x_t)` - """ - def __init__(self, x0, r): - """ - Initialize with state x0 and parameter r - """ - self.x, self.r = x0, r - - def update(self): - "Apply the map to update state." - self.x = self.r * self.x *(1 - self.x) - - def generate_sequence(self, n): - "Generate and return a sequence of length n." - path = [] - for i in range(n): - path.append(self.x) - self.update() - return path diff --git a/examples/chaotic_ts.py b/examples/chaotic_ts.py deleted file mode 100644 index fef5876f3..000000000 --- a/examples/chaotic_ts.py +++ /dev/null @@ -1,16 +0,0 @@ -""" -Filename: choatic_ts.py -Reference: http://quant-econ.net/py/python_oop.html -""" -from chaos_class import Chaos -import matplotlib.pyplot as plt - -ch = Chaos(0.1, 4.0) -ts_length = 250 - -fig, ax = plt.subplots() -ax.set_xlabel(r'$t$', fontsize=14) -ax.set_ylabel(r'$x_t$', fontsize=14) -x = ch.generate_sequence(ts_length) -ax.plot(range(ts_length), x, 'bo-', alpha=0.5, lw=2, label=r'$x_t$') -plt.show() diff --git a/examples/clt3d.py b/examples/clt3d.py deleted file mode 100644 index 0834c3787..000000000 --- a/examples/clt3d.py +++ /dev/null @@ -1,80 +0,0 @@ -""" -Origin: QE by John Stachurski and Thomas J. Sargent -Filename: clt3d.py - -Visual illustration of the central limit theorem. Produces a 3D figure -showing the density of the scaled sample mean \sqrt{n} \bar X_n plotted -against n. -""" - -import numpy as np -from scipy.stats import beta, gaussian_kde -from mpl_toolkits.mplot3d import Axes3D -from matplotlib.collections import PolyCollection -import matplotlib.pyplot as plt - -beta_dist = beta(2, 2) - - -def gen_x_draws(k): - """ - Returns a flat array containing k independent draws from the - distribution of X, the underlying random variable. This distribution is - itself a convex combination of three beta distributions. - """ - bdraws = beta_dist.rvs((3, k)) - # == Transform rows, so each represents a different distribution == # - bdraws[0, :] -= 0.5 - bdraws[1, :] += 0.6 - bdraws[2, :] -= 1.1 - # == Set X[i] = bdraws[j, i], where j is a random draw from {0, 1, 2} == # - js = np.random.random_integers(0, 2, size=k) - X = bdraws[js, np.arange(k)] - # == Rescale, so that the random variable is zero mean == # - m, sigma = X.mean(), X.std() - return (X - m) / sigma - -nmax = 5 -reps = 100000 -ns = list(range(1, nmax + 1)) - -# == Form a matrix Z such that each column is reps independent draws of X == # -Z = np.empty((reps, nmax)) -for i in range(nmax): - Z[:, i] = gen_x_draws(reps) -# == Take cumulative sum across columns -S = Z.cumsum(axis=1) -# == Multiply j-th column by sqrt j == # -Y = (1 / np.sqrt(ns)) * S - -# == Plot == # - -fig = plt.figure() -ax = fig.gca(projection='3d') - -a, b = -3, 3 -gs = 100 -xs = np.linspace(a, b, gs) - -# == Build verts == # -greys = np.linspace(0.3, 0.7, nmax) -verts = [] -for n in ns: - density = gaussian_kde(Y[:, n-1]) - ys = density(xs) - verts.append(list(zip(xs, ys))) - -poly = PolyCollection(verts, facecolors=[str(g) for g in greys]) -poly.set_alpha(0.85) -ax.add_collection3d(poly, zs=ns, zdir='x') - -# ax.text(np.mean(rhos), a-1.4, -0.02, r'$\beta$', fontsize=16) -# ax.text(np.max(rhos)+0.016, (a+b)/2, -0.02, r'$\log(y)$', fontsize=16) -ax.set_xlim3d(1, nmax) -ax.set_xticks(ns) -ax.set_xlabel("n") -ax.set_yticks((-3, 0, 3)) -ax.set_ylim3d(a, b) -ax.set_zlim3d(0, 0.4) -ax.set_zticks((0.2, 0.4)) -plt.show() diff --git a/examples/consumer.py b/examples/consumer.py deleted file mode 100644 index b6de2ccf6..000000000 --- a/examples/consumer.py +++ /dev/null @@ -1,17 +0,0 @@ -class Consumer: - - def __init__(self, w): - "Initialize consumer with w dollars of wealth" - self.wealth = w - - def earn(self, y): - "The consumer earns y dollars" - self.wealth += y - - def spend(self, x): - "The consumer spends x dollars if feasible" - new_wealth = self.wealth - x - if new_wealth < 0: - print("Insufficent funds") - else: - self.wealth = new_wealth diff --git a/examples/dice.py b/examples/dice.py deleted file mode 100644 index 115be4940..000000000 --- a/examples/dice.py +++ /dev/null @@ -1,16 +0,0 @@ -""" -Filename: dice.py -""" - -import random - - -class Dice: - - faces = (1, 2, 3, 4, 5, 6) - - def __init__(self): - self.current_face = 1 - - def roll(self): - self.current_face = random.choice(Dice.faces) diff --git a/examples/duopoly_lqnash.py b/examples/duopoly_lqnash.py deleted file mode 100644 index 4702fa6b4..000000000 --- a/examples/duopoly_lqnash.py +++ /dev/null @@ -1,48 +0,0 @@ -""" -Filename: lqnash.py -Authors: Chase Coleman, Thomas Sargent - -This file provides an example of a Markov Perfect Equilibrium for a -simple duopoly example. - -See the lecture at http://quant-econ.net/py/markov_perf.html for a -description of the model. - -""" -from __future__ import division -from numpy import array, eye -from quantecon.lqnash import nnash - - -# ---------------------------------------------------------------------# -# Set up parameter values and LQ matrices -# Remember state is x_t = [1, y_{1, t}, y_{2, t}] and -# control is u_{i, t} = [y_{i, t+1} - y_{i, t}] -# ---------------------------------------------------------------------# -a0 = 10. -a1 = 1. -beta = 1. -d = .5 - -a = eye(3) -b1 = array([[0.], [1.], [0.]]) -b2 = array([[0.], [0.], [1.]]) - -r1 = array([[a0, 0., 0.], - [0., -a1, -a1/2.], - [0, -a1/2., 0.]]) - -r2 = array([[a0, 0., 0.], - [0., 0., -a1/2.], - [0, -a1/2., -a1]]) - -q1 = array([[-.5*d]]) -q2 = array([[-.5*d]]) - - -# ---------------------------------------------------------------------# -# Solve using QE's nnash function -# ---------------------------------------------------------------------# - -f1, f2, p1, p2 = nnash(a, b1, b2, r1, r2, q1, q2, 0., 0., 0., 0., 0., 0., - tol=1e-8, max_iter=1000) diff --git a/examples/duopoly_mpe.py b/examples/duopoly_mpe.py deleted file mode 100644 index 124b64927..000000000 --- a/examples/duopoly_mpe.py +++ /dev/null @@ -1,48 +0,0 @@ -""" -@authors: Chase Coleman, Thomas Sargent, John Stachurski - -Markov Perfect Equilibrium for the simple duopoly example. - -See the lecture at http://quant-econ.net/py/markov_perf.html for a -description of the model. -""" - -from __future__ import division -import numpy as np -import quantecon as qe - -# == Parameters == # -a0 = 10.0 -a1 = 2.0 -beta = 0.96 -gamma = 12.0 - -# == In LQ form == # - -A = np.eye(3) - -B1 = np.array([[0.], [1.], [0.]]) -B2 = np.array([[0.], [0.], [1.]]) - - -R1 = [[0., -a0/2, 0.], - [-a0/2., a1, a1/2.], - [0, a1/2., 0.]] - -R2 = [[0., 0., -a0/2], - [0., 0., a1/2.], - [-a0/2, a1/2., a1]] - -Q1 = Q2 = gamma - -S1 = S2 = W1 = W2 = M1 = M2 = 0.0 - -# == Solve using QE's nnash function == # -F1, F2, P1, P2 = qe.nnash(A, B1, B2, R1, R2, Q1, Q2, S1, S2, W1, W2, M1, M2, - beta=beta) - -# == Display policies == # -print("Computed policies for firm 1 and firm 2:\n") -print("F1 = {}".format(F1)) -print("F2 = {}".format(F2)) -print("\n") diff --git a/examples/duopoly_mpe_dynamics.py b/examples/duopoly_mpe_dynamics.py deleted file mode 100644 index e52f12109..000000000 --- a/examples/duopoly_mpe_dynamics.py +++ /dev/null @@ -1,20 +0,0 @@ -import matplotlib.pyplot as plt -from duopoly_mpe import * - -AF = A - B1.dot(F1) - B2.dot(F2) -n = 20 -x = np.empty((3, n)) -x[:, 0] = 1, 1, 1 -for t in range(n-1): - x[:, t+1] = np.dot(AF, x[:, t]) -q1 = x[1, :] -q2 = x[2, :] -q = q1 + q2 # Total output, MPE -p = a0 - a1 * q # Price, MPE - -fig, ax = plt.subplots(figsize=(9, 5.8)) -ax.plot(q, 'b-', lw=2, alpha=0.75, label='total output') -ax.plot(p, 'g-', lw=2, alpha=0.75, label='price') -ax.set_title('Output and prices, duopoly MPE') -ax.legend(frameon=False) -plt.show() diff --git a/examples/eigenvec.py b/examples/eigenvec.py deleted file mode 100644 index 3af24e498..000000000 --- a/examples/eigenvec.py +++ /dev/null @@ -1,57 +0,0 @@ -""" -Filename: eigenvec.py -Authors: Tom Sargent and John Stachurski. - -Illustrates eigenvectors. -""" - -import matplotlib.pyplot as plt -import numpy as np -from scipy.linalg import eig - -A = ((1, 2), - (2, 1)) -A = np.array(A) -evals, evecs = eig(A) -evecs = evecs[:, 0], evecs[:, 1] - -fig, ax = plt.subplots() -# Set the axes through the origin -for spine in ['left', 'bottom']: - ax.spines[spine].set_position('zero') -for spine in ['right', 'top']: - ax.spines[spine].set_color('none') -ax.grid(alpha=0.4) - -xmin, xmax = -3, 3 -ymin, ymax = -3, 3 -ax.set_xlim(xmin, xmax) -ax.set_ylim(ymin, ymax) -# ax.set_xticks(()) -# ax.set_yticks(()) - -# Plot each eigenvector -for v in evecs: - ax.annotate('', xy=v, xytext=(0, 0), - arrowprops=dict(facecolor='blue', - shrink=0, - alpha=0.6, - width=0.5)) - -# Plot the image of each eigenvector -for v in evecs: - v = np.dot(A, v) - ax.annotate('', xy=v, xytext=(0, 0), - arrowprops=dict(facecolor='red', - shrink=0, - alpha=0.6, - width=0.5)) - -# Plot the lines they run through -x = np.linspace(xmin, xmax, 3) -for v in evecs: - a = v[1] / v[0] - ax.plot(x, a * x, 'b-', lw=0.4) - - -plt.show() diff --git a/examples/evans_sargent.py b/examples/evans_sargent.py deleted file mode 100644 index 8b537cb0d..000000000 --- a/examples/evans_sargent.py +++ /dev/null @@ -1,179 +0,0 @@ -""" -Created on Mon Dec 16 19:12:17 2013 -@author: dgevans -Edited by: Chase Coleman, John Stachurski - -This file corresponds to the Ramsey model from the QE lecture on -history dependent policies: - - http://quant-econ.net/py/hist_dep_policies.html - -In the following, ``uhat`` and ``tauhat`` are what the planner would choose if -he could reset at time t, ``uhatdif`` and ``tauhatdif`` are the difference -between those and what the planner is constrained to choose. The variable -``mu`` is the Lagrange multiplier associated with the constraint at time t. - -For more complete description of inputs and outputs see the website. - -""" - -import numpy as np -from quantecon import LQ -from quantecon.matrix_eqn import solve_discrete_lyapunov -from scipy.optimize import root - - -def computeG(A0, A1, d, Q0, tau0, beta, mu): - """ - Compute government income given mu and return tax revenues and - policy matrixes for the planner. - - Parameters - ---------- - A0 : float - A constant parameter for the inverse demand function - A1 : float - A constant parameter for the inverse demand function - d : float - A constant parameter for quadratic adjustment cost of production - Q0 : float - An initial condition for production - tau0 : float - An initial condition for taxes - beta : float - A constant parameter for discounting - mu : float - Lagrange multiplier - - Returns - ------- - T0 : array(float) - Present discounted value of government spending - A : array(float) - One of the transition matrices for the states - B : array(float) - Another transition matrix for the states - F : array(float) - Policy rule matrix - P : array(float) - Value function matrix - """ - # Create Matrices for solving Ramsey problem - R = np.array([[0, -A0/2, 0, 0], - [-A0/2, A1/2, -mu/2, 0], - [0, -mu/2, 0, 0], - [0, 0, 0, d/2]]) - - A = np.array([[1, 0, 0, 0], - [0, 1, 0, 1], - [0, 0, 0, 0], - [-A0/d, A1/d, 0, A1/d+1/beta]]) - - B = np.array([0, 0, 1, 1/d]).reshape(-1, 1) - - Q = 0 - - # Use LQ to solve the Ramsey Problem. - lq = LQ(Q, -R, A, B, beta=beta) - P, F, d = lq.stationary_values() - - # Need y_0 to compute government tax revenue. - P21 = P[3, :3] - P22 = P[3, 3] - z0 = np.array([1, Q0, tau0]).reshape(-1, 1) - u0 = -P22**(-1) * P21.dot(z0) - y0 = np.vstack([z0, u0]) - - # Define A_F and S matricies - AF = A - B.dot(F) - S = np.array([0, 1, 0, 0]).reshape(-1, 1).dot(np.array([[0, 0, 1, 0]])) - - # Solves equation (25) - temp = beta * AF.T.dot(S).dot(AF) - Omega = solve_discrete_lyapunov(np.sqrt(beta) * AF.T, temp) - T0 = y0.T.dot(Omega).dot(y0) - - return T0, A, B, F, P - - -# == Primitives == # -T = 20 -A0 = 100.0 -A1 = 0.05 -d = 0.20 -beta = 0.95 - -# == Initial conditions == # -mu0 = 0.0025 -Q0 = 1000.0 -tau0 = 0.0 - - -def gg(mu): - """ - Computes the tax revenues for the government given Lagrangian - multiplier mu. - """ - return computeG(A0, A1, d, Q0, tau0, beta, mu) - -# == Solve the Ramsey problem and associated government revenue == # -G0, A, B, F, P = gg(mu0) - -# == Compute the optimal u0 == # -P21 = P[3, :3] -P22 = P[3, 3] -z0 = np.array([1, Q0, tau0]).reshape(-1, 1) -u0 = -P22**(-1) * P21.dot(z0) - - -# == Initialize vectors == # -y = np.zeros((4, T)) -uhat = np.zeros(T) -uhatdif = np.zeros(T) -tauhat = np.zeros(T) -tauhatdif = np.zeros(T-1) -mu = np.zeros(T) -G = np.zeros(T) -GPay = np.zeros(T) - -# == Initial conditions == # -G[0] = G0 -mu[0] = mu0 -uhatdif[0] = 0 -uhat[0] = u0 -y[:, 0] = np.vstack([z0, u0]).flatten() - -for t in range(1, T): - # Iterate government policy - y[:, t] = (A-B.dot(F)).dot(y[:, t-1]) - - # update G - G[t] = (G[t-1] - beta*y[1, t]*y[2, t])/beta - GPay[t] = beta*y[1, t]*y[2, t] - - # Compute the mu if the government were able to reset its plan - # ff is the tax revenues the government would receive if they reset the - # plan with Lagrange multiplier mu minus current G - - ff = lambda mu: (gg(mu)[0]-G[t]).flatten() - - # find ff = 0 - mu[t] = root(ff, mu[t-1]).x - temp, Atemp, Btemp, Ftemp, Ptemp = gg(mu[t]) - - # Compute alternative decisions - P21temp = Ptemp[3, :3] - P22temp = P[3, 3] - uhat[t] = -P22temp**(-1)*P21temp.dot(y[:3, t]) - - yhat = (Atemp-Btemp.dot(Ftemp)).dot(np.hstack([y[0:3, t-1], uhat[t-1]])) - tauhat[t] = yhat[3] - tauhatdif[t-1] = tauhat[t]-y[3, t] - uhatdif[t] = uhat[t]-y[3, t] - - -if __name__ == '__main__': - print("1 Q tau u") - print(y) - print("-F") - print(-F) diff --git a/examples/evans_sargent_plot1.py b/examples/evans_sargent_plot1.py deleted file mode 100644 index a9b34bc9d..000000000 --- a/examples/evans_sargent_plot1.py +++ /dev/null @@ -1,44 +0,0 @@ -""" -Plot 1 from the Evans Sargent model. - -@author: David Evans -Edited by: John Stachurski - -""" -import numpy as np -import matplotlib.pyplot as plt -from evans_sargent import T, y - -tt = np.arange(T) # tt is used to make the plot time index correct. - -n_rows = 3 -fig, axes = plt.subplots(n_rows, 1, figsize=(10, 12)) - -plt.subplots_adjust(hspace=0.5) -for ax in axes: - ax.grid() - ax.set_xlim(0, 15) - -bbox = (0., 1.02, 1., .102) -legend_args = {'bbox_to_anchor': bbox, 'loc': 3, 'mode': 'expand'} -p_args = {'lw': 2, 'alpha': 0.7} - -ax = axes[0] -ax.plot(tt, y[1, :], 'b-', label="output", **p_args) -ax.set_ylabel(r"$Q$", fontsize=16) -ax.legend(ncol=1, **legend_args) - -ax = axes[1] -ax.plot(tt, y[2, :], 'b-', label="tax rate", **p_args) -ax.set_ylabel(r"$\tau$", fontsize=16) -ax.set_yticks((0.0, 0.2, 0.4, 0.6, 0.8)) -ax.legend(ncol=1, **legend_args) - -ax = axes[2] -ax.plot(tt, y[3, :], 'b-', label="first difference in output", **p_args) -ax.set_ylabel(r"$u$", fontsize=16) -ax.set_yticks((0, 100, 200, 300, 400)) -ax.legend(ncol=1, **legend_args) -ax.set_xlabel(r'time', fontsize=16) - -plt.show() diff --git a/examples/evans_sargent_plot2.py b/examples/evans_sargent_plot2.py deleted file mode 100644 index dcf9923b0..000000000 --- a/examples/evans_sargent_plot2.py +++ /dev/null @@ -1,60 +0,0 @@ -""" -Plot 2 from the Evans Sargent model. - -@author: David Evans -Edited by: John Stachurski - -""" -import numpy as np -import matplotlib.pyplot as plt -from evans_sargent import T, uhatdif, tauhatdif, mu, G - -tt = np.arange(T) # tt is used to make the plot time index correct. -tt2 = np.arange(T-1) - -n_rows = 4 -fig, axes = plt.subplots(n_rows, 1, figsize=(10, 16)) - -plt.subplots_adjust(hspace=0.5) -for ax in axes: - ax.grid(alpha=.5) - ax.set_xlim(-0.5, 15) - -bbox = (0., 1.02, 1., .102) -legend_args = {'bbox_to_anchor': bbox, 'loc': 3, 'mode': 'expand'} -p_args = {'lw': 2, 'alpha': 0.7} - -ax = axes[0] -ax.plot(tt2, tauhatdif, label=r'time inconsistency differential for tax rate', - **p_args) -ax.set_ylabel(r"$\Delta\tau$", fontsize=16) -ax.set_ylim(-0.1, 1.4) -ax.set_yticks((0.0, 0.4, 0.8, 1.2)) -ax.legend(ncol=1, **legend_args) - -ax = axes[1] -ax.plot(tt, uhatdif, label=r'time inconsistency differential for $u$', - **p_args) -ax.set_ylabel(r"$\Delta u$", fontsize=16) -ax.set_ylim(-3, .1) -ax.set_yticks((-3.0, -2.0, -1.0, 0.0)) -ax.legend(ncol=1, **legend_args) - -ax = axes[2] -ax.plot(tt, mu, label='Lagrange multiplier', **p_args) -ax.set_ylabel(r"$\mu$", fontsize=16) -ax.set_ylim(2.34e-3, 2.52e-3) -ax.set_yticks((2.34e-3, 2.43e-3, 2.52e-3)) -ax.legend(ncol=1, **legend_args) - -ax = axes[3] -ax.plot(tt, G, label='government revenue', **p_args) -ax.set_ylabel(r"$G$", fontsize=16) -ax.set_ylim(9100, 9800) -ax.set_yticks((9200, 9400, 9600, 9800)) -ax.legend(ncol=1, **legend_args) - -ax.set_xlabel(r'time', fontsize=16) - -plt.show() -# lines = plt.plot(tt, GPay, "o") diff --git a/examples/finite_dp_og_example.py b/examples/finite_dp_og_example.py deleted file mode 100644 index ab13eb810..000000000 --- a/examples/finite_dp_og_example.py +++ /dev/null @@ -1,49 +0,0 @@ -""" -A simple optimal growth model, for testing the DiscreteDP class. - -Filename: finite_dp_og_example.py -""" -import numpy as np - -class SimpleOG(object): - - def __init__(self, B=10, M=5, alpha=0.5, beta=0.9): - """ - Set up R, Q and beta, the three elements that define an instance of - the DiscreteDP class. - """ - - self.B, self.M, self.alpha, self.beta = B, M, alpha, beta - self.n = B + M + 1 - self.m = M + 1 - - self.R = np.empty((self.n, self.m)) - self.Q = np.zeros((self.n, self.m, self.n)) - - self.populate_Q() - self.populate_R() - - def u(self, c): - return c**self.alpha - - def populate_R(self): - """ - Populate the R matrix, with R[s, a] = -np.inf for infeasible - state-action pairs. - """ - for s in range(self.n): - for a in range(self.m): - self.R[s, a] = self.u(s - a) if a <= s else -np.inf - - def populate_Q(self): - """ - Populate the Q matrix by setting - - Q[s, a, s'] = 1 / (1 + B) if a <= s' <= a + B - - and zero otherwise. - """ - - for a in range(self.m): - self.Q[:, a, a:(a + self.B + 1)] = 1.0 / (self.B + 1) - diff --git a/examples/first_notebook.ipynb b/examples/first_notebook.ipynb deleted file mode 100644 index c1e8e4eea..000000000 --- a/examples/first_notebook.ipynb +++ /dev/null @@ -1,93 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:1c9b10f6aa5899245b1bdbc936804f20f2b6e72d639e8fb2d0495120f94e3c49" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print 'foobar'" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "foobar\n" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "\n", - "N = 50\n", - "x = np.random.rand(N)\n", - "y = np.random.rand(N)\n", - "area = np.pi * (15 * np.random.rand(N))**2 # 0 to 15 point radiuses\n", - "\n", - "plt.scatter(x, y, s=area, alpha=0.5)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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SE5PAxIkLiIyc0u34pqYi4uO/4tFH7x6kyEc3MbgrDLn9+w9w/HgwaWkDb40l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\nBQ1xP/EnA3UXPa4H8obY/wFgu5vv6Tfq6+t5/vm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- "text": [ - "" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "np.rank?" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 11 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If $\\{A_n\\}$ is pairwise disjoint, then\n", - "\n", - "$$ \\mu(\\cup_n A_n) = \\sum_n \\mu(A_n) $$" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/examples/gaussian_contours.py b/examples/gaussian_contours.py deleted file mode 100644 index 9b24abbb9..000000000 --- a/examples/gaussian_contours.py +++ /dev/null @@ -1,101 +0,0 @@ -""" -Filename: gaussian_contours.py -Authors: John Stachurski and Thomas Sargent - -Plots of bivariate Gaussians to illustrate the Kalman filter. -""" - -from scipy import linalg -import numpy as np -import matplotlib.cm as cm -from matplotlib.mlab import bivariate_normal -import matplotlib.pyplot as plt - -# == Set up the Gaussian prior density p == # -Sigma = [[0.4, 0.3], [0.3, 0.45]] -Sigma = np.matrix(Sigma) -x_hat = np.matrix([0.2, -0.2]).T -# == Define the matrices G and R from the equation y = G x + N(0, R) == # -G = [[1, 0], [0, 1]] -G = np.matrix(G) -R = 0.5 * Sigma -# == The matrices A and Q == # -A = [[1.2, 0], [0, -0.2]] -A = np.matrix(A) -Q = 0.3 * Sigma -# == The observed value of y == # -y = np.matrix([2.3, -1.9]).T - -# == Set up grid for plotting == # -x_grid = np.linspace(-1.5, 2.9, 100) -y_grid = np.linspace(-3.1, 1.7, 100) -X, Y = np.meshgrid(x_grid, y_grid) - - -def gen_gaussian_plot_vals(mu, C): - "Z values for plotting the bivariate Gaussian N(mu, C)" - m_x, m_y = float(mu[0]), float(mu[1]) - s_x, s_y = np.sqrt(C[0, 0]), np.sqrt(C[1, 1]) - s_xy = C[0, 1] - return bivariate_normal(X, Y, s_x, s_y, m_x, m_y, s_xy) - -fig, ax = plt.subplots() -ax.xaxis.grid(True, zorder=0) -ax.yaxis.grid(True, zorder=0) - -# == Code for the 4 plots, choose one below == # - - -def plot1(): - Z = gen_gaussian_plot_vals(x_hat, Sigma) - ax.contourf(X, Y, Z, 6, alpha=0.6, cmap=cm.jet) - cs = ax.contour(X, Y, Z, 6, colors="black") - ax.clabel(cs, inline=1, fontsize=10) - - -def plot2(): - Z = gen_gaussian_plot_vals(x_hat, Sigma) - ax.contourf(X, Y, Z, 6, alpha=0.6, cmap=cm.jet) - cs = ax.contour(X, Y, Z, 6, colors="black") - ax.clabel(cs, inline=1, fontsize=10) - ax.text(float(y[0]), float(y[1]), r"$y$", fontsize=20, color="black") - - -def plot3(): - Z = gen_gaussian_plot_vals(x_hat, Sigma) - cs1 = ax.contour(X, Y, Z, 6, colors="black") - ax.clabel(cs1, inline=1, fontsize=10) - M = Sigma * G.T * linalg.inv(G * Sigma * G.T + R) - x_hat_F = x_hat + M * (y - G * x_hat) - Sigma_F = Sigma - M * G * Sigma - new_Z = gen_gaussian_plot_vals(x_hat_F, Sigma_F) - cs2 = ax.contour(X, Y, new_Z, 6, colors="black") - ax.clabel(cs2, inline=1, fontsize=10) - ax.contourf(X, Y, new_Z, 6, alpha=0.6, cmap=cm.jet) - ax.text(float(y[0]), float(y[1]), r"$y$", fontsize=20, color="black") - - -def plot4(): - # Density 1 - Z = gen_gaussian_plot_vals(x_hat, Sigma) - cs1 = ax.contour(X, Y, Z, 6, colors="black") - ax.clabel(cs1, inline=1, fontsize=10) - # Density 2 - M = Sigma * G.T * linalg.inv(G * Sigma * G.T + R) - x_hat_F = x_hat + M * (y - G * x_hat) - Sigma_F = Sigma - M * G * Sigma - Z_F = gen_gaussian_plot_vals(x_hat_F, Sigma_F) - cs2 = ax.contour(X, Y, Z_F, 6, colors="black") - ax.clabel(cs2, inline=1, fontsize=10) - # Density 3 - new_x_hat = A * x_hat_F - new_Sigma = A * Sigma_F * A.T + Q - new_Z = gen_gaussian_plot_vals(new_x_hat, new_Sigma) - cs3 = ax.contour(X, Y, new_Z, 6, colors="black") - ax.clabel(cs3, inline=1, fontsize=10) - ax.contourf(X, Y, new_Z, 6, alpha=0.6, cmap=cm.jet) - ax.text(float(y[0]), float(y[1]), r"$y$", fontsize=20, color="black") - -# == Choose a plot to generate == # -plot1() -plt.show() diff --git a/examples/gd.xls b/examples/gd.xls deleted file mode 100644 index 452132e8b..000000000 Binary files a/examples/gd.xls and /dev/null differ diff --git a/examples/ifp_savings_plots.py b/examples/ifp_savings_plots.py deleted file mode 100644 index 3340bb38b..000000000 --- a/examples/ifp_savings_plots.py +++ /dev/null @@ -1,30 +0,0 @@ -""" -Origin: QE by John Stachurski and Thomas J. Sargent -Filename: ifp_savings_plots.py -Authors: John Stachurski, Thomas J. Sargent -LastModified: 11/08/2013 - -""" - -from matplotlib import pyplot as plt -from quantecon import compute_fixed_point -from quantecon.models import ConsumerProblem - -# === solve for optimal consumption === # -m = ConsumerProblem(r=0.03, grid_max=4) -v_init, c_init = m.initialize() - -# Coleman Operator takes in (c)? -c = compute_fixed_point(m.coleman_operator, c_init) -a = m.asset_grid -R, z_vals = m.R, m.z_vals - -# === generate savings plot === # -fig, ax = plt.subplots() -ax.plot(a, R * a + z_vals[0] - c[:, 0], label='low income') -ax.plot(a, R * a + z_vals[1] - c[:, 1], label='high income') -ax.plot(a, a, 'k--') -ax.set_xlabel('current assets') -ax.set_ylabel('next period assets') -ax.legend(loc='upper left') -plt.show() diff --git a/examples/illustrates_clt.py b/examples/illustrates_clt.py deleted file mode 100644 index 53c427b87..000000000 --- a/examples/illustrates_clt.py +++ /dev/null @@ -1,42 +0,0 @@ -""" -Filename: illustrates_clt.py -Authors: John Stachurski and Thomas J. Sargent - -Visual illustration of the central limit theorem. Histograms draws of - - Y_n := \sqrt{n} (\bar X_n - \mu) - -for a given distribution of X_i, and a given choice of n. -""" -import numpy as np -from scipy.stats import expon, norm -import matplotlib.pyplot as plt -from matplotlib import rc - -# == Specifying font, needs LaTeX integration == # -rc('font', **{'family': 'serif', 'serif': ['Palatino']}) -rc('text', usetex=True) - -# == Set parameters == # -n = 250 # Choice of n -k = 100000 # Number of draws of Y_n -distribution = expon(2) # Exponential distribution, lambda = 1/2 -mu, s = distribution.mean(), distribution.std() - -# == Draw underlying RVs. Each row contains a draw of X_1,..,X_n == # -data = distribution.rvs((k, n)) -# == Compute mean of each row, producing k draws of \bar X_n == # -sample_means = data.mean(axis=1) -# == Generate observations of Y_n == # -Y = np.sqrt(n) * (sample_means - mu) - -# == Plot == # -fig, ax = plt.subplots() -xmin, xmax = -3 * s, 3 * s -ax.set_xlim(xmin, xmax) -ax.hist(Y, bins=60, alpha=0.5, normed=True) -xgrid = np.linspace(xmin, xmax, 200) -ax.plot(xgrid, norm.pdf(xgrid, scale=s), 'k-', lw=2, label=r'$N(0, \sigma^2)$') -ax.legend() - -plt.show() diff --git a/examples/illustrates_lln.py b/examples/illustrates_lln.py deleted file mode 100644 index 49ff2e880..000000000 --- a/examples/illustrates_lln.py +++ /dev/null @@ -1,57 +0,0 @@ -""" -Filename: illustrates_lln.py -Authors: John Stachurski and Thomas J. Sargent - -Visual illustration of the law of large numbers. -""" - -import random -import numpy as np -from scipy.stats import t, beta, lognorm, expon, gamma, poisson -import matplotlib.pyplot as plt - -n = 100 - -# == Arbitrary collection of distributions == # -distributions = {"student's t with 10 degrees of freedom": t(10), - "beta(2, 2)": beta(2, 2), - "lognormal LN(0, 1/2)": lognorm(0.5), - "gamma(5, 1/2)": gamma(5, scale=2), - "poisson(4)": poisson(4), - "exponential with lambda = 1": expon(1)} - -# == Create a figure and some axes == # -num_plots = 3 -fig, axes = plt.subplots(num_plots, 1, figsize=(10, 10)) - -# == Set some plotting parameters to improve layout == # -bbox = (0., 1.02, 1., .102) -legend_args = {'ncol': 2, - 'bbox_to_anchor': bbox, - 'loc': 3, - 'mode': 'expand'} -plt.subplots_adjust(hspace=0.5) - -for ax in axes: - # == Choose a randomly selected distribution == # - name = random.choice(list(distributions.keys())) - distribution = distributions.pop(name) - - # == Generate n draws from the distribution == # - data = distribution.rvs(n) - - # == Compute sample mean at each n == # - sample_mean = np.empty(n) - for i in range(n): - sample_mean[i] = np.mean(data[:i+1]) - - # == Plot == # - ax.plot(list(range(n)), data, 'o', color='grey', alpha=0.5) - axlabel = r'$\bar X_n$' + ' for ' + r'$X_i \sim$' + ' ' + name - ax.plot(list(range(n)), sample_mean, 'g-', lw=3, alpha=0.6, label=axlabel) - m = distribution.mean() - ax.plot(list(range(n)), [m] * n, 'k--', lw=1.5, label=r'$\mu$') - ax.vlines(list(range(n)), m, data, lw=0.2) - ax.legend(**legend_args) - -plt.show() diff --git a/examples/jv_test.py b/examples/jv_test.py deleted file mode 100644 index 3e1bdf116..000000000 --- a/examples/jv_test.py +++ /dev/null @@ -1,28 +0,0 @@ -""" -Origin: QE by John Stachurski and Thomas J. Sargent -Filename: jv_test.py -Authors: John Stachurski and Thomas Sargent -LastModified: 11/08/2013 - -Tests jv.py with a particular parameterization. - -""" -import matplotlib.pyplot as plt -from quantecon import compute_fixed_point -from quantecon.models import JvWorker - -# === solve for optimal policy === # -wp = JvWorker(grid_size=25) -v_init = wp.x_grid * 0.5 -V = compute_fixed_point(wp.bellman_operator, v_init, max_iter=40) -s_policy, phi_policy = wp.bellman_operator(V, return_policies=True) - -# === plot policies === # -fig, ax = plt.subplots() -ax.set_xlim(0, max(wp.x_grid)) -ax.set_ylim(-0.1, 1.1) -ax.plot(wp.x_grid, phi_policy, 'b-', label='phi') -ax.plot(wp.x_grid, s_policy, 'g-', label='s') -ax.set_xlabel("x") -ax.legend() -plt.show() diff --git a/examples/lakemodel_example.py b/examples/lakemodel_example.py deleted file mode 100644 index 75a19d0e8..000000000 --- a/examples/lakemodel_example.py +++ /dev/null @@ -1,151 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Created on Fri Feb 27 18:08:44 2015 - -Author: David Evans - -Example Usage of LakeModel in quantecon.models -""" -import numpy as np -import matplotlib.pyplot as plt -from quantecon.models import LakeModel, LakeModelAgent, LakeModel_Equilibrium - -import pandas as pd -pd.set_option('display.mpl_style', 'default') # Make the graphs a bit prettier - -#Initialize Parameters -alpha = 0.013 -lamb = 0.283#0.2486 -b = 0.0124 -d = 0.00822 -g = b-d -N0 = 150. -e0 = 0.92 -u0 = 1-e0 -T = 50 - -LM = LakeModel(lamb,alpha,b,d) - -#Find steady state -xbar = LM.find_steady_state() - -#simulate stocks for T periods -E0 = e0*N0 -U0 = u0*N0 -X_path = np.vstack( LM.simulate_stock_path([E0,U0],T) ) -plt.figure(figsize=[10,9]) -plt.subplot(3,1,1) -plt.plot(X_path[:,0]) -plt.title(r'Employment') -plt.subplot(3,1,2) -plt.plot(X_path[:,1]) -plt.title(r'Unemployment') -plt.subplot(3,1,3) -plt.plot(X_path.sum(1)) -plt.title(r'Labor Force') -plt.tight_layout() -plt.savefig('example_stock_path.png') - -#simulate rates for T periods - -x_path = np.vstack( LM.simulate_rate_path([e0,u0],T) ) -plt.figure(figsize=[10,6]) -plt.subplot(2,1,1) -plt.plot(x_path[:,0]) -plt.hlines(xbar[0],0,T,'r','--') -plt.title(r'Employment Rate') -plt.subplot(2,1,2) -plt.plot(x_path[:,1]) -plt.hlines(xbar[1],0,T,'r','--') -plt.title(r'Unemployment Rate') -plt.tight_layout() -plt.savefig('example_rate_path.png') - - -#Simulate a single agent -T = 5000 - -A = LakeModelAgent(lamb,alpha) -pi_bar = A.compute_ergodic().flatten() - -sHist = np.hstack(A.simulate(1,T)) - -pi_u = np.cumsum(sHist)/(np.arange(T) + 1.) # time spent in unemployment after T periods -pi_e = 1- pi_u #time spent employed - -plt.figure(figsize=[10,6]) -plt.subplot(2,1,1) -plt.plot(range(50,T),pi_e[50:]) -plt.hlines(pi_bar[0],0,T,'r','--') -plt.title('Percent of Time Employed') -plt.subplot(2,1,2) -plt.plot(range(50,T),pi_u[50:]) -plt.hlines(pi_bar[1],0,T,'r','--') -plt.xlabel('Time') -plt.title('Percent of Time Unemployed') -plt.tight_layout() -plt.savefig('example_averages.png') - - -#============================================================================== -# Now add McCall Search Model -#============================================================================== -from scipy.stats import norm - -#using quaterly data -alpha_q = (1-(1-alpha)**3) -gamma = 1. - -logw_dist = norm(np.log(20.),1) -w = np.linspace(0.,175,201)# wage grid - -#compute probability of each wage level -cdf = logw_dist.cdf(np.log(w)) -pdf = cdf[1:]-cdf[:-1] -pdf /= pdf.sum() -w = (w[1:] + w[:1])/2 - -#Find the quilibirum -LME = LakeModel_Equilibrium(alpha_q,gamma,0.99,2.00,pdf,w) - -#possible levels of unemployment insurance -cvec = np.linspace(1.,75,25) -T,W,U,EV,pi = map(np.vstack,zip(* [LME.find_steady_state_tax(c) for c in cvec])) -W= W[:] -T = T[:] -U = U[:] -EV = EV[:] -i_max = np.argmax(W) - -plt.figure(figsize=[10,6]) -plt.subplot(221) -plt.plot(cvec,W) -plt.xlabel(r'$c$') -plt.title(r'Welfare' ) -axes = plt.gca() -plt.vlines(cvec[i_max],axes.get_ylim()[0],max(W),'k','-.') - -plt.subplot(222) -plt.plot(cvec,T) -axes = plt.gca() -plt.vlines(cvec[i_max],axes.get_ylim()[0],T[i_max],'k','-.') -plt.xlabel(r'$c$') -plt.title(r'Taxes' ) - - -plt.subplot(223) -plt.plot(cvec,pi[:,0]) -axes = plt.gca() -plt.vlines(cvec[i_max],axes.get_ylim()[0],pi[i_max,0],'k','-.') -plt.xlabel(r'$c$') -plt.title(r'Employment Rate' ) - - -plt.subplot(224) -plt.plot(cvec,pi[:,1]) -axes = plt.gca() -plt.vlines(cvec[i_max],axes.get_ylim()[0],pi[i_max,1],'k','-.') -plt.xlabel(r'$c$') -plt.title(r'Unemployment Rate' ) -plt.tight_layout() -plt.savefig('welfare_plot.png') \ No newline at end of file diff --git a/examples/lin_interp_3d_plot.py b/examples/lin_interp_3d_plot.py deleted file mode 100644 index 50413e770..000000000 --- a/examples/lin_interp_3d_plot.py +++ /dev/null @@ -1,56 +0,0 @@ -""" -Origin: QE by John Stachurski and Thomas J. Sargent -Filename: lin_inter_3d_plot.py -Authors: John Stachurski, Thomas J. Sargent -LastModified: 21/08/2013 -""" -from scipy.interpolate import LinearNDInterpolator -import matplotlib.pyplot as plt -from mpl_toolkits.mplot3d.axes3d import Axes3D -import numpy as np - -alpha = 0.7 -phi_ext = 2 * 3.14 * 0.5 - - -def f(a, b): - # return 2 + alpha - 2 * np.cos(b)*np.cos(a) - alpha*np.cos(phi_ext - 2*b) - return a + np.sqrt(b) - -x_max = 3 -y_max = 2.5 - -# === the approximation grid === # -Nx0, Ny0 = 25, 25 -x0 = np.linspace(0, x_max, Nx0) -y0 = np.linspace(0, y_max, Ny0) -X0, Y0 = np.meshgrid(x0, y0) -points = np.column_stack((X0.ravel(1), Y0.ravel(1))) - -# === generate the function values on the grid === # -Z0 = np.empty(Nx0 * Ny0) -for i in range(len(Z0)): - a, b = points[i, :] - Z0[i] = f(a, b) - -g = LinearNDInterpolator(points, Z0) - -# === a grid for plotting === # -Nx1, Ny1 = 100, 100 -x1 = np.linspace(0, x_max, Nx1) -y1 = np.linspace(0, y_max, Ny1) -X1, Y1 = np.meshgrid(x1, y1) - -# === the approximating function, as a matrix, for plotting === # -# ZA = np.empty((Ny1, Nx1)) -# for i in range(Ny1): -# for j in range(Nx1): -# ZA[i, j] = g(x1[j], y1[i]) -ZA = g(X1, Y1) -ZF = f(X1, Y1) - -# === plot === # -fig = plt.figure(figsize=(8, 6)) -ax = fig.add_subplot(1, 1, 1, projection='3d') -p = ax.plot_wireframe(X1, Y1, ZF, rstride=4, cstride=4) -plt.show() diff --git a/examples/linapprox.py b/examples/linapprox.py deleted file mode 100644 index 5fd147702..000000000 --- a/examples/linapprox.py +++ /dev/null @@ -1,28 +0,0 @@ -import numpy as np -import scipy as sp -import matplotlib.pyplot as plt - - -def f(x): - y1 = 2 * np.cos(6 * x) + np.sin(14 * x) - return y1 + 2.5 - -c_grid = np.linspace(0, 1, 6) - - -def Af(x): - return sp.interp(x, c_grid, f(c_grid)) - -f_grid = np.linspace(0, 1, 150) - -fig, ax = plt.subplots() -ax.set_xlim(0, 1) - -ax.plot(f_grid, f(f_grid), 'b-', lw=2, alpha=0.8, label='true function') -ax.plot(f_grid, Af(f_grid), 'g-', lw=2, alpha=0.8, - label='linear approximation') - -ax.vlines(c_grid, c_grid * 0, f(c_grid), linestyle='dashed', alpha=0.5) -ax.legend(loc='upper center') - -plt.show() diff --git a/examples/lq_permanent_1.py b/examples/lq_permanent_1.py deleted file mode 100644 index 9fe72be4e..000000000 --- a/examples/lq_permanent_1.py +++ /dev/null @@ -1,66 +0,0 @@ -""" -Filename: lq_permanent_1.py -Authors: John Stachurski and Thomas J. Sargent - -A permanent income / life-cycle model with iid income -""" - -import numpy as np -import matplotlib.pyplot as plt -from quantecon import LQ - -# == Model parameters == # -r = 0.05 -beta = 1 / (1 + r) -T = 45 -c_bar = 2 -sigma = 0.25 -mu = 1 -q = 1e6 - -# == Formulate as an LQ problem == # -Q = 1 -R = np.zeros((2, 2)) -Rf = np.zeros((2, 2)) -Rf[0, 0] = q -A = [[1 + r, -c_bar + mu], - [0, 1]] -B = [[-1], - [0]] -C = [[sigma], - [0]] - -# == Compute solutions and simulate == # -lq = LQ(Q, R, A, B, C, beta=beta, T=T, Rf=Rf) -x0 = (0, 1) -xp, up, wp = lq.compute_sequence(x0) - -# == Convert back to assets, consumption and income == # -assets = xp[0, :] # a_t -c = up.flatten() + c_bar # c_t -income = wp[0, 1:] + mu # y_t - -# == Plot results == # -n_rows = 2 -fig, axes = plt.subplots(n_rows, 1, figsize=(12, 10)) - -plt.subplots_adjust(hspace=0.5) -for i in range(n_rows): - axes[i].grid() - axes[i].set_xlabel(r'Time') -bbox = (0., 1.02, 1., .102) -legend_args = {'bbox_to_anchor': bbox, 'loc': 3, 'mode': 'expand'} -p_args = {'lw': 2, 'alpha': 0.7} - -axes[0].plot(list(range(1, T+1)), income, 'g-', label="non-financial income", - **p_args) -axes[0].plot(list(range(T)), c, 'k-', label="consumption", **p_args) -axes[0].legend(ncol=2, **legend_args) - -axes[1].plot(list(range(1, T+1)), np.cumsum(income - mu), 'r-', - label="cumulative unanticipated income", **p_args) -axes[1].plot(list(range(T+1)), assets, 'b-', label="assets", **p_args) -axes[1].plot(list(range(T)), np.zeros(T), 'k-') -axes[1].legend(ncol=2, **legend_args) - -plt.show() diff --git a/examples/lqramsey.py b/examples/lqramsey.py deleted file mode 100644 index 72ba777c3..000000000 --- a/examples/lqramsey.py +++ /dev/null @@ -1,296 +0,0 @@ -""" -Filename: lqramsey.py -Authors: Thomas Sargent, Doc-Jin Jang, Jeong-hun Choi, John Stachurski - -This module provides code to compute Ramsey equilibria in a LQ economy with -distortionary taxation. The program computes allocations (consumption, -leisure), tax rates, revenues, the net present value of the debt and other -related quantities. - -Functions for plotting the results are also provided below. - -See the lecture at http://quant-econ.net/py/lqramsey.html for a description of -the model. - -""" - -import sys -import numpy as np -from numpy import sqrt, eye, dot, zeros, cumsum -from numpy.random import randn -import scipy.linalg -import matplotlib.pyplot as plt -from collections import namedtuple -from quantecon import nullspace, mc_sample_path, var_quadratic_sum - - -# == Set up a namedtuple to store data on the model economy == # -Economy = namedtuple('economy', - ('beta', # Discount factor - 'Sg', # Govt spending selector matrix - 'Sd', # Exogenous endowment selector matrix - 'Sb', # Utility parameter selector matrix - 'Ss', # Coupon payments selector matrix - 'discrete', # Discrete or continuous -- boolean - 'proc')) # Stochastic process parameters - -# == Set up a namedtuple to store return values for compute_paths() == # -Path = namedtuple('path', - ('g', # Govt spending - 'd', # Endowment - 'b', # Utility shift parameter - 's', # Coupon payment on existing debt - 'c', # Consumption - 'l', # Labor - 'p', # Price - 'tau', # Tax rate - 'rvn', # Revenue - 'B', # Govt debt - 'R', # Risk free gross return - 'pi', # One-period risk-free interest rate - 'Pi', # Cumulative rate of return, adjusted - 'xi')) # Adjustment factor for Pi - - -def compute_paths(T, econ): - """ - Compute simulated time paths for exogenous and endogenous variables. - - Parameters - =========== - T: int - Length of the simulation - - econ: a namedtuple of type 'Economy', containing - beta - Discount factor - Sg - Govt spending selector matrix - Sd - Exogenous endowment selector matrix - Sb - Utility parameter selector matrix - Ss - Coupon payments selector matrix - discrete - Discrete exogenous process (True or False) - proc - Stochastic process parameters - - Returns - ======== - path: a namedtuple of type 'Path', containing - g - Govt spending - d - Endowment - b - Utility shift parameter - s - Coupon payment on existing debt - c - Consumption - l - Labor - p - Price - tau - Tax rate - rvn - Revenue - B - Govt debt - R - Risk free gross return - pi - One-period risk-free interest rate - Pi - Cumulative rate of return, adjusted - xi - Adjustment factor for Pi - - The corresponding values are flat numpy ndarrays. - - """ - - # == Simplify names == # - beta, Sg, Sd, Sb, Ss = econ.beta, econ.Sg, econ.Sd, econ.Sb, econ.Ss - - if econ.discrete: - P, x_vals = econ.proc - else: - A, C = econ.proc - - # == Simulate the exogenous process x == # - if econ.discrete: - state = mc_sample_path(P, init=0, sample_size=T) - x = x_vals[:, state] - else: - # == Generate an initial condition x0 satisfying x0 = A x0 == # - nx, nx = A.shape - x0 = nullspace((eye(nx) - A)) - x0 = -x0 if (x0[nx-1] < 0) else x0 - x0 = x0 / x0[nx-1] - - # == Generate a time series x of length T starting from x0 == # - nx, nw = C.shape - x = zeros((nx, T)) - w = randn(nw, T) - x[:, 0] = x0.T - for t in range(1, T): - x[:, t] = dot(A, x[:, t-1]) + dot(C, w[:, t]) - - # == Compute exogenous variable sequences == # - g, d, b, s = (dot(S, x).flatten() for S in (Sg, Sd, Sb, Ss)) - - # == Solve for Lagrange multiplier in the govt budget constraint == # - # In fact we solve for nu = lambda / (1 + 2*lambda). Here nu is the - # solution to a quadratic equation a(nu**2 - nu) + b = 0 where - # a and b are expected discounted sums of quadratic forms of the state. - Sm = Sb - Sd - Ss - # == Compute a and b == # - if econ.discrete: - ns = P.shape[0] - F = scipy.linalg.inv(np.identity(ns) - beta * P) - a0 = 0.5 * dot(F, dot(Sm, x_vals).T**2)[0] - H = dot(Sb - Sd + Sg, x_vals) * dot(Sg - Ss, x_vals) - b0 = 0.5 * dot(F, H.T)[0] - a0, b0 = float(a0), float(b0) - else: - H = dot(Sm.T, Sm) - a0 = 0.5 * var_quadratic_sum(A, C, H, beta, x0) - H = dot((Sb - Sd + Sg).T, (Sg + Ss)) - b0 = 0.5 * var_quadratic_sum(A, C, H, beta, x0) - - # == Test that nu has a real solution before assigning == # - warning_msg = """ - Hint: you probably set government spending too {}. Elect a {} - Congress and start over. - """ - disc = a0**2 - 4 * a0 * b0 - if disc >= 0: - nu = 0.5 * (a0 - sqrt(disc)) / a0 - else: - print("There is no Ramsey equilibrium for these parameters.") - print(warning_msg.format('high', 'Republican')) - sys.exit(0) - - # == Test that the Lagrange multiplier has the right sign == # - if nu * (0.5 - nu) < 0: - print("Negative multiplier on the government budget constraint.") - print(warning_msg.format('low', 'Democratic')) - sys.exit(0) - - # == Solve for the allocation given nu and x == # - Sc = 0.5 * (Sb + Sd - Sg - nu * Sm) - Sl = 0.5 * (Sb - Sd + Sg - nu * Sm) - c = dot(Sc, x).flatten() - l = dot(Sl, x).flatten() - p = dot(Sb - Sc, x).flatten() # Price without normalization - tau = 1 - l / (b - c) - rvn = l * tau - - # == Compute remaining variables == # - if econ.discrete: - H = dot(Sb - Sc, x_vals) * dot(Sl - Sg, x_vals) - dot(Sl, x_vals)**2 - temp = dot(F, H.T).flatten() - B = temp[state] / p - H = dot(P[state, :], dot(Sb - Sc, x_vals).T).flatten() - R = p / (beta * H) - temp = dot(P[state, :], dot(Sb - Sc, x_vals).T).flatten() - xi = p[1:] / temp[:T-1] - else: - H = dot(Sl.T, Sl) - dot((Sb - Sc).T, Sl - Sg) - L = np.empty(T) - for t in range(T): - L[t] = var_quadratic_sum(A, C, H, beta, x[:, t]) - B = L / p - Rinv = (beta * dot(dot(Sb - Sc, A), x)).flatten() / p - R = 1 / Rinv - AF1 = dot(Sb - Sc, x[:, 1:]) - AF2 = dot(dot(Sb - Sc, A), x[:, :T-1]) - xi = AF1 / AF2 - xi = xi.flatten() - - pi = B[1:] - R[:T-1] * B[:T-1] - rvn[:T-1] + g[:T-1] - Pi = cumsum(pi * xi) - - # == Prepare return values == # - path = Path(g=g, - d=d, - b=b, - s=s, - c=c, - l=l, - p=p, - tau=tau, - rvn=rvn, - B=B, - R=R, - pi=pi, - Pi=Pi, - xi=xi) - - return path - - -def gen_fig_1(path): - """ - The parameter is the path namedtuple returned by compute_paths(). See - the docstring of that function for details. - """ - - T = len(path.c) - - # == Prepare axes == # - num_rows, num_cols = 2, 2 - fig, axes = plt.subplots(num_rows, num_cols, figsize=(14, 10)) - plt.subplots_adjust(hspace=0.4) - for i in range(num_rows): - for j in range(num_cols): - axes[i, j].grid() - axes[i, j].set_xlabel(r'Time') - bbox = (0., 1.02, 1., .102) - legend_args = {'bbox_to_anchor': bbox, 'loc': 3, 'mode': 'expand'} - p_args = {'lw': 2, 'alpha': 0.7} - - # == Plot consumption, govt expenditure and revenue == # - ax = axes[0, 0] - ax.plot(path.rvn, label=r'$\tau_t \ell_t$', **p_args) - ax.plot(path.g, label=r'$g_t$', **p_args) - ax.plot(path.c, label=r'$c_t$', **p_args) - ax.legend(ncol=3, **legend_args) - - # == Plot govt expenditure and debt == # - ax = axes[0, 1] - ax.plot(list(range(1, T+1)), path.rvn, label=r'$\tau_t \ell_t$', **p_args) - ax.plot(list(range(1, T+1)), path.g, label=r'$g_t$', **p_args) - ax.plot(list(range(1, T)), path.B[1:T], label=r'$B_{t+1}$', **p_args) - ax.legend(ncol=3, **legend_args) - - # == Plot risk free return == # - ax = axes[1, 0] - ax.plot(list(range(1, T+1)), path.R - 1, label=r'$R_t - 1$', **p_args) - ax.legend(ncol=1, **legend_args) - - # == Plot revenue, expenditure and risk free rate == # - ax = axes[1, 1] - ax.plot(list(range(1, T+1)), path.rvn, label=r'$\tau_t \ell_t$', **p_args) - ax.plot(list(range(1, T+1)), path.g, label=r'$g_t$', **p_args) - axes[1, 1].plot(list(range(1, T)), path.pi, label=r'$\pi_{t+1}$', **p_args) - ax.legend(ncol=3, **legend_args) - - plt.show() - - -def gen_fig_2(path): - """ - The parameter is the path namedtuple returned by compute_paths(). See - the docstring of that function for details. - """ - - T = len(path.c) - - # == Prepare axes == # - num_rows, num_cols = 2, 1 - fig, axes = plt.subplots(num_rows, num_cols, figsize=(10, 10)) - plt.subplots_adjust(hspace=0.5) - bbox = (0., 1.02, 1., .102) - bbox = (0., 1.02, 1., .102) - legend_args = {'bbox_to_anchor': bbox, 'loc': 3, 'mode': 'expand'} - p_args = {'lw': 2, 'alpha': 0.7} - - # == Plot adjustment factor == # - ax = axes[0] - ax.plot(list(range(2, T+1)), path.xi, label=r'$\xi_t$', **p_args) - ax.grid() - ax.set_xlabel(r'Time') - ax.legend(ncol=1, **legend_args) - - # == Plot adjusted cumulative return == # - ax = axes[1] - ax.plot(list(range(2, T+1)), path.Pi, label=r'$\Pi_t$', **p_args) - ax.grid() - ax.set_xlabel(r'Time') - ax.legend(ncol=1, **legend_args) - - plt.show() diff --git a/examples/lqramsey_ar1.py b/examples/lqramsey_ar1.py deleted file mode 100644 index 0eea50061..000000000 --- a/examples/lqramsey_ar1.py +++ /dev/null @@ -1,35 +0,0 @@ -""" -Filename: lqramsey_ar1.py -Authors: Thomas Sargent, Doc-Jin Jang, Jeong-hun Choi, John Stachurski - -Example 1: Govt spending is AR(1) and state is (g, 1). - -""" - -import numpy as np -from numpy import array -import lqramsey - -# == Parameters == # -beta = 1 / 1.05 -rho, mg = .7, .35 -A = np.identity(2) -A[0, :] = rho, mg * (1-rho) -C = np.zeros((2, 1)) -C[0, 0] = np.sqrt(1 - rho**2) * mg / 10 -Sg = array((1, 0)).reshape(1, 2) -Sd = array((0, 0)).reshape(1, 2) -Sb = array((0, 2.135)).reshape(1, 2) -Ss = array((0, 0)).reshape(1, 2) - -economy = lqramsey.Economy(beta=beta, - Sg=Sg, - Sd=Sd, - Sb=Sb, - Ss=Ss, - discrete=False, - proc=(A, C)) - -T = 50 -path = lqramsey.compute_paths(T, economy) -lqramsey.gen_fig_1(path) diff --git a/examples/lqramsey_discrete.py b/examples/lqramsey_discrete.py deleted file mode 100644 index 5db8c157d..000000000 --- a/examples/lqramsey_discrete.py +++ /dev/null @@ -1,38 +0,0 @@ -""" -Filename: lqramsey_discrete.py -Authors: Thomas Sargent, Doc-Jin Jang, Jeong-hun Choi, John Stachurski - -LQ Ramsey model with discrete exogenous process. - -""" -from numpy import array -import lqramsey - -# == Parameters == # -beta = 1 / 1.05 -P = array([[0.8, 0.2, 0.0], - [0.0, 0.5, 0.5], - [0.0, 0.0, 1.0]]) -# == Possible states of the world == # -# Each column is a state of the world. The rows are [g d b s 1] -x_vals = array([[0.5, 0.5, 0.25], - [0.0, 0.0, 0.0], - [2.2, 2.2, 2.2], - [0.0, 0.0, 0.0], - [1.0, 1.0, 1.0]]) -Sg = array((1, 0, 0, 0, 0)).reshape(1, 5) -Sd = array((0, 1, 0, 0, 0)).reshape(1, 5) -Sb = array((0, 0, 1, 0, 0)).reshape(1, 5) -Ss = array((0, 0, 0, 1, 0)).reshape(1, 5) - -economy = lqramsey.Economy(beta=beta, - Sg=Sg, - Sd=Sd, - Sb=Sb, - Ss=Ss, - discrete=True, - proc=(P, x_vals)) - -T = 15 -path = lqramsey.compute_paths(T, economy) -lqramsey.gen_fig_1(path) diff --git a/examples/lucas_stokey.py b/examples/lucas_stokey.py deleted file mode 100644 index 8a74ce84b..000000000 --- a/examples/lucas_stokey.py +++ /dev/null @@ -1,437 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Created on Wed Feb 18 15:43:37 2015 - -@author: dgevans -""" -import numpy as np -from scipy.optimize import root -from scipy.optimize import fmin_slsqp -from scipy.interpolate import UnivariateSpline -from quantecon import compute_fixed_point -from quantecon.markov import mc_sample_path - - -class Planners_Allocation_Sequential(object): - ''' - Class returns planner's allocation as a function of the multiplier on the - implementability constraint mu - ''' - def __init__(self,Para): - ''' - Initializes the class from the calibration Para - ''' - self.beta = Para.beta - self.Pi = Para.Pi - self.G = Para.G - self.S = len(Para.Pi) # number of states - self.Theta = Para.Theta - self.Para = Para - #now find the first best allocation - self.find_first_best() - - def find_first_best(self): - ''' - Find the first best allocation - ''' - Para = self.Para - S,Theta,Uc,Un,G = self.S,self.Theta,Para.Uc,Para.Un,self.G - - def res(z): - c = z[:S] - n = z[S:] - return np.hstack( - [Theta*Uc(c,n)+Un(c,n), Theta*n - c - G] - ) - res = root(res,0.5*np.ones(2*S)) - - if not res.success: - raise Exception('Could not find first best') - - self.cFB = res.x[:S] - self.nFB = res.x[S:] - self.XiFB = Uc(self.cFB,self.nFB) #multiplier on the resource constraint. - self.zFB = np.hstack([self.cFB,self.nFB,self.XiFB]) - - def time1_allocation(self,mu): - ''' - Computes optimal allocation for time t\geq 1 for a given \mu - ''' - Para = self.Para - S,Theta,G,Uc,Ucc,Un,Unn = self.S,self.Theta,self.G,Para.Uc,Para.Ucc,Para.Un,Para.Unn - def FOC(z): - c = z[:S] - n = z[S:2*S] - Xi = z[2*S:] - return np.hstack([ - Uc(c,n) - mu*(Ucc(c,n)*c+Uc(c,n)) -Xi, #foc c - Un(c,n) - mu*(Unn(c,n)*n+Un(c,n)) + Theta*Xi, #foc n - Theta*n - c - G #resource constraint - ]) - - #find the root of the FOC - res = root(FOC,self.zFB) - if not res.success: - raise Exception('Could not find LS allocation.') - z = res.x - c,n,Xi = z[:S],z[S:2*S],z[2*S:] - - #now compute x - I = Uc(c,n)*c + Un(c,n)*n - x = np.linalg.solve(np.eye(S) - self.beta*self.Pi, I ) - - return c,n,x,Xi - - def time0_allocation(self,B_,s_0): - ''' - Finds the optimal allocation given initial government debt B_ and state s_0 - ''' - Para,Pi,Theta,G,beta = self.Para,self.Pi,self.Theta,self.G,self.beta - Uc,Ucc,Un,Unn = Para.Uc,Para.Ucc,Para.Un,Para.Unn - - #first order conditions of planner's problem - def FOC(z): - mu,c,n,Xi = z - xprime = self.time1_allocation(mu)[2] - return np.hstack([ - Uc(c,n)*(c-B_) + Un(c,n)*n + beta*Pi[s_0].dot(xprime), - Uc(c,n) - mu*(Ucc(c,n)*(c-B_) + Uc(c,n)) - Xi, - Un(c,n) - mu*(Unn(c,n)*n+Un(c,n)) + Theta[s_0]*Xi, - (Theta*n - c - G)[s_0] - ]) - - #find root - res = root(FOC,np.array([0.,self.cFB[s_0],self.nFB[s_0],self.XiFB[s_0]])) - if not res.success: - raise Exception('Could not find time 0 LS allocation.') - - return res.x - - def time1_value(self,mu): - ''' - Find the value associated with multiplier mu - ''' - c,n,x,Xi = self.time1_allocation(mu) - U = self.Para.U(c,n) - V = np.linalg.solve(np.eye(self.S) - self.beta*self.Pi, U ) - return c,n,x,V - - def Tau(self,c,n): - ''' - Computes Tau given c,n - ''' - Para = self.Para - Uc,Un = Para.Uc(c,n),Para.Un(c,n) - - return 1+Un/(self.Theta * Uc) - - def simulate(self,B_,s_0,T,sHist=None): - ''' - Simulates planners policies for T periods - ''' - Para,Pi,beta = self.Para,self.Pi,self.beta - Uc = Para.Uc - - - if sHist == None: - sHist = mc_sample_path(Pi,s_0,T) - - cHist,nHist,Bhist,TauHist,muHist = np.zeros((5,T)) - RHist = np.zeros(T-1) - #time0 - mu,cHist[0],nHist[0],_ = self.time0_allocation(B_,s_0) - TauHist[0] = self.Tau(cHist[0],nHist[0])[s_0] - Bhist[0] = B_ - muHist[0] = mu - - #time 1 onward - for t in range(1,T): - c,n,x,Xi = self.time1_allocation(mu) - Tau = self.Tau(c,n) - u_c = Uc(c,n) - s = sHist[t] - Eu_c = Pi[sHist[t-1]].dot(u_c) - - cHist[t],nHist[t],Bhist[t],TauHist[t] = c[s],n[s],x[s]/u_c[s],Tau[s] - - RHist[t-1] = Uc(cHist[t-1],nHist[t-1])/(beta*Eu_c) - muHist[t] = mu - - return cHist,nHist,Bhist,TauHist,sHist,muHist,RHist - - - - -class Planners_Allocation_Bellman(object): - ''' - Compute the planner's allocation by solving Bellman - equation. - ''' - def __init__(self,Para,mugrid): - ''' - Initializes the class from the calibration Para - ''' - self.beta = Para.beta - self.Pi = Para.Pi - self.G = Para.G - self.S = len(Para.Pi) # number of states - self.Theta = Para.Theta - self.Para = Para - self.mugrid = mugrid - - #now find the first best allocation - self.solve_time1_bellman() - self.T.time_0 = True #Bellman equation now solves time 0 problem - - def solve_time1_bellman(self): - ''' - Solve the time 1 Bellman equation for calibration Para and initial grid mugrid0 - ''' - Para,mugrid0 = self.Para,self.mugrid - S = len(Para.Pi) - - #First get initial fit - PP = Planners_Allocation_Sequential(Para) - c,n,x,V = map(np.vstack, zip(*map(lambda mu: PP.time1_value(mu),mugrid0)) ) - - Vf,cf,nf,xprimef = {},{},{},{} - for s in range(2): - cf[s] = UnivariateSpline(x[:,s],c[:,s]) - nf[s] = UnivariateSpline(x[:,s],n[:,s]) - Vf[s] = UnivariateSpline(x[:,s],V[:,s]) - for sprime in range(S): - xprimef[s,sprime] = UnivariateSpline(x[:,s],x[:,s]) - policies = [cf,nf,xprimef] - - - #create xgrid - xbar = [x.min(0).max(),x.max(0).min()] - xgrid = np.linspace(xbar[0],xbar[1],len(mugrid0)) - self.xgrid = xgrid - - #Now iterate on bellman equation - T = BellmanEquation(Para,xgrid,policies) - diff = 1. - while diff > 1e-5: - PF = T(Vf) - - Vfnew,policies = self.fit_policy_function(PF) - - diff = 0. - for s in range(S): - diff = max(diff, np.abs((Vf[s](xgrid)-Vfnew[s](xgrid))/Vf[s](xgrid)).max() ) - - print(diff) - Vf = Vfnew - - #store value function policies and Bellman Equations - self.Vf = Vf - self.policies = policies - self.T = T - - def fit_policy_function(self,PF): - ''' - Fits the policy functions PF using the points xgrid using UnivariateSpline - ''' - xgrid,S = self.xgrid,self.S - - Vf,cf,nf,xprimef = {},{},{},{} - for s in range(S): - PFvec = np.vstack(map(lambda x:PF(x,s),xgrid)) - Vf[s] = UnivariateSpline(xgrid,PFvec[:,0],s=0) - cf[s] = UnivariateSpline(xgrid,PFvec[:,1],s=0,k=1) - nf[s] = UnivariateSpline(xgrid,PFvec[:,2],s=0,k=1) - for sprime in range(S): - xprimef[s,sprime] = UnivariateSpline(xgrid,PFvec[:,3+sprime],s=0,k=1) - - return Vf,[cf,nf,xprimef] - - def Tau(self,c,n): - ''' - Computes Tau given c,n - ''' - Para = self.Para - Uc,Un = Para.Uc(c,n),Para.Un(c,n) - - return 1+Un/(self.Theta * Uc) - - def time0_allocation(self,B_,s0): - ''' - Finds the optimal allocation given initial government debt B_ and state s_0 - ''' - PF = self.T(self.Vf) - - z0 = PF(B_,s0) - c0,n0,xprime0 = z0[1],z0[2],z0[3:] - return c0,n0,xprime0 - - def simulate(self,B_,s_0,T,sHist=None): - ''' - Simulates Ramsey plan for T periods - ''' - Para,Pi = self.Para,self.Pi - Uc = Para.Uc - cf,nf,xprimef = self.policies - - if sHist == None: - sHist = mc_sample_path(Pi,s_0,T) - - cHist,nHist,Bhist,TauHist,muHist = np.zeros((5,T)) - RHist = np.zeros(T-1) - #time0 - cHist[0],nHist[0],xprime = self.time0_allocation(B_,s_0) - TauHist[0] = self.Tau(cHist[0],nHist[0])[s_0] - Bhist[0] = B_ - muHist[0] = 0. - - #time 1 onward - for t in range(1,T): - s,x = sHist[t],xprime[sHist[t]] - c,n,xprime = np.empty(self.S),nf[s](x),np.empty(self.S) - for shat in range(self.S): - c[shat] = cf[shat](x) - for sprime in range(self.S): - xprime[sprime] = xprimef[s,sprime](x) - - Tau = self.Tau(c,n)[s] - u_c = Uc(c,n) - Eu_c = Pi[sHist[t-1]].dot(u_c) - muHist[t] = self.Vf[s](x,1) - - RHist[t-1] = Uc(cHist[t-1],nHist[t-1])/(self.beta*Eu_c) - - cHist[t],nHist[t],Bhist[t],TauHist[t] = c[s],n,x/u_c[s],Tau - - return cHist,nHist,Bhist,TauHist,sHist,muHist,RHist - -class BellmanEquation(object): - ''' - Bellman equation for the continuation of the Lucas-Stokey Problem - ''' - def __init__(self,Para,xgrid,policies0): - ''' - Initializes the class from the calibration Para - ''' - self.beta = Para.beta - self.Pi = Para.Pi - self.G = Para.G - self.S = len(Para.Pi) # number of states - self.Theta = Para.Theta - self.Para = Para - - self.xbar = [min(xgrid),max(xgrid)] - self.time_0 = False - - self.z0 = {} - cf,nf,xprimef = policies0 - for s in range(self.S): - for x in xgrid: - xprime0 = np.empty(self.S) - for sprime in range(self.S): - xprime0[sprime] = xprimef[s,sprime](x) - self.z0[x,s] = np.hstack([cf[s](x),nf[s](x),xprime0]) - - self.find_first_best() - - def find_first_best(self): - ''' - Find the first best allocation - ''' - Para = self.Para - S,Theta,Uc,Un,G = self.S,self.Theta,Para.Uc,Para.Un,self.G - - def res(z): - c = z[:S] - n = z[S:] - return np.hstack( - [Theta*Uc(c,n)+Un(c,n), Theta*n - c - G] - ) - res = root(res,0.5*np.ones(2*S)) - if not res.success: - raise Exception('Could not find first best') - - self.cFB = res.x[:S] - self.nFB = res.x[S:] - IFB = Uc(self.cFB,self.nFB)*self.cFB + Un(self.cFB,self.nFB)*self.nFB - - self.xFB = np.linalg.solve(np.eye(S) - self.beta*self.Pi, IFB) - - self.zFB = {} - for s in range(S): - self.zFB[s] = np.hstack([self.cFB[s],self.nFB[s],self.xFB]) - - - - def __call__(self,Vf): - ''' - Given continuation value function next period return value function this - period return T(V) and optimal policies - ''' - if not self.time_0: - PF = lambda x,s: self.get_policies_time1(x,s,Vf) - else: - PF = lambda B_,s0: self.get_policies_time0(B_,s0,Vf) - return PF - - def get_policies_time1(self,x,s,Vf): - ''' - Finds the optimal policies - ''' - Para,beta,Theta,G,S,Pi = self.Para,self.beta,self.Theta,self.G,self.S,self.Pi - U,Uc,Un = Para.U,Para.Uc,Para.Un - - def objf(z): - c,n,xprime = z[0],z[1],z[2:] - Vprime = np.empty(S) - for sprime in range(S): - Vprime[sprime] = Vf[sprime](xprime[sprime]) - - return -(U(c,n)+beta*Pi[s].dot(Vprime)) - - def cons(z): - c,n,xprime = z[0],z[1],z[2:] - return np.hstack([ - x - Uc(c,n)*c-Un(c,n)*n - beta*Pi[s].dot(xprime), - (Theta*n - c - G)[s] - ]) - - - out,fx,_,imode,smode = fmin_slsqp(objf,self.z0[x,s],f_eqcons=cons, - bounds=[(0.,100),(0.,100)]+[self.xbar]*S,full_output=True,iprint=0) - - if imode >0: - raise Exception(smode) - - self.z0[x,s] = out - return np.hstack([-fx,out]) - - def get_policies_time0(self,B_,s0,Vf): - ''' - Finds the optimal policies - ''' - Para,beta,Theta,G,S,Pi = self.Para,self.beta,self.Theta,self.G,self.S,self.Pi - U,Uc,Un = Para.U,Para.Uc,Para.Un - - def objf(z): - c,n,xprime = z[0],z[1],z[2:] - Vprime = np.empty(S) - for sprime in range(S): - Vprime[sprime] = Vf[sprime](xprime[sprime]) - - return -(U(c,n)+beta*Pi[s0].dot(Vprime)) - - def cons(z): - c,n,xprime = z[0],z[1],z[2:] - return np.hstack([ - -Uc(c,n)*(c-B_)-Un(c,n)*n - beta*Pi[s0].dot(xprime), - (Theta*n - c - G)[s0] - ]) - - - out,fx,_,imode,smode = fmin_slsqp(objf,self.zFB[s0],f_eqcons=cons, - bounds=[(0.,100),(0.,100)]+[self.xbar]*S,full_output=True,iprint=0) - - if imode >0: - raise Exception(smode) - - return np.hstack([-fx,out]) \ No newline at end of file diff --git a/examples/lucas_tree_price1.py b/examples/lucas_tree_price1.py deleted file mode 100644 index 99ce92269..000000000 --- a/examples/lucas_tree_price1.py +++ /dev/null @@ -1,22 +0,0 @@ - -from __future__ import division # Omit for Python 3.x -import matplotlib.pyplot as plt -from quantecon.models import LucasTree - -fig, ax = plt.subplots() - -tree = LucasTree(gamma=2, beta=0.95, alpha=0.90, sigma=0.1) -grid, price_vals = tree.grid, tree.compute_lt_price() -ax.plot(grid, price_vals, lw=2, alpha=0.7, label=r'$p^*(y)$') -ax.set_xlim(min(grid), max(grid)) - -# tree = LucasTree(gamma=3, beta=0.95, alpha=0.90, sigma=0.1) -# grid, price_vals = tree.grid, tree.compute_lt_price() -# ax.plot(grid, price_vals, lw=2, alpha=0.7, label='more patient') -# ax.set_xlim(min(grid), max(grid)) - -ax.set_xlabel(r'$y$', fontsize=16) -ax.set_ylabel(r'price', fontsize=16) -ax.legend(loc='upper left') - -plt.show() diff --git a/examples/main_LS.py b/examples/main_LS.py deleted file mode 100644 index 95bbe16f2..000000000 --- a/examples/main_LS.py +++ /dev/null @@ -1,162 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Created on Fri Feb 20 14:07:56 2015 - -@author: dgevans -""" -import matplotlib.pyplot as plt -import numpy as np -import lucas_stokey as LS -from calibrations.BGP import M1 -from calibrations.CES import M2 -from calibrations.CES import M_time_example - - -''' -Time Varying Example -''' - -PP_seq_time = LS.Planners_Allocation_Sequential(M_time_example) #solve sequential problem - -sHist_h = np.array([0,1,2,3,5,5,5]) -sHist_l = np.array([0,1,2,4,5,5,5]) - -sim_seq_h = PP_seq_time.simulate(1.,0,7,sHist_h) -sim_seq_l = PP_seq_time.simulate(1.,0,7,sHist_l) - -plt.figure(figsize=[14,10]) -plt.subplot(3,2,1) -plt.title('Consumption') -plt.plot(sim_seq_l[0],'-ok') -plt.plot(sim_seq_h[0],'-or') -plt.subplot(3,2,2) -plt.title('Labor Supply') -plt.plot(sim_seq_l[1],'-ok') -plt.plot(sim_seq_h[1],'-or') -plt.subplot(3,2,3) -plt.title('Government Debt') -plt.plot(sim_seq_l[2],'-ok') -plt.plot(sim_seq_h[2],'-or') -plt.subplot(3,2,4) -plt.title('Taxe Rate') -plt.plot(sim_seq_l[3],'-ok') -plt.plot(sim_seq_h[3],'-or') -plt.subplot(3,2,5) -plt.title('Government Spending') -plt.plot(M_time_example.G[sHist_l],'-ok') -plt.plot(M_time_example.G[sHist_h],'-or') -plt.subplot(3,2,6) -plt.title('Output') -plt.plot(M_time_example.Theta[sHist_l]*sim_seq_l[1],'-ok') -plt.plot(M_time_example.Theta[sHist_h]*sim_seq_h[1],'-or') - -plt.tight_layout() -plt.savefig('TaxSequence_time_varying.png') - -plt.figure(figsize=[8,5]) -plt.title('Gross Interest Rate') -plt.plot(sim_seq_l[-1],'-ok') -plt.plot(sim_seq_h[-1],'-or') -plt.tight_layout() -plt.savefig('InterestRate_time_varying.png') - -''' -Time 0 example -''' -PP_seq_time0 = LS.Planners_Allocation_Sequential(M2) #solve sequential problem - -B_vec = np.linspace(-1.5,1.,100) -taxpolicy = np.vstack([PP_seq_time0.simulate(B_,0,2)[3] for B_ in B_vec]) -interest_rate = np.vstack([PP_seq_time0.simulate(B_,0,3)[-1] for B_ in B_vec]) - -plt.figure(figsize=[14,6]) -plt.subplot(211) -plt.plot(B_vec,taxpolicy[:,0],linewidth=2.) -plt.plot(B_vec,taxpolicy[:,1],linewidth=2.) - -plt.title('Tax Rate') -plt.legend((r'Time $t=0$', 'Time $t\geq1$'),loc=2,shadow=True) -plt.subplot(212) -plt.title('Gross Interest Rate') -plt.plot(B_vec,interest_rate[:,0],linewidth=2.) -plt.plot(B_vec,interest_rate[:,1],linewidth=2.) -plt.xlabel('Initial Government Debt') -plt.tight_layout() - -plt.savefig('Time0_taxpolicy.png') - - - - -#compute the debt entered with at time 1 -B1_vec = np.hstack([PP_seq_time0.simulate(B_,0,2)[2][1] for B_ in B_vec]) -#now compute the optimal policy if the government could reset -tau1_reset = np.hstack([PP_seq_time0.simulate(B1,0,1)[3] for B1 in B1_vec]) - -plt.figure(figsize=[10,6]) -plt.plot(B_vec,taxpolicy[:,1],linewidth=2.) -plt.plot(B_vec,tau1_reset,linewidth=2.) -plt.xlabel('Initial Government Debt') -plt.title('Tax Rate') -plt.legend((r'$\tau_1$', r'$\tau_1^R$'),loc=2,shadow=True) -plt.tight_layout() - -plt.savefig('Time0_inconsistent.png') - - -''' -BGP Example -''' -#initialize mugrid for value function iteration -muvec = np.linspace(-0.6,0.0,200) - - -PP_seq = LS.Planners_Allocation_Sequential(M1) #solve sequential problem -PP_bel = LS.Planners_Allocation_Bellman(M1,muvec) #solve recursive problem - -T = 20 -#sHist = utilities.simulate_markov(M1.Pi,0,T) -sHist = np.array([0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0],dtype=int) - -#simulate -sim_seq = PP_seq.simulate(0.5,0,T,sHist) -sim_bel = PP_bel.simulate(0.5,0,T,sHist) - -#plot policies -plt.figure(figsize=[14,10]) -plt.subplot(3,2,1) -plt.title('Consumption') -plt.plot(sim_seq[0],'-ok') -plt.plot(sim_bel[0],'-xk') -plt.legend(('Sequential','Recursive'),loc='best') -plt.subplot(3,2,2) -plt.title('Labor Supply') -plt.plot(sim_seq[1],'-ok') -plt.plot(sim_bel[1],'-xk') -plt.subplot(3,2,3) -plt.title('Government Debt') -plt.plot(sim_seq[2],'-ok') -plt.plot(sim_bel[2],'-xk') -plt.subplot(3,2,4) -plt.title('Tax Rate') -plt.plot(sim_seq[3],'-ok') -plt.plot(sim_bel[3],'-xk') -plt.subplot(3,2,5) -plt.title('Government Spending') -plt.plot(M1.G[sHist],'-ok') -plt.plot(M1.G[sHist],'-xk') -plt.plot(M1.G[sHist],'-^k') -plt.subplot(3,2,6) -plt.title('Output') -plt.plot(M1.Theta[sHist]*sim_seq[1],'-ok') -plt.plot(M1.Theta[sHist]*sim_bel[1],'-xk') - -plt.tight_layout() -plt.savefig('TaxSequence_LS.png') - -plt.figure(figsize=[8,5]) -plt.title('Gross Interest Rate') -plt.plot(sim_seq[-1],'-ok') -plt.plot(sim_bel[-1],'-xk') -plt.legend(('Sequential','Recursive'),loc='best') -plt.tight_layout() diff --git a/examples/market.py b/examples/market.py deleted file mode 100644 index 335e4f2ef..000000000 --- a/examples/market.py +++ /dev/null @@ -1,58 +0,0 @@ -""" -Filename: market.py -Reference: http://quant-econ.net/py/python_oop.html -""" - -from __future__ import division -from scipy.integrate import quad - -class Market: - - def __init__(self, ad, bd, az, bz, tax): - """ - Set up market parameters. All parameters are scalars. See - http://quant-econ.net/py/python_oop.html for interpretation. - - """ - self.ad, self.bd, self.az, self.bz, self.tax = ad, bd, az, bz, tax - if ad < az: - raise ValueError('Insufficient demand.') - - def price(self): - "Return equilibrium price" - return (self.ad - self.az + self.bz*self.tax)/(self.bd + self.bz) - - def quantity(self): - "Compute equilibrium quantity" - return self.ad - self.bd * self.price() - - def consumer_surp(self): - "Compute consumer surplus" - # == Compute area under inverse demand function == # - integrand = lambda x: (self.ad/self.bd) - (1/self.bd)* x - area, error = quad(integrand, 0, self.quantity()) - return area - self.price() * self.quantity() - - def producer_surp(self): - "Compute producer surplus" - # == Compute area above inverse supply curve, excluding tax == # - integrand = lambda x: -(self.az/self.bz) + (1/self.bz) * x - area, error = quad(integrand, 0, self.quantity()) - return (self.price() - self.tax) * self.quantity() - area - - def taxrev(self): - "Compute tax revenue" - return self.tax * self.quantity() - - def inverse_demand(self,x): - "Compute inverse demand" - return self.ad/self.bd - (1/self.bd)* x - - def inverse_supply(self,x): - "Compute inverse supply curve" - return -(self.az/self.bz) + (1/self.bz) * x + self.tax - - def inverse_supply_no_tax(self,x): - "Compute inverse supply curve without tax" - return -(self.az/self.bz) + (1/self.bz) * x - diff --git a/examples/market.py~ b/examples/market.py~ deleted file mode 100644 index 335e4f2ef..000000000 --- a/examples/market.py~ +++ /dev/null @@ -1,58 +0,0 @@ -""" -Filename: market.py -Reference: http://quant-econ.net/py/python_oop.html -""" - -from __future__ import division -from scipy.integrate import quad - -class Market: - - def __init__(self, ad, bd, az, bz, tax): - """ - Set up market parameters. All parameters are scalars. See - http://quant-econ.net/py/python_oop.html for interpretation. - - """ - self.ad, self.bd, self.az, self.bz, self.tax = ad, bd, az, bz, tax - if ad < az: - raise ValueError('Insufficient demand.') - - def price(self): - "Return equilibrium price" - return (self.ad - self.az + self.bz*self.tax)/(self.bd + self.bz) - - def quantity(self): - "Compute equilibrium quantity" - return self.ad - self.bd * self.price() - - def consumer_surp(self): - "Compute consumer surplus" - # == Compute area under inverse demand function == # - integrand = lambda x: (self.ad/self.bd) - (1/self.bd)* x - area, error = quad(integrand, 0, self.quantity()) - return area - self.price() * self.quantity() - - def producer_surp(self): - "Compute producer surplus" - # == Compute area above inverse supply curve, excluding tax == # - integrand = lambda x: -(self.az/self.bz) + (1/self.bz) * x - area, error = quad(integrand, 0, self.quantity()) - return (self.price() - self.tax) * self.quantity() - area - - def taxrev(self): - "Compute tax revenue" - return self.tax * self.quantity() - - def inverse_demand(self,x): - "Compute inverse demand" - return self.ad/self.bd - (1/self.bd)* x - - def inverse_supply(self,x): - "Compute inverse supply curve" - return -(self.az/self.bz) + (1/self.bz) * x + self.tax - - def inverse_supply_no_tax(self,x): - "Compute inverse supply curve without tax" - return -(self.az/self.bz) + (1/self.bz) * x - diff --git a/examples/market_deadweight.py b/examples/market_deadweight.py deleted file mode 100644 index 0eb8a6e9b..000000000 --- a/examples/market_deadweight.py +++ /dev/null @@ -1,11 +0,0 @@ - -from market import Market - -def deadw(m): - "Computes deadweight loss for market m." - # == Create analogous market with no tax == # - m_no_tax = Market(m.ad, m.bd, m.az, m.bz, 0) - # == Compare surplus, return difference == # - surp1 = m_no_tax.consumer_surp() + m_no_tax.producer_surp() - surp2 = m.consumer_surp() + m.producer_surp() + m.taxrev() - return surp1 - surp2 diff --git a/examples/mc_convergence_plot.py b/examples/mc_convergence_plot.py deleted file mode 100644 index 2bc034075..000000000 --- a/examples/mc_convergence_plot.py +++ /dev/null @@ -1,40 +0,0 @@ -""" -Filename: mc_convergence_plot.py -Authors: John Stachurski, Thomas J. Sargent - -""" -import numpy as np -from mpl_toolkits.mplot3d import Axes3D -import matplotlib.pyplot as plt -from quantecon import mc_compute_stationary - -P = ((0.971, 0.029, 0.000), - (0.145, 0.778, 0.077), - (0.000, 0.508, 0.492)) -P = np.array(P) - -psi = (0.0, 0.2, 0.8) # Initial condition - -fig = plt.figure() -ax = fig.add_subplot(111, projection='3d') - -ax.set_xlim(0, 1) -ax.set_ylim(0, 1) -ax.set_zlim(0, 1) -ax.set_xticks((0.25, 0.5, 0.75)) -ax.set_yticks((0.25, 0.5, 0.75)) -ax.set_zticks((0.25, 0.5, 0.75)) - -x_vals, y_vals, z_vals = [], [], [] -for t in range(20): - x_vals.append(psi[0]) - y_vals.append(psi[1]) - z_vals.append(psi[2]) - psi = np.dot(psi, P) - -ax.scatter(x_vals, y_vals, z_vals, c='r', s=60) - -psi_star = mc_compute_stationary(P)[0] -ax.scatter(psi_star[0], psi_star[1], psi_star[2], c='k', s=60) - -plt.show() diff --git a/examples/nds.py b/examples/nds.py deleted file mode 100644 index 58adaa30f..000000000 --- a/examples/nds.py +++ /dev/null @@ -1,14 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -from scipy.stats import norm -from random import uniform - -fig, ax = plt.subplots() -x = np.linspace(-4, 4, 150) -for i in range(3): - m, s = uniform(-1, 1), uniform(1, 2) - y = norm.pdf(x, loc=m, scale=s) - current_label = r'$\mu = {0:.2f}$'.format(m) - ax.plot(x, y, linewidth=2, alpha=0.6, label=current_label) -ax.legend() -plt.show() diff --git a/examples/nx_demo.py b/examples/nx_demo.py deleted file mode 100644 index df40a0645..000000000 --- a/examples/nx_demo.py +++ /dev/null @@ -1,22 +0,0 @@ -""" -Filename: nx_demo.py -Authors: John Stachurski and Thomas J. Sargent -""" - -import networkx as nx -import matplotlib.pyplot as plt -import numpy as np - -G = nx.random_geometric_graph(200, 0.12) # Generate random graph -pos = nx.get_node_attributes(G, 'pos') # Get positions of nodes -# find node nearest the center point (0.5,0.5) -dists = [(x - 0.5)**2 + (y - 0.5)**2 for x, y in list(pos.values())] -ncenter = np.argmin(dists) -# Plot graph, coloring by path length from central node -p = nx.single_source_shortest_path_length(G, ncenter) -plt.figure() -nx.draw_networkx_edges(G, pos, alpha=0.4) -nx.draw_networkx_nodes(G, pos, nodelist=list(p.keys()), - node_size=120, alpha=0.5, - node_color=list(p.values()), cmap=plt.cm.jet_r) -plt.show() diff --git a/examples/odu_plot_densities.py b/examples/odu_plot_densities.py deleted file mode 100644 index 281efd605..000000000 --- a/examples/odu_plot_densities.py +++ /dev/null @@ -1,16 +0,0 @@ -""" -Filename: odu_plot_densities.py -Authors: John Stachurski, Thomas J. Sargent - -""" -import numpy as np -import matplotlib.pyplot as plt -from quantecon.models import SearchProblem - -sp = SearchProblem(F_a=1, F_b=1, G_a=3, G_b=1.2) -grid = np.linspace(0, 2, 150) -fig, ax = plt.subplots() -ax.plot(grid, sp.f(grid), label=r'$f$', lw=2) -ax.plot(grid, sp.g(grid), label=r'$g$', lw=2) -ax.legend(loc=0) -plt.show() diff --git a/examples/odu_vfi_plots.py b/examples/odu_vfi_plots.py deleted file mode 100644 index e4fc74430..000000000 --- a/examples/odu_vfi_plots.py +++ /dev/null @@ -1,55 +0,0 @@ -""" -Filename: odu_vfi_plots.py -Authors: John Stachurski and Thomas Sargent -""" - -import matplotlib.pyplot as plt -from mpl_toolkits.mplot3d.axes3d import Axes3D -from matplotlib import cm -from scipy.interpolate import LinearNDInterpolator -import numpy as np -from quantecon import compute_fixed_point -from quantecon.models import SearchProblem - - -sp = SearchProblem(w_grid_size=100, pi_grid_size=100) -v_init = np.zeros(len(sp.grid_points)) + sp.c / (1 - sp.beta) -v = compute_fixed_point(sp.bellman_operator, v_init) -policy = sp.get_greedy(v) - -# Make functions from these arrays by interpolation -vf = LinearNDInterpolator(sp.grid_points, v) -pf = LinearNDInterpolator(sp.grid_points, policy) - -pi_plot_grid_size, w_plot_grid_size = 100, 100 -pi_plot_grid = np.linspace(0.001, 0.99, pi_plot_grid_size) -w_plot_grid = np.linspace(0, sp.w_max, w_plot_grid_size) - -# plot_choice = 'value_function' -plot_choice = 'policy_function' - -if plot_choice == 'value_function': - Z = np.empty((w_plot_grid_size, pi_plot_grid_size)) - for i in range(w_plot_grid_size): - for j in range(pi_plot_grid_size): - Z[i, j] = vf(w_plot_grid[i], pi_plot_grid[j]) - fig, ax = plt.subplots() - ax.contourf(pi_plot_grid, w_plot_grid, Z, 12, alpha=0.6, cmap=cm.jet) - cs = ax.contour(pi_plot_grid, w_plot_grid, Z, 12, colors="black") - ax.clabel(cs, inline=1, fontsize=10) - ax.set_xlabel('pi', fontsize=14) - ax.set_ylabel('wage', fontsize=14) -else: - Z = np.empty((w_plot_grid_size, pi_plot_grid_size)) - for i in range(w_plot_grid_size): - for j in range(pi_plot_grid_size): - Z[i, j] = pf(w_plot_grid[i], pi_plot_grid[j]) - fig, ax = plt.subplots() - ax.contourf(pi_plot_grid, w_plot_grid, Z, 1, alpha=0.6, cmap=cm.jet) - ax.contour(pi_plot_grid, w_plot_grid, Z, 1, colors="black") - ax.set_xlabel('pi', fontsize=14) - ax.set_ylabel('wage', fontsize=14) - ax.text(0.4, 1.0, 'reject') - ax.text(0.7, 1.8, 'accept') - -plt.show() diff --git a/examples/oligopoly.py b/examples/oligopoly.py deleted file mode 100644 index 74c97e40e..000000000 --- a/examples/oligopoly.py +++ /dev/null @@ -1,172 +0,0 @@ -""" -Filename: oligopoly.py -Authors: Chase Coleman, Tom Sargent, Balint Szoke -This is an example for the lecture dyn_stack.rst from the QuantEcon -series of lectures by Tom Sargent and John Stachurski. -We deal with a large monopolistic firm who faces costs: -C_t = e Q_t + .5 g Q_t^2 + .5 c (Q_{t+1} - Q_t)^2 -where the fringe firms face: -sigma_t = d q_t + .5 h q_t^2 + .5 c (q_{t+1} - q_t)^2 -Additionally, there is a linear inverse demand curve of the form: -p_t = A_0 - A_1 (Q_t + \bar{q_t}) + \eta_t, -where: -.. math - \eta_{t+1} = \rho \eta_t + C_{\varepsilon} \varepsilon_{t+1}; - \varepsilon_{t+1} \sim N(0, 1) -For more details, see the lecture. -""" -import numpy as np -import scipy.linalg as la -from quantecon import LQ -from quantecon.matrix_eqn import solve_discrete_lyapunov -from scipy.optimize import root - - -def setup_matrices(params): - """ - This function sets up the A, B, R, Q for the oligopoly problem - described in the lecture. - Parameters - ---------- - params : Array(Float, ndim=1) - Contains the parameters that describe the problem in the order - [a0, a1, rho, c_eps, c, d, e, g, h, beta] - Returns - ------- - (A, B, Q, R) : Array(Float, ndim=2) - These matrices describe the oligopoly problem. - """ - - # Left hand side of (37) - Alhs = np.eye(5) - Alhs[4, :] = np.array([a0-d, 1., -a1, -a1-h, c]) - Alhsinv = la.inv(Alhs) - - # Right hand side of (37) - Brhs = np.array([[0., 0., 1., 0., 0.]]).T - Arhs = np.eye(5) - Arhs[1, 1] = rho - Arhs[3, 4] = 1. - Arhs[4, 4] = c / beta - - # R from equation (40) - R = np.array([[0., 0., (a0-e)/2., 0., 0.], - [0., 0., 1./2., 0., 0.], - [(a0-e)/2., 1./2, -a1 - .5*g, -a1/2, 0.], - [0., 0., -a1/2, 0., 0.], - [0., 0., 0., 0., 0.]]) - - Rf = np.array([[0., 0., 0., 0., 0., (a0-d)/2.], - [0., 0., 0., 0., 0., 1./2.], - [0., 0., 0., 0., 0., -a1/2.], - [0., 0., 0., 0., 0., -a1/2.], - [0., 0., 0., 0., 0., 0.], - [(a0-d)/2., 1./2., -a1/2., -a1/2., 0., -h/2.]]) - - Q = np.array([[c/2]]) - - A = Alhsinv.dot(Arhs) - B = Alhsinv.dot(Brhs) - - return A, B, Q, R, Rf - - -def find_PFd(A, B, Q, R, Rf, beta=.95): - """ - Taking the parameters A, B, Q, R as found in the `setup_matrices`, - we find the value function of the optimal linear regulator problem. - This is steps 2 and 3 in the lecture notes. - Parameters - ---------- - (A, B, Q, R) : Array(Float, ndim=2) - The matrices that describe the oligopoly problem - Returns - ------- - (P, F, d) : Array(Float, ndim=2) - The matrix that describes the value function of the optimal - linear regulator problem. - """ - - lq = LQ(Q, -R, A, B, beta=beta) - P, F, d = lq.stationary_values() - - Af = np.vstack((np.hstack([A-np.dot(B,F), np.array([[0., 0., 0., 0., 0.]]).T]),np.array([[0., 0., 0., 0., 0., 1.]]))) - Bf = np.array([[0., 0., 0., 0., 0., 1.]]).T - - lqf = LQ(Q, -Rf, Af, Bf, beta=beta) - Pf, Ff, df = lqf.stationary_values() - - return P, F, d, Pf, Ff, df - - -def solve_for_opt_policy(params, eta0=0., Q0=0., q0=0.): - """ - Taking the parameters as given, solve for the optimal decision rules - for the firm. - Parameters - ---------- - params : Array(Float, ndim=1) - This holds all of the model parameters in an array - Returns - ------- - out : - """ - # Step 1/2: Formulate/Solve the optimal linear regulator - (A, B, Q, R, Rf) = setup_matrices(params) - (P, F, d, Pf, Ff, df) = find_PFd(A, B, Q, R, Rf, beta=beta) - - # Step 3: Convert implementation into state variables (Find coeffs) - P22 = P[-1, -1] - P21 = P[-1, :-1] - P22inv = P22**(-1) - - # Step 4: Find optimal x_0 and \mu_{x, 0} - z0 = np.array([1., eta0, Q0, q0]) - x0 = -P22inv*np.dot(P21, z0) - D0 = -np.dot(P22inv, P21) - - # Return -F and -Ff because we use u_t = -F y_t - return P, -F, D0, Pf, -Ff - - -# Parameter values -a0 = 100. -a1 = 1. -rho = .8 -c_eps = .2 -c = 1. -d = 20. -e = 20. -g = .2 -h = .2 -beta = .95 -params = np.array([a0, a1, rho, c_eps, c, d, e, g, h, beta]) - - -P, F, D0, Pf,Ff = solve_for_opt_policy(params) - - -# Checking time-inconsistency: -A, B, Q, R, Rf = setup_matrices(params) -# arbitrary initial z_0 -y0 = np.array([[1, 1, 1, 1]]).T -# optimal x_0 = i_0 -i0 = np.dot(D0,y0) -# iterate one period using the closed-loop system -y1 = np.dot( A + np.dot(B,F) , np.vstack([y0, i0]) ) -# the last element of y_1 is x_1 = i_1 -i1_0 = y1[-1,0] - -# compare this to the case when the leader solves a Stackelberg problem -# in period 1. if in period 1 the leader could choose i1 given -# (1, v_1, Q_1, \bar{q}_1) -i1_1 = np.dot(D0, y1[0:-1,0]) - - -print("P = {}".format(P)) -print("-F = {}".format(F)) -print("D0 = {}".format(D0)) -print("Pf = {}".format(Pf)) -print("-Ff = {}".format(Ff)) -print("i1_0 = {}".format(i1_0)) -print("i1_1 = {}".format(i1_1)) diff --git a/examples/oligopoly.py~ b/examples/oligopoly.py~ deleted file mode 100644 index a596f0b33..000000000 --- a/examples/oligopoly.py~ +++ /dev/null @@ -1,181 +0,0 @@ -""" -Filename: oligopoly.py -Authors: Chase Coleman - -This is an example for the lecture dyn_stack.rst from the QuantEcon -series of lectures by Tom Sargent and John Stachurski. - -We deal with a large monopolistic firm who faces costs: - -C_t = e Q_t + .5 g Q_t^2 + .5 c (Q_{t+1} - Q_t)^2 - -where the fringe firms face: - -sigma_t = d q_t + .5 h q_t^2 + .5 c (q_{t+1} - q_t)^2 - -Additionally, there is a linear inverse demand curve of the form: - -p_t = A_0 - A_1 (Q_t + \bar{q_t}) + \eta_t, - -where: - -.. math - \eta_{t+1} = \rho \eta_t + C_{\varepsilon} \varepsilon_{t+1}; - \varepsilon_{t+1} \sim N(0, 1) - -For more details, see the lecture. -""" -import numpy as np -import scipy.linalg as la -from quantecon import LQ -from quantecon.matrix_eqn import solve_discrete_lyapunov -from scipy.optimize import root - - -def setup_matrices(params): - """ - This function sets up the A, B, R, Q for the oligopoly problem - described in the lecture. - - Parameters - ---------- - params : Array(Float, ndim=1) - Contains the parameters that describe the problem in the order - [a0, a1, rho, c_eps, c, d, e, g, h, beta] - - Returns - ------- - (A, B, Q, R) : Array(Float, ndim=2) - These matrices describe the oligopoly problem. - """ - - # Left hand side of (37) - Alhs = np.eye(5) - Alhs[4, :] = np.array([a0-d, 1., -a1, -a1-h, c]) - Alhsinv = la.inv(Alhs) - - # Right hand side of (37) - Brhs = np.array([[0., 0., 1., 0., 0.]]).T - Arhs = np.eye(5) - Arhs[1, 1] = rho - Arhs[3, 4] = 1. - Arhs[4, 4] = c / beta - - # R from equation (40) - R = np.array([[0., 0., (a0-e)/2., 0., 0.], - [0., 0., 1./2., 0., 0.], - [(a0-e)/2., 1./2, -a1 - .5*g, -a1/2, 0.], - [0., 0., -a1/2, 0., 0.], - [0., 0., 0., 0., 0.]]) - Q = np.array([[c/2]]) - - A = Alhsinv.dot(Arhs) - B = Alhsinv.dot(Brhs) - - return A, B, Q, R - - -def find_PFd(A, B, Q, R, beta=.95): - """ - Taking the parameters A, B, Q, R as found in the `setup_matrices`, - we find the value function of the optimal linear regulator problem. - This is steps 2 and 3 in the lecture notes. - - Parameters - ---------- - (A, B, Q, R) : Array(Float, ndim=2) - The matrices that describe the oligopoly problem - - Returns - ------- - (P, F, d) : Array(Float, ndim=2) - The matrix that describes the value function of the optimal - linear regulator problem. - - """ - - lq = LQ(Q, -R, A, B, beta=beta) - P, F, d = lq.stationary_values() - - return P, F, d - - -def solve_for_opt_policy(params, eta0=0., Q0=0., q0=0.): - """ - Taking the parameters as given, solve for the optimal decision rules - for the firm. - - Parameters - ---------- - params : Array(Float, ndim=1) - This holds all of the model parameters in an array - - Returns - ------- - out : - - """ - # Step 1/2: Formulate/Solve the optimal linear regulator - (A, B, Q, R) = setup_matrices(params) - (P, F, d) = find_PFd(A, B, Q, R, beta=beta) - - # Step 3: Convert implementation into state variables (Find coeffs) - P22 = P[-1, -1] - P21 = P[-1, :-1] - P22inv = P22**(-1) - dotmat = np.empty((5, 5)) - upper = np.eye(4, 5) # Gives me 4x4 identity with a column of 0s - lower = np.hstack([-P22inv*P21, P22inv]) - dotmat[:-1, :] = upper - dotmat[-1, :] = lower - - coeffs = np.dot(-F, dotmat) - - # Step 4: Find optimal x_0 and \mu_{x, 0} - z0 = np.array([1., eta0, Q0, q0]) - x0 = -P22inv*np.dot(P21, z0) - - # Do some rearranging for convenient representation of policy - # TODO: Finish getting the equations into the from - # u_t = rho u_{t-1} + gamma_1 z_t + gamma_2 z_{t-1} - - part1 = np.vstack([np.eye(4, 5), P[-1, :]]) - part2 = A - np.dot(B, F) - part3 = dotmat - m = np.dot(part1, part2).dot(part3) - m12 = m[-1, :-1] - m22 = m[-1, -1] - - f = np.dot(-F, dotmat) - f11 = f[-1, :-1] - f12 = f[-1, -1] - - coeff_utm1 = f12*m22*f12**(-1) - coeff_zt = coeffs[0, :-1] - coeff_ztm1 = f12*(m12 - f12**(-1)*m22*f11) - - return coeffs, x0, (coeff_utm1, coeff_zt, coeff_ztm1) - - -# Parameter values -a0 = 100. -a1 = 1. -rho = .8 -c_eps = .2 -c = 1. -d = 20. -e = 20. -g = .2 -h = .2 -beta = .95 -params = np.array([a0, a1, rho, c_eps, c, d, e, g, h, beta]) - - -coefficients, x0, alt_coeffs = solve_for_opt_policy(params) - -print("The original coefficients are") -print("u_t = {} [z_t mu_[x, t]]'".format(coefficients)) -print("or in other terms") -print("u_t = {} u_[t-1] \n + {} z_t \n + {} z_[t-1]".format(alt_coeffs[0], - alt_coeffs[1], - alt_coeffs[2])) diff --git a/examples/optgrowth_v0.py b/examples/optgrowth_v0.py deleted file mode 100644 index 39b52dc13..000000000 --- a/examples/optgrowth_v0.py +++ /dev/null @@ -1,71 +0,0 @@ -""" -Filename: optgrowth_v0.py -Authors: John Stachurski and Thomas Sargent - -A first pass at solving the optimal growth problem via value function -iteration. A more general version is provided in optgrowth.py. - -""" -from __future__ import division # Omit for Python 3.x -import matplotlib.pyplot as plt -import numpy as np -from numpy import log -from scipy.optimize import fminbound -from scipy import interp - -# Primitives and grid -alpha = 0.65 -beta = 0.95 -grid_max = 2 -grid_size = 150 -grid = np.linspace(1e-6, grid_max, grid_size) -# Exact solution -ab = alpha * beta -c1 = (log(1 - ab) + log(ab) * ab / (1 - ab)) / (1 - beta) -c2 = alpha / (1 - ab) - - -def v_star(k): - return c1 + c2 * log(k) - - -def bellman_operator(w): - """ - The approximate Bellman operator, which computes and returns the updated - value function Tw on the grid points. - - * w is a flat NumPy array with len(w) = len(grid) - - The vector w represents the value of the input function on the grid - points. - """ - # === Apply linear interpolation to w === # - Aw = lambda x: interp(x, grid, w) - - # === set Tw[i] equal to max_c { log(c) + beta w(f(k_i) - c)} === # - Tw = np.empty(grid_size) - for i, k in enumerate(grid): - objective = lambda c: - log(c) - beta * Aw(k**alpha - c) - c_star = fminbound(objective, 1e-6, k**alpha) - Tw[i] = - objective(c_star) - - return Tw - -# === If file is run directly, not imported, produce figure === # -if __name__ == '__main__': - - w = 5 * log(grid) - 25 # An initial condition -- fairly arbitrary - n = 35 - fig, ax = plt.subplots() - ax.set_ylim(-40, -20) - ax.set_xlim(np.min(grid), np.max(grid)) - lb = 'initial condition' - ax.plot(grid, w, color=plt.cm.jet(0), lw=2, alpha=0.6, label=lb) - for i in range(n): - w = bellman_operator(w) - ax.plot(grid, w, color=plt.cm.jet(i / n), lw=2, alpha=0.6) - lb = 'true value function' - ax.plot(grid, v_star(grid), 'k-', lw=2, alpha=0.8, label=lb) - ax.legend(loc='upper left') - - plt.show() diff --git a/examples/paths_and_hist.py b/examples/paths_and_hist.py deleted file mode 100644 index 6fc891e29..000000000 --- a/examples/paths_and_hist.py +++ /dev/null @@ -1,49 +0,0 @@ - -import numpy as np -import matplotlib.pyplot as plt -from quantecon import LinearStateSpace -import random - -phi_1, phi_2, phi_3, phi_4 = 0.5, -0.2, 0, 0.5 -sigma = 0.1 - -A = [[phi_1, phi_2, phi_3, phi_4], - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 1, 0]] -C = [[sigma], [0], [0], [0]] -G = [1, 0, 0, 0] - -T = 30 -ar = LinearStateSpace(A, C, G, mu_0=np.ones(4)) - -ymin, ymax = -0.8, 1.25 - -fig, axes = plt.subplots(1, 2, figsize=(8, 3)) - -for ax in axes: - ax.grid(alpha=0.4) - -ax = axes[0] - -ax.set_ylim(ymin, ymax) -ax.set_ylabel(r'$y_t$', fontsize=16) -ax.vlines((T,), -1.5, 1.5) - -ax.set_xticks((T,)) -ax.set_xticklabels((r'$T$',)) - -sample = [] -for i in range(20): - rcolor = random.choice(('c', 'g', 'b', 'k')) - x, y = ar.simulate(ts_length=T+15) - y = y.flatten() - ax.plot(y, color=rcolor, lw=1, alpha=0.5) - ax.plot((T,), (y[T],), 'ko', alpha=0.5) - sample.append(y[T]) - -y = y.flatten() -axes[1].set_ylim(ymin, ymax) -axes[1].hist(sample, bins=16, normed=True, orientation='horizontal', alpha=0.5) - -plt.show() diff --git a/examples/paths_and_stationarity.py b/examples/paths_and_stationarity.py deleted file mode 100644 index 97bcdce7b..000000000 --- a/examples/paths_and_stationarity.py +++ /dev/null @@ -1,43 +0,0 @@ - -import numpy as np -import matplotlib.pyplot as plt -from quantecon import LinearStateSpace -import random - -phi_1, phi_2, phi_3, phi_4 = 0.5, -0.2, 0, 0.5 -sigma = 0.1 - -A = [[phi_1, phi_2, phi_3, phi_4], - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 1, 0]] -C = [[sigma], [0], [0], [0]] -G = [1, 0, 0, 0] - -T0 = 10 -T1 = 50 -T2 = 75 -T4 = 100 - -ar = LinearStateSpace(A, C, G, mu_0=np.ones(4)) -ymin, ymax = -0.8, 1.25 - -fig, ax = plt.subplots(figsize=(8, 5)) - -ax.grid(alpha=0.4) -ax.set_ylim(ymin, ymax) -ax.set_ylabel(r'$y_t$', fontsize=16) -ax.vlines((T0, T1, T2), -1.5, 1.5) - -ax.set_xticks((T0, T1, T2)) -ax.set_xticklabels((r"$T$", r"$T'$", r"$T''$"), fontsize=14) - -sample = [] -for i in range(80): - rcolor = random.choice(('c', 'g', 'b')) - x, y = ar.simulate(ts_length=T4) - y = y.flatten() - ax.plot(y, color=rcolor, lw=0.8, alpha=0.5) - ax.plot((T0, T1, T2), (y[T0], y[T1], y[T2],), 'ko', alpha=0.5) - -plt.show() diff --git a/examples/perm_inc_figs.py b/examples/perm_inc_figs.py deleted file mode 100644 index 7786f9bf5..000000000 --- a/examples/perm_inc_figs.py +++ /dev/null @@ -1,65 +0,0 @@ -""" -Plots consumption, income and debt for the simple infinite horizon LQ -permanent income model with Gaussian iid income. -""" - - -import random -import numpy as np -import matplotlib.pyplot as plt - -r = 0.05 -beta = 1 / (1 + r) -T = 60 -sigma = 0.15 -mu = 1 - - -def time_path(): - w = np.random.randn(T+1) # w_0, w_1, ..., w_T - w[0] = 0 - b = np.zeros(T+1) - for t in range(1, T+1): - b[t] = w[1:t].sum() - b = - sigma * b - c = mu + (1 - beta) * (sigma * w - b) - return w, b, c - - -# == Figure showing a typical realization == # - -if 1: - fig, ax = plt.subplots() - - p_args = {'lw': 2, 'alpha': 0.7} - ax.grid() - ax.set_xlabel(r'Time') - bbox = (0., 1.02, 1., .102) - legend_args = {'bbox_to_anchor': bbox, 'loc': 'upper left', - 'mode': 'expand'} - - w, b, c = time_path() - ax.plot(list(range(T+1)), mu + sigma * w, 'g-', - label="non-financial income", **p_args) - ax.plot(list(range(T+1)), c, 'k-', label="consumption", **p_args) - ax.plot(list(range(T+1)), b, 'b-', label="debt", **p_args) - ax.legend(ncol=3, **legend_args) - - plt.show() - -# == Figure showing multiple consumption paths == # - -if 0: - fig, ax = plt.subplots() - - p_args = {'lw': 0.8, 'alpha': 0.7} - ax.grid() - ax.set_xlabel(r'Time') - ax.set_ylabel(r'Consumption') - b_sum = np.zeros(T+1) - for i in range(250): - rcolor = random.choice(('c', 'g', 'b', 'k')) - w, b, c = time_path() - ax.plot(list(range(T+1)), c, color=rcolor, **p_args) - - plt.show() diff --git a/examples/perm_inc_ir.py b/examples/perm_inc_ir.py deleted file mode 100644 index a63cd1b8e..000000000 --- a/examples/perm_inc_ir.py +++ /dev/null @@ -1,58 +0,0 @@ -""" -Impulse response functions for the LQ permanent income model permanent and -transitory shocks. -""" - - -import numpy as np -import matplotlib.pyplot as plt - -r = 0.05 -beta = 1 / (1 + r) -T = 20 # Time horizon -S = 5 # Impulse date -sigma1 = sigma2 = 0.15 - - -def time_path(permanent=False): - "Time path of consumption and debt given shock sequence" - w1 = np.zeros(T+1) - w2 = np.zeros(T+1) - b = np.zeros(T+1) - c = np.zeros(T+1) - if permanent: - w1[S+1] = 1.0 - else: - w2[S+1] = 1.0 - for t in range(1, T): - b[t+1] = b[t] - sigma2 * w2[t] - c[t+1] = c[t] + sigma1 * w1[t+1] + (1 - beta) * sigma2 * w2[t+1] - return b, c - - -fig, axes = plt.subplots(2, 1) -plt.subplots_adjust(hspace=0.5) -p_args = {'lw': 2, 'alpha': 0.7} - -L = 0.175 - -for ax in axes: - ax.grid(alpha=0.5) - ax.set_xlabel(r'Time') - ax.set_ylim(-L, L) - ax.plot((S, S), (-L, L), 'k-', lw=0.5) - -ax = axes[0] -b, c = time_path(permanent=0) -ax.set_title('impulse-response, transitory income shock') -ax.plot(list(range(T+1)), c, 'g-', label="consumption", **p_args) -ax.plot(list(range(T+1)), b, 'b-', label="debt", **p_args) -ax.legend(loc='upper right') - -ax = axes[1] -b, c = time_path(permanent=1) -ax.set_title('impulse-response, permanent income shock') -ax.plot(list(range(T+1)), c, 'g-', label="consumption", **p_args) -ax.plot(list(range(T+1)), b, 'b-', label="debt", **p_args) -ax.legend(loc='lower right') -plt.show() diff --git a/examples/plot_example_1.py b/examples/plot_example_1.py deleted file mode 100644 index 441bfb4d6..000000000 --- a/examples/plot_example_1.py +++ /dev/null @@ -1,7 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -fig, ax = plt.subplots() -x = np.linspace(0, 10, 200) -y = np.sin(x) -ax.plot(x, y, 'b-', linewidth=2) -plt.show() diff --git a/examples/plot_example_2.py b/examples/plot_example_2.py deleted file mode 100644 index e7c4915c0..000000000 --- a/examples/plot_example_2.py +++ /dev/null @@ -1,8 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -fig, ax = plt.subplots() -x = np.linspace(0, 10, 200) -y = np.sin(x) -ax.plot(x, y, 'r-', lw=2, label='sine function', alpha=0.6) -ax.legend(loc='upper center') -plt.show() diff --git a/examples/plot_example_3.py b/examples/plot_example_3.py deleted file mode 100644 index 2b8a8ab16..000000000 --- a/examples/plot_example_3.py +++ /dev/null @@ -1,8 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -fig, ax = plt.subplots() -x = np.linspace(0, 10, 200) -y = np.sin(x) -ax.plot(x, y, 'r-', lw=2, label=r'$y=\sin(x)$', alpha=0.6) -ax.legend(loc='upper center') -plt.show() diff --git a/examples/plot_example_4.py b/examples/plot_example_4.py deleted file mode 100644 index 4bb052f5b..000000000 --- a/examples/plot_example_4.py +++ /dev/null @@ -1,13 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -from scipy.stats import norm -from random import uniform -fig, ax = plt.subplots() -x = np.linspace(-4, 4, 150) -for i in range(3): - m, s = uniform(-1, 1), uniform(1, 2) - y = norm.pdf(x, loc=m, scale=s) - current_label = r'$\mu = {0:.2f}$'.format(m) - ax.plot(x, y, lw=2, alpha=0.6, label=current_label) -ax.legend() -plt.show() diff --git a/examples/plot_example_5.py b/examples/plot_example_5.py deleted file mode 100644 index b924d9731..000000000 --- a/examples/plot_example_5.py +++ /dev/null @@ -1,15 +0,0 @@ -import matplotlib.pyplot as plt -from scipy.stats import norm -from random import uniform -num_rows, num_cols = 2, 3 -fig, axes = plt.subplots(num_rows, num_cols, figsize=(12, 8)) -for i in range(num_rows): - for j in range(num_cols): - m, s = uniform(-1, 1), uniform(1, 2) - x = norm.rvs(loc=m, scale=s, size=100) - axes[i, j].hist(x, alpha=0.6, bins=20) - t = r'$\mu = {0:.1f},\; \sigma = {1:.1f}$'.format(m, s) - axes[i, j].set_title(t) - axes[i, j].set_xticks([-4, 0, 4]) - axes[i, j].set_yticks([]) -plt.show() diff --git a/examples/plot_market.py b/examples/plot_market.py deleted file mode 100644 index 8e35443a5..000000000 --- a/examples/plot_market.py +++ /dev/null @@ -1,24 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -from market import Market - -# Baseline ad, bd, az, bz, tax -baseline_params = 15, .5, -2, .5, 3 -m = Market(*baseline_params) - -q_max = m.quantity() * 2 -q_grid = np.linspace(0.0, q_max, 100) -pd = m.inverse_demand(q_grid) -ps = m.inverse_supply(q_grid) -psno = m.inverse_supply_no_tax(q_grid) - -fig, ax = plt.subplots() -ax.plot(q_grid, pd, lw=2, alpha=0.6, label='demand') -ax.plot(q_grid, ps, lw=2, alpha=0.6, label='supply') -ax.plot(q_grid, psno, '--k', lw=2, alpha=0.6, label='supply without tax') -ax.set_xlabel('quantity', fontsize=14) -ax.set_xlim(0, q_max) -ax.set_ylabel('price', fontsize=14) -ax.legend(loc='lower right', frameon=False, fontsize=14) -plt.show() - diff --git a/examples/preim1.py b/examples/preim1.py deleted file mode 100644 index aed9b6144..000000000 --- a/examples/preim1.py +++ /dev/null @@ -1,53 +0,0 @@ -""" -QE by Tom Sargent and John Stachurski. -Illustrates preimages of functions -""" -import matplotlib.pyplot as plt -import numpy as np - - -def f(x): - return 0.6 * np.cos(4 * x) + 1.4 - - -xmin, xmax = -1, 1 -x = np.linspace(xmin, xmax, 160) -y = f(x) -ya, yb = np.min(y), np.max(y) - -fig, axes = plt.subplots(2, 1, figsize=(8, 8)) - -for ax in axes: - # Set the axes through the origin - for spine in ['left', 'bottom']: - ax.spines[spine].set_position('zero') - for spine in ['right', 'top']: - ax.spines[spine].set_color('none') - - ax.set_ylim(-0.6, 3.2) - ax.set_xlim(xmin, xmax) - ax.set_yticks(()) - ax.set_xticks(()) - - ax.plot(x, y, 'k-', lw=2, label=r'$f$') - ax.fill_between(x, ya, yb, facecolor='blue', alpha=0.05) - ax.vlines([0], ya, yb, lw=3, color='blue', label=r'range of $f$') - ax.text(0.04, -0.3, '$0$', fontsize=16) - -ax = axes[0] - -ax.legend(loc='upper right', frameon=False) -ybar = 1.5 -ax.plot(x, x * 0 + ybar, 'k--', alpha=0.5) -ax.text(0.05, 0.8 * ybar, r'$y$', fontsize=16) -for i, z in enumerate((-0.35, 0.35)): - ax.vlines(z, 0, f(z), linestyle='--', alpha=0.5) - ax.text(z, -0.2, r'$x_{}$'.format(i), fontsize=16) - -ax = axes[1] - -ybar = 2.6 -ax.plot(x, x * 0 + ybar, 'k--', alpha=0.5) -ax.text(0.04, 0.91 * ybar, r'$y$', fontsize=16) - -plt.show() diff --git a/examples/pylab_eg.py b/examples/pylab_eg.py deleted file mode 100644 index 27a1e9f1e..000000000 --- a/examples/pylab_eg.py +++ /dev/null @@ -1,5 +0,0 @@ -from pylab import * # Depreciated -x = linspace(0, 10, 200) -y = sin(x) -plot(x, y, 'b-', linewidth=2) -show() diff --git a/examples/pylab_eg2.py b/examples/pylab_eg2.py deleted file mode 100644 index 202142ba1..000000000 --- a/examples/pylab_eg2.py +++ /dev/null @@ -1,6 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -x = np.linspace(0, 10, 200) -y = np.sin(x) -plt.plot(x, y, 'b-', linewidth=2) -plt.show() diff --git a/examples/qm_plot.py b/examples/qm_plot.py deleted file mode 100644 index 7ee08f850..000000000 --- a/examples/qm_plot.py +++ /dev/null @@ -1,16 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np - - -def qm(x0, n): - x = np.empty(n+1) - x[0] = x0 - for t in range(n): - x[t+1] = 4 * x[t] * (1 - x[t]) - return x - -x = qm(0.1, 250) -fig, ax = plt.subplots(figsize=(10, 6.5)) -ax.plot(x, 'b-', lw=2, alpha=0.8) -ax.set_xlabel('time', fontsize=16) -plt.show() diff --git a/examples/qs.py b/examples/qs.py deleted file mode 100644 index d7d93c44c..000000000 --- a/examples/qs.py +++ /dev/null @@ -1,47 +0,0 @@ - -import matplotlib.pyplot as plt -import numpy as np -from scipy.stats import norm -from matplotlib import cm - -xmin, xmax = -4, 12 -x = 10 -alpha = 0.5 - -m, v = x, 10 - -xgrid = np.linspace(xmin, xmax, 200) - -fig, ax = plt.subplots() - -ax.spines['right'].set_color('none') -ax.spines['top'].set_color('none') -ax.spines['left'].set_color('none') -ax.xaxis.set_ticks_position('bottom') -ax.spines['bottom'].set_position(('data', 0)) - -ax.set_ylim(-0.05, 0.5) -ax.set_xticks((x,)) -ax.set_xticklabels((r'$x$',), fontsize=18) -ax.set_yticks(()) - -K = 3 -for i in range(K): - m = alpha * m - v = alpha * alpha * v + 1 - f = norm(loc=m, scale=np.sqrt(v)) - k = (i + 0.5) / K - ax.plot(xgrid, f.pdf(xgrid), lw=1, color='black', alpha=0.4) - ax.fill_between(xgrid, 0 * xgrid, f.pdf(xgrid), color=cm.jet(k), alpha=0.4) - - -ax.annotate(r'$Q(x,\cdot)$', xy=(6.6, 0.2), xycoords='data', - xytext=(20, 90), textcoords='offset points', fontsize=16, - arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=-0.2")) -ax.annotate(r'$Q^2(x,\cdot)$', xy=(3.6, 0.24), xycoords='data', - xytext=(20, 90), textcoords='offset points', fontsize=16, - arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=-0.2")) -ax.annotate(r'$Q^3(x,\cdot)$', xy=(-0.2, 0.28), xycoords='data', - xytext=(-90, 90), textcoords='offset points', fontsize=16, - arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=0.2")) -fig.show() diff --git a/examples/quadmap_class.py b/examples/quadmap_class.py deleted file mode 100644 index ba32d8059..000000000 --- a/examples/quadmap_class.py +++ /dev/null @@ -1,26 +0,0 @@ -""" -Filename: quadmap_class.py -Authors: John Stachurski, Thomas J. Sargent - -""" - - -class QuadMap(object): - - def __init__(self, initial_state): - self.x = initial_state - - def update(self): - "Apply the quadratic map to update the state." - self.x = 4 * self.x * (1 - self.x) - - def generate_series(self, n): - """ - Generate and return a trajectory of length n, starting at the - current state. - """ - trajectory = [] - for i in range(n): - trajectory.append(self.x) - self.update() - return trajectory diff --git a/examples/robust_monopolist.py b/examples/robust_monopolist.py deleted file mode 100644 index b4431ddf6..000000000 --- a/examples/robust_monopolist.py +++ /dev/null @@ -1,193 +0,0 @@ -""" -Filename: robust_monopolist.py -Authors: Chase Coleman, Spencer Lyon, Thomas Sargent, John Stachurski - -The robust control problem for a monopolist with adjustment costs. The -inverse demand curve is: - - p_t = a_0 - a_1 y_t + d_t - -where d_{t+1} = \rho d_t + \sigma_d w_{t+1} for w_t ~ N(0, 1) and iid. -The period return function for the monopolist is - - r_t = p_t y_t - gamma (y_{t+1} - y_t)^2 / 2 - c y_t - -The objective of the firm is E_t \sum_{t=0}^\infty \beta^t r_t - -For the linear regulator, we take the state and control to be - - x_t = (1, y_t, d_t) and u_t = y_{t+1} - y_t - -""" -import pandas as pd -import numpy as np -from scipy.linalg import eig -from scipy import interp -import matplotlib.pyplot as plt - -import quantecon as qe - -# == model parameters == # - -a_0 = 100 -a_1 = 0.5 -rho = 0.9 -sigma_d = 0.05 -beta = 0.95 -c = 2 -gamma = 50.0 - -theta = 0.002 -ac = (a_0 - c) / 2.0 - -# == Define LQ matrices == # - -R = np.array([[0., ac, 0.], - [ac, -a_1, 0.5], - [0., 0.5, 0.]]) - -R = -R # For minimization -Q = gamma / 2 - -A = np.array([[1., 0., 0.], - [0., 1., 0.], - [0., 0., rho]]) -B = np.array([[0.], - [1.], - [0.]]) -C = np.array([[0.], - [0.], - [sigma_d]]) - -# -------------------------------------------------------------------------- # -# Functions -# -------------------------------------------------------------------------- # - - -def evaluate_policy(theta, F): - """ - Given theta (scalar, dtype=float) and policy F (array_like), returns the - value associated with that policy under the worst case path for {w_t}, as - well as the entropy level. - """ - rlq = qe.robustlq.RBLQ(Q, R, A, B, C, beta, theta) - K_F, P_F, d_F, O_F, o_F = rlq.evaluate_F(F) - x0 = np.array([[1.], [0.], [0.]]) - value = - x0.T.dot(P_F.dot(x0)) - d_F - entropy = x0.T.dot(O_F.dot(x0)) + o_F - return list(map(float, (value, entropy))) - - -def value_and_entropy(emax, F, bw, grid_size=1000): - """ - Compute the value function and entropy levels for a theta path - increasing until it reaches the specified target entropy value. - - Parameters - ========== - emax: scalar - The target entropy value - - F: array_like - The policy function to be evaluated - - bw: str - A string specifying whether the implied shock path follows best - or worst assumptions. The only acceptable values are 'best' and - 'worst'. - - Returns - ======= - df: pd.DataFrame - A pandas DataFrame containing the value function and entropy - values up to the emax parameter. The columns are 'value' and - 'entropy'. - - """ - if bw == 'worst': - thetas = 1 / np.linspace(1e-8, 1000, grid_size) - else: - thetas = -1 / np.linspace(1e-8, 1000, grid_size) - - df = pd.DataFrame(index=thetas, columns=('value', 'entropy')) - - for theta in thetas: - df.ix[theta] = evaluate_policy(theta, F) - if df.ix[theta, 'entropy'] >= emax: - break - - df = df.dropna(how='any') - return df - - -# -------------------------------------------------------------------------- # -# Main -# -------------------------------------------------------------------------- # - - -# == Compute the optimal rule == # -optimal_lq = qe.lqcontrol.LQ(Q, R, A, B, C, beta) -Po, Fo, do = optimal_lq.stationary_values() - -# == Compute a robust rule given theta == # -baseline_robust = qe.robustlq.RBLQ(Q, R, A, B, C, beta, theta) -Fb, Kb, Pb = baseline_robust.robust_rule() - -# == Check the positive definiteness of worst-case covariance matrix to == # -# == ensure that theta exceeds the breakdown point == # -test_matrix = np.identity(Pb.shape[0]) - np.dot(C.T, Pb.dot(C)) / theta -eigenvals, eigenvecs = eig(test_matrix) -assert (eigenvals >= 0).all(), 'theta below breakdown point.' - - -emax = 1.6e6 - -optimal_best_case = value_and_entropy(emax, Fo, 'best') -robust_best_case = value_and_entropy(emax, Fb, 'best') -optimal_worst_case = value_and_entropy(emax, Fo, 'worst') -robust_worst_case = value_and_entropy(emax, Fb, 'worst') - -fig, ax = plt.subplots() - -ax.set_xlim(0, emax) -ax.set_ylabel("Value") -ax.set_xlabel("Entropy") -ax.grid() - -for axis in 'x', 'y': - plt.ticklabel_format(style='sci', axis=axis, scilimits=(0, 0)) - -plot_args = {'lw': 2, 'alpha': 0.7} - -colors = 'r', 'b' - -df_pairs = ((optimal_best_case, optimal_worst_case), - (robust_best_case, robust_worst_case)) - - -class Curve(object): - - def __init__(self, x, y): - self.x, self.y = x, y - - def __call__(self, z): - return interp(z, self.x, self.y) - - -for c, df_pair in zip(colors, df_pairs): - curves = [] - for df in df_pair: - # == Plot curves == # - x, y = df['entropy'], df['value'] - x, y = (np.asarray(a, dtype='float') for a in (x, y)) - egrid = np.linspace(0, emax, 100) - curve = Curve(x, y) - print(ax.plot(egrid, curve(egrid), color=c, **plot_args)) - curves.append(curve) - # == Color fill between curves == # - ax.fill_between(egrid, - curves[0](egrid), - curves[1](egrid), - color=c, alpha=0.1) - -plt.show() diff --git a/examples/sine2.py b/examples/sine2.py deleted file mode 100644 index e4be028a2..000000000 --- a/examples/sine2.py +++ /dev/null @@ -1,8 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -fig, ax = plt.subplots() -x = np.linspace(0, 10, 200) -y = np.sin(x) -ax.plot(x, y, 'r-', linewidth=2, label='sine function', alpha=0.6) -ax.legend() -plt.show() diff --git a/examples/sine3.py b/examples/sine3.py deleted file mode 100644 index de2b8a466..000000000 --- a/examples/sine3.py +++ /dev/null @@ -1,8 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -fig, ax = plt.subplots() -x = np.linspace(0, 10, 200) -y = np.sin(x) -ax.plot(x, y, 'r-', linewidth=2, label='sine function', alpha=0.6) -ax.legend(loc='upper center') -plt.show() diff --git a/examples/sine4.py b/examples/sine4.py deleted file mode 100644 index 4e5cac4c6..000000000 --- a/examples/sine4.py +++ /dev/null @@ -1,8 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -fig, ax = plt.subplots() -x = np.linspace(0, 10, 200) -y = np.sin(x) -ax.plot(x, y, 'r-', linewidth=2, label=r'$y=\sin(x)$', alpha=0.6) -ax.legend(loc='upper center') -plt.show() diff --git a/examples/sine5.py b/examples/sine5.py deleted file mode 100644 index 9cb6e2100..000000000 --- a/examples/sine5.py +++ /dev/null @@ -1,10 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -fig, ax = plt.subplots() -x = np.linspace(0, 10, 200) -y = np.sin(x) -ax.plot(x, y, 'r-', linewidth=2, label=r'$y=\sin(x)$', alpha=0.6) -ax.legend(loc='upper center') -ax.set_yticks([-1, 0, 1]) -ax.set_title('Test plot') -plt.show() diff --git a/examples/six_hists.py b/examples/six_hists.py deleted file mode 100644 index 21386e33a..000000000 --- a/examples/six_hists.py +++ /dev/null @@ -1,15 +0,0 @@ -import matplotlib.pyplot as plt -from scipy.stats import norm -from random import uniform -num_rows, num_cols = 3, 2 -fig, axes = plt.subplots(num_rows, num_cols, figsize=(8, 12)) -for i in range(num_rows): - for j in range(num_cols): - m, s = uniform(-1, 1), uniform(1, 2) - x = norm.rvs(loc=m, scale=s, size=100) - axes[i, j].hist(x, alpha=0.6, bins=20) - t = r'$\mu = {0:.1f}, \quad \sigma = {1:.1f}$'.format(m, s) - axes[i, j].set_title(t) - axes[i, j].set_xticks([-4, 0, 4]) - axes[i, j].set_yticks([]) -plt.show() diff --git a/examples/solow.py b/examples/solow.py deleted file mode 100644 index 11156cb85..000000000 --- a/examples/solow.py +++ /dev/null @@ -1,47 +0,0 @@ -""" -Filename: solow.py -Reference: http://quant-econ.net/py/python_oop.html -""" -from __future__ import division # Omit for Python 3.x -import numpy as np - -class Solow: - """ - Implements the Solow growth model with update rule - - .. math:: - k_{t+1} = \frac{s z k^{\alpha}_t}{1 + n} + k_t \frac{1 + d}{1 + n} - - """ - - def __init__(self, n, s, d, alpha, z, k): - """ - Solow growth model with Cobb Douglas production function. All - parameters are scalars. See http://quant-econ.net/py/python_oop.html - for interpretation. - """ - self.n, self.s, self.d, self.alpha, self.z = n, s, d, alpha, z - self.k = k - - - def h(self,x): - "Evaluate the h function" - temp = self.s * self.z * self.k**self.alpha + self.k * (1 - self.d) - return temp / (1 + self.n) - - def update(self): - "Update the current state (i.e., the capital stock)." - self.k = self.h(self.k) - - def steady_state(self): - "Compute the steady state value of capital." - return ((self.s * self.z) / (self.n + self.d))**(1 / (1 - self.alpha)) - - def generate_sequence(self, t): - "Generate and return a time series of length t" - path = [] - for i in range(t): - path.append(self.k) - self.update() - return path - diff --git a/examples/stochasticgrowth.py b/examples/stochasticgrowth.py deleted file mode 100644 index 79db69b0b..000000000 --- a/examples/stochasticgrowth.py +++ /dev/null @@ -1,59 +0,0 @@ -""" -Neoclassical growth model with constant savings rate, where the dynamics are -given by - - k_{t+1} = s A_{t+1} f(k_t) + (1 - delta) k_t - -Marginal densities are computed using the look-ahead estimator. Thus, the -estimate of the density psi_t of k_t is - - (1/n) sum_{i=0}^n p(k_{t-1}^i, y) - -This is a density in y. -""" -import numpy as np -import matplotlib.pyplot as plt -from scipy.stats import lognorm, beta -from quantecon import LAE - -# == Define parameters == # -s = 0.2 -delta = 0.1 -a_sigma = 0.4 # A = exp(B) where B ~ N(0, a_sigma) -alpha = 0.4 # We set f(k) = k**alpha -psi_0 = beta(5, 5, scale=0.5) # Initial distribution -phi = lognorm(a_sigma) - - -def p(x, y): - """ - Stochastic kernel for the growth model with Cobb-Douglas production. - Both x and y must be strictly positive. - """ - d = s * x**alpha - return phi.pdf((y - (1 - delta) * x) / d) / d - -n = 10000 # Number of observations at each date t -T = 30 # Compute density of k_t at 1,...,T+1 - -# == Generate matrix s.t. t-th column is n observations of k_t == # -k = np.empty((n, T)) -A = phi.rvs((n, T)) -k[:, 0] = psi_0.rvs(n) # Draw first column from initial distribution -for t in range(T-1): - k[:, t+1] = s * A[:, t] * k[:, t]**alpha + (1 - delta) * k[:, t] - -# == Generate T instances of LAE using this data, one for each date t == # -laes = [LAE(p, k[:, t]) for t in range(T)] - -# == Plot == # -fig, ax = plt.subplots() -ygrid = np.linspace(0.01, 4.0, 200) -greys = [str(g) for g in np.linspace(0.0, 0.8, T)] -greys.reverse() -for psi, g in zip(laes, greys): - ax.plot(ygrid, psi(ygrid), color=g, lw=2, alpha=0.6) -ax.set_xlabel('capital') -title = r'Density of $k_1$ (lighter) to $k_T$ (darker) for $T={}$' -ax.set_title(title.format(T)) -plt.show() diff --git a/examples/subplots.py b/examples/subplots.py deleted file mode 100644 index d955a4936..000000000 --- a/examples/subplots.py +++ /dev/null @@ -1,25 +0,0 @@ - -import matplotlib.pyplot as plt -import numpy as np - - -def subplots(): - "Custom subplots with axes throught the origin" - fig, ax = plt.subplots() - - # Set the axes through the origin - for spine in ['left', 'bottom']: - ax.spines[spine].set_position('zero') - for spine in ['right', 'top']: - ax.spines[spine].set_color('none') - - ax.grid() - return fig, ax - - -fig, ax = subplots() # Call the local version, not plt.subplots() -x = np.linspace(-2, 10, 200) -y = np.sin(x) -ax.plot(x, y, 'r-', linewidth=2, label='sine function', alpha=0.6) -ax.legend(loc='lower right') -plt.show() diff --git a/examples/temp.py b/examples/temp.py deleted file mode 100644 index 8b1378917..000000000 --- a/examples/temp.py +++ /dev/null @@ -1 +0,0 @@ - diff --git a/examples/test_program_1.py b/examples/test_program_1.py deleted file mode 100644 index f08e3e735..000000000 --- a/examples/test_program_1.py +++ /dev/null @@ -1,9 +0,0 @@ -from random import normalvariate -import matplotlib.pyplot as plt -ts_length = 100 -epsilon_values = [] # An empty list -for i in range(ts_length): - e = normalvariate(0, 1) - epsilon_values.append(e) -plt.plot(epsilon_values, 'b-') -plt.show() diff --git a/examples/test_program_2.py b/examples/test_program_2.py deleted file mode 100644 index 0282bb875..000000000 --- a/examples/test_program_2.py +++ /dev/null @@ -1,11 +0,0 @@ -from random import normalvariate -import matplotlib.pyplot as plt -ts_length = 100 -epsilon_values = [] -i = 0 -while i < ts_length: - e = normalvariate(0, 1) - epsilon_values.append(e) - i = i + 1 -plt.plot(epsilon_values, 'b-') -plt.show() diff --git a/examples/test_program_3.py b/examples/test_program_3.py deleted file mode 100644 index 80bf134ec..000000000 --- a/examples/test_program_3.py +++ /dev/null @@ -1,14 +0,0 @@ -from random import normalvariate -import matplotlib.pyplot as plt - - -def generate_data(n): - epsilon_values = [] - for i in range(n): - e = normalvariate(0, 1) - epsilon_values.append(e) - return epsilon_values - -data = generate_data(100) -plt.plot(data, 'b-') -plt.show() diff --git a/examples/test_program_4.py b/examples/test_program_4.py deleted file mode 100644 index 0b68e7d35..000000000 --- a/examples/test_program_4.py +++ /dev/null @@ -1,17 +0,0 @@ -from random import normalvariate, uniform -import matplotlib.pyplot as plt - - -def generate_data(n, generator_type): - epsilon_values = [] - for i in range(n): - if generator_type == 'U': - e = uniform(0, 1) - else: - e = normalvariate(0, 1) - epsilon_values.append(e) - return epsilon_values - -data = generate_data(100, 'U') -plt.plot(data, 'b-') -plt.show() diff --git a/examples/test_program_5.py b/examples/test_program_5.py deleted file mode 100644 index 516714670..000000000 --- a/examples/test_program_5.py +++ /dev/null @@ -1,14 +0,0 @@ -from random import normalvariate, uniform -import matplotlib.pyplot as plt - - -def generate_data(n, generator_type): - epsilon_values = [] - for i in range(n): - e = uniform(0, 1) if generator_type == 'U' else normalvariate(0, 1) - epsilon_values.append(e) - return epsilon_values - -data = generate_data(100, 'U') -plt.plot(data, 'b-') -plt.show() diff --git a/examples/test_program_5_short.py b/examples/test_program_5_short.py deleted file mode 100644 index 6744c2c39..000000000 --- a/examples/test_program_5_short.py +++ /dev/null @@ -1,19 +0,0 @@ -import pylab -from random import normalvariate, uniform - - -def generate_data(n, generator_type): - epsilon_values = [] - for i in range(n): - if generator_type == "U": - e = uniform(0, 1) - else: - e = normalvariate(0, 1) - - epsilon_values.append(e) - return epsilon_values - -ts_length = 100 -data = generate_data(ts_length, 'U') -pylab.plot(data, 'b-') -pylab.show() diff --git a/examples/test_program_6.py b/examples/test_program_6.py deleted file mode 100644 index ed20f96e9..000000000 --- a/examples/test_program_6.py +++ /dev/null @@ -1,14 +0,0 @@ -from random import uniform -import matplotlib.pyplot as plt - - -def generate_data(n, generator_type): - epsilon_values = [] - for i in range(n): - e = generator_type(0, 1) - epsilon_values.append(e) - return epsilon_values - -data = generate_data(100, uniform) -plt.plot(data, 'b-') -plt.show() diff --git a/examples/tests/__init__.py b/examples/tests/__init__.py deleted file mode 100644 index e69de29bb..000000000 diff --git a/examples/tests/test_directory_pyfiles.py b/examples/tests/test_directory_pyfiles.py deleted file mode 100644 index 532271b82..000000000 --- a/examples/tests/test_directory_pyfiles.py +++ /dev/null @@ -1,27 +0,0 @@ -""" -Simple Test Script which can be used to run a directoy of py files - -Just run this file using `python $filename` - -""" -#-Subprocess Recipe-# -from subprocess import call -import glob -files = glob.glob("*.py") -for fl in files: - print "Testing File: %s" % fl - call(["python", fl]) - print "------------ END (%s) -----------------" % fl - -#-IPYTHON NOTEBOOK Recipe-# -#-Instructions-# -#--------------# -#-1. Open an IPython Notebook in quantecon.py/examples/ folder -#-2. Copy the following code recipe into the notebook and run -import glob -files = glob.glob("*.py") -%pylab inline -for fl in files: - print "----RUNNING (%s)----"%fl - %run $fl - print "----END (%s)-----"%fl \ No newline at end of file diff --git a/examples/tsh_hg.py b/examples/tsh_hg.py deleted file mode 100644 index 0ffc2caa4..000000000 --- a/examples/tsh_hg.py +++ /dev/null @@ -1,37 +0,0 @@ - -import numpy as np -import matplotlib.pyplot as plt -from scipy.stats import norm -from quantecon import LinearStateSpace - -phi_1, phi_2, phi_3, phi_4 = 0.5, -0.2, 0, 0.5 -sigma = 0.1 - -A = [[phi_1, phi_2, phi_3, phi_4], - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 1, 0]] -C = [[sigma], [0], [0], [0]] -G = [1, 0, 0, 0] - -T = 30 -ar = LinearStateSpace(A, C, G) - -ymin, ymax = -0.8, 1.25 - -fig, ax = plt.subplots(figsize=(8, 4)) - -ax.set_xlim(ymin, ymax) -ax.set_xlabel(r'$y_t$', fontsize=16) - -x, y = ar.replicate(T=T, num_reps=100000) -mu_x, mu_y, Sigma_x, Sigma_y = ar.stationary_distributions() -f_y = norm(loc=float(mu_y), scale=float(np.sqrt(Sigma_y))) - -y = y.flatten() -ax.hist(y, bins=50, normed=True, alpha=0.4) - -ygrid = np.linspace(ymin, ymax, 150) -ax.plot(ygrid, f_y.pdf(ygrid), 'k-', lw=2, alpha=0.8, label='true density') -ax.legend() -plt.show() diff --git a/examples/us_cities.py b/examples/us_cities.py deleted file mode 100644 index 7c6f41dcb..000000000 --- a/examples/us_cities.py +++ /dev/null @@ -1,7 +0,0 @@ -data_file = open('us_cities.txt', 'r') -for line in data_file: - city, population = line.split(':') # Tuple unpacking - city = city.title() # Capitalize city names - population = '{0:,}'.format(int(population)) # Add commas to numbers - print(city.ljust(15) + population) -data_file.close() diff --git a/examples/us_cities.txt b/examples/us_cities.txt deleted file mode 100644 index 9be9260fc..000000000 --- a/examples/us_cities.txt +++ /dev/null @@ -1,9 +0,0 @@ -new york: 8244910 -los angeles: 3819702 -chicago: 2707120 -houston: 2145146 -philadelphia: 1536471 -phoenix: 1469471 -san antonio: 1359758 -san diego: 1326179 -dallas: 1223229 diff --git a/examples/utilities.py b/examples/utilities.py deleted file mode 100644 index 3d941c9f4..000000000 --- a/examples/utilities.py +++ /dev/null @@ -1,108 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Created on Sun Feb 22 10:47:42 2015 - -@author: dgevans -""" -import numpy as np -from scipy.interpolate import UnivariateSpline - -class interpolate_wrapper(object): - ''' - Wrapper to interpolate vector function - ''' - def __init__(self,F): - ''' - Inits with array of interpolated functions - ''' - self.F = F - - def __getitem__(self,index): - ''' - Uses square brakets operator - ''' - return interpolate_wrapper(np.asarray(self.F[index])) - - - def reshape(self,*args): - ''' - Reshapes F - ''' - self.F = self.F.reshape(*args) - return self - - def transpose(self): - ''' - Transpose F - ''' - self.F = self.F.transpose() - - def __len__(self): - ''' - return length - ''' - return len(self.F) - - def __call__(self,xvec): - ''' - Evaluates F at X for each element of F, keeping track of the shape of F - ''' - x = np.atleast_1d(xvec) - shape = self.F.shape - if len(x) == 1: - fhat = np.hstack([f(x) for f in self.F.flatten()]) - return fhat.reshape(shape) - else: - fhat = np.vstack([f(x) for f in self.F.flatten()]) - return fhat.reshape( np.hstack((shape,len(x))) ) - -class interpolator_factory(object): - ''' - Generates an interpolator factory which will interpolate vector functions - ''' - def __init__(self,k,s): - ''' - Inits with types, orders and k - ''' - self.k = k - self.s = s - - def __call__(self,xgrid,Fs): - ''' - Interpolates function given function values Fs at domain X - ''' - shape,m = Fs.shape[:-1],Fs.shape[-1] - Fs = Fs.reshape((-1,m)) - F = [] - for Fhat in Fs: - #F.append(interpolate(X,Fs[:,i],self.INFO)) - F.append(UnivariateSpline(xgrid,Fhat,k=self.k,s=self.s)) - return interpolate_wrapper(np.array(F).reshape(shape)) - - -def fun_vstack(fun_list): - ''' - Performs vstack on interpolator wrapper - ''' - Fs = [IW.F for IW in fun_list] - return interpolate_wrapper(np.vstack(Fs)) - -def fun_hstack(fun_list): - ''' - Performs vstack on interpolator wrapper - ''' - Fs = [IW.F for IW in fun_list] - return interpolate_wrapper(np.hstack(Fs)) - -def simulate_markov(Pi,s_0,T): - ''' - Simulates markov chain Pi for T periods starting at s_0 - ''' - - sHist = np.empty(T,dtype = int) - sHist[0] = s_0 - S = len(Pi) - for t in range(1,T): - sHist[t] = np.random.choice(np.arange(S),p=Pi[sHist[t-1]]) - - return sHist \ No newline at end of file diff --git a/examples/vecs.py b/examples/vecs.py deleted file mode 100644 index 326f30c2e..000000000 --- a/examples/vecs.py +++ /dev/null @@ -1,26 +0,0 @@ -""" -QE by Tom Sargent and John Stachurski. -Illustrates vectors in the plane. -""" -import matplotlib.pyplot as plt - -fig, ax = plt.subplots() -# Set the axes through the origin -for spine in ['left', 'bottom']: - ax.spines[spine].set_position('zero') -for spine in ['right', 'top']: - ax.spines[spine].set_color('none') - - -ax.set_xlim(-5, 5) -ax.set_ylim(-5, 5) -ax.grid() -vecs = ((2, 4), (-3, 3), (-4, -3.5)) -for v in vecs: - ax.annotate('', xy=v, xytext=(0, 0), - arrowprops=dict(facecolor='blue', - shrink=0, - alpha=0.7, - width=0.5)) - ax.text(1.1 * v[0], 1.1 * v[1], str(v)) -plt.show() diff --git a/examples/vecs2.py b/examples/vecs2.py deleted file mode 100644 index fe3c85d42..000000000 --- a/examples/vecs2.py +++ /dev/null @@ -1,38 +0,0 @@ -""" -QE by Tom Sargent and John Stachurski. -Illustrates scalar multiplication. -""" -import matplotlib.pyplot as plt -import numpy as np - -fig, ax = plt.subplots() -# Set the axes through the origin -for spine in ['left', 'bottom']: - ax.spines[spine].set_position('zero') -for spine in ['right', 'top']: - ax.spines[spine].set_color('none') - -ax.set_xlim(-5, 5) -ax.set_ylim(-5, 5) - -x = (2, 2) -ax.annotate('', xy=x, xytext=(0, 0), - arrowprops=dict(facecolor='blue', - shrink=0, - alpha=1, - width=0.5)) -ax.text(x[0] + 0.4, x[1] - 0.2, r'$x$', fontsize='16') - - -scalars = (-2, 2) -x = np.array(x) - -for s in scalars: - v = s * x - ax.annotate('', xy=v, xytext=(0, 0), - arrowprops=dict(facecolor='red', - shrink=0, - alpha=0.5, - width=0.5)) - ax.text(v[0] + 0.4, v[1] - 0.2, r'${} x$'.format(s), fontsize='16') -plt.show() diff --git a/examples/wb_download.py b/examples/wb_download.py deleted file mode 100644 index 40f61e3c9..000000000 --- a/examples/wb_download.py +++ /dev/null @@ -1,37 +0,0 @@ -""" -Origin: QE by John Stachurski and Thomas J. Sargent -Filename: wb_download.py -Authors: John Stachurski, Tomohito Okabe -LastModified: 29/08/2013 - -Dowloads data from the World Bank site on GDP per capita and plots result for -a subset of countries. - -NOTE: This is not dually compatible with Python 3. Python 2 and Python -3 call the urllib package differently. -""" -import sys -import matplotlib.pyplot as plt -from pandas.io.excel import ExcelFile - -if sys.version_info[0] == 2: - from urllib import urlretrieve -elif sys.version_info[0] == 3: - from urllib.request import urlretrieve - -# == Get data and read into file gd.xls == # -wb_data_file_dir = "http://api.worldbank.org/datafiles/" -file_name = "GC.DOD.TOTL.GD.ZS_Indicator_MetaData_en_EXCEL.xls" -url = wb_data_file_dir + file_name -urlretrieve(url, "gd.xls") - -# == Parse data into a DataFrame == # -gov_debt_xls = ExcelFile('gd.xls') -govt_debt = gov_debt_xls.parse('Sheet1', index_col=1, na_values=['NA']) - -# == Take desired values and plot == # -govt_debt = govt_debt.transpose() -govt_debt = govt_debt[['AUS', 'DEU', 'FRA', 'USA']] -govt_debt = govt_debt[36:] -govt_debt.plot(lw=2) -plt.show() diff --git a/examples/web_network.py b/examples/web_network.py deleted file mode 100644 index 01e6ba724..000000000 --- a/examples/web_network.py +++ /dev/null @@ -1,51 +0,0 @@ -import numpy as np -import re - -alphabet = 'abcdefghijklmnopqrstuvwxyz' - - -def gen_rw_mat(n): - "Generate an n x n matrix of zeros and ones." - Q = np.random.randn(n, n) - 0.8 - Q = np.where(Q > 0, 1, 0) - # Make sure that no row contains only zeros - for i in range(n): - if Q[i, :].sum() == 0: - Q[i, np.random.randint(0, n, 1)] = 1 - return Q - - -def adj_matrix_to_dot(Q, outfile='/tmp/foo_out.dot'): - """ - Convert an adjacency matrix to a dot file. - """ - n = Q.shape[0] - f = open(outfile, 'w') - f.write('digraph {\n') - for i in range(n): - for j in range(n): - if Q[i, j]: - f.write(' {0} -> {1};\n'.format(alphabet[i], alphabet[j])) - f.write('}\n') - f.close() - - -def dot_to_adj_matrix(node_num, infile='/tmp/foo_out.dot'): - Q = np.zeros((node_num, node_num), dtype=int) - f = open(infile, 'r') - lines = f.readlines() - f.close() - edges = lines[1:-1] # Drop first and last lines - for edge in edges: - from_node, to_node = re.findall('\w', edge) - i, j = alphabet.index(from_node), alphabet.index(to_node) - Q[i, j] = 1 - return Q - - -def adj_matrix_to_markov(Q): - n = Q.shape[0] - P = np.empty((n, n)) - for i in range(n): - P[i, :] = Q[i, :] / float(Q[i, :].sum()) - return P diff --git a/examples/white_noise_plot.py b/examples/white_noise_plot.py deleted file mode 100644 index c1e3109f6..000000000 --- a/examples/white_noise_plot.py +++ /dev/null @@ -1,7 +0,0 @@ -from pylab import plot, show, legend -from random import normalvariate - -x = [normalvariate(0, 1) for i in range(100)] -plot(x, 'b-', label="white noise") -legend() -show() diff --git a/quantecon/__init__.py b/quantecon/__init__.py index 43742faf7..8c71c3fe9 100644 --- a/quantecon/__init__.py +++ b/quantecon/__init__.py @@ -2,11 +2,23 @@ Import the main names to top level. """ -from . import models as models +try: + import numba +except: + raise ImportError("Cannot import numba from current anaconda distribution. Please run `conda install numba` to install the latest version.") + +#-Modules-# +from . import distributions +from . import game_theory +from . import quad +from . import random + +#-Objects-# from .compute_fp import compute_fixed_point from .discrete_rv import DiscreteRV from .ecdf import ECDF from .estspec import smooth, periodogram, ar_periodogram +# from .game_theory import #Place Holder if we wish to promote any general objects to the qe namespace. from .graph_tools import DiGraph from .gridtools import cartesian, mlinspace from .kalman import Kalman @@ -18,13 +30,12 @@ from .matrix_eqn import solve_discrete_lyapunov, solve_discrete_riccati from .quadsums import var_quadratic_sum, m_quadratic_sum #->Propose Delete From Top Level -from .markov import MarkovChain, random_markov_chain, random_stochastic_matrix, gth_solve, tauchen #Promote to keep current examples working -from .markov import mc_compute_stationary, mc_sample_path #Imports that Should be Deprecated with markov package +from .markov import MarkovChain, random_markov_chain, random_stochastic_matrix, gth_solve, tauchen #Promote to keep current examples working +from .markov import mc_compute_stationary, mc_sample_path #Imports that Should be Deprecated with markov package #<- from .rank_nullspace import rank_est, nullspace from .robustlq import RBLQ -from . import quad as quad -from .util import searchsorted +from .util import searchsorted, fetch_nb_dependencies -#Add Version Attribute +#-Add Version Attribute-# from .version import version as __version__ diff --git a/quantecon/discrete_rv.py b/quantecon/discrete_rv.py index fd27f0044..4b5567d1e 100644 --- a/quantecon/discrete_rv.py +++ b/quantecon/discrete_rv.py @@ -8,6 +8,7 @@ """ +import numpy as np from numpy import cumsum from numpy.random import uniform @@ -31,7 +32,7 @@ class DiscreteRV(object): """ def __init__(self, q): - self._q = q + self._q = np.asarray(q) self.Q = cumsum(q) def __repr__(self): @@ -54,7 +55,7 @@ def q(self, val): Setter method for q. """ - self._q = val + self._q = np.asarray(val) self.Q = cumsum(val) def draw(self, k=1): diff --git a/quantecon/game_theory/__init__.py b/quantecon/game_theory/__init__.py new file mode 100644 index 000000000..b7beb74cf --- /dev/null +++ b/quantecon/game_theory/__init__.py @@ -0,0 +1,6 @@ +""" +Game Theory SubPackage + +""" +from .normal_form_game import Player, NormalFormGame +from .normal_form_game import pure2mixed, best_response_2p diff --git a/quantecon/game_theory/normal_form_game.py b/quantecon/game_theory/normal_form_game.py new file mode 100644 index 000000000..2619bffa3 --- /dev/null +++ b/quantecon/game_theory/normal_form_game.py @@ -0,0 +1,671 @@ +r""" +Authors: Tomohiro Kusano, Daisuke Oyama + +Tools for normal form games. + +Definitions and Basic Concepts +------------------------------ + +An :math:`N`-player *normal form game* :math:`g = (I, (A_i)_{i \in I}, +(u_i)_{i \in I})` consists of + +- the set of *players* :math:`I = \{0, \ldots, N-1\}`, +- the set of *actions* :math:`A_i = \{0, \ldots, n_i-1\}` for each + player :math:`i \in I`, and +- the *payoff function* :math:`u_i \colon A_i \times A_{i+1} \times + \cdots \times A_{i+N-1} \to \mathbb{R}` for each player :math:`i \in + I`, + +where :math:`i+j` is understood modulo :math:`N`. Note that we adopt the +convention that the 0-th argument of the payoff function :math:`u_i` is +player :math:`i`'s own action and the :math:`j`-th argument is player +(:math:`i+j`)'s action (modulo :math:`N`). A mixed action for player +:math:`i` is a probability distribution on :math:`A_i` (while an element +of :math:`A_i` is referred to as a pure action). A pure action +:math:`a_i \in A_i` is identified with the mixed action that assigns +probability one to :math:`a_i`. Denote the set of mixed actions of +player :math:`i` by :math:`X_i`. We also denote :math:`A_{-i} = A_{i+1} +\times \cdots \times A_{i+N-1}` and :math:`X_{-i} = X_{i+1} \times +\cdots \times X_{i+N-1}`. + +The (pure-action) *best response correspondence* :math:`b_i \colon +X_{-i} \to A_i` for each player :math:`i` is defined by + +.. math:: + + b_i(x_{-i}) = \{a_i \in A_i \mid + u_i(a_i, x_{-i}) \geq u_i(a_i', x_{-i}) + \ \forall\,a_i' \in A_i\}, + +where :math:`u_i(a_i, x_{-i}) = \sum_{a_{-i} \in A_{-i}} u_i(a_i, +a_{-i}) \prod_{j=1}^{N-1} x_{i+j}(a_j)` is the expected payoff to action +:math:`a_i` against mixed actions :math:`x_{-i}`. A profile of mixed +actions :math:`x^* \in X_0 \times \cdots \times X_{N-1}` is a *Nash +equilibrium* if for all :math:`i \in I` and :math:`a_i \in A_i`, + +.. math:: + + x_i^*(a_i) > 0 \Rightarrow a_i \in b_i(x_{-i}^*), + +or equivalently, :math:`x_i^* \cdot v_i(x_{-i}^*) \geq x_i \cdot +v_i(x_{-i}^*)` for all :math:`x_i \in X_i`, where :math:`v_i(x_{-i})` is +the vector of player :math:`i`'s payoffs when the opponent players play +mixed actions :math:`x_{-i}`. + +Creating a NormalFormGame +------------------------- + +There are three ways to construct a `NormalFormGame` instance. + +The first is to pass an array of payoffs for all the players: + +>>> matching_pennies_bimatrix = [[(1, -1), (-1, 1)], [(-1, 1), (1, -1)]] +>>> g = NormalFormGame(matching_pennies_bimatrix) +>>> print(g.players[0]) +Player in a 2-player normal form game with payoff array: +[[ 1, -1], + [-1, 1]] +>>> print(g.players[1]) +Player in a 2-player normal form game with payoff array: +[[-1, 1], + [ 1, -1]] + +If a square matrix (2-dimensional array) is given, then it is considered +to be a symmetric two-player game: + +>>> coordination_game_matrix = [[4, 0], [3, 2]] +>>> g = NormalFormGame(coordination_game_matrix) +>>> print(g) +2-player NormalFormGame with payoff profile array: +[[[4, 4], [0, 3]], + [[3, 0], [2, 2]]] + +The second is to specify the sizes of the action sets of the players, +which gives a `NormalFormGame` instance filled with payoff zeros, and +then set the payoff values to each entry: + +>>> g = NormalFormGame((2, 2)) +>>> print(g) +2-player NormalFormGame with payoff profile array: +[[[ 0., 0.], [ 0., 0.]], + [[ 0., 0.], [ 0., 0.]]] +>>> g[0, 0] = 1, 1 +>>> g[0, 1] = -2, 3 +>>> g[1, 0] = 3, -2 +>>> print(g) +2-player NormalFormGame with payoff profile array: +[[[ 1., 1.], [-2., 3.]], + [[ 3., -2.], [ 0., 0.]]] + +The third is to pass an array of `Player` instances, as explained in the +next section. + +Creating a Player +----------------- + +A `Player` instance is created by passing a payoff array: + +>>> player0 = Player([[3, 1], [0, 2]]) +>>> player0.payoff_array +array([[3, 1], + [0, 2]]) + +Passing an array of `Player` instances is the third way to create a +`NormalFormGame` instance. + +>>> player1 = Player([[2, 0], [1, 3]]) +>>> player1.payoff_array +array([[2, 0], + [1, 3]]) +>>> g = NormalFormGame((player0, player1)) +>>> print(g) +2-player NormalFormGame with payoff profile array: +[[[3, 2], [1, 1]], + [[0, 0], [2, 3]]] + +Beware that in `payoff_array[h, k]`, `h` refers to the player's own +action, while `k` refers to the opponent player's action. + +""" +import re +import numbers +import numpy as np +from numba import jit + +from ..util import check_random_state + + +class Player(object): + """ + Class representing a player in an N-player normal form game. + + Parameters + ---------- + payoff_array : array_like(float) + Array representing the player's payoff function, where + `payoff_array[a_0, a_1, ..., a_{N-1}]` is the payoff to the + player when the player plays action `a_0` while his N-1 + opponents play actions `a_1`, ..., `a_{N-1}`, respectively. + + Attributes + ---------- + payoff_array : ndarray(float, ndim=N) + See Parameters. + + num_actions : scalar(int) + The number of actions available to the player. + + num_opponents : scalar(int) + The number of opponent players. + + """ + def __init__(self, payoff_array): + self.payoff_array = np.asarray(payoff_array) + + if self.payoff_array.ndim == 0: + raise ValueError('payoff_array must be an array_like') + + self.num_opponents = self.payoff_array.ndim - 1 + self.num_actions = self.payoff_array.shape[0] + + self.tol = 1e-8 + + def __repr__(self): + N = self.num_opponents + 1 + s = 'Player in a {N}-player normal form game'.format(N=N) + return s + + def __str__(self): + s = self.__repr__() + s += ' with payoff array:\n' + s += np.array2string(self.payoff_array, separator=', ') + return s + + def payoff_vector(self, opponents_actions): + """ + Return an array of payoff values, one for each own action, given + a profile of the opponents' actions. + + Parameters + ---------- + opponents_actions : see `best_response`. + + Returns + ------- + payoff_vector : ndarray(float, ndim=1) + An array representing the player's payoff vector given the + profile of the opponents' actions. + + """ + def reduce_last_player(payoff_array, action): + """ + Given `payoff_array` with ndim=M, return the payoff array + with ndim=M-1 fixing the last player's action to be `action`. + + """ + if isinstance(action, numbers.Integral): # pure action + return payoff_array.take(action, axis=-1) + else: # mixed action + return payoff_array.dot(action) + + if self.num_opponents == 1: + payoff_vector = \ + reduce_last_player(self.payoff_array, opponents_actions) + elif self.num_opponents >= 2: + payoff_vector = self.payoff_array + for i in reversed(range(self.num_opponents)): + payoff_vector = \ + reduce_last_player(payoff_vector, opponents_actions[i]) + else: # Trivial case with self.num_opponents == 0 + payoff_vector = self.payoff_array + + return payoff_vector + + def is_best_response(self, own_action, opponents_actions): + """ + Return True if `own_action` is a best response to + `opponents_actions`. + + Parameters + ---------- + own_action : scalar(int) or array_like(float, ndim=1) + An integer representing a pure action, or an array of floats + representing a mixed action. + + opponents_actions : see `best_response` + + Returns + ------- + bool + True if `own_action` is a best response to + `opponents_actions`; False otherwise. + + """ + payoff_vector = self.payoff_vector(opponents_actions) + payoff_max = payoff_vector.max() + + if isinstance(own_action, numbers.Integral): + return payoff_vector[own_action] >= payoff_max - self.tol + else: + return np.dot(own_action, payoff_vector) >= payoff_max - self.tol + + def best_response(self, opponents_actions, tie_breaking='smallest', + payoff_perturbation=None, random_state=None): + """ + Return the best response action(s) to `opponents_actions`. + + Parameters + ---------- + opponents_actions : array_like(int or array_like(float)) or + array_like(int, ndim=1) or scalar(int) + A profile of N-1 opponents' actions. If N=2, then it must be + a 1-dimensional array of floats (in which case it is treated + as the opponent's mixed action) or a scalar of integer (in + which case it is treated as the opponent's pure action). If + N>2, then it must be an array of N-1 objects, where each + object must be an integer (pure action) or an array of + floats (mixed action). + + tie_breaking : {'smallest', 'random', False}, + optional(default='smallest') + Control how, or whether, to break a tie (see Returns for + details). + + payoff_perturbation : array_like(float), optional(default=None) + Array of length equal to the number of actions of the player + containing the values ("noises") to be added to the payoffs + in determining the best response. + + random_state : scalar(int) or np.random.RandomState, + optional(default=None) + Random seed (integer) or np.random.RandomState instance to + set the initial state of the random number generator for + reproducibility. If None, a randomly initialized RandomState + is used. Relevant only when tie_breaking='random'. + + Returns + ------- + scalar(int) or ndarray(int, ndim=1) + If tie_breaking=False, returns an array containing all the + best response pure actions. If tie_breaking='smallest', + returns the best response action with the smallest index; if + tie_breaking='random', returns an action randomly chosen + from the best response actions. + + """ + payoff_vector = self.payoff_vector(opponents_actions) + if payoff_perturbation is not None: + try: + payoff_vector += payoff_perturbation + except TypeError: # type mismatch + payoff_vector = payoff_vector + payoff_perturbation + + if tie_breaking == 'smallest': + best_response = np.argmax(payoff_vector) + return best_response + else: + best_responses = \ + np.where(payoff_vector >= payoff_vector.max() - self.tol)[0] + if tie_breaking == 'random': + return self.random_choice(best_responses, + random_state=random_state) + elif tie_breaking is False: + return best_responses + else: + msg = "tie_breaking must be one of 'smallest', 'random' " + \ + "or False" + raise ValueError(msg) + + def random_choice(self, actions=None, random_state=None): + """ + Return a pure action chosen randomly from `actions`. + + Parameters + ---------- + actions : array_like(int), optional(default=None) + An array of integers representing pure actions. + + random_state : scalar(int) or np.random.RandomState, + optional(default=None) + Random seed (integer) or np.random.RandomState instance to + set the initial state of the random number generator for + reproducibility. If None, a randomly initialized RandomState + is used. + + Returns + ------- + scalar(int) + If `actions` is given, returns an integer representing a + pure action chosen randomly from `actions`; if not, an + action is chosen randomly from the player's all actions. + + """ + random_state = check_random_state(random_state) + + if actions is not None: + n = len(actions) + else: + n = self.num_actions + + if n == 1: + idx = 0 + else: + idx = random_state.randint(n) + + if actions is not None: + return actions[idx] + else: + return idx + + +class NormalFormGame(object): + """ + Class representing an N-player normal form game. + + Parameters + ---------- + data : array_like(Player) or array_like(int, ndim=1) or + array_like(float, ndim=2 or N+1) + Data to initialize a NormalFormGame. `data` may be an array of + Players, in which case the shapes of the Players' payoff arrays + must be consistent. If `data` is an array of N integers, then + these integers are treated as the numbers of actions of the N + players and a NormalFormGame is created consisting of payoffs + all 0 with `data[i]` actions for each player `i`. `data` may + also be an (N+1)-dimensional array representing payoff profiles. + If `data` is a square matrix (2-dimensional array), then the + game will be a symmetric two-player game where the payoff matrix + of each player is given by the input matrix. + + Attributes + ---------- + players : tuple(Player) + Tuple of the Player instances of the game. + + N : scalar(int) + The number of players. + + nums_actions : tuple(int) + Tuple of the numbers of actions, one for each player. + + """ + def __init__(self, data): + # data represents an array_like of Players + if hasattr(data, '__getitem__') and isinstance(data[0], Player): + N = len(data) + + # Check that the shapes of the payoff arrays are consistent + shape_0 = data[0].payoff_array.shape + for i in range(1, N): + shape = data[i].payoff_array.shape + if not ( + len(shape) == N and + shape == shape_0[i:] + shape_0[:i] + ): + raise ValueError( + 'shapes of payoff arrays must be consistent' + ) + + self.players = tuple(data) + + # data represents action sizes or a payoff array + else: + data = np.asarray(data) + + if data.ndim == 0: # data represents action size + # Trivial game consisting of one player + N = 1 + self.players = (Player(np.zeros(data)),) + + elif data.ndim == 1: # data represents action sizes + N = data.size + # N instances of Player created + # with payoff_arrays filled with zeros + # Payoff values set via __setitem__ + self.players = tuple( + Player(np.zeros(tuple(data[i:]) + tuple(data[:i]))) + for i in range(N) + ) + + elif data.ndim == 2 and data.shape[1] >= 2: + # data represents a payoff array for symmetric two-player game + # Number of actions must be >= 2 + if data.shape[0] != data.shape[1]: + raise ValueError( + 'symmetric two-player game must be represented ' + + 'by a square matrix' + ) + N = 2 + self.players = tuple(Player(data) for i in range(N)) + + else: # data represents a payoff array + # data must be of shape (n_0, ..., n_{N-1}, N), + # where n_i is the number of actions available to player i, + # and the last axis contains the payoff profile + N = data.ndim - 1 + if data.shape[-1] != N: + raise ValueError( + 'size of innermost array must be equal to ' + + 'the number of players' + ) + self.players = tuple( + Player( + data.take(i, axis=-1).transpose(list(range(i, N)) + + list(range(i))) + ) for i in range(N) + ) + + self.N = N # Number of players + self.nums_actions = tuple( + player.num_actions for player in self.players + ) + + @property + def payoff_profile_array(self): + N = self.N + dtype = \ + np.result_type(*(player.payoff_array for player in self.players)) + payoff_profile_array = \ + np.empty(self.players[0].payoff_array.shape + (N,), dtype=dtype) + for i, player in enumerate(self.players): + payoff_profile_array[..., i] = \ + player.payoff_array.transpose(list(range(N-i, N)) + + list(range(N-i))) + return payoff_profile_array + + def __repr__(self): + s = '{N}-player NormalFormGame'.format(N=self.N) + return s + + def __str__(self): + s = self.__repr__() + s += ' with payoff profile array:\n' + s += _payoff_profile_array2string(self.payoff_profile_array) + return s + + def __getitem__(self, action_profile): + if self.N == 1: # Trivial game with 1 player + if not isinstance(action_profile, numbers.Integral): + raise TypeError('index must be an integer') + return self.players[0].payoff_array[action_profile] + + # Non-trivial game with 2 or more players + try: + if len(action_profile) != self.N: + raise IndexError('index must be of length {0}'.format(self.N)) + except TypeError: + raise TypeError('index must be a tuple') + + payoff_profile = [ + player.payoff_array[ + tuple(action_profile[i:]) + tuple(action_profile[:i]) + ] + for i, player in enumerate(self.players) + ] + + return payoff_profile + + def __setitem__(self, action_profile, payoff_profile): + if self.N == 1: # Trivial game with 1 player + if not isinstance(action_profile, numbers.Integral): + raise TypeError('index must be an integer') + self.players[0].payoff_array[action_profile] = payoff_profile + return None + + # Non-trivial game with 2 or more players + try: + if len(action_profile) != self.N: + raise IndexError('index must be of length {0}'.format(self.N)) + except TypeError: + raise TypeError('index must be a tuple') + + try: + if len(payoff_profile) != self.N: + raise ValueError( + 'value must be an array_like of length {0}'.format(self.N) + ) + except TypeError: + raise TypeError('value must be a tuple') + + for i, player in enumerate(self.players): + player.payoff_array[ + tuple(action_profile[i:]) + tuple(action_profile[:i]) + ] = payoff_profile[i] + + def is_nash(self, action_profile): + """ + Return True if `action_profile` is a Nash equilibrium. + + Parameters + ---------- + action_profile : array_like(int or array_like(float)) + An array of N objects, where each object must be an integer + (pure action) or an array of floats (mixed action). + + Returns + ------- + bool + True if `action_profile` is a Nash equilibrium; False + otherwise. + + """ + if self.N == 2: + for i, player in enumerate(self.players): + own_action, opponent_action = \ + action_profile[i], action_profile[1-i] + if not player.is_best_response(own_action, opponent_action): + return False + + elif self.N >= 3: + for i, player in enumerate(self.players): + own_action = action_profile[i] + opponents_actions = \ + tuple(action_profile[i+1:]) + tuple(action_profile[:i]) + + if not player.is_best_response(own_action, opponents_actions): + return False + + else: # Trivial case with self.N == 1 + if not self.players[0].is_best_response(action_profile[0], None): + return False + + return True + + +def _payoff_array2string(payoff_array, class_name=None): + prefix, suffix = '', '' + if class_name is not None: + prefix = class_name + '(' + suffix = ')' + s = np.array2string(payoff_array, separator=', ', prefix=prefix) + return prefix + s + suffix + + +def _payoff_profile_array2string(payoff_profile_array, class_name=None): + s = np.array2string(payoff_profile_array, separator=', ') + + # Remove one linebreak + s = re.sub(r'(\n+)', lambda x: x.group(0)[0:-1], s) + + if class_name is not None: + prefix = class_name + '(' + next_line_prefix = ' ' * len(prefix) + suffix = ')' + l = s.splitlines() + l[0] = prefix + l[0] + for i in range(1, len(l)): + if l[i]: + l[i] = next_line_prefix + l[i] + l[-1] += suffix + s = '\n'.join(l) + + return s + + +def pure2mixed(num_actions, action): + """ + Convert a pure action to the corresponding mixed action. + + Parameters + ---------- + num_actions : scalar(int) + The number of the pure actions (= the length of a mixed action). + + action : scalar(int) + The pure action to convert to the corresponding mixed action. + + Returns + ------- + ndarray(float, ndim=1) + The mixed action representation of the given pure action. + + """ + mixed_action = np.zeros(num_actions) + mixed_action[action] = 1 + return mixed_action + + +# Numba jitted functions # + +@jit(nopython=True) +def best_response_2p(payoff_matrix, opponent_mixed_action): + """ + Numba-optimized version of `Player.best_response` compilied in + nopython mode, specialized for 2-player games (where there is only + one opponent). + + Return the best response action (with the smallest index if more + than one) to `opponent_mixed_action` under `payoff_matrix`. + + Parameters + ---------- + payoff_matrix : ndarray(float, ndim=2) + Payoff matrix. + + opponent_mixed_action : ndarray(float, ndim=1) + Opponent's mixed action. Its length must be equal to + `payoff_matrix.shape[1]`. + + Return + ------ + scalar(int) + Best response action. + + """ + n, m = payoff_matrix.shape + + best_response = 0 + payoff_0 = 0 + for b in range(m): + payoff_0 += payoff_matrix[0, b] * opponent_mixed_action[b] + payoff_max = payoff_0 + + for a in range(1, n): + payoff = 0 + for b in range(m): + payoff += payoff_matrix[a, b] * opponent_mixed_action[b] + if payoff > payoff_max: + payoff_max = payoff + best_response = a + + return best_response diff --git a/quantecon/game_theory/tests/test_normal_form_game.py b/quantecon/game_theory/tests/test_normal_form_game.py new file mode 100644 index 000000000..bc0b30f45 --- /dev/null +++ b/quantecon/game_theory/tests/test_normal_form_game.py @@ -0,0 +1,375 @@ +""" +Author: Daisuke Oyama + +Tests for normal_form_game.py + +""" +from __future__ import division + +import numpy as np +from numpy.testing import assert_array_equal +from nose.tools import eq_, ok_, raises + +from quantecon.game_theory import ( + Player, NormalFormGame, pure2mixed, best_response_2p +) + + +# Player # + +class TestPlayer_1opponent: + """Test the methods of Player with one opponent player""" + + def setUp(self): + """Setup a Player instance""" + coordination_game_matrix = [[4, 0], [3, 2]] + self.player = Player(coordination_game_matrix) + + def test_best_response_against_pure(self): + eq_(self.player.best_response(1), 1) + + def test_best_response_against_mixed(self): + eq_(self.player.best_response([1/2, 1/2]), 1) + + def test_best_response_list_when_tie(self): + """best_response with tie_breaking=False""" + assert_array_equal( + sorted(self.player.best_response([2/3, 1/3], tie_breaking=False)), + sorted([0, 1]) + ) + + def test_best_response_with_random_tie_breaking(self): + """best_response with tie_breaking='random'""" + ok_(self.player.best_response([2/3, 1/3], tie_breaking='random') + in [0, 1]) + + seed = 1234 + br0 = self.player.best_response([2/3, 1/3], tie_breaking='random', + random_state=seed) + br1 = self.player.best_response([2/3, 1/3], tie_breaking='random', + random_state=seed) + eq_(br0, br1) + + def test_best_response_with_smallest_tie_breaking(self): + """best_response with tie_breaking='smallest' (default)""" + eq_(self.player.best_response([2/3, 1/3]), 0) + + def test_best_response_with_payoff_perturbation(self): + """best_response with payoff_perturbation""" + eq_(self.player.best_response([2/3, 1/3], + payoff_perturbation=[0, 0.1]), + 1) + eq_(self.player.best_response([2, 1], # int + payoff_perturbation=[0, 0.1]), + 1) + + def test_is_best_response_against_pure(self): + ok_(self.player.is_best_response(0, 0)) + + def test_is_best_response_against_mixed(self): + ok_(self.player.is_best_response([1/2, 1/2], [2/3, 1/3])) + + +class TestPlayer_2opponents: + """Test the methods of Player with two opponent players""" + + def setUp(self): + """Setup a Player instance""" + payoffs_2opponents = [[[3, 6], + [4, 2]], + [[1, 0], + [5, 7]]] + self.player = Player(payoffs_2opponents) + + def test_payoff_vector_against_pure(self): + assert_array_equal(self.player.payoff_vector((0, 1)), [6, 0]) + + def test_is_best_response_against_pure(self): + ok_(not self.player.is_best_response(0, (1, 0))) + + def test_best_response_against_pure(self): + eq_(self.player.best_response((1, 1)), 1) + + def test_best_response_list_when_tie(self): + """ + best_response against a mixed action profile with + tie_breaking=False + """ + assert_array_equal( + sorted(self.player.best_response(([3/7, 4/7], [1/2, 1/2]), + tie_breaking=False)), + sorted([0, 1]) + ) + + +def test_random_choice(): + n, m = 5, 4 + payoff_matrix = np.zeros((n, m)) + player = Player(payoff_matrix) + + eq_(player.random_choice([0]), 0) + + actions = list(range(player.num_actions)) + ok_(player.random_choice() in actions) + + +# NormalFormGame # + +class TestNormalFormGame_Sym2p: + """Test the methods of NormalFormGame with symmetric two players""" + + def setUp(self): + """Setup a NormalFormGame instance""" + coordination_game_matrix = [[4, 0], [3, 2]] + self.g = NormalFormGame(coordination_game_matrix) + + def test_getitem(self): + assert_array_equal(self.g[0, 1], [0, 3]) + + def test_is_nash_pure(self): + ok_(self.g.is_nash((0, 0))) + + def test_is_nash_mixed(self): + ok_(self.g.is_nash(([2/3, 1/3], [2/3, 1/3]))) + + +class TestNormalFormGame_Asym2p: + """Test the methods of NormalFormGame with asymmetric two players""" + + def setUp(self): + """Setup a NormalFormGame instance""" + matching_pennies_bimatrix = [[(1, -1), (-1, 1)], + [(-1, 1), (1, -1)]] + self.g = NormalFormGame(matching_pennies_bimatrix) + + def test_getitem(self): + assert_array_equal(self.g[1, 0], [-1, 1]) + + def test_is_nash_against_pure(self): + ok_(not self.g.is_nash((0, 0))) + + def test_is_nash_against_mixed(self): + ok_(self.g.is_nash(([1/2, 1/2], [1/2, 1/2]))) + + +class TestNormalFormGame_3p: + """Test the methods of NormalFormGame with three players""" + + def setUp(self): + """Setup a NormalFormGame instance""" + payoffs_2opponents = [[[3, 6], + [4, 2]], + [[1, 0], + [5, 7]]] + player = Player(payoffs_2opponents) + self.g = NormalFormGame([player for i in range(3)]) + + def test_getitem(self): + assert_array_equal(self.g[0, 0, 1], [6, 4, 1]) + + def test_is_nash_pure(self): + ok_(self.g.is_nash((0, 0, 0))) + ok_(not self.g.is_nash((0, 0, 1))) + + def test_is_nash_mixed(self): + p = (1 + np.sqrt(65)) / 16 + ok_(self.g.is_nash(([1 - p, p], [1 - p, p], [1 - p, p]))) + + +def test_normalformgame_input_action_sizes(): + g = NormalFormGame((2, 3, 4)) + + eq_(g.N, 3) # Number of players + + assert_array_equal( + g.players[0].payoff_array, + np.zeros((2, 3, 4)) + ) + assert_array_equal( + g.players[1].payoff_array, + np.zeros((3, 4, 2)) + ) + assert_array_equal( + g.players[2].payoff_array, + np.zeros((4, 2, 3)) + ) + + +def test_normalformgame_setitem(): + g = NormalFormGame((2, 2)) + g[0, 0] = (0, 10) + g[0, 1] = (0, 10) + g[1, 0] = (3, 5) + g[1, 1] = (-2, 0) + + assert_array_equal( + g.players[0].payoff_array, + [[0, 0], [3, -2]] + ) + assert_array_equal( + g.players[1].payoff_array, + [[10, 5], [10, 0]] + ) + + +def test_normalformgame_constant_payoffs(): + g = NormalFormGame((2, 2)) + + ok_(g.is_nash((0, 0))) + ok_(g.is_nash((0, 1))) + ok_(g.is_nash((1, 0))) + ok_(g.is_nash((1, 1))) + + +def test_normalformgame_payoff_profile_array(): + nums_actions = (2, 3, 4) + for N in range(1, len(nums_actions)+1): + payoff_arrays = [ + np.arange(np.prod(nums_actions[0:N])).reshape(nums_actions[i:N] + + nums_actions[0:i]) + for i in range(N) + ] + players = [Player(payoff_array) for payoff_array in payoff_arrays] + g = NormalFormGame(players) + g_new = NormalFormGame(g.payoff_profile_array) + for player_new, payoff_array in zip(g_new.players, payoff_arrays): + assert_array_equal(player_new.payoff_array, payoff_array) + + +# Trivial cases with one player # + +class TestPlayer_0opponents: + """Test for trivial Player with no opponent player""" + + def setUp(self): + """Setup a Player instance""" + payoffs = [0, 1] + self.player = Player(payoffs) + + def test_payoff_vector(self): + """Trivial player: payoff_vector""" + assert_array_equal(self.player.payoff_vector(None), [0, 1]) + + def test_is_best_response(self): + """Trivial player: is_best_response""" + ok_(self.player.is_best_response(1, None)) + + def test_best_response(self): + """Trivial player: best_response""" + eq_(self.player.best_response(None), 1) + + +class TestNormalFormGame_1p: + """Test for trivial NormalFormGame with a single player""" + + def setUp(self): + """Setup a NormalFormGame instance""" + data = [[0], [1], [1]] + self.g = NormalFormGame(data) + + def test_construction(self): + """Trivial game: construction""" + ok_(self.g.N == 1) + assert_array_equal(self.g.players[0].payoff_array, [0, 1, 1]) + + def test_getitem(self): + """Trivial game: __getitem__""" + eq_(self.g[0], 0) + + def test_is_nash_pure(self): + """Trivial game: is_nash with pure action""" + ok_(self.g.is_nash((1,))) + ok_(not self.g.is_nash((0,))) + + def test_is_nash_mixed(self): + """Trivial game: is_nash with mixed action""" + ok_(self.g.is_nash(([0, 1/2, 1/2],))) + + +def test_normalformgame_input_action_sizes_1p(): + g = NormalFormGame(2) + + eq_(g.N, 1) # Number of players + + assert_array_equal( + g.players[0].payoff_array, + np.zeros(2) + ) + + +def test_normalformgame_setitem_1p(): + g = NormalFormGame(2) + + eq_(g.N, 1) # Number of players + + g[0] = 10 # Set payoff 10 for action 0 + eq_(g.players[0].payoff_array[0], 10) + + +# Invalid inputs # + +@raises(ValueError) +def test_normalformgame_invalid_input_players_shape_inconsistent(): + p0 = Player(np.zeros((2, 3))) + p1 = Player(np.zeros((2, 3))) + g = NormalFormGame([p0, p1]) + + +@raises(ValueError) +def test_normalformgame_invalid_input_players_num_inconsistent(): + p0 = Player(np.zeros((2, 2, 2))) + p1 = Player(np.zeros((2, 2, 2))) + g = NormalFormGame([p0, p1]) + + +@raises(ValueError) +def test_normalformgame_invalid_input_nosquare_matrix(): + g = NormalFormGame(np.zeros((2, 3))) + + +@raises(ValueError) +def test_normalformgame_invalid_input_payoff_profiles(): + g = NormalFormGame(np.zeros((2, 2, 1))) + + +# Utility functions # + +def test_pure2mixed(): + num_actions = 3 + pure_action = 0 + mixed_action = [1., 0., 0.] + + assert_array_equal(pure2mixed(num_actions, pure_action), mixed_action) + + +# Numba jitted functions # + +def test_best_response_2p(): + test_case0 = { + 'payoff_array': np.array([[4, 0], [3, 2], [0, 3]]), + 'mixed_actions': + [np.array([1, 0]), np.array([0.5, 0.5]), np.array([0, 1])], + 'brs_expected': [0, 1, 2] + } + test_case1 = { + 'payoff_array': np.zeros((2, 3)), + 'mixed_actions': [np.array([1, 0, 0]), np.array([1/3, 1/3, 1/3])], + 'brs_expected': [0, 0] + } + + for test_case in [test_case0, test_case1]: + for mixed_action, br_expected in zip(test_case['mixed_actions'], + test_case['brs_expected']): + br_computed = \ + best_response_2p(test_case['payoff_array'], mixed_action) + eq_(br_computed, br_expected) + + +if __name__ == '__main__': + import sys + import nose + + argv = sys.argv[:] + argv.append('--verbose') + argv.append('--nocapture') + nose.main(argv=argv, defaultTest=__file__) diff --git a/quantecon/kalman.py b/quantecon/kalman.py index 023e91b9c..dd3e64396 100644 --- a/quantecon/kalman.py +++ b/quantecon/kalman.py @@ -9,6 +9,7 @@ import numpy as np from numpy import dot from scipy.linalg import inv +from quantecon.lss import LinearStateSpace from quantecon.matrix_eqn import solve_discrete_riccati @@ -83,6 +84,70 @@ def __str__(self): """ return dedent(m.format(n=self.ss.n, k=self.ss.k)) + def whitener_lss(self): + r""" + This function takes the linear state space system + that is an input to the Kalman class and it converts + that system to the time-invariant whitener represenation + given by + + \tilde{x}_{t+1}^* = \tilde{A} \tilde{x} + \tilde{C} v + a = \tilde{G} \tilde{x} + + where + + \tilde{x}_t = [x+{t}, \hat{x}_{t}, v_{t}] + + and + + \tilde{A} = [A 0 0 + KG A-KG KH + 0 0 0] + + \tilde{C} = [C 0 + 0 0 + 0 I] + + \tilde{G} = [G -G H] + + with A, C, G, H coming from the linear state space system + that defines the Kalman instance + + + Returns + ------- + whitened_lss : LinearStateSpace + This is the linear state space system that represents + the whitened system + """ + # Check for steady state Sigma and K + if self.K_infinity is None: + Sig, K = self.stationary_values() + self.Sigma_infinity = Sig + self.K_infinity = K + else: + K = self.K_infinity + + # Get the matrix sizes + n, k, m, l = self.ss.n, self.ss.k, self.ss.m, self.ss.l + A, C, G, H = self.ss.A, self.ss.C, self.ss.G, self.ss.H + + Atil = np.vstack([np.hstack([A, np.zeros((n, n)), np.zeros((n, l))]), + np.hstack([dot(K, G), A-dot(K, G), dot(K, H)]), + np.zeros((l, 2*n + l))]) + + Ctil = np.vstack([np.hstack([C, np.zeros((n, l))]), + np.zeros((n, m+l)), + np.hstack([np.zeros((l, m)), np.eye(l)])]) + + Gtil = np.hstack([G, -G, H]) + + whitened_lss = LinearStateSpace(Atil, Ctil, Gtil) + self.whitened_lss = whitened_lss + + return whitened_lss + + def prior_to_filtered(self, y): r""" Updates the moments (x_hat, Sigma) of the time t prior to the @@ -192,17 +257,21 @@ def stationary_coefficients(self, j, coeff_type='ma'): if K_infinity is None: S, K_infinity = self.stationary_values() # == compute and return coefficients == # - coeffs = [np.identity(self.ss.k)] + coeffs = [] i = 1 if coeff_type == 'ma': - P = A + coeffs.append(np.identity(self.ss.k)) + P_mat = A + P = np.identity(self.ss.n) # Create a copy elif coeff_type == 'var': - P = A - dot(K_infinity, G) + coeffs.append(dot(G, K_infinity)) + P_mat = A - dot(K_infinity, G) + P = np.copy(P_mat) # Create a copy else: raise ValueError("Unknown coefficient type") while i <= j: coeffs.append(dot(dot(G, P), K_infinity)) - P = dot(P, P) + P = dot(P, P_mat) i += 1 return coeffs diff --git a/quantecon/lqcontrol.py b/quantecon/lqcontrol.py index e61712852..0690c3e89 100644 --- a/quantecon/lqcontrol.py +++ b/quantecon/lqcontrol.py @@ -100,7 +100,7 @@ class LQ(object): def __init__(self, Q, R, A, B, C=None, N=None, beta=1, T=None, Rf=None): # == Make sure all matrices can be treated as 2D arrays == # - converter = lambda X: np.atleast_2d(np.asarray(X, dtype='float32')) + converter = lambda X: np.atleast_2d(np.asarray(X, dtype='float')) self.A, self.B, self.Q, self.R, self.N = list(map(converter, (A, B, Q, R, N))) # == Record dimensions == # @@ -123,7 +123,7 @@ def __init__(self, Q, R, A, B, C=None, N=None, beta=1, T=None, Rf=None): if T: # == Model is finite horizon == # self.T = T - self.Rf = np.asarray(Rf, dtype='float32') + self.Rf = np.asarray(Rf, dtype='float') self.P = self.Rf self.d = 0 else: diff --git a/quantecon/lss.py b/quantecon/lss.py index 4df6ec464..dbfc2d029 100644 --- a/quantecon/lss.py +++ b/quantecon/lss.py @@ -141,7 +141,7 @@ def convert(self, x): well formed 2D NumPy arrays """ - return np.atleast_2d(np.asarray(x, dtype='float32')) + return np.atleast_2d(np.asarray(x, dtype='float')) def simulate(self, ts_length=100): """ @@ -336,3 +336,42 @@ def geometric_sums(self, beta, x_t): S_y = self.G.dot(S_x) return S_x, S_y + + def impulse_response(self, j=5): + """ + Pulls off the imuplse response coefficients to a shock + in w_{t} for x and y + + Important to note: We are uninterested in the shocks to + v for this method + + * x coefficients are C, AC, A^2 C... + * y coefficients are GC, GAC, GA^2C... + + Parameters + ---------- + j : Scalar(int) + Number of coefficients that we want + + Returns + ------- + xcoef : list(array_like(float, 2)) + The coefficients for x + ycoef : list(array_like(float, 2)) + The coefficients for y + """ + # Pull out matrices + A, C, G, H = self.A, self.C, self.G, self.H + Apower = np.copy(A) + + # Create room for coefficients + xcoef = [C] + ycoef = [np.dot(G, C)] + + for i in range(j): + xcoef.append(np.dot(Apower, C)) + ycoef.append(np.dot(G, np.dot(Apower, C))) + Apower = np.dot(Apower, A) + + return xcoef, ycoef + diff --git a/quantecon/markov/ddp.py b/quantecon/markov/ddp.py index c4b30daad..20aefaa6e 100644 --- a/quantecon/markov/ddp.py +++ b/quantecon/markov/ddp.py @@ -1,4 +1,4 @@ -""" +r""" Filename: ddp.py Author: Daisuke Oyama @@ -23,16 +23,16 @@ \Delta(S)`, where :math:`q(s'|s, a)` is the probability that the state in the next period is :math:`s'` when the current state is :math:`s` and the action chosen is :math:`a`; and -* discount factor :math:`\beta \in [0, 1)`. +* discount factor :math:`0 \leq \beta < 1`. For a policy function :math:`\sigma`, let :math:`r_{\sigma}` and :math:`Q_{\sigma}` be the reward vector and the transition probability matrix for :math:`\sigma`, which are defined by :math:`r_{\sigma}(s) = r(s, \sigma(s))` and :math:`Q_{\sigma}(s, s') = q(s'|s, \sigma(s))`, respectively. The policy value function :math:`v_{\sigma}` for -:math`\sigma` is defined by +:math:`\sigma` is defined by -..math:: +.. math:: v_{\sigma}(s) = \sum_{t=0}^{\infty} \beta^t (Q_{\sigma}^t r_{\sigma})(s) @@ -45,7 +45,7 @@ The *Bellman equation* is written as -..math:: +.. math:: v(s) = \max_{a \in A(s)} r(s, a) + \beta \sum_{s' \in S} q(s'|s, a) v(s') \quad (s \in S). @@ -53,7 +53,7 @@ The *Bellman operator* :math:`T` is defined by the right hand side of the Bellman equation: -..math:: +.. math:: (T v)(s) = \max_{a \in A(s)} r(s, a) + \beta \sum_{s' \in S} q(s'|s, a) v(s') \quad (s \in S). @@ -61,7 +61,7 @@ For a policy function :math:`\sigma`, the operator :math:`T_{\sigma}` is defined by -..math:: +.. math:: (T_{\sigma} v)(s) = r(s, \sigma(s)) + \beta \sum_{s' \in S} q(s'|s, \sigma(s)) v(s') @@ -117,7 +117,7 @@ class DiscreteDP(object): - """ + r""" Class for dealing with a discrete dynamic program. There are two ways to represent the data for instantiating a @@ -141,7 +141,7 @@ class DiscreteDP(object): with parameters: - * length L reward vector R, + * length L reward vector `R`, * L x n transition probability array `Q`, * discount factor `beta`, * length L array `s_indices`, and @@ -165,7 +165,7 @@ class DiscreteDP(object): Transition probability array. beta : scalar(float) - Discount factor. Must be in [0, 1). + Discount factor. Must be 0 <= beta < 1. s_indices : array_like(int, ndim=1), optional(default=None) Array containing the indices of the states. @@ -297,7 +297,7 @@ def __init__(self, R, Q, beta, s_indices=None, a_indices=None): raise ValueError('R must be 1- or 2-dimensional') msg_dimension = 'dimensions of R and Q must be either 1 and 2, ' \ - 'of 2 and 3' + 'or 2 and 3' msg_shape = 'shapes of R and Q must be either (n, m) and (n, m, n), ' \ 'or (L,) and (L, n)' @@ -451,8 +451,8 @@ def _check_action_feasibility(self): def RQ_sigma(self, sigma): """ - Given a policy `sigma`, return the reward vector R_sigma and the - transition probability matrix Q_sigma. + Given a policy `sigma`, return the reward vector `R_sigma` and + the transition probability matrix `Q_sigma`. Parameters ---------- @@ -483,7 +483,7 @@ def RQ_sigma(self, sigma): def bellman_operator(self, v, Tv=None, sigma=None): """ The Bellman operator, which computes and returns the updated - value function Tv for a value function v. + value function `Tv` for a value function `v`. Parameters ---------- @@ -538,7 +538,7 @@ def compute_greedy(self, v, sigma=None): Value function vector, of length n. sigma : ndarray(int, ndim=1), optional(default=None) - Optional output array for sigma. + Optional output array for `sigma`. Returns ------- @@ -708,12 +708,12 @@ def value_iteration(self, v_init=None, epsilon=None, max_iter=None): sigma = self.compute_greedy(v) res = DPSolveResult(v=v, - sigma=sigma, - num_iter=num_iter, - mc=self.controlled_mc(sigma), - method='value iteration', - epsilon=epsilon, - max_iter=max_iter) + sigma=sigma, + num_iter=num_iter, + mc=self.controlled_mc(sigma), + method='value iteration', + epsilon=epsilon, + max_iter=max_iter) return res @@ -745,11 +745,11 @@ def policy_iteration(self, v_init=None, max_iter=None): num_iter = i + 1 res = DPSolveResult(v=v_sigma, - sigma=sigma, - num_iter=num_iter, - mc=self.controlled_mc(sigma), - method='policy iteration', - max_iter=max_iter) + sigma=sigma, + num_iter=num_iter, + mc=self.controlled_mc(sigma), + method='policy iteration', + max_iter=max_iter) return res @@ -798,13 +798,13 @@ def midrange(z): num_iter = i + 1 res = DPSolveResult(v=v, - sigma=sigma, - num_iter=num_iter, - mc=self.controlled_mc(sigma), - method='modified policy iteration', - epsilon=epsilon, - max_iter=max_iter, - k=k) + sigma=sigma, + num_iter=num_iter, + mc=self.controlled_mc(sigma), + method='modified policy iteration', + epsilon=epsilon, + max_iter=max_iter, + k=k) return res @@ -820,7 +820,7 @@ def controlled_mc(self, sigma): Returns ------- mc : MarkovChain - Controlled Markov Chain. + Controlled Markov chain. """ _, Q_sigma = self.RQ_sigma(sigma) diff --git a/quantecon/markov/tests/test_random.py b/quantecon/markov/tests/test_random.py index dee4c7013..62cddb630 100644 --- a/quantecon/markov/tests/test_random.py +++ b/quantecon/markov/tests/test_random.py @@ -81,6 +81,16 @@ def test_random_stochastic_matrix_dense_vs_sparse(): assert_array_equal(P_dense, P_sparse.toarray()) +def test_random_stochastic_matrix_k_1(): + n, k = 3, 1 + P_dense = random_stochastic_matrix(n, k, sparse=False) + P_sparse = random_stochastic_matrix(n, k, sparse=True) + assert_array_equal(P_dense[P_dense != 0], np.ones(n)) + assert_array_equal(P_sparse.data, np.ones(n)) + for P in [P_dense, P_sparse]: + assert_array_almost_equal_nulp(P.sum(axis=1), np.ones(n)) + + class TestRandomDiscreteDP: def setUp(self): self.num_states, self.num_actions = 5, 4 diff --git a/quantecon/models/__init__.py b/quantecon/models/__init__.py index 5b76969b5..1ebf46304 100644 --- a/quantecon/models/__init__.py +++ b/quantecon/models/__init__.py @@ -1,22 +1 @@ -""" -models directory imports - -objects imported here will live in the `quantecon.models` namespace - -""" - -__all__ = ["AssetPrices", "CareerWorkerProblem", "ConsumerProblem", - "JvWorker", "LakeModel", "LakeModelAgent", "LakeModel_Equilibrium", "LucasTree", - "SearchProblem", "GrowthModel", "solow"] - -from . import solow as solow -from .asset_pricing import AssetPrices -from .career import CareerWorkerProblem -from .ifp import ConsumerProblem -from .jv import JvWorker -from .lake import LakeModel, LakeModelAgent, LakeModel_Equilibrium -from .lucastree import LucasTree -from .odu import SearchProblem -from .optgrowth import GrowthModel -from .arellano_vfi import Arellano_Economy -from .uncertainty_traps import UncertaintyTrapEcon +raise ImportError("The code previously contained in the quantecon.models subpackage has been migrated to the QuantEcon.applications (https://github.com/QuantEcon/QuantEcon.applications) repo") \ No newline at end of file diff --git a/quantecon/models/arellano_vfi.py b/quantecon/models/arellano_vfi.py deleted file mode 100644 index 56a82d423..000000000 --- a/quantecon/models/arellano_vfi.py +++ /dev/null @@ -1,251 +0,0 @@ -""" -Filename: arellano_vfi.py - -Authors: Chase Coleman, John Stachurski - -Solve the Arellano default risk model - -References ----------- - -http://quant-econ.net/py/arellano.html - -.. Arellano, Cristina. "Default risk and income fluctuations in emerging - economies." The American Economic Review (2008): 690-712. - -""" -from __future__ import division -import numpy as np -import random -import quantecon as qe -from numba import jit - - -class Arellano_Economy(object): - """ - Arellano 2008 deals with a small open economy whose government - invests in foreign assets in order to smooth the consumption of - domestic households. Domestic households receive a stochastic - path of income. - - Parameters - ---------- - beta : float - Time discounting parameter - gamma : float - Risk-aversion parameter - r : float - int lending rate - rho : float - Persistence in the income process - eta : float - Standard deviation of the income process - theta : float - Probability of re-entering financial markets in each period - ny : int - Number of points in y grid - nB : int - Number of points in B grid - tol : float - Error tolerance in iteration - maxit : int - Maximum number of iterations - """ - - def __init__(self, - beta=.953, # time discount rate - gamma=2., # risk aversion - r=0.017, # international interest rate - rho=.945, # persistence in output - eta=0.025, # st dev of output shock - theta=0.282, # prob of regaining access - ny=21, # number of points in y grid - nB=251, # number of points in B grid - tol=1e-8, # error tolerance in iteration - maxit=10000): - - # Save parameters - self.beta, self.gamma, self.r = beta, gamma, r - self.rho, self.eta, self.theta = rho, eta, theta - self.ny, self.nB = ny, nB - - # Create grids and discretize Markov process - self.Bgrid = np.linspace(-.45, .45, nB) - log_ygrid, Py = qe.markov.tauchen(rho, eta, 3, ny) - self.ygrid = np.exp(log_ygrid) - self.Py = Py - - # Output when in default - ymean = np.mean(self.ygrid) - self.def_y = np.minimum(0.969 * ymean, self.ygrid) - - # Allocate memory - self.Vd = np.zeros(ny) - self.Vc = np.zeros((ny, nB)) - self.V = np.zeros((ny, nB)) - self.Q = np.ones((ny, nB)) * .95 # Initial guess for prices - self.default_prob = np.empty((ny, nB)) - - # Compute the value functions, prices, and default prob - self.solve(tol=tol, maxit=maxit) - # Compute the optimal savings policy conditional on no default - self.compute_savings_policy() - - - def solve(self, tol=1e-8, maxit=10000): - # Iteration Stuff - it = 0 - dist = 10. - - # Alloc memory to store next iterate of value function - V_upd = np.zeros((self.ny, self.nB)) - - # == Main loop == # - while dist > tol and maxit > it: - - # Compute expectations for this iteration - Vs = self.V, self.Vd, self.Vc - EV, EVd, EVc = (np.dot(self.Py, v) for v in Vs) - - # Run inner loop to update value functions Vc and Vd. - # Note that Vc and Vd are updated in place. Other objects - # are not modified. - _inner_loop(self.ygrid, self.def_y, self.Bgrid, self.Vd, self.Vc, - EVc, EVd, EV, self.Q, - self.beta, self.theta, self.gamma) - - # Update prices - Vd_compat = np.repeat(self.Vd, self.nB).reshape(self.ny, self.nB) - default_states = Vd_compat > self.Vc - self.default_prob[:, :] = np.dot(self.Py, default_states) - self.Q[:, :] = (1 - self.default_prob)/(1 + self.r) - - # Update main value function and distance - V_upd[:, :] = np.maximum(self.Vc, Vd_compat) - dist = np.max(np.abs(V_upd - self.V)) - self.V[:, :] = V_upd[:, :] - - it += 1 - if it % 25 == 0: - print("Running iteration {} with dist of {}".format(it, dist)) - - return None - - - def compute_savings_policy(self): - """ - Compute optimal savings B' conditional on not defaulting. - The policy is recorded as an index value in Bgrid. - """ - - # Allocate memory - self.next_B_index = np.empty((self.ny, self.nB)) - EV = np.dot(self.Py, self.V) - - _compute_savings_policy(self.ygrid, self.Bgrid, self.Q, EV, - self.gamma, self.beta, self.next_B_index) - - - def simulate(self, T, y_init=None, B_init=None): - """ - Simulate time series for output, consumption, B'. - """ - # Find index i such that Bgrid[i] is near 0 - zero_B_index = np.searchsorted(self.Bgrid, 0) - - if y_init is None: - # Set to index near the mean of the ygrid - y_init = np.searchsorted(self.ygrid, self.ygrid.mean()) - if B_init is None: - B_init = zero_B_index - # Start off not in default - in_default = False - # Initialize Markov chain for output - mc = qe.markov.MarkovChain(self.Py) - - y_sim_indices = mc.simulate(T, init=y_init) - B_sim_indices = np.empty(T, dtype=np.int64) - B_sim_indices[0] = B_init - q_sim = np.empty(T) - in_default_series = np.zeros(T, dtype=np.int64) - - for t in range(T-1): - yi, Bi = y_sim_indices[t], B_sim_indices[t] - if not in_default: - if self.Vc[yi, Bi] < self.Vd[yi]: - in_default = True - Bi_next = zero_B_index - else: - new_index = self.next_B_index[yi, Bi] - Bi_next = new_index - else: - in_default_series[t] = 1 - Bi_next = zero_B_index - if random.uniform(0, 1) < self.theta: - in_default = False - B_sim_indices[t+1] = Bi_next - q_sim[t] = self.Q[yi, Bi_next] - - q_sim[-1] = q_sim[-2] # Extrapolate for the last price - return_vecs = (self.ygrid[y_sim_indices], - self.Bgrid[B_sim_indices], - q_sim, - in_default_series) - - return return_vecs - - -@jit(nopython=True) -def u(c, gamma): - return c**(1-gamma)/(1-gamma) - - -@jit(nopython=True) -def _inner_loop(ygrid, def_y, Bgrid, Vd, Vc, EVc, - EVd, EV, qq, beta, theta, gamma): - """ - This is a numba version of the inner loop of the solve in the - Arellano class. It updates Vd and Vc in place. - """ - ny, nB = len(ygrid), len(Bgrid) - zero_ind = nB // 2 # Integer division - for iy in range(ny): - y = ygrid[iy] # Pull out current y - - # Compute Vd - Vd[iy] = u(def_y[iy], gamma) + \ - beta * (theta * EVc[iy, zero_ind] + (1 - theta) * EVd[iy]) - - # Compute Vc - for ib in range(nB): - B = Bgrid[ib] # Pull out current B - - current_max = -1e14 - for ib_next in range(nB): - c = max(y - qq[iy, ib_next] * Bgrid[ib_next] + B, 1e-14) - m = u(c, gamma) + beta * EV[iy, ib_next] - if m > current_max: - current_max = m - Vc[iy, ib] = current_max - - return None - - -@jit(nopython=True) -def _compute_savings_policy(ygrid, Bgrid, Q, EV, gamma, beta, next_B_index): - # Compute best index in Bgrid given iy, ib - ny, nB = len(ygrid), len(Bgrid) - for iy in range(ny): - y = ygrid[iy] - for ib in range(nB): - B = Bgrid[ib] - current_max = -1e10 - for ib_next in range(nB): - c = max(y - Q[iy, ib_next] * Bgrid[ib_next] + B, 1e-14) - m = u(c, gamma) + beta * EV[iy, ib_next] - if m > current_max: - current_max = m - current_max_index = ib_next - next_B_index[iy, ib] = current_max_index - return None - diff --git a/quantecon/models/asset_pricing.py b/quantecon/models/asset_pricing.py deleted file mode 100644 index 312da91ef..000000000 --- a/quantecon/models/asset_pricing.py +++ /dev/null @@ -1,216 +0,0 @@ -""" -Filename: asset_pricing.py - -Authors: David Evans, John Stachurski and Thomas J. Sargent - -Computes asset prices in an endowment economy when the endowment obeys -geometric growth driven by a finite state Markov chain. The transition -matrix of the Markov chain is P, and the set of states is s. The -discount factor is beta, and gamma is the coefficient of relative risk -aversion in the household's utility function. - -References ----------- - - http://quant-econ.net/py/markov_asset.html - -""" -from textwrap import dedent -import numpy as np -from numpy.linalg import solve - - -class AssetPrices(object): - r""" - A class to compute asset prices when the endowment follows a finite - Markov chain. - - Parameters - ---------- - beta : scalar, float - Discount factor - P : array_like(float) - Transition matrix - s : array_like(float) - Growth rate of consumption - gamma : scalar(float) - Coefficient of risk aversion - - Attributes - ---------- - beta, P, s, gamma : see Parameters - n : scalar(int) - The number of rows in P - - Examples - -------- - - >>> n = 5 - >>> P = 0.0125 * np.ones((n, n)) - >>> P += np.diag(0.95 - 0.0125 * np.ones(5)) - >>> s = np.array([1.05, 1.025, 1.0, 0.975, 0.95]) - >>> gamma = 2.0 - >>> beta = 0.94 - >>> ap = AssetPrices(beta, P, s, gamma) - >>> zeta = 1.0 - >>> v = ap.tree_price() - >>> print("Lucas Tree Prices: %s" % v) - Lucas Tree Prices: [ 12.72221763 14.72515002 17.57142236 - 21.93570661 29.47401578] - - >>> v_consol = ap.consol_price(zeta) - >>> print("Consol Bond Prices: %s" % v_consol) - Consol Bond Prices: [ 87.56860139 109.25108965 148.67554548 - 242.55144082 753.87100476] - - >>> p_s = 150.0 - >>> w_bar, w_bars = ap.call_option(zeta, p_s, T = [10,20,30]) - >>> w_bar - array([ 64.30843769, 80.05179282, 108.67734545, 176.83933585, - 603.87100476]) - >>> w_bars - {10: array([ 44.79815889, 50.81409953, 58.61386544, - 115.69837047, 603.87100476]), - 20: array([ 56.73357192, 68.51905592, 86.69038119, - 138.45961867, 603.87100476]), - 30: array([ 60.62653565, 74.67608505, 98.38386204, - 153.80497466, 603.87100476])} - - """ - def __init__(self, beta, P, s, gamma): - self.beta, self.gamma = beta, gamma - self.P, self.s = P, s - self.n = self.P.shape[0] - - def __repr__(self): - m = "AssetPrices(beta={b:g}, P='{n:g} by {n:g}', s={s}, gamma={g:g})" - return m.format(b=self.beta, n=self.P.shape[0], s=self.s, g=self.gamma) - - def __str__(self): - m = """\ - AssetPrices (Merha and Prescott, 1985): - - beta (discount factor) : {b:g} - - P (Transition matrix) : {n:g} by {n:g} - - s (growth rate of consumption) : {s:s} - - gamma (Coefficient of risk aversion) : {g:g} - """ - - return dedent(m.format(b=self.beta, n=self.P.shape[0], s=repr(self.s), - g=self.gamma)) - - @property - def P_tilde(self): - P, s, gamma = self.P, self.s, self.gamma - return P * s**(1.0-gamma) # using broadcasting - - @property - def P_check(self): - P, s, gamma = self.P, self.s, self.gamma - return P * s**(-gamma) # using broadcasting - - def tree_price(self): - """ - Computes the function v such that the price of the lucas tree is - v(lambda)C_t - - Returns - ------- - v : array_like(float) - Lucas tree prices - - """ - # == Simplify names == # - beta = self.beta - - # == Compute v == # - P_tilde = self.P_tilde - I = np.identity(self.n) - O = np.ones(self.n) - v = beta * solve(I - beta * P_tilde, P_tilde.dot(O)) - - return v - - def consol_price(self, zeta): - """ - Computes price of a consol bond with payoff zeta - - Parameters - ---------- - zeta : scalar(float) - Coupon of the console - - Returns - ------- - p_bar : array_like(float) - Console bond prices - - """ - # == Simplify names == # - beta = self.beta - - # == Compute price == # - P_check = self.P_check - I = np.identity(self.n) - O = np.ones(self.n) - p_bar = beta * solve(I - beta * P_check, P_check.dot(zeta * O)) - - return p_bar - - def call_option(self, zeta, p_s, T=[], epsilon=1e-8): - """ - Computes price of a call option on a consol bond, both finite - and infinite horizon - - Parameters - ---------- - zeta : scalar(float) - Coupon of the console - - p_s : scalar(float) - Strike price - - T : iterable(integers) - Length of option in the finite horizon case - - epsilon : scalar(float), optional(default=1e-8) - Tolerance for infinite horizon problem - - Returns - ------- - w_bar : array_like(float) - Infinite horizon call option prices - - w_bars : dict - A dictionary of key-value pairs {t: vec}, where t is one of - the dates in the list T and vec is the option prices at that - date - - """ - # == Simplify names, initialize variables == # - beta = self.beta - P_check = self.P_check - - # == Compute consol price == # - v_bar = self.consol_price(zeta) - - # == Compute option price == # - w_bar = np.zeros(self.n) - error = epsilon + 1 - t = 0 - w_bars = {} - while error > epsilon: - if t in T: - w_bars[t] = w_bar - - # == Maximize across columns == # - to_stack = (beta*P_check.dot(w_bar), v_bar-p_s) - w_bar_new = np.amax(np.vstack(to_stack), axis=0) - - # == Find maximal difference of each component == # - error = np.amax(np.abs(w_bar-w_bar_new)) - - # == Update == # - w_bar = w_bar_new - t += 1 - - return w_bar, w_bars diff --git a/quantecon/models/career.py b/quantecon/models/career.py deleted file mode 100644 index fe5fbca7a..000000000 --- a/quantecon/models/career.py +++ /dev/null @@ -1,166 +0,0 @@ -""" -Filename: career.py - -Authors: Thomas Sargent, John Stachurski - -A class to solve the career / job choice model due to Derek Neal. - -References ----------- - -http://quant-econ.net/py/career.html - -.. [Neal1999] Neal, D. (1999). The Complexity of Job Mobility among - Young Men, Journal of Labor Economics, 17(2), 237-261. - -""" -from textwrap import dedent -import numpy as np -from quantecon.distributions import BetaBinomial - - -class CareerWorkerProblem(object): - """ - An instance of the class is an object with data on a particular - problem of this type, including probabilites, discount factor and - sample space for the variables. - - Parameters - ---------- - beta : scalar(float), optional(default=5.0) - Discount factor - B : scalar(float), optional(default=0.95) - Upper bound of for both epsilon and theta - N : scalar(int), optional(default=50) - Number of possible realizations for both epsilon and theta - F_a : scalar(int or float), optional(default=1) - Parameter `a` from the career distribution - F_b : scalar(int or float), optional(default=1) - Parameter `b` from the career distribution - G_a : scalar(int or float), optional(default=1) - Parameter `a` from the job distribution - G_b : scalar(int or float), optional(default=1) - Parameter `b` from the job distribution - - Attributes - ---------- - beta, B, N : see Parameters - theta : array_like(float, ndim=1) - A grid of values from 0 to B - epsilon : array_like(float, ndim=1) - A grid of values from 0 to B - F_probs : array_like(float, ndim=1) - The probabilities of different values for F - G_probs : array_like(float, ndim=1) - The probabilities of different values for G - F_mean : scalar(float) - The mean of the distribution for F - G_mean : scalar(float) - The mean of the distribution for G - - """ - - def __init__(self, B=5.0, beta=0.95, N=50, F_a=1, F_b=1, G_a=1, - G_b=1): - self.beta, self.N, self.B = beta, N, B - self.theta = np.linspace(0, B, N) # set of theta values - self.epsilon = np.linspace(0, B, N) # set of epsilon values - self.F_probs = BetaBinomial(N-1, F_a, F_b).pdf() - self.G_probs = BetaBinomial(N-1, G_a, G_b).pdf() - self.F_mean = np.sum(self.theta * self.F_probs) - self.G_mean = np.sum(self.epsilon * self.G_probs) - - # Store these parameters for str and repr methods - self._F_a, self._F_b = F_a, F_b - self._G_a, self._G_b = G_a, G_b - - def __repr__(self): - m = "CareerWorkerProblem(beta={b:g}, B={B:g}, N={n:g}, F_a={fa:g}, " - m += "F_b={fb:g}, G_a={ga:g}, G_b={gb:g})" - return m.format(b=self.beta, B=self.B, n=self.N, fa=self._F_a, - fb=self._F_b, ga=self._G_a, gb=self._G_b) - - def __str__(self): - m = """\ - CareerWorkerProblem (Neal, 1999) - - beta (discount factor) : {b:g} - - B (upper bound for epsilon and theta) : {B:g} - - N (number of realizations of epsilon and theta) : {n:g} - - F_a (parameter a from career distribution) : {fa:g} - - F_b (parameter b from career distribution) : {fb:g} - - G_a (parameter a from job distribution) : {ga:g} - - G_b (parameter b from job distribution) : {gb:g} - """ - return dedent(m.format(b=self.beta, B=self.B, n=self.N, fa=self._F_a, - fb=self._F_b, ga=self._G_a, gb=self._G_b)) - - def bellman_operator(self, v): - """ - The Bellman operator for the career / job choice model of Neal. - - Parameters - ---------- - v : array_like(float) - A 2D NumPy array representing the value function - Interpretation: :math:`v[i, j] = v(\theta_i, \epsilon_j)` - - Returns - ------- - new_v : array_like(float) - The updated value function Tv as an array of shape v.shape - - """ - new_v = np.empty(v.shape) - for i in range(self.N): - for j in range(self.N): - # stay put - v1 = self.theta[i] + self.epsilon[j] + self.beta * v[i, j] - - # new job - v2 = (self.theta[i] + self.G_mean + self.beta * - np.dot(v[i, :], self.G_probs)) - - # new life - v3 = (self.G_mean + self.F_mean + self.beta * - np.dot(self.F_probs, np.dot(v, self.G_probs))) - new_v[i, j] = max(v1, v2, v3) - return new_v - - def get_greedy(self, v): - """ - Compute optimal actions taking v as the value function. - - Parameters - ---------- - v : array_like(float) - A 2D NumPy array representing the value function - Interpretation: :math:`v[i, j] = v(\theta_i, \epsilon_j)` - - Returns - ------- - policy : array_like(float) - A 2D NumPy array, where policy[i, j] is the optimal action - at :math:`(\theta_i, \epsilon_j)`. - - The optimal action is represented as an integer in the set - 1, 2, 3, where 1 = 'stay put', 2 = 'new job' and 3 = 'new - life' - - """ - policy = np.empty(v.shape, dtype=int) - for i in range(self.N): - for j in range(self.N): - v1 = self.theta[i] + self.epsilon[j] + self.beta * v[i, j] - v2 = (self.theta[i] + self.G_mean + self.beta * - np.dot(v[i, :], self.G_probs)) - v3 = (self.G_mean + self.F_mean + self.beta * - np.dot(self.F_probs, np.dot(v, self.G_probs))) - if v1 > max(v2, v3): - action = 1 - elif v2 > max(v1, v3): - action = 2 - else: - action = 3 - policy[i, j] = action - - return policy diff --git a/quantecon/models/ifp.py b/quantecon/models/ifp.py deleted file mode 100644 index f6baea40d..000000000 --- a/quantecon/models/ifp.py +++ /dev/null @@ -1,221 +0,0 @@ -""" -Filename: ifp.py - -Authors: Thomas Sargent, John Stachurski - -Tools for solving the standard optimal savings / income fluctuation -problem for an infinitely lived consumer facing an exogenous income -process that evolves according to a Markov chain. - -References ----------- - -http://quant-econ.net/py/ifp.html - -""" -from textwrap import dedent -import numpy as np -from scipy.optimize import fminbound, brentq -from scipy import interp - - -class ConsumerProblem(object): - """ - A class for solving the income fluctuation problem. Iteration with - either the Coleman or Bellman operators from appropriate initial - conditions leads to convergence to the optimal consumption policy. - The income process is a finite state Markov chain. Note that the - Coleman operator is the preferred method, as it is almost always - faster and more accurate. The Bellman operator is only provided for - comparison. - - Parameters - ---------- - r : scalar(float), optional(default=0.01) - A strictly positive scalar giving the interest rate - beta : scalar(float), optional(default=0.96) - The discount factor, must satisfy (1 + r) * beta < 1 - Pi : array_like(float), optional(default=((0.60, 0.40),(0.05, 0.95)) - A 2D NumPy array giving the Markov matrix for {z_t} - z_vals : array_like(float), optional(default=(0.5, 0.95)) - The state space of {z_t} - b : scalar(float), optional(default=0) - The borrowing constraint - grid_max : scalar(float), optional(default=16) - Max of the grid used to solve the problem - grid_size : scalar(int), optional(default=50) - Number of grid points to solve problem, a grid on [-b, grid_max] - u : callable, optional(default=np.log) - The utility function - du : callable, optional(default=lambda x: 1/x) - The derivative of u - - Attributes - ---------- - r, beta, Pi, z_vals, b, u, du : see Parameters - asset_grid : np.ndarray - One dimensional grid for assets - - """ - - def __init__(self, r=0.01, beta=0.96, Pi=((0.6, 0.4), (0.05, 0.95)), - z_vals=(0.5, 1.0), b=0, grid_max=16, grid_size=50, - u=np.log, du=lambda x: 1/x): - self.u, self.du = u, du - self.r, self.R = r, 1 + r - self.beta, self.b = beta, b - self.Pi, self.z_vals = np.array(Pi), tuple(z_vals) - self.asset_grid = np.linspace(-b, grid_max, grid_size) - - def __repr__(self): - m = "ConsumerProblem(r={r:g}, beta={be:g}, Pi='{n:g} by {n:g}', " - m += "z_vals={z}, b={b:g}, grid_max={gm:g}, grid_size={gs:g}, " - m += "u={u}, du={du})" - return m.format(r=self.r, be=self.beta, n=self.Pi.shape[0], - z=self.z_vals, b=self.b, - gm=self.asset_grid.max(), gs=self.asset_grid.size, - u=self.u, du=self.du) - - def __str__(self): - m = """ - Consumer Problem (optimal savings): - - r (interest rate) : {r:g} - - beta (discount rate) : {be:g} - - Pi (transition matrix) : {n} by {n} - - z_vals (state space of shocks) : {z} - - b (borrowing constraint) : {b:g} - - grid_max (maximum of asset grid) : {gm:g} - - grid_size (number of points in asset grid) : {gs:g} - - u (utility function) : {u} - - du (marginal utility function) : {du} - """ - return dedent(m.format(r=self.r, be=self.beta, n=self.Pi.shape[0], - z=self.z_vals, b=self.b, - gm=self.asset_grid.max(), - gs=self.asset_grid.size, u=self.u, - du=self.du)) - - def bellman_operator(self, V, return_policy=False): - """ - The approximate Bellman operator, which computes and returns the - updated value function TV (or the V-greedy policy c if - return_policy is True). - - Parameters - ---------- - V : array_like(float) - A NumPy array of dim len(cp.asset_grid) times len(cp.z_vals) - return_policy : bool, optional(default=False) - Indicates whether to return the greed policy given V or the - updated value function TV. Default is TV. - - Returns - ------- - array_like(float) - Returns either the greed policy given V or the updated value - function TV. - - """ - # === Simplify names, set up arrays === # - R, Pi, beta, u, b = self.R, self.Pi, self.beta, self.u, self.b - asset_grid, z_vals = self.asset_grid, self.z_vals - new_V = np.empty(V.shape) - new_c = np.empty(V.shape) - z_idx = list(range(len(z_vals))) - - # === Linear interpolation of V along the asset grid === # - vf = lambda a, i_z: interp(a, asset_grid, V[:, i_z]) - - # === Solve r.h.s. of Bellman equation === # - for i_a, a in enumerate(asset_grid): - for i_z, z in enumerate(z_vals): - def obj(c): # objective function to be *minimized* - y = sum(vf(R * a + z - c, j) * Pi[i_z, j] for j in z_idx) - return - u(c) - beta * y - c_star = fminbound(obj, np.min(z_vals), R * a + z + b) - new_c[i_a, i_z], new_V[i_a, i_z] = c_star, -obj(c_star) - - if return_policy: - return new_c - else: - return new_V - - def coleman_operator(self, c): - """ - The approximate Coleman operator. - - Iteration with this operator corresponds to policy function - iteration. Computes and returns the updated consumption policy - c. The array c is replaced with a function cf that implements - univariate linear interpolation over the asset grid for each - possible value of z. - - Parameters - ---------- - c : array_like(float) - A NumPy array of dim len(cp.asset_grid) times len(cp.z_vals) - - Returns - ------- - array_like(float) - The updated policy, where updating is by the Coleman - operator. function TV. - - """ - # === simplify names, set up arrays === # - R, Pi, beta, du, b = self.R, self.Pi, self.beta, self.du, self.b - asset_grid, z_vals = self.asset_grid, self.z_vals - z_size = len(z_vals) - gamma = R * beta - vals = np.empty(z_size) - - # === linear interpolation to get consumption function === # - def cf(a): - """ - The call cf(a) returns an array containing the values c(a, - z) for each z in z_vals. For each such z, the value c(a, z) - is constructed by univariate linear approximation over asset - space, based on the values in the array c - """ - for i in range(z_size): - vals[i] = interp(a, asset_grid, c[:, i]) - return vals - - # === solve for root to get Kc === # - Kc = np.empty(c.shape) - for i_a, a in enumerate(asset_grid): - for i_z, z in enumerate(z_vals): - def h(t): - expectation = np.dot(du(cf(R * a + z - t)), Pi[i_z, :]) - return du(t) - max(gamma * expectation, du(R * a + z + b)) - Kc[i_a, i_z] = brentq(h, np.min(z_vals), R * a + z + b) - - return Kc - - def initialize(self): - """ - Creates a suitable initial conditions V and c for value function - and policy function iteration respectively. - - Returns - ------- - V : array_like(float) - Initial condition for value function iteration - c : array_like(float) - Initial condition for Coleman operator iteration - - """ - # === Simplify names, set up arrays === # - R, beta, u, b = self.R, self.beta, self.u, self.b - asset_grid, z_vals = self.asset_grid, self.z_vals - shape = len(asset_grid), len(z_vals) - V, c = np.empty(shape), np.empty(shape) - - # === Populate V and c === # - for i_a, a in enumerate(asset_grid): - for i_z, z in enumerate(z_vals): - c_max = R * a + z + b - c[i_a, i_z] = c_max - V[i_a, i_z] = u(c_max) / (1 - beta) - - return V, c diff --git a/quantecon/models/jv.py b/quantecon/models/jv.py deleted file mode 100644 index 50cebc7ed..000000000 --- a/quantecon/models/jv.py +++ /dev/null @@ -1,198 +0,0 @@ -""" -Filename: jv.py - -Authors: Thomas Sargent, John Stachurski - -References ------------ - -http://quant-econ.net/py/jv.html - -""" -from textwrap import dedent -import sys -import numpy as np -from scipy.integrate import fixed_quad as integrate -from scipy.optimize import minimize -import scipy.stats as stats -from scipy import interp - -# The SLSQP method is faster and more stable, but it didn't give the -# correct answer in python 3. So, if we are in python 2, use SLSQP, otherwise -# use the only other option (to handle constraints): COBYLA -if sys.version_info[0] == 2: - method = "SLSQP" -else: - # python 3 - method = "COBYLA" - -epsilon = 1e-4 # A small number, used in the optimization routine - - -class JvWorker(object): - r""" - A Jovanovic-type model of employment with on-the-job search. The - value function is given by - - .. math:: - - V(x) = \max_{\phi, s} w(x, \phi, s) - - for - - .. math:: - - w(x, \phi, s) := x(1 - \phi - s) - + \beta (1 - \pi(s)) V(G(x, \phi)) - + \beta \pi(s) E V[ \max(G(x, \phi), U)] - - Here - - * x = human capital - * s = search effort - * :math:`\phi` = investment in human capital - * :math:`\pi(s)` = probability of new offer given search level s - * :math:`x(1 - \phi - s)` = wage - * :math:`G(x, \phi)` = new human capital when current job retained - * U = RV with distribution F -- new draw of human capital - - Parameters - ---------- - A : scalar(float), optional(default=1.4) - Parameter in human capital transition function - alpha : scalar(float), optional(default=0.6) - Parameter in human capital transition function - beta : scalar(float), optional(default=0.96) - Discount factor - grid_size : scalar(int), optional(default=50) - Grid size for discretization - G : function, optional(default=lambda x, phi: A * (x * phi)**alpha) - Transition function for human captial - pi : function, optional(default=sqrt) - Function mapping search effort (:math:`s \in (0,1)`) to - probability of getting new job offer - F : distribution, optional(default=Beta(2,2)) - Distribution from which the value of new job offers is drawn - - Attributes - ---------- - A, alpha, beta : see Parameters - x_grid : array_like(float) - The grid over the human capital - - """ - - def __init__(self, A=1.4, alpha=0.6, beta=0.96, grid_size=50, - G=None, pi=np.sqrt, F=stats.beta(2, 2)): - self.A, self.alpha, self.beta = A, alpha, beta - - # === set defaults for G, pi and F === # - self.G = G if G is not None else lambda x, phi: A * (x * phi)**alpha - self.pi = pi - self.F = F - - # === Set up grid over the state space for DP === # - # Max of grid is the max of a large quantile value for F and the - # fixed point y = G(y, 1). - grid_max = max(A**(1 / (1 - alpha)), self.F.ppf(1 - epsilon)) - self.x_grid = np.linspace(epsilon, grid_max, grid_size) - - def __repr__(self): - m = "JvWorker(A={a:g}, alpha={al:g}, beta={b:g}, grid_size={gs})" - return m.format(a=self.A, al=self.alpha, b=self.beta, - gs=self.x_grid.size) - - def __str__(self): - m = """\ - Jovanovic worker (on the job search): - - A (parameter in human capital transition function) : {a:g} - - alpha (parameter in human capital transition function) : {al:g} - - beta (parameter in human capital transition function) : {b:g} - - grid_size (number of grid points for human capital) : {gs} - - grid_max (maximum of grid for human capital) : {gm:g} - """ - return dedent(m.format(a=self.A, al=self.alpha, b=self.beta, - gs=self.x_grid.size, gm=self.x_grid.max())) - - def bellman_operator(self, V, brute_force=False, return_policies=False): - """ - Returns the approximate value function TV by applying the - Bellman operator associated with the model to the function V. - - Returns TV, or the V-greedy policies s_policy and phi_policy when - return_policies=True. In the function, the array V is replaced below - with a function Vf that implements linear interpolation over the - points (V(x), x) for x in x_grid. - - - Parameters - ---------- - V : array_like(float) - Array representing an approximate value function - brute_force : bool, optional(default=False) - Default is False. If the brute_force flag is True, then grid - search is performed at each maximization step. - return_policies : bool, optional(default=False) - Indicates whether to return just the updated value function - TV or both the greedy policy computed from V and TV - - - Returns - ------- - s_policy : array_like(float) - The greedy policy computed from V. Only returned if - return_policies == True - new_V : array_like(float) - The updated value function Tv, as an array representing the - values TV(x) over x in x_grid. - - """ - # === simplify names, set up arrays, etc. === # - G, pi, F, beta = self.G, self.pi, self.F, self.beta - Vf = lambda x: interp(x, self.x_grid, V) - N = len(self.x_grid) - new_V, s_policy, phi_policy = np.empty(N), np.empty(N), np.empty(N) - a, b = F.ppf(0.005), F.ppf(0.995) # Quantiles, for integration - c1 = lambda z: 1.0 - sum(z) # used to enforce s + phi <= 1 - c2 = lambda z: z[0] - epsilon # used to enforce s >= epsilon - c3 = lambda z: z[1] - epsilon # used to enforce phi >= epsilon - guess = (0.2, 0.2) - constraints = [{"type": "ineq", "fun": i} for i in [c1, c2, c3]] - - # === solve r.h.s. of Bellman equation === # - for i, x in enumerate(self.x_grid): - - # === set up objective function === # - def w(z): - s, phi = z - h = lambda u: Vf(np.maximum(G(x, phi), u)) * F.pdf(u) - integral, err = integrate(h, a, b) - q = pi(s) * integral + (1.0 - pi(s)) * Vf(G(x, phi)) - # == minus because we minimize == # - return - x * (1.0 - phi - s) - beta * q - - # === either use SciPy solver === # - if not brute_force: - max_s, max_phi = minimize(w, guess, constraints=constraints, - options={"disp": 0}, - method=method)["x"] - max_val = -w((max_s, max_phi)) - - # === or search on a grid === # - else: - search_grid = np.linspace(epsilon, 1.0, 15) - max_val = -1.0 - for s in search_grid: - for phi in search_grid: - current_val = -w((s, phi)) if s + phi <= 1.0 else -1.0 - if current_val > max_val: - max_val, max_s, max_phi = current_val, s, phi - - # === store results === # - new_V[i] = max_val - s_policy[i], phi_policy[i] = max_s, max_phi - - if return_policies: - return s_policy, phi_policy - else: - return new_V diff --git a/quantecon/models/lake.py b/quantecon/models/lake.py deleted file mode 100644 index e3901b992..000000000 --- a/quantecon/models/lake.py +++ /dev/null @@ -1,394 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Created on Fri Feb 27 18:08:44 2015 - -Author: David Evans - -Provides a class call LakeModel that simulates the dynamics of unemployment and -employment. -""" - -import numpy as np -from scipy.stats import norm -from scipy.optimize import brentq -import quantecon as qe - -class LakeModel(object): - r""" - This class solves the lake model and simulates :math:`E_t` and :math:`U_t` - with the following parameters - - Parameters: - ------------ - lamb: The job finding rate for currently unemployed workers. - - alpha: The dismissal rate for currently employed workers. - - b : Entry rate into the labor force. - - d : Exit rate from the labor force. - - Attributes - ------------ - - In solving the lake model the program computes - - A : Matrix governing law of motion for :math:`E_t` and :math:`U_t` - - hatA : Matrix governing the law of motion for the rates :math:`e_t` - and :math:`u_t` - - """ - def __init__(self,lamb,alpha,b,d): - self.lamb = lamb - self.alpha= alpha - self.b = b - self.d = d - self.g = b-d - - self.A = self.ConstructA_matrix() - self.Ahat = self.Construct_ScaledA_matrix() - - def ConstructA_matrix(self): - r''' - Constructs the A matrix for :math:`X_{t+1} = A X_{t}` where :math:`X_t = (E_t,U_t)` - - Returns - -------- - A : (2x2) matrix governing state dynamics - ''' - lamb,alpha,b,d = self.lamb,self.alpha,self.b,self.d - - return np.array([ [(1-d)*(1-alpha), (1-d)*lamb], - [(1-d)*alpha + b, (1-lamb)*(1-d) + b ]]) - - def Construct_ScaledA_matrix(self): - r''' - Constructs the scaled A matrix for :math:`x_{t+1} = Ahat x_{t}` where - :math:`x_t = (E_t/N_t,U_t/N_t) = (e_t,u_t)` - - Returns - -------- - Ahat : (2x2) matrix governing state dynamics for employment rates. - ''' - A = self.ConstructA_matrix() - return A/(1+self.g) - - def find_steady_state(self): - r""" - Finds the steady state of the system :math:`x_{t+1} = \hat A x_{t}` - - Returns - -------- - - xbar : steady state vector of employment and unemployment rates - """ - x = np.ones(2)/2. - diff = 1. - while diff > 1e-6: - xprime = self.Ahat.dot(x) - diff = np.abs(xprime-x).max() - x = xprime - - return x - - def simulate_stock_path(self,X0,T): - r''' - Simulates the the sequence of Employment and Unemployent stocks - - Parameters - ------------ - - X0 : array containing initial values (E0,U0) - - T : Number of periods to simulate - - Returns - --------- - - X : iterator containing sequence of Employment and Unemployment stocks - ''' - X = np.atleast_1d(X0) # recast as array just in case - for t in range(T): - yield X - X = self.A.dot(X) - - def simulate_rate_path(self,x0,T): - r''' - Simulates the the sequence of Employment and Unemployent rates - - Parameters - ------------ - - x0 : array containing initial values (e0,u0) - - T : Number of periods to simulate - - Returns - --------- - - x : iterator containing sequence of Employment and Unemployment rates - ''' - x = np.atleast_1d(x0) # recast as array just in case - for t in range(T): - yield x - x = self.Ahat.dot(x) - - - -class LakeModelAgent(object): - r''' - This class holds methods necessary to simulate the life course of an agent - who lives in the lake model economy with the following parameters - - Parameters: - ------------ - lamb: The job finding rate if agent is currently unemployed. - - alpha: The dismissal rate if agent is currently employed. - ''' - def __init__(self,lamb,alpha): - self.lamb = lamb - self.alpha = alpha - - self.P = self.compute_P() - - def compute_P(self): - r''' - This method computes the transition matrix for the agent. - - Return - --------- - - P(2d-array) : Transition matrix for the agent - ''' - alpha,lamb = self.alpha,self.lamb - return np.array([ - [(1-alpha), alpha], - [lamb, 1-lamb] - ]) - - def compute_ergodic(self): - r''' - Computes the ergodic distribution over the unemployment and employment - states - - Returns - --------- - - pibar(1d-array) : the ergodic distribution of P - ''' - return qe.mc_compute_stationary(self.P) - - def simulate(self,s0,T): - r''' - Simulates the life of an agent for T periods - - Parameters - ------------- - - s0(int) : initial state - - T(int) : number of periods to simulate - - Returns - ----------- - - sHist(iterator) : history of employment(s==0) and unemployment(s==1) - ''' - pi0 = np.arange(2) == s0 - return qe.mc_sample_path(self.P,pi0,T) - - -class LakeModel_Equilibrium(object): - r''' - Solves for the steady state General Equilibirium of a Lake Model economy - using the McCall Search Model to model the behavior - - Parameters - ------------- - - alpha - (float) Exogenous firing rate. - - beta - (float) The discount factor. - - gamma - (float) Arrival rate of wage offer - - sigma - (float) Degree of risk aversion. - - pdf - (1d - array) pdf[s] Probability of receiving a wage wstar[s] - - wstar - (1d -array) Distribution of wages. - ''' - - def __init__(self,alpha,gamma,beta,sigma,pdf,wstar): - self.alpha = alpha - self.beta = beta - self.gamma = gamma - self.sigma = sigma - self.pdf = pdf - self.wstar = wstar - - def U(self,c): - r''' - Utility function of the agent - - Parameters - ------------- - - c - (array or float) consumption of the agent - - Returns - ---------- - - U - (array or float) Utility of the agent for each level of consumption - ''' - sigma = self.sigma - negative_c = c < 0. - if sigma == 1.: - U = np.log(c) - else: - U= (c**(1-sigma) - 1)/(1-sigma) - U[negative_c] = -9999999. - return U - - - - def solve_for_steadystate(self,c,T): - r''' - Solve for workers steady state policies given tax policy - - Paramaters - ------------ - - c - (float) Level of unemployment benefit - - T - (float) Lump sum tax - - Results - --------- - - V - (array) Value function of the worker - - C - (array) optimal policy function of the worker - - pi - (array) distribution between employed and unemployed - - W - (float) Welfare at steady state - ''' - - V,C = self.solveMcCallModel(c-T,self.wstar-T) - - U = self.U(np.array([c-T])) + self.beta*self.pdf.dot(V) # value of unemployment - - lamb = self.gamma * self.pdf.dot(C) # probability of accepting a job - - LM = LakeModel(lamb,self.alpha,0,0) #no birth or death - - pi = LM.find_steady_state() - - #Expected value of being employed - EV = (C*V).dot(self.pdf)/(C.dot(self.pdf)) - - W = pi[0]*EV + pi[1] * U - - return V,C,pi,W,U,EV - - def find_steady_state_tax(self,c): - r''' - Finds the lump sum tax that balances budget at steady state - - Parameters - ----------- - - c - (float) Level of unemployment benefit - - Results - ---------- - - T - (float) Lump sum tax that balances budget - - W - (float) Steady State Wealfare at that balanced budget tax - ''' - - #budget at steady state - def SS_budget(T): - V,C,pi,W,U,EV= self.solve_for_steadystate(c,T) - #return inflows minus outflows - return T - pi[1]*c - - T = brentq(SS_budget, 0., 0.9*c) - - V,C,pi,W,U,EV = self.solve_for_steadystate(c,T) - - return T,W,U,EV,pi - - - def iterateValueFunction(self,c,w,V): - r''' - Iterates McCall search value function v - - Parameters - ---------- - - c - (float) Level of unemployment insurance - - w - (float) Vector of possible wages - - V - (n array) continuation value function if offered w[s] next period - - Returns - -------- - - V_new - (n array) current value function if offered w[s] this period - - Choice - (n array) do we accept or reject wage w[s] - ''' - p,beta,alpha,gamma = self.pdf,self.beta,self.alpha,self.gamma - S = len(p) - Q = p.dot(V)# value before wage offer - V_U = (self.U(c*np.ones(S)) + beta*gamma*Q)/( 1-beta*(1-gamma) ) - #stack value of accepting and rejecting offer on top of each other - stacked_values = np.vstack([ V_U, - self.U(w) + (1-alpha)*beta*V + alpha*beta*V_U ]) - - #find whether it is optimal to accept or reject offer - V_new = np.amax(stacked_values, axis = 0) - Choice = np.argmax(stacked_values, axis = 0) - return V_new,Choice - - def solveMcCallModel(self,c,w,eps = 1e-6): - r''' - Solves the infinite horizon McCall search model - - Parameters - ----------- - - c - (float) Level of unemployment insurance - - w - (float) Vector of possible wages - - eps - (float) convergence criterion for infinite horizon - - Returns - -------- - - V - (1d-array) Value function that solves the infinite horizon problem - - Choice - (1d-array) Optimal policy of workers - ''' - - S = len(self.pdf) - v = np.zeros(S) #intialize with zero - diff = 1 #holds difference v_{t+1}-v_t - while diff > eps: - v_new,choice = self.iterateValueFunction(c,w,v) - diff = np.amax( np.abs(v-v_new) )#compute difference between value - v = v_new #copy v_new into v #add in infinte horizon solution - - return v,choice - - - - - \ No newline at end of file diff --git a/quantecon/models/lucastree.py b/quantecon/models/lucastree.py deleted file mode 100644 index afbd17884..000000000 --- a/quantecon/models/lucastree.py +++ /dev/null @@ -1,278 +0,0 @@ -r""" -Filename: lucastree.py - -Authors: Thomas Sargent, John Stachurski, Spencer Lyon - -Solves the price function for the Lucas tree in a continuous state -setting, using piecewise linear approximation for the sequence of -candidate price functions. The consumption endownment follows the log -linear AR(1) process - -.. math:: - - log y' = \alpha log y + \sigma \epsilon - -where y' is a next period y and epsilon is an iid standard normal shock. -Hence - -.. math:: - - y' = y^{\alpha} * \xi, - -where - -.. math:: - - \xi = e^(\sigma * \epsilon) - -The distribution phi of xi is - -.. math:: - - \phi = LN(0, \sigma^2), - -where LN means lognormal. - -""" -from __future__ import division # == Omit for Python 3.x == # -from textwrap import dedent -import numpy as np -from scipy import interp -from scipy.stats import lognorm -from scipy.integrate import fixed_quad -from ..compute_fp import compute_fixed_point - - -class LucasTree(object): - """ - Class to solve for the price of a the Lucas tree in the Lucas - asset pricing model - - Parameters - ---------- - gamma : scalar(float) - The coefficient of risk aversion in the household's CRRA utility - function - beta : scalar(float) - The household's discount factor - alpha : scalar(float) - The correlation coefficient in the shock process - sigma : scalar(float) - The volatility of the shock process - grid : array_like(float), optional(default=None) - The grid points on which to evaluate the asset prices. Grid - points should be nonnegative. If None is passed, we will create - a reasonable one for you - - Attributes - ---------- - gamma, beta, alpha, sigma, grid : see Parameters - grid_min, grid_max, grid_size : scalar(int) - Properties for grid upon which prices are evaluated - phi : scipy.stats.lognorm - The distribution for the shock process - - Examples - -------- - >>> tree = LucasTree(gamma=2, beta=0.95, alpha=0.90, sigma=0.1) - >>> grid, price_vals = tree.grid, tree.compute_lt_price() - - """ - - def __init__(self, gamma, beta, alpha, sigma, grid=None): - self.gamma = gamma - self.beta = beta - self.alpha = alpha - self.sigma = sigma - - # == set up grid == # - if grid is None: - (self.grid, self.grid_min, - self.grid_max, self.grid_size) = self._new_grid() - else: - self.grid = np.asarray(grid) - self.grid_min = min(grid) - self.grid_max = max(grid) - self.grid_size = len(grid) - - # == set up distribution for shocks == # - self.phi = lognorm(sigma) - - # == set up integration bounds. 4 Standard deviations. Make them - # private attributes b/c users don't need to see them, but we - # only want to compute them once. == # - self._int_min = np.exp(-4.0 * sigma) - self._int_max = np.exp(4.0 * sigma) - - # == Set up h from the Lucas Operator == # - self.h = self._init_h() - - def __repr__(self): - m = "LucasTree(gamma={g}, beta={b}, alpha={a}, sigma={s})" - return m.format(g=self.gamma, b=self.beta, a=self.alpha, s=self.sigma) - - def __str__(self): - m = """\ - Lucas Pricing Model (Lucas, 1978): - - gamma (coefficient of risk aversion) : {g} - - beta (discount parameter) : {b} - - alpha (correlation coefficient in shock process) : {a} - - sigma (volatility of shock process) : {s} - - grid bounds (bounds for where to compute prices) : ({gl:g}, {gu:g}) - - grid points (number of grid points) : {gs} - """ - return dedent(m.format(g=self.gamma, b=self.beta, a=self.alpha, - s=self.sigma, gl=self.grid_min, - gu=self.grid_max, gs=self.grid_size)) - - def _init_h(self): - """ - Compute the function h in the Lucas operator as a vector of - values on the grid - - Recall that h(y) = beta * int u'(G(y,z)) G(y,z) phi(dz) - """ - alpha, gamma, beta = self.alpha, self.gamma, self.beta - grid, grid_size = self.grid, self.grid_size - - h = np.empty(grid_size) - - for i, y in enumerate(grid): - # == u'(G(y,z)) G(y,z) == # - integrand = lambda z: (y**alpha * z)**(1 - gamma) - h[i] = beta * self.integrate(integrand) - - return h - - def _new_grid(self): - """ - Construct the default grid for the problem - - This is defined to be np.linspace(0, 10, 100) when alpha > 1 - and 100 evenly spaced points covering 4 standard deviations - when alpha < 1 - """ - grid_size = 100 - if abs(self.alpha) >= 1.0: - grid_min, grid_max = 0.0, 10.0 - else: - # == Set the grid interval to contain most of the mass of the - # stationary distribution of the consumption endowment == # - ssd = self.sigma / np.sqrt(1 - self.alpha**2) - grid_min, grid_max = np.exp(-4 * ssd), np.exp(4 * ssd) - - grid = np.linspace(grid_min, grid_max, grid_size) - - return grid, grid_min, grid_max, grid_size - - def integrate(self, g, int_min=None, int_max=None): - """ - Integrate the function g(z) * self.phi(z) from int_min to - int_max. - - Parameters - ---------- - g : function - The function which to integrate - - int_min, int_max : scalar(float), optional - The bounds of integration. If either of these parameters are - `None` (the default), they will be set to 4 standard - deviations above and below the mean. - - Returns - ------- - result : scalar(float) - The result of the integration - - """ - # == Simplify notation == # - phi = self.phi - if int_min is None: - int_min = self._int_min - if int_max is None: - int_max = self._int_max - - # == set up integrand and integrate == # - integrand = lambda z: g(z) * phi.pdf(z) - result, error = fixed_quad(integrand, int_min, int_max) - return result - - def lucas_operator(self, f, Tf=None): - """ - The approximate Lucas operator, which computes and returns the - updated function Tf on the grid points. - - Parameters - ---------- - f : array_like(float) - A candidate function on R_+ represented as points on a grid - and should be flat NumPy array with len(f) = len(grid) - - Tf : array_like(float) - Optional storage array for Tf - - Returns - ------- - Tf : array_like(float) - The updated function Tf - - Notes - ----- - The argument `Tf` is optional, but recommended. If it is passed - into this function, then we do not have to allocate any memory - for the array here. As this function is often called many times - in an iterative algorithm, this can save significant computation - time. - - """ - grid, h = self.grid, self.h - alpha, beta = self.alpha, self.beta - - # == set up storage if needed == # - if Tf is None: - Tf = np.empty_like(f) - - # == Apply the T operator to f == # - Af = lambda x: interp(x, grid, f) # Piecewise linear interpolation - - for i, y in enumerate(grid): - Tf[i] = h[i] + beta * self.integrate(lambda z: Af(y**alpha * z)) - - return Tf - - def compute_lt_price(self, error_tol=1e-3, max_iter=50, verbose=0): - """ - Compute the equilibrium price function associated with Lucas - tree lt - - Parameters - ---------- - error_tol, max_iter, verbose - Arguments to be passed directly to - `quantecon.compute_fixed_point`. See that docstring for more - information - - Returns - ------- - price : array_like(float) - The prices at the grid points in the attribute `grid` of the - object - - """ - # == simplify notation == # - grid, grid_size = self.grid, self.grid_size - lucas_operator, gamma = self.lucas_operator, self.gamma - - # == Create storage array for compute_fixed_point. Reduces memory - # allocation and speeds code up == # - Tf = np.empty(grid_size) - - # == Initial guess, just a vector of zeros == # - f_init = np.zeros(grid_size) - f = compute_fixed_point(lucas_operator, f_init, error_tol, - max_iter, verbose, Tf=Tf) - - price = f * grid**gamma - - return price diff --git a/quantecon/models/odu.py b/quantecon/models/odu.py deleted file mode 100644 index 1aafc8e1b..000000000 --- a/quantecon/models/odu.py +++ /dev/null @@ -1,233 +0,0 @@ -""" -Filename: odu.py - -Authors: Thomas Sargent, John Stachurski - -Solves the "Offer Distribution Unknown" Model by value function -iteration and a second faster method discussed in the corresponding -quantecon lecture. - -""" -from textwrap import dedent -from scipy.interpolate import LinearNDInterpolator -from scipy.integrate import fixed_quad -from scipy.stats import beta as beta_distribution -from scipy import interp -from numpy import maximum as npmax -import numpy as np - - -class SearchProblem(object): - """ - A class to store a given parameterization of the "offer distribution - unknown" model. - - Parameters - ---------- - beta : scalar(float), optional(default=0.95) - The discount parameter - c : scalar(float), optional(default=0.6) - The unemployment compensation - F_a : scalar(float), optional(default=1) - First parameter of beta distribution on F - F_b : scalar(float), optional(default=1) - Second parameter of beta distribution on F - G_a : scalar(float), optional(default=3) - First parameter of beta distribution on G - G_b : scalar(float), optional(default=1.2) - Second parameter of beta distribution on G - w_max : scalar(float), optional(default=2) - Maximum wage possible - w_grid_size : scalar(int), optional(default=40) - Size of the grid on wages - pi_grid_size : scalar(int), optional(default=40) - Size of the grid on probabilities - - Attributes - ---------- - beta, c, w_max : see Parameters - w_grid : np.ndarray - Grid points over wages, ndim=1 - pi_grid : np.ndarray - Grid points over pi, ndim=1 - grid_points : np.ndarray - Combined grid points, ndim=2 - F : scipy.stats._distn_infrastructure.rv_frozen - Beta distribution with params (F_a, F_b), scaled by w_max - G : scipy.stats._distn_infrastructure.rv_frozen - Beta distribution with params (G_a, G_b), scaled by w_max - f : function - Density of F - g : function - Density of G - pi_min : scalar(float) - Minimum of grid over pi - pi_max : scalar(float) - Maximum of grid over pi - """ - - def __init__(self, beta=0.95, c=0.6, F_a=1, F_b=1, G_a=3, G_b=1.2, - w_max=2, w_grid_size=40, pi_grid_size=40): - - self.beta, self.c, self.w_max = beta, c, w_max - self.F = beta_distribution(F_a, F_b, scale=w_max) - self.G = beta_distribution(G_a, G_b, scale=w_max) - self.f, self.g = self.F.pdf, self.G.pdf # Density functions - self.pi_min, self.pi_max = 1e-3, 1 - 1e-3 # Avoids instability - self.w_grid = np.linspace(0, w_max, w_grid_size) - self.pi_grid = np.linspace(self.pi_min, self.pi_max, pi_grid_size) - x, y = np.meshgrid(self.w_grid, self.pi_grid) - self.grid_points = np.column_stack((x.ravel(1), y.ravel(1))) - - def __repr__(self): - m = "SearchProblem(beta={b}, c={c}, F_a={fa}, F_b={fb}, G_a={ga}, " - m += "G_b={gb}, w_max={wu}, w_grid_size={wgs}, pi_grid_size={pgs})" - fa, fb = self.F.args - ga, gb = self.G.args - return m.format(b=self.beta, c=self.c, fa=fa, fb=fb, ga=ga, - gb=gb, wu=self.w_grid.max(), - wgs=self.w_grid.size, pgs=self.pi_grid.size) - - def __str__(self): - m = """\ - SearchProblem (offer distribution unknown): - - beta (discount factor) : {b:g} - - c (unemployment compensation) : {c} - - F (distribution F) : Beta({fa}, {fb:g}) - - G (distribution G) : Beta({ga}, {gb:g}) - - w bounds (bounds for wage offers) : ({wl:g}, {wu:g}) - - w grid size (number of points in grid for wage) : {wgs} - - pi bounds (bounds for probability of dist f) : ({pl:g}, {pu:g}) - - pi grid size (number of points in grid for pi) : {pgs} - """ - fa, fb = self.F.args - ga, gb = self.G.args - return dedent(m.format(b=self.beta, c=self.c, fa=fa, fb=fb, ga=ga, - gb=gb, - wl=self.w_grid.min(), wu=self.w_grid.max(), - wgs=self.w_grid.size, - pl=self.pi_grid.min(), pu=self.pi_grid.max(), - pgs=self.pi_grid.size)) - - def q(self, w, pi): - """ - Updates pi using Bayes' rule and the current wage observation w. - - Returns - ------- - - new_pi : scalar(float) - The updated probability - - """ - - new_pi = 1.0 / (1 + ((1 - pi) * self.g(w)) / (pi * self.f(w))) - - # Return new_pi when in [pi_min, pi_max] and else end points - new_pi = np.maximum(np.minimum(new_pi, self.pi_max), self.pi_min) - - return new_pi - - def bellman_operator(self, v): - """ - - The Bellman operator. Including for comparison. Value function - iteration is not recommended for this problem. See the - reservation wage operator below. - - Parameters - ---------- - v : array_like(float, ndim=1, length=len(pi_grid)) - An approximate value function represented as a - one-dimensional array. - - Returns - ------- - new_v : array_like(float, ndim=1, length=len(pi_grid)) - The updated value function - - """ - # == Simplify names == # - f, g, beta, c, q = self.f, self.g, self.beta, self.c, self.q - - vf = LinearNDInterpolator(self.grid_points, v) - N = len(v) - new_v = np.empty(N) - - for i in range(N): - w, pi = self.grid_points[i, :] - v1 = w / (1 - beta) - integrand = lambda m: vf(m, q(m, pi)) * (pi * f(m) - + (1 - pi) * g(m)) - integral, error = fixed_quad(integrand, 0, self.w_max) - v2 = c + beta * integral - new_v[i] = max(v1, v2) - - return new_v - - def get_greedy(self, v): - """ - Compute optimal actions taking v as the value function. - - Parameters - ---------- - v : array_like(float, ndim=1, length=len(pi_grid)) - An approximate value function represented as a - one-dimensional array. - - Returns - ------- - policy : array_like(float, ndim=1, length=len(pi_grid)) - The decision to accept or reject an offer where 1 indicates - accept and 0 indicates reject - - """ - # == Simplify names == # - f, g, beta, c, q = self.f, self.g, self.beta, self.c, self.q - - vf = LinearNDInterpolator(self.grid_points, v) - N = len(v) - policy = np.zeros(N, dtype=int) - - for i in range(N): - w, pi = self.grid_points[i, :] - v1 = w / (1 - beta) - integrand = lambda m: vf(m, q(m, pi)) * (pi * f(m) + - (1 - pi) * g(m)) - integral, error = fixed_quad(integrand, 0, self.w_max) - v2 = c + beta * integral - policy[i] = v1 > v2 # Evaluates to 1 or 0 - - return policy - - def res_wage_operator(self, phi): - """ - - Updates the reservation wage function guess phi via the operator - Q. - - Parameters - ---------- - phi : array_like(float, ndim=1, length=len(pi_grid)) - This is reservation wage guess - - Returns - ------- - new_phi : array_like(float, ndim=1, length=len(pi_grid)) - The updated reservation wage guess. - - """ - # == Simplify names == # - beta, c, f, g, q = self.beta, self.c, self.f, self.g, self.q - # == Turn phi into a function == # - phi_f = lambda p: interp(p, self.pi_grid, phi) - - new_phi = np.empty(len(phi)) - for i, pi in enumerate(self.pi_grid): - def integrand(x): - "Integral expression on right-hand side of operator" - return npmax(x, phi_f(q(x, pi))) * (pi*f(x) + (1 - pi)*g(x)) - integral, error = fixed_quad(integrand, 0, self.w_max) - new_phi[i] = (1 - beta) * c + beta * integral - - return new_phi diff --git a/quantecon/models/optgrowth.py b/quantecon/models/optgrowth.py deleted file mode 100644 index f5516bfb3..000000000 --- a/quantecon/models/optgrowth.py +++ /dev/null @@ -1,110 +0,0 @@ -""" -Filename: optgrowth.py - -Authors: John Stachurski and Thomas Sargent - -Solving the optimal growth problem via value function iteration. - -""" -from __future__ import division # Omit for Python 3.x -from textwrap import dedent -import numpy as np -from scipy.optimize import fminbound -from scipy import interp - - -class GrowthModel(object): - """ - - This class defines the primitives representing the growth model. - - Parameters - ---------- - f : function, optional(default=k**.65) - The production function; the default is the Cobb-Douglas - production function with power of .65 - beta : scalar(int), optional(default=.95) - The utility discounting parameter - u : function, optional(default=np.log) - The utility function. Default is log utility - grid_max : scalar(int), optional(default=2) - The maximum grid value - grid_size : scalar(int), optional(default=150) - The size of grid to use. - - Attributes - ---------- - f, beta, u : see Parameters - grid : array_like(float, ndim=1) - The grid over savings. - - """ - def __init__(self, f=lambda k: k**0.65, beta=0.95, u=np.log, - grid_max=2, grid_size=150): - - self.u, self.f, self.beta = u, f, beta - self.grid = np.linspace(1e-6, grid_max, grid_size) - - def __repr__(self): - m = "GrowthModel(beta={b}, grid_max={gm}, grid_size={gs})" - return m.format(b=self.beta, gm=self.grid.max(), gs=self.grid.size) - - def __str__(self): - m = """\ - GrowthModel: - - beta (discount factor) : {b} - - u (utility function) : {u} - - f (production function) : {f} - - grid bounds (bounds for grid over savings values) : ({gl}, {gm}) - - grid points (number of points in grid for savings) : {gs} - """ - return dedent(m.format(b=self.beta, u=self.u, f=self.f, - gl=self.grid.min(), gm=self.grid.max(), - gs=self.grid.size)) - - def bellman_operator(self, w, compute_policy=False): - """ - The approximate Bellman operator, which computes and returns the - updated value function Tw on the grid points. - - Parameters - ---------- - w : array_like(float, ndim=1) - The value of the input function on different grid points - compute_policy : Boolean, optional(default=False) - Whether or not to compute policy function - - """ - # === Apply linear interpolation to w === # - Aw = lambda x: interp(x, self.grid, w) - - if compute_policy: - sigma = np.empty(len(w)) - - # == set Tw[i] equal to max_c { u(c) + beta w(f(k_i) - c)} == # - Tw = np.empty(len(w)) - for i, k in enumerate(self.grid): - objective = lambda c: - self.u(c) - self.beta * Aw(self.f(k) - c) - c_star = fminbound(objective, 1e-6, self.f(k)) - if compute_policy: - # sigma[i] = argmax_c { u(c) + beta w(f(k_i) - c)} - sigma[i] = c_star - Tw[i] = - objective(c_star) - - if compute_policy: - return Tw, sigma - else: - return Tw - - def compute_greedy(self, w): - """ - Compute the w-greedy policy on the grid points. - - Parameters - ---------- - w : array_like(float, ndim=1) - The value of the input function on different grid points - - """ - Tw, sigma = self.bellman_operator(w, compute_policy=True) - return sigma diff --git a/quantecon/models/solow/__init__.py b/quantecon/models/solow/__init__.py deleted file mode 100644 index d4aeccd96..000000000 --- a/quantecon/models/solow/__init__.py +++ /dev/null @@ -1,14 +0,0 @@ -""" -models directory imports - -objects imported here will live in the `quantecon.models.solow` namespace - -""" -__all__ = ['Model', 'CobbDouglasModel', 'CESModel'] - -from . model import Model -from . import model -from . cobb_douglas import CobbDouglasModel -from . import cobb_douglas -from . ces import CESModel -from . import ces diff --git a/quantecon/models/solow/ces.py b/quantecon/models/solow/ces.py deleted file mode 100644 index c46d90f2a..000000000 --- a/quantecon/models/solow/ces.py +++ /dev/null @@ -1,134 +0,0 @@ -""" -Solow model with constant elasticity of substitution (CES) production. - -@author : David R. Pugh -@date : 2014-12-11 - -""" -from __future__ import division -from textwrap import dedent - -import sympy as sym - -from . import model - -# declare key variables for the model -A, k, K, L, Y = sym.symbols('A, k, K, L, Y') - -# declare required model parameters -g, n, s, alpha, delta, sigma = sym.symbols('g, n, s, alpha, delta, sigma') - - -class CESModel(model.Model): - - _required_params = ['g', 'n', 's', 'alpha', 'delta', 'sigma', 'A0', 'L0'] - - def __init__(self, params): - """ - Create an instance of the Solow growth model with constant elasticity - of subsitution (CES) aggregate production. - - Parameters - ---------- - params : dict - Dictionary of model parameters. - - """ - rho = (sigma - 1) / sigma - ces_output = (alpha * K**rho + (1 - alpha) * (A * L)**rho)**(1 / rho) - super(CESModel, self).__init__(ces_output, params) - - def __str__(self): - """Human readable summary of a CESModel instance.""" - m = super(CESModel, self).__str__() - m += " - alpha (capital's weight in output) : {alpha:g}\n" - m += " - sigma (elasticity of substitution) : {sigma:g}" - formatted_str = dedent(m.format(alpha=self.params['alpha'], - sigma=self.params['sigma'])) - return formatted_str - - @property - def solow_residual(self): - """ - Symbolic expression for the Solow residual which is used as a measure - of technology. - - :getter: Return the symbolic expression. - :type: sym.Basic - - """ - rho = (sigma - 1) / sigma - residual = (((1 / (1 - alpha)) * (Y / L)**rho - - (alpha / (1 - alpha)) * (K / L)**rho)**(1 / rho)) - return residual - - @property - def steady_state(self): - r""" - Steady state value of capital stock (per unit effective labor). - - :getter: Return the current steady state value. - :type: float - - Notes - ----- - The steady state value of capital stock (per unit effective labor) - with CES production is defined as - - .. math:: - - k^* = \left[\frac{1-\alpha}{\bigg(\frac{g+n+\delta}{s}\bigg)^{\rho}-\alpha}\right]^{\frac{1}{rho}} - - where `s` is the savings rate, :math:`g + n + \delta` is the effective - depreciation rate, and :math:`\alpha` controls the importance of - capital stock relative to effective labor in the production of output. - Finally, - - ..math:: - - \rho=\frac{\sigma-1}{\sigma} - - where `:math:`sigma` is the elasticity of substitution between capital - and effective labor in production. - - """ - g = self.params['g'] - n = self.params['n'] - s = self.params['s'] - alpha = self.params['alpha'] - delta = self.params['delta'] - sigma = self.params['sigma'] - - ratio_investment_rates = (g + n + delta) / s - rho = (sigma - 1) / sigma - k_star = ((1 - alpha) / (ratio_investment_rates**rho - alpha))**(1 / rho) - - return k_star - - def _isdeterminate_steady_state(self, params): - """Check that parameters are consistent with determinate steady state.""" - g = params['g'] - n = params['n'] - s = params['s'] - alpha = params['alpha'] - delta = params['delta'] - sigma = params['sigma'] - - ratio_investment_rates = (g + n + delta) / s - rho = (sigma - 1) / sigma - - return ratio_investment_rates**rho - alpha > 0 - - def _validate_params(self, params): - """Validate the model parameters.""" - params = super(CESModel, self)._validate_params(params) - if params['alpha'] < 0.0 or params['alpha'] > 1.0: - raise AttributeError('Capital weight must be in (0, 1).') - elif params['sigma'] <= 0.0: - mesg = 'Elasticity of substitution must be strictly positive.' - raise AttributeError(mesg) - elif not self._isdeterminate_steady_state(params): - mesg = 'Steady state is indeterminate.' - raise AttributeError(mesg) - else: - return params diff --git a/quantecon/models/solow/cobb_douglas.py b/quantecon/models/solow/cobb_douglas.py deleted file mode 100644 index 8c612780c..000000000 --- a/quantecon/models/solow/cobb_douglas.py +++ /dev/null @@ -1,114 +0,0 @@ -""" -Solow growth model with Cobb-Douglas aggregate production. - -@author : David R. Pugh -@date : 2014-11-27 - -""" -from __future__ import division -from textwrap import dedent - -import numpy as np -import sympy as sym - -from . import model - -# declare key variables for the model -t, X = sym.symbols('t'), sym.DeferredVector('X') -A, k, K, L = sym.symbols('A, k, K, L') - -# declare required model parameters -g, n, s, alpha, delta = sym.symbols('g, n, s, alpha, delta') - - -class CobbDouglasModel(model.Model): - - _required_params = ['g', 'n', 's', 'alpha', 'delta', 'A0', 'L0'] - - def __init__(self, params): - """ - Create an instance of the Solow growth model with Cobb-Douglas - aggregate production. - - Parameters - ---------- - params : dict - Dictionary of model parameters. - - """ - cobb_douglas_output = K**alpha * (A * L)**(1 - alpha) - super(CobbDouglasModel, self).__init__(cobb_douglas_output, params) - - def __str__(self): - """Human readable summary of a CESModel instance.""" - m = super(CobbDouglasModel, self).__str__() - m += " - alpha (output elasticity) : {alpha:g}\n" - formatted_str = dedent(m.format(alpha=self.params['alpha'])) - return formatted_str - - @property - def steady_state(self): - r""" - Steady state value of capital stock (per unit effective labor). - - :getter: Return the current steady state value. - :type: float - - Notes - ----- - The steady state value of capital stock (per unit effective labor) - with Cobb-Douglas production is defined as - - .. math:: - - k^* = \bigg(\frac{s}{g + n + \delta}\bigg)^\frac{1}{1-\alpha} - - where `s` is the savings rate, :math:`g + n + \delta` is the effective - depreciation rate, and :math:`\alpha` is the elasticity of output with - respect to capital (i.e., capital's share). - - """ - s = self.params['s'] - alpha = self.params['alpha'] - return (s / self.effective_depreciation_rate)**(1 / (1 - alpha)) - - def _validate_params(self, params): - """Validate the model parameters.""" - params = super(CobbDouglasModel, self)._validate_params(params) - if params['alpha'] <= 0.0 or params['alpha'] >= 1.0: - raise AttributeError('Output elasticity must be in (0, 1).') - else: - return params - - def analytic_solution(self, t, k0): - """ - Compute the analytic solution for the Solow model with Cobb-Douglas - production technology. - - Parameters - ---------- - t : numpy.ndarray (shape=(T,)) - Array of points at which the solution is desired. - k0 : (float) - Initial condition for capital stock (per unit of effective labor) - - Returns - ------- - analytic_traj : ndarray (shape=t.size, 2) - Array representing the analytic solution trajectory. - - """ - s = self.params['s'] - alpha = self.params['alpha'] - - # lambda governs the speed of convergence - lmbda = self.effective_depreciation_rate * (1 - alpha) - - # analytic solution for Solow model at time t - k_t = (((s / (self.effective_depreciation_rate)) * (1 - np.exp(-lmbda * t)) + - k0**(1 - alpha) * np.exp(-lmbda * t))**(1 / (1 - alpha))) - - # combine into a (T, 2) array - analytic_traj = np.hstack((t[:, np.newaxis], k_t[:, np.newaxis])) - - return analytic_traj diff --git a/quantecon/models/solow/impulse_response.py b/quantecon/models/solow/impulse_response.py deleted file mode 100644 index e9df439e1..000000000 --- a/quantecon/models/solow/impulse_response.py +++ /dev/null @@ -1,343 +0,0 @@ -""" -Classes for generating and plotting impulse response functions. - -@author : David R. Pugh -@date : 2014-10-06 - -""" -from __future__ import division -from textwrap import dedent - -import matplotlib.pyplot as plt -import numpy as np - - -class ImpulseResponse(object): - """Base class representing an impulse response function for a Model.""" - - # number of points to use for "padding" - N = 10 - - # length of impulse response - T = 100 - - def __init__(self, model): - """ - Create an instance of the ImpulseResponse class. - - Parameters - ---------- - model : model.Model - Instance of the model.Model class representing a Solow model. - - """ - self.model = model - - def __repr__(self): - """Machine readable summary of a ImpulseResponse instance.""" - return self.__str__() - - def __str__(self): - """Human readable summary of a ImpulseResponse instance.""" - m = """ - Impulse response function (IRF): - - N (number of points used for padding) : {N:d} - - T (length of the impulse response) : {T:d} - """ - formatted_str = dedent(m.format(N=self.N, T=self.T)) - return formatted_str - - @property - def _padding(self): - """ - Impulse response functions are "padded" for pretty plotting. - - :getter: Return the current "padding" values. - :type: numpy.ndarray - - """ - return np.hstack((self._padding_time, self._padding_variables)) - - @property - def _padding_scaling_factor(self): - """ - Scaling factor used in constructing the impulse response function - "padding". - - :getter: Return the current scaling factor. - :type: numpy.ndarray - - """ - # extract the relevant parameters - A0 = self.model.params['A0'] - L0 = self.model.params['L0'] - g = self.model.params['g'] - n = self.model.params['n'] - - if self.kind == 'per_capita': - factor = A0 * np.exp(g * self._padding_time) - elif self.kind == 'levels': - factor = A0 * L0 * np.exp((g + n) * self._padding_time) - else: - factor = np.ones(self.N) - - return factor.reshape((self.N, 1)) - - @property - def _padding_time(self): - """ - The independent variable, time, is "padded" using values from -N to -1. - - :getter: Return the current "padding" values. - :type: numpy.ndarray - - """ - return np.linspace(-self.N, -1, self.N).reshape((self.N, 1)) - - @property - def _padding_variables(self): - """ - Impulse response functions for endogenous variables are "padded" with - N periods of steady state values. - - :getter: Return current "padding" values. - :kind: numpy.ndarray - - """ - # economy is initial in steady state - k0 = self.model.steady_state - y0 = self.model.evaluate_intensive_output(k0) - c0 = self.model.evaluate_consumption(k0) - i0 = self.model.evaluate_actual_investment(k0) - intitial_condition = np.array([[k0, y0, c0, i0]]) - - return self._padding_scaling_factor * intitial_condition - - @property - def _response(self): - """ - Response functions combined independent and endogenous variables. - - :getter: Return the current response values. - :type: numpy.ndarray - - """ - return np.hstack((self._response_time, self._response_variables)) - - @property - def _response_time(self): - """ - The independent variable, time, for the response ranges from 0 to T. - - :getter: Return the current resonse time values. - :type: numpy.ndarray - - """ - return np.linspace(0, self.T, self.T + 1).reshape((self.T + 1, 1)) - - @property - def _response_variables(self): - """ - Response of endogenous variables to exogenous impulse. - - :getter: Return the current response. - :type: numpy.ndarray - - """ - # economy is initial in steady state - k0 = self.model.steady_state - - # apply the impulse...force validate params! - tmp_params = self.model.params.copy() - tmp_params.update(self.impulse) - self.model.params = tmp_params - - # ...and generate the response - soln = self.model.ivp.solve(t0=0.0, y0=k0, h=1.0, T=self.T, - integrator='dop853') - # gather the results - k = soln[:, 1][:, np.newaxis] - y = self.model.evaluate_intensive_output(k) - c = self.model.evaluate_consumption(k) - i = self.model.evaluate_actual_investment(k) - - return self._response_scaling_factor * np.hstack((k, y, c, i)) - - @property - def _response_scaling_factor(self): - """ - Scaling factor used in constructing the impulse response. - - :getter: Return the current scaling factor. - :type: numpy.ndarray - - """ - # extract the relevant parameters - A0 = self.model.params['A0'] - L0 = self.model.params['L0'] - g = self.model.params['g'] - n = self.model.params['n'] - - if self.kind == 'per_capita': - factor = A0 * np.exp(g * self._response_time) - elif self.kind == 'levels': - factor = A0 * L0 * np.exp((g + n) * self._response_time) - else: - factor = np.ones(self.T + 1) - - return factor.reshape((self.T + 1, 1)) - - @property - def impulse(self): - """ - Dictionary of new parameter values representing an impulse. - - :getter: Return the current impulse dictionary. - :setter: Set a new impulse dictionary. - :type: dictionary - - """ - return self._impulse - - @property - def kind(self): - """ - The kind of impulse response function to generate. Must be one of: - 'levels', 'per_capita', 'efficiency_units'. - - :getter: Return the current kind of impulse responses. - :setter: Set a new value for the kind of impulse responses. - :type: str - - """ - return self._kind - - @property - def impulse_response(self): - """ - Impulse response functions generated by a shock to model parameter(s). - - :getter: Return the current impulse response functions. - :type: numpy.ndarray - - """ - orig_params = self.model.params.copy() - - # create the irf - tmp_irf = np.vstack((self._padding, self._response)) - - # reset the model parameters - self.model.params = orig_params - - return tmp_irf - - @impulse.setter - def impulse(self, params): - """Set a new impulse dictionary.""" - self._impulse = self._validate_impulse(params) - - @kind.setter - def kind(self, value): - """Set a new value for the kind attribute.""" - self._kind = self._validate_kind(value) - - def _validate_impulse(self, params): - """Validates the impulse attribute.""" - if not isinstance(params, dict): - mesg = "ImpulseResponse.impulse must have type dict, not {}." - raise AttributeError(mesg.format(params.__class__)) - elif not set(params.keys()) <= set(self.model.params.keys()): - mesg = "Invalid parameter included in the impulse dictionary.""" - raise AttributeError(mesg) - else: - return params - - @staticmethod - def _validate_kind(value): - """Validates the kind attribute.""" - valid_kinds = ['levels', 'per_capita', 'efficiency_units'] - - if value not in valid_kinds: - mesg = "The 'kind' attribute must be in {}." - raise AttributeError(mesg.format(valid_kinds)) - else: - return value - - def plot_impulse_response(self, ax, variable, log=False): - """ - Plot an impulse response function. - - Parameters - ---------- - ax : `matplotlib.axes.AxesSubplot` - An instance of `matplotlib.axes.AxesSubplot`. - variable : str - Variable whose impulse response functions you wish to plot. - impulse : dict - Dictionary of new parameter values representing the impulse whose - model response you wish to plot. - kind : str (default='efficiency_units') - Whether you want impulse response functions in 'levels', - 'per_capita', or 'efficiency_units'. - log : boolean (default=False) - Whether or not to have logarithmic scales on the vertical axes. - Useful when plotting impulse response functions with - kind='per_capita' or kind='levels'. - - Returns - ------- - A list containing: - - irf_line : maplotlib.lines.Line2D - A Line2D object representing the impulse response for the requested - variable. - bgp_line : maplotlib.lines.Line2D - A Line2D object representing the pre-impulse balanced growth path - for the model. - - """ - # create a mapping from variables to column indices - irf = self.impulse_response - irf_dict = {'capital': irf[:, [0, 1]], - 'output': irf[:, [0, 2]], - 'consumption': irf[:, [0, 3]], - 'investment': irf[:, [0, 4]], - } - - # create the plot - traj = irf_dict[variable] - irf_line = ax.plot(traj[:, 0], traj[:, 1]) - - # add the old balanced growth path - g = self.model.params['g'] - n = self.model.params['n'] - t = self.N + traj[:, 0] - - if self.kind == 'per_capita': - bgp_line = ax.plot(traj[:, 0], traj[0, 1] * np.exp(g * t), 'k--', - label='Original BGP') - ax.set_ylabel(variable.title() + ' (per capita)', fontsize=15, - family='serif') - elif self.kind == 'levels': - bgp_line = ax.plot(traj[:, 0], traj[0, 1] * np.exp((g + n) * t), - 'k--', label='Original BGP') - ax.set_ylabel(variable.title(), fontsize=15, family='serif') - else: - bgp_line = ax.axhline(traj[0, 1], linestyle='dashed', color='k', - label='Original BGP') - ax.set_ylabel(variable.title() + ' (per unit effective labor)', - fontsize=15, family='serif') - - # format axes, labels, title, legend, etc - ax.set_xlabel('Time', fontsize=15, family='serif') - ax.set_ylim(0.95 * traj[:, 1].min(), 1.05 * traj[:, 1].max()) - - if log is True: - ax.set_yscale('log') - - ax.set_title('Impulse response function', fontsize=20, family='serif') - ax.grid('on') - ax.legend(loc=0, frameon=False, bbox_to_anchor=(1.0, 1.0), - prop={'family': 'serif'}) - - return [irf_line, bgp_line] diff --git a/quantecon/models/solow/model.py b/quantecon/models/solow/model.py deleted file mode 100644 index 3ca98868f..000000000 --- a/quantecon/models/solow/model.py +++ /dev/null @@ -1,1132 +0,0 @@ -r""" -====================== -The Solow Growth Model -====================== - -The following summary of the [solow1956] model of economic growth -largely follows [romer2011]. - -Assumptions -=========== - -The production function ----------------------------------------------- - -The [solow1956] model of economic growth focuses on the behavior of four -variables: output, `Y`, capital, `K`, labor, `L`, and knowledge (or -technology or the ``effectiveness of labor''), `A`. At each point in -time the economy has some amounts of capital, labor, and knowledge that -can be combined to produce output according to some production function, -`F`. - -.. math:: - - Y(t) = F(K(t), A(t)L(t)) - -where `t` denotes time. - -The evolution of the inputs to production ------------------------------------------ - -The initial levels of capital, :math:`K_0`, labor, :math:`L_0`, and -technology, :math:`A_0`, are taken as given. Labor and technology are -assumed to grow at constant rates: - -.. math:: - - \dot{A}(t) = gA(t) - \dot{L}(t) = nL(t) - -where the rate of technological progrss, `g`, and the population growth -rate, `n`, are exogenous parameters. - -Output is divided between consumption and investment. The fraction of -output devoted to investment, :math:`0 < s < 1`, is exogenous and -constant. One unit of output devoted to investment yields one unit of -new capital. Capital is assumed to decpreciate at a rate :math:`0\le -\delta`. Thus aggregate capital stock evolves according to - -.. math:: - - \dot{K}(t) = sY(t) - \delta K(t). - -Although no restrictions are placed on the rates of technological -progress and population growth, the sum of `g`, `n`, and :math:`delta` -is assumed to be positive. - -The dynamics of the model -========================= - -Because the economy is growing over time (due to exogenous technological -progress and population growth) it is useful to focus on the behavior of -capital stock per unit of effective labor, :math:`k\equiv K/AL`. -Applying the chain rule to the equation of motion for capital stock -yields (after a bit of algebra!) an equation of motion for capital stock -per unit of effective labor. - -.. math:: - - \dot{k}(t) = s f(k) - (g + n + \delta)k(t) - -References -========== -.. [romer2011] D. Romer. *Advanced Macroeconomics, 4th edition*, MacGraw Hill, 2011. -.. [solow1956] R. Solow. *A contribution to the theory of economic growth*, Quarterly Journal of Economics, 70(1):64-95, 1956. - -@author : David R. Pugh -@date : 2014-11-27 - -""" -from __future__ import division -import collections -from textwrap import dedent - -import matplotlib.pyplot as plt -import numpy as np -from scipy import optimize -import sympy as sym - -from ... import ivp -from . import impulse_response - -# declare key variables for the model -t, X = sym.symbols('t'), sym.DeferredVector('X') -A, k, K, L, Y = sym.symbols('A, k, K, L, Y') - -# declare required model parameters -g, n, s, delta = sym.symbols('g, n, s, delta') - - -class Model(object): - - __intensive_output = None - - __mpk = None - - __numeric_jacobian = None - - __numeric_solow_residual = None - - __numeric_system = None - - _modules = [{'ImmutableMatrix': np.array}, "numpy"] - - _required_params = ['g', 'n', 's', 'delta', 'A0', 'L0'] - - def __init__(self, output, params): - """ - Create an instance of the Solow growth model. - - Parameters - ---------- - output : sym.Basic - Symbolic expression defining the aggregate production - function. - params : dict - Dictionary of model parameters. - - """ - self.irf = impulse_response.ImpulseResponse(self) - self.output = output - self.params = params - - def __repr__(self): - """Machine readable summary of a Model instance.""" - return self.__str__() - - def __str__(self): - """Human readable summary of a Model instance.""" - m = """ - Solow (1956) model of economic growth: - - Output : {Y} - - A0 (initial level of technology) : {A0:g} - - L0 (initial amount of available labor) : {L0:g} - - g (growth rate of technology) : {g:g} - - n (growth rate of the labor force) : {n:g} - - s (savings rate) : {s:g} - - delta (depreciation rate of physical capital) : {delta:g} - """ - formatted_str = dedent(m.format(Y=self.output, - A0=self.params['A0'], - L0=self.params['L0'], - g=self.params['g'], - n=self.params['n'], - s=self.params['s'], - delta=self.params['delta'])) - return formatted_str - - @property - def _intensive_output(self): - """ - :getter: Return vectorized symbolic intensive aggregate production. - :type: function - - """ - if self.__intensive_output is None: - args = [k] + sym.symbols(list(self.params.keys())) - self.__intensive_output = sym.lambdify(args, self.intensive_output, - self._modules) - return self.__intensive_output - - @property - def _mpk(self): - """ - :getter: Return vectorized symbolic marginal product capital. - :type: function - - """ - if self.__mpk is None: - args = [k] + sym.symbols(list(self.params.keys())) - self.__mpk = sym.lambdify(args, self.marginal_product_capital, - self._modules) - return self.__mpk - - @property - def _numeric_jacobian(self): - """ - Vectorized, numpy-aware function defining the Jacobian matrix of - partial derivatives. - - :getter: Return vectorized Jacobian matrix of partial derivatives. - :type: function - - """ - if self.__numeric_jacobian is None: - self.__numeric_jacobian = sym.lambdify(self._symbolic_args, - self._symbolic_jacobian, - self._modules) - return self.__numeric_jacobian - - @property - def _numeric_solow_residual(self): - """ - Vectorized, numpy-aware function defining the Solow residual. - - :getter: Return vectorized symbolic Solow residual. - :type: function - - """ - if self.__numeric_solow_residual is None: - tmp_args = [Y, K, L] + sym.symbols(list(self.params.keys())) - self.__numeric_solow_residual = sym.lambdify(tmp_args, - self.solow_residual, - self._modules) - return self.__numeric_solow_residual - - @property - def _numeric_system(self): - """ - Vectorized, numpy-aware function defining the system of ODEs. - - :getter: Return vectorized symbolic system of ODEs. - :type: function - - """ - if self.__numeric_system is None: - self.__numeric_system = sym.lambdify(self._symbolic_args, - self._symbolic_system, - self._modules) - return self.__numeric_system - - @property - def _symbolic_args(self): - """ - List of symbolic arguments used in constructing vectorized - versions of _symbolic_system and _symbolic_jacobian. - - :getter: Return list of symbolic arguments. - :type: list - - """ - args = [t, X] + sym.symbols(list(self.params.keys())) - return args - - @property - def _symbolic_jacobian(self): - """ - Symbolic Jacobian matrix for the system of ODEs. - - :getter: Return the symbolic Jacobian matrix. - :type: sym.MutableDenseMatrix - - """ - N = self._symbolic_system.shape[0] - return self._symbolic_system.jacobian([X[i] for i in range(N)]) - - @property - def _symbolic_system(self): - """ - Symbolic matrix defining the system of ODEs. - - :getter: Return the matrix defining the system of ODEs. - :type: sym.MutableDenseMatrix - - """ - change_of_vars = {k: X[0]} - return sym.Matrix([self.k_dot]).subs(change_of_vars) - - @property - def effective_depreciation_rate(self): - """ - Effective depreciation rate for capital stock (per unit - effective labor). - - :getter: Return the current effective depreciation rate. - :type: float - - Notes - ----- - The effective depreciation rate of physical capital takes into - account both technological progress and population growth, as - well as physical depreciation. - - """ - return sum(self.params[key] for key in ['g', 'n', 'delta']) - - @property - def intensive_output(self): - r""" - Symbolic expression for the intensive form of aggregate - production. - - :getter: Return the current intensive production function. - :type: sym.Basic - - Notes - ----- - The assumption of constant returns to scale allows us to work - the the intensive form of the aggregate production function, - `F`. Defining :math:`c=1/AL` one can write - - ..math:: - - F\bigg(\frac{K}{AL}, 1\bigg) = \frac{1}{AL}F(A, K, L) - - Defining :math:`k=K/AL` and :math:`y=Y/AL` to be capital per - unit effective labor and output per unit effective labor, - respectively, the intensive form of the production function can - be written as - - .. math:: - - y = f(k). - - Additional assumptions are that `f` satisfies :math:`f(0)=0`, is - concave (i.e., :math:`f'(k) > 0, f''(k) < 0`), and satisfies the - Inada conditions: - - .. math:: - :type: eqnarray - - \lim_{k \rightarrow 0} &=& \infty \\ - \lim_{k \rightarrow \infty} &=& 0 - - The [inada1964]_ conditions are sufficient (but not necessary!) - to ensure that the time path of capital per effective worker - does not explode. - - .. [inada1964] K. Inda. *Some structural characteristics of Turnpike Theorems*, Review of Economic Studies, 31(1):43-58, 1964. - - """ - return self.output.subs({'A': 1.0, 'K': k, 'L': 1.0}) - - @property - def ivp(self): - r""" - Initial value problem - - :getter: Return an instance of the ivp.IVP class representing - the Solow model. - :type: ivp.IVP - - Notes - ----- - The Solow model with can be formulated as an initial value - problem (IVP) as follows. - - .. math:: - - \dot{k}(t) = sf(k(t)) - (g + n + \delta)k(t),\ t\ge t_0,\ k(t_0) = k_0 - - The solution to this IVP is a function :math:`k(t)` describing - the time path of capital stock (per unit effective labor). - - """ - tmp_ivp = ivp.IVP(self._numeric_system, self._numeric_jacobian) - tmp_ivp.f_params = tuple(self.params.values()) - tmp_ivp.jac_params = tuple(self.params.values()) - return tmp_ivp - - @property - def k_dot(self): - r""" - Symbolic expression for the equation of motion for capital (per - unit effective labor). - - :getter: Return the current equation of motion for capital (per - unit effective labor). - :type: sym.Basic - - Notes - ----- - Because the economy is growing over time due to technological - progress, `g`, and population growth, `n`, it makes sense to - focus on the capital stock per unit effective labor, `k`, rather - than aggregate physical capital, `K`. Since, by definition, - :math:`k=K/AL`, we can apply the chain rule to the time derative - of `k`. - - .. math:: - :type: eqnarray - - \dot{k}(t) =& \frac{\dot{K}(t)}{A(t)L(t)} - \frac{K(t)}{[A(t)L(t)]^2}\bigg[\dot{A}(t)L(t) + \dot{L}(t)A(t)\bigg] \\ - =& \frac{\dot{K}(t)}{A(t)L(t)} - \bigg(\frac{\dot{A}(t)}{A(t)} + \frac{\dot{L}(t)}{L(t)}\bigg)\frac{K(t)}{A(t)L(t)} - - By definition, math:`k=K/AL`, and by assumption - :math:`\dot{A}/A` and :math:`\dot{L}/L` are `g` and `n` - respectively. Aggregate capital stock evolves according to - - .. math:: - - \dot{K}(t) = sF(K(t), A(t)L(t)) - \delta K(t). - - Substituting these facts into the above equation yields the - equation of motion for capital stock (per unit effective labor). - - .. math:: - :type: eqnarray - - \dot{k}(t) =& \frac{sF(K(t), A(t)L(t)) - \delta K(t)}{A(t)L(t)} - (g + n)k(t) \\ - =& \frac{sY(t)}{A(t)L(t)} - (g + n + \delta)k(t) \\ - =& sf(k(t)) - (g + n + \delta)k(t) - - """ - return s * self.intensive_output - (g + n + delta) * k - - @property - def marginal_product_capital(self): - r""" - Symbolic expression for the marginal product of capital (per - unit effective labor). - - :getter: Return the current marginal product of capital (per - unit effective labor). - :type: sym.Basic - - Notes - ----- - The marginal product of capital is defined as follows: - - .. math:: - - \frac{\partial F(K, AL)}{\partial K} \equiv f'(k) - - where :math:`k=K/AL` is capital stock (per unit effective labor) - - """ - return sym.diff(self.intensive_output, k) - - @property - def output(self): - r""" - Symbolic expression for the aggregate production function. - - :getter: Return the current aggregate production function. - :setter: Set a new aggregate production function - :type: sym.Basic - - Notes - ----- - At each point in time the economy has some amounts of capital, - `K`, labor, `L`, and knowledge (or technology), `A`, that can be - combined to produce output, `Y`, according to some function, - `F`. - - .. math:: - - Y(t) = F(K(t), A(t)L(t)) - - where `t` denotes time. Note that `A` and `L` are assumed to - enter multiplicatively. Typically `A(t)L(t)` denotes "effective - labor", and technology that enters in this fashion is known as - labor-augmenting or "Harrod neutral." - - A key assumption of the model is that the function `F` exhibits - constant returns to scale in capital and labor inputs. - Specifically, - - .. math:: - - F(cK(t), cA(t)L(t)) = cF(K(t), A(t)L(t)) = cY(t) - - for any :math:`c \ge 0`. - - """ - return self._output - - @property - def params(self): - """ - Dictionary of model parameters. - - :getter: Return the current dictionary of model parameters. - :setter: Set a new dictionary of model parameters. - :type: dict - - Notes - ----- - The following parameters are required: - - A0: float - Initial level of technology. Must satisfy :math:`A_0 > 0 `. - L0: float - Initial amount of available labor. Must satisfy - :math:`L_0 > 0 `. - g : float - Growth rate of technology. - n : float - Growth rate of the labor force. - s : float - Savings rate. Must satisfy `0 < s < 1`. - delta : float - Depreciation rate of physical capital. Must satisfy - :math:`0 < \delta`. - - Although no restrictions are placed on the rates of - technological progress and population growth, the sum of `g`, - `n`, and :math:`delta` is assumed to be positive. The user mus - also specify any additional model parameters specific to the - chosen aggregate production function. - - """ - return self._params - - @property - def solow_residual(self): - """ - Symbolic expression for the Solow residual which is used as a - measure of technology. - - :getter: Return the symbolic expression. - :type: sym.Basic - - """ - return sym.solve(Y - self.output, A)[0] - - @property - def speed_of_convergence(self): - r""" - The speed of convergence for the Solow model. - - :getter: Return the current speed of convergence. - :type: float - - Notes - ----- - The following is a derivation for the speed of convergence - :math:`\lambda`: - - .. :math:: - :type: eqnarray - - \lambda \equiv -\frac{\partial \dot{k}(k(t))}{\partial k(t)}\bigg|_{k(t)=k^*} =& -[sf'(k^*) - (g + n+ \delta)] \\ - =& (g + n+ \delta) - sf'(k^*) \\ - =& (g + n + \delta) - (g + n + \delta)\frac{k^*f'(k^*)}{f(k^*)} \\ - =& (1 - \alpha_K(k^*))(g + n + \delta) - - where the elasticity of output with respect to capital, - $\alpha_K(k)$, is defined as - - .. :math:: - - \alpha_K(k) = \frac{k'(k)}{f(k)}. - - """ - alpha_K = self.evaluate_output_elasticity(self.steady_state) - return (1 - alpha_K) * self.effective_depreciation_rate - - @property - def steady_state(self): - r""" - Steady state value of capital stock (per unit effective labor). - - :getter: Return the current steady state value. - :type: float - - Notes - ----- - The steady state value of capital stock (per unit effective - labor), `k`, is defined as the value of `k` that solves - - .. math:: - - 0 = sf(k) - (g + n + \delta)k - - where `s` is the savings rate, `f(k)` is intensive output, and - :math:`g + n + \delta` is the effective depreciation rate. - - """ - lower, upper = 1e-12, 1e12 - return self.find_steady_state(lower, upper) - - @output.setter - def output(self, value): - """Set a new production function.""" - self._output = self._validate_output(value) - self._clear_cache() - - @params.setter - def params(self, value): - """Set a new parameter dictionary.""" - valid_params = self._validate_params(value) - self._params = self._order_params(valid_params) - - def _clear_cache(self): - """Clear cached values.""" - self.__intensive_output = None - self.__mpk = None - self.__numeric_jacobian = None - self.__numeric_solow_residual = None - self.__numeric_system = None - - @staticmethod - def _order_params(params): - """Cast a dictionary to an order dictionary.""" - return collections.OrderedDict(sorted(params.items())) - - def _validate_output(self, output): - """Validate the production function.""" - if not isinstance(output, sym.Basic): - mesg = ("Output must be an instance of {}.".format(sym.Basic)) - raise AttributeError(mesg) - elif not ({A, K, L} < output.atoms()): - mesg = ("Output must be an expression of technology, 'A', " + - "capital, 'K', and labor, 'L'.") - raise AttributeError(mesg) - else: - return output - - def _validate_params(self, params): - """Validate the model parameters.""" - if not isinstance(params, dict): - mesg = "SolowModel.params must be a dict, not a {}." - raise AttributeError(mesg.format(params.__class__)) - elif not set(self._required_params) <= set(params.keys()): - mesg = "One of the required params in {} has not been specified." - raise AttributeError(mesg.format(self._required_params)) - elif params['s'] <= 0.0 or params['s'] >= 1.0: - raise AttributeError('Savings rate must be in (0, 1).') - elif params['delta'] <= 0.0 or params['delta'] >= 1.0: - raise AttributeError('Depreciation rate must be in (0, 1).') - elif params['g'] + params['n'] + params['delta'] <= 0.0: - raise AttributeError("Sum of g, n, and delta must be positive.") - elif params['A0'] <= 0.0: - mesg = "Initial value for technology must be strictly positive." - raise AttributeError(mesg) - elif params['L0'] <= 0.0: - mesg = "Initial value for labor supply must be strictly positive." - raise AttributeError(mesg) - else: - return params - - def evaluate_actual_investment(self, k): - """ - Return the amount of output (per unit of effective labor) - invested in the production of new capital. - - Parameters - ---------- - k : array_like (float) - Capital stock (per unit of effective labor) - - Returns - ------- - actual_inv : array_like (float) - Investment (per unit of effective labor) - - """ - actual_inv = self.params['s'] * self.evaluate_intensive_output(k) - return actual_inv - - def evaluate_consumption(self, k): - """ - Return the amount of consumption (per unit of effective labor). - - Parameters - ---------- - k : ndarray (float) - Capital stock (per unit of effective labor) - - Returns - ------- - c : ndarray (float) - Consumption (per unit of effective labor) - - """ - c = (self.evaluate_intensive_output(k) - - self.evaluate_actual_investment(k)) - return c - - def evaluate_effective_depreciation(self, k): - """ - Return amount of Capital stock (per unit of effective labor) - that depreciaties due to technological progress, population - growth, and physical depreciation. - - Parameters - ---------- - k : array_like (float) - Capital stock (per unit of effective labor) - - Returns - ------- - effective_depreciation : array_like (float) - Amount of depreciated Capital stock (per unit of effective - labor) - - """ - effective_depreciation = self.effective_depreciation_rate * k - return effective_depreciation - - def evaluate_intensive_output(self, k): - """ - Return the amount of output (per unit of effective labor). - - Parameters - ---------- - k : ndarray (float) - Capital stock (per unit of effective labor) - - Returns - ------- - y : ndarray (float) - Output (per unit of effective labor) - - """ - y = self._intensive_output(k, *self.params.values()) - return y - - def evaluate_k_dot(self, k): - """ - Return time derivative of capital stock (per unit of effective - labor). - - Parameters - ---------- - k : ndarray (float) - Capital stock (per unit of effective labor) - - Returns - ------- - k_dot : ndarray (float) - Time derivative of capital stock (per unit of effective - labor). - - """ - k_dot = (self.evaluate_actual_investment(k) - - self.evaluate_effective_depreciation(k)) - return k_dot - - def evaluate_mpk(self, k): - """ - Return marginal product of capital stock (per unit of effective - labor). - - Parameters - ---------- - k : ndarray (float) - Capital stock (per unit of effective labor) - - Returns - ------- - mpk : ndarray (float) - Marginal product of capital stock (per unit of effective - labor). - - """ - mpk = self._mpk(k, *self.params.values()) - return mpk - - def evaluate_output_elasticity(self, k): - """ - Return elasticity of output with respect to capital stock (per - unit effective labor). - - Parameters - ---------- - k : array_like (float) - Capital stock (per unit of effective labor) - - Returns - ------- - alpha_k : array_like (float) - Elasticity of output with respect to capital stock (per unit - effective labor). - - Notes - ----- - Under the additional assumption that markets are perfectly - competitive, the elasticity of output with respect to capital - stock is equivalent to capital's share of income. Since, under - perfect competition, firms earn zero profits it must be true - capital's share and labor's share must sum to one. - - """ - alpha_k = (k*self.evaluate_mpk(k)) / self.evaluate_intensive_output(k) - return alpha_k - - def evaluate_solow_residual(self, Y, K, L): - """ - Return Solow residual. - - Parameters - ---------- - k : array_like (float) - Capital stock (per unit of effective labor) - - Returns - ------- - residual : array_like (float) - Solow residual - - """ - residual = self._numeric_solow_residual(Y, K, L, *self.params.values()) - assert residual.all() > 0, "Solow residual show always be positive!" - return residual - - def find_steady_state(self, a, b, method='brentq', **kwargs): - """ - Compute the equilibrium value of capital stock (per unit - effective labor). - - Parameters - ---------- - a : float - One end of the bracketing interval [a,b]. - b : float - The other end of the bracketing interval [a,b] - method : str (default=`brentq`) - Method to use when computing the steady state. Supported - methods are `bisect`, `brenth`, `brentq`, `ridder`. See - `scipy.optimize` for more details (including references). - kwargs : optional - Additional keyword arguments. Keyword arguments are method - specific see `scipy.optimize` for details. - - Returns - ------- - x0 : float - Zero of `f` between `a` and `b`. - r : RootResults (present if ``full_output = True``) - Object containing information about the convergence. In - particular, ``r.converged`` is True if the routine - converged. - - """ - if method == 'bisect': - result = optimize.bisect(self.evaluate_k_dot, a, b, **kwargs) - elif method == 'brenth': - result = optimize.brenth(self.evaluate_k_dot, a, b, **kwargs) - elif method == 'brentq': - result = optimize.brentq(self.evaluate_k_dot, a, b, **kwargs) - elif method == 'ridder': - result = optimize.ridder(self.evaluate_k_dot, a, b, **kwargs) - else: - mesg = ("Method must be one of : 'bisect', 'brenth', 'brentq', " + - "or 'ridder'.") - raise ValueError(mesg) - - return result - - def linearized_solution(self, t, k0): - """ - Compute the linearized solution for the Solow model. - - Parameters - ---------- - t : ndarray (shape=(T,)) - Array of points at which the solution is desired. - k0 : (float) - Initial condition for capital stock (per unit of effective - labor) - - Returns - ------- - linearized_traj : ndarray (shape=t.size, 2) - Array representing the linearized solution trajectory. - - """ - kt = (self.steady_state + np.exp(-self.speed_of_convergence * t) * - (k0 - self.steady_state)) - linearized_traj = np.hstack((t[:, np.newaxis], kt[:, np.newaxis])) - - return linearized_traj - - def plot_factor_shares(self, ax, Nk=1e3, **new_params): - """ - Plot income/output shares of capital and labor inputs to - production. - - Parameters - ---------- - ax : `matplotlib.axes.AxesSubplot` - An instance of `matplotlib.axes.AxesSubplot`. - Nk : float (default=1e3) - Number of capital stock (per unit of effective labor) grid - points. - new_params : dict (optional) - Optional dictionary of parameter values to change. - - Returns - ------- - A list containing... - - capitals_share_line : maplotlib.lines.Line2D - A Line2D object representing the time path for capital's - share of income. - labors_share_line : maplotlib.lines.Line2D - A Line2D object representing the time path for labor's - share of income. - - """ - # create tmp_params dict to force check for valid params - tmp_params = self.params.copy() - tmp_params.update(new_params) - self.params = tmp_params # forces check for valid params! - - # create the plot - k_grid = np.linspace(0, 2 * self.steady_state, Nk) - capitals_share = self.evaluate_output_elasticity(k_grid) - labors_share = 1 - capitals_share - - capitals_share_line, = ax.plot(k_grid, capitals_share, 'r-', - label=r'$\alpha_K(k(t))$') - labors_share_line, = ax.plot(k_grid, labors_share, 'b-', - label=r'$1 - \alpha_K(k(t))$') - ax.set_xlabel('Capital (per unit effective labor), $k(t)$', - family='serif', fontsize=15) - ax.set_title('Factor shares', family='serif', fontsize=20) - ax.grid(True) - ax.legend(loc=0, frameon=False, prop={'family': 'serif'}, - bbox_to_anchor=(1.0, 1.0)) - - return [capitals_share_line, labors_share_line] - - def plot_intensive_output(self, ax, Nk=1e3, **new_params): - """ - Plot intensive form of the aggregate production function. - - Parameters - ---------- - ax : `matplotlib.axes.AxesSubplot` - An instance of `matplotlib.axes.AxesSubplot`. - Nk : float (default=1e3) - Number of capital stock (per unit of effective labor) grid - points. - new_params : dict (optional) - Optional dictionary of parameter values to change. - - Returns - ------- - A list containing... - - intensive_output : maplotlib.lines.Line2D - A Line2D object representing intensive output as a function - of capital stock (per unit effective labor). - - """ - # create tmp_params dict to force check for valid params - tmp_params = self.params.copy() - tmp_params.update(new_params) - self.params = tmp_params # forces check for valid params! - - # create the plot - k_grid = np.linspace(0, 2 * self.steady_state, Nk) - y_grid = self.evaluate_intensive_output(k_grid) - intensive_output_line, = ax.plot(k_grid, y_grid, 'r-') - ax.set_xlabel('Capital (per unit effective labor), $k(t)$', - family='serif', fontsize=15) - ax.set_ylabel('$f(k(t))$', family='serif', fontsize=20, - rotation='horizontal') - ax.yaxis.set_label_coords(-0.1, 0.5) - ax.set_title('Output (per unit effective labor)', - family='serif', fontsize=20) - ax.grid(True) - - return [intensive_output_line] - - def plot_intensive_investment(self, ax, Nk=1e3, **new_params): - """ - Plot actual investment (per unit effective labor) and effective - depreciation. The steady state value of capital stock (per unit - effective labor) balance acual investment and effective - depreciation. - - Parameters - ---------- - ax : `matplotlib.axes.AxesSubplot` - An instance of `matplotlib.axes.AxesSubplot`. - Nk : float (default=1e3) - Number of capital stock (per unit of effective labor) grid - points. - new_params : dict (optional) - Optional dictionary of parameter values to change. - - Returns - ------- - A list containing... - - actual_investment_line : maplotlib.lines.Line2D - A Line2D object representing the level of actual investment - as a function of capital stock (per unit effective labor). - breakeven_investment_line : maplotlib.lines.Line2D - A Line2D object representing the "break-even" level of - investment as a function of capital stock (per unit - effective labor). - ss_line : maplotlib.lines.Line2D - A Line2D object representing the steady state level of - investment. - - """ - # create tmp_params dict to force check for valid params - tmp_params = self.params.copy() - tmp_params.update(new_params) - self.params = tmp_params # forces check for valid params! - - # create the plot - k_grid = np.linspace(0, 2 * self.steady_state, Nk) - actual_investment_grid = self.evaluate_actual_investment(k_grid) - breakeven_investment_grid = self.evaluate_effective_depreciation(k_grid) - ss_investment = self.evaluate_actual_investment(self.steady_state) - - actual_investment_line, = ax.plot(k_grid, actual_investment_grid, 'g-', - label='$sf(k(t))$') - breakeven_investment_line, = ax.plot(k_grid, breakeven_investment_grid, - 'b-', label='$(g + n + \delta)k(t)$') - ss_line, = ax.plot(self.steady_state, ss_investment, 'ko', - label='$k^*={0:.4f}$'.format(self.steady_state)) - ax.set_xlabel('Capital (per unit effective labor), $k(t)$', - family='serif', fontsize=15) - ax.set_ylabel('Investment (per unit effective labor)', family='serif', - fontsize=15) - ax.set_title('Output (per unit effective labor)', - family='serif', fontsize=20) - ax.grid(True) - ax.legend(loc=0, frameon=False, prop={'family': 'serif'}, - bbox_to_anchor=(1.0, 1.0)) - - return [actual_investment_line, breakeven_investment_line, ss_line] - - def plot_phase_diagram(self, ax, Nk=1e3, **new_params): - """ - Plot the model's phase diagram. - - Parameters - ---------- - ax : `matplotlib.axes.AxesSubplot` - An instance of `matplotlib.axes.AxesSubplot`. - Nk : float (default=1e3) - Number of capital stock (per unit of effective labor) grid - points. - new_params : dict (optional) - Optional dictionary of parameter values to change. - - Returns - ------- - A list containing... - - k_dot_line : maplotlib.lines.Line2D - A Line2D object representing the rate of change of capital - stock (per unit effective labor) as a function of its level. - origin_line : maplotlib.lines.Line2D - A Line2D object representing the origin (i.e., locus of - points where k_dot is zero). - ss_line : maplotlib.lines.Line2D - A Line2D object representing the steady state level of - capital stock (per unit effective labor). - - """ - # create tmp_params dict to force check for valid params - tmp_params = self.params.copy() - tmp_params.update(new_params) - self.params = tmp_params # forces check for valid params! - - # create the plot - k_grid = np.linspace(0, 2 * self.steady_state, Nk) - k_dot_line, = ax.plot(k_grid, self.evaluate_k_dot(k_grid), - color='orange') - origin_line = ax.axhline(0, color='k') - ss_line, = ax.plot(self.steady_state, 0.0, 'ko', - label='$k^*={0:.4f}$'.format(self.steady_state)) - ax.set_xlabel('Capital (per unit effective labor), $k(t)$', - family='serif', fontsize=15) - ax.set_ylabel('$\dot{k}(t)$', family='serif', fontsize=25, - rotation='horizontal') - ax.yaxis.set_label_coords(-0.1, 0.5) - ax.set_title('Phase diagram', family='serif', fontsize=20) - ax.grid(True) - - return [k_dot_line, origin_line, ss_line] - - def plot_solow_diagram(self, ax, Nk=1e3, **new_params): - """ - Plot the classic Solow diagram. - - Parameters - ---------- - ax : `matplotlib.axes.AxesSubplot` - An instance of `matplotlib.axes.AxesSubplot`. - Nk : float (default=1e3) - Number of capital stock (per unit of effective labor) grid - points. - new_params : dict (optional) - Optional dictionary of parameter values to change. - - Returns - ------- - A list containing... - - actual_investment_line : maplotlib.lines.Line2D - A Line2D object representing the level of actual investment - as a function of capital stock (per unit effective labor). - breakeven_investment_line : maplotlib.lines.Line2D - A Line2D object representing the "break-even" level of - investment as a function of capital stock (per unit - effective labor). - ss_line : maplotlib.lines.Line2D - A Line2D object representing the steady state level of - investment. - - """ - # create tmp_params dict to force check for valid params - tmp_params = self.params.copy() - tmp_params.update(new_params) - self.params = tmp_params # forces check for valid params! - - # create the plot - k_grid = np.linspace(0, 2 * self.steady_state, Nk) - intensive_output_grid = self.evaluate_intensive_output(k_grid) - actual_investment_grid = self.evaluate_actual_investment(k_grid) - breakeven_investment_grid = self.evaluate_effective_depreciation(k_grid) - ss_investment = self.evaluate_actual_investment(self.steady_state) - - intensive_output_line, = ax.plot(k_grid, intensive_output_grid, 'r-', - label='$f(k(t)$') - actual_investment_line, = ax.plot(k_grid, actual_investment_grid, 'g-', - label='$sf(k(t))$') - breakeven_investment_line, = ax.plot(k_grid, breakeven_investment_grid, - 'b-', label='$(g + n + \delta)k(t)$') - ss_line, = ax.plot(self.steady_state, ss_investment, 'ko', - label='$k^*={0:.4f}$'.format(self.steady_state)) - ax.set_xlabel('Capital (per unit effective labor), $k(t)$', - family='serif', fontsize=15) - ax.set_title('Solow diagram', - family='serif', fontsize=20) - ax.grid(True) - ax.legend(loc=0, frameon=False, prop={'family': 'serif'}, - bbox_to_anchor=(1, 1)) - - lines = [intensive_output_line, actual_investment_line, - breakeven_investment_line, ss_line] - - return lines diff --git a/quantecon/models/uncertainty_traps.py b/quantecon/models/uncertainty_traps.py deleted file mode 100644 index 878150234..000000000 --- a/quantecon/models/uncertainty_traps.py +++ /dev/null @@ -1,62 +0,0 @@ -from __future__ import division -import numpy as np - -class UncertaintyTrapEcon(object): - - def __init__(self, - a=1.5, # Risk aversion - gx=0.5, # Production shock precision - rho=0.99, # Correlation coefficient for theta - sig_theta=0.5, # Std dev of theta shock - num_firms=100, # Number of firms - sig_F=1.5, # Std dev of fixed costs - c=-420, # External opportunity cost - mu_init=0, # Initial value for mu - gamma_init=4, # Initial value for gamma - theta_init=0): # Initial value for theta - - # == Record values == # - self.a, self.gx, self.rho, self.sig_theta = a, gx, rho, sig_theta - self.num_firms, self.sig_F, self.c, = num_firms, sig_F, c - self.sd_x = np.sqrt(1/ gx) - - # == Initialize states == # - self.gamma, self.mu, self.theta = gamma_init, mu_init, theta_init - - def psi(self, F): - temp1 = -self.a * (self.mu - F) - temp2 = self.a**2 * (1/self.gamma + 1/self.gx) / 2 - return (1 / self.a) * (1 - np.exp(temp1 + temp2)) - self.c - - def update_beliefs(self, X, M): - """ - Update beliefs (mu, gamma) based on aggregates X and M. - """ - # Simplify names - gx, rho, sig_theta = self.gx, self.rho, self.sig_theta - # Update mu - temp1 = rho * (self.gamma * self.mu + M * gx * X) - temp2 = self.gamma + M * gx - self.mu = temp1 / temp2 - # Update gamma - self.gamma = 1 / (rho**2 / (self.gamma + M * gx) + sig_theta**2) - - def update_theta(self, w): - """ - Update the fundamental state theta given shock w. - """ - self.theta = self.rho * self.theta + self.sig_theta * w - - def gen_aggregates(self): - """ - Generate aggregates based on current beliefs (mu, gamma). This - is a simulation step that depends on the draws for F. - """ - F_vals = self.sig_F * np.random.randn(self.num_firms) - M = np.sum(self.psi(F_vals) > 0) # Counts number of active firms - if M > 0: - x_vals = self.theta + self.sd_x * np.random.randn(M) - X = x_vals.mean() - else: - X = 0 - return X, M diff --git a/quantecon/random/utilities.py b/quantecon/random/utilities.py index 67dc4e8a1..98944f01f 100644 --- a/quantecon/random/utilities.py +++ b/quantecon/random/utilities.py @@ -38,6 +38,10 @@ def probvec(m, k, random_state=None): [ 0.43772774, 0.34763084, 0.21464142]]) """ + if k == 1: + return np.ones((m, k)) + + # if k >= 2 random_state = check_random_state(random_state) r = random_state.random_sample(size=(m, k-1)) diff --git a/quantecon/tests/tests_models/__init__.py b/quantecon/tests/tests_models/__init__.py deleted file mode 100644 index e69de29bb..000000000 diff --git a/quantecon/tests/tests_models/test_asset_pricing.py b/quantecon/tests/tests_models/test_asset_pricing.py deleted file mode 100644 index c6d6c0e91..000000000 --- a/quantecon/tests/tests_models/test_asset_pricing.py +++ /dev/null @@ -1,94 +0,0 @@ -""" -Filename: test_asset_pricing.py -Authors: Spencer Lyon -Date: 2014-07-30 - -Tests for quantecon.asset_pricing module - -TODO: come up with some simple examples we can check by hand for price - methods. - -""" -from __future__ import division -import unittest -import numpy as np -from numpy.testing import assert_allclose -from quantecon.models import AssetPrices - -# parameters for object -n = 5 -P = 0.0125 * np.ones((n, n)) -P += np.diag(0.95 - 0.0125 * np.ones(5)) -s = np.array([1.05, 1.025, 1.0, 0.975, 0.95]) # state values -gamma = 2.0 -bet = 0.94 -zeta = 1.0 -p_s = 150.0 - - -class TestAssetPrices(unittest.TestCase): - - @classmethod - def setUpClass(cls): - cls.ap = AssetPrices(bet, P, s, gamma) - - def test_P_shape(self): - "asset_pricing: is P square" - shp = self.ap.P.shape - assert shp[0] == shp[1] - - def test_n(self): - "asset_pricing: n computed correctly" - assert self.ap.n == self.ap.P.shape[0] - - def test_P_tilde(self): - "asset_pricing: test P_tilde by hand using nested loops" - # unpack variables and allocate memory for new P_tilde - n, s, P, gam = (self.ap.n, self.ap.s, self.ap.P, self.ap.gamma) - p_tilde_2 = np.empty_like(self.ap.P) - - # fill in new p_tilde by hand - for i in range(n): - for k in range(n): - p_tilde_2[i, k] = P[i, k] * s[k] ** (1.0 - gam) - - assert_allclose(self.ap.P_tilde, p_tilde_2) - - def test_P_check(self): - "asset_pricing: test P_check by hand using nested loops" - # unpack variables and allocate memory for new P_tilde - n, s, P, gam = (self.ap.n, self.ap.s, self.ap.P, self.ap.gamma) - p_check_2 = np.empty_like(self.ap.P) - - # fill in new p_check by hand - for i in range(n): - for k in range(n): - p_check_2[i, k] = P[i, k] * s[k] ** (-gam) - - assert_allclose(self.ap.P_check, p_check_2) - - def test_tree_price_size(self): - "asset_pricing: test lucas_tree price size" - assert self.ap.tree_price().size == self.ap.n - - def test_consol_price_size(self): - "asset_pricing: test consol_price price size" - assert self.ap.consol_price(zeta).size == self.ap.n - - def test_call_option_size(self): - "asset_pricing: test call_option price size" - assert self.ap.call_option(zeta, p_s)[0].size == self.ap.n - - def test_tree_price(self): - pass - - def test_consol_price(self): - pass - - def test_call_option_price(self): - pass - - def test_multiple_periods_call_option(self): - "asset_pricing: T option works to return multiple periods" - w_bars = self.ap.call_option(zeta, p_s, T=[5, 7])[1] - self.assertEqual(len(w_bars), 2) diff --git a/quantecon/tests/tests_models/test_career.py b/quantecon/tests/tests_models/test_career.py deleted file mode 100644 index 97c9aab1b..000000000 --- a/quantecon/tests/tests_models/test_career.py +++ /dev/null @@ -1,48 +0,0 @@ -""" -Tests for quantecon.carrer module - -@author : Spencer Lyon -@date : 2014-07-31 - -""" -from __future__ import division -import unittest -import numpy as np -from quantecon.models import CareerWorkerProblem - - -class TestCareerWorkerProblem(unittest.TestCase): - - @classmethod - def setUpClass(cls): - cls.cp = CareerWorkerProblem() - cls.v_init = np.random.rand(cls.cp.N, cls.cp.N) - cls.v_prime = cls.cp.bellman_operator(cls.v_init) - cls.greedy = cls.cp.get_greedy(cls.v_init) - - def test_bellman_shape(self): - "career: bellman shape" - assert self.v_init.shape == self.v_prime.shape - - def test_greedy_shape(self): - "career: greedy shape" - assert self.v_init.shape == self.greedy.shape - - def test_greedy_new_life(self): - "career: want new life with worst job/career?" - if (self.greedy == 3).any(): - # if we ever want a new life, it will be with worst possible - # theta and worst epsilon - assert self.greedy[0, 0] == 3 - - def test_greedy_new_job(self): - "career: want new job with best carrer/worst job?" - # we should want a new job with best career and worst job - assert self.greedy[-1, 0] == 2 - - def test_greedy_stay_put(self): - "career: want to stayw with best career/job?" - if (self.greedy == 1).any(): - # if we ever want to stay put, it will be with best possible - # theta and best epsilon - assert self.greedy[-1, -1] == 1 diff --git a/quantecon/tests/tests_models/test_ifp.py b/quantecon/tests/tests_models/test_ifp.py deleted file mode 100644 index a29bb71b4..000000000 --- a/quantecon/tests/tests_models/test_ifp.py +++ /dev/null @@ -1,157 +0,0 @@ -""" -tests for quantecon.ifp - -@author : Spencer Lyon -@date : 2014-08-01 12:09:17 - -""" -from __future__ import division -import unittest -import numpy as np -from quantecon.models import ConsumerProblem -from quantecon import compute_fixed_point -from quantecon.tests import get_h5_data_file, write_array, max_abs_diff - - -def _solve_via_vfi(cp, v_init, return_both=False): - "compute policy rule using value function iteration" - v = compute_fixed_point(cp.bellman_operator, v_init, verbose=False, - error_tol=1e-5, - max_iter=1000) - - # Run one more time to get the policy - p = cp.bellman_operator(v, return_policy=True) - - if return_both: - return v, p - else: - return p - - -def _solve_via_pfi(cp, c_init): - "compute policy rule using policy function iteration" - p = compute_fixed_point(cp.coleman_operator, c_init, verbose=False, - error_tol=1e-5, - max_iter=1000) - - return p - - -def _get_vfi_pfi_guesses(cp, force_new=False): - """ - load precomputed vfi/pfi solutions, or compute them if requested - or we can't find old ones - """ - # open the data file - with get_h5_data_file() as f: - - # See if the ifp group already exists - group_existed = True - try: - ifp_group = f.getNode("/ifp") - except: - # doesn't exist - group_existed = False - ifp_group = f.create_group("/", "ifp", "data for ifp.py tests") - - if force_new or not group_existed: - # group doesn't exist, or forced to create new data. - # This function updates f in place and returns v_vfi, c_vfi, c_pfi - v_vfi, c_vfi, c_pfi = _new_solutions(cp, f, ifp_group) - - # We have what we need, so return - return v_vfi, c_pfi - - # if we made it here, the group exists and we should try to read - # existing solutions - try: # read in vfi - # Try reading vfi - c_vfi = ifp_group.c_vfi[:] - v_vfi = ifp_group.v_vfi[:] - - except: - # doesn't exist. Let's create it - v_vfi, c_vfi = _new_solutions(cp, f, ifp_group, which="vfi") - - try: # read in pfi - # Try reading pfi - c_pfi = ifp_group.c_pfi[:] - - except: - # doesn't exist. Let's create it - c_pfi = _new_solutions(cp, f, ifp_group, which="pfi") - - return v_vfi, c_pfi - - -def _new_solutions(cp, f, grp, which="both"): - v_init, c_init = cp.initialize() - if which == "both": - - v_vfi, c_vfi = _solve_via_vfi(cp, v_init, return_both=True) - c_pfi = _solve_via_pfi(cp, c_init) - - # Store solutions in chunked arrays... - write_array(f, grp, c_vfi, "c_vfi") - write_array(f, grp, v_vfi, "v_vfi") - write_array(f, grp, c_pfi, "c_pfi") - - return v_vfi, c_vfi, c_pfi - - elif which == "vfi": - v_vfi, c_vfi = _solve_via_vfi(cp, v_init, return_both=True) - write_array(f, grp, c_vfi, "c_vfi") - write_array(f, grp, v_vfi, "v_vfi") - - return v_vfi, c_vfi - - elif which == "pfi": - c_pfi = _solve_via_pfi(cp, c_init) - write_array(f, grp, c_pfi, "c_pfi") - - return c_pfi - - -class TestConsumerProblem(unittest.TestCase): - - @classmethod - def setUpClass(cls): - cls.cp = ConsumerProblem() - - # get precomputed answer for each method - print("reading old solutions") - old_vfi_sol, old_pfi_sol = _get_vfi_pfi_guesses(cls.cp) - cls.v_vfi = old_vfi_sol - - # compute answers again, using something close to old answer as - # initial value so it goes really fast - print("computing new vfi") - cls.c_vfi = _solve_via_vfi(cls.cp, old_vfi_sol * 0.99999) - print("computing new pfi") - cls.c_pfi = _solve_via_pfi(cls.cp, old_pfi_sol * 0.99999) - - def test_bellman_coleman_solutions_agree(self): - "ifp: bellman and coleman solutions agree" - self.assertLessEqual(max_abs_diff(self.c_vfi, self.c_pfi), 0.2) - - def test_bellman_fp(self): - "ifp: solution to bellman is a fixed point" - new_v = self.cp.bellman_operator(self.v_vfi) - self.assertLessEqual(max_abs_diff(self.v_vfi, new_v), 1e-3) - - def test_coleman_fp(self): - "ifp: solution to coleman is a fixed point" - new_c = self.cp.coleman_operator(self.c_pfi) - self.assertLessEqual(max_abs_diff(self.c_pfi, new_c), 1e-3) - - def test_initialize(self): - "ifp: initialize function works" - i = self.cp.initialize() - - # returned two things? - self.assertEqual(len(i), 2) - - shapes = (len(self.cp.asset_grid), len(self.cp.z_vals)) - self.assertEqual(i[0].shape, shapes) - self.assertEqual(i[1].shape, shapes) - diff --git a/quantecon/tests/tests_models/test_jv.py b/quantecon/tests/tests_models/test_jv.py deleted file mode 100644 index 2772b3e0d..000000000 --- a/quantecon/tests/tests_models/test_jv.py +++ /dev/null @@ -1,113 +0,0 @@ -""" -tests for quantecon.jv - -@author : Spencer Lyon -@date : 2014-08-01 13:53:29 - -""" -from __future__ import division -import sys -import unittest -from nose.plugins.skip import SkipTest -from quantecon.models import JvWorker -from quantecon import compute_fixed_point -from quantecon.tests import get_h5_data_file, write_array, max_abs_diff - -# specify params -- use defaults -A = 1.4 -alpha = 0.6 -beta = 0.96 -grid_size = 50 - -if sys.version_info[0] == 2: - v_nm = "V" -else: # python 3 - raise SkipTest("Python 3 tests aren't ready.") - v_nm = "V_py3" - - -def _new_solution(jv, f, grp): - "gets new solution and updates data file" - V = _solve_via_vfi(jv) - write_array(f, grp, V, v_nm) - - return V - - -def _solve_via_vfi(jv): - "compute policy rules via value function iteration" - v_init = jv.x_grid * 0.6 - V = compute_fixed_point(jv.bellman_operator, v_init, - max_iter=3000, - error_tol=1e-5) - return V - - -def _get_vf_guess(jv, force_new=False): - with get_h5_data_file() as f: - - # See if the jv group already exists - group_existed = True - try: - jv_group = f.getNode("/jv") - except: - # doesn't exist - group_existed = False - jv_group = f.create_group("/", "jv", "data for jv.py tests") - - if force_new or not group_existed: - # group doesn't exist, or forced to create new data. - # This function updates f in place and returns v_vfi, c_vfi, c_pfi - V = _new_solution(jv, f, jv_group) - - return V - - # if we made it here, the group exists and we should try to read - # existing solutions - try: - # Try reading vfi - if sys.version_info[0] == 2: - V = jv_group.V[:] - else: # python 3 - V = jv_group.V_py3[:] - - except: - # doesn't exist. Let's create it - V = _new_solution(jv, f, jv_group) - - return V - - -class TestJvWorkder(unittest.TestCase): - - @classmethod - def setUpClass(cls): - jv = JvWorker(A=A, alpha=alpha, beta=beta, grid_size=grid_size) - cls.jv = jv - - # compute solution - v_init = _get_vf_guess(jv) - cls.V = compute_fixed_point(jv.bellman_operator, v_init) - cls.s_pol, cls.phi_pol = jv.bellman_operator(cls.V * 0.999, - return_policies=True) - - def test_low_x_prefer_s(self): - "jv: s preferred to phi with low x?" - # low x is an early index - self.assertGreaterEqual(self.s_pol[0], self.phi_pol[0]) - - def test_high_x_prefer_phi(self): - "jv: phi preferred to s with high x?" - # low x is an early index - self.assertGreaterEqual(self.phi_pol[-1], self.s_pol[-1]) - - def test_policy_sizes(self): - "jv: policies correct size" - n = self.jv.x_grid.size - self.assertEqual(self.s_pol.size, n) - self.assertEqual(self.phi_pol.size, n) - - def test_bellman_sol_fixed_point(self): - "jv: solution to bellman is fixed point" - new_V = self.jv.bellman_operator(self.V) - self.assertLessEqual(max_abs_diff(new_V, self.V), 1e-4) diff --git a/quantecon/tests/tests_models/test_lucastree.py b/quantecon/tests/tests_models/test_lucastree.py deleted file mode 100644 index f20148e2f..000000000 --- a/quantecon/tests/tests_models/test_lucastree.py +++ /dev/null @@ -1,108 +0,0 @@ -""" -Tests for quantecon.models.lucastree - -@author : Spencer Lyon -@date : 2014-08-05 09:15:45 - -""" -from __future__ import division -from nose.tools import (assert_equal, assert_true, assert_less_equal) -import numpy as np -from quantecon.models import LucasTree -from quantecon.tests import (get_h5_data_file, get_h5_data_group, write_array, - max_abs_diff) - -# helper parameters -_tol = 1e-6 - - -# helper functions -def _new_solution(tree, f, grp): - "gets a new set of prices and updates the file" - prices = tree.compute_lt_price(error_tol=_tol, max_iter=5000) - write_array(f, grp, prices, "prices") - return prices - - -def _get_price_data(tree, force_new=False): - "get price data from file, or create if necessary" - with get_h5_data_file() as f: - existed, grp = get_h5_data_group("lucastree") - - if force_new or not existed: - if existed: - grp.prices._f_remove() - prices = _new_solution(tree, f, grp) - - return prices - - # if we made it here, the group exists and we should try to read - # existing solutions - try: - # Try reading vfi - prices = grp.prices[:] - - except: - # doesn't exist. Let's create it - prices = _new_solution(tree, f, grp) - - return prices - - -# model parameters -gamma = 2.0 -beta = 0.95 -alpha = 0.90 -sigma = 0.1 - -# model object -tree = LucasTree(gamma, beta, alpha, sigma) -grid = tree.grid -prices = _get_price_data(tree) - - -def test_h5_access(): - "lucastree: test access to data file" - assert_true(prices is not None) - - -def test_prices_shape(): - "lucastree: test access shape of computed prices" - assert_equal(prices.shape, grid.shape) - - -def test_integrate(): - "lucastree: integrate function" - # just have it be a 1. Then integrate should give cdf - g = lambda x: x*0.0 + 1.0 - - # estimate using integrate function - est = tree.integrate(g) - - # compute exact solution - exact = tree.phi.cdf(tree._int_max) - tree.phi.cdf(tree._int_min) - - assert_less_equal(est - exact, .1) - - -def test_lucas_op_fixed_point(): - "lucastree: are prices a fixed point of lucas_operator" - # transform from p to f - old_f = prices / (grid ** gamma) - - # compute new f - new_f = tree.lucas_operator(old_f) - - # transform from f to p - new_p = new_f * grid**gamma - - # test if close. Make it one order of magnitude less than tol used - # to compute prices - assert_less_equal(max_abs_diff(new_p, prices), _tol*10) - - -def test_lucas_prices_increasing(): - "lucastree: test prices are increasing in y" - # sort the array and test that it is the same - sorted = np.sort(np.copy(prices)) - np.testing.assert_array_equal(sorted, prices) diff --git a/quantecon/tests/tests_models/test_odu.py b/quantecon/tests/tests_models/test_odu.py deleted file mode 100644 index 983f3d6a7..000000000 --- a/quantecon/tests/tests_models/test_odu.py +++ /dev/null @@ -1,138 +0,0 @@ -""" -tests for quantecon.models.odu - -@author : Spencer Lyon -@date : 2014-08-05 10:20:53 - -""" -from __future__ import division -import numpy as np -from nose.tools import (assert_equal, assert_true, assert_less_equal) -from quantecon import compute_fixed_point -from quantecon.models import SearchProblem -from quantecon.tests import (get_h5_data_file, get_h5_data_group, write_array, - max_abs_diff) - -# helper parameters -_tol = 1e-6 - - -# helper functions -def _new_solution(sp, f, grp): - "gets a new set of solution objects and updates the data file" - - # compute value function and policy rule using vfi - v_init = np.zeros(len(sp.grid_points)) + sp.c / (1 - sp.beta) - v = compute_fixed_point(sp.bellman_operator, v_init, error_tol=_tol, - max_iter=5000) - phi_vfi = sp.get_greedy(v) - - # also run v through bellman so I can test if it is a fixed point - # bellman_operator takes a long time, so store result instead of compute - new_v = sp.bellman_operator(v) - - # compute policy rule using pfi - - phi_init = np.ones(len(sp.pi_grid)) - phi_pfi = compute_fixed_point(sp.res_wage_operator, phi_init, - error_tol=_tol, max_iter=5000) - - # write all arrays to file - write_array(f, grp, v, "v") - write_array(f, grp, phi_vfi, "phi_vfi") - write_array(f, grp, phi_pfi, "phi_pfi") - write_array(f, grp, new_v, "new_v") - - # return data - return v, phi_vfi, phi_pfi, new_v - - -def _get_data(sp, force_new=False): - "get solution data from file, or create if necessary" - with get_h5_data_file() as f: - existed, grp = get_h5_data_group("odu") - - if force_new or not existed: - if existed: - grp.v._f_remove() - grp.phi_vfi._f_remove() - grp.phi_pfi._f_remove() - grp.new_v._f_remove() - v, phi_vfi, phi_pfi, new_v = _new_solution(sp, f, grp) - - return v, phi_vfi, phi_pfi, new_v - - # if we made it here, the group exists and we should try to read - # existing solutions - try: - # Try reading data - v = grp.v[:] - phi_vfi = grp.phi_vfi[:] - phi_pfi = grp.phi_pfi[:] - new_v = grp.new_v[:] - - except: - # doesn't exist. Let's create it - v, phi_vfi, phi_pfi, new_v = _new_solution(sp, f, grp) - - return v, phi_vfi, phi_pfi, new_v - -# model parameters -beta = 0.95 -c = 0.6 -F_a = 1 -F_b = 1 -G_a = 3 -G_b = 1.2 -w_max = 2 -w_grid_size = 40 -pi_grid_size = 40 - -sp = SearchProblem(beta, c, F_a, F_b, G_a, G_b, w_max, w_grid_size, - pi_grid_size) - -v, phi_vfi, phi_pfi, new_v = _get_data(sp) - - -def test_h5_access(): - "odu: test access to data file" - assert_true(v is not None) - assert_true(phi_vfi is not None) - assert_true(phi_pfi is not None) - - -def test_vfi_v_phi_same_shape(): - "odu: vfi value and policy same shape" - assert_equal(v.shape, phi_vfi.shape) - - -def test_phi_vfi_increasing(): - "odu: phi from vfi is increasing" - phi_mat = phi_vfi.reshape(w_grid_size, pi_grid_size) - sorted = np.sort(np.copy(phi_mat)) - np.testing.assert_array_equal(sorted, phi_mat) - - -def test_phi_pfi_increasing(): - "odu: phi from pfi is increasing" - sorted = np.sort(np.copy(phi_pfi))[::-1] # ascending - np.testing.assert_array_equal(sorted, phi_pfi) - - -def test_v_vfi_increasing(): - "odu: v from vfi is increasing" - # order so it sorts along the correct dimension (ascending) - v_mat = v[::-1].reshape(w_grid_size, pi_grid_size) - sorted = np.sort(np.copy(v_mat)) - np.testing.assert_array_equal(sorted, v_mat) - - -def test_v_vfi_fixed_point(): - "odu: v from vfi is fixed point" - assert_less_equal(max_abs_diff(v, new_v), _tol*10) - - -def test_phi_pfi_fixed_point(): - "odu: phi from pfi is fixed point" - new_phi = sp.res_wage_operator(phi_pfi) - assert_less_equal(max_abs_diff(new_phi, phi_pfi), _tol*10) diff --git a/quantecon/tests/tests_models/test_optgrowth.py b/quantecon/tests/tests_models/test_optgrowth.py deleted file mode 100644 index e76b0c1ce..000000000 --- a/quantecon/tests/tests_models/test_optgrowth.py +++ /dev/null @@ -1,114 +0,0 @@ -""" -tests for quantecon.models.optgrowth - -@author : Spencer Lyon -@date : 2014-08-05 10:20:53 - -TODO: I'd really like to see why the solutions only match analytical - counter part up to 1e-2. Seems like we should be able to do better - than that. -""" -from __future__ import division -from math import log -import numpy as np -from nose.tools import (assert_equal, assert_true, assert_less_equal) -from quantecon import compute_fixed_point -from quantecon.models import GrowthModel -from quantecon.tests import (get_h5_data_file, get_h5_data_group, write_array, - max_abs_diff) - - -# helper parameters -_tol = 1e-6 - - -# helper functions -def _new_solution(gm, f, grp): - "gets a new set of solution objects and updates the data file" - - # compute value function and policy rule using vfi - v_init = 5 * gm.u(gm.grid) - 25 - v = compute_fixed_point(gm.bellman_operator, v_init, error_tol=_tol, - max_iter=5000) - # sigma = gm.get_greedy(v) - - # write all arrays to file - write_array(f, grp, v, "v") - - # return data - return v - - -def _get_data(gm, force_new=False): - "get solution data from file, or create if necessary" - with get_h5_data_file() as f: - existed, grp = get_h5_data_group("optgrowth") - - if force_new or not existed: - if existed: - grp.w._f_remove() - v = _new_solution(gm, f, grp) - - return v - - # if we made it here, the group exists and we should try to read - # existing solutions - try: - # Try reading data - v = grp.v[:] - - except: - # doesn't exist. Let's create it - v = _new_solution(gm, f, grp) - - return v - -# model parameters -alpha = 0.65 -f = lambda k: k ** alpha -beta = 0.95 -u = np.log -grid_max = 2 -grid_size = 150 - -gm = GrowthModel(f, beta, u, grid_max, grid_size) - -v = _get_data(gm) - -# compute analytical policy function -true_sigma = (1 - alpha * beta) * gm.grid**alpha - -# compute analytical value function -ab = alpha * beta -c1 = (log(1 - ab) + log(ab) * ab / (1 - ab)) / (1 - beta) -c2 = alpha / (1 - ab) -def v_star(k): - return c1 + c2 * np.log(k) - - -def test_h5_access(): - "optgrowth: test access to data file" - assert_true(v is not None) - - -def test_bellman_return_both(): - "optgrowth: bellman_operator compute_policy option works" - assert_equal(len(gm.bellman_operator(v, compute_policy=True)), 2) - - -def test_analytical_policy(): - "optgrowth: approx sigma matches analytical" - sigma = gm.compute_greedy(v) - assert_less_equal(max_abs_diff(sigma, true_sigma), 1e-2) - - -def test_analytical_vf(): - "optgrowth: approx v matches analytical" - true_v = v_star(gm.grid) - assert_less_equal(max_abs_diff(v[1:-1], true_v[1:-1]), 5e-2) - - -def test_vf_fixed_point(): - "optgrowth: solution is fixed point of bellman" - new_v = gm.bellman_operator(v) - assert_less_equal(max_abs_diff(v[1:-1], new_v[1:-1]), 5e-2) diff --git a/quantecon/tests/tests_models/tests_solow/__init__.py b/quantecon/tests/tests_models/tests_solow/__init__.py deleted file mode 100644 index e69de29bb..000000000 diff --git a/quantecon/tests/tests_models/tests_solow/test_ces.py b/quantecon/tests/tests_models/tests_solow/test_ces.py deleted file mode 100644 index b39266ad5..000000000 --- a/quantecon/tests/tests_models/tests_solow/test_ces.py +++ /dev/null @@ -1,68 +0,0 @@ -""" -Test suite for ces.py module. - -@author : David R. Pugh -@date : 2014-12-08 - -""" -import nose - -import numpy as np - -from .... models.solow import ces - -params = {'A0': 1.0, 'g': 0.02, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'sigma': 1.1, 'delta': 0.05} -model = ces.CESModel(params) - - -def test_steady_state(): - """Compare analytic steady state with numerical steady state.""" - eps = 1e-1 - for g in np.linspace(eps, 0.05, 4): - for n in np.linspace(eps, 0.05, 4): - for s in np.linspace(eps, 1-eps, 4): - for alpha in np.linspace(eps, 1-eps, 4): - for delta in np.linspace(eps, 1-eps, 4): - for sigma in np.linspace(eps, 2.0, 4): - - tmp_params = {'A0': 1.0, 'g': g, 'L0': 1.0, 'n': n, - 's': s, 'alpha': alpha, 'delta': delta, - 'sigma': sigma} - try: - model.params = tmp_params - - # use root finder to compute the steady state - actual_ss = model.steady_state - expected_ss = model.find_steady_state(1e-12, 1e9) - - # conduct the test (numerical precision limits!) - nose.tools.assert_almost_equals(actual_ss, - expected_ss, - places=6) - - # handles params with non finite steady state - except AttributeError: - continue - - -def test_validate_params(): - """Testing validation of params attribute.""" - invalid_params_0 = {'A0': 1.0, 'g': 0.02, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 1.33, 'delta': 0.03, 'sigma': 1.2} - invalid_params_1 = {'A0': 1.0, 'g': 0.02, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'delta': 0.03, 'sigma': 0.0} - invalid_params_2 = {'A0': 1.0, 'g': 0.01, 'L0': 1.0, 'n': 0.01, 's': 0.12, - 'alpha': 0.75, 'delta': 0.01, 'sigma': 2.0} - - # alpha must be in (0, 1) - with nose.tools.assert_raises(AttributeError): - ces.CESModel(invalid_params_0) - - # sigma must be strictly positive - with nose.tools.assert_raises(AttributeError): - ces.CESModel(invalid_params_1) - - # parameters inconsistent with finite steady state - with nose.tools.assert_raises(AttributeError): - ces.CESModel(invalid_params_2) diff --git a/quantecon/tests/tests_models/tests_solow/test_cobb_douglas.py b/quantecon/tests/tests_models/tests_solow/test_cobb_douglas.py deleted file mode 100644 index ddd15a092..000000000 --- a/quantecon/tests/tests_models/tests_solow/test_cobb_douglas.py +++ /dev/null @@ -1,84 +0,0 @@ -""" -Test suite for solow.cobb_douglas.py module. - -@author : David R. Pugh - -""" -import nose - -import numpy as np - -from .... models.solow import cobb_douglas - -params = {'A0': 1.0, 'g': 0.02, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'delta': 0.05} -model = cobb_douglas.CobbDouglasModel(params) - - -def test_ivp_solve(): - """Testing computation of solution to the initial value problem.""" - eps = 1e-1 - for g in np.linspace(eps, 0.05, 4): - for n in np.linspace(eps, 0.05, 4): - for s in np.linspace(eps, 1-eps, 4): - for alpha in np.linspace(eps, 1-eps, 4): - for delta in np.linspace(eps, 1-eps, 4): - - tmp_params = {'A0': 1.0, 'g': g, 'L0': 1.0, 'n': n, - 's': s, 'alpha': alpha, 'delta': delta} - model.params = tmp_params - - # solve the initial value problem - t0, k0 = 0, 0.5 * model.steady_state - numeric_soln = model.ivp.solve(t0, k0, T=100) - - # compute the analytic solution - tmp_ti = numeric_soln[:, 0] - analytic_soln = model.analytic_solution(tmp_ti, k0) - - # conduct the test - np.testing.assert_allclose(numeric_soln, analytic_soln) - - -def test_root_finders(): - """Testing conditional logic in find_steady_state.""" - valid_methods = ['brenth', 'brentq', 'ridder', 'bisect'] - for method in valid_methods: - actual_ss = model.find_steady_state(1e-6, 1e6, method=method) - expected_ss = model.steady_state - nose.tools.assert_almost_equals(actual_ss, expected_ss) - - -def test_steady_state(): - """Compare analytic steady state with numerical steady state.""" - eps = 1e-1 - for g in np.linspace(eps, 0.05, 4): - for n in np.linspace(eps, 0.05, 4): - for s in np.linspace(eps, 1-eps, 4): - for alpha in np.linspace(eps, 1-eps, 4): - for delta in np.linspace(eps, 1-eps, 4): - - tmp_params = {'A0': 1.0, 'g': g, 'L0': 1.0, 'n': n, - 's': s, 'alpha': alpha, 'delta': delta} - model.params = tmp_params - - # use root finder to compute the steady state - actual_ss = model.steady_state - expected_ss = model.find_steady_state(1e-12, 1e12) - - # conduct the test - nose.tools.assert_almost_equals(actual_ss, expected_ss) - - -def test_valid_methods(): - """Testing invalid method passed to find_steady_state.""" - with nose.tools.assert_raises(ValueError): - model.find_steady_state(1e-12, 1e12, method='invalid_method') - - -def test_valid_parameters(): - """Testing invalid value for output elasticity.""" - with nose.tools.assert_raises(AttributeError): - invalid_params = {'A0': 1.0, 'g': 0.02, 'L0': 1.0, 'n': 0.02, - 's': 0.15, 'alpha': 1.1, 'delta': 0.03} - cobb_douglas.CobbDouglasModel(invalid_params) diff --git a/quantecon/tests/tests_models/tests_solow/test_impulse_response.py b/quantecon/tests/tests_models/tests_solow/test_impulse_response.py deleted file mode 100644 index 0e6d46836..000000000 --- a/quantecon/tests/tests_models/tests_solow/test_impulse_response.py +++ /dev/null @@ -1,150 +0,0 @@ -""" -Test suite for the impulse_response.py module. - -@author : David R. Pugh - -""" -from __future__ import division -import nose - -import matplotlib.pyplot as plt -import numpy as np - -from .... models.solow import cobb_douglas - -params = {'A0': 1.0, 'g': 0.02, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'delta': 0.05} -model = cobb_douglas.CobbDouglasModel(params) - - -def test_valid_impulse(): - """Testing validation of impulse attribute.""" - # impulse attribute must be a dict - with nose.tools.assert_raises(AttributeError): - model.irf.impulse = (('alpha', 0.75), ('g', 0.04)) - - # impulse sttribute must have valid keys - with nose.tools.assert_raises(AttributeError): - model.irf.impulse = {'alpha': 0.56, 'bad_key': 0.55} - - -def test_impulse_response(): - """Testing computation of impulse response.""" - original_params = {'A0': 1.0, 'g': 0.01, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'delta': 0.05} - model = cobb_douglas.CobbDouglasModel(original_params) - - # generate the impulse response - impulse = {'s': 0.30} - model.irf.impulse = impulse - model.irf.kind = 'efficiency_units' - model.irf.T = 500 # need to get "close" to new BGP - actual_ss = model.irf.impulse_response[-1, 1] - - # compute steady state following the impulse - model.params.update(impulse) - expected_ss = model.steady_state - - nose.tools.assert_almost_equals(actual_ss, expected_ss) - - -def test_per_capita_impulse_response(): - """Testing computation of per capita impulse response.""" - original_params = {'A0': 1.0, 'g': 0.01, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'delta': 0.05} - model = cobb_douglas.CobbDouglasModel(original_params) - - # generate the per capita impulse response - impulse = {'alpha': 0.15} - model.irf.impulse = impulse - model.irf.kind = 'per_capita' - model.irf.T = 500 # need to get "close" to new BGP - actual_c = model.irf.impulse_response[-1, 3] - - # compute steady state following the impulse - model.params.update(impulse) - A0, g = model.params['A0'], model.params['g'] - scaling_factor = A0 * np.exp(g * model.irf.T) - c_ss = model.evaluate_consumption(model.steady_state) - expected_c = c_ss * scaling_factor - - nose.tools.assert_almost_equals(actual_c, expected_c) - - -def test_levels_impulse_response(): - """Testing computation of levels impulse response.""" - original_params = {'A0': 1.0, 'g': 0.01, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'delta': 0.05} - model = cobb_douglas.CobbDouglasModel(original_params) - - # generate the per capita impulse response - impulse = {'delta': 0.15} - model.irf.impulse = impulse - model.irf.kind = 'levels' - model.irf.T = 500 # need to get "close" to new BGP - actual_y = model.irf.impulse_response[-1, 2] - - # compute steady state following the impulse - model.params.update(impulse) - A0, g = model.params['A0'], model.params['g'] - L0, n = model.params['L0'], model.params['n'] - scaling_factor = A0 * L0 * np.exp((g + n) * model.irf.T) - y_ss = model.evaluate_intensive_output(model.steady_state) - expected_y = y_ss * scaling_factor - - nose.tools.assert_almost_equals(actual_y, expected_y) - - -def test_plot_efficiency_units_impulse_response(): - """Testing return type for plot_impulse_response.""" - original_params = {'A0': 1.0, 'g': 0.02, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'delta': 0.05} - model = cobb_douglas.CobbDouglasModel(original_params) - - # initialize the impulse - model.irf.impulse = {'delta': 0.25} - model.irf.kind = 'efficiency_units' - - fig, ax = plt.subplots(1, 1) - tmp_lines = model.irf.plot_impulse_response(ax, variable='output') - nose.tools.assert_is_instance(tmp_lines, list) - - -def test_plot_levels_impulse_response(): - """Testing return type for plot_impulse_response.""" - original_params = {'A0': 1.0, 'g': 0.02, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'delta': 0.05} - model = cobb_douglas.CobbDouglasModel(original_params) - - # initialize the impulse - model.irf.impulse = {'alpha': 0.25} - model.irf.kind = 'levels' - - fig, ax = plt.subplots(1, 1) - tmp_lines = model.irf.plot_impulse_response(ax, variable='output', - log=False) - nose.tools.assert_is_instance(tmp_lines, list) - - -def test_plot_per_capita_impulse_response(): - """Testing return type for plot_impulse_response.""" - original_params = {'A0': 1.0, 'g': 0.02, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'delta': 0.05} - model = cobb_douglas.CobbDouglasModel(original_params) - - # initialize the impulse - model.irf.impulse = {'g': 0.05} - model.irf.kind = 'per_capita' - - fig, ax = plt.subplots(1, 1) - tmp_lines = model.irf.plot_impulse_response(ax, variable='output', - log=True) - nose.tools.assert_is_instance(tmp_lines, list) - - -def test_valid_kind(): - """Testing validation of the kind attribute.""" - - # kind sttribute must be a valid string - with nose.tools.assert_raises(AttributeError): - model.irf.kind = 'invalid_kind' diff --git a/quantecon/tests/tests_models/tests_solow/test_model.py b/quantecon/tests/tests_models/tests_solow/test_model.py deleted file mode 100644 index f9488fc48..000000000 --- a/quantecon/tests/tests_models/tests_solow/test_model.py +++ /dev/null @@ -1,147 +0,0 @@ -""" -Test suite for solow module. - -@author : David R. Pugh -@date : 2014-11-27 - -""" -from __future__ import division -import nose - -import matplotlib.pyplot as plt -import numpy as np -import sympy as sym - -from .... models import solow - -# declare key variables for the model -A, E, k, K, L = sym.symbols('A, E, k, K, L') - -# declare required model parameters -g, n, s, alpha, delta = sym.symbols('g, n, s, alpha, delta') - - -# two different ways in which output can fail -def invalid_output_1(A, K, L, alpha): - """Output must be of type sym.basic, not function.""" - return K**alpha * (A * L)**(1 - alpha) - -invalid_output_2 = K**alpha * (A * E)**(1 - alpha) - -valid_output = K**alpha * (A * L)**(1 - alpha) - -valid_params = {'A0': 1.0, 'g': 0.02, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'delta': 0.05} - - -# testing functions -def test_plot_factor_shares(): - """Testing return type for plot_factor_shares.""" - tmp_mod = solow.Model(output=valid_output, params=valid_params) - fig, ax = plt.subplots(1, 1) - tmp_lines = tmp_mod.plot_factor_shares(ax) - nose.tools.assert_is_instance(tmp_lines, list) - - -def test_plot_intensive_investment(): - """Testing return type for plot_intensive_investment.""" - tmp_mod = solow.Model(output=valid_output, params=valid_params) - fig, ax = plt.subplots(1, 1) - tmp_lines = tmp_mod.plot_intensive_investment(ax) - nose.tools.assert_is_instance(tmp_lines, list) - - -def test_plot_intensive_output(): - """Testing return type for plot_intensive_output.""" - tmp_mod = solow.Model(output=valid_output, params=valid_params) - fig, ax = plt.subplots(1, 1) - tmp_lines = tmp_mod.plot_intensive_output(ax) - nose.tools.assert_is_instance(tmp_lines, list) - - -def test_plot_phase_diagram(): - """Testing return type for plot_phase_diagram.""" - tmp_mod = solow.Model(output=valid_output, params=valid_params) - fig, ax = plt.subplots(1, 1) - tmp_lines = tmp_mod.plot_phase_diagram(ax) - nose.tools.assert_is_instance(tmp_lines, list) - - -def test_plot_solow_diagram(): - """Testing return type for plot_solow_diagram.""" - tmp_mod = solow.Model(output=valid_output, params=valid_params) - fig, ax = plt.subplots(1, 1) - tmp_lines = tmp_mod.plot_solow_diagram(ax) - nose.tools.assert_is_instance(tmp_lines, list) - - -def test_validate_output(): - """Testing validation of output attribute.""" - # output must have type sym.Basic - with nose.tools.assert_raises(AttributeError): - solow.Model(output=invalid_output_1, params=valid_params) - - # output must be function of K, A, L - with nose.tools.assert_raises(AttributeError): - solow.Model(output=invalid_output_2, params=valid_params) - - -def test_validate_params(): - """Testing validation of params attribute.""" - # four different ways in which params can fail - invalid_params_0 = (1.0, 1.0, 0.02, 0.02, 0.15, 0.33, 0.03) - invalid_params_1 = {'A0': 1.0, 'g': -0.02, 'L0': 1.0, 'n': -0.02, 's': 0.15, - 'alpha': 0.33, 'delta': 0.03} - invalid_params_2 = {'A0': 1.0, 'g': 0.02, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'delta': -0.03} - invalid_params_3 = {'A0': 1.0, 'g': 0.02, 'L0': 1.0, 'n': 0.02, 's': -0.15, - 'alpha': 0.33, 'delta': 0.03} - invalid_params_4 = {'A0': -1.0, 'g': 0.02, 'L0': 1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'delta': 0.03} - invalid_params_3 = {'A0': 1.0, 'g': 0.02, 'L0': -1.0, 'n': 0.02, 's': 0.15, - 'alpha': 0.33, 'delta': 0.03} - - # params must be a dict - with nose.tools.assert_raises(AttributeError): - solow.Model(output=valid_output, params=invalid_params_0) - - # effective depreciation rate must be positive - with nose.tools.assert_raises(AttributeError): - solow.Model(output=valid_output, params=invalid_params_1) - - # physical depreciation rate must be positive - with nose.tools.assert_raises(AttributeError): - solow.Model(output=valid_output, params=invalid_params_2) - - # savings rate must be positive - with nose.tools.assert_raises(AttributeError): - solow.Model(output=valid_output, params=invalid_params_3) - - # initial condition for A must be positive - with nose.tools.assert_raises(AttributeError): - solow.Model(output=valid_output, params=invalid_params_4) - - -def test_evaluate_output_elasticity(): - """Testing computation of elasticity of output with respect to capital.""" - eps = 1e-1 - for g in np.linspace(eps, 0.05, 4): - for n in np.linspace(eps, 0.05, 4): - for s in np.linspace(eps, 1-eps, 4): - for alpha in np.linspace(eps, 1-eps, 4): - for delta in np.linspace(eps, 1-eps, 4): - - tmp_params = {'A0': 1.0, 'g': g, 'L0': 1.0, 'n': n, - 's': s, 'alpha': alpha, 'delta': delta} - tmp_mod = solow.Model(output=valid_output, - params=tmp_params) - - # use root finder to compute the steady state - tmp_k_star = tmp_mod.steady_state - - actual_elasticity = tmp_mod.evaluate_output_elasticity(tmp_k_star) - expected_elasticity = tmp_params['alpha'] - - # conduct the test - nose.tools.assert_almost_equals(actual_elasticity, - expected_elasticity) diff --git a/quantecon/util/__init__.py b/quantecon/util/__init__.py index 85ff46e77..39dcf0b0e 100644 --- a/quantecon/util/__init__.py +++ b/quantecon/util/__init__.py @@ -4,5 +4,6 @@ from .array import searchsorted from .external import jit, numba_installed +from .notebooks import fetch_nb_dependencies from .random import check_random_state from .timing import tic, tac, toc \ No newline at end of file diff --git a/quantecon/util/notebooks.py b/quantecon/util/notebooks.py new file mode 100644 index 000000000..7f5924d2a --- /dev/null +++ b/quantecon/util/notebooks.py @@ -0,0 +1,67 @@ +""" +Support functions to Support QuantEcon.notebooks + +The purpose of these utilities is to implement simple support functions to allow for automatic downloading +of any support files (python modules, or data) that may be required to run demonstration notebooks. + +Note +---- +Files on the REMOTE Github Server can be organised into folders but they will end up at the root level of +when downloaded as a support File + +"https://github.com/QuantEcon/QuantEcon.notebooks/raw/master/dependencies/mpi/something.py" --> ./somthing.py + +TODO +---- +1. Write Style guide for QuantEcon.notebook contributions +2. Write an interface for Dat Server +3. Platform Agnostic (replace wget usage) + +""" + +import os +import requests + +#-Remote Structure-# +REPO = "https://github.com/QuantEcon/QuantEcon.notebooks" +RAW = "raw" +BRANCH = "master" +DEPS = "dependencies" #Hard Coded Dependencies Folder on QuantEcon.notebooks + +def fetch_nb_dependencies(files, repo=REPO, raw=RAW, branch=BRANCH, deps=DEPS, verbose=True): + """ + Retrieve raw files from QuantEcon.notebooks Github repo + + Parameters + ---------- + file_list list or dict + A list of files to specify a collection of filenames + A dict of dir : list(files) to specify a directory + repo str, optional(default=REPO) + branch str, optional(default=BRANCH) + deps str, optional(default=DEPS) + verbose bool, optional(default=True) + + TODO + ---- + 1. Should we update this to allow people to specify their own folders on a different GitHub repo? + + """ + + #-Generate Common Data Structure-# + if type(files) == list: + files = {"" : files} + + #-Obtain each requested file-# + for directory in files.keys(): + if directory != "": + if verbose: print("Parsing directory: %s") + for fl in files[directory]: + if directory != "": + fl = directory+"/"+fl + if verbose: print("Fetching file: %s"%fl) + url = "/".join([repo,raw,branch,deps,fl]) + r = requests.get(url) + with open(fl, "wb") as fl: + fl.write(r.content) + diff --git a/quantecon/version.py b/quantecon/version.py index 61f299333..c9eab20eb 100644 --- a/quantecon/version.py +++ b/quantecon/version.py @@ -1,4 +1,4 @@ """ This is a VERSION file and should NOT be manually altered """ -version = '0.2.0' \ No newline at end of file +version = '0.3.1' \ No newline at end of file diff --git a/scripts/common.py b/scripts/common.py deleted file mode 100644 index d95a97d74..000000000 --- a/scripts/common.py +++ /dev/null @@ -1,20 +0,0 @@ -""" -Provides Context Manager for Test Scripts -""" - -import sys - -class RedirectStdStreams(object): - def __init__(self, stdout=None, stderr=None): - self._stdout = stdout or sys.stdout - self._stderr = stderr or sys.stderr - - def __enter__(self): - self.old_stdout, self.old_stderr = sys.stdout, sys.stderr - self.old_stdout.flush(); self.old_stderr.flush() - sys.stdout, sys.stderr = self._stdout, self._stderr - - def __exit__(self, exc_type, exc_value, traceback): - self._stdout.flush(); self._stderr.flush() - sys.stdout = self.old_stdout - sys.stderr = self.old_stderr \ No newline at end of file diff --git a/scripts/example-tests.log b/scripts/example-tests.log deleted file mode 100644 index d2d250fd8..000000000 --- a/scripts/example-tests.log +++ /dev/null @@ -1,200 +0,0 @@ ----Executing '3dplot.py'--- ----END '3dplot.py'--- ----Executing '3dvec.py'--- ----END '3dvec.py'--- ----Executing 'amss.py'--- ----END 'amss.py'--- ----Executing 'amss_figures.py'--- ----END 'amss_figures.py'--- ----Executing 'ar1_acov.py'--- ----END 'ar1_acov.py'--- ----Executing 'ar1_cycles.py'--- ----END 'ar1_cycles.py'--- ----Executing 'ar1_sd.py'--- ----END 'ar1_sd.py'--- ----Executing 'beta-binomial.py'--- ----END 'beta-binomial.py'--- ----Executing 'bifurcation_diagram.py'--- ----END 'bifurcation_diagram.py'--- ----Executing 'binom_df.py'--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/matplotlib/figure.py:387: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure - "matplotlib is currently using a non-GUI backend, " ----END 'binom_df.py'--- ----Executing 'bisection.py'--- ----END 'bisection.py'--- ----Executing 'boxplot_example.py'--- ----END 'boxplot_example.py'--- ----Executing 'career_vf_plot.py'--- ----END 'career_vf_plot.py'--- ----Executing 'cauchy_samples.py'--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/numpy/core/_methods.py:59: RuntimeWarning: Mean of empty slice. - warnings.warn("Mean of empty slice.", RuntimeWarning) -/home/matthewmckay/anaconda/lib/python2.7/site-packages/numpy/core/_methods.py:71: RuntimeWarning: invalid value encountered in double_scalars - ret = ret.dtype.type(ret / rcount) -/home/matthewmckay/anaconda/lib/python2.7/site-packages/matplotlib/figure.py:387: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure - "matplotlib is currently using a non-GUI backend, " ----END 'cauchy_samples.py'--- ----Executing 'chaos_class.py'--- ----END 'chaos_class.py'--- ----Executing 'chaotic_ts.py'--- ----END 'chaotic_ts.py'--- ----Executing 'clt3d.py'--- ----END 'clt3d.py'--- ----Executing 'consumer.py'--- ----END 'consumer.py'--- ----Executing 'dice.py'--- ----END 'dice.py'--- ----Executing 'duopoly_lqnash.py'--- ----END 'duopoly_lqnash.py'--- ----Executing 'duopoly_mpe.py'--- ----END 'duopoly_mpe.py'--- ----Executing 'duopoly_mpe_dynamics.py'--- ----END 'duopoly_mpe_dynamics.py'--- ----Executing 'eigenvec.py'--- ----END 'eigenvec.py'--- ----Executing 'evans_sargent.py'--- ----END 'evans_sargent.py'--- ----Executing 'evans_sargent_plot1.py'--- ----END 'evans_sargent_plot1.py'--- ----Executing 'evans_sargent_plot2.py'--- ----END 'evans_sargent_plot2.py'--- ----Executing 'gaussian_contours.py'--- ----END 'gaussian_contours.py'--- ----Executing 'ifp_savings_plots.py'--- ----END 'ifp_savings_plots.py'--- ----Executing 'illustrates_clt.py'--- ----END 'illustrates_clt.py'--- ----Executing 'illustrates_lln.py'--- ----END 'illustrates_lln.py'--- ----Executing 'jv_test.py'--- ----END 'jv_test.py'--- ----Executing 'lakemodel_example.py'--- ----END 'lakemodel_example.py'--- ----Executing 'lin_interp_3d_plot.py'--- ----END 'lin_interp_3d_plot.py'--- ----Executing 'linapprox.py'--- ----END 'linapprox.py'--- ----Executing 'lq_permanent_1.py'--- ----END 'lq_permanent_1.py'--- ----Executing 'lqramsey.py'--- ----END 'lqramsey.py'--- ----Executing 'lqramsey_ar1.py'--- ----END 'lqramsey_ar1.py'--- ----Executing 'lqramsey_discrete.py'--- ----END 'lqramsey_discrete.py'--- ----Executing 'lucas_stokey.py'--- ----END 'lucas_stokey.py'--- ----Executing 'lucas_tree_price1.py'--- ----END 'lucas_tree_price1.py'--- ----Executing 'main_LS.py'--- ----END 'main_LS.py'--- ----Executing 'market.py'--- ----END 'market.py'--- ----Executing 'market_deadweight.py'--- ----END 'market_deadweight.py'--- ----Executing 'mc_convergence_plot.py'--- ----END 'mc_convergence_plot.py'--- ----Executing 'nds.py'--- ----END 'nds.py'--- ----Executing 'nx_demo.py'--- ----END 'nx_demo.py'--- ----Executing 'odu_plot_densities.py'--- ----END 'odu_plot_densities.py'--- ----Executing 'odu_vfi_plots.py'--- ----END 'odu_vfi_plots.py'--- ----Executing 'oligopoly.py'--- ----END 'oligopoly.py'--- ----Executing 'optgrowth_v0.py'--- ----END 'optgrowth_v0.py'--- ----Executing 'paths_and_hist.py'--- ----END 'paths_and_hist.py'--- ----Executing 'paths_and_stationarity.py'--- ----END 'paths_and_stationarity.py'--- ----Executing 'perm_inc_figs.py'--- ----END 'perm_inc_figs.py'--- ----Executing 'perm_inc_ir.py'--- ----END 'perm_inc_ir.py'--- ----Executing 'plot_example_1.py'--- ----END 'plot_example_1.py'--- ----Executing 'plot_example_2.py'--- ----END 'plot_example_2.py'--- ----Executing 'plot_example_3.py'--- ----END 'plot_example_3.py'--- ----Executing 'plot_example_4.py'--- ----END 'plot_example_4.py'--- ----Executing 'plot_example_5.py'--- ----END 'plot_example_5.py'--- ----Executing 'plot_market.py'--- ----END 'plot_market.py'--- ----Executing 'preim1.py'--- ----END 'preim1.py'--- ----Executing 'pylab_eg.py'--- ----END 'pylab_eg.py'--- ----Executing 'pylab_eg2.py'--- ----END 'pylab_eg2.py'--- ----Executing 'qm_plot.py'--- ----END 'qm_plot.py'--- ----Executing 'qs.py'--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/matplotlib/figure.py:387: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure - "matplotlib is currently using a non-GUI backend, " ----END 'qs.py'--- ----Executing 'quadmap_class.py'--- ----END 'quadmap_class.py'--- ----Executing 'robust_monopolist.py'--- -Traceback (most recent call last): - File "_robust_monopolist.py", line 132, in - Po, Fo, do = optimal_lq.stationary_values() - File "/home/matthewmckay/anaconda/lib/python2.7/site-packages/quantecon/lqcontrol.py", line 209, in stationary_values - P = solve_discrete_riccati(A0, B0, R, Q, N) - File "/home/matthewmckay/anaconda/lib/python2.7/site-packages/quantecon/matrix_eqn.py", line 197, in solve_discrete_riccati - raise ValueError(fail_msg.format(i)) -ValueError: Convergence failed after 5001 iterations. ----END 'robust_monopolist.py'--- ----Executing 'sine2.py'--- ----END 'sine2.py'--- ----Executing 'sine3.py'--- ----END 'sine3.py'--- ----Executing 'sine4.py'--- ----END 'sine4.py'--- ----Executing 'sine5.py'--- ----END 'sine5.py'--- ----Executing 'six_hists.py'--- ----END 'six_hists.py'--- ----Executing 'solow.py'--- ----END 'solow.py'--- ----Executing 'stochasticgrowth.py'--- ----END 'stochasticgrowth.py'--- ----Executing 'subplots.py'--- ----END 'subplots.py'--- ----Executing 'temp.py'--- ----END 'temp.py'--- ----Executing 'test_program_1.py'--- ----END 'test_program_1.py'--- ----Executing 'test_program_2.py'--- ----END 'test_program_2.py'--- ----Executing 'test_program_3.py'--- ----END 'test_program_3.py'--- ----Executing 'test_program_4.py'--- ----END 'test_program_4.py'--- ----Executing 'test_program_5.py'--- ----END 'test_program_5.py'--- ----Executing 'test_program_5_short.py'--- ----END 'test_program_5_short.py'--- ----Executing 'test_program_6.py'--- ----END 'test_program_6.py'--- ----Executing 'tsh_hg.py'--- ----END 'tsh_hg.py'--- ----Executing 'us_cities.py'--- ----END 'us_cities.py'--- ----Executing 'utilities.py'--- ----END 'utilities.py'--- ----Executing 'vecs.py'--- ----END 'vecs.py'--- ----Executing 'vecs2.py'--- ----END 'vecs2.py'--- ----Executing 'wb_download.py'--- ----END 'wb_download.py'--- ----Executing 'web_network.py'--- ----END 'web_network.py'--- ----Executing 'white_noise_plot.py'--- ----END 'white_noise_plot.py'--- diff --git a/scripts/solutions-tests.log b/scripts/solutions-tests.log deleted file mode 100644 index fb0e79e89..000000000 --- a/scripts/solutions-tests.log +++ /dev/null @@ -1,3357 +0,0 @@ ----> Executing 'arellano_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:42:10 PM INFO: Reading notebook arellano_solutions.ipynb -09/11/2015 03:42:11 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:42:12 PM INFO: Cell returned -09/11/2015 03:42:12 PM INFO: Running cell: -from __future__ import division -import numpy as np -import matplotlib.pyplot as plt -import quantecon as qe -from quantecon.models import Arellano_Economy - -09/11/2015 03:42:15 PM INFO: Cell returned -09/11/2015 03:42:15 PM INFO: Running cell: -ae = Arellano_Economy(beta=.953, # time discount rate - gamma=2., # risk aversion - r=0.017, # international interest rate - rho=.945, # persistence in output - eta=0.025, # st dev of output shock - theta=0.282, # prob of regaining access - ny=21, # number of points in y grid - nB=251, # number of points in B grid - tol=1e-8, # error tolerance in iteration - maxit=10000) - -09/11/2015 03:42:30 PM INFO: Cell returned -09/11/2015 03:42:30 PM INFO: Running cell: - -# Create "Y High" and "Y Low" values as 5% devs from mean -high, low = np.mean(ae.ygrid)*1.05, np.mean(ae.ygrid)*.95 -iy_high, iy_low = (np.searchsorted(ae.ygrid, x) for x in (high, low)) - -fig, ax = plt.subplots(figsize=(10, 6.5)) -ax.set_title("Bond price schedule $q(y, B')$") - -# Extract a suitable plot grid -x = [] -q_low = [] -q_high = [] -for i in range(ae.nB): - b = ae.Bgrid[i] - if -0.35 <= b <= 0: # To match fig 3 of Arellano - x.append(b) - q_low.append(ae.Q[iy_low, i]) - q_high.append(ae.Q[iy_high, i]) -ax.plot(x, q_high, label=r"$y_H$", lw=2, alpha=0.7) -ax.plot(x, q_low, label=r"$y_L$", lw=2, alpha=0.7) -ax.set_xlabel(r"$B'$") -ax.legend(loc='upper left', frameon=False) -plt.show() - -09/11/2015 03:42:31 PM INFO: Cell returned -09/11/2015 03:42:31 PM INFO: Running cell: - -# Create "Y High" and "Y Low" values as 5% devs from mean -high, low = np.mean(ae.ygrid)*1.05, np.mean(ae.ygrid)*.95 -iy_high, iy_low = (np.searchsorted(ae.ygrid, x) for x in (high, low)) - -fig, ax = plt.subplots(figsize=(10, 6.5)) -ax.set_title("Value Functions") -ax.plot(ae.Bgrid, ae.V[iy_high], label=r"$y_H$", lw=2, alpha=0.7) -ax.plot(ae.Bgrid, ae.V[iy_low], label=r"$y_L$", lw=2, alpha=0.7) -ax.legend(loc='upper left') -ax.set_xlabel(r"$B$") -ax.set_ylabel(r"$V(y, B)$") -ax.set_xlim(ae.Bgrid.min(), ae.Bgrid.max()) -plt.show() - -09/11/2015 03:42:32 PM INFO: Cell returned -09/11/2015 03:42:32 PM INFO: Running cell: - -xx, yy = ae.Bgrid, ae.ygrid -zz = ae.default_prob - -# Create figure -fig, ax = plt.subplots(figsize=(10, 6.5)) -fig.suptitle("Probability of Default") -hm = ax.pcolormesh(xx, yy, zz) -cax = fig.add_axes([.92, .1, .02, .8]) -fig.colorbar(hm, cax=cax) -ax.axis([xx.min(), 0.05, yy.min(), yy.max()]) -ax.set_xlabel(r"$B'$") -ax.set_ylabel(r"$y$") -plt.show() - -09/11/2015 03:42:32 PM INFO: Cell returned -09/11/2015 03:42:32 PM INFO: Running cell: -T = 250 -y_vec, B_vec, q_vec, default_vec = ae.simulate(T) - -# Pick up default start and end dates -start_end_pairs = [] -i = 0 -while i < len(default_vec): - if default_vec[i] == 0: - i += 1 - else: - # If we get to here we're in default - start_default = i - while i < len(default_vec) and default_vec[i] == 1: - i += 1 - end_default = i - 1 - start_end_pairs.append((start_default, end_default)) - -plot_series = y_vec, B_vec, q_vec -titles = 'output', 'foreign assets', 'bond price' - -fig, axes = plt.subplots(len(plot_series), 1, figsize=(10, 12)) -p_args = {'lw': 2, 'alpha': 0.7} -fig.subplots_adjust(hspace=0.3) - -for ax, series, title in zip(axes, plot_series, titles): - # determine suitable y limits - s_max, s_min = max(series), min(series) - s_range = s_max - s_min - y_max = s_max + s_range * 0.1 - y_min = s_min - s_range * 0.1 - ax.set_ylim(y_min, y_max) - for pair in start_end_pairs: - ax.fill_between(pair, (y_min, y_min), (y_max, y_max), color='k', alpha=0.3) - - ax.grid() - ax.set_title(title) - ax.plot(range(T), series, **p_args) - ax.set_xlabel(r"time") - -plt.show() - -09/11/2015 03:42:34 PM INFO: Cell returned -09/11/2015 03:42:34 PM INFO: Running cell: - - -09/11/2015 03:42:34 PM INFO: Cell returned -09/11/2015 03:42:34 PM INFO: Shutdown kernel ----> END 'arellano_solutions.ipynb' <--- - ----> Executing 'asset_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:42:35 PM INFO: Reading notebook asset_solutions.ipynb -09/11/2015 03:42:36 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:42:36 PM INFO: Cell returned -09/11/2015 03:42:36 PM INFO: Running cell: -from __future__ import division # Omit for Python 3.x -import numpy as np -import matplotlib.pyplot as plt -from quantecon.models import AssetPrices - -09/11/2015 03:42:38 PM INFO: Cell returned -09/11/2015 03:42:38 PM INFO: Running cell: -# == Define primitives == # -n = 5 -P = 0.0125 * np.ones((n, n)) -P += np.diag(0.95 - 0.0125 * np.ones(5)) -s = np.array([1.05, 1.025, 1.0, 0.975, 0.95]) -gamma = 2.0 -beta = 0.94 -zeta = 1.0 - -ap = AssetPrices(beta, P, s, gamma) - -v = ap.tree_price() -print("Lucas Tree Prices: ", v) - -v_consol = ap.consol_price(zeta) -print("Consol Bond Prices: ", v_consol) - -P_tilde = P * s**(1-gamma) -temp = beta * P_tilde.dot(v) + beta * P_tilde.dot(np.ones(n)) -print("Should be 0: ", v - temp) - -p_s = 150.0 -w_bar, w_bars = ap.call_option(zeta, p_s, T = [10,20,30]) - - -09/11/2015 03:42:38 PM INFO: Cell returned -09/11/2015 03:42:38 PM INFO: Running cell: - - -09/11/2015 03:42:38 PM INFO: Cell returned -09/11/2015 03:42:38 PM INFO: Shutdown kernel ----> END 'asset_solutions.ipynb' <--- - ----> Executing 'career_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:42:39 PM INFO: Reading notebook career_solutions.ipynb -09/11/2015 03:42:40 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:42:40 PM INFO: Cell returned -09/11/2015 03:42:40 PM INFO: Running cell: -import numpy as np -import matplotlib.pyplot as plt -from quantecon import DiscreteRV, compute_fixed_point -from quantecon.models import CareerWorkerProblem - -09/11/2015 03:42:42 PM INFO: Cell returned -09/11/2015 03:42:42 PM INFO: Running cell: -wp = CareerWorkerProblem() -v_init = np.ones((wp.N, wp.N))*100 -v = compute_fixed_point(wp.bellman_operator, v_init, verbose=False) -optimal_policy = wp.get_greedy(v) -F = DiscreteRV(wp.F_probs) -G = DiscreteRV(wp.G_probs) - -def gen_path(T=20): - i = j = 0 - theta_index = [] - epsilon_index = [] - for t in range(T): - if optimal_policy[i, j] == 1: # Stay put - pass - elif optimal_policy[i, j] == 2: # New job - j = int(G.draw()) - else: # New life - i, j = int(F.draw()), int(G.draw()) - theta_index.append(i) - epsilon_index.append(j) - return wp.theta[theta_index], wp.epsilon[epsilon_index] - -theta_path, epsilon_path = gen_path() - -fig, axes = plt.subplots(2, 1, figsize=(10, 8)) -for ax in axes: - ax.plot(epsilon_path, label='epsilon') - ax.plot(theta_path, label='theta') - ax.legend(loc='lower right') - -plt.show() - - - -09/11/2015 03:42:45 PM INFO: Cell returned -09/11/2015 03:42:45 PM INFO: Running cell: - -wp = CareerWorkerProblem() -v_init = np.ones((wp.N, wp.N))*100 -v = compute_fixed_point(wp.bellman_operator, v_init) -optimal_policy = wp.get_greedy(v) -F = DiscreteRV(wp.F_probs) -G = DiscreteRV(wp.G_probs) - -def gen_first_passage_time(): - t = 0 - i = j = 0 - while 1: - if optimal_policy[i, j] == 1: # Stay put - return t - elif optimal_policy[i, j] == 2: # New job - j = int(G.draw()) - else: # New life - i, j = int(F.draw()), int(G.draw()) - t += 1 - -M = 25000 # Number of samples -samples = np.empty(M) -for i in range(M): - samples[i] = gen_first_passage_time() -print(np.median(samples)) - - -09/11/2015 03:42:53 PM INFO: Cell returned -09/11/2015 03:42:53 PM INFO: Running cell: -from matplotlib import cm - -wp = CareerWorkerProblem() -v_init = np.ones((wp.N, wp.N))*100 -v = compute_fixed_point(wp.bellman_operator, v_init) -optimal_policy = wp.get_greedy(v) - -fig, ax = plt.subplots(figsize=(6,6)) -tg, eg = np.meshgrid(wp.theta, wp.epsilon) -lvls=(0.5, 1.5, 2.5, 3.5) -ax.contourf(tg, eg, optimal_policy.T, levels=lvls, cmap=cm.winter, alpha=0.5) -ax.contour(tg, eg, optimal_policy.T, colors='k', levels=lvls, linewidths=2) -ax.set_xlabel('theta', fontsize=14) -ax.set_ylabel('epsilon', fontsize=14) -ax.text(1.8, 2.5, 'new life', fontsize=14) -ax.text(4.5, 2.5, 'new job', fontsize=14, rotation='vertical') -ax.text(4.0, 4.5, 'stay put', fontsize=14) - - - -09/11/2015 03:42:57 PM INFO: Cell returned -09/11/2015 03:42:57 PM INFO: Shutdown kernel ----> END 'career_solutions.ipynb' <--- - ----> Executing 'estspec_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:42:59 PM INFO: Reading notebook estspec_solutions.ipynb -09/11/2015 03:43:00 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:43:00 PM INFO: Cell returned -09/11/2015 03:43:00 PM INFO: Running cell: -import numpy as np -import matplotlib.pyplot as plt -from quantecon import ARMA, periodogram, ar_periodogram - -09/11/2015 03:43:02 PM INFO: Cell returned -09/11/2015 03:43:02 PM INFO: Running cell: - -## Data -n = 400 -phi = 0.5 -theta = 0, -0.8 -lp = ARMA(phi, theta) -X = lp.simulation(ts_length=n) - -fig, ax = plt.subplots(3, 1, figsize=(10, 12)) - -for i, wl in enumerate((15, 55, 175)): # window lengths - - x, y = periodogram(X) - ax[i].plot(x, y, 'b-', lw=2, alpha=0.5, label='periodogram') - - x_sd, y_sd = lp.spectral_density(two_pi=False, res=120) - ax[i].plot(x_sd, y_sd, 'r-', lw=2, alpha=0.8, label='spectral density') - - x, y_smoothed = periodogram(X, window='hamming', window_len=wl) - ax[i].plot(x, y_smoothed, 'k-', lw=2, label='smoothed periodogram') - - ax[i].legend() - ax[i].set_title('window length = {}'.format(wl)) - - -09/11/2015 03:43:05 PM INFO: Cell returned -09/11/2015 03:43:05 PM INFO: Running cell: -lp = ARMA(-0.9) -wl = 65 - - -fig, ax = plt.subplots(3, 1, figsize=(10,12)) - -for i in range(3): - X = lp.simulation(ts_length=150) - ax[i].set_xlim(0, np.pi) - - x_sd, y_sd = lp.spectral_density(two_pi=False, res=180) - ax[i].semilogy(x_sd, y_sd, 'r-', lw=2, alpha=0.75, label='spectral density') - - x, y_smoothed = periodogram(X, window='hamming', window_len=wl) - ax[i].semilogy(x, y_smoothed, 'k-', lw=2, alpha=0.75, label='standard smoothed periodogram') - - x, y_ar = ar_periodogram(X, window='hamming', window_len=wl) - ax[i].semilogy(x, y_ar, 'b-', lw=2, alpha=0.75, label='AR smoothed periodogram') - - ax[i].legend(loc='upper left') - - - - -09/11/2015 03:43:15 PM INFO: Cell returned -09/11/2015 03:43:15 PM INFO: Shutdown kernel ----> END 'estspec_solutions.ipynb' <--- - ----> Executing 'finite_mc_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:43:17 PM INFO: Reading notebook finite_mc_solutions.ipynb -09/11/2015 03:43:19 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:43:19 PM INFO: Cell returned -09/11/2015 03:43:19 PM INFO: Running cell: -from __future__ import print_function, division # Omit for Python 3.x -import numpy as np -import matplotlib.pyplot as plt -from quantecon import mc_compute_stationary, mc_sample_path - - -09/11/2015 03:43:22 PM INFO: Cell returned -09/11/2015 03:43:22 PM INFO: Running cell: - -alpha = beta = 0.1 -N = 10000 -p = beta / (alpha + beta) - -P = ((1 - alpha, alpha), # Careful: P and p are distinct - (beta, 1 - beta)) -P = np.array(P) - -fig, ax = plt.subplots(figsize=(9, 6)) -ax.set_ylim(-0.25, 0.25) -ax.grid() -ax.hlines(0, 0, N, lw=2, alpha=0.6) # Horizonal line at zero - -for x0, col in ((0, 'blue'), (1, 'green')): - # == Generate time series for worker that starts at x0 == # - X = mc_sample_path(P, x0, N) - # == Compute fraction of time spent unemployed, for each n == # - X_bar = (X == 0).cumsum() / (1 + np.arange(N, dtype=float)) - # == Plot == # - ax.fill_between(range(N), np.zeros(N), X_bar - p, color=col, alpha=0.1) - ax.plot(X_bar - p, color=col, label=r'$X_0 = \, {} $'.format(x0)) - ax.plot(X_bar - p, 'k-', alpha=0.6) # Overlay in black--make lines clearer - -ax.legend(loc='upper right') - - - -09/11/2015 03:43:23 PM INFO: Cell returned -09/11/2015 03:43:23 PM INFO: Running cell: -%%file web_graph_data.txt -a -> d; -a -> f; -b -> j; -b -> k; -b -> m; -c -> c; -c -> g; -c -> j; -c -> m; -d -> f; -d -> h; -d -> k; -e -> d; -e -> h; -e -> l; -f -> a; -f -> b; -f -> j; -f -> l; -g -> b; -g -> j; -h -> d; -h -> g; -h -> l; -h -> m; -i -> g; -i -> h; -i -> n; -j -> e; -j -> i; -j -> k; -k -> n; -l -> m; -m -> g; -n -> c; -n -> j; -n -> m; - - -09/11/2015 03:43:23 PM INFO: Cell returned -09/11/2015 03:43:23 PM INFO: Running cell: -""" -Return list of pages, ordered by rank -""" -import numpy as np -from operator import itemgetter -import re - -infile = 'web_graph_data.txt' -alphabet = 'abcdefghijklmnopqrstuvwxyz' - -n = 14 # Total number of web pages (nodes) - -# == Create a matrix Q indicating existence of links == # -# * Q[i, j] = 1 if there is a link from i to j -# * Q[i, j] = 0 otherwise -Q = np.zeros((n, n), dtype=int) -f = open(infile, 'r') -edges = f.readlines() -f.close() -for edge in edges: - from_node, to_node = re.findall('\w', edge) - i, j = alphabet.index(from_node), alphabet.index(to_node) - Q[i, j] = 1 -# == Create the corresponding Markov matrix P == # -P = np.empty((n, n)) -for i in range(n): - P[i,:] = Q[i,:] / Q[i,:].sum() -# == Compute the stationary distribution r == # -r = mc_compute_stationary(P)[0] -ranked_pages = {alphabet[i] : r[i] for i in range(n)} -# == Print solution, sorted from highest to lowest rank == # -print('Rankings\n ***') -for name, rank in sorted(ranked_pages.items(), key=itemgetter(1), reverse=1): - print('{0}: {1:.4}'.format(name, rank)) - - - -09/11/2015 03:43:24 PM INFO: Cell returned -09/11/2015 03:43:24 PM INFO: Running cell: - - -09/11/2015 03:43:24 PM INFO: Cell returned -09/11/2015 03:43:24 PM INFO: Running cell: - - -09/11/2015 03:43:24 PM INFO: Cell returned -09/11/2015 03:43:24 PM INFO: Running cell: - - -09/11/2015 03:43:24 PM INFO: Cell returned -09/11/2015 03:43:24 PM INFO: Shutdown kernel ----> END 'finite_mc_solutions.ipynb' <--- - ----> Executing 'ifp_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:43:26 PM INFO: Reading notebook ifp_solutions.ipynb -09/11/2015 03:43:27 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:43:27 PM INFO: Cell returned -09/11/2015 03:43:27 PM INFO: Running cell: -import numpy as np -import matplotlib.pyplot as plt -from quantecon import compute_fixed_point -from quantecon.models import ConsumerProblem - -09/11/2015 03:43:29 PM INFO: Cell returned -09/11/2015 03:43:29 PM INFO: Running cell: -cp = ConsumerProblem() -K = 80 - -# Bellman iteration -V, c = cp.initialize() -print("Starting value function iteration") -for i in range(K): - # print "Current iterate = " + str(i) - V = cp.bellman_operator(V) -c1 = cp.bellman_operator(V, return_policy=True) - -# Policy iteration -print("Starting policy function iteration") -V, c2 = cp.initialize() -for i in range(K): - # print "Current iterate = " + str(i) - c2 = cp.coleman_operator(c2) - -fig, ax = plt.subplots(figsize=(10, 8)) -ax.plot(cp.asset_grid, c1[:, 0], label='value function iteration') -ax.plot(cp.asset_grid, c2[:, 0], label='policy function iteration') -ax.set_xlabel('asset level') -ax.set_ylabel('consumption (low income)') -ax.legend(loc='upper left') -plt.show() - -09/11/2015 03:43:42 PM INFO: Cell returned -09/11/2015 03:43:42 PM INFO: Running cell: - -r_vals = np.linspace(0, 0.04, 4) - -fig, ax = plt.subplots(figsize=(10, 8)) -for r_val in r_vals: - cp = ConsumerProblem(r=r_val) - v_init, c_init = cp.initialize() - c = compute_fixed_point(cp.coleman_operator, c_init, verbose=False) - ax.plot(cp.asset_grid, c[:, 0], label=r'$r = %.3f$' % r_val) - -ax.set_xlabel('asset level') -ax.set_ylabel('consumption (low income)') -ax.legend(loc='upper left') -plt.show() - -09/11/2015 03:43:52 PM INFO: Cell returned -09/11/2015 03:43:52 PM INFO: Running cell: - -from scipy import interp -from quantecon import mc_sample_path - -def compute_asset_series(cp, T=500000, verbose=False): - """ - Simulates a time series of length T for assets, given optimal savings - behavior. Parameter cp is an instance of consumerProblem - """ - - Pi, z_vals, R = cp.Pi, cp.z_vals, cp.R # Simplify names - v_init, c_init = cp.initialize() - c = compute_fixed_point(cp.coleman_operator, c_init, verbose=verbose) - cf = lambda a, i_z: interp(a, cp.asset_grid, c[:, i_z]) - a = np.zeros(T+1) - z_seq = mc_sample_path(Pi, sample_size=T) - for t in range(T): - i_z = z_seq[t] - a[t+1] = R * a[t] + z_vals[i_z] - cf(a[t], i_z) - return a - -cp = ConsumerProblem(r=0.03, grid_max=4) -a = compute_asset_series(cp) -fig, ax = plt.subplots(figsize=(10, 8)) -ax.hist(a, bins=20, alpha=0.5, normed=True) -ax.set_xlabel('assets') -ax.set_xlim(-0.05, 0.75) -plt.show() - -09/11/2015 03:44:00 PM INFO: Cell returned -09/11/2015 03:44:00 PM INFO: Running cell: - -M = 25 -r_vals = np.linspace(0, 0.04, M) -fig, ax = plt.subplots(figsize=(10,8)) - -for b in (1, 3): - asset_mean = [] - for r_val in r_vals: - cp = ConsumerProblem(r=r_val, b=b) - mean = np.mean(compute_asset_series(cp, T=250000)) - asset_mean.append(mean) - ax.plot(asset_mean, r_vals, label=r'$b = %d$' % b) - print("Finished iteration b=%i" % b) - -ax.set_yticks(np.arange(.0, 0.045, .01)) -ax.set_xticks(np.arange(-3, 2, 1)) -ax.set_xlabel('capital') -ax.set_ylabel('interest rate') -ax.grid(True) -ax.legend(loc='upper left') -plt.show() - -09/11/2015 03:47:07 PM INFO: Cell returned -09/11/2015 03:47:07 PM INFO: Shutdown kernel ----> END 'ifp_solutions.ipynb' <--- - ----> Executing 'jv_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:47:09 PM INFO: Reading notebook jv_solutions.ipynb -09/11/2015 03:47:10 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:47:10 PM INFO: Cell returned -09/11/2015 03:47:10 PM INFO: Running cell: -import numpy as np -import matplotlib.pyplot as plt -import random -from quantecon import compute_fixed_point -from quantecon.models import JvWorker - -09/11/2015 03:47:12 PM INFO: Cell returned -09/11/2015 03:47:12 PM INFO: Running cell: - -wp = JvWorker(grid_size=25) -G, pi, F = wp.G, wp.pi, wp.F # Simplify names - -v_init = wp.x_grid * 0.5 -print("Computing value function") -V = compute_fixed_point(wp.bellman_operator, v_init, max_iter=40, verbose=False) -print("Computing policy functions") -s_policy, phi_policy = wp.bellman_operator(V, return_policies=True) - -# Turn the policy function arrays into actual functions -s = lambda y: np.interp(y, wp.x_grid, s_policy) -phi = lambda y: np.interp(y, wp.x_grid, phi_policy) - -def h(x, b, U): - return (1 - b) * G(x, phi(x)) + b * max(G(x, phi(x)), U) - -plot_grid_max, plot_grid_size = 1.2, 100 -plot_grid = np.linspace(0, plot_grid_max, plot_grid_size) -fig, ax = plt.subplots(figsize=(8,8)) -ax.set_xlim(0, plot_grid_max) -ax.set_ylim(0, plot_grid_max) -ticks = (0.25, 0.5, 0.75, 1.0) -ax.set_xticks(ticks) -ax.set_yticks(ticks) -ax.set_xlabel(r'$x_t$', fontsize=16) -ax.set_ylabel(r'$x_{t+1}$', fontsize=16, rotation='horizontal') - -ax.plot(plot_grid, plot_grid, 'k--') # 45 degree line -for x in plot_grid: - for i in range(50): - b = 1 if random.uniform(0, 1) < pi(s(x)) else 0 - U = wp.F.rvs(1) - y = h(x, b, U) - ax.plot(x, y, 'go', alpha=0.25) - -plt.show() - -09/11/2015 03:47:46 PM INFO: Cell returned -09/11/2015 03:47:46 PM INFO: Running cell: - -wp = JvWorker(grid_size=25) - -def xbar(phi): - return (wp.A * phi**wp.alpha)**(1 / (1 - wp.alpha)) - -phi_grid = np.linspace(0, 1, 100) -fig, ax = plt.subplots(figsize=(9, 7)) -ax.set_xlabel(r'$\phi$', fontsize=16) -ax.plot(phi_grid, [xbar(phi) * (1 - phi) for phi in phi_grid], 'b-', label=r'$w^*(\phi)$') -ax.legend(loc='upper left') - -plt.show() - -09/11/2015 03:47:47 PM INFO: Cell returned -09/11/2015 03:47:47 PM INFO: Shutdown kernel ----> END 'jv_solutions.ipynb' <--- - ----> Executing 'kalman_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:47:49 PM INFO: Reading notebook kalman_solutions.ipynb -09/11/2015 03:47:50 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:47:50 PM INFO: Cell returned -09/11/2015 03:47:50 PM INFO: Running cell: -import numpy as np -import matplotlib.pyplot as plt -from quantecon import Kalman -from quantecon import LinearStateSpace -from scipy.stats import norm - -09/11/2015 03:47:51 PM INFO: Cell returned -09/11/2015 03:47:51 PM INFO: Running cell: -# == parameters == # -theta = 10 # Constant value of state x_t -A, C, G, H = 1, 0, 1, 1 -ss = LinearStateSpace(A, C, G, H, mu_0=theta) - -# == set prior, initialize kalman filter == # -x_hat_0, Sigma_0 = 8, 1 -kalman = Kalman(ss, x_hat_0, Sigma_0) - -# == draw observations of y from state space model == # -N = 5 -x, y = ss.simulate(N) -y = y.flatten() - -# == set up plot == # -fig, ax = plt.subplots(figsize=(10,8)) -xgrid = np.linspace(theta - 5, theta + 2, 200) - -for i in range(N): - # == record the current predicted mean and variance == # - m, v = [float(z) for z in (kalman.x_hat, kalman.Sigma)] - # == plot, update filter == # - ax.plot(xgrid, norm.pdf(xgrid, loc=m, scale=np.sqrt(v)), label=r'$t=%d$' % i) - kalman.update(y[i]) - -ax.set_title(r'First %d densities when $\theta = %.1f$' % (N, theta)) -ax.legend(loc='upper left') - -09/11/2015 03:47:53 PM INFO: Cell returned -09/11/2015 03:47:53 PM INFO: Running cell: -from scipy.integrate import quad - -epsilon = 0.1 -theta = 10 # Constant value of state x_t -A, C, G, H = 1, 0, 1, 1 -ss = LinearStateSpace(A, C, G, H, mu_0=theta) - -x_hat_0, Sigma_0 = 8, 1 -kalman = Kalman(ss, x_hat_0, Sigma_0) - -T = 600 -z = np.empty(T) -x, y = ss.simulate(T) -y = y.flatten() - -for t in range(T): - # Record the current predicted mean and variance, and plot their densities - m, v = [float(temp) for temp in (kalman.x_hat, kalman.Sigma)] - - f = lambda x: norm.pdf(x, loc=m, scale=np.sqrt(v)) - integral, error = quad(f, theta - epsilon, theta + epsilon) - z[t] = 1 - integral - - kalman.update(y[t]) - -fig, ax = plt.subplots(figsize=(9, 7)) -ax.set_ylim(0, 1) -ax.set_xlim(0, T) -ax.plot(range(T), z) -ax.fill_between(range(T), np.zeros(T), z, color="blue", alpha=0.2) - -09/11/2015 03:47:55 PM INFO: Cell returned -09/11/2015 03:47:55 PM INFO: Running cell: -from __future__ import print_function # Remove for Python 3.x -from numpy.random import multivariate_normal -from scipy.linalg import eigvals - - -# === Define A, C, G, H === # -G = np.identity(2) -H = np.sqrt(0.5) * np.identity(2) - -A = [[0.5, 0.4], - [0.6, 0.3]] -C = np.sqrt(0.3) * np.identity(2) - -# === Set up state space mode, initial value x_0 set to zero === # -ss = LinearStateSpace(A, C, G, H, mu_0 = np.zeros(2)) - -# === Define the prior density === # -Sigma = [[0.9, 0.3], - [0.3, 0.9]] -Sigma = np.array(Sigma) -x_hat = np.array([8, 8]) - -# === Initialize the Kalman filter === # -kn = Kalman(ss, x_hat, Sigma) - -# == Print eigenvalues of A == # -print("Eigenvalues of A:") -print(eigvals(A)) - -# == Print stationary Sigma == # -S, K = kn.stationary_values() -print("Stationary prediction error variance:") -print(S) - -# === Generate the plot === # -T = 50 -x, y = ss.simulate(T) - -e1 = np.empty(T-1) -e2 = np.empty(T-1) - -for t in range(1, T): - kn.update(y[:,t]) - e1[t-1] = np.sum((x[:,t] - kn.x_hat.flatten())**2) - e2[t-1] = np.sum((x[:,t] - np.dot(A, x[:,t-1]))**2) - -fig, ax = plt.subplots(figsize=(9,6)) -ax.plot(range(1, T), e1, 'k-', lw=2, alpha=0.6, label='Kalman filter error') -ax.plot(range(1, T), e2, 'g-', lw=2, alpha=0.6, label='conditional expectation error') -ax.legend() - - - -09/11/2015 03:47:56 PM INFO: Cell returned -09/11/2015 03:47:56 PM INFO: Running cell: - - -09/11/2015 03:47:56 PM INFO: Cell returned -09/11/2015 03:47:56 PM INFO: Shutdown kernel ----> END 'kalman_solutions.ipynb' <--- - ----> Executing 'lakemodel_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:47:57 PM INFO: Reading notebook lakemodel_solutions.ipynb -09/11/2015 03:47:57 PM INFO: Running cell: -%pylab inline -from quantecon.models import LakeModel - -alpha = 0.012 -lamb = 0.2486 -b = 0.001808 -d = 0.0008333 -g = b-d -N0 = 100. -e0 = 0.92 -u0 = 1-e0 -T = 50 - -09/11/2015 03:47:59 PM INFO: Cell returned -09/11/2015 03:47:59 PM INFO: Running cell: -LM0 = LakeModel(lamb,alpha,b,d) -x0 = LM0.find_steady_state()# initial conditions - -print "Initial Steady State: ", x0 - -09/11/2015 03:47:59 PM INFO: Cell returned -09/11/2015 03:47:59 PM INFO: Running cell: -LM1 = LakeModel(0.2,alpha,b,d) - -09/11/2015 03:47:59 PM INFO: Cell returned -09/11/2015 03:47:59 PM INFO: Running cell: -xbar = LM1.find_steady_state() # new steady state -X_path = vstack(LM1.simulate_stock_path(x0*N0,T)) # simulate stocks -x_path = vstack(LM1.simulate_rate_path(x0,T)) # simulate rates -print "New Steady State: ", xbar - -09/11/2015 03:47:59 PM INFO: Cell returned -09/11/2015 03:47:59 PM INFO: Running cell: -figure(figsize=[10,9]) -subplot(3,1,1) -plot(X_path[:,0]) -title(r'Employment') -subplot(3,1,2) -plot(X_path[:,1]) -title(r'Unemployment') -subplot(3,1,3) -plot(X_path.sum(1)) -title(r'Labor Force') - -09/11/2015 03:48:00 PM INFO: Cell returned -09/11/2015 03:48:00 PM INFO: Running cell: -figure(figsize=[10,6]) -subplot(2,1,1) -plot(x_path[:,0]) -hlines(xbar[0],0,T,'r','--') -title(r'Employment Rate') -subplot(2,1,2) -plot(x_path[:,1]) -hlines(xbar[1],0,T,'r','--') -title(r'Unemployment Rate') - -09/11/2015 03:48:01 PM INFO: Cell returned -09/11/2015 03:48:01 PM INFO: Running cell: -bhat = 0.003 -T_hat = 20 -LM1 = LakeModel(lamb,alpha,bhat,d) - -09/11/2015 03:48:01 PM INFO: Cell returned -09/11/2015 03:48:01 PM INFO: Running cell: -X_path1 = vstack(LM1.simulate_stock_path(x0*N0,T_hat)) # simulate stocks -x_path1 = vstack(LM1.simulate_rate_path(x0,T_hat)) # simulate rates - -09/11/2015 03:48:01 PM INFO: Cell returned -09/11/2015 03:48:01 PM INFO: Running cell: -X_path2 = vstack(LM0.simulate_stock_path(X_path1[-1,:2],T-T_hat+1)) # simulate stocks -x_path2 = vstack(LM0.simulate_rate_path(x_path1[-1,:2],T-T_hat+1)) # simulate rates - -09/11/2015 03:48:01 PM INFO: Cell returned -09/11/2015 03:48:01 PM INFO: Running cell: -x_path = vstack([x_path1,x_path2[1:]]) # note [1:] to avoid doubling period 20 -X_path = vstack([X_path1,X_path2[1:]]) # note [1:] to avoid doubling period 20 - -09/11/2015 03:48:01 PM INFO: Cell returned -09/11/2015 03:48:01 PM INFO: Running cell: -figure(figsize=[10,9]) -subplot(3,1,1) -plot(X_path[:,0]) -title(r'Employment') -subplot(3,1,2) -plot(X_path[:,1]) -title(r'Unemployment') -subplot(3,1,3) -plot(X_path.sum(1)) -title(r'Labor Force') - -09/11/2015 03:48:02 PM INFO: Cell returned -09/11/2015 03:48:02 PM INFO: Running cell: -figure(figsize=[10,6]) -subplot(2,1,1) -plot(x_path[:,0]) -hlines(x0[0],0,T,'r','--') -title(r'Employment Rate') -subplot(2,1,2) -plot(x_path[:,1]) -hlines(x0[1],0,T,'r','--') -title(r'Unemployment Rate') - -09/11/2015 03:48:02 PM INFO: Cell returned -09/11/2015 03:48:02 PM INFO: Running cell: - - -09/11/2015 03:48:02 PM INFO: Cell returned -09/11/2015 03:48:02 PM INFO: Shutdown kernel ----> END 'lakemodel_solutions.ipynb' <--- - ----> Executing 'lln_clt_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:48:04 PM INFO: Reading notebook lln_clt_solutions.ipynb -09/11/2015 03:48:04 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:48:05 PM INFO: Cell returned -09/11/2015 03:48:05 PM INFO: Running cell: -import numpy as np -import matplotlib.pyplot as plt - -09/11/2015 03:48:05 PM INFO: Cell returned -09/11/2015 03:48:05 PM INFO: Running cell: -""" -Illustrates the delta method, a consequence of the central limit theorem. -""" - -from scipy.stats import uniform, norm -from matplotlib import rc - -# == Specifying font, needs LaTeX integration == # -rc('font',**{'family':'serif','serif':['Palatino']}) -rc('text', usetex=True) - -# == Set parameters == # -n = 250 -replications = 100000 -distribution = uniform(loc=0, scale=(np.pi / 2)) -mu, s = distribution.mean(), distribution.std() - -g = np.sin -g_prime = np.cos - -# == Generate obs of sqrt{n} (g(\bar X_n) - g(\mu)) == # -data = distribution.rvs((replications, n)) -sample_means = data.mean(axis=1) # Compute mean of each row -error_obs = np.sqrt(n) * (g(sample_means) - g(mu)) - -# == Plot == # -asymptotic_sd = g_prime(mu) * s -fig, ax = plt.subplots(figsize=(10, 6)) -xmin = -3 * g_prime(mu) * s -xmax = -xmin -ax.set_xlim(xmin, xmax) -ax.hist(error_obs, bins=60, alpha=0.5, normed=True) -xgrid = np.linspace(xmin, xmax, 200) -lb = r"$N(0, g'(\mu)^2 \sigma^2)$" -ax.plot(xgrid, norm.pdf(xgrid, scale=asymptotic_sd), 'k-', lw=2, label=lb) -ax.legend() -plt.show() - -09/11/2015 03:50:33 PM INFO: Cell returned -09/11/2015 03:50:33 PM INFO: Running cell: -from scipy.stats import uniform, chi2 -from scipy.linalg import inv, sqrtm - -# == Set parameters == # -n = 250 -replications = 50000 -dw = uniform(loc=-1, scale=2) # Uniform(-1, 1) -du = uniform(loc=-2, scale=4) # Uniform(-2, 2) -sw, su = dw.std(), du.std() -vw, vu = sw**2, su**2 -Sigma = ((vw, vw), (vw, vw + vu)) -Sigma = np.array(Sigma) - -# == Compute Sigma^{-1/2} == # -Q = inv(sqrtm(Sigma)) - -# == Generate observations of the normalized sample mean == # -error_obs = np.empty((2, replications)) -for i in range(replications): - # == Generate one sequence of bivariate shocks == # - X = np.empty((2, n)) - W = dw.rvs(n) - U = du.rvs(n) - # == Construct the n observations of the random vector == # - X[0, :] = W - X[1, :] = W + U - # == Construct the i-th observation of Y_n == # - error_obs[:, i] = np.sqrt(n) * X.mean(axis=1) - -# == Premultiply by Q and then take the squared norm == # -temp = np.dot(Q, error_obs) -chisq_obs = np.sum(temp**2, axis=0) - -# == Plot == # -fig, ax = plt.subplots(figsize=(10, 6)) -xmax = 8 -ax.set_xlim(0, xmax) -xgrid = np.linspace(0, xmax, 200) -lb = "Chi-squared with 2 degrees of freedom" -ax.plot(xgrid, chi2.pdf(xgrid, 2), 'k-', lw=2, label=lb) -ax.legend() -ax.hist(chisq_obs, bins=50, normed=True) -plt.show() - -09/11/2015 03:50:44 PM INFO: Cell returned -09/11/2015 03:50:44 PM INFO: Shutdown kernel ----> END 'lln_clt_solutions.ipynb' <--- - ----> Executing 'lqcontrol_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:50:45 PM INFO: Reading notebook lqcontrol_solutions.ipynb -09/11/2015 03:50:46 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:50:47 PM INFO: Cell returned -09/11/2015 03:50:47 PM INFO: Running cell: -from __future__ import division -import numpy as np -import matplotlib.pyplot as plt -from quantecon import LQ - -09/11/2015 03:50:49 PM INFO: Cell returned -09/11/2015 03:50:49 PM INFO: Running cell: -# == Model parameters == # -r = 0.05 -beta = 1 / (1 + r) -T = 50 -c_bar = 1.5 -sigma = 0.15 -mu = 2 -q = 1e4 -m1 = T * (mu / (T/2)**2) -m2 = - (mu / (T/2)**2) - -# == Formulate as an LQ problem == # -Q = 1 -R = np.zeros((4, 4)) -Rf = np.zeros((4, 4)) -Rf[0, 0] = q -A = [[1 + r, -c_bar, m1, m2], - [0, 1, 0, 0], - [0, 1, 1, 0], - [0, 1, 2, 1]] -B = [[-1], - [0], - [0], - [0]] -C = [[sigma], - [0], - [0], - [0]] - -# == Compute solutions and simulate == # -lq = LQ(Q, R, A, B, C, beta=beta, T=T, Rf=Rf) -x0 = (0, 1, 0, 0) -xp, up, wp = lq.compute_sequence(x0) - -# == Convert results back to assets, consumption and income == # -ap = xp[0, :] # Assets -c = up.flatten() + c_bar # Consumption -time = np.arange(1, T+1) -income = wp[0, 1:] + m1 * time + m2 * time**2 # Income - - -# == Plot results == # -n_rows = 2 -fig, axes = plt.subplots(n_rows, 1, figsize=(12, 10)) - -plt.subplots_adjust(hspace=0.5) -for i in range(n_rows): - axes[i].grid() - axes[i].set_xlabel(r'Time') -bbox = (0., 1.02, 1., .102) -legend_args = {'bbox_to_anchor' : bbox, 'loc' : 3, 'mode' : 'expand'} -p_args = {'lw' : 2, 'alpha' : 0.7} - -axes[0].plot(range(1, T+1), income, 'g-', label="non-financial income", **p_args) -axes[0].plot(range(T), c, 'k-', label="consumption", **p_args) -axes[0].legend(ncol=2, **legend_args) - -axes[1].plot(range(T+1), ap.flatten(), 'b-', label="assets", **p_args) -axes[1].plot(range(T+1), np.zeros(T+1), 'k-') -axes[1].legend(ncol=1, **legend_args) - -plt.show() - -09/11/2015 03:50:50 PM INFO: Cell returned -09/11/2015 03:50:50 PM INFO: Running cell: -# == Model parameters == # -r = 0.05 -beta = 1 / (1 + r) -T = 60 -K = 40 -c_bar = 4 -sigma = 0.35 -mu = 4 -q = 1e4 -s = 1 -m1 = 2 * mu / K -m2 = - mu / K**2 - -# == Formulate LQ problem 1 (retirement) == # -Q = 1 -R = np.zeros((4, 4)) -Rf = np.zeros((4, 4)) -Rf[0, 0] = q -A = [[1 + r, s - c_bar, 0, 0], - [0, 1, 0, 0], - [0, 1, 1, 0], - [0, 1, 2, 1]] -B = [[-1], - [0], - [0], - [0]] -C = [[0], - [0], - [0], - [0]] - -# == Initialize LQ instance for retired agent == # -lq_retired = LQ(Q, R, A, B, C, beta=beta, T=T-K, Rf=Rf) -# == Iterate back to start of retirement, record final value function == # -for i in range(T-K): - lq_retired.update_values() -Rf2 = lq_retired.P - -# == Formulate LQ problem 2 (working life) == # -R = np.zeros((4, 4)) -A = [[1 + r, -c_bar, m1, m2], - [0, 1, 0, 0], - [0, 1, 1, 0], - [0, 1, 2, 1]] -B = [[-1], - [0], - [0], - [0]] -C = [[sigma], - [0], - [0], - [0]] - -# == Set up working life LQ instance with terminal Rf from lq_retired == # -lq_working = LQ(Q, R, A, B, C, beta=beta, T=K, Rf=Rf2) - -# == Simulate working state / control paths == # -x0 = (0, 1, 0, 0) -xp_w, up_w, wp_w = lq_working.compute_sequence(x0) -# == Simulate retirement paths (note the initial condition) == # -xp_r, up_r, wp_r = lq_retired.compute_sequence(xp_w[:, K]) - -# == Convert results back to assets, consumption and income == # -xp = np.column_stack((xp_w, xp_r[:, 1:])) -assets = xp[0, :] # Assets - -up = np.column_stack((up_w, up_r)) -c = up.flatten() + c_bar # Consumption - -time = np.arange(1, K+1) -income_w = wp_w[0, 1:K+1] + m1 * time + m2 * time**2 # Income -income_r = np.ones(T-K) * s -income = np.concatenate((income_w, income_r)) - -# == Plot results == # -n_rows = 2 -fig, axes = plt.subplots(n_rows, 1, figsize=(12, 10)) - -plt.subplots_adjust(hspace=0.5) -for i in range(n_rows): - axes[i].grid() - axes[i].set_xlabel(r'Time') -bbox = (0., 1.02, 1., .102) -legend_args = {'bbox_to_anchor' : bbox, 'loc' : 3, 'mode' : 'expand'} -p_args = {'lw' : 2, 'alpha' : 0.7} - -axes[0].plot(range(1, T+1), income, 'g-', label="non-financial income", **p_args) -axes[0].plot(range(T), c, 'k-', label="consumption", **p_args) -axes[0].legend(ncol=2, **legend_args) - -axes[1].plot(range(T+1), assets, 'b-', label="assets", **p_args) -axes[1].plot(range(T+1), np.zeros(T+1), 'k-') -axes[1].legend(ncol=1, **legend_args) - -plt.show() - -09/11/2015 03:50:51 PM INFO: Cell returned -09/11/2015 03:50:51 PM INFO: Running cell: -# == Model parameters == # -a0 = 5 -a1 = 0.5 -sigma = 0.15 -rho = 0.9 -gamma = 1 -beta = 0.95 -c = 2 -T = 120 - -# == Useful constants == # -m0 = (a0 - c) / (2 * a1) -m1 = 1 / (2 * a1) - -# == Formulate LQ problem == # -Q = gamma -R = [[a1, -a1, 0], - [-a1, a1, 0], - [0, 0, 0]] -A = [[rho, 0, m0 * (1 - rho)], - [0, 1, 0], - [0, 0, 1]] - -B = [[0], - [1], - [0]] -C = [[m1 * sigma], - [0], - [0]] - -lq = LQ(Q, R, A, B, C=C, beta=beta) - -# == Simulate state / control paths == # -x0 = (m0, 2, 1) -xp, up, wp = lq.compute_sequence(x0, ts_length=150) -q_bar = xp[0, :] -q = xp[1, :] - -# == Plot simulation results == # -fig, ax = plt.subplots(figsize=(10, 6.5)) -ax.set_xlabel('Time') - -# == Some fancy plotting stuff -- simplify if you prefer == # -bbox = (0., 1.01, 1., .101) -legend_args = {'bbox_to_anchor' : bbox, 'loc' : 3, 'mode' : 'expand'} -p_args = {'lw' : 2, 'alpha' : 0.6} - -time = range(len(q)) -ax.set_xlim(0, max(time)) -ax.plot(time, q_bar, 'k-', lw=2, alpha=0.6, label=r'$\bar q_t$') -ax.plot(time, q, 'b-', lw=2, alpha=0.6, label=r'$q_t$') -ax.legend(ncol=2, **legend_args) -s = r'dynamics with $\gamma = {}$'.format(gamma) -ax.text(max(time) * 0.6, 1 * q_bar.max(), s, fontsize=14) -plt.show() - -09/11/2015 03:50:52 PM INFO: Cell returned -09/11/2015 03:50:52 PM INFO: Shutdown kernel ----> END 'lqcontrol_solutions.ipynb' <--- - ----> Executing 'lqramsey_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:50:53 PM INFO: Reading notebook lqramsey_solutions.ipynb -09/11/2015 03:50:54 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:50:55 PM INFO: Cell returned -09/11/2015 03:50:55 PM INFO: Running cell: -import sys -import os -import numpy as np -import matplotlib.pyplot as plt - -# lqramsy.py lives in the examples folder. We need -# to append it to the path so we can import it below -sys.path.append(os.path.abspath("../examples")) - -09/11/2015 03:50:55 PM INFO: Cell returned -09/11/2015 03:50:55 PM INFO: Running cell: -from numpy import array -from lqramsey import * - -# == Parameters == # -beta = 1 / 1.05 -rho, mg = .95, .35 -A = array([[0, 0, 0, rho, mg*(1-rho)], - [1, 0, 0, 0, 0], - [0, 1, 0, 0, 0], - [0, 0, 1, 0, 0], - [0, 0, 0, 0, 1]]) -C = np.zeros((5, 1)) -C[0, 0] = np.sqrt(1 - rho**2) * mg / 8 -Sg = array((1, 0, 0, 0, 0)).reshape(1, 5) -Sd = array((0, 0, 0, 0, 0)).reshape(1, 5) -Sb = array((0, 0, 0, 0, 2.135)).reshape(1, 5) # Chosen st. (Sc + Sg) * x0 = 1 -Ss = array((0, 0, 0, 0, 0)).reshape(1, 5) - -economy = Economy(beta=beta, - Sg=Sg, - Sd=Sd, - Sb=Sb, - Ss=Ss, - discrete=False, - proc=(A, C)) - -T = 50 -path = compute_paths(T, economy) -gen_fig_1(path) - -09/11/2015 03:50:59 PM INFO: Cell returned -09/11/2015 03:50:59 PM INFO: Shutdown kernel ----> END 'lqramsey_solutions.ipynb' <--- - ----> Executing 'lss_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:51:00 PM INFO: Reading notebook lss_solutions.ipynb -09/11/2015 03:51:01 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:51:02 PM INFO: Cell returned -09/11/2015 03:51:02 PM INFO: Running cell: -import numpy as np -import matplotlib.pyplot as plt -from quantecon import LinearStateSpace - -09/11/2015 03:51:04 PM INFO: Cell returned -09/11/2015 03:51:04 PM INFO: Running cell: -phi_0, phi_1, phi_2 = 1.1, 0.8, -0.8 - -A = [[1, 0, 0], - [phi_0, phi_1, phi_2], - [0, 1, 0]] -C = np.zeros((3, 1)) -G = [0, 1, 0] - -ar = LinearStateSpace(A, C, G, mu_0=np.ones(3)) -x, y = ar.simulate(ts_length=50) - -fig, ax = plt.subplots(figsize=(8, 4.6)) -y = y.flatten() -ax.plot(y, 'b-', lw=2, alpha=0.7) -ax.grid() -ax.set_xlabel('time') -ax.set_ylabel(r'$y_t$', fontsize=16) -plt.show() - -09/11/2015 03:51:05 PM INFO: Cell returned -09/11/2015 03:51:05 PM INFO: Running cell: -phi_1, phi_2, phi_3, phi_4 = 0.5, -0.2, 0, 0.5 -sigma = 0.2 - -A = [[phi_1, phi_2, phi_3, phi_4], - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 1, 0]] -C = [[sigma], - [0], - [0], - [0]] -G = [1, 0, 0, 0] - -ar = LinearStateSpace(A, C, G, mu_0=np.ones(4)) -x, y = ar.simulate(ts_length=200) - -fig, ax = plt.subplots(figsize=(8, 4.6)) -y = y.flatten() -ax.plot(y, 'b-', lw=2, alpha=0.7) -ax.grid() -ax.set_xlabel('time') -ax.set_ylabel(r'$y_t$', fontsize=16) -plt.show() - - -09/11/2015 03:51:05 PM INFO: Cell returned -09/11/2015 03:51:05 PM INFO: Running cell: -from __future__ import division -from scipy.stats import norm -import random - -phi_1, phi_2, phi_3, phi_4 = 0.5, -0.2, 0, 0.5 -sigma = 0.1 - -A = [[phi_1, phi_2, phi_3, phi_4], - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 1, 0]] -C = [[sigma], - [0], - [0], - [0]] -G = [1, 0, 0, 0] - -I = 20 -T = 50 -ar = LinearStateSpace(A, C, G, mu_0=np.ones(4)) -ymin, ymax = -0.5, 1.15 - -fig, ax = plt.subplots(figsize=(8, 5)) - -ax.set_ylim(ymin, ymax) -ax.set_xlabel(r'time', fontsize=16) -ax.set_ylabel(r'$y_t$', fontsize=16) - -ensemble_mean = np.zeros(T) -for i in range(I): - x, y = ar.simulate(ts_length=T) - y = y.flatten() - ax.plot(y, 'c-', lw=0.8, alpha=0.5) - ensemble_mean = ensemble_mean + y - -ensemble_mean = ensemble_mean / I -ax.plot(ensemble_mean, color='b', lw=2, alpha=0.8, label=r'$\bar y_t$') - -m = ar.moment_sequence() -population_means = [] -for t in range(T): - mu_x, mu_y, Sigma_x, Sigma_y = next(m) - population_means.append(float(mu_y)) -ax.plot(population_means, color='g', lw=2, alpha=0.8, label=r'$G\mu_t$') -ax.legend(ncol=2) -plt.show() - -09/11/2015 03:51:06 PM INFO: Cell returned -09/11/2015 03:51:06 PM INFO: Running cell: -phi_1, phi_2, phi_3, phi_4 = 0.5, -0.2, 0, 0.5 -sigma = 0.1 - -A = [[phi_1, phi_2, phi_3, phi_4], - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 1, 0]] -C = [[sigma], - [0], - [0], - [0]] -G = [1, 0, 0, 0] - -T0 = 10 -T1 = 50 -T2 = 75 -T4 = 100 - -ar = LinearStateSpace(A, C, G, mu_0=np.ones(4)) -ymin, ymax = -0.6, 0.6 - -fig, ax = plt.subplots(figsize=(8, 5)) - -ax.grid(alpha=0.4) -ax.set_ylim(ymin, ymax) -ax.set_ylabel(r'$y_t$', fontsize=16) -ax.vlines((T0, T1, T2), -1.5, 1.5) - -ax.set_xticks((T0, T1, T2)) -ax.set_xticklabels((r"$T$", r"$T'$", r"$T''$"), fontsize=14) - -mu_x, mu_y, Sigma_x, Sigma_y = ar.stationary_distributions() -ar.mu_0 = mu_x -ar.Sigma_0 = Sigma_x - -for i in range(80): - rcolor = random.choice(('c', 'g', 'b')) - x, y = ar.simulate(ts_length=T4) - y = y.flatten() - ax.plot(y, color=rcolor, lw=0.8, alpha=0.5) - ax.plot((T0, T1, T2), (y[T0], y[T1], y[T2],), 'ko', alpha=0.5) - - -09/11/2015 03:51:08 PM INFO: Cell returned -09/11/2015 03:51:08 PM INFO: Running cell: - - -09/11/2015 03:51:08 PM INFO: Cell returned -09/11/2015 03:51:08 PM INFO: Shutdown kernel ----> END 'lss_solutions.ipynb' <--- - ----> Executing 'lucas_asset_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:51:10 PM INFO: Reading notebook lucas_asset_solutions.ipynb -09/11/2015 03:51:10 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:51:11 PM INFO: Cell returned -09/11/2015 03:51:11 PM INFO: Running cell: -from __future__ import division # Omit for Python 3.x -import numpy as np -import matplotlib.pyplot as plt -from quantecon.models import LucasTree - -09/11/2015 03:51:13 PM INFO: Cell returned -09/11/2015 03:51:13 PM INFO: Running cell: -fig, ax = plt.subplots(figsize=(10,7)) - -ax.set_xlabel(r'$y$', fontsize=16) -ax.set_ylabel(r'price', fontsize=16) - -for beta in (.95, 0.98): - print("Comuting at beta = {}".format(beta)) - tree = LucasTree(gamma=2, beta=beta, alpha=0.90, sigma=0.1) - grid, price_vals = tree.grid, tree.compute_lt_price() - label = r'$\beta = {}$'.format(beta) - ax.plot(grid, price_vals, lw=2, alpha=0.7, label=label) - -ax.legend(loc='upper left') -ax.set_xlim(min(grid), max(grid)) - -09/11/2015 03:51:17 PM INFO: Cell returned -09/11/2015 03:51:17 PM INFO: Running cell: - - -09/11/2015 03:51:17 PM INFO: Cell returned -09/11/2015 03:51:17 PM INFO: Shutdown kernel ----> END 'lucas_asset_solutions.ipynb' <--- - ----> Executing 'mpe_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:51:17 PM INFO: Reading notebook mpe_solutions.ipynb -09/11/2015 03:51:18 PM INFO: Running cell: -import numpy as np -import quantecon as qe -import matplotlib.pyplot as plt -from numpy import dot - -09/11/2015 03:51:21 PM INFO: Cell returned -09/11/2015 03:51:21 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:51:21 PM INFO: Cell returned -09/11/2015 03:51:21 PM INFO: Running cell: -# == Parameters == # -a0 = 10.0 -a1 = 2.0 -beta = 0.96 -gamma = 12.0 - -# == In LQ form == # - -A = np.eye(3) - -B1 = np.array([[0.], [1.], [0.]]) -B2 = np.array([[0.], [0.], [1.]]) - - -R1 = [[0., -a0/2, 0.], - [-a0/2., a1, a1/2.], - [0, a1/2., 0.]] - -R2 = [[0., 0., -a0/2], - [0., 0., a1/2.], - [-a0/2, a1/2., a1]] - -Q1 = Q2 = gamma - -S1 = S2 = W1 = W2 = M1 = M2 = 0.0 - -# == Solve using QE's nnash function == # -F1, F2, P1, P2 = qe.nnash(A, B1, B2, R1, R2, Q1, Q2, S1, S2, W1, W2, M1, M2, - beta=beta) - -09/11/2015 03:51:21 PM INFO: Cell returned -09/11/2015 03:51:21 PM INFO: Running cell: -AF = A - B1.dot(F1) - B2.dot(F2) -n = 20 -x = np.empty((3, n)) -x[:, 0] = 1, 1, 1 -for t in range(n-1): - x[:, t+1] = np.dot(AF, x[:, t]) -q1 = x[1, :] -q2 = x[2, :] -q = q1 + q2 # Total output, MPE -p = a0 - a1 * q # Price, MPE - -09/11/2015 03:51:21 PM INFO: Cell returned -09/11/2015 03:51:21 PM INFO: Running cell: -R = a1 -Q = gamma -A = B = 1 -lq_alt = qe.LQ(Q, R, A, B, beta=beta) -P, F, d = lq_alt.stationary_values() -q_bar = a0 / (2.0 * a1) -qm = np.empty(n) -qm[0] = 2 -x0 = qm[0] - q_bar -x = x0 -for i in range(1, n): - x = A * x - B * F * x - qm[i] = float(x) + q_bar -pm = a0 - a1 * qm - -09/11/2015 03:51:21 PM INFO: Cell returned -09/11/2015 03:51:21 PM INFO: Running cell: -fig, axes = plt.subplots(2, 1, figsize=(9, 9)) - -ax = axes[0] -ax.plot(qm, 'b-', lw=2, alpha=0.75, label='monopolist output') -ax.plot(q, 'g-', lw=2, alpha=0.75, label='MPE total output') -ax.set_ylabel("output") -ax.set_xlabel("time") -ax.set_ylim(2, 4) -ax.legend(loc='upper left', frameon=0) - - -ax = axes[1] -ax.plot(pm, 'b-', lw=2, alpha=0.75, label='monopolist price') -ax.plot(p, 'g-', lw=2, alpha=0.75, label='MPE price') -ax.set_ylabel("price") -ax.set_xlabel("time") -ax.legend(loc='upper right', frameon=0) - -09/11/2015 03:51:22 PM INFO: Cell returned -09/11/2015 03:51:22 PM INFO: Running cell: -delta = 0.02 -D = np.array([[-1, 0.5], [0.5, -1]]) -b = np.array([25, 25]) -c1 = c2 = np.array([1, -2, 1]) -e1 = e2 = np.array([10, 10, 3]) - -delta_1 = 1 - delta - -09/11/2015 03:51:22 PM INFO: Cell returned -09/11/2015 03:51:22 PM INFO: Running cell: -# == Create matrices needed to compute the Nash feedback equilibrium == # - -A = np.array([[delta_1, 0, -delta_1*b[0]], - [0, delta_1, -delta_1*b[1]], - [0, 0, 1]]) - -B1 = delta_1 * np.array([[1, -D[0, 0]], - [0, -D[1, 0]], - [0, 0]]) -B2 = delta_1 * np.array([[0, -D[0, 1]], - [1, -D[1, 1]], - [0, 0]]) - -R1 = -np.array([[0.5*c1[2], 0, 0.5*c1[1]], - [0, 0, 0], - [0.5*c1[1], 0, c1[0]]]) -R2 = -np.array([[0, 0, 0], - [0, 0.5*c2[2], 0.5*c2[1]], - [0, 0.5*c2[1], c2[0]]]) - -Q1 = np.array([[-0.5*e1[2], 0], [0, D[0, 0]]]) -Q2 = np.array([[-0.5*e2[2], 0], [0, D[1, 1]]]) - -S1 = np.zeros((2, 2)) -S2 = np.copy(S1) - -W1 = np.array([[0, 0], - [0, 0], - [-0.5*e1[1], b[0]/2.]]) -W2 = np.array([[0, 0], - [0, 0], - [-0.5*e2[1], b[1]/2.]]) - -M1 = np.array([[0, 0], [0, D[0, 1] / 2.]]) -M2 = np.copy(M1) - -09/11/2015 03:51:22 PM INFO: Cell returned -09/11/2015 03:51:22 PM INFO: Running cell: -F1, F2, P1, P2 = qe.nnash(A, B1, B2, R1, R2, Q1, Q2, S1, S2, W1, W2, M1, M2) - -print("\nFirm 1's feedback rule:\n") -print(F1) - -print("\nFirm 2's feedback rule:\n") -print(F2) - -09/11/2015 03:51:22 PM INFO: Cell returned -09/11/2015 03:51:22 PM INFO: Running cell: -AF = A - B1.dot(F1) - B2.dot(F2) -n = 25 -x = np.empty((3, n)) -x[:, 0] = 2, 0, 1 -for t in range(n-1): - x[:, t+1] = np.dot(AF, x[:, t]) -I1 = x[0, :] -I2 = x[1, :] -fig, ax = plt.subplots(figsize=(9, 5)) -ax.plot(I1, 'b-', lw=2, alpha=0.75, label='inventories, firm 1') -ax.plot(I2, 'g-', lw=2, alpha=0.75, label='inventories, firm 2') -ax.set_title(r'$\delta = {}$'.format(delta)) -ax.legend() - -09/11/2015 03:51:23 PM INFO: Cell returned -09/11/2015 03:51:23 PM INFO: Running cell: - - -09/11/2015 03:51:23 PM INFO: Cell returned -09/11/2015 03:51:23 PM INFO: Shutdown kernel ----> END 'mpe_solutions.ipynb' <--- - ----> Executing 'numpy_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:51:24 PM INFO: Reading notebook numpy_solutions.ipynb -09/11/2015 03:51:25 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:51:26 PM INFO: Cell returned -09/11/2015 03:51:26 PM INFO: Running cell: -import numpy as np -import matplotlib.pyplot as plt - -09/11/2015 03:51:26 PM INFO: Cell returned -09/11/2015 03:51:26 PM INFO: Running cell: -def p(x, coef): - X = np.empty(len(coef)) - X[0] = 1 - X[1:] = x - y = np.cumprod(X) # y = [1, x, x**2,...] - return np.dot(coef, y) - -09/11/2015 03:51:26 PM INFO: Cell returned -09/11/2015 03:51:26 PM INFO: Running cell: -coef = np.ones(3) -print(coef) -print(p(1, coef)) -# For comparison -q = np.poly1d(coef) -print(q(1)) - -09/11/2015 03:51:26 PM INFO: Cell returned -09/11/2015 03:51:26 PM INFO: Running cell: -from numpy import cumsum -from numpy.random import uniform - -class discreteRV: - """ - Generates an array of draws from a discrete random variable with vector of - probabilities given by q. - """ - - def __init__(self, q): - """ - The argument q is a NumPy array, or array like, nonnegative and sums - to 1 - """ - self.q = q - self.Q = cumsum(q) - - def draw(self, k=1): - """ - Returns k draws from q. For each such draw, the value i is returned - with probability q[i]. - """ - return self.Q.searchsorted(uniform(0, 1, size=k)) - -09/11/2015 03:51:26 PM INFO: Cell returned -09/11/2015 03:51:26 PM INFO: Running cell: -q = (0.1, 0.9) -d = discreteRV(q) -d.q = (0.5, 0.5) - -09/11/2015 03:51:26 PM INFO: Cell returned -09/11/2015 03:51:26 PM INFO: Running cell: -""" -Modifies ecdf.py from QuantEcon to add in a plot method - -""" - -import numpy as np -import matplotlib.pyplot as plt - - -class ECDF(object): - """ - One-dimensional empirical distribution function given a vector of - observations. - - Parameters - ---------- - observations : array_like - An array of observations - - Attributes - ---------- - observations : array_like - An array of observations - - """ - - def __init__(self, observations): - self.observations = np.asarray(observations) - - def __call__(self, x): - """ - Evaluates the ecdf at x - - Parameters - ---------- - x : scalar(float) - The x at which the ecdf is evaluated - - Returns - ------- - scalar(float) - Fraction of the sample less than x - - """ - return np.mean(self.observations <= x) - - def plot(self, a=None, b=None): - """ - Plot the ecdf on the interval [a, b]. - - Parameters - ---------- - a : scalar(float), optional(default=None) - Lower end point of the plot interval - b : scalar(float), optional(default=None) - Upper end point of the plot interval - - """ - - # === choose reasonable interval if [a, b] not specified === # - if a is None: - a = self.observations.min() - self.observations.std() - if b is None: - b = self.observations.max() + self.observations.std() - - # === generate plot === # - x_vals = np.linspace(a, b, num=100) - f = np.vectorize(self.__call__) - plt.plot(x_vals, f(x_vals)) - plt.show() - -09/11/2015 03:51:26 PM INFO: Cell returned -09/11/2015 03:51:26 PM INFO: Running cell: -X = np.random.randn(1000) -F = ECDF(X) -F.plot() - -09/11/2015 03:51:26 PM INFO: Cell returned -09/11/2015 03:51:26 PM INFO: Running cell: - - -09/11/2015 03:51:26 PM INFO: Cell returned -09/11/2015 03:51:26 PM INFO: Shutdown kernel ----> END 'numpy_solutions.ipynb' <--- - ----> Executing 'odu_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:51:27 PM INFO: Reading notebook odu_solutions.ipynb -09/11/2015 03:51:28 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:51:29 PM INFO: Cell returned -09/11/2015 03:51:29 PM INFO: Running cell: -import numpy as np -import matplotlib.pyplot as plt -from quantecon import compute_fixed_point -from quantecon.models import SearchProblem - -09/11/2015 03:51:30 PM INFO: Cell returned -09/11/2015 03:51:30 PM INFO: Running cell: -sp = SearchProblem(pi_grid_size=50) - -phi_init = np.ones(len(sp.pi_grid)) -w_bar = compute_fixed_point(sp.res_wage_operator, phi_init) - -fig, ax = plt.subplots(figsize=(9, 7)) -ax.plot(sp.pi_grid, w_bar, linewidth=2, color='black') -ax.set_ylim(0, 2) -ax.grid(axis='x', linewidth=0.25, linestyle='--', color='0.25') -ax.grid(axis='y', linewidth=0.25, linestyle='--', color='0.25') -ax.fill_between(sp.pi_grid, 0, w_bar, color='blue', alpha=0.15) -ax.fill_between(sp.pi_grid, w_bar, 2, color='green', alpha=0.15) -ax.text(0.42, 1.2, 'reject') -ax.text(0.7, 1.8, 'accept') -plt.show() - -09/11/2015 03:51:31 PM INFO: Cell returned -09/11/2015 03:51:31 PM INFO: Running cell: -from scipy import interp -# Set up model and compute the function w_bar -sp = SearchProblem(pi_grid_size=50, F_a=1, F_b=1) -pi_grid, f, g, F, G = sp.pi_grid, sp.f, sp.g, sp.F, sp.G -phi_init = np.ones(len(sp.pi_grid)) -w_bar_vals = compute_fixed_point(sp.res_wage_operator, phi_init) -w_bar = lambda x: interp(x, pi_grid, w_bar_vals) - - -class Agent(object): - """ - Holds the employment state and beliefs of an individual agent. - """ - - def __init__(self, pi=1e-3): - self.pi = pi - self.employed = 1 - - def update(self, H): - "Update self by drawing wage offer from distribution H." - if self.employed == 0: - w = H.rvs() - if w >= w_bar(self.pi): - self.employed = 1 - else: - self.pi = 1.0 / (1 + ((1 - self.pi) * g(w)) / (self.pi * f(w))) - - -num_agents = 5000 -separation_rate = 0.025 # Fraction of jobs that end in each period -separation_num = int(num_agents * separation_rate) -agent_indices = list(range(num_agents)) -agents = [Agent() for i in range(num_agents)] -sim_length = 600 -H = G # Start with distribution G -change_date = 200 # Change to F after this many periods - -unempl_rate = [] -for i in range(sim_length): - if i % 20 == 0: - print("date =", i) - if i == change_date: - H = F - # Randomly select separation_num agents and set employment status to 0 - np.random.shuffle(agent_indices) - separation_list = agent_indices[:separation_num] - for agent_index in separation_list: - agents[agent_index].employed = 0 - # Update agents - for agent in agents: - agent.update(H) - employed = [agent.employed for agent in agents] - unempl_rate.append(1 - np.mean(employed)) - -fig, ax = plt.subplots(figsize=(9, 7)) -ax.plot(unempl_rate, lw=2, alpha=0.8, label='unemployment rate') -ax.axvline(change_date, color="red") -ax.legend() -plt.show() - -09/11/2015 03:53:47 PM INFO: Cell returned -09/11/2015 03:53:47 PM INFO: Shutdown kernel ----> END 'odu_solutions.ipynb' <--- - ----> Executing 'oop_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:53:48 PM INFO: Reading notebook oop_solutions.ipynb -09/11/2015 03:53:48 PM INFO: Running cell: -class ECDF(object): - - def __init__(self, observations): - self.observations = observations - - def __call__(self, x): - counter = 0.0 - for obs in self.observations: - if obs <= x: - counter += 1 - return counter / len(self.observations) - -09/11/2015 03:53:48 PM INFO: Cell returned -09/11/2015 03:53:48 PM INFO: Running cell: -# == test == # - -from random import uniform -samples = [uniform(0, 1) for i in range(10)] -F = ECDF(samples) - -print(F(0.5)) # Evaluate ecdf at x = 0.5 - -F.observations = [uniform(0, 1) for i in range(1000)] - -print(F(0.5)) - -09/11/2015 03:53:49 PM INFO: Cell returned -09/11/2015 03:53:49 PM INFO: Running cell: -class Polynomial(object): - - def __init__(self, coefficients): - """ - Creates an instance of the Polynomial class representing - - p(x) = a_0 x^0 + ... + a_N x^N, - - where a_i = coefficients[i]. - """ - self.coefficients = coefficients - - def __call__(self, x): - "Evaluate the polynomial at x." - y = 0 - for i, a in enumerate(self.coefficients): - y += a * x**i - return y - - def differentiate(self): - "Reset self.coefficients to those of p' instead of p." - new_coefficients = [] - for i, a in enumerate(self.coefficients): - new_coefficients.append(i * a) - # Remove the first element, which is zero - del new_coefficients[0] - # And reset coefficients data to new values - self.coefficients = new_coefficients - - -09/11/2015 03:53:49 PM INFO: Cell returned -09/11/2015 03:53:49 PM INFO: Shutdown kernel ----> END 'oop_solutions.ipynb' <--- - ----> Executing 'optgrowth_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:53:50 PM INFO: Reading notebook optgrowth_solutions.ipynb -09/11/2015 03:53:50 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:53:51 PM INFO: Cell returned -09/11/2015 03:53:51 PM INFO: Running cell: -import numpy as np -import matplotlib.pyplot as plt -from quantecon import compute_fixed_point -from quantecon.models import GrowthModel - -09/11/2015 03:53:53 PM INFO: Cell returned -09/11/2015 03:53:53 PM INFO: Running cell: -alpha, beta = 0.65, 0.95 -gm = GrowthModel() -true_sigma = (1 - alpha * beta) * gm.grid**alpha -w = 5 * gm.u(gm.grid) - 25 # Initial condition - -fig, ax = plt.subplots(3, 1, figsize=(8, 10)) - -for i, n in enumerate((2, 4, 6)): - ax[i].set_ylim(0, 1) - ax[i].set_xlim(0, 2) - ax[i].set_yticks((0, 1)) - ax[i].set_xticks((0, 2)) - - v_star = compute_fixed_point(gm.bellman_operator, w, max_iter=n) - sigma = gm.compute_greedy(v_star) - - ax[i].plot(gm.grid, sigma, 'b-', lw=2, alpha=0.8, label='approximate optimal policy') - ax[i].plot(gm.grid, true_sigma, 'k-', lw=2, alpha=0.8, label='true optimal policy') - ax[i].legend(loc='upper left') - ax[i].set_title('{} value function iterations'.format(n)) - -09/11/2015 03:53:55 PM INFO: Cell returned -09/11/2015 03:53:55 PM INFO: Running cell: -from scipy import interp - -gm = GrowthModel() -w = 5 * gm.u(gm.grid) - 25 # To be used as an initial condition -discount_factors = (0.9, 0.94, 0.98) -series_length = 25 - -fig, ax = plt.subplots(figsize=(8,5)) -ax.set_xlabel("time") -ax.set_ylabel("capital") - -for beta in discount_factors: - - # Compute the optimal policy given the discount factor - gm.beta = beta - v_star = compute_fixed_point(gm.bellman_operator, w, max_iter=20) - sigma = gm.compute_greedy(v_star) - - # Compute the corresponding time series for capital - k = np.empty(series_length) - k[0] = 0.1 - sigma_function = lambda x: interp(x, gm.grid, sigma) - for t in range(1, series_length): - k[t] = gm.f(k[t-1]) - sigma_function(k[t-1]) - ax.plot(k, 'o-', lw=2, alpha=0.75, label=r'$\beta = {}$'.format(beta)) - -ax.legend(loc='lower right') -plt.show() - -09/11/2015 03:54:03 PM INFO: Cell returned -09/11/2015 03:54:03 PM INFO: Shutdown kernel ----> END 'optgrowth_solutions.ipynb' <--- - ----> Executing 'pandas_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:54:05 PM INFO: Reading notebook pandas_solutions.ipynb -09/11/2015 03:54:06 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:54:07 PM INFO: Cell returned -09/11/2015 03:54:07 PM INFO: Running cell: -import numpy as np -import pandas as pd -import datetime as dt -import pandas.io.data as web -import matplotlib.pyplot as plt - -09/11/2015 03:54:07 PM INFO: Cell returned -09/11/2015 03:54:07 PM INFO: Running cell: -ticker_list = {'INTC': 'Intel', - 'MSFT': 'Microsoft', - 'IBM': 'IBM', - 'BHP': 'BHP', - 'RSH': 'RadioShack', - 'TM': 'Toyota', - 'AAPL': 'Apple', - 'AMZN': 'Amazon', - 'BA': 'Boeing', - 'QCOM': 'Qualcomm', - 'KO': 'Coca-Cola', - 'GOOG': 'Google', - 'SNE': 'Sony', - 'PTR': 'PetroChina'} - -start = dt.datetime(2013, 1, 1) -end = dt.datetime.today() - -price_change = {} - -for ticker in ticker_list: - prices = web.DataReader(ticker, 'yahoo', start, end) - closing_prices = prices['Close'] - change = 100 * (closing_prices[-1] - closing_prices[0]) / closing_prices[0] - name = ticker_list[ticker] - price_change[name] = change - -pc = pd.Series(price_change) -pc.sort() -fig, ax = plt.subplots(figsize=(10,8)) -pc.plot(kind='bar', ax=ax) - -09/11/2015 03:54:10 PM INFO: Cell returned -09/11/2015 03:54:10 PM INFO: Shutdown kernel ----> END 'pandas_solutions.ipynb' <--- - ----> Executing 'pbe_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:54:11 PM INFO: Reading notebook pbe_solutions.ipynb -09/11/2015 03:54:12 PM INFO: Running cell: -def factorial(n): - k = 1 - for i in range(n): - k = k * (i + 1) - return k - -factorial(4) - -09/11/2015 03:54:12 PM INFO: Cell returned -09/11/2015 03:54:12 PM INFO: Running cell: -from random import uniform - -def binomial_rv(n, p): - count = 0 - for i in range(n): - U = uniform(0, 1) - if U < p: - count = count + 1 # Or count += 1 - return count - -binomial_rv(10, 0.5) - -09/11/2015 03:54:12 PM INFO: Cell returned -09/11/2015 03:54:12 PM INFO: Running cell: -from __future__ import division # Omit if using Python 3.x -from math import sqrt - -n = 100000 - -count = 0 -for i in range(n): - u, v = uniform(0, 1), uniform(0, 1) - d = sqrt((u - 0.5)**2 + (v - 0.5)**2) - if d < 0.5: - count += 1 - -area_estimate = count / n - -print(area_estimate * 4) # dividing by radius**2 - -09/11/2015 03:54:12 PM INFO: Cell returned -09/11/2015 03:54:12 PM INFO: Running cell: -payoff = 0 -count = 0 - -for i in range(10): - U = uniform(0, 1) - count = count + 1 if U < 0.5 else 0 - if count == 3: - payoff = 1 - -print(payoff) - -09/11/2015 03:54:12 PM INFO: Cell returned -09/11/2015 03:54:12 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:54:13 PM INFO: Cell returned -09/11/2015 03:54:13 PM INFO: Running cell: -import matplotlib.pyplot as plt -from random import normalvariate - -alpha = 0.9 -ts_length = 200 -current_x = 0 - -x_values = [] -for i in range(ts_length + 1): - x_values.append(current_x) - current_x = alpha * current_x + normalvariate(0, 1) -plt.plot(x_values, 'b-') - - -09/11/2015 03:54:13 PM INFO: Cell returned -09/11/2015 03:54:13 PM INFO: Running cell: -alphas = [0.0, 0.8, 0.98] -ts_length = 200 - -for alpha in alphas: - x_values = [] - current_x = 0 - for i in range(ts_length): - x_values.append(current_x) - current_x = alpha * current_x + normalvariate(0, 1) - plt.plot(x_values, label='alpha = ' + str(alpha)) -plt.legend() - -09/11/2015 03:54:13 PM INFO: Cell returned -09/11/2015 03:54:13 PM INFO: Running cell: - - -09/11/2015 03:54:13 PM INFO: Cell returned -09/11/2015 03:54:13 PM INFO: Shutdown kernel ----> END 'pbe_solutions.ipynb' <--- - ----> Executing 'py_adv_feat_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:54:15 PM INFO: Reading notebook py_adv_feat_solutions.ipynb -09/11/2015 03:54:16 PM INFO: Running cell: -def x(t): - if t == 0: - return 0 - if t == 1: - return 1 - else: - return x(t-1) + x(t-2) - - -09/11/2015 03:54:16 PM INFO: Cell returned -09/11/2015 03:54:16 PM INFO: Running cell: -print([x(i) for i in range(10)]) - -09/11/2015 03:54:16 PM INFO: Cell returned -09/11/2015 03:54:16 PM INFO: Running cell: -def column_iterator(target_file, column_number): - """A generator function for CSV files. - When called with a file name target_file (string) and column number - column_number (integer), the generator function returns a generator - which steps through the elements of column column_number in file - target_file. - """ - f = open(target_file, 'r') - for line in f: - yield line.split(',')[column_number - 1] - f.close() - -dates = column_iterator('test_table.csv', 1) - -i = 1 -for date in dates: - print(date) - if i == 10: - break - i += 1 - -09/11/2015 03:54:16 PM INFO: Cell returned -09/11/2015 03:54:16 PM INFO: Running cell: -%%file numbers.txt -prices -3 -8 - -7 -21 - -09/11/2015 03:54:16 PM INFO: Cell returned -09/11/2015 03:54:16 PM INFO: Running cell: -f = open('numbers.txt') - -total = 0.0 -for line in f: - try: - total += float(line) - except ValueError: - pass - -f.close() - -print(total) - - -09/11/2015 03:54:16 PM INFO: Cell returned -09/11/2015 03:54:16 PM INFO: Shutdown kernel ----> END 'py_adv_feat_solutions.ipynb' <--- - ----> Executing 'pyess_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:54:17 PM INFO: Reading notebook pyess_solutions.ipynb -09/11/2015 03:54:18 PM INFO: Running cell: -from __future__ import division # Omit for Python 3.x - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Running cell: -x_vals = [1, 2, 3] -y_vals = [1, 1, 1] -sum([x * y for x, y in zip(x_vals, y_vals)]) - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Running cell: -sum(x * y for x, y in zip(x_vals, y_vals)) - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Running cell: -sum([x % 2 == 0 for x in range(100)]) - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Running cell: -sum(x % 2 == 0 for x in range(100)) - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Running cell: -len([x for x in range(100) if x % 2 == 0]) - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Running cell: -sum([1 for x in range(100) if x % 2 == 0]) - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Running cell: -pairs = ((2, 5), (4, 2), (9, 8), (12, 10)) -sum([x % 2 == 0 and y % 2 == 0 for x, y in pairs]) - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Running cell: -def p(x, coeff): - return sum(a * x**i for i, a in enumerate(coeff)) - - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Running cell: -p(1, (2, 4)) - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Running cell: -def f(string): - count = 0 - for letter in string: - if letter == letter.upper() and letter.isalpha(): - count += 1 - return count -f('The Rain in Spain') - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Running cell: -def f(seq_a, seq_b): - is_subset = True - for a in seq_a: - if a not in seq_b: - is_subset = False - return is_subset - -# == test == # - -print(f([1, 2], [1, 2, 3])) -print(f([1, 2, 3], [1, 2])) - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Running cell: -def f(seq_a, seq_b): - return set(seq_a).issubset(set(seq_b)) - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Running cell: -def linapprox(f, a, b, n, x): - """ - Evaluates the piecewise linear interpolant of f at x on the interval - [a, b], with n evenly spaced grid points. - - Parameters - =========== - f : function - The function to approximate - - x, a, b : scalars (floats or integers) - Evaluation point and endpoints, with a <= x <= b - - n : integer - Number of grid points - - Returns - ========= - A float. The interpolant evaluated at x - - """ - length_of_interval = b - a - num_subintervals = n - 1 - step = length_of_interval / num_subintervals - - # === find first grid point larger than x === # - point = a - while point <= x: - point += step - - # === x must lie between the gridpoints (point - step) and point === # - u, v = point - step, point - - return f(u) + (x - u) * (f(v) - f(u)) / (v - u) - - -09/11/2015 03:54:18 PM INFO: Cell returned -09/11/2015 03:54:18 PM INFO: Shutdown kernel ----> END 'pyess_solutions.ipynb' <--- - ----> Executing 'ree_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:54:19 PM INFO: Reading notebook ree_solutions.ipynb -09/11/2015 03:54:20 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:54:20 PM INFO: Cell returned -09/11/2015 03:54:20 PM INFO: Running cell: -from __future__ import print_function -import numpy as np -import matplotlib.pyplot as plt - -09/11/2015 03:54:20 PM INFO: Cell returned -09/11/2015 03:54:20 PM INFO: Running cell: -from quantecon import LQ - -09/11/2015 03:54:22 PM INFO: Cell returned -09/11/2015 03:54:22 PM INFO: Running cell: - -# == Model parameters == # - -a0 = 100 -a1 = 0.05 -beta = 0.95 -gamma = 10.0 - -# == Beliefs == # - -kappa0 = 95.5 -kappa1 = 0.95 - -# == Formulate the LQ problem == # - -A = np.array([[1, 0, 0], [0, kappa1, kappa0], [0, 0, 1]]) -B = np.array([1, 0, 0]) -B.shape = 3, 1 -R = np.array([[0, a1/2, -a0/2], [a1/2, 0, 0], [-a0/2, 0, 0]]) -Q = 0.5 * gamma - -# == Solve for the optimal policy == # - -lq = LQ(Q, R, A, B, beta=beta) -P, F, d = lq.stationary_values() -F = F.flatten() -out1 = "F = [{0:.3f}, {1:.3f}, {2:.3f}]".format(F[0], F[1], F[2]) -h0, h1, h2 = -F[2], 1 - F[0], -F[1] -out2 = "(h0, h1, h2) = ({0:.3f}, {1:.3f}, {2:.3f})".format(h0, h1, h2) - -print(out1) -print(out2) - - -09/11/2015 03:54:22 PM INFO: Cell returned -09/11/2015 03:54:22 PM INFO: Running cell: - -candidates = ( - (94.0886298678, 0.923409232937), - (93.2119845412, 0.984323478873), - (95.0818452486, 0.952459076301) - ) - -for kappa0, kappa1 in candidates: - - # == Form the associated law of motion == # - A = np.array([[1, 0, 0], [0, kappa1, kappa0], [0, 0, 1]]) - - # == Solve the LQ problem for the firm == # - lq = LQ(Q, R, A, B, beta=beta) - P, F, d = lq.stationary_values() - F = F.flatten() - h0, h1, h2 = -F[2], 1 - F[0], -F[1] - - # == Test the equilibrium condition == # - if np.allclose((kappa0, kappa1), (h0, h1 + h2)): - print('Equilibrium pair =', kappa0, kappa1) - print('(h0, h1, h2) = ', h0, h1, h2) - break - - - - -09/11/2015 03:54:22 PM INFO: Cell returned -09/11/2015 03:54:22 PM INFO: Running cell: - -# == Formulate the planner's LQ problem == # - -A = np.array([[1, 0], [0, 1]]) -B = np.array([[1], [0]]) -R = np.array([[a1 / 2, -a0 / 2], [-a0 / 2, 0]]) -Q = gamma / 2 - -# == Solve for the optimal policy == # - -lq = LQ(Q, R, A, B, beta=beta) -P, F, d = lq.stationary_values() - -# == Print the results == # - -F = F.flatten() -kappa0, kappa1 = -F[1], 1 - F[0] -print(kappa0, kappa1) - - -09/11/2015 03:54:22 PM INFO: Cell returned -09/11/2015 03:54:22 PM INFO: Running cell: - -A = np.array([[1, 0], [0, 1]]) -B = np.array([[1], [0]]) -R = np.array([[a1, -a0 / 2], [-a0 / 2, 0]]) -Q = gamma / 2 - -lq = LQ(Q, R, A, B, beta=beta) -P, F, d = lq.stationary_values() - -F = F.flatten() -m0, m1 = -F[1], 1 - F[0] -print(m0, m1) - - -09/11/2015 03:54:22 PM INFO: Cell returned -09/11/2015 03:54:22 PM INFO: Shutdown kernel ----> END 'ree_solutions.ipynb' <--- - ----> Executing 'schelling_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:54:23 PM INFO: Reading notebook schelling_solutions.ipynb -09/11/2015 03:54:23 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:54:24 PM INFO: Cell returned -09/11/2015 03:54:24 PM INFO: Running cell: -from random import uniform, seed -from math import sqrt -import matplotlib.pyplot as plt - -seed(10) # for reproducible random numbers - -class Agent: - - def __init__(self, type): - self.type = type - self.draw_location() - - def draw_location(self): - self.location = uniform(0, 1), uniform(0, 1) - - def get_distance(self, other): - "Computes euclidean distance between self and other agent." - a = (self.location[0] - other.location[0])**2 - b = (self.location[1] - other.location[1])**2 - return sqrt(a + b) - - def happy(self, agents): - "True if sufficient number of nearest neighbors are of the same type." - distances = [] - # distances is a list of pairs (d, agent), where d is distance from - # agent to self - for agent in agents: - if self != agent: - distance = self.get_distance(agent) - distances.append((distance, agent)) - # == Sort from smallest to largest, according to distance == # - distances.sort() - # == Extract the neighboring agents == # - neighbors = [agent for d, agent in distances[:num_neighbors]] - # == Count how many neighbors have the same type as self == # - num_same_type = sum(self.type == agent.type for agent in neighbors) - return num_same_type >= require_same_type - - def update(self, agents): - "If not happy, then randomly choose new locations until happy." - while not self.happy(agents): - self.draw_location() - - -def plot_distribution(agents, cycle_num): - "Plot the distribution of agents after cycle_num rounds of the loop." - x_values_0, y_values_0 = [], [] - x_values_1, y_values_1 = [], [] - # == Obtain locations of each type == # - for agent in agents: - x, y = agent.location - if agent.type == 0: - x_values_0.append(x) - y_values_0.append(y) - else: - x_values_1.append(x) - y_values_1.append(y) - fig, ax = plt.subplots(figsize=(8, 8)) - plot_args = {'markersize' : 8, 'alpha' : 0.6} - ax.set_axis_bgcolor('azure') - ax.plot(x_values_0, y_values_0, 'o', markerfacecolor='orange', **plot_args) - ax.plot(x_values_1, y_values_1, 'o', markerfacecolor='green', **plot_args) - ax.set_title('Cycle {}'.format(cycle_num - 1)) - plt.show() - -# == Main == # - -num_of_type_0 = 250 -num_of_type_1 = 250 -num_neighbors = 10 # Number of agents regarded as neighbors -require_same_type = 7 # Want at least this many neighbors to be same type - -# == Create a list of agents == # -agents = [Agent(0) for i in range(num_of_type_0)] -agents.extend(Agent(1) for i in range(num_of_type_1)) - - -count = 1 -# == Loop until none wishes to move == # -while 1: - print('Entering loop ', count) - plot_distribution(agents, count) - count += 1 - no_one_moved = True - for agent in agents: - old_location = agent.location - agent.update(agents) - if agent.location != old_location: - no_one_moved = False - if no_one_moved: - break - -print('Converged, terminating.') - - -09/11/2015 03:54:34 PM INFO: Cell returned -09/11/2015 03:54:34 PM INFO: Shutdown kernel ----> END 'schelling_solutions.ipynb' <--- - ----> Executing 'scipy_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:54:35 PM INFO: Reading notebook scipy_solutions.ipynb -09/11/2015 03:54:35 PM INFO: Running cell: -def bisect(f, a, b, tol=10e-5): - """ - Implements the bisection root finding algorithm, assuming that f is a - real-valued function on [a, b] satisfying f(a) < 0 < f(b). - """ - lower, upper = a, b - if upper - lower < tol: - return 0.5 * (upper + lower) - else: - middle = 0.5 * (upper + lower) - print('Current mid point = {}'.format(middle)) - if f(middle) > 0: # Implies root is between lower and middle - bisect(f, lower, middle) - else: # Implies root is between middle and upper - bisect(f, middle, upper) - - -09/11/2015 03:54:35 PM INFO: Cell returned -09/11/2015 03:54:35 PM INFO: Running cell: -import numpy as np -f = lambda x: np.sin(4 * (x - 0.25)) + x + x**20 - 1 - -bisect(f, 0, 1) - -09/11/2015 03:54:36 PM INFO: Cell returned -09/11/2015 03:54:36 PM INFO: Shutdown kernel ----> END 'scipy_solutions.ipynb' <--- - ----> Executing 'short_path_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:54:37 PM INFO: Reading notebook short_path_solutions.ipynb -09/11/2015 03:54:38 PM INFO: Running cell: -%%file graph.txt -node0, node1 0.04, node8 11.11, node14 72.21 -node1, node46 1247.25, node6 20.59, node13 64.94 -node2, node66 54.18, node31 166.80, node45 1561.45 -node3, node20 133.65, node6 2.06, node11 42.43 -node4, node75 3706.67, node5 0.73, node7 1.02 -node5, node45 1382.97, node7 3.33, node11 34.54 -node6, node31 63.17, node9 0.72, node10 13.10 -node7, node50 478.14, node9 3.15, node10 5.85 -node8, node69 577.91, node11 7.45, node12 3.18 -node9, node70 2454.28, node13 4.42, node20 16.53 -node10, node89 5352.79, node12 1.87, node16 25.16 -node11, node94 4961.32, node18 37.55, node20 65.08 -node12, node84 3914.62, node24 34.32, node28 170.04 -node13, node60 2135.95, node38 236.33, node40 475.33 -node14, node67 1878.96, node16 2.70, node24 38.65 -node15, node91 3597.11, node17 1.01, node18 2.57 -node16, node36 392.92, node19 3.49, node38 278.71 -node17, node76 783.29, node22 24.78, node23 26.45 -node18, node91 3363.17, node23 16.23, node28 55.84 -node19, node26 20.09, node20 0.24, node28 70.54 -node20, node98 3523.33, node24 9.81, node33 145.80 -node21, node56 626.04, node28 36.65, node31 27.06 -node22, node72 1447.22, node39 136.32, node40 124.22 -node23, node52 336.73, node26 2.66, node33 22.37 -node24, node66 875.19, node26 1.80, node28 14.25 -node25, node70 1343.63, node32 36.58, node35 45.55 -node26, node47 135.78, node27 0.01, node42 122.00 -node27, node65 480.55, node35 48.10, node43 246.24 -node28, node82 2538.18, node34 21.79, node36 15.52 -node29, node64 635.52, node32 4.22, node33 12.61 -node30, node98 2616.03, node33 5.61, node35 13.95 -node31, node98 3350.98, node36 20.44, node44 125.88 -node32, node97 2613.92, node34 3.33, node35 1.46 -node33, node81 1854.73, node41 3.23, node47 111.54 -node34, node73 1075.38, node42 51.52, node48 129.45 -node35, node52 17.57, node41 2.09, node50 78.81 -node36, node71 1171.60, node54 101.08, node57 260.46 -node37, node75 269.97, node38 0.36, node46 80.49 -node38, node93 2767.85, node40 1.79, node42 8.78 -node39, node50 39.88, node40 0.95, node41 1.34 -node40, node75 548.68, node47 28.57, node54 53.46 -node41, node53 18.23, node46 0.28, node54 162.24 -node42, node59 141.86, node47 10.08, node72 437.49 -node43, node98 2984.83, node54 95.06, node60 116.23 -node44, node91 807.39, node46 1.56, node47 2.14 -node45, node58 79.93, node47 3.68, node49 15.51 -node46, node52 22.68, node57 27.50, node67 65.48 -node47, node50 2.82, node56 49.31, node61 172.64 -node48, node99 2564.12, node59 34.52, node60 66.44 -node49, node78 53.79, node50 0.51, node56 10.89 -node50, node85 251.76, node53 1.38, node55 20.10 -node51, node98 2110.67, node59 23.67, node60 73.79 -node52, node94 1471.80, node64 102.41, node66 123.03 -node53, node72 22.85, node56 4.33, node67 88.35 -node54, node88 967.59, node59 24.30, node73 238.61 -node55, node84 86.09, node57 2.13, node64 60.80 -node56, node76 197.03, node57 0.02, node61 11.06 -node57, node86 701.09, node58 0.46, node60 7.01 -node58, node83 556.70, node64 29.85, node65 34.32 -node59, node90 820.66, node60 0.72, node71 0.67 -node60, node76 48.03, node65 4.76, node67 1.63 -node61, node98 1057.59, node63 0.95, node64 4.88 -node62, node91 132.23, node64 2.94, node76 38.43 -node63, node66 4.43, node72 70.08, node75 56.34 -node64, node80 47.73, node65 0.30, node76 11.98 -node65, node94 594.93, node66 0.64, node73 33.23 -node66, node98 395.63, node68 2.66, node73 37.53 -node67, node82 153.53, node68 0.09, node70 0.98 -node68, node94 232.10, node70 3.35, node71 1.66 -node69, node99 247.80, node70 0.06, node73 8.99 -node70, node76 27.18, node72 1.50, node73 8.37 -node71, node89 104.50, node74 8.86, node91 284.64 -node72, node76 15.32, node84 102.77, node92 133.06 -node73, node83 52.22, node76 1.40, node90 243.00 -node74, node81 1.07, node76 0.52, node78 8.08 -node75, node92 68.53, node76 0.81, node77 1.19 -node76, node85 13.18, node77 0.45, node78 2.36 -node77, node80 8.94, node78 0.98, node86 64.32 -node78, node98 355.90, node81 2.59 -node79, node81 0.09, node85 1.45, node91 22.35 -node80, node92 121.87, node88 28.78, node98 264.34 -node81, node94 99.78, node89 39.52, node92 99.89 -node82, node91 47.44, node88 28.05, node93 11.99 -node83, node94 114.95, node86 8.75, node88 5.78 -node84, node89 19.14, node94 30.41, node98 121.05 -node85, node97 94.51, node87 2.66, node89 4.90 -node86, node97 85.09 -node87, node88 0.21, node91 11.14, node92 21.23 -node88, node93 1.31, node91 6.83, node98 6.12 -node89, node97 36.97, node99 82.12 -node90, node96 23.53, node94 10.47, node99 50.99 -node91, node97 22.17 -node92, node96 10.83, node97 11.24, node99 34.68 -node93, node94 0.19, node97 6.71, node99 32.77 -node94, node98 5.91, node96 2.03 -node95, node98 6.17, node99 0.27 -node96, node98 3.32, node97 0.43, node99 5.87 -node97, node98 0.30 -node98, node99 0.33 -node99, - -09/11/2015 03:54:38 PM INFO: Cell returned -09/11/2015 03:54:38 PM INFO: Running cell: - -def read_graph(in_file): - """ Read in the graph from the data file. The graph is stored - as a dictionary, where the keys are the nodes, and the values - are a list of pairs (d, c), where d is a node and c is a number. - If (d, c) is in the list for node n, then d can be reached from - n at cost c. - """ - graph = {} - infile = open(in_file) - for line in infile: - elements = line.split(',') - node = elements.pop(0).strip() - graph[node] = [] - if node != 'node99': - for element in elements: - destination, cost = element.split() - graph[node].append((destination.strip(), float(cost))) - infile.close() - return graph - -def update_J(J, graph): - "The Bellman operator." - next_J = {} - for node in graph: - if node == 'node99': - next_J[node] = 0 - else: - next_J[node] = min(cost + J[dest] for dest, cost in graph[node]) - return next_J - -def print_best_path(J, graph): - """ Given a cost-to-go function, computes the best path. At each node n, - the function prints the current location, looks at all nodes that can be - reached from n, and moves to the node m which minimizes c + J[m], where c - is the cost of moving to m. - """ - sum_costs = 0 - current_location = 'node0' - while current_location != 'node99': - print(current_location) - running_min = 1e100 # Any big number - for destination, cost in graph[current_location]: - cost_of_path = cost + J[destination] - if cost_of_path < running_min: - running_min = cost_of_path - minimizer_cost = cost - minimizer_dest = destination - current_location = minimizer_dest - sum_costs += minimizer_cost - - print('node99\n') - print('Cost: ', sum_costs) - - -## Main loop - -graph = read_graph('graph.txt') -M = 1e10 -J = {} -for node in graph: - J[node] = M -J['node99'] = 0 - -while 1: - next_J = update_J(J, graph) - if next_J == J: - break - else: - J = next_J -print_best_path(J, graph) - -09/11/2015 03:54:38 PM INFO: Cell returned -09/11/2015 03:54:38 PM INFO: Shutdown kernel ----> END 'short_path_solutions.ipynb' <--- - ----> Executing 'speed_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:54:40 PM INFO: Reading notebook speed_solutions.ipynb -09/11/2015 03:54:40 PM INFO: Running cell: -import matplotlib.pyplot as plt -import numpy as np -from numba import jit - -09/11/2015 03:54:41 PM INFO: Cell returned -09/11/2015 03:54:41 PM INFO: Running cell: -p, q = 0.1, 0.2 # Prob of leaving low and high state respectively - -09/11/2015 03:54:41 PM INFO: Cell returned -09/11/2015 03:54:41 PM INFO: Running cell: -def compute_series(n): - x = np.empty(n, dtype=int) - x[0] = 1 # Start in state 1 - U = np.random.uniform(0, 1, size=n) - for t in range(1, n): - current_x = x[t-1] - if current_x == 0: - x[t] = U[t] < p - else: - x[t] = U[t] > q - return x - -09/11/2015 03:54:41 PM INFO: Cell returned -09/11/2015 03:54:41 PM INFO: Running cell: -n = 100000 -x = compute_series(n) -print(np.mean(x == 0)) # Fraction of time x is in state 0 - -09/11/2015 03:54:41 PM INFO: Cell returned -09/11/2015 03:54:41 PM INFO: Running cell: -%timeit compute_series(n) - -09/11/2015 03:54:47 PM INFO: Cell returned -09/11/2015 03:54:47 PM INFO: Running cell: -compute_series_numba = jit(compute_series) - -09/11/2015 03:54:47 PM INFO: Cell returned -09/11/2015 03:54:47 PM INFO: Running cell: -x = compute_series_numba(n) -print(np.mean(x == 0)) - -09/11/2015 03:54:47 PM INFO: Cell returned -09/11/2015 03:54:47 PM INFO: Running cell: -%timeit compute_series_numba(n) - -09/11/2015 03:54:49 PM INFO: Cell returned -09/11/2015 03:54:49 PM INFO: Running cell: -%load_ext cythonmagic - -09/11/2015 03:54:50 PM INFO: Cell returned -09/11/2015 03:54:50 PM INFO: Running cell: -%%cython -import numpy as np -from numpy cimport int_t, float_t - -def compute_series_cy(int n): - # == Create NumPy arrays first == # - x_np = np.empty(n, dtype=int) - U_np = np.random.uniform(0, 1, size=n) - # == Now create memoryviews of the arrays == # - cdef int_t [:] x = x_np - cdef float_t [:] U = U_np - # == Other variable declarations == # - cdef float p = 0.1 - cdef float q = 0.2 - cdef int t - # == Main loop == # - x[0] = 1 - for t in range(1, n): - current_x = x[t-1] - if current_x == 0: - x[t] = U[t] < p - else: - x[t] = U[t] > q - return np.asarray(x) - -09/11/2015 03:54:50 PM INFO: Cell returned -09/11/2015 03:54:50 PM INFO: Running cell: -compute_series_cy(10) - -09/11/2015 03:54:50 PM INFO: Cell returned -09/11/2015 03:54:50 PM INFO: Running cell: -x = compute_series_cy(n) -print(np.mean(x == 0)) - -09/11/2015 03:54:50 PM INFO: Cell returned -09/11/2015 03:54:50 PM INFO: Running cell: -%timeit compute_series_cy(n) - -09/11/2015 03:54:53 PM INFO: Cell returned -09/11/2015 03:54:53 PM INFO: Shutdown kernel ----> END 'speed_solutions.ipynb' <--- - ----> Executing 'statd_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:54:53 PM INFO: Reading notebook statd_solutions.ipynb -09/11/2015 03:54:54 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:54:55 PM INFO: Cell returned -09/11/2015 03:54:55 PM INFO: Running cell: -import numpy as np -import matplotlib.pyplot as plt - -09/11/2015 03:54:55 PM INFO: Cell returned -09/11/2015 03:54:55 PM INFO: Running cell: -from scipy.stats import norm, gaussian_kde -from quantecon import LAE - -phi = norm() -n = 500 -theta = 0.8 -# == Frequently used constants == # -d = np.sqrt(1 - theta**2) -delta = theta / d - -def psi_star(y): - "True stationary density of the TAR Model" - return 2 * norm.pdf(y) * norm.cdf(delta * y) - -def p(x, y): - "Stochastic kernel for the TAR model." - return phi.pdf((y - theta * np.abs(x)) / d) / d - -Z = phi.rvs(n) -X = np.empty(n) -for t in range(n-1): - X[t+1] = theta * np.abs(X[t]) + d * Z[t] -psi_est = LAE(p, X) -k_est = gaussian_kde(X) - -fig, ax = plt.subplots(figsize=(10,7)) -ys = np.linspace(-3, 3, 200) -ax.plot(ys, psi_star(ys), 'b-', lw=2, alpha=0.6, label='true') -ax.plot(ys, psi_est(ys), 'g-', lw=2, alpha=0.6, label='look ahead estimate') -ax.plot(ys, k_est(ys), 'k-', lw=2, alpha=0.6, label='kernel based estimate') -ax.legend(loc='upper left') -plt.show() - -09/11/2015 03:54:57 PM INFO: Cell returned -09/11/2015 03:54:57 PM INFO: Running cell: -from scipy.stats import lognorm, beta - -# == Define parameters == # -s = 0.2 -delta = 0.1 -a_sigma = 0.4 # A = exp(B) where B ~ N(0, a_sigma) -alpha = 0.4 # f(k) = k**alpha - -phi = lognorm(a_sigma) - -def p(x, y): - "Stochastic kernel, vectorized in x. Both x and y must be positive." - d = s * x**alpha - return phi.pdf((y - (1 - delta) * x) / d) / d - -n = 1000 # Number of observations at each date t -T = 40 # Compute density of k_t at 1,...,T - -fig, axes = plt.subplots(2, 2, figsize=(11, 8)) -axes = axes.flatten() -xmax = 6.5 - -for i in range(4): - ax = axes[i] - ax.set_xlim(0, xmax) - psi_0 = beta(5, 5, scale=0.5, loc=i*2) # Initial distribution - - # == Generate matrix s.t. t-th column is n observations of k_t == # - k = np.empty((n, T)) - A = phi.rvs((n, T)) - k[:, 0] = psi_0.rvs(n) - for t in range(T-1): - k[:, t+1] = s * A[:,t] * k[:, t]**alpha + (1 - delta) * k[:, t] - - # == Generate T instances of lae using this data, one for each t == # - laes = [LAE(p, k[:, t]) for t in range(T)] - - ygrid = np.linspace(0.01, xmax, 150) - greys = [str(g) for g in np.linspace(0.0, 0.8, T)] - greys.reverse() - for psi, g in zip(laes, greys): - ax.plot(ygrid, psi(ygrid), color=g, lw=2, alpha=0.6) - ax.set_xlabel('capital') - -09/11/2015 03:55:05 PM INFO: Cell returned -09/11/2015 03:55:05 PM INFO: Running cell: -n = 20 -k = 5000 -J = 6 - -theta = 0.9 -d = np.sqrt(1 - theta**2) -delta = theta / d - -fig, axes = plt.subplots(J, 1, figsize=(10, 4*J)) -initial_conditions = np.linspace(8, 0, J) -X = np.empty((k, n)) - -for j in range(J): - - axes[j].set_ylim(-4, 8) - title = 'time series from t = ' + str(initial_conditions[j]) - axes[j].set_title(title) - - Z = np.random.randn(k, n) - X[:,0] = initial_conditions[j] - for t in range(1, n): - X[:, t] = theta * np.abs(X[:, t-1]) + d * Z[:, t] - axes[j].boxplot(X) - -plt.show() - -09/11/2015 03:55:10 PM INFO: Cell returned -09/11/2015 03:55:10 PM INFO: Shutdown kernel ----> END 'statd_solutions.ipynb' <--- - ----> Executing 'uncertainty_traps_solutions.ipynb' <--- -/home/matthewmckay/anaconda/lib/python2.7/site-packages/IPython/nbformat/current.py:19: UserWarning: IPython.nbformat.current is deprecated. - -- use IPython.nbformat for read/write/validate public API -- use IPython.nbformat.vX directly to composing notebooks of a particular version - - """) -09/11/2015 03:55:11 PM INFO: Reading notebook uncertainty_traps_solutions.ipynb -09/11/2015 03:55:12 PM INFO: Running cell: -%matplotlib inline - -09/11/2015 03:55:13 PM INFO: Cell returned -09/11/2015 03:55:13 PM INFO: Running cell: -from __future__ import division -import matplotlib.pyplot as plt -import numpy as np -import quantecon as qe -import seaborn as sns -import itertools - -09/11/2015 03:55:14 PM INFO: Cell returned -09/11/2015 03:55:14 PM INFO: Running cell: -palette = itertools.cycle(sns.color_palette()) -econ = qe.models.UncertaintyTrapEcon() -rho, sig_theta, gx = econ.rho, econ.sig_theta, econ.gx # simplify names -g = np.linspace(1e-10, 3, 200) # gamma grid -fig, ax = plt.subplots(figsize=(9, 9)) -ax.plot(g, g, 'k-') # 45 degree line -for M in range(7): - g_next = 1 / (rho**2 / (g + M * gx) + sig_theta**2) - label_string = r"$M = {}$".format(M) - ax.plot(g, g_next, lw=2, label=label_string, color=next(palette)) -ax.legend(loc='lower right', fontsize=14) -ax.set_xlabel(r'$\gamma$', fontsize=16) -ax.set_ylabel(r"$\gamma'$", fontsize=16) -ax.grid() -plt.show() - -09/11/2015 03:55:16 PM INFO: Cell returned -09/11/2015 03:55:16 PM INFO: Running cell: -sim_length=2000 - -mu_vec = np.empty(sim_length) -theta_vec = np.empty(sim_length) -gamma_vec = np.empty(sim_length) -X_vec = np.empty(sim_length) -M_vec = np.empty(sim_length) - -mu_vec[0] = econ.mu -gamma_vec[0] = econ.gamma -theta_vec[0] = 0 - -w_shocks = np.random.randn(sim_length) - -for t in range(sim_length-1): - X, M = econ.gen_aggregates() - X_vec[t] = X - M_vec[t] = M - - econ.update_beliefs(X, M) - econ.update_theta(w_shocks[t]) - - mu_vec[t+1] = econ.mu - gamma_vec[t+1] = econ.gamma - theta_vec[t+1] = econ.theta - -# Record final values of aggregates -X, M = econ.gen_aggregates() -X_vec[-1] = X -M_vec[-1] = M - -09/11/2015 03:55:16 PM INFO: Cell returned -09/11/2015 03:55:16 PM INFO: Running cell: -fig, ax = plt.subplots(figsize=(9, 6)) -ax.plot(range(sim_length), theta_vec, alpha=0.6, lw=2, label=r"$\theta$") -ax.plot(range(sim_length), mu_vec, alpha=0.6, lw=2, label=r"$\mu$") -ax.legend(fontsize=16) -plt.show() - -09/11/2015 03:55:17 PM INFO: Cell returned -09/11/2015 03:55:17 PM INFO: Running cell: -fig, axes = plt.subplots(4, 1, figsize=(12, 20)) -# Add some spacing -fig.subplots_adjust(hspace=0.3) - -series = (theta_vec, mu_vec, gamma_vec, M_vec) -names = r'$\theta$', r'$\mu$', r'$\gamma$', r'$M$' - -for ax, vals, name in zip(axes, series, names): - # determine suitable y limits - s_max, s_min = max(vals), min(vals) - s_range = s_max - s_min - y_max = s_max + s_range * 0.1 - y_min = s_min - s_range * 0.1 - ax.set_ylim(y_min, y_max) - # Plot series - ax.plot(range(sim_length), vals, alpha=0.6, lw=2) - ax.set_title("time series for {}".format(name), fontsize=16) - ax.grid() - -plt.show() - -09/11/2015 03:55:19 PM INFO: Cell returned -09/11/2015 03:55:19 PM INFO: Running cell: - - -09/11/2015 03:55:19 PM INFO: Cell returned -09/11/2015 03:55:19 PM INFO: Shutdown kernel ----> END 'uncertainty_traps_solutions.ipynb' <--- - diff --git a/scripts/test-examples.py b/scripts/test-examples.py deleted file mode 100644 index 9dd187617..000000000 --- a/scripts/test-examples.py +++ /dev/null @@ -1,90 +0,0 @@ -#!/usr/bin/python -""" -Test script for QuantEcon executables -===================================== - examples/*.py - solutions/*.ipynb - -This script uses a context manager to redirect stdout and stderr -to capture runtime errors for writing to the log file. It also -reports basic execution statistics on the command line (pass/fail) - -Usage ------ -python test.py - -Default Logs ------------- - examples/*.py => example-tests.log -""" - -import sys -import os -import glob -import subprocess -import re - -from common import RedirectStdStreams - -set_backend = "import matplotlib\nmatplotlib.use('Agg')\n" - -def generate_temp(fl): - """ - Modify file to supress matplotlib figures - Preserve __future__ imports at front of file for python intertpreter - """ - doc = open(fl).read() - doc = set_backend+doc - #-Adjust Future Imports-# - if re.search(r"from __future__ import division", doc): - doc = doc.replace("from __future__ import division", "") - doc = "from __future__ import division\n" + doc - return doc - -def example_tests(test_dir='examples/', log_path='../scripts/example-tests.log'): - """ - Execute each Python Example File and check exit status. - The stdout and stderr is also captured and added to the log file - """ - os.chdir(test_dir) - test_files = glob.glob('*.py') - test_files.sort() - passed = [] - failed = [] - with open(log_path, 'w') as f: - for i,fname in enumerate(test_files): - print("Checking program %s (%s/%s) ..."%(fname,i,len(test_files))) - with RedirectStdStreams(stdout=f, stderr=f): - print("---Executing '%s'---" % fname) - sys.stdout.flush() - #-Generate tmp File-# - tmpfl = "_" + fname - fl = open(tmpfl,'w') - fl.write(generate_temp(fname)) - fl.close() - #-Run Program-# - exit_code = subprocess.call(["python",tmpfl], stderr=f) - if exit_code == 0: - passed.append(fname) - else: - failed.append(fname) - #-Remove tmp file-# - os.remove(tmpfl) - print("---END '%s'---" % fname) - sys.stdout.flush() - #-Report-# - print("[examples/*.py] Passed %i/%i: " %(len(passed), len(test_files))) - if len(failed) == 0: - print("Failed Files:\n\tNone") - else: - print("Failed Files:\n\t" + '\n\t'.join(failed)) - print(">> See %s for details" % log_path) - os.chdir('../') - return passed, failed - - -if __name__ == '__main__': - print("-------------------------") - print("Running all examples/*.py") - print("-------------------------") - example_tests(*sys.argv[1:]) \ No newline at end of file diff --git a/scripts/test-solutions.py b/scripts/test-solutions.py deleted file mode 100644 index 0078a4cf4..000000000 --- a/scripts/test-solutions.py +++ /dev/null @@ -1,58 +0,0 @@ -#!/usr/bin/python -""" -Test solutions/*.ipynb - -Notes ------ - 1. This script should be run from the root level "python scripts/test-solutions.py" - -""" - -import sys -import os -import glob -import subprocess - -from common import RedirectStdStreams - -def solutions_tests(test_dir='solutions/', log_path='../scripts/solutions-tests.log'): - """ - Execute each Jupyter Notebook - """ - os.chdir(test_dir) - test_files = glob.glob(os.path.join('*.ipynb')) - test_files.sort() - passed = [] - failed = [] - with open(log_path, 'w') as f: - for i,fname in enumerate(test_files): - print("Checking notebook %s (%s/%s) ..."%(fname,i,len(test_files))) - with RedirectStdStreams(stdout=f, stderr=f): - print("---> Executing '%s' <---" % fname) - sys.stdout.flush() - #-Run Program-# - exit_code = subprocess.call(["runipy",fname], stdout=open(os.devnull, 'wb'), stderr=f) - sys.stderr.flush() - if exit_code == 0: - passed.append(fname) - else: - failed.append(fname) - print("---> END '%s' <---" % fname) - print - sys.stdout.flush() - #-Report-# - print("[solutions/*.py] Passed %i/%i: " %(len(passed), len(test_files))) - if len(failed) == 0: - print("Failed Notebooks:\n\tNone") - else: - print("Failed Notebooks:\n\t" + '\n\t'.join(failed)) - print(">> See %s for details" % log_path) - os.chdir('../') - return passed, failed - - -if __name__ == '__main__': - print("-----------------------------") - print("Running all solutions/*.ipynb") - print("-----------------------------") - solutions_tests(*sys.argv[1:]) \ No newline at end of file diff --git a/setup.py b/setup.py index 477efcab2..4c1a46ca7 100644 --- a/setup.py +++ b/setup.py @@ -4,7 +4,7 @@ #-Write Versions File-# #~~~~~~~~~~~~~~~~~~~~~# -VERSION = '0.2.0' +VERSION = '0.3.1' def write_version_py(filename=None): """ @@ -12,10 +12,10 @@ def write_version_py(filename=None): """ doc = "\"\"\"\nThis is a VERSION file and should NOT be manually altered\n\"\"\"" doc += "\nversion = '%s'" % VERSION - + if not filename: filename = os.path.join(os.path.dirname(__file__), 'quantecon', 'version.py') - + fl = open(filename, 'w') try: fl.write(doc) @@ -30,12 +30,12 @@ def write_version_py(filename=None): DESCRIPTION = "QuantEcon is a package to support all forms of quantitative economic modelling." #'Core package of the QuantEcon library' LONG_DESCRIPTION = """ -**QuantEcon** is an organization run by economists for economists with the aim of coordinating -distributed development of high quality open source code for all forms of quantitative economic modelling. +**QuantEcon** is an organization run by economists for economists with the aim of coordinating +distributed development of high quality open source code for all forms of quantitative economic modelling. The project website is located at `http://quantecon.org/ `_. This website provides -more information with regards to the **quantecon** library, documentation, in addition to some resources -in regards to how you can use and/or contribute to the package. +more information with regards to the **quantecon** library, documentation, in addition to some resources +in regards to how you can use and/or contribute to the package. The **quantecon** Package ------------------------- @@ -68,7 +68,7 @@ def write_version_py(filename=None): Additional Links ---------------- -1. `QuantEcon Course Website `_ +1. `QuantEcon Course Website `_ """ @@ -84,8 +84,7 @@ def write_version_py(filename=None): 'Programming Language :: Python :: 2', 'Programming Language :: Python :: 3', 'Programming Language :: Python :: 2.7', - 'Programming Language :: Python :: 3.3', - 'Programming Language :: Python :: 3.4', + 'Programming Language :: Python :: 3.5', 'Topic :: Scientific/Engineering', ] @@ -94,12 +93,13 @@ def write_version_py(filename=None): setup(name='quantecon', packages=['quantecon', - 'quantecon.markov', - 'quantecon.models', - 'quantecon.models.solow', + 'quantecon.game_theory', + 'quantecon.markov', 'quantecon.random', 'quantecon.tests', 'quantecon.util', + #-Deprecated-# + 'quantecon.models', ], version=VERSION, description=DESCRIPTION, diff --git a/solutions/arellano_solutions.ipynb b/solutions/arellano_solutions.ipynb deleted file mode 100644 index bb5eb505a..000000000 --- a/solutions/arellano_solutions.ipynb +++ /dev/null @@ -1,326 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# quant-econ Solutions: Default Risk and Income Fluctuations" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/arellano.html" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "from __future__ import division\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "import quantecon as qe\n", - "from quantecon.models import Arellano_Economy" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Compute the value function, policy and equilibrium prices" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Running iteration 25 with dist of 0.34324232989\n", - "Running iteration 50 with dist of 0.0983915577985\n", - "Running iteration 75 with dist of 0.0292120955917\n", - "Running iteration 100 with dist of 0.00874510696905\n", - "Running iteration 125 with dist of 0.00262314121558\n", - "Running iteration 150 with dist of 0.000787192669915\n", - "Running iteration 175 with dist of 0.000236259111634\n", - "Running iteration 200 with dist of 7.09100062899e-05\n", - "Running iteration 225 with dist of 2.1282821141e-05\n", - "Running iteration 250 with dist of 6.38780295859e-06\n", - "Running iteration 275 with dist of 1.91722896759e-06\n", - "Running iteration 300 with dist of 5.75435290529e-07\n", - "Running iteration 325 with dist of 1.72710617363e-07\n", - "Running iteration 350 with dist of 5.1837215409e-08\n", - "Running iteration 375 with dist of 1.555838125e-08\n" - ] - } - ], - "source": [ - "ae = Arellano_Economy(beta=.953, # time discount rate\n", - " gamma=2., # risk aversion\n", - " r=0.017, # international interest rate\n", - " rho=.945, # persistence in output \n", - " eta=0.025, # st dev of output shock\n", - " theta=0.282, # prob of regaining access \n", - " ny=21, # number of points in y grid\n", - " nB=251, # number of points in B grid\n", - " tol=1e-8, # error tolerance in iteration\n", - " maxit=10000)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Compute the bond price schedule as seen in figure 3 of Arellano (2008)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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BIyMjOumkk9Tb2xvbuAA0Fv1YyIqdgzslSdPapyU8EtSKKBxhzZo1WrhwoTaGfwqvXLlS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\nH37bEb7Y4kWRsnYW4kSPSU2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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "\n", - "# Create \"Y High\" and \"Y Low\" values as 5% devs from mean\n", - "high, low = np.mean(ae.ygrid)*1.05, np.mean(ae.ygrid)*.95\n", - "iy_high, iy_low = (np.searchsorted(ae.ygrid, x) for x in (high, low))\n", - "\n", - "fig, ax = plt.subplots(figsize=(10, 6.5))\n", - "ax.set_title(\"Bond price schedule $q(y, B')$\")\n", - "\n", - "# Extract a suitable plot grid\n", - "x = []\n", - "q_low = []\n", - "q_high = []\n", - "for i in range(ae.nB):\n", - " b = ae.Bgrid[i]\n", - " if -0.35 <= b <= 0: # To match fig 3 of Arellano\n", - " x.append(b)\n", - " q_low.append(ae.Q[iy_low, i])\n", - " q_high.append(ae.Q[iy_high, i])\n", - "ax.plot(x, q_high, label=r\"$y_H$\", lw=2, alpha=0.7)\n", - "ax.plot(x, q_low, label=r\"$y_L$\", lw=2, alpha=0.7)\n", - "ax.set_xlabel(r\"$B'$\")\n", - "ax.legend(loc='upper left', frameon=False)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Draw a plot of the value functions" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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iIpIazN2jrqGBmRUARe4eM7PnAdz9GTO7B3gRmAmMBlYBk9091uT5pcB33P1t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\nACalyAEATOoPX53Pm74ffOwAAAAASUVORK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "\n", - "# Create \"Y High\" and \"Y Low\" values as 5% devs from mean\n", - "high, low = np.mean(ae.ygrid)*1.05, np.mean(ae.ygrid)*.95\n", - "iy_high, iy_low = (np.searchsorted(ae.ygrid, x) for x in (high, low))\n", - "\n", - "fig, ax = plt.subplots(figsize=(10, 6.5))\n", - "ax.set_title(\"Value Functions\")\n", - "ax.plot(ae.Bgrid, ae.V[iy_high], label=r\"$y_H$\", lw=2, alpha=0.7)\n", - "ax.plot(ae.Bgrid, ae.V[iy_low], label=r\"$y_L$\", lw=2, alpha=0.7)\n", - "ax.legend(loc='upper left')\n", - "ax.set_xlabel(r\"$B$\")\n", - "ax.set_ylabel(r\"$V(y, B)$\")\n", - "ax.set_xlim(ae.Bgrid.min(), ae.Bgrid.max())\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Draw a heat map for default probability" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "\n", - "xx, yy = ae.Bgrid, ae.ygrid\n", - "zz = ae.default_prob\n", - "\n", - "# Create figure\n", - "fig, ax = plt.subplots(figsize=(10, 6.5))\n", - "fig.suptitle(\"Probability of Default\")\n", - "hm = ax.pcolormesh(xx, yy, zz)\n", - "cax = fig.add_axes([.92, .1, .02, .8])\n", - "fig.colorbar(hm, cax=cax)\n", - "ax.axis([xx.min(), 0.05, yy.min(), yy.max()])\n", - "ax.set_xlabel(r\"$B'$\")\n", - "ax.set_ylabel(r\"$y$\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot a time series of major variables simulated from the model." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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f+hRw003AU0/lv60wxpg1N2tm7xMnMi9r+6+Q3GX5kk6YPf209o3NSJ9448yG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AF8+SVQXQ1kZyfu2loMjh3L1rKvvgKef563LV8O/PGPbNUT/zLBa4jFTLAV8VNyL5J37iaS/GvV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\nh2w2W9PracSxxd5vR0dHRZ9nn2v0/VRzvGEDAOjxh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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "T = 250\n", - "y_vec, B_vec, q_vec, default_vec = ae.simulate(T)\n", - "\n", - "# Pick up default start and end dates\n", - "start_end_pairs = []\n", - "i = 0\n", - "while i < len(default_vec):\n", - " if default_vec[i] == 0:\n", - " i += 1\n", - " else:\n", - " # If we get to here we're in default\n", - " start_default = i\n", - " while i < len(default_vec) and default_vec[i] == 1:\n", - " i += 1\n", - " end_default = i - 1\n", - " start_end_pairs.append((start_default, end_default))\n", - " \n", - "plot_series = y_vec, B_vec, q_vec\n", - "titles = 'output', 'foreign assets', 'bond price'\n", - "\n", - "fig, axes = plt.subplots(len(plot_series), 1, figsize=(10, 12))\n", - "p_args = {'lw': 2, 'alpha': 0.7}\n", - "fig.subplots_adjust(hspace=0.3)\n", - "\n", - "for ax, series, title in zip(axes, plot_series, titles):\n", - " # determine suitable y limits\n", - " s_max, s_min = max(series), min(series)\n", - " s_range = s_max - s_min\n", - " y_max = s_max + s_range * 0.1\n", - " y_min = s_min - s_range * 0.1\n", - " ax.set_ylim(y_min, y_max)\n", - " for pair in start_end_pairs:\n", - " ax.fill_between(pair, (y_min, y_min), (y_max, y_max), color='k', alpha=0.3)\n", - " \n", - " ax.grid()\n", - " ax.set_title(title)\n", - " ax.plot(range(T), series, **p_args)\n", - " ax.set_xlabel(r\"time\")\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.10" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/solutions/asset_solutions.ipynb b/solutions/asset_solutions.ipynb deleted file mode 100644 index 53da01cb2..000000000 --- a/solutions/asset_solutions.ipynb +++ /dev/null @@ -1,116 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:f95d50b3abd5dc694309bb15b01ad17d5b2269d03da61295961b5e7daef40de5" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: The Lucas Asset Pricing Model" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/markov_asset.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import division # Omit for Python 3.x\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from quantecon.models import AssetPrices" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 3 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# == Define primitives == #\n", - "n = 5\n", - "P = 0.0125 * np.ones((n, n))\n", - "P += np.diag(0.95 - 0.0125 * np.ones(5))\n", - "s = np.array([1.05, 1.025, 1.0, 0.975, 0.95])\n", - "gamma = 2.0\n", - "beta = 0.94\n", - "zeta = 1.0\n", - "\n", - "ap = AssetPrices(beta, P, s, gamma)\n", - "\n", - "v = ap.tree_price()\n", - "print(\"Lucas Tree Prices: \", v)\n", - "\n", - "v_consol = ap.consol_price(zeta)\n", - "print(\"Consol Bond Prices: \", v_consol)\n", - "\n", - "P_tilde = P * s**(1-gamma)\n", - "temp = beta * P_tilde.dot(v) + beta * P_tilde.dot(np.ones(n))\n", - "print(\"Should be 0: \", v - temp)\n", - "\n", - "p_s = 150.0\n", - "w_bar, w_bars = ap.call_option(zeta, p_s, T = [10,20,30])\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "('Lucas Tree Prices: ', array([ 12.72221763, 14.72515002, 17.57142236, 21.93570661, 29.47401578]))\n", - "('Consol Bond Prices: ', array([ 87.56860139, 109.25108965, 148.67554548, 242.55144082,\n", - " 753.87100476]))\n", - "('Should be 0: ', array([ -1.77635684e-15, -1.77635684e-15, 0.00000000e+00,\n", - " 0.00000000e+00, 0.00000000e+00]))\n" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/career_solutions.ipynb b/solutions/career_solutions.ipynb deleted file mode 100644 index f613c9228..000000000 --- a/solutions/career_solutions.ipynb +++ /dev/null @@ -1,723 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:b9dea1cbbf559fd5acb0661f63a244effc42bfd147016309292bad583956912a" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Modeling Career Choice" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/career.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from quantecon import DiscreteRV, compute_fixed_point\n", - "from quantecon.models import CareerWorkerProblem" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "Simulate job / career paths. \n", - "\n", - "In reading the code, recall that `optimal_policy[i, j]` = policy at\n", - "$(\\theta_i, \\epsilon_j)$ = either 1, 2 or 3; meaning 'stay put', 'new job' and\n", - "'new life'.\n", - "\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "wp = CareerWorkerProblem()\n", - "v_init = np.ones((wp.N, wp.N))*100\n", - "v = compute_fixed_point(wp.bellman_operator, v_init, verbose=False)\n", - "optimal_policy = wp.get_greedy(v)\n", - "F = DiscreteRV(wp.F_probs)\n", - "G = DiscreteRV(wp.G_probs)\n", - "\n", - "def gen_path(T=20):\n", - " i = j = 0 \n", - " theta_index = []\n", - " epsilon_index = []\n", - " for t in range(T):\n", - " if optimal_policy[i, j] == 1: # Stay put\n", - " pass\n", - " elif optimal_policy[i, j] == 2: # New job\n", - " j = int(G.draw())\n", - " else: # New life\n", - " i, j = int(F.draw()), int(G.draw())\n", - " theta_index.append(i)\n", - " epsilon_index.append(j)\n", - " return wp.theta[theta_index], wp.epsilon[epsilon_index]\n", - "\n", - "theta_path, epsilon_path = gen_path()\n", - "\n", - "fig, axes = plt.subplots(2, 1, figsize=(10, 8))\n", - "for ax in axes:\n", - " ax.plot(epsilon_path, label='epsilon')\n", - " ax.plot(theta_path, label='theta')\n", - " ax.legend(loc='lower right')\n", - "\n", - "plt.show()\n", - "\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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ZZ9yMqHKffmqSNy8SJTC9Uvv3w7Zt3lw/3s2bB1dfrURJRKQ6ieRPfg9gONALWFPy6O9k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\nJEmSJEkS8C9yUPOCOjPh9AAAAABJRU5ErkJggg==\n", - "text": [ - "" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The median for the original parameterization can be computed as follows" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "wp = CareerWorkerProblem()\n", - "v_init = np.ones((wp.N, wp.N))*100\n", - "v = compute_fixed_point(wp.bellman_operator, v_init)\n", - "optimal_policy = wp.get_greedy(v)\n", - "F = DiscreteRV(wp.F_probs)\n", - "G = DiscreteRV(wp.G_probs)\n", - "\n", - "def gen_first_passage_time():\n", - " t = 0\n", - " i = j = 0\n", - " while 1:\n", - " if optimal_policy[i, j] == 1: # Stay put\n", - " return t\n", - " elif optimal_policy[i, j] == 2: # New job\n", - " j = int(G.draw())\n", - " else: # New life\n", - " i, j = int(F.draw()), int(G.draw())\n", - " t += 1\n", - "\n", - "M = 25000 # Number of samples\n", - "samples = np.empty(M)\n", - "for i in range(M): \n", - " samples[i] = gen_first_passage_time()\n", - "print(np.median(samples))\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Computed iterate 1 with error 5.000000\n", - "Computed iterate 2 with error 4.750000\n", - "Computed iterate 3 with error 4.512500" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 4 with error 4.286875\n", - "Computed iterate 5 with error 4.072531" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 6 with error 3.868905\n", - "Computed iterate 7 with error 3.675459" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 8 with error 3.491686\n", - "Computed iterate 9 with error 3.317102" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 10 with error 3.151247\n", - "Computed iterate 11 with error 2.993685" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 12 with error 2.844000\n", - "Computed iterate 13 with error 2.701800" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 14 with error 2.566710\n", - "Computed iterate 15 with error 2.438375" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 16 with error 2.316456\n", - "Computed iterate 17 with error 2.200633" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 18 with error 2.090602\n", - "Computed iterate 19 with error 1.986072" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 20 with error 1.886768\n", - "Computed iterate 21 with error 1.792430" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 22 with error 1.702808\n", - "Computed iterate 23 with error 1.617668" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 24 with error 1.536784\n", - "Computed iterate 25 with error 1.459945" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 26 with error 1.386948\n", - "Computed iterate 27 with error 1.317600" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 28 with error 1.251720\n", - "Computed iterate 29 with error 1.189134" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 30 with error 1.129678\n", - "Computed iterate 31 with error 1.073194" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 32 with error 1.019534\n", - "Computed iterate 33 with error 0.968557" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 34 with error 0.920130\n", - "Computed iterate 35 with error 0.874123" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 36 with error 0.830417\n", - "Computed iterate 37 with error 0.788896" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 38 with error 0.749451\n", - "Computed iterate 39 with error 0.711979" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 40 with error 0.676380\n", - "Computed iterate 41 with error 0.642561" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 42 with error 0.610433\n", - "Computed iterate 43 with error 0.579911" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 44 with error 0.550916\n", - "Computed iterate 45 with error 0.523370" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 46 with error 0.497201\n", - "Computed iterate 47 with error 0.472341" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 48 with error 0.448724\n", - "Computed iterate 49 with error 0.426288" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 50 with error 0.404974\n", - "7.0" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To compute the median with $\\beta=0.99$ instead of the default value $\\beta=0.95$,\n", - "replace `wp = CareerWorkerProblem()` with `wp = CareerWorkerProblem(beta=0.99)`\n", - "\n", - "The medians are subject to randomness, but should be about 7 and 11\n", - "respectively. Not surprisingly, more patient workers will wait longer to settle down to their final job\n", - "\n" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 3" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here\u2019s the code to reproduce the original figure" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from matplotlib import cm\n", - "\n", - "wp = CareerWorkerProblem()\n", - "v_init = np.ones((wp.N, wp.N))*100\n", - "v = compute_fixed_point(wp.bellman_operator, v_init)\n", - "optimal_policy = wp.get_greedy(v)\n", - "\n", - "fig, ax = plt.subplots(figsize=(6,6))\n", - "tg, eg = np.meshgrid(wp.theta, wp.epsilon)\n", - "lvls=(0.5, 1.5, 2.5, 3.5)\n", - "ax.contourf(tg, eg, optimal_policy.T, levels=lvls, cmap=cm.winter, alpha=0.5)\n", - "ax.contour(tg, eg, optimal_policy.T, colors='k', levels=lvls, linewidths=2)\n", - "ax.set_xlabel('theta', fontsize=14)\n", - "ax.set_ylabel('epsilon', fontsize=14)\n", - "ax.text(1.8, 2.5, 'new life', fontsize=14)\n", - "ax.text(4.5, 2.5, 'new job', fontsize=14, rotation='vertical')\n", - "ax.text(4.0, 4.5, 'stay put', fontsize=14)\n", - "\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Computed iterate 1 with error 5.000000\n", - "Computed iterate 2 with error 4.750000\n", - "Computed iterate 3 with error 4.512500" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 4 with error 4.286875\n", - "Computed iterate 5 with error 4.072531" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 6 with error 3.868905\n", - "Computed iterate 7 with error 3.675459" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 8 with error 3.491686\n", - "Computed iterate 9 with error 3.317102" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 10 with error 3.151247\n", - "Computed iterate 11 with error 2.993685" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 12 with error 2.844000\n", - "Computed iterate 13 with error 2.701800" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 14 with error 2.566710\n", - "Computed iterate 15 with error 2.438375" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 16 with error 2.316456\n", - "Computed iterate 17 with error 2.200633" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 18 with error 2.090602\n", - "Computed iterate 19 with error 1.986072" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 20 with error 1.886768\n", - "Computed iterate 21 with error 1.792430" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 22 with error 1.702808\n", - "Computed iterate 23 with error 1.617668" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 24 with error 1.536784\n", - "Computed iterate 25 with error 1.459945" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 26 with error 1.386948\n", - "Computed iterate 27 with error 1.317600" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 28 with error 1.251720\n", - "Computed iterate 29 with error 1.189134" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 30 with error 1.129678\n", - "Computed iterate 31 with error 1.073194" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 32 with error 1.019534\n", - "Computed iterate 33 with error 0.968557" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 34 with error 0.920130\n", - "Computed iterate 35 with error 0.874123" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 36 with error 0.830417\n", - "Computed iterate 37 with error 0.788896" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 38 with error 0.749451\n", - "Computed iterate 39 with error 0.711979" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 40 with error 0.676380\n", - "Computed iterate 41 with error 0.642561" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 42 with error 0.610433\n", - "Computed iterate 43 with error 0.579911" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 44 with error 0.550916\n", - "Computed iterate 45 with error 0.523370" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 46 with error 0.497201\n", - "Computed iterate 47 with error 0.472341" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 48 with error 0.448724\n", - "Computed iterate 49 with error 0.426288" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 50 with error 0.404974\n" - ] - }, - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 5, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we want to set `G_a = G_b = 100` and generate a new figure with these parameters. \n", - "\n", - "To do this replace:\n", - "\n", - " wp = CareerWorkerProblem()\n", - "\n", - "with:\n", - "\n", - " wp = CareerWorkerProblem(G_a=100, G_b=100)\n", - "\n", - "In the new figure, you will see that the region for which the worker will stay put has grown because the distribution for $\\epsilon$ has become more concentrated around the mean, making high-paying jobs less realistic\n" - ] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/discrete_dp_solutions.ipynb b/solutions/discrete_dp_solutions.ipynb deleted file mode 100644 index ca15c0d3f..000000000 --- a/solutions/discrete_dp_solutions.ipynb +++ /dev/null @@ -1,1071 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## quant-econ Solutions: Discrete Dynamic Programming" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/discrete_dp.html" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Prepared by **Daisuke Oyama**, Faculty of Economics, University of Tokyo" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The exercise is to replicate numerically the analytical solution for the benchmark model in [this lecture](http://quant-econ.net/py/dp_intro.html) of quant-econ, using the `DiscreteDP` class. " - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "from __future__ import division, print_function\n", - "import numpy as np\n", - "import scipy.sparse as sparse\n", - "import matplotlib.pyplot as plt\n", - "from quantecon import compute_fixed_point\n", - "from quantecon.markov import DiscreteDP" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Setup" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To recall, we consider the following problem:\n", - "$$\n", - "\\begin{aligned}\n", - "&\\max_{\\{c_t\\}_{t=0}^{\\infty}} \\sum_{t=0}^{\\infty} \\beta^t u(c_t) \\\\\n", - "&\\ \\text{ s.t. }\\ k_{t+1} = f(k_t) - c_t,\n", - " \\quad \\text{$k_0$: given},\n", - "\\end{aligned}\n", - "$$\n", - "where\n", - "$k_t$ and $c_t$ are the capital stock and consumption at time $t$, respectively,\n", - "$u$ is the utility function,\n", - "$f$ is the production function, and\n", - "$\\beta \\in (0, 1)$ is the discount factor." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As in the lecture,\n", - "we let $f(k) = k^{\\alpha}$ with $\\alpha = 0.65$, $u(c) = \\log c$, and $\\beta = 0.95$." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "alpha = 0.65\n", - "f = lambda k: k**alpha\n", - "u = np.log\n", - "beta = 0.95" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we want to solve a finite state version of the continuous state model above.\n", - "We discretize the state space into a grid of size `grid_size=1500`,\n", - "from $10^{-6}$ to `grid_max=2`.\n", - "\n", - "The grid size in [the lecture](http://quant-econ.net/py/dp_intro.html#computation) is 150,\n", - "where the value functions are approximated by linear interpolation,\n", - "while we choose a finer grid since we fill the gaps with discrete points." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "grid_max = 2\n", - "grid_size = 1500\n", - "grid = np.linspace(1e-6, grid_max, grid_size)" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 1.00000000e-06 1.33522215e-03 2.66944430e-03 ..., 1.99733156e+00\n", - " 1.99866578e+00 2.00000000e+00]\n" - ] - } - ], - "source": [ - "print(grid)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We choose the action to be the amount of capital to save for the next period\n", - "(the state is the capical stock at the beginning of the period).\n", - "Thus the state indices and the action indices are both `0`, ..., `grid_size-1`.\n", - "Action (indexed by) `a` is feasible at state (indexed by) `s` if and only if\n", - "`grid[a] < f([grid[s])`\n", - "(zero consumption is not allowed because of the log utility).\n", - "\n", - "Thus the Bellman equation is:\n", - "$$\n", - "v(k) = \\max_{0 < k' < f(k)} u(f(k) - k') + \\beta v(k'),\n", - "$$\n", - "where $k'$ is the capital stock in the next period." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The transition probability array `Q` will be highly sparse\n", - "(in fact it is degenerate as the model is deterministic),\n", - "so we formulate the problem with state-action pairs, to represent `Q` in\n", - "[scipy sparse matrix format](http://docs.scipy.org/doc/scipy/reference/sparse.html)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We first construct indices for state-action pairs:" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Consumption matrix, with nonpositive consumption included\n", - "C = f(grid).reshape(grid_size, 1) - grid.reshape(1, grid_size)\n", - "\n", - "# State-action indices\n", - "s_indices, a_indices = np.where(C > 0)\n", - "\n", - "# Number of state-action pairs\n", - "L = len(s_indices)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1069790\n", - "[ 0 1 1 ..., 1499 1499 1499]\n", - "[ 0 0 1 ..., 1174 1175 1176]\n" - ] - } - ], - "source": [ - "print(L)\n", - "print(s_indices)\n", - "print(a_indices)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Reward vector `R` (of length `L`):" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "R = u(C[s_indices, a_indices])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "(Degenerate) transition probability matrix `Q` (of shape `(L, grid_size)`),\n", - "where we choose the [scipy.sparse.lil_matrix](http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.lil_matrix.html)\n", - "format,\n", - "while any format will do\n", - "(internally it will be converted to the csr format):" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "Q = sparse.lil_matrix((L, grid_size))\n", - "Q[np.arange(L), a_indices] = 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "(If you are familar with the data structure of\n", - "[scipy.sparse.csr_matrix](http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csr_matrix.html),\n", - "the following is the most efficient way to create the `Q` matrix in the current case.)" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# data = np.ones(L)\n", - "# indptr = np.arange(L+1)\n", - "# Q = sparse.csr_matrix((data, a_indices, indptr), shape=(L, grid_size))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Discrete growth model:" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "ddp = DiscreteDP(R, Q, beta, s_indices, a_indices)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**Notes**\n", - "\n", - "Here we intensively vectorized the operations on arrays to simplify the code.\n", - "As [noted](http://quant-econ.net/py/need_for_speed.html#pros-and-cons-of-vectorization),\n", - "however, vectorization is memory consumptive,\n", - "and it can be prohibitively so for grids with large size." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Solving the model" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solve the dynamic optimization problem:" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "res = ddp.solve(method='policy_iteration')\n", - "v, sigma, num_iter = res.v, res.sigma, res.num_iter" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": false, - "scrolled": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "14" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "num_iter" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that `sigma` contains the *indices* of the optimal *capital stocks*\n", - "to save for the next period.\n", - "The following translates `sigma` to the corresponding consumption vector." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Optimal consumption in the discrete version\n", - "c = f(grid) - grid[sigma]" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Exact solution of the continuous version\n", - "ab = alpha * beta\n", - "c1 = (np.log(1 - ab) + np.log(ab) * ab / (1 - ab)) / (1 - beta)\n", - "c2 = alpha / (1 - ab)\n", - "def v_star(k):\n", - " return c1 + c2 * np.log(k)\n", - "\n", - "def c_star(k):\n", - " return (1 - ab) * k**alpha" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let us compare the solution of the discrete model with that of the original continuous model." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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mTp06PPbYY9jY2DB8+HCcnJxo1KgRXbp0MWw3QIMGDZgwYQKmpqYMGTKEgIAA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\nHEjmrbcmU6hQOQYObJndlxcREfFMcjJMmrSP1q2f4aefplC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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(1, 2, figsize=(14, 4))\n", - "ax[0].set_ylim(-40, -32)\n", - "ax[0].set_xlim(grid[0], grid[-1])\n", - "ax[1].set_xlim(grid[0], grid[-1])\n", - "\n", - "lb0 = 'discrete value function'\n", - "ax[0].plot(grid, v, lw=2, alpha=0.6, label=lb0)\n", - "\n", - "lb0 = 'continuous value function'\n", - "ax[0].plot(grid, v_star(grid), 'k-', lw=1.5, alpha=0.8, label=lb0)\n", - "ax[0].legend(loc='upper left')\n", - "\n", - "lb1 = 'discrete optimal consumption'\n", - "ax[1].plot(grid, c, 'b-', lw=2, alpha=0.6, label=lb1)\n", - "\n", - "lb1 = 'continuous optimal consumption'\n", - "ax[1].plot(grid, c_star(grid), 'k-', lw=1.5, alpha=0.8, label=lb1)\n", - "ax[1].legend(loc='upper left')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The outcomes appear very close to those of the continuous version." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Except for the \"boundary\" point, the value functions are very close:" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "121.49819147053378" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.abs(v - v_star(grid)).max()" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "0.0038595076780651993" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.abs(v - v_star(grid))[1:].max()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The optimal consumption functions are close as well:" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "0.0013020872868430011" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.abs(c - c_star(grid)).max()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In fact, the optimal consumption obtained in the discrete version is not really monotone,\n", - "but the decrements are quit small:" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "False" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "diff = np.diff(c)\n", - "(diff >= 0).all()" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "dec_ind = np.where(diff < 0)[0]" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "521" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(dec_ind)" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "0.00065355751082307734" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.abs(diff[dec_ind]).max()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The value function is monotone:" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "True" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "(np.diff(v) > 0).all()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Comparison of the solution methods" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let us solve the problem by the other two methods." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Value iteration" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "ddp.epsilon = 1e-4\n", - "ddp.max_iter = 500\n", - "res1 = ddp.solve(method='value_iteration')" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "294" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "res1.num_iter" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "True" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.array_equal(sigma, res1.sigma)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Modified policy iteration" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "res2 = ddp.solve(method='modified_policy_iteration')" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "16" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "res2.num_iter" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "True" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.array_equal(sigma, res2.sigma)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Speed comparison" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": { - "collapsed": false, - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1 loops, best of 3: 2.83 s per loop\n", - "1 loops, best of 3: 201 ms per loop\n", - "1 loops, best of 3: 204 ms per loop\n" - ] - } - ], - "source": [ - "%timeit ddp.solve(method='value_iteration')\n", - "%timeit ddp.solve(method='policy_iteration')\n", - "%timeit ddp.solve(method='modified_policy_iteration')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As is often the case, policy iteration and modified policy iteration are much faster\n", - "than value iteration." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Replication of the figures" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Using `DiscreteDP` we replicate the figures shown in the lecture." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Convergence of value iteration" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let us first visualize the convergence of the value iteration algorithm as in the lecture,\n", - "where we use `ddp.bellman_operator` implemented as a method of `DiscreteDP`." - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": { - "collapsed": false, - "scrolled": false - }, - "outputs": [ - { - "data": { - "image/png": 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vvDOEt98elI2DNps1uOYaGkE3NVmZoLOIi1Lki3lgIIhAoLhtWYyWa2rMqK21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\n5UjUchijGvpgKAdaGbStWEFw4vH2wECjZb1z55947rnniMVi3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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "w = 5 * np.log(grid) - 25 # Initial condition\n", - "n = 35\n", - "fig, ax = plt.subplots(figsize=(8,5))\n", - "ax.set_ylim(-40, -20)\n", - "ax.set_xlim(np.min(grid), np.max(grid))\n", - "lb = 'initial condition'\n", - "ax.plot(grid, w, color=plt.cm.jet(0), lw=2, alpha=0.6, label=lb)\n", - "for i in range(n):\n", - " w = ddp.bellman_operator(w)\n", - " ax.plot(grid, w, color=plt.cm.jet(i / n), lw=2, alpha=0.6)\n", - "lb = 'true value function'\n", - "ax.plot(grid, v_star(grid), 'k-', lw=2, alpha=0.8, label=lb)\n", - "ax.legend(loc='upper left')\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We next plot the consumption policies along the value iteration." - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Iteration Distance Elapsed (seconds)\n", - "---------------------------------------------\n", - "1 6.924e+00 9.756e-03 \n", - "2 4.107e+00 1.951e-02 \n", - "Iteration Distance Elapsed (seconds)\n", - "---------------------------------------------\n", - "1 6.924e+00 9.754e-03 \n", - "2 4.107e+00 1.950e-02 \n", - "3 3.866e+00 3.034e-02 \n", - "4 3.673e+00 4.010e-02 \n", - "Iteration Distance Elapsed (seconds)\n", - "---------------------------------------------\n", - "1 6.924e+00 9.911e-03 \n", - "2 4.107e+00 1.975e-02 \n", - "3 3.866e+00 3.082e-02 \n", - "4 3.673e+00 4.225e-02 \n", - "5 3.489e+00 5.175e-02 \n", - "6 3.315e+00 6.115e-02 \n" - ] - }, - { - "data": { - "image/png": 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8cN1118HT01Or6W7evBk33ngj/P3921ynEOLyddnVdA4ePNhVm27VpVxbMiMj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ZNPPplwjx4R2UzLgM3IyMDPf/5z5OTkICoqCgUFBViyZIndOldddRXKysoQHh6Obdu24a9//ava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\nmtQsFguqqqpQWFiIg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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "w = 5 * u(grid) - 25 # Initial condition\n", - "\n", - "fig, ax = plt.subplots(3, 1, figsize=(8, 10))\n", - "true_c = c_star(grid)\n", - "\n", - "for i, n in enumerate((2, 4, 6)):\n", - " ax[i].set_ylim(0, 1)\n", - " ax[i].set_xlim(0, 2)\n", - " ax[i].set_yticks((0, 1))\n", - " ax[i].set_xticks((0, 2))\n", - "\n", - " w = 5 * u(grid) - 25 # Initial condition\n", - " compute_fixed_point(ddp.bellman_operator, w, max_iter=n, print_skip=1)\n", - " sigma = ddp.compute_greedy(w) # Policy indices\n", - " c_policy = f(grid) - grid[sigma]\n", - "\n", - " ax[i].plot(grid, c_policy, 'b-', lw=2, alpha=0.8,\n", - " label='approximate optimal consumption policy')\n", - " ax[i].plot(grid, true_c, 'k-', lw=2, alpha=0.8,\n", - " label='true optimal consumption policy')\n", - " ax[i].legend(loc='upper left')\n", - " ax[i].set_title('{} value function iterations'.format(n))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Dynamics of the capital stock" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally, let us work on [Exercise 2](http://quant-econ.net/py/dp_intro.html#exercise-2),\n", - "where we plot the trajectories of the capital stock for three different discount factors,\n", - "$0.9$, $0.94$, and $0.98$, with initial condition $k_0 = 0.1$." - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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vt9lg0CBITIThw63nAQPgiy/UVS4iHc9ZE71pmitaMI4OzxsWZiV6gPh4/3Vf\n7a2UzsM0TbYc20JFVAVRYVH+JA/gsAVeT1tSWQl/+EMWO3akUlRkjatbUikstMbWExJg2DAroQ8b\nBkOG1N2Bqpq6ykWkIzrvGL1hGEOBJ4GRQPU/n6ZpmgODGVhHkzxkCOk+H6lOp7UhMrDY6WR8SkrA\ndby7/V0qe1UStjGM/tf09yd5Z46TlDsDr6e1lZXBunWwejWsWQNZWTVj62Fh1qz1qCgYMsTGK6/4\nOz8Copa4iHQ0gUzGWwL8AvgdcD3wbaDhTYDlwpgmSVu3Qr9+ZPTtiy0+Hp/DwfiUlIDH53ed3MWf\n1v2J2Itjue/S+9i2aRtunxuHzUHKnSlMGh/4OH9rKCiwkvrq1ZCdTZ3u+C5dvHTpAl26WAm+Wt++\nvkYleRGRjiiQRO80TfNjw9qdZi/whGEY64GfBzm2jiMnB3btImnAAJL+8Y+6p4oEwF3pZv7K+VR4\nK/j64K/z8BUPQzuYKnnokJXYV6+GL7+0tocFayb8qFFwxRXWY//+5htbFxHpaAJJ9G7DMOzATsMw\n/hs4BEQHN6wO5p//tJ5nzGh0kgd4bu1z7Cvax8WxF/PwZQ83c3BNc+Zs+cmTkyktTWL1amt2fLXw\ncBg3zkrskyZBt241n/Xtq7F1EZELdd4tcA3DGA/kAbHAAqAz8GvTNNcGP7xzC4ktcA8dsk6mCwuD\nf/wDujZu17qPdn3Ek6ufJMIewV9u+AsDug4IUqCNVz1b/uTJVE6csLaR9XrT6dcvmdjYJKKjYeJE\nK7lPmFC3W15ERBoWjC1wB5imuQ4oBu6t+pLbgVZP9CHhX/+y+qynTm10kj9w6gC/X/t7AB6e8HCb\nSvIAL7yQRV5eKgUFNdfCw1OJjs7gN79JIinpgjowRESkEQJJ9I8DrwVwTRqrpATee896fcstjSrq\n8XqY/+l8yirLuOriq7hhyA1BCPDCHDsGL78MH31kp6zMGnPv3t3qjo+KgkGDbCQnt3aUIiIdw7l2\nxpsOfB1IMAzjj0B1N0EM4DlbuTPquB74A9Ys/cWmaT5zxud3AY9W1V0MfN80zU2BlA0Jy5ZZu78k\nJVmLvxvhL1l/YcfJHVwUcxE/mfgT/1K61lRQYJ2Z/s471np3w/DSrRv06mXtQlfN4fC1XpAiIh2M\n7RyfHQKyAXfVc/XjHWDa+SqumsC3EGtJ3gjgTsMwhp9x225gsmmaY7DG///aiLLtm88Hb75pvW5k\na371vtXK4JioAAAgAElEQVS8mfcmYbYw5k2eR3RE686NLC6G9HS46y544w0ryU+dCgsXJpOYmF4n\nyVuz5ce1XrAiIh3MuXbGywFyDMP4m2maAbXgzzAB2Gma5h4AwzBeBWYA/oM5TdNcU+v+z4E+gZZt\n99autU5a6dXLmo0WoKOnj/Lrz34NwANjHyAxLjFYEZ5XWZn1t8qrr8Lp09a1SZPgvvusLWghiZ49\nNVteRKQ1navr/nXTNG8D1jfQLWxWtcLPJQHYX+v9AeCyc9yfCrx3gWXbnzfesJ5nzrQ2Zw9Apa+S\ntJVpFFcUM7HPRG4dcWsQAzy7igp4912rm756ot3YsZCaCiNG1L1XO9GJiLSuc03G+2HV8zcusO6A\n170ZhnEVcB9Q3bQNuOwTTzzhfz1lyhSmTJkSaNHWs2sXrF8PTid8/esBF3tx44t8efxLekT1YM4V\nc1p8XN7rhQ8+sCbaHTtmXRsxwkrwY8e2aCgiIh3GihUrWLFixQWXP1fX/aGq5z2GYfTCalH7gHWm\naR4JoO6DQN9a7/titczrMAxjDLAIuN40zYLGlIW6ib7dqB6bnz7d2rg9AFmHsliauxSbYeNnX/sZ\nXRxdghhg3Y1uwsO9DB+ezLp1SRyo+q8wcKCV4CdOtGbVi4hIcJzZiP3lL3/ZqPKBHGpzPzAPWF51\naaFhGPNN00w/T9EsYIhhGBdjTey7A7jzjLr7AW8Cs03T3NmYsu1WYSF8/LGVHW++OaAiJ8tO8uSq\nJzExuTfpXpJ6BbcrvPaxsEVFcOQIvPZaOv36wahRSXz72zBlSsAjDiIi0ooCWUf/KHCpaZonAAzD\n6A6sAc6Z6E3TrKzaMncZ1hK5dNM0txqG8d2qz1/A+gOiK/B8VTe0xzTNCWcre0E/YVvz7rvWIPfE\nidCnz3lv95k+nlr1FAXuAi7tdSmzx8wOeoiZmVmcPp3Kvn3WbnZgbXSTkJDBiy8mYdeRRiIi7UYg\niT4fOF3r/emqa+dlmub7wPtnXHuh1uv7gfsDLdvueTzw9tvW61sDm0j399y/k3U4i1hHLD/92k+x\nGcFvRh8+bCcvzwrXbrcWBsTFQa9eNiV5EZF2JpBEvwtYaxhGVYZiBrDJMIyfYM2+/13Qogs1n34K\nJ07AgAFw6aXnvf3LY1+yZOMSAB6/8nHiouKCGp7XC6+8Al984cXjsaYP9O9fs9mNNroREWl/Ak30\nu6iZCf921etOwQoqJJlmzSl1t9xy3hlsp8pPsWDlAryml1kjZzEhYUJQwzt2DNLSIDcXevZMxuNJ\np3v3VH+YOhZWRKR9Om+iN03ziRaII/Rt3gzbtkGXLnDNNee81TRNfvPZbzhWcowRcSNIHZt6zvub\natUq+M1vrB3uuneH3/0uibIybXQjIhIKApl1H481IW8E4Ky6bJqmOTWYgYWc6g1yvvENiIxs8BbX\nOheZyzLZdmIbecfzuHjExcydOZcwWyAdL41XXg7PP18zbeDyy2HOHIiNBdBGNyIioSCQDPI34B/A\njcB3sY6qPR7EmELP0aNWs9luhxkzGrzFtc5F2qtpnBh+gh3hOzB7mXj3evkq7yt6j+/d7CHt2QML\nFsDu3dZRsd/9rrVJn9bEi4iElkCmcHc3TXMxUGGa5qemaX4bUGu+Md5+25rpNmWKNX29AZnLMikZ\nXcLewr2YmHR3dsd5mZOly5Y2ayimCf/v/8H3vmcl+T59YOHCgKYNiIhIOxRIi76i6vmIYRg3Ym1g\n0zV4IYUYt9taOw/nPKWuwlfB8ZLjlHvLcYQ5SOicYBX3uZstlNOn4dlnoXonxWnT4Ic/tHbiFRGR\n0BRIok8zDCMW+Anwf0Bn4H+CGlUoWbbMyrAjR8Lwc5y064OjJUcB6NO5j3+9vMPmaJYwvvwSfvUr\na5c7pxN+/OPzzgkUEZEQEEjX/e2AYZpmrmmaU4BrgMD2bu3oGnHmfOzAWFgPMRExdIqwVi46c5yk\nTEtpcgiZmfCjH1lJPjERFi1SkhcR6SgCadGPqXXYDKZpnjQM4/y7vQhkZcG+fdCjB3zta2e97ejp\no+Tacuk3vB8jT4zEUezAYXOQcmcKk8ZPavTXVh9Ic+qUndxcLzZbMrGxSdxxh3UQTXh4U34oERFp\nTwJJ9IZhGN1M0zxZ9aYb1v7zcj7VS+puvhnCzv6rfinnJSq8FcycMpOf/9fPm/SV1QfSHD1q7VVf\nWQmRkek89BDcf7+Wy4mIdDSBJPpngTWGYbwGGMBtwK+CGlUo2LsXvvjCWjN/ww1nvW1P4R6W7VqG\n3bBz36X3NflrMzOz2L8/1X+cbEwM9O+fysaNGYASvYhIRxPIzngvG4aRjbWkzgRuNk1zS9Aja++q\nx+avuw46dz7rbenr0/GZPmYkzvDPtG+KXbvs/iTfuzf07Gm9drt1pqyISEcU0JZrpmluBjYHOZbQ\nceoUfPih9XrmzLPetuX4FlbvX40jzMHdY+5u8td+8gl8+aUXgIQEa2pANR1IIyLSMamZFwzvvWet\nnx8/Hi6+uMFbTNNkUfYiAG4dfivdo7o36StXrYKnnoL4+GT69Uuvk+StA2nGNal+ERFpn4KziXpH\n5vXCv/5lvT7Hkrp1h9ax8ehGYiJiuGPUHU36yi++gPnzra9+6KEkRozQgTQiImJRom9uq1ZZZ772\n62e16BvgM33+1vxdo+/yr5u/EBs3ws9/bs2uv+UWa/mcYehAGhERsajrvrlVL6mbORNsDf96l3+1\nnJ0FO+kR1YObht10wV+1eTP89KdQUWEdivfQQ9qvXkRE6lKib055edZes506WbPtG+DxesjYmAHA\nvZfcS2RYw0fWns/27fDYY1BWBtdea+18pyQvIiJnUqJvTtWt+RtvPOtJMe/teI9DxYfo16Uf0wZN\nu6Cv+eorePRRawv9yZOtM+TP0nkgIiIdnMbom0GOy0XW4sXYP/gAr2GQnJDQ4NY07ko3L296GYD7\nL70fu63xGwzu3w+PPAJFRXD55TB3rnXMvYiISEOU6Jsox+UiKy2N1N27rX702FjS//xn6NaNpEl1\n96n/55Z/crLsJMO6D+PKflc2+ruOHIGf/AROnoSxY+GXv9S+9SIicm7q8G2irMxMUktL4cQJ60KP\nHqSWlZG9dGmd+06Vn+LVL18F4IFxD2A0ckA9P986Wvb4cRg92jpyNiKiWX4EEREJYUr0TWSvqLB2\nwqustMblo6MBsLndde5bmruUEk8J4y8az6W9G3f4X0GB1ZI/fNg6Zvapp8DRPMfUi4hIiFOibyJv\nRAQUFlpvunb1X/fVysTHSo7xrzxrE537x97fqPpPnbLG5Pftg0GD4Ne/9v8tISIicl5K9E2UfNtt\npBcXW29iYwFY7HQyLiXFf89LG61jaK+6+CqGdh8acN0lJdbs+t27rf13fvObc56PIyIiUo8m4zVR\nkmFAnz5kVFZiGz4cn8PB+JQU/0S8vYV7+WDXB40+htbthscfh23b4KKL4Nln63QYiIiIBESJvqmW\nLycpNpakhx6CW2+t93HGhgx8po9vDv0mfTr3OWdVLlcOmZlZlJXZ2bDBi2EkM2RIEs8+C3FxwfoB\nREQklCnRN0VJCaxda21JN2VKvY+3Ht/Kyn0ribRHcnfSuY+hdblySEvLorQ0la++ssbmIyPTmTcP\nevXSvvUiInJhNEbfFJ99Zm00n5RUr8ltmiZ/zf4rALeOuJW4qHM3ya2WfCp791pJPiwMBgxI5ZNP\nsoMWvoiIhD4l+qZYvtx6vuqqeh9lH872H0M7a9Ss81ZVUWHn2DFrAr/dDgMHWkvo3G79JxIRkQun\nLHKhTp2CdeusrDx5cp2PfKbP35pPGZ0S0DG0breXw4et1/37Q1SU9drh8DVr2CIi0rEo0V+oVavA\n67X2oq1aVlft0z2fsuPkDuKi4rh52M3nrcrjgaKiZAwjne7da5bQOZ2LSUkZF4zoRUSkg9BkvAv1\nn/9Yz2d021f6KknfkA7At5K+FdAxtC+/DKdPJzFuHAwYkIHXa8Ph8JGSMp5JkzQRT0RELpwS/YUo\nKICNG60Zc1fWPZzmvR3vcbD4IH0792X64OnnrWrzZli61Jq4/+yzSYwercQuIiLNR133F+LTT8Hn\ngwkTICbGf9ld6ealnJcASL009bzH0Lrd8PTTVlWzZlmH1YiIiDQnJfoLUd1tP3VqnctvbHmDk2Un\nSeyeyOT+kxsoWNcLL8CBAzBgAHz728EIVEREOjp13TfWsWOQmwuRkVC1za1rnYuMf2fw4Vcf4vV6\nueeue857DG1WFrz1ljVp//HHda68iIgEh1r0jfXpp9bz5ZeD04lrnYu0V9NY1X0VxSOKsY+z8/rH\nr+Na5zprFadPW6fQAdx7LwwZEvywRUSkY1Kib6wzuu0zl2VSPLKY46XHAegd05uyMWUsXbb0rFX8\n3//B8eMwYgTceWfQIxYRkQ5Mib4xDh2CvDxwOuGyywCo8FVwouwEJiadIzsTFW7tdOP2uRusYtUq\n+PBDq+f/scesrnsREZFgUaJvjOotb6+4wsrUQLgRTn5pPgA9onr4b3XYHPWKFxRYx80CPPAA9O0b\n3HBFRESU6BujOtHXmm2fdGkS3mwvkfZIYiKspXbOHCcp01LqFDVNK8kXFVmb6d10U4tFLSIiHZhm\n3Qdqzx7YtQs6dYLkZP/lXRG76De8Hz0P96RPaR8cNgcpd6YwafykOsWXLbMOu4uOhjlzwKY/sURE\npAUo0QdqxQrrefJk/1q4/UX7yTqcRc9BPXn9tteJiYxpsOjRo7BwofX6Bz+A+PgWiFdERAR13QfG\nNBs8kvadbe8AcPWAq8+a5H0+ayldSYm1W+611wY9WhERET8l+kDs2gX79lmn1F16KWBtd/vBrg8A\nmDFsxlmLvvUWrF9vFf3xj6097UVERFqKEn0gqtfOT5niXw/38e6POV1xmhFxIxjafWiDxfbts7a5\nBSvJd+3aArGKiIjUokR/PrW77adMqbpk8nbe2wDcNKzh6fNer3VgTUUFTJsGX/taSwQrIiJSlxL9\n+eTlwZEjEBfnP15u8/HN7CzYSawjlikXT2mw2NKlsHWrNfHuv/+7BeMVERGpRYn+fKq77a+6yr8m\nrro1f8OQGwi31z+NZvt2eMk6rZY5c6wVeSIiIq1Bif5cfL6aZXVVs+0LygpYsXcFNsPGN4Z+o16R\nigqry97rhZkzrc1xREREWosS/bnk5kJ+PvTqBcOGAfDvHf+m0lfJxD4T6dmpZ70iS5bAV19Z29t+\n5zstHbCIiEhdSvTnUnvLW8PA6/P61843NAlv0yb4xz+sHv7HHwdH/e3uRUREWpR2xjsbr7fm7Pmq\nve3XHFjD8dLj9Onch7G9a/rkXa4cXnwxi08+seN2e7nnnmSGD09qjahFRETqUKI/mw0boLAQ+vWD\ngQMBeCvvLQBmJM7AZlidIS5XDmlpWWzfnsrJk9YJths2pONywaRJSvYiItK61HV/NrW3vDUM9hft\nJ/twNpH2SKYNmua/LTMzixMnUjlxwtr1rn9/KC9PZenS7FYKXEREpIYSfUM8Hli50npdNdv+7W3W\nkrprBl5TZ1/7igo7R45Yr3v0qBmXd7v1qxURkdanbNSQrCw4fRoGDYL+/SnzlPHBTmtf+zMn4ZWU\neDl1ypqAV/tUOofD15IRi4iINEiJviG1N8kBPvnqE0o8JYzqMYrB3QbXudVuT8ZmSycuDsKqZjw4\nnYtJSRnXkhGLiIg0KKiT8QzDuB74A2AHFpum+cwZnw8DlgCXAj8zTfPZWp/tAU4BXsBjmuaEYMbq\n53bDZ59Zr6+6CtM0aybhnXFK3ZYtcPBgEkOHwqhRGZimDYfDR0rKeE3EExGRNiFoid4wDDuwELgG\nOAisMwzjHdM0t9a67QTwMNDQyTAmMMU0zZPBirFBn38OZWUwfDhcdBFfHs1lV8EuYh2x/Ff//6pz\n64svWs+pqUncf78Su4iItD3BbNFPAHaaprkHwDCMV4EZgD/Rm6Z5HDhuGMYNZ6mj5U9vrz3bnpol\ndTcOubHOvvZffgnr1kFUFNx+e4tHKSLSZhhGy/9T3VGYptnkOoKZ6BOA/bXeHwAua0R5E/jYMAwv\n8IJpmouaM7gGlZbCmjXW6ylTOFl2kpX7VmIzbNw49MY6t1a35m+5BTp3DnpkIiJtWnMkJKmruf6A\nCmaib+p/9StM0zxsGEYP4CPDMPJM01zVHIGdlctlnUozZgz06MG/c16h0lfJlX2vrLOvfW4uZGdD\ndDTcdltQIxIREWmSYCb6g0DfWu/7YrXqA2Ka5uGq5+OGYfwLayigXqJ/4okn/K+nTJnClClTLixa\nqNNt7/V5eXf7u0D9SXjVrflbb4WYGERERIJmxYoVrKg+SfUCGMHqbjEMIwzYBlwNHAK+AO48YzJe\n9b1PAMXVs+4Nw4gC7KZpFhuGEQ18CPzSNM0PzyhnNlv8xcXWubI+H/zzn6w69SXzVsyjb+e+vHjT\ni/4tb3Ny4Ec/ss6Y//vfdda8iIhhGOq6D4Kz/V6rrgfcrx+0Fr1pmpWGYfw3sAxreV26aZpbDcP4\nbtXnLxiG0QtYB3QGfIZh/BAYAcQDb1aNT4QBfzszyTe71auhshLGjYOuXXnri/r72kNNa/6225Tk\nRUSk7QvqOnrTNN8H3j/j2gu1Xh+hbvd+tdPAJcGMrZ7qTXKmTmVv4V7WH1mPI8zBtME1+9pv2AAb\nN1oJ/pZbWjQ6ERGRC6LT6wAKCqwsbrfDlVfyztaXALhmwDV0irCa7aZZ05q//XZrIp6IiHQ8b731\nFlu2bMFms5GQkMDdd99d756MjAwOHTpEeHg4iYmJ3HRTQ9vFtAwlerAOsPF64fLLKXOGs2zXMqDu\nvvYbNsCmTdZSupkzWytQERFpio0bN7J7924AduzYwZw5cxpVvqioiAULFpCdbZ1QOnHiRKZPn05c\nXJz/ntzcXJYsWcKqVdb88WuvvZbrr78eR/WpZy1MiR5qZttPncpHuz+ixFPC6PjRDOo2CLBa80uW\nWLeoNS8iEjiXK4fMzCwqKuxERHiZPTu5UVuEN7V8bbm5uRQWFjKzqrU2derURif6lStXMmLECP/7\npKQkli9fzm211lp/8MEHDBgwwP8+Pj6ezz77jKuvvvqC4m6qDp3oc1wushYvxv7++3jDwhhnGLyd\nZx1HOyOxZklddra1E16XLnDzza0VrYhI++Jy5ZCWlkVZWar/WlpaOnPnElCybmr5M23ZsoU77rgD\ngOzsbEaNGgXA7t27WbTo7HuyXX755cyYYeWEAwcOEBsb6/8sNjaWHTt21Lk/JiYGj8fjf+92u9m6\ndasSfUvLcbnISksjdd8+6yCbLl34/VO/ZNvE08SPHsDk/pOBuq35O+6wtrwVEZHzy8y0kvTGjbWv\npnLbbRkMHXr+RL19exalpTVJ/pJLoKwslaVLMxqd6A8fPkxCQgK5ubksXryYr776ihdesOaGDxw4\nkKeeeiqgegoLC+t0wUdERHD69Ok698ycOZOMjAxM0+T06dNs27aN8ePHNyre5tRhj6nNyswktazM\nmogH0LUrN588QNe1x7hhyA3+fe3XrbNOqevSBVpxLoWISLtTUWFv8LrPF1jq8fkaLu92Nz51ff75\n51x++eWMHj2a5557junTp5ORkdHoemJiYuqsbS8rK6Nbt2517omPj2fJkiUsWrSIFStWMHr0aOLj\n4xv9Xc2lw7bo7RUV4PFY+9sbBp5OTgrz9+D0OPlG4jeAuq35O+8Ep7MVAxYRaWciIryA1RKvbeRI\nHwsXnr/8gw962VpvizVwOHyNjsXtdhMWVpPytmzZwpAhQ4DGdd0PGjSIrKws/2f5+fmMHTu2XpkR\nI0YwcuRIAObPn8+CBQsaHXNz6bCJ3hsRAadOWW9iYjjhLsAEunZNID7a+svr888hLw+6doUZM85e\nl4iI1Dd7djJpael1xtidzsWkpATWjd3U8rWtXLmSWbNmAVZyXrNmDU8++STQuK77yZMn8+ijj/rf\nr1+/nmeeeQaAXbt2MXDgQPbu3cuMGTPIyclh69at9O/fn8GDBzc65uYStC1wW0JTtsDNcbnIuvtu\nUk+exOzTh83mUf5g83Jt2m+545vfxjTh+9+HbdvgwQd1eI2IyNmcawtclyuHpUuzcbttOBw+UlLG\nNXrWfVPKA2zevJmdO3dSXFxMVFQUmzZtIjU1lb59G9qv7fxeeeUV9u7di8/nY9CgQdx1110AjB07\nlvT0dEaNGkVaWho9e/Zkx44dzJs3j65duzb6e5prC9wOm+gpLydn8mSyDxzg+ISRrC7eTOQ1Y3h9\nznsYhoHLBT/7GXTrBn/7G7TS8kcRkTavre91/9prr3H77be3dhiN1ub3um/z1q8nKSqKpG98gx/f\nHMXpIx6+PeE7Vb/Aml3wUlKU5EVE2jObrcPOOwc6cqJfs4ai4iJePbSJv7/yFRG2CLoM6QLAZ5/B\njh3QvTvceGMrxykiIk1y6623tnYIrap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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "discount_factors = (0.9, 0.94, 0.98)\n", - "k_init = 0.1\n", - "\n", - "# Search for the index corresponding to k_init\n", - "k_init_ind = np.searchsorted(grid, k_init)\n", - "\n", - "sample_size = 25\n", - "\n", - "fig, ax = plt.subplots(figsize=(8,5))\n", - "ax.set_xlabel(\"time\")\n", - "ax.set_ylabel(\"capital\")\n", - "ax.set_ylim(0.10, 0.30)\n", - "\n", - "# Create a new instance, not to modify the one used above\n", - "ddp0 = DiscreteDP(R, Q, beta, s_indices, a_indices)\n", - "\n", - "for beta in discount_factors:\n", - " ddp0.beta = beta\n", - " res0 = ddp0.solve()\n", - " k_path_ind = res0.mc.simulate(init=k_init_ind, ts_length=sample_size)\n", - " k_path = grid[k_path_ind]\n", - " ax.plot(k_path, 'o-', lw=2, alpha=0.75, label=r'$\\beta = {}$'.format(beta))\n", - "\n", - "ax.legend(loc='lower right')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.10" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/solutions/estspec_solutions.ipynb b/solutions/estspec_solutions.ipynb deleted file mode 100644 index 4b889f662..000000000 --- a/solutions/estspec_solutions.ipynb +++ /dev/null @@ -1,145 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:ced859d6b4e0d7b96eb89edb3dc7dd9f5eb939faca76ce076900f1f0d1671a25" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Estimation of Spectra" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/estspec.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from quantecon import ARMA, periodogram, ar_periodogram" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "## Data\n", - "n = 400\n", - "phi = 0.5\n", - "theta = 0, -0.8\n", - "lp = ARMA(phi, theta)\n", - "X = lp.simulation(ts_length=n)\n", - "\n", - "fig, ax = plt.subplots(3, 1, figsize=(10, 12))\n", - "\n", - "for i, wl in enumerate((15, 55, 175)): # window lengths\n", - " \n", - " x, y = periodogram(X)\n", - " ax[i].plot(x, y, 'b-', lw=2, alpha=0.5, label='periodogram')\n", - "\n", - " x_sd, y_sd = lp.spectral_density(two_pi=False, res=120)\n", - " ax[i].plot(x_sd, y_sd, 'r-', lw=2, alpha=0.8, label='spectral density')\n", - "\n", - " x, y_smoothed = periodogram(X, window='hamming', window_len=wl)\n", - " ax[i].plot(x, y_smoothed, 'k-', lw=2, label='smoothed periodogram')\n", - "\n", - " ax[i].legend()\n", - " ax[i].set_title('window length = {}'.format(wl))\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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Em266yRNuveqqq1i2bBk9e/akfv36NGnSxHN+Zff23HPPZfjw4TRo0AClFE2a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JM07yZqjMn9HWUMUzaKkVrLW0DyE6Go/Hg81mY+zYsfzsZz9j7dq1Ua03ZcoUXn75ZVwuFwBP\nPfWUr8D8wgsvZPXq1Rw4cACA119/nX79+pGenu5bPzU1lWPHjvnaEI3JkyfzxhtvsGfPHt9z1oV+\n5MiRfPrpp5w6dQrDMGK6q84wDJYsWUJ9fT319fUsXLiQSy65pMV9hv4/FpMnT+bvf/87YGa9Xnjh\nBaZMmQKY2bLXX38dwzCoqqqipKTEt15Lx/a3v/0tTz/9NIsWLeKmm26Kuj07d+7E6XRy++23M2zY\nMDZs2NCuQVQgyVCJM05oAJVsAZVhmEGhLcLXnUQG9rTWsTJVQiSLV199lWeeecbX3fXHP/4x7HKB\n2SeACRMmsHnzZqZPn45SiiFDhnDbbbcBZqH9n//8Z2666SaUUuTk5PD4448HbW/ixIk8/PDDXHbZ\nZWRlZfGPf/yDTp06Be0jVK9evXj44YeZM2eOL4tz7733MmbMGAoKCrj77ruZPn06eXl5jBw5Muq7\n45RSDBgwgBtuuIHS0lKmT5/OmDFjWtyntW40+wld5pe//CV33XUX06ZNw+12c+211/q6W7/1rW+x\nfPlyJk6cSEFBAd27d/et39KxPe+885g7dy6FhYUopejevTt/+MMffF2hkdo6ZMgQevTowfjx4+ne\nvTsXX3wxR48ebdL+9rjjULUU2WmaNh54EFih6/rt3uf+ApyLmeH6oa7ru8OtW1JSYgwfPrx1WyxE\nCw4cULzwQqrv8Q9+4KK4uGN8g2nOww+nUltrfgj88pd1eDP5TTz6aCpVVYqcHIMf/9gV0z6WLXOw\nerWDfv08XHNNfaJNFmeY0tJSunXr1t7NEBEsWLCAjIyMoLvwktXVV1/NH//4R/r164fL5WL27Nnc\ncccdXHrppadl/5HO9XXr1jF58uS4orFoMlSpwAPARdYTuq7/CEDTtEnA7cCP49m5EG3BrJnyS56B\nPVXA/yMvl0gNlWSohEhuZ8pYTxdccAFz5swhLS0Nj8fD7NmzT1sw1VZaDKh0XV+qadqECC9XAvI1\nV3Qo4Qb2TAaB7W6uximRcaishLQEVEIkn8BhG5LdlkoQAwAAIABJREFUPffcwz333NPezWhViRal\n3wg80RoNEaK1NC1K7/jf6Ky6KUtzBeeJjEMV7dAMQgghYhN3QKVp2kxgm67rW1uxPUIkLBmL0g0j\neG6+SBkqwwgMqOK5y8/82dDQ8YNMIYRIJtEGVEGfvpqmjQAm6Lr+f63fJCESk4yTI0cbBAY+L3f5\nidZmt9upqalp72YI0aZqamraZCqaFmuoNE27A7gcKNY0LVvX9TnAv4D9mqYtAzbquv5frd4yIeKU\njBmq0DZGylCFBlSGAbHUqCYy5II48xUVFXH06FFOnTrV3k0Ros3Y7XaKiopafbvRFKUvABaEPNe3\n1VsiRCsJvcsvGYKHaAvpQwOtWAMqa7vS5SfCUUrRpUuX9m6GEElJRkoXEW3aZOfgweS78DYNTjr+\ne2iaoQrf5kSzb4EjpXeQwYWFEOKMIAGVCKuiAt56y8k770QYXbIDS8YaqtCgL3INVWLZt2iHZhBC\nCBEbCahEWHV1yvuznRsSh2Scyy+eGiqIPVgMXF8K04UQovVIQCXCsi7oyRCMhDoTitIjtTk00JIM\nlRBCdAwSUImwrK6lZOguC5WMXX5NA6roaqhirQ8LPBaR6rSEEELETgIqEZY/Q5V8F93QICM5A6pI\nyyX23gKPjXT5CSFE65GASoRlXWyTsVsoGaeeCQ0Co62hki4/IYToGCSgEmFZF9vQOeaSgRU02GzB\njzuy9qmh6viBphBCJAsJqERYgVmdZAhIAlkBoNMZ/Lgji7+GKv79SJefEEK0HgmoRFiBmZBkC6is\n9jocRtDjjizaDFWiQ0IEF6XHtq4QQojImp16RtO08cCDwApd12/3PjcF+I13kd/ouv5B2zZRtIfA\n7EUyBCSBrKAhJQWqq5MzQxUp2AntpjNrr6If8jww8yVdfkII0XpaylClAg9YDzRNswH3AdO8/+7V\nNE0+ldtAaali2TJHu2URkrvLz2y702llqDr+KRr9SOmh68W2H+nyE0KIttFsQKXr+lLgRMBTA4Dt\nuq7X6rpeC+wC+rdh+85aq1Y5WL3awd697dMrG9zl1/EDkkBWkOFwBD/uyKKtoZKBPYUQomNqtssv\njHzglKZp/+t9XA50Bna0aqsE9fXK+7N99p/MNVShRenJ0P7AOxM9nugzVLG8N48neEJk6fITQojW\nE2tAVQbkAj8BFPA4cLy1GyX8F8qGhva56CVzQGW119/l146NiZLVxtRUg9pa1cw4VPEP7Bl6HKTL\nTwghWk80/UmBn+C7gIEBjwfour6zdZskwB/QtF+GKplrqMyfVpdfMrTfHwQGP460nCWRgEq6/IQQ\novU0G1BpmnYHcC8wU9O0v+q67sYsSn8feM/7mmgD1sWvvbplAi+2yVCDFMg6dikp5k8j+pvg2o1V\nlJ6aaj6OfmDP6M8PCaiEEKLtNNvlp+v6AmBByHPvYQZTog1ZF8r26pYJvNiaQV0SRCVeVgCVTHf5\nBXdTqjYZ2DN0WamhEkKI1iMDe3ZQVkDTXgFV4IU7GbrMAlnBSDJ2+VkZqmhrqGIrSg9eV2qohBCi\n9UhA1UFZF9T2yiIEFsMnQ0ASKJnv8mupkD60OzOW9yZdfkII0XYkoOqg/Hf5tc/+z6S7/JKhBsxq\nY7Q1VPG8t6YBlXT5CSFEa5GAqoOyunba6y6/wItvaFdRR5eckyObxzglpfm6r9AMVSy/Gxk2QQgh\n2o4EVB2QYbR/l9+ZMGyCv8uv4weEoYFSpO44fyYr9jG2AgcPbW4fQgghYicBVQcUOKJ1olmEQ4cU\nlZWxrxe432S78PrHoUq+gT1bqo2yAt14sm/+oRmMoG0JIYRInARUHVBgAJNIQFVZCf/4RypvvpmS\nUBuSISAJ5J8c2Xrcjo2Jkj+gavuidKtOS7r8hBCi9UhA1QEFT2AbfxahqkphGFBZGfs2knvYBPNn\nMt3l17QovfnJkeOZVidwehuQgEoIIVqTBFQdUGtlqBK5UzAwkEveovTkucvPCqCsNrdUQxXPKPBN\ns1vJ9XsVQoiOTAKqDijwQpdIQGWNJRVrliuwKN5sT/xtaA9NM1QdP3AIDZTc7vDBkr+GKvZR4K3j\nkpYmGSohhGhtElB1QMEZqviDAf+dgvHvH5IvoErOYRPMnw4H2O3Bz4VbrqXxqsIJrC2z2czjkmy/\nWyGE6KiancuvOZqmfR/4KdAI3KPr+rJWa9VZLvAi19BgZipUHHGVlYFwu82Lpy3K8Dk0oJK7/Nqe\nf0gDA4fDfOx2+6fPsVi/C6t4PZ65/Ox2c7v19eb2rABOCCFE/BLJUM0DLgIuB/7QOs0R0HoBTWB3\nUCzbCF02GTI8gcLd5RdLrVF7CAx27PbIdVSJTKtjLWsGVNLtJ4QQrSnuDBWwGZgAFAOrWqc5AprW\nxTQ0+C+gsQi8WDY0+OtzWhJac5UMNUiBgoMTf4auI2dirGNsszXf5Wf9bhIZNsFmM0Lqyzp4tCmE\nEEkgkYDqPeA2IAV4rHWaI6D1MlTBg3NGf+FM9hqqwBHBbTZ/91nHDqjMn1YQaD7X9HcWOk9hPHf5\n2Wz+rkTJUAkhROuIq8tP07S+wAxd12fpun4ZcLumaZ1at2lnr9AApr4+vgxRa3X5BbZnzx4bx493\n3IyVYfhrzsxsT3LUUQV3xwU/ZzGMxO5gDMzcWQGZBFRCCNE64q2hsuPNbmmapoBOSL9BqwkNaOK9\n6IV2+UUr9EJuPa6uBl1P4c034+h/PE1C56uzfiZLQGWzGRFrqKIJuprfh/Kt31y3ohBCiNjFFVDp\nur4DWKVp2mJgCfCYrut1rdqys1ho1iHe0dIDL8ixZajC11DV1Jgjr1dVddwMlZWFsQIpK3Do6IX1\noXVfEDmwtdv97y+W9xW4vpXhSmRYDiGEEH5x11Dpui539rWR1spQBQZGsdRQWfuzCrqtC7HVLpdL\nxT2UQ6xi3Y8/aDDfqz/w6NjF1+GzR8Ftto6/w2Fgs8U/9YzdbkiXnxBCtDIZ2LMDCr1Ixh9QxbcN\naz1rzjd/QKV8j09HV9GmTXYeeSSVgwdjrxMKzVB19K6taLrzArsz48m8hVs/2cYYE0KIjkoCqg6o\n6V1+8aWCgu/yi349K1sSOhp34PZcrriaFJO9e23U1ioOHoz+NA2toUqGgCqw2Ly5cais34vDEZp5\ni05wUTrefUiXnxBCtAYJqDqgcONQxbcd//9juXCGZqisC3FgO+K98zAWdXVWe6Lfl2H4x3MCf3DS\nkWuomt6ZaD7fXA1VPIFiYLdiS5MwCyGEiI0EVB1Q02ET4ttOYMFxLEGZtayVoQrs6rOcjgxVXZ25\n31jef2DQAf76q46coQptc3ANlV9gDVU8AVW4wveOUkO1ZYuNjz5ydPgR7YUQIhIJqDog68Lpr3M5\nvXf5WRdpa744f5efvx2nJ0OlvPv9/9l78yBHzvPM85eZuIEq1H1X381ms0mK7CabzUMUKcm6Ja8k\nu7xyyObYcszaYXtidsMOO7x/TDhi/tqYsb0zntVKWoctWbY8JYmiDsqSaIrizSbZzb67WX3XfaFQ\nhftIZO4fX33IRAKoQqGK3U0xnwgEUEAi88tEVn5PPu/zvm/j36mf5XfrhrachKoRD5U0pTeX5Wfe\nciG/55/38tJLHpaWtmY8xSIkk1uyKhcuXLhoCC6hugUhJ75AYHOZWJWEaiMhP2V1+5XjudEeKhny\n20hqv6XCmKvP4u93h0JVOeZGPFTNtZ6xe6iaGfHWQ/7WW0WonnzSx1e+EiCT2ZLVuXDhwsW6cAnV\nLQhJaIKrtee3pmzCRr4nnp0KlX0dN1Khaibk926qQ1U95tolEWp5qDayX3b1Tm7jVgj5maZ1PsXj\nW3NeLS4q6DosL98aCpwLFy5++eESqlsQcuKUpvCtyPJrxkMlFSo5EdvH0ayvq1HoujWOjZBBOVbp\nnVqvXtO1aypf+5qf6embN/HKcGS1h6pyuco6VJXfbQSVpnS5zptPOGTzaoCVla0ZTz6vVDy7cOHC\nxTsNl1DdgpATZzC4ORWhujlyY5ATr6VQVXuZ3umQX85Wd38japiTnKwXGrt4USUWU7h8+eZ1Tq7v\noXJWrBfPa2UCNroduY2bEfI7d07lhResmsJ2ch6Pb/6SZBjWOnNu/wYXLlzcILiE6haE5aESz82q\nQZttjmxl+VWv450O+clwH2yVKb328tKflcncPCWjXpaf8zer156m0cy4SkJ180J+v/iFl1de8ZTV\nKLtHbitCfs2ScRcuXLjYDJpuPTMyMjIE/OPqOt4YHR39P7ZsVO9xWKbwmxPyc3qoDENM2vZx3EiF\naiOm9HrkpF5oTJLVdHqjI9w6VJvSa4cp5fH3eERIU1Eqa1g1uh1VNfF6lYp13kjY1aNotPKGYWVF\nwTAsQtwM7GE+V6Fy4cLFjULThAr4L8D/OTo6+spWDcaFgJz4NmNKN4xKVWYjoSFJqLzeyn5+N7Kw\n51YpVOuF/G4lhWq96u61yKKui/cbISB2hetmhvzkuSN/VzuhMgxIJBTa2povSGUnUa6HyoULFzcK\nTd0HjoyMaMBul0y9M5CTnKVQbXwdThKyEZXHroTYJ/et8lDF4wovvOBZcx3NEiq7CgPre43kZH4z\nCZXT91XPQ2XVJ2uuJITdlF4v5Kfr76z6aDegS7LjPDc3G/azk6gbUd7DhQsXLqB5haobCIyMjDwF\ntAL/fXR09HtbN6z3NiyFSk56G59gnCSsmZCfIFQmoFAqObP8mp/03nhD4/hxD8Ggyf3312YD2az1\nemOmdPFsKVRrZ/nJ45JO33yFaj0PlXM5sW9Kw6UT7N+vV4fqn//Zx8qKwh/8Qb5M7LYSdjVKkh2n\nRzAeV9i5s/lt2BUqOzF34cKFi3cSzToVYsAK8HngY8BfjIyMBLdsVO9xOAtrNhPyc3pjmgn5aVpl\nixP75LuZO39JXmZn659+dpVB1xuvtyQN2tUeqtrLS7KWz9+8IpfVhKpeHSpLOYSNF/esneVnHWfT\nhLk5lXRa2bKCmKVS5blSK2zsvGHYbO0oV6Fy4cLFzUBThGp0dLQITAB9o6OjBcC9bG0htqJSerVC\ntfGQn/RQiTEpW+ahkt+dm6t/+tkVKmj8GEjS4fRQ1TOl2yfcm1VVu16Ycj2FaqNtdSz1ziw3R3Ym\nLshtbJX3aHTUx1e+4i9vp7J9kdyWeJbn+2ZDfq5C5cKFi5uBzZRN+DPgayMjIy8D3x4dHc2u9wUX\njcHyUInnZkJ+VnHOjZOyypCfeO0M+W3mzl9+NxZT6paEcE6EjY6/XtmE9UzpcPPCfvXqUDmJktND\nZZHFxrZTy5RuPy6V5QYaW+daME2YnlbJZBRSqepaZpJYy2319Ij9Wl7eXDWXSoXKJVQuXLi4MWja\nJTE6OjoOfGILx+JiFdWV0htPjZewk7Jcrrk6VM6QX6Wa0fxEJSc504T5eYWhoeqMLidhE9tbP/Or\nnopTi1CZZuU+CWN689llzaJepfRGFapmTOnyXLL/jnYSK8jO5o5FoWAdX/l72rfnfK+nx2B8XGV5\nWdnw+W6H/dxxQ34uXLi4UXALe96CsIfcpHl4o2G/zdSykhO0ZUqv7aFqtKCkE/ZJrp6PKpvdrEJl\nVjzXUnGKxcp9uHUUqsY8VPW8Vo1sx35eyWNgJ1RbQUSkKiW2s75C1dJiEgqZFIuQSjW/3cr9cBUq\nFy5c3Bi4hOoWhJ3Q1PK6NAK5vKxltTGFyiJ0duOzk5Q1Gxay+6/q+ajkROjzbWxbzppOaxm3neu8\n2R4qZ7uc9bP8xPNGs/xUVag/ToWr2czKerATVHms7cdcvpZky+eDaHTzYT+nQnUrN8Z24cLFLw9c\nQnWLQRbkVBQx8dXKxmoE9mrnqirW2YiSYQ+DeTyVfh75figkJr1mVAx7nzVYS6ESzy0tG1PYpNrS\nSOsZZ9jyZitUUk2zjnnt5aSCtZEsP1ntXp5XYFXCt8zhW61QWa/lNmqV3pCf+XzQ3i4JVfO/hdN/\n54b9XLhwcSPgEqpbDHZDOGxcobHWY4WH5LoaUbnsKohdxSgULKInVa9mVAw5uUn1a3FRqRqXaVqT\nYmtr5aS//vhr+5FqZcJVK1Q3h1DZzeL2ZyeJlOdGNVlcf9xOdQuspAcZXn0nFSpJXmvVoZK/v9dr\nlgnVZjL9nGE+N+znwoWLGwGXUN1isAiVWfG8HhkyTTh+XGNyUvZoE+97vdY6Ggn7OQmd9OnIScnr\ntZSNZu785UQdDJp0dpplY7pzDKWSGIOVpbjR0gBy/OK5dsivcp03j1DVq5TuXI6K5TYS8qtFqKTS\nKPf7nfRQOckT2MOAVshPtpyRjZObgbMMg9vPz4ULFzcCLqG6xeCc+KyK1mtPMOPjKj/7mZdnnhFf\nkBOXppkNr0MsI56dYSU5KXk8Jn6/eL0Zhcrvh95ewQScPiqplAQCZlmh26gp3Uk61vJQSWJxsxok\n166AXk2A7aqjfflGQn7OBsxgJ1TibzuJeqcUqso6VJWqlddrlsfkTErYCCT5l34sV6Fy4cLFjYBL\nqG4xOENWjWb5jY2Jn1KqAnI9QqESyzSmUNWetOWk5PFsTqGyzOYmfX2C/Th9VFIpCQYtYmd5cGBy\nsn67FUkcFKUyy28tQiVVkZvtoaquQ7X2chvJ8nOa9QFCIfEsFSo7idkKhaqWKX0thcrvt9otNZsg\nYBhi7Ipi+e9chcqFCxc3Ai6husXgDLk1EvIzTbh4Ucyy2axSYSwXpRcazxSs3r54tnufLF9X8wpV\nIECZUM3N1fa8+P2WQiWJ3tGjHr75TT8XLtQ+deuF/NYypUtCJY/djUb9SulrF/aUdZoaCfk5w4pA\nlRpUXYdqc7ArflaldOs9+TtbpnSz7M9rVqGyFFCz7BHbin1x4cKFi/XgEqpbDM5MrkbCdXNzComE\n+Fxm0dUqztlMyM+pUHm9ZrngaDNlE+yTZ0eHWI8cu4QM+QWDVrhSfm9pSSxbL62+nsHbMESD54kJ\ntbyMXGcwaBIImBhGdcubG4F6CtV6Hqr1+hSu9V2oDnXa932rPVS1+vbJ2mZ28i8VquYJlaV2yfPU\nVahcuHBxI+ASqlsMFhESz41k+V26pFX8ncspFaZ0i5Q1vn2nKd3yUG1WobJPeNZ7dmVIKiV+f7W6\nVisjzQ6pxNSqQ/Xaax7+6Z98nD+vra7TMkOHw2K5m2FMd6pHsk6ULKEhUd9D1VyWnzPkZ/caNUOW\nL19WOXlSK2/PfiwlQXOuN5+vNKX7/WL/7TcFG4E8TwMBS6FyPVQuXLi4EXAJ1S0Gp4eqkZDfxYvi\nZ5QhoGy2cvLdWMivctKWhMTuoZJ3/k4V4+JFla9/3bdmyrs9JCMrdhtG5djsk6LlIRPrlN4ae3jq\n8mWVr37Vz+yssmZ7FnmcFher6x9Zas2Nn3xrkZ1a6spmCnuuZUq3Qn7W8hslIaYJP/qRl3/9Vy/x\nuFJl8Je/n1MlzWaFH07TrFIdm/FRuQqVCxcubhY2RahGRkb8IyMj10dGRv5wqwb0XodTIVov5Ley\nojA3p+LzwcCAmFlzOaWitk+93nCNbF9+V05KXq9ZV6E6e1ZjZkbl6tX6p5V9wgPL4G6f9OymdPm5\nU6GyLz82prG0pHD5slbloZK+pExGKWcTynXUyi67GZl+a6lH9tCX00PVTJaf3ZRuJy722l+w8cr8\niYRSHuvcnFIR7oPaldLBCgvK3xlq73ujkOeF3UPlKlQuXLi4EdisQvX7wDFuRkfZLYKs3yRVi5uN\neh6qehOczO7btatEJGJNkPbQYTNlE5yTdqVCJd+r/G6t0JETdg8VUNM4bJ8UnUVJ5aRvn/xl+C+Z\nVOoavGMxK6wol7eHmsLhyppMNxLOMYOd7FjjqS4J0XiW31qm9HRaKfdmtJIQNmbQtycWzM+rZaVP\nZto5TelyHJJQyXMUNuejkudeIOAqVC5cuLixaJpQjYyMhIBfAb4P3BpspAlMTIj6Tc8+611/4RsA\nZzXs9UJ+ExNiwT17jPKdvfBQVZdNaKxSeuUEJ79rKVTVLUskrAKR9ddv90dB7RIMlQoVq9sSZEku\nV0moxOtkUqmhUFWPoZZCtREP1cmTGmfOaOsu1yjWLrppvVcvHNt8YU/xnM0q5eMZCgkSWyo13nQZ\nBImSWFhQyoRKVj53mtIlgZXtaeTvDJsL+dnJuN2j58KFCxfvNDajUP0H4G+3aiA3C7Jn2GZaXWwl\nJKFpNOQn7/Db2gxbZWgr5CdazzReKd3+PbBUEEuhqj9RyXBZIwqVVA9qhWXk5C48VBahtE+wdlO6\nRajqZ8LZIZe3m9Ib9VDpOvzkJ8IrtFVNd2urR+JZEjzTrB+O3UjrGTvBlGqjYVj/B8Gg2VSdMbtC\nNTen1iBU4jN5flmEysoeldhMyK+WQuX28nPhwsWNQFOEamRkJAo8Mjo6+hPexeoUWBf0ZPLm1CBy\norqX39olCuTEFQ5brTaEKV2uZ3OV0p0+HXthT/uYSiVrAlxrAqvnoapUqFhdptKUblel6oX8nFl+\ntQiVJGa1TOnrqSLZrCA3Iott7WUbRS31yBn2ymQE8QkGzZqG+8a3UXmSy/2W5SgCgeayOBcWrEtJ\nIqGUQ+jt7UbFuiShkuFpy0NlrUvuu7PJcSNwPVQuXLi4WWhWoXoYCIyMjHwL4aP6nZGRkTu2blg3\nDsmkuNiWSjev9YgdTg/VWlXOTdNSMMJhqyiiPeS30ebIzrINTkJiL+xpn6js5GIjHqpaaletkF+x\nWG3QLhbFMbBKKShlYmYRKotADA4a5eUqi5+aZcVkPYXKPslvld+qkZCfHFckYi1TL+R37ZrKK694\nOH9eLRObWgqVfTuxmCS65oaVnVxOKFwej1Ws9fp1saFo1ERRxO8lsjkr96OWKX0rsvxchcqFCxc3\nGp5mvjQ6Ovpj4McAIyMjTwDh0dHRc1s5sBuFZNL+WinfOd8sOD1UzrIBdhQKghRIklNLodpoc2Sn\nh8pJqOopVHYi0oiHSqoHtSY9e9kEqRo6Q35yOZ+vklDI0JUct2I7bLt2GSwsqBQKlfWP/H6LuK1H\nkuyESuzz5s8XZ7scqA75WUqktUy91jPf/763gnx+5CPFMnF1/p6SUMXj4oQLBp2m/fX3T6pTXV0G\nvb0ms7PWuFtaRFZoPi9+L10Xv4ncbi2FanMhP/Fs91DlcoJAK1vDf9/VmJxUGBvTePRRvXyj5cKF\ni63Bpv+lRkdHv74VA7lZkAoViFBFf//NJVTVHqr6pnTnJGuvK7T55sjyufJ41GuOXFnEsXmFyp6+\nHwhYZMEZ8gOxnJNMyGPizPID2L69xKlTGoWCUqFmeb3WMUqn15587d6trapZtVYVc0kqJPGwE6pa\njZ+lkqeqovn0zIzKzIzK8LBRtQ2xHfFshfzMulmc9SD9U729Jj09BmBtJBwWv3U+r5TPEXtiw1oh\nv+bKJljnjqaJ9RYK4iH3672Ml1/2cvWqyvbtBrt3b5EJ0IULF4Bb2LOCUNlfN78++MpX/LzwQnNc\ntV4dqlokRSo2cpKVqo+daGy0ObKdiEF1iEiuT1XF+uQ67YSqnkJlmtUeKqdCVSgIguHzVZZ8EApV\nNaGqFxayK3yaJrbX329WhJPspnS/X5CJWkqYc5sSMkNts3AWc4XqsJcMR9ciVHbvnyR8oZDJI4/o\nq+OsLnjq3M7Kit2ULj5r1EMlFaruboOenkoCHg5b65ME1E7KLSXV+p5dad0o7AqV/dkN+wnIa9zN\nKA/iwsUvO97Toq+uV15YnD3lmsGZMx7icYWLF4WsvlE4zcOtrWZ5bE7lRN7dSzXDPhFJsmDP8ttI\n2QRnJpmE1yvG4PebZLMKhYJY1k4u6ilUui72T9Os9TsVKqlKyH1RFPB5DMxMlvx0mmiigFfPopUK\nqG+l0Up5do2baEYR1dBRS0VUUyf6szze1hJew+BLfhOvxyT4HZP3ndIYmFcIfkfnzhM+TFUl/EMd\nVJVD1wPEEx5KPzDx9Gjlvj2mKDeP6fOhXArRlgijaz4KCx4oeK2D0iRqkR1nXaxaClWt1jNy+VDI\n7guzq2C1TemSlFW2BGps/HaFqrvbUj1kKFWQJat6us9X6ZmS71ljqtyXjaA6pCxucnI5pfy/9F6G\n/D/dqoQKFy5cWHhPEypnNefNKlSmKaqFQ/MGd6cpXJhrxeSWzVqTjdhGpcHXbkqXE6jdlN5MyM9J\nqOSE7POJ8RQKCqGQWTH5SeXK6dHIJ/K0pOK0E0c7uoCSSDBwfoUjb2UYvLRM4ESC1pkEv346R1RN\nEnkuBek0f3A9j2GI43A4j8grNSH6ihjLJ5er96vroolnVd3abnv/7mWFXBZaL5o8klBQVAhMiPU8\nGFfI56DtnEkgWPv43JVU2LU6KQWehpa/NkFVMYNBCAQwQyHxOhgUr8NhzHAYVp/NSKTy0dqKlu5C\nMVscCpV4zmQEka5lSq+V5ScJaTBYmUlXz5Qu629JBALmupmldhgGLC5aClUgIIzoKytKmdA5FSp7\nYoOEXaHaaMjPMMQx8HrtCqhdoVJW339vE6pisXZhXBcuXGwN3uOESjyrqrgob1ahmpuz0sVlj7Ja\nhSXXglMhUhSIRg3m51VWVpSyogDVHiq7ZwQs4WQjzZFlmEVOSLUUKuvzVR+SaVKYX6EntkAkNUck\ns4Dny9MEkouoCwsoS0so8TjB5RT/bkFB80BolQwN5iG4pODzg/eKSSAPfUsKfj8oqlSpFIreILo/\nQNoXRAkGyRp+GNYwvH6uzwTQAh6yJS+G4sFQPdz3gEmwZbU5nGwSB0yOqYxPeNi+TWf8uorfW6L9\noQKYJnNjJtPjBju3FxnqLaAUi+Jglkoo+TwUiySvF0kqBTylHIonB1pWfJ5OQzqNEos18jNX4Dfn\nFUqGQtfLEbSOVsyWFsxolI+c7STtbUP9Zpjus51kkx10zUVQOloxOzpQVcGu7aZ8+fsFg6JYqaoK\nUiYVy3ohP+vv2pmX9RCLiUbcbW1WmYKeHoPPyyyZAAAgAElEQVSVFc1GqCozKL1es8rPZCdYMtxb\nLFpJF2vhySe9TE+r/PZvF8jnpYIqPrPC4Ovuyi897J6/ZvxpLly4WBvvaUIlCVRPj8HsrLppherc\nOWu2EqoCtLRsbB1OhQjEHf/8vPC52E3z9vCORDBolr0vVumFxkN+y8uCAba1SUK16qUqFYmmpmk7\nfRXviSkeeHEOJqfpe2uKSGKWD80UKNhCRMGrZpVCZage0qF2jPZ22u9twWxrI6G28dqpDoK9ER79\nVJDLC20890aU7QeCfPDTPsxwmG/+UxuLS1qZLO7caXD1qspDD+koCrz8soc9e0pcumQd/9t+P4/a\nVq1ITL7s4eUXPSzuK/F2j0Z7u8n9/5sY+OwxjWef8XLPPSW6PiYOViymoGnW8Xj2KS8XLojtdHeb\nfOlLefGjZbMoqw8yGfE6k7GIVjqNkkqJRzoNqRRKMomSTFKIp/HkUmjJBGomUR7rHfNCWQrOmxyM\nK7xPh67T1nG92wzSke7E+2oHwWNt4rgmOrnjWg9DwTa0sShdZj8LRmf5XK+X5Sfh929MoVpYUFaP\nhcXqentNLl60FDJnBqXdlC5hJ1SyQXIqpZDNVhKqlRWFVAoGBy3vl/zdn3/eU94HGYGVNwYbqan1\nywp7WN4N+blwsfV4TxMqSaD6+0WqdyrVnKoEQiWQhMrjsfxZspdZo6hVgFF6P6RxWKKWUTkYNMvL\nWZl64nk9hco0ITOXoj92ld5XL+Kfvs7AhQl+6+g0rakZVKNE54smXh/sWxLqlDdtQgDy3ghLoT5S\nkV4SoR7u/lA70b1dGJ2dmF1dmB0dXI1F+ZfRANu3G/R9QczW6SWFN77qp73d5KEP55k9qjF73cvQ\ndh2zRwzY61cwTZNUKk0+v0Ims8LsbJ6TJ1Pk81kuXsxTKqU5ezaPrmcpFrMUi0kMI0s2Kx6FQoFi\nscjCgs7MTAmPp0A2q6NpBZ58soCu6ySTBVZWFHw+k//8n4UCF4spKIpCV5c4xsvL6irREJl0//iP\nJsrq7K3YfFS1Xnu9Xnw+X+VzOMzFaBe0ahy8s0RQNQmpKiHTZOqiipo2eN/2PLFSiUghz90dGVrz\nGUKpFFqugJ5I0pKfQEuAR1EYSCp8KAWRUxD+vskXFxUKuor54w72Kd20j3UQeLMdo6sLs6uLtmAX\nHctDJEM9FH3hCoWqERIiyy10dlrn4N69JU6e1Ni7V5zMzpCfz1etUNlDfiCIXiolMgPt3qcnn/Qy\nP6/yxBN5+vpMzp+3/lnPnxf/f/Z1W90D1t2VX3pUljZxCaYLF1sNl1AhQmqhkEomo5Tv4v7hH/zc\ndVeJxx9vzFg+Pq6SSim0tZlEoybXr6urd+QbI1ROD5UYn2VMt6OWUVmGOGCd9jW6jnr9OuqVK2hX\nrqBeuYI5dpkvXYijqtByYlWZKkJbQsFUFFZaBgjf04+5Z4BzM8NcSAxx3692s+vhbv7+H7pIpwXx\nWFxU6PlkgdAuoVoYhkEymeTa+CQLCzkgzs9+FieRSLCwkOC11zIYRoJLl+JcvJhkairJ00+v8Jd/\nuUIikSAWS5HNJjDNxpvLPf98w4ty5Ur1e1NTlX/Pztb+br33m8Gp03U+OGN7fbn2It4ZDy2BAEHF\nT8Dw0K2rdGbAnzaIFEtEU5OEUeme1+h+S6ND02jXNDo0D5+KeWhVNIq+CH3nOgj6esjN9xOa6cKr\ndGL09GD29mJ0d1eeYFgkX56jIBSqP/xDS66UZEneAAiPf32FCiwPmQhNWZl6c3OCQL3xhodPf7pY\nVgtbW83y/4ckUbCx8OUvO+yeUTfk58LF1uM9TajkBaa11aS1VRirk0mFmRlBhk6e1PjAB/SGFCup\nTh04UCr3BWymTpHTQwVWuMmpUFlV0q337JOJnLQ8RoHexctsu36BwH85h3rpEtqVK1WSVaEARU+Q\nXN822h8fxti+neXoNr75wi4W/K2kimk+/vEZSqU4LyVSnLt+idd+9gZtr8d5/vkUudwKmrZMPJ7g\n299eIZ8XhCjVYH2Bl15a+3OvN4Tf30pHR4RcLkwkEsTnC1IsBtm1K0AsFsI0Q3g8QR56yENra4hA\nIEAwGMTv9+P1elle9vHqqwFU1YemeRka0vjwh4V6pChevvnNIJoGv/VbeS5eVHnpJfG7fu5zRaJR\ng+98x0vCisoxMpInFALTVrtAvra/ZxgGpVKJQqFQVssKhQLpdJGnnzYxzQKPPZahUMiTy+XIZrOc\nPZtndjZLe3ua6eksppmhqytNNpslk8mQTGZZWclSLKYo6nmWUilAHOvL9ZIi6vwUGtCmeuhe0GhX\nPUQMD51vaQz8RKPT46HD46FT0+iIRunq66N7aIjo8DA9V4fZneujd7EDZbkXMxqtyniUZMlec6ra\nQ+X0clWXTpDhRRBq1N13l5idVfH74bOfLfD1r4uV2tctQ36uQuX0UN3Egbhw8UuK9zShkgpVS4uo\n6Dw7K1Qg2TYjl1OYnlYYGlpfZZqdFevatatUDj00k+lXz0MFsLJiMTt75ldFyC9g0rYyTt/CGfae\nPUvojXOExi4xMm2gquC5YJAwDGK6zkJHBwudnSxGIiwEAowtezhxWcejxAi89hqxp58mFouzuBjD\nMISn6Ktf3fg+AUQiEQKBKBClo6OFbdtaaGlpobW1lQsXOvD5Wvn4x0NcutROPN7Ghz8c5MAB8fnL\nL3dw7Vo7muYlGDT5/OcLfPObfvr7DQxDqBZPPJHn5z/3MjEhjtF//I85p5gCwPy8wuKiNePefnuJ\nI0csc9nLL/tJpxV27MgxN+eht1f8ENu2Fdi+3eDnP/cTColQbjKpsGuXCD01i4sXVcbHfQwNGXzx\ni5WmpWef9fDGGx727i1x8aJGf7/BE09Yy1y/rvKtb/nYts3g859Pkkwm+ad/ynL1aoqHH44RDid4\n880Up0+nKRQS5PMJuruX8fmWicfjxONxlpaWmJuLUyikiBk6sbwOrKpLeaDWOXzyJCAuHl2qly7V\nw3ef9tDr9dAbCNDV3k5Pby/dAwN0b9+Oz9hD99wdZPJD4GvH4xE+ME2zQtxOhcpZ2BQsdQpEiP37\n3xfS6969Jfr7TfbtK/H221qZRMHWK1TJJIyO+jl0SOeeexpXTG8FOBUqt3q8CxdbC5dQIcyzdp+S\nnJQBrlzRGBpaO+xnmpaXpKPDLJtxm1OoxLPdQ2URKusiKJLODJTiAtP/9jIrx48TP3eOxbPXyMaT\nHDN0nlN0/sqjE9NLTBUVlkyD5HwOvZFuug54vWGCwQ62bWuns7OdQKCNmZl2otEohw5FOHOmk66u\nKDt3Rrh+vZOHHw7xyCNhWltbiUQiaJrGyy97ePFFDw89pFfU6Ppv/81PJqPwxS/m+N73fExNqbz/\n/fkykT13zsvEhCCpqxUJADFJSgIaClHhV6vVFFl8f+1QUzRqkk4rrKyoFRO49NflcgqKIn7nZFJp\nKqxrhyTv27dXV62WRFmWJXC2RbL38vP7/fj9flpafPT1qTz6aJ7eXpP+fg2fz3J1f+xjxSoi8I1v\n+JiY0PH5FvnUp+a4di3Ot7+dRNOWuPPOeZaWllhaWiK+tERsfp7F+XkWYzFWMhlmjSKzRpEzduVr\nZgbOVXaiUoAOxUOvx8fxSCv/1tdOsTBAILKDQPtupvfvJnDkbiK9vYAz5CcwPy92+MCBEmfPamWF\ndv9+sT+PPaaTTCocOGDtn1Rst8qEPT6usbCgcPas9q4jVPbrUankVo934WKr8Z4lVKZp3bFFImZ5\nMr50SStPmqYJV66oPPro2utKpUQGXSgkGhQ3U5iwWCwSj8eZmkoyMbHML34xh2EsllWEF19cIZWK\n8dMfz7OyMMtSbIl4JkMJk/9rg/seiUTo6Oioeiwu9pBMdvLQQ23cc08bnZ2dBALtfOtbA3i9Yob7\nkz/J4fGIC/Jf/VWAUgk+97kCTz7pY3jYYNcug1LJQ3+/zvBwJRGVhSKd4R2/X0x4+bxSUUdJwlmj\nyG40luUAAgGzglDVC9MGHfWlnF6etjaT6WnRE1BWAAfxG9t7DG6GNNshyfu2bdWESo5V9ie016AC\nq72OnR/Lc04SRycJq0U0w2ETTfPR09PH/v0dDA7CyZMBIhGTP/qj+tU95+dz/M3fJDGMOR5/fIr5\n+XkWpqZYHB9nYXqahbk5FuJxZpcTxAs5YqZOrKhzLp6B+Cxwvryuv/mFeI5qGoPhMF2hdnxqLwsv\nDHLtwR307d3LiUvvI6/v4H3vC7GyojA5qRIMmuzYIY5de7vJb/92pcrX3i72X97wbBay9+dWFAG+\n0XAq5rmcUqHmuXDhYnNoilCNjIz8v8A+ROua3xkdHa1h6721IatHh0Kij5tUqCYnxYX3jjtE+GB2\nViWVqp7M7KguNZAmkUhx4cIiLS1zxGKxMjGyP+zvJezGHOBb32psP1oUlc5ggM62Ntp7evC0bmMh\nPUww2MmOHR188IOtdHZ28oMf9OHzdfIXfxEmHK59W/rNb/qYnFT57GcL5Qk+nwevV8TOZEknsY8i\nVX52Vi2rLOGwaWv1UT3hONvOSNhrWkklwa4k2dPmBaESr2XYQtbfaoRQeTxWoVSorVABXLumVlQK\nT6WUiirc9irkzSKTEWEsjwcGB6sJlbOKuT20C9ZvIetQmSZVhLSaUFVPoHJZe3VxWD/LL58P0dra\nxsDAIB/96J11lxsbU/n2txUymXny8Svs7jyFt3iRoy9OEItNs5xZIGGsMJXNsFIqsZJIIIxq12Ea\n/v61yvX9f/+Ph75wKyFPN4ODAySvDtO/dy8Du3YxMDDAwMAAnZ2dqKpKR4ckVM1n8NohVe1kcmvW\ndyMhxy4L8WYyEI3e5EG5cPFLhKYI1ejo6O8DjIyMfBD4U+APtnJQNwL2cB8IQmWaBoVCmkJhBVVd\nQtfTXLmS5O/+bolodJlEIsHKimW0lubiqakEU1NxdH2JP//zGLkmHLCqqtLe3o6qdBBWA+zrMOgt\n5uhKpehUVQJ5Dy0lD8NtPnoP7KYwdIijiUeIPnI3n/lNi6FcvKjy3e8KlnDHHSU+8xnhD3rzzQD5\nPKhq/bFJJaStzZrc7YqGs8NKT4/wnV25IhYKh80109SdfdYk5ASeyyllddCuJFU2zq0uYBoMirpD\nklCp6trekEDArKqoLSFJ8eXLlTNlOq2UjbyBgNXWxVltfyOQ6tTAgFFVswuqw5NOQmWF/MQYVmuQ\nrrZ7Wfs7djhbF1m9/FiTNNTK8KsFUajTS0vLIC0tgzz4sSPcc0+JwCqB1zT40z/NYRoG8StXmDlz\nhnOvjfHmS9fQixPoxiyTsTgTyTTTRpGMrnNlZQlY4kzsbX56qsY2NY3+jg4G+vrI6dvxRnajaX3s\n2dPPwMAA/f399Pb24ql14NeA/L0NQ6iWra0b+vpNg2FY6mVXl8n4uFKRQenChYvNY7MhvyTQQPm/\nrUepVCKfz5cznlKpFOl0mkwmQzqdJp1Ok0qlKv6Wr1OpFAsLGSYmMpjmCn/91yskEsLUKy8wX/6y\nta3vfGdjY/P5fPh8nYTDHezd2057ezudnZ10dHTQ3t5OR0cHptnBa6/1MzDQzu9/JknnhQv4jh9n\n7sen0LJpur0mWsAL0Silffs4GzzIq4X7UT63jx2P+Tl2TGPqGS+9XTpghdbqKTsej1nhOXKiWBST\nhabVbm8i12FHT48BaOWsxnB4bROwVDzqZXhJQicJUq3tyv0LBKwCppJ8SUJVzz9lX4ckA84q3JIc\nSDWqr89YVSkthSoYtDIrN9Nkdny8vn8KKtsMQX2FSob8LHXKWi4SoRy+tn+n1nolsZKVxvN5Qaqk\ncpVOwy9+4eX++3V6esyGCVV1iYRK4ib/VlSVjj17xOMBhcttfnp7DX7ndwqcOaPxr983ubt7kof3\nXGD23DlmLl9mZnyc6dlZphYXmcrlmCwWmSoWiZdKXF9Y4PrCAiDqUbz+RuW4VFWlr6uLgeFhduzc\nyfbt29mxYwc7duxg+/bt9PX1VREue/HfROLd0x8wnRbngL3Ho5v56MLF1mKzhOp3gf97rQW+9KUv\nEVyd8UqlUsVDppLLh67r5fd0XSefFynkhUKBXC5HPp8vv9Yb6aPSBIT5upXe3gihUJSVlSihUCsH\nD0aIRluJRqNEo1HC4TA+nw+Px8Pp0x3EYt185jMtHD7cht8f5r/+1yCqKu68q9SSbJbrT55mx8TL\nbD/6GoM/mSirAN68Qiy6nchn7kE7cgj97ruhpYXFNzTGn/XSVRAESnp3nJOuXdmxE5HKWlTVk4B9\ncrQrEopiteZx3sz39VUSgVDIXDNNvZ5CJSdsScyc+1TZOFd8Nxi06g5JAiEnt1phrcpx1l43WAqV\nxK5dglCl0/aQn73xcPOE6vp1wW5q+afEOCvHUs8PJQlVrXCpqor1yHHWIlR33FFieVnh4EHLjOXz\nCQJuJ1Rvvunh9GmNQgE++9li+fg3olDZIc8jSaRqtZZx+hDn5hRKmpeWO7cReWiAPR/8IHvsXzBN\nlHgcdXoaZWaG3NWrzF68yPS1a4yNTTMVXyamFZkzC0wWi0wXi8zpOtPz80zPz/PmsWNVY9A0jf6+\nPoa3bWN4eJjh4WEuXtyB37+N1tZtzM/3MjRUI5X0FoTVC9Isnx9r3QxcuqRy5ozGxz9efFca148d\n04hGTfbsqf2/5cLFO4GmCdXIyMingbdHR0cvrLXc9773vWY3sSYURSEQCOD3+wmHw4TDYSKRCKFQ\nqPx3OBwmFAoRiUSq3rtypZXLl6M8+GCYRx8N0drayje+0Ukm4+XQIZ1f+RUd04SvfMXP8rLCE0/k\nK9q+2LG05MPrVbn99nx50gsETHI5pdzQWJmcxHP0qHicOMGOeImu1cyoXGsL3vcfonT//XzjjYeI\n+3r53/8oV3Ehc5ZOqFUyQW5Xwk6A5Ot67WescF/1PmqaIFTOia+7u3LZUMjyN63loXJOsLUUqlqf\nQ7XPR7wnDdjwwAN61TFxolLFq1y2pcWsUHR27SrxyiuechsU+f3NEqpUChYXFbxeEfKrBb+/srRA\ndZaf+Ft6qKRC5SSkkcjahCochl/5lcobFL9fGLDtTYWvXhXn3uSkimk2HvJzEmj5+8vf0Hk+QGWD\nZNO0MvyEKloDioLZ0UGpowPuvBMPMLT6UN/UmPvXIr86NM4Hdo+jTk+jzsxQmJhg7upVJqenuZrL\ncbVQ4EqhwNV8nmuFArO6zuTUFJNTU7z66qtVm/y7v4POzk6Gh4cZGhpi27ZtbN++nW3btpUfYWf3\n6ZsE63pR2US9FgwDfvpTL8mkwt69RkXW5LsBsZjCM894CYVM/viP825pCBc3DM2a0g8BHxgdHf2T\n9Zb92te+RiaTQVEUNE0rP1RVrfjb+fB4POVU8EAggM/nKxMoWaRR2cR/yo9+5KVQ0LjrriLbtokL\nRkeHRiZjKQaKIia75WWNxUWV/v7qC4uzZIJES6BI19WTeP/HS4RPv4o6OWl9SVFY6NvPqfCDjA8+\nwI5P7OWxD4nvJs4EoFStBjmLe0o1oppQWa+dIT+oH/Kr5Z+yf7dYVKrIh98vsqiskF9jCpWd9NnH\nLI+jU5mxHwt7yE/CTiAaqWxvJ1TOyVzThNK1siLJjommibHLcI/dlN5sOr4M9w0NGXVDlPaedlBN\nlKSSuFbIDwTRnJuT+9dYiEqQWKX8m6VSMDtrkfnlZWUDIb/Kv6VyailU1d/3eq0WTsWiqB8GaxCq\nNdDZaVL0hrjmu42HH91R8Vk30K3rHJydFUTL9ihOTDA1Ps54KsV4ocC1fIGxRJGpUoEpo8B0qUgs\nFiMWi3HixIk627YI18DAEMnkDu6+e5AjR4YYGhqio6NjU9exRmHPaK5VNNWOy5etvqax2LuPjchz\nJZNRSKfXTihy4WIr0axC9W1gYmRk5Dng9Ojo6H+ot+DnP//5JjfxzkISCHtm2OOPFxkf19i717po\nS5JU78JSUTIht4zn+aN4Xn2VL/z4GGYyQ6TDRPWD2dKCfv/96A88QOn++/nRUz3lCco7awAFTNOa\nHJ1GYHudLHvJByf50DTL/7KRkJ8kRbUmRzmWWhN/T49BPC5N6aypUEnP03oK1dohP/FsD206CcR6\nqAz5VX83GhWEqrtbFEONRMTf8hwIBER5DEURF+1SqfaxeeklD6YJ739/NcmbmhIHdXh4bYIge9oF\ng9XNpp1ZfrVCflCpbDWalSaPuShLYXL1auUOTkyo5ZDfej6i6t+78rlWSElRxL4nEgqjoz6yWYVQ\nyNxws3GAzk5xgOqSA48Hc2iI0tAQzlumXsOgLxbjyPQ0y2emOfaDBaLJKaLJaXr0CUxPjOuFAuOF\nAtcLBa4WClwrFLiWz3O9WJtw2TN4Q6EQQ0OCXMmwov11LR9XM7Ar2vJ/p17I7623rO29GwmVrNsm\nX0cibtjPxY1Bs1l+u7Z6IDcS8bjC1JRIV7f7gAYHTQYHKye/jg7x+dJSjQuLaZI+Nc59p49yR+xl\nIt8/U44V+YsKU227KHz0MF2fPULpjjvKM6BpwtKS9U8/M6NSKlkTo8dTnaUWCIiJMpsV6c6WJ6J6\nWDKLbSMhP6k21Av5QW2vS2+vydtvi9ehkFUBW9fFQ27XMOqXKpAkTKpnTkJgJ4ZSmbIrVE7Faz3U\nM+5LtLWZjI+LfQMxCa2sKOULdTBY6U1Kp6uzvdJpQahAVPJ2VlOfmbEy/NaCJH+1IkfOLL96IT+7\nirmeYV9CEk35m125IjYmFckLFzRKJbHuWsfQDk2rDF3K5ddSqAAOH9Z54QVvuZRJT4/ZVPimpUVs\nM5NRyOWq2hGuDVXF7O6m1N3NTPBeXpvwEYkIktvTY/C7vx7j7ulp7nGoW8rMDOb8PHPFYplwXUoW\nuZItMFUqMKcWGC8WSWQyjI2NMTY2VnPzmqbR399fJljDw8MMDg4yPDzMwMAAg4ODtLa28vrrGmfP\navzarxVqkk7Z/UkQqsrECzuWl5VyaBcqr1PvFkiFCkS7oh07bt5YXLy38J4s7Hn8uIZpigrLzsnH\nCalQlS8sxSLayZN4XnkFz2uvMXRllpYVRdz1dWno99yD/uCDvFJ4hJevDvOhDxVpv6vyvjedFtlT\nwaBJKCTuAmdnlfK2nNl0EtGoIFSLi6rNlF69rMxiqyRUYrn6Ib/KWlp2WISq+rPeXkEIfD674mCW\nJy9J+GSJA7+/WiWp18fN+rz6M/ukuN5v6IR9/bXUkT17Spw7p7Fvn/jdpMIjFTQZ1pTepHS6OtvL\nXmX95EkPfX0Wky2VrM+dxv56Y63lC2sky88+fvt31oO9FpVhiLpcAI88ovPDH3rLf68X7pPw+czy\n+OR5tJaHCuC++0ocOFDi5EmNsTGNQ4eaS0QRle0N5uZUYjGFwcHqMSeT8N3v+jh0qMRdd9X2DMkw\n2OCgwdtva8LP2NJC6bZ9XPLup+d+o/IGJ58nOjfH+6anuXd6mjM/nad4dYbW5DQ7/VOE1BwrpVKZ\ncI0XBMmaKBS4XiwyruvM5PNMTk4yOTlZ08cF0NLSQiAwRCQyxM9+1s+99wqiNTg4WCZdqVQbsH7I\n78QJcW287bYSY2MaS0vvvnpbToWKKt3RhYt3Bu85QlUowOnTYlY5eHD9C3RHh0kwF6fn9VcJTLyA\n59ibKDbjTDbQzvnuh4h8/Ai3P3FPWUrQXvHA1dqyut0A3tNjEotpTE2pRKPiH7/exUvWffr2t33l\nekO1Db3i2a4cyAl/dlZl377KSdw01zel25/t6OsTNZSkkgeVlc/lZC7DQ7XUJCepcZKHysKeVK1n\noyG/elXYJW67zeBP/sQygTnN4BbJEX/Xaj8jw7kAZ89qPP54sfxbzc+LMGFnp7muWiIJs3MMUEmo\nTLN+yM9+PBsP+VkK1fS0qFnU3m5y++0lfvITb1npbJRQeb3WBC5/z127SuzeLZoc10MwCEeOlDhy\nZHOTYkeHydycuDEaHKxe1/nzoojvSy8p3HlnqaYSJglVT4/J1avi2ORyQm0cHfURCok+k2XC5vdj\nbNsG27ZRAp6b97O8U6zj4L1FPnrfPN7pafbOzrJvagp1Zqb8UGIxAPKGwUSxyPV8gbFkkRkzz5RR\nZKJUYqJUYjKbJZlMkkyeZ2HhPFevwk9/Wj32UKidcHiQV17pZ2hogImJYbq7Bxge7iabHWJ8fBut\nra0sLIiT6vBhnZkZ4aVaWRG//dmzGm+9pfGrv1pbBbsVUChY1zKobKjtwsU7jfccoTp3TrSWGRgw\n6mbtYZqoly7hOXqU0Kuv8u9feBtDN1G7TRQPGDt3oj/4IPqDD/Kj83fx9iUfn3msAGGLVMiJsFYW\nmFS7OjpMBgcNTp7UmJy0iE49y8RjjxXRdbEPUFu1AOEZuXpVJRq1xrNvn8GxY2LiePRRvWLCSKWE\nciXKHlSvTxiZlZqhnXAYfud38hUER1Y+txvTZRHLWhXBnVlgzvYwcnIPBMwyidiqkF89dcQOZ1hV\nkiD5G585ozE+rtLXZ7B/v9i/mRkrq65QEL+Z7P0mw33rqVP2bdciVIpi1ZiyV0mvleUn0YxCJf1T\nu3aV0DTo7zfKpvpGCZX9vJLnUWsr/Pqv35gydp2dUmmuPcFKT9vKisLcnFKz4bX0Lba0iN6fi4sK\niYRSDodmMgrf+pafT36yUD4PJPL5yol+fMKD+dFOSp2dcNdd1QPK51FnZ1FmZhiansZ/co7gq3M8\nlptmX2QKNSfYqWmaXF0yuJouMG0UmS4VWPEXmFJhwjSZzOeZSqfJZOJkMnEWFs5UbOapp6zXXm+E\nlpYBOjsHGB/vZ3l5iFJpkKee6uXee3t57rlhstleTp3y8PDD70zZmvl50Sfx4Yf1hv43nVhcFB5T\nGZZdXFTdJtAubhjeU4TKNEW4D+DQIcddajqN5623yqUNlMXF8keqz8fV3oPkPv8AXf/LYcz+/vJn\n8aPiEMqeYRJysq2VBSYN4O3tJkND4vQ7MAUAABmzSURBVMI7NaWWw3H1CFUoBJ/5jGhu+9JLHnbv\nrn3X/vjjOvfeWypPIiCyycJhk+VlhZkZhYEB6zM5mTjLIEisFfIDKrYDTmO6+GytJsBOEletsIhQ\nkz2BwE66mg35KUr9Y125fef+ib/leM6fFwdIVWH79hyhkKVQPfCAziuveDhxoppQ9fevT6gOHNBJ\npeDee2v/1h6P8MXl8/VDfpUteTaS5Qevv+4phxR37RLjHRqyCFWjhS3FuSPC0DcjfCQV1Foma9O0\nWk4BjI1p9PVVEwapUDkJlTy3h4cNJiZUvv99H1BJqhYXxXc7O4XRfnFReO/qVlXw+zG2b4ft2ykB\nr4W8nAiK8+xTnyxw17Y4yvQ0xtQsZ74ZI7g8w73mNPfNzTKkzdDit4iqaZicmykxXSqSay0wVSxy\nLqkyrqikIzqX4nkW8ivkiymWlsZYWhrj4kVrKM88Y71WFJWvfKWbnTt76e3tpa+vj76+vgpj/eDg\nYLn24Ebx3HNerl5V8fvhoYc2TtpkuG94WJyj6bT4jRol/i5cbAbvakJVLArJvVH5eWJCZX5eJRQy\n2Xebjnr5Cp4338Tz+utop05VdJk1OzrQjxxBP3KEl5cP8/qZVj54qEinrXSCvWSCk1Ct1ZpE3iW3\nt5u0t5tlc/MPfyhu3et5qCS2bTP4zd+sf2evadUkR1Xh9ttLHDvm4cIFjYEB62K1XsVuSagaTTZy\nlk4wzbWbADsVqlq+sEcecdZJaj7kFw4LIuCsyF4P1SE/8fy+95VIp0U5ifFxjYUFhStXNHbsKJFM\nKvj98OCDOm+9JcJJMzMK/f3mhghVa2t1jSg7enoMpqZUrl5V1wj5Wa8bVaikIV+a0qNRs/zbyZsA\n+X4jcFZFv9Go8kLasLysVCjJY2NCxXXC3q5KEsm5OXFN8XjgN36jwNGjHl580cPTT/toackzNCSW\nkxN9X59BS4vCtWsqExMqt9/eWAaaJG0Abx7zcODOKEo0ytvqAY7e7qOvz6DtiM5TT/kY6NN54tNz\nQuGanUUfn2HmqSU6sjPc2z+NOjvL/JSOUYK2iMmyruBpH8TTrjO1Wml+0jS5WPIxllaIeYosmVmm\nVtIk8iskk3OcOjW35ng7Ozvp6ekpP7q7uyv+lu91dXWhrZ6Uum5dJ06e1HjwQX3DypIM8XV3m2Sz\n4rq6sOASKhc3Bu9qQvXUUz6uX1f53d/NV9SAqofTP19i3+UTPOw5StsX3kBZWrI+VFVKBw6gHz6M\n/sADGHv2lG+lW9/U4Iy8GFuEKpm0SiY4vTBrtSaR0n97u4GiwI4dBufOaWVVw0nOtgr791uE6vHH\nrYuVVbG7tgqyUULlLJ2wsCA8OC0tZk2PllOhakRxkqRGUTaYtYX4WX/v9/INKyV2hUr0pROv29pM\nPvEJYSY6dszkmWe8jI2pZQWrt9fA64U77yzxxhsejh718PGPF4nFRIsfSVo2g337SkxNqbz9tlbR\nGscO0cjaJJ2ubcKvhZ07Df7wD3OUSgqaJpIn5H4PDBjlUGPjHiqZcNHY9rcaazVJlgrt7t0G09NC\nPYrFlIqbEnupEqlQgQj3giCZHo9QVZJJhRMnNJ580sdv/VaB9naznHnW3W3Q0bExQrWyohCPK6uF\nXk1mZ1WmphSGhsyyOrp/f4ndu8X5Nj3rYcXbSeuBTjhwgMVFhefm/HR0mNz27/NgGDz5txkK1+e4\ns3Oa+Ll5bm+bYV90hv1zc9wxP4+SSlHIw1JewesL4vW2klGgiMliqUgqUGSp1cOUx8dVXWVe05nI\nZphMJJhcWiqXizh//vya+6aqapl8tbT0kEj0EQ73EAx2kEq1sGdPlPb29vKjra2NlpaWurW7JHHt\n7jbIZEQyxeKiwp49NRd34WJL8a4lVEtLSrmB7blzWpWCAaAsL6OdOoV24gTGq8d57OQEAD3dJooG\nZmcn+n33ifpQ991Xt9NpPf+FbApci8zZK2nbY/i1VK2PfrTIgQMlPB4x8WzFRFsLg4NiIkgklPIF\nOZEQYRCfj7qesrXKJtSCVI+kumEP99W6Dnq9Vnsbn6/xMJzPJ9SCZvwRG/Fn2BWqen6tvXtLPPOM\nl2vXtPL5ID1S99+v89Zbgsj29xuYprjgbwW52LfP4Oc/h0uXNAyj0mdmxxe/mEfXG1eoQCq/1fsb\nCMA995SIx5WGbmSguvbUjYbPR/ncf/NNjfvvt4znMtw3PFwiFFI5fVpkFR4+rJe9cYoivHA+nyCl\nklDJ8L1UdxUFPvKRYtlb9ZOfePnCFwrlib6ryyp+Oz6uYe/DWQ/y/2fbthJdXSavvurh9dc9pNMl\nLl+2CJXXK3xub7+t8fbbYh/BKnlRThxRVejsYC7TRSJ4B9k7FQY+VSR7p+2GKp0mc2WeH3x1hc7i\nLF36LObsAjtDs4SuLTBYnKfbUyAWU9B1k7Y2lUAkApEIpf5+5nWdyUyRC0kfM34/Zr/KHCZzpRJz\nuRzz6TTziQSx5WUWFhZYWFgAzlbs9wsv1D4emqaVCVY0Gq0gW2Nj3WhaB319EQqFTqanuzh9Osre\nvRGi0eiW1PRy4aIe3rVnl8zUAxgbU3nkYRNlZgbt7Fk8p0+jnTqFOj5eXiaRUCh6guTvuJv2z9+L\nft99GDt2NORWrFXcs1CAF18Uh69WtqDXKy6+hYIgFlJFSaXEe6GQVWDP7xd3x+80FEWE/V5/3cP5\n8xpDQzoTE+I4Dg/Xr9gtfTfrhSIl5L5KxUSGFOv1rBPNeM1y8cZG4PXCE0/k6/q6thKhkGX+rhde\nbG0VitTcnMrJk+JASkLV2gqHDukcPerh+ecFK12v/lSjiEbNcgNnqFanJPz+xtWpRvDRj9YpaFYH\nkkQ0eg69Ezh8WOff/s3Lz3/uJRZT+chHimiapVANDRl0dpqcPi2y2U6c0FhZUdi92+Cxx8T+SgLv\n9I7Z1V1VhU9/usCXvxzg+nWVhQWlHIrq6TEIhcRNw8LCOj6qVdhvSG67rcTRox7GxgTpA/G/K+8F\n9+0ThOrUKQ+HDgnSKAt12rMp7a19oMb5GA4TvHMnMzsDXF91F2j74I/+KMc/fDlAMW+wtyvG8tuL\nRDIL7AjO8v59sygLC6iLi/TOL+A5H2NYK4Bu0JYsEZDnpjwZOzoomiYLpRKzgQBvxUNc0zWMbri4\nqLJslgj35lku5IilMiQySVYSCVKpFIuLiyzafK5OPPts5d9/9mfiuaWlhba2tvJD9ma1v2d/v729\nne7ublpbW29IRXsX7268KwmVYcClo8tsn7pE79IFeubP4f/eGXzp5coF/X5K+/eTvfNe/vnCA0y1\n3cG/+70ShZ6NXdRbW0XxQtEgVxCGo0c9pNMiW9CZ0SMRCpkUCsKfIZWNteo93Qjs3y8I1ZkzHh58\nUK+4+60HeVO3UYWqUBC/1Vr+Kes7Iq1+I34op0/snYKqCkUslVLWDC/u3SsIlZyk7IrfkSM6J09a\nYbm6GaZNYN8+O6G6Nb0iVjHPmzeG++4rEQqZ/PjHPk6eFG2mPvGJIgsLIgTb12dimkL5lGU+QLRi\n2blTHF9p8LcTKr+/+vcMBuHOO3WOHxeeqkxGhOxaWgQ5377d4PJllRdf9PKxj9Unp6ZZSahaW4V3\n78QJjYEBgz17DO6807qhu+02g9ZWk4UFhVOnNFpaRCFWZ6NgZ6eBWjYDWb9LnlsDAwbBIOzeXeL8\neY2xWDf+wW7ixn6uFGHPr1nWi2vXVP7lW14ChQSR9Dw7I/N87OAMyuIi6tISysICSiyGJxZjYHmZ\nvoLOQDqJAvQUTZZNhXwOvNPCW2WaIaJtQQI7dpCPRlkKhVgKBIh5vSxpGnFFYTxh8sYFg6IvT8dA\nilgixdtvJ8jl4sASy8vLqyUmkkxMTKx1qlTB5/MRjUYJBoMEg0FCoVD5WddDJJNhtm0L0NcXIBQK\nlT93Llvv/UAg4BK2XwLc+oQqnUYdH0cbH0e9fh31yhXypy7zv15dQvOIC3UuC8UWE+9glNL+/ZTu\nvhv97rvJ79jLbMzPyZMaE/MaO3ca9PRsPHNEUYTfaX5eZWlJ1FZ6/XVx6D74wWJdkUtm1V2/rtLZ\nKQiLDBs2GirZavT1mezZU+LSJY1f/MK7riEdrPBlrdT9WrArVPPzCrmcuKCvRSJlqYWNZuzdKMg0\n7LVKNOzZUypXRw8EKvc3GIQHHijx/PPi80ZKJjSK226z1tuownejIYlUo6T8ncIddxi0t+f5n//T\nx8WLGk89Jf4fZT01gEceKXLpksY99+hcv65x8qTGK6+IDyWhsjfR3ratVNOPd/BgiePHPWUlqavL\nCnk/9liRa9f8nDghCsju3ClKnczNKdxzT6n8P7S0pJBKCeW2q0ts+yMfKfKhDxVrhow9HrHuH/zA\nxwsveMrfufdevWKMduI9MFA/bN7ZKWrfgdUm6bbbSmXv1ic/WeDiRY3Tp8Vxevxx0VT+pZdEu4d7\nHwvz1lt7eCO3lzsO1WkwXypx6egyLz65ws7WRX7l3jmS5+OMvbxMKLtEKLdEKBvDTC/R688QyGQY\nAAYcq8mkBREOhiCqm6BpXI+0k4ruYMc9ETy9UVYCAeIeD3FVJQ6cmVBYKuoYgTxFb45kLs3y8jLx\n+DJXriRIJuNkswvk86nVsGR9HDu25sfrwkm2nH/LnrZerxefz4fH46l49nq9Fa+dD+eytT7XbGEK\n0zQrXsu/h4eHXfJXB00TqpGRkQ8D/2n1z/80Ojr68w2vpFRCicdRlpZQlpbEncvcnChuNztbUeDO\njmRcoeAN4z2wi/zevTw7dzfmgf18/o87mZtXOXVKY/oNlbkfqeV2LiAk/2bR0WEyPy+63r/0kkax\nKOR1mcVTC7t3iwysn/3My+Kiwv33l95x4/l6UBT40Id0rl3TyobaYHBt39Yjj+js3m2sSbrssDxU\nStlntpY6BdaEe6sqLJJMrpUN3ttr0tJikkwq9PZWT1KHDunlUPVWqmudnSbd3UKVaDJb/R2HDM3e\niBDteujvN/nMZ4p8+9u+svpjz1w8fLjE4cPiBqiry1xVs6wMPxBetEhE/Nb1zu2uLpMdO4xyVfke\nmzLe3W3yyCM6zz/v4V//1cvAgMGFC+LcOHbMw0c/WmT3bqPcBsbuP1yv3Mf+/QbHjolrz/i4KFXh\nLJ5aSajq/2/az1O5n3v3Gtx1V4mBAYPbbjMIhUSY9PRpkR05Pq4yOakSDJocOaKj6/DGGx6OHfPw\nqU/VUOM0jUuJPua6Brn9AzrFB3Win4TsYQ8ZU4z9pz/1Mn5d4YEDyzx29yInf77C/PllDu5YZCAU\npzQfZ+xoAjMQZ1tLHFOJo6TTtBZi+HMxzDfBHzHpAXpWN5tOw702JVJRINSqEe6PMJ2OstA2TL6n\nlZyvhVzYR99+FV+Pl5xXI6VppEyFn7/uZS6hQNBgKW1SLGXZtStJJJIhm82SyVjP8rV82D/L5/Pl\nZW51zMzM4N9K/8AvEZoiVCMjIyrwl8CHV9/66cjIyHOjo6NVV8vgn/85FHUKmRKZ5SJmKkOglMJf\nTKMVsigKGCXI5RVyeRFe8frMcu+vIl4yXcOke3eQ7t5OvH0nx9O3sxwe4A/+sEDQD1f/e4BiBl47\nWuSll7zlek6KIjwLg4NCldm5s3lVQCpKzzzjpVQSCsRjj61N0B58UMfnM3nuOS/Hj3s4ftw63O3t\nN69hZ3u7yQMP6Lz8shjPtm21zeISgQAbOnZSxZmcVMuG2Ho1s5zfuVUVFllgcy2FSlGEOf34cU/N\nkgg+nyiCqqpbX4vp9ttLLCx4btn0cKvC/c0dh8SuXQYf+ECRX/xCSGa1Cs6CIEGyvhRU1vQaGDC4\nfFlb0/948KDOtWvibqGrq3K5Bx7QGRtTmZlRSSQ0vF5LCf/Od3zlRA0QmcCNQlGEcv6P/ygmvQMH\nqlts2Yn3WoRKGtlV1VrO44FPftIiRoODQj1bXFR48klfmUDef38Jv1/U/HvzTeHbPHhQL9fAy2ZF\nvTbDsIzzO3ZY3SLs19cPf7jIP/yDn9fPt3N9KcrsvAqdcDwJh/frXDNV5g+rtLaa/PZv50lFgEKB\nq68neP77GQKFFY7si7G/bwklkSAxnuDC0RSB8Aq9wQQsr6AkE5grWbLJFTzGCgMqtLeZJOcVigXg\ntBiXzwfq6vx0MAeaB7o6TVJpheVcgMK1MNH+EO1DQQgFMXt7MUMhCAYp+kNokaD4OxDADAQgFEL3\neMgqChkgYxhkTJO0rpPVdTLFYpmEFQoFdF2nWCyWXxcKBYrFYtX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- "text": [ - "" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "lp = ARMA(-0.9)\n", - "wl = 65\n", - "\n", - "\n", - "fig, ax = plt.subplots(3, 1, figsize=(10,12))\n", - "\n", - "for i in range(3):\n", - " X = lp.simulation(ts_length=150)\n", - " ax[i].set_xlim(0, np.pi)\n", - "\n", - " x_sd, y_sd = lp.spectral_density(two_pi=False, res=180)\n", - " ax[i].semilogy(x_sd, y_sd, 'r-', lw=2, alpha=0.75, label='spectral density')\n", - "\n", - " x, y_smoothed = periodogram(X, window='hamming', window_len=wl)\n", - " ax[i].semilogy(x, y_smoothed, 'k-', lw=2, alpha=0.75, label='standard smoothed periodogram')\n", - "\n", - " x, y_ar = ar_periodogram(X, window='hamming', window_len=wl)\n", - " ax[i].semilogy(x, y_ar, 'b-', lw=2, alpha=0.75, label='AR smoothed periodogram')\n", - "\n", - " ax[i].legend(loc='upper left')\n", - "\n", - "\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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Gjx5NXFwct912W6PnrPbII4/UCVeNKSoqIj09nSlTpgDg6+vL2LFjOXjwIFOn\nTuXAgQOsX78esD1oOiQkxL5vY/dWo9Hg4OBAcXExGo2Gbt264eDgUOvc/fr1a3D2dJ1Ox7fffktq\naioODg7k5ubi4eEBwJAhQzh9+jRDhgzB1dXV/jkQQoiOoKKigoKCAn7++WcuXvyZ6OgubN0aQEmh\niv5iMsMd/06s7gg7lWAKn3sOq7Vl81w5OTnh5OREly5d6NKli/13R0dHHBwccHBwqPNar9djMBjQ\n6/X2xWAwoNPp0Ov1aLXaBpea34VX6vQBqzm1Tq3pm2++ISoqCldXV8D2yJSazYSqquLv788DDzzA\nn/70J9asWdOk4z700EPMnz+fqKgoHnnkEZYsWWIPE1ejKJcffKmqqj3caDSaWtsURam3D1FD/Yoa\nCl56vZ7ly5dz11131dmm0+lq7Xetnfyv3Lc6mDR2zuaeq759at6jK6+lpqvd2+eff57bb7+dQYMG\n8e677za5PCdPnuTRRx/loYceIiwsjF69etVbho4+eEIIcWOxWCxcvHiR/Pz8Wj+rl+pQVf0/1BZL\nNzIy7qWwcCgo+bhYovHQ/51sbRmKZwBU1T5VVx5069aNbt261Xrt7OxMt27d6Nq1K87OzrV+du3a\nFUdHR/v3XVuJjY1tcFunD1jt6cyZM3Tr1s0ergBuv/12vvnmG+6///5a733iiSeIiIhg//79RERc\nfU4Pq9VK165dmTVrFufPnyc2NrbBgKWqqv0LdtKkSXz44Yf85S9/obS0lE8//ZTnnnsOgMmTJ7Nq\n1Srmz5+Po6Mj69ats9fWVHNyciIvLw+whYSmfFhnzJjBW2+9xYQJE+jWrRuqqtrDRWRkJOvWreP+\n+++npKSEqKioJl1/teo+Uunp6Rw5coShQ4de9ZzN1b17d/z9/dmxYwfTpk0jOTmZgwcP2pvcJkyY\nwJdffsmSJUtITEwkLi7Ovm9j97ayspLXXnuN6OhoevXqdU1l2rNnD1OnTuXBBx/k1KlTpKamSpgS\nQlx3xcXF5OXlkZubS25uLnl5eeTk5JCXl0d+fn6dPqgN0el0WK3jyMj4f6hqd/q6lDKVd4nouhfX\n/kNwevRRenh50aNHD1xcXOytADeCNglYRqPxFUBvMpn+ty3O11a++uor7rzzzlrr7rzzTlavXm0P\nWNVf+l26dOGFF15g6dKl/PDDD/bOzg155plnOHLkCIqi4O7uzt///nf78aqPWfNn9ev//d//ZcWK\nFUydOhVTHSyQAAAgAElEQVSr1cr8+fPtnbQnTpzIqVOnmDFjhr0v0BNPPFHrvL/4xS9YvHgxX331\nFYMHD641pUJDAWbevHlkZ2cze/Zse6duk8lEt27duPPOO/n++++57bbb6N27N97e3tcUhAwGA3Pm\nzCE/P59XX32VblWPTm/snFcrb2Peffddli5dyptvvomiKKxdu5YePXoAsHTpUh555BEmT55MYGAg\ngYGB9v0au7cGg4E+ffrwi1/8AicnJ3Q6HSNHjuT555+/alnnzp3LggUL7H3sIiIiyM3NrfM+Gc0o\nhLgWVquVvLw8srOzycnJISsri+zsbPvvV+vKodVq6dmzJ7169bIvvXv3xs3NDTc3N3r27Ile35ON\nG3vzww8G/P1ghONJ/lj8J/o6/Izl1rmYf/c7cHRsoytue5q2+L9ho9GoBV4zmUxPNva+qKgodeTI\nkXXWZ2Zm4uXldb2KJzqo2bNn8+c//5lhw4a1d1FaJCMjgyVLlvCPf/wDFxcXMjMziYyM5Pjx43Tt\n2rW9i9chyb95IVpOURTy8vLIzMy0L1lZWWRkZJCbm9tofydHR0fc3d3p06cP7u7u9tfVv/fs2bPR\nioIDB3S8+64TFy9qcNRb+U2Pz5iT/yFaLZT/6ldUzp0LN8D/GMbGxjJp0qR6L6RNarBMJpNiNBrb\n4lRCdDiurq44ODhgNBrtHSnfe+89CVdCiFZRWlpKRkYG6enptZasrCwsFkuD+/Xq1Yu+ffvi6elp\n/+nh4YGHhwcuLi7Nqhm/cEHDe+85cuCALV6E+BXyVOmz+OYfQ+3mTNnSpVhHjWr2tXYmzQpYRqMx\nEngN2GMymZbVWD8ZeLbq12dNJtOulhdR3Ky+/vrr9i5Cq3B2drbPeSWEEM1VUlJCampqrSU9PZ0L\nFy40uE/Pnj3x8vKqs3h4eODYis1zigLffmvg448dKC3V4OQEv55wmnn7nkJXWozi60vZypWo3t6t\nds6Orrk1WI7AKmBc9YqqZsDngeq57b8FdhmNRk31e41G42STydSxpzIXQggh2lFlZSXp6ekkJSXZ\ng1RKSop9ANKV9Ho9Xl5e+Pr64uPjg4+PD97e3nh5ebVJTXlqqpY1axw5dcrWZDj2lkoW99qAz7fr\nQVWxjBmD+cknwdn5upelI2lWwDKZTDuNRuPEK1YHA+dMJlMZgNFoPG80GoNNJlM8sLyF5RRCCCFu\nOAUFBSQlJZGUlERKSgpJSUmkpaXV2z/KYDDg4+ODv78//v7++Pj44Ovri4eHR5tPTwBQWQlffOHA\nF184YLWCq6vKo/fmcMcPf0H/0ynQaqm47z4qjEZoh/K1t9bsg+UGFBiNxjeqfr8E9AKa/zRdIYQQ\n4gagqioXL14kISGB8+fPk5iYSEJCAhcvXqzzXo1Gg6enJwEBAQQEBODv74+fnx+enp5XHYHeFlQV\nYmJ0fPihI1lZtuB0552VPDTkR3qvewNNURGqmxvmpUuxhoa2c2nbT2sGrAuAK/AYoAHWAPmtcWCd\nTkdpaal0ChbiBlf9JXTlTPdCdDaXLl3i7NmzxMfHc/78eRISEigoKKjzvi5duhAYGIi/vz+BgYH2\nQNWlS5d2KPXVpaRoef99R44dswU9X1+F3z5SwqjD/8Twuu0ZqtZRozA/8QRq1RQ3N6uWBKwrhxec\nBwbU+D3YZDIltOD4du7u7uTm5tb74RRC3DhUVaVHjx615jMToqMrLy/n/PnznDt3jnPnzhEfH09O\nTk6d9zk7O9O/f3/70q9fP7y8vNqlee9aFRbCxo2O/Oc/BhQFunVTue++CmaEJtJt9RtoExJAp6N8\nwQIq77nnpmwSvFJzRxE+BUwDPIxGo4vJZFpkMpmsRqPxeeC/VW97rpXKiEajoW/fvq11OCGEEKJZ\nVFUlOzubs2fP2pekpKQ6faYcHR0JCgpi4MCBBAUF0b9/f/tD2jsTiwW2bzfw2WcOlJRo0OlgxoxK\n7ptvptfuLTguXQ+Vlaju7pQtXYoyaFB7F7nDaJOJRpuqoYlGhRBCiPZQXl5OfHw8p0+f5ty5c5w9\ne7ZOa4pWq8XPz4/g4GAGDhxIcHAwfn5+HaK/VHNV97P65BNH0tNttVHDh1tZuLAcf0MGTm++ie7U\nKQAqJ0+m/OGHb7pRgtABJhoVQgghOoPCwkJOnz7N6dOnOXXqFPHx8XVqp1xcXBg0aBADBw60B6qO\n2meqOU6d0vLxx46cPm0LiF5eCg8+WM6YWyw4fPsfHD/8EMxmVFdXzI8/jnXMmHYuccckAUsIIcRN\n6+LFi5w4cYKTJ09y8uRJUlNTa23XaDQEBgYyePBgBg4cyKBBgzplU19TpKZqWb/egZgYWzTo0UPl\n3nsruPPOShwu5uD0/Bp0R44AYImMxLxoEbi4tGeROzQJWEIIIW4aFy5c4MSJExw/fpyTJ0+SkZFR\na7vBYCA4OJiQkBBCQkIYPHgwzjd409eFCxo2bHBg1y5bB3YnJ7j77grmzKnA2dGCYcsWHD/7DCoq\nUF1cKH/0USwTJrR3sTs8CVhCCCFuWBcuXOD48eMcP36cEydOkJWVVWu7k5MTgwcPJjQ0lCFDhhAU\nFHTTTBNSWAibNzvwzTcOVFaCTgfTplUyf34FPXuqaM+exWnNGrRJSYCt1qp84ULUnj3bueSdgwQs\nIYQQN4yCggKOHz9OXFwcJ06cqFND1aVLF0JCQggNDSU0NJT+/fuj199cX4WlpfDNNw78+98GSktt\nTZ3jx1u4//5yfHxUKCnB8b1PMWzfDqqK6u6O+dFHsY4e3c4l71xurk+VEEKIG0phYSEnT54kLi6O\nuLg40tLSam13cnJiyJAhhIaGEhYWRv/+/Tv16L6WqKiwTbmwaZMDhYW2YDV8uJUFC8oZMEABVUW/\nNxrHf/4TzYULoNNRMWcOFfPn29oNxTWRgCWEEKLTKCsr4+TJk/ZaqsTERGpON+To6MjgwYMJCwsj\nLCyMoKCgm66G6koWC0RFGfj8cwcuXLAFq0GDrDzwQAVhYbYRktrz53Fct84+9YJ14EDKH3sMJTCw\n3crd2d3cnzohhBAdmsVi4dy5cxw7doxjx45x9uzZWtMm6PV6Bg0axNChQwkLC2PAgAEYDIZ2LHHH\nYTbDrl0Gtmwx2J8ZGBiosGBBOaNHW9FoQHPpEg6fforhu+9szYE9elD+wANYJk+W2dhbSAKWEEKI\nDkNVVTIyMjhy5Ii92a+srMy+XavVMnDgQMLCwhg6dCiDBg3CSZqvaiko0LB9u4Ht2w32pkAvL4X7\n769g/HiLLTdZLBi2bcPh88/RlJSATkflzJmU33svyKOqWoUELCGEEO2qsrKS48ePc/DgQQ4ePEh+\nfn6t7T4+PgwbNoxhw4YRFhZ2w0+b0Fzp6Rq2bLFNt1BZaVsXHKxwzz0VRERY0Omw9bP6cR8O69ej\nzcwEwDpiBOULF6L4+rZf4W9AErCEEEK0ucLCQg4dOsTBgweJjY3FbDbbt/Xo0cMeqIYPH06fPn3a\nsaQdm6rCiRM6tmwxcPDg5a/0sWMtzJlTyZAhtqZAAN2JEzh89BG6c+cAULy8KH/wQdtM7DfgxKnt\nTQKWEEKINpGdnc2BAwc4cOAAZ86cQVEU+7bAwEDGjBnDmDFj6N+/P1rp/9OoigrYs0fP1q0OJCXZ\n7pXBAHfcUcmcORW26RaqaJOTcfjkE/SHDgGgurpSMX8+lVOnwk0+AOB6kjsrhBDiulBVlZSUFA4c\nOMD+/ftJqpqwEkCn0zF8+HB7qHJ3d2/HknYeFy9q2LHDwH/+Y+DSJVutk6uryl13VTJ9eiWurpeD\nlSYzEweTCcPu3baqLicnKubOpWLOHLiBnp3YUUnAEkII0WoUReHs2bPExMSwf//+WjOnOzk5MXr0\naCIiIhg5cqT0pboG8fFavvnGgb179VQPouzXT2HWrApuvdVCzYGTmqwsHL74whasrFZbB/Zp06gw\nGlFdXdvnAm5CErCEEEK0SEVFBXFxccTExBATE0NBQYF9m4uLC2PGjCEiIoJhw4bdNI+haQ0lJbBn\nj4HvvjOQmGhrBtRqISLCwqxZtftXAWhycmw1Vrt2XQ5WkydT8YtfoHp6ttNV3LwkYAkhhLhmRUVF\nHD58mAMHDtTppN6nTx/Cw8OJiIhg8ODBN+3M6c2hqnDmjJbvvjMQHW2gvNy2vnt3lUmTKpkxo5K+\nfdVa+2iysnDYvBnDzp22YKXVUnnHHbYaKy+vdrgKARKwhBBCNFFJSQkHDhxg7969HDt2rNaEn4GB\ngYwdO5bw8HACAwPRyKi0a1JYCN9/b6utSk293ME/LMzK1KmVRERYuLLyT5uUhMOXX6KPjgZFAa0W\ny223UW40ovr4tPEViCtJwBJCCNGgsrIyDh48SHR0NIcPH8ZisQC2TuphYWGEh4czZswY+vbt284l\n7XwsFoiN1REVZZtioTqvurqq3HFHJVOmVOLtrdbZT3vqFA6bNtlHBaLTUTlpEhXz5kmw6kAkYAkh\nhKjl0qVLHDt2jH379nHo0CEqKioA0Gg0hIWFERkZSUREBD169GjnknZOKSlaoqL0fP+9gYICW02f\nVgsjR9pqq265pXandQAUBd1PP+Hw1VfoTp60rXNwoPLOO6mYMwdVRmF2OBKwhBDiJldRUcHp06c5\ncuQIx44d4/z587W2h4SEMH78eMaPH4+bm1s7lbJzKyjQsHevnt27DSQkXG4C9PFRmDSpkttus9Cr\nV93aKsxmDLt2Yfj6a/vM66qzM5XTp1M5ezaqhNwOSwKWEELcZBRFITk5mWPHjnH06FFOnjxpr6UC\nMBgMhISEMGrUKMaPHy8zqTdTSQns36/nhx8MxMXpqJ5X1dlZJTLSwqRJlQwYoNQ7ibrm4kUM27Zh\n+M9/0BQVAaD26UPFrFlUTpkCMsVFhycBSwghbnCqqpKWlsbx48eJi4vjxIkTFFV9aVcLDAxk+PDh\nDB8+nJCQEBwdHduptJ1beTkcOqTnhx/0HDqktz8TUKeDW26xMHGihfDwuh3WAVBVtKdP47Bjh63j\nelWnLOvAgVTOmYMlIsJ2INEpSMASQogbkKqqxMTEEB0dTVxcXK25qcA2lcLQoUPtz/tzlQkom628\nHI4c0fHjj7bO6mVltvUaDYSGWpk40UJERCUuLg0coLQUw549GLZvR5uSYlun1WKJiKBizhyUkJA2\nuQ7RuiRgCSHEDURVVX766Sc2btxIYmKifb2rqytDhw5l6NChhIWF4eHhIVMptIDZDEeO6ImO1vPT\nT3pqTANGUJDCrbdWEhnZQL+qKtrUVAzbt9tmXK9KZaqrK5VTplB5553Scb2Tk4AlhBA3AFVVOXLk\nCBs3buTcuXMA9OzZkzlz5nDLLbfg4+MjgaqFzGZb89+PP9qa/6onAQXo319h/HjbfFX1Ta1gV1mJ\nPiYGw/bt6E6csK+2hoRQOX26rRmwzhBC0RlJwBJCiE4uLi6OjRs3curUKcBWWzV37lymTZsmfala\nqKzMFqqio/UcPqynxlgAgoMVxo2rZNw4C56ejYQqQJuSgj4qCsPu3WguXbKtdHKi8vbbqZw2DSUg\n4PpdhGgXErCEEKITKigoICYmhu+//56TVfMiubi4cM899zBjxgycnJzauYSdV1kZ/PSTrabqylA1\ncKCVceMsjBtnqfPImjqKizH88AOGqCi08fH21YqfH5XTplF5220yGvAGJgFLCCE6iaysLA4cOEBM\nTAynT59GVW1f8M7Oztx9993MnDkTZ/nCbpbcXA2HD+s5dEjH0aOXR/8BDBp0OVS5u18lVCkKurg4\nDFFR6Pfto/pAqrMzlshIKidPRgkOpt65GcQNRQKWEEJ0UIqikJiYyMGDBzlw4ADJycn2bXq9nuHD\nhxMeHs64cePo1q1b+xW0E7Ja4exZLT/9ZOtPlZKirbV98ODLoapPn6uEKkCTnm4bCbh7N5rc3KqV\nGqzDhlE5eTKW8HCQ5tqbigQsIYToQIqLizl69CiHDx/m8OHDtaZX6NKlC6NHjyY8PJyRI0dKbdU1\n+vlnDUeO6IiN1RMbq6O4+HItkpMTDB9u4ZZbLIwcaW109F81zYUL6H/4AcMPP6CtMfu96u5O5eTJ\nVN5xh4wEvIlJwBJCiHakqirJycn2QHXmzBms1U/9BXr16sXo0aMZO3Ysw4YNwyAjzJrMYoEzZ3TE\nxtpCVWJi7VoqLy+F0aOtjB5tYcgQa9MG7xUVod+/H8OePbZRgFXNtGrXrljGjcNy221YQ0NtDxcU\nNzUJWEII0cYKCgo4cuQIR48e5ciRI7VqqXQ6HaGhoYwaNYpRo0bh7+8v0ys0kapCRoaGuDg9R4/q\nOHbs8qSfAA4OMHSohREjrIwceZXpFGoym9EfOoR+zx70hw/bkhuAwYBl9Ggst92GZdQo6p+eXdys\nJGAJIcR1VvNhykeOHCEpKanWdjc3N0aOHMmoUaMYNmyY9Ke6BhcuaDh2TEdcnC1QXbhQO4z6+iqM\nGmULVUOGWJuegUpL0f/0E/p9+2yhqnoooVZr61d16622OavkbyUaIAFLCCFamaqqZGZmEhsby5Ej\nRzh+/DjlNWaldHBwIDQ0lOHDhzNy5Eh8fX2llqqJCgo0nDih48QJW6hKT6/dFNejh0pYmJVhw6yM\nGNGEUX81FRejP3gQ/f796GNjqTmU0DpwIJYJE7BERqK6ubXW5YgbmAQsIYRoBWVlZcTFxREbG0ts\nbCw5OTm1tgcGBjJixAhGjBjB4MGDcZDmpCa5cOFyoDp5sm6gcnKC0FALQ4faQpW/v3JN3Z80ly6h\nO3gQw7596I4etT9gGY0Ga0iIrV9VRARqnz6teFXiZiABSwghWkBVVXbu3MlHH31EUVGRfX337t3t\nNVQjRozATWo9rkpVIStLw8mTOk6f1nHqlI7MzNppydHRNi9VaKiVsDALAwYo6K/xm0yTno4+Jgb9\nTz+hO3MGFMW2QavFGhaGZfx4LOHhUlMlWkQClhBCNFN6ejpr167l+PHjAAQFBTFmzBhGjBhBcHAw\nWhlJ1iirFZKStJw6pbOHqoKC2k2lTk62OanCwmwj/YKClGt/VJ+ioD1zxhaqDh5Em5FxeZtOh3XE\nCFtN1dixqK6uLb8wIZCAJYQQ16yyspLNmzdjMpmorKzExcWFhQsXMnHiROlL1YjiYjh71hakzpzR\nce6cDrO59nt69FAZPNhKSIiVwYNtgUqna97J9MeOofvpJ/SHDqEpLLRvUrt1wzp6NJYxY7CMGCGP\nqxHXhQQsIYS4BqdOneKdd94hLS0NgEmTJvHggw/i4uLSziXrWFQVsrM1nDplC1OnT+tIS9NWTxtl\n5+mpEBJyOVB5e6vNe4qMoqBNTEQfG4suNhbd2bOX+1MBiqcnlrFjsY4Zg3XwYJqX2oRoOglYQghx\nFcXFxSQnJ7Nnzx6+/fZbALy8vHjssccYOnRoO5euY6ieg+rkSb29U/qVUybo9RAcbGXQIFuYGjRI\nwdX1Gkb5XUFz6RK6I0dsoerIETSXLl3eqNNhDQ3FMmoU1jFjUHx85Pl/ok1JwBJCiCqqqpKXl0dS\nUhJJSUkkJiaSmJhIbvWz5bBNBDpv3jyMRuNNPRLQbIbERC2JiTp7H6qff64dYLp3V+01U9XNfS2a\niN5qRXv2LPqqUKVNSKBmlZjau7ctUI0ciWXoUGn6E+1KApYQ4qajqioXL14kNTWVlJQU0tLS7EtJ\nSUmd9xsMBgICAujXrx8zZ87E39+/HUrdfoqKIClJR0KClqQkHefPa8nIqNvc16OHLVCFhdlG+fn5\nXduUCXWoKtq0NHTHjqGLi0N34gSamn8fvd5WSzVyJNZRo6SWSnQoErCEEDeFvLw8oqOjiYmJISUl\npd4gBeDi4kJgYCD9+vWjX79+BAYG4u3tje4m6bNTVATnz9tCVHy8jvPndeTk1A0tOp1tlvT+/a0E\nByuEhlrx9VVanG802dnojh+3dVCPi0NT4zFCYOtLZR01yhaqQkNtwwyF6IAkYAkhblg///wzP/74\nI9HR0Zw6darWNhcXF3x9ffH19cXPz8++9OjR46YYCaiqcPGihqQkLcnJWnuoys6uW+Xk4ACBgVb6\n9VOqFtuEnq3RQqq5eBHd8ePojh1DHxeHpkZzLIDq6op12DAsQ4diDQtD9fBo+UmFaAPXPWAZjUYX\n4G9Vv75sMpnOX+9zCiFuXgUFBcTExLB3715OnDiBUjWJpMFgYMyYMURGRhISEnLTBCmwPfElPV1r\nD1OJiTqSk7UUFta9fgcH6NfPSv/+ttqpoCAFX99mTpVQD01+PrqTJ9GdOoXuxAm0VaMxq6nOzljD\nwrAOHYp16FAUX19p9hOdUlvUYN0NvAXEA88A/9cG5xRC3CTMZjMnTpwgLi6Oo0ePkpycbN+m0+ns\noeqWW26ha9eu7VfQNqCqkJenISVFS3Kyruqnrb9UjRkL7JydVQIDlaql9cMUqoomIwN9daA6ebJO\nDRWOjliHDMESFoZ12DCUfv1oWcctITqGtghY3lXnmQ50aYPzCSFuYIqiEB8fz9GjRzl27BinT5/G\nWiM9GAwGQkNDmTBhAuHh4XTv3r0dS3v9mM3Yg1R1zVRKipaSkrq1PRoNeHkpBATYwlRAgJXAQIU+\nfZo551RDrFa0iYmXa6hOn649dQKgdu2KMmiQLVQNGYISHEzLhhYK0TE1K2AZjcZI4DVgj8lkWlZj\n/WTg2apfnzWZTLuATOAYkAIsbVlxhRA3I0VROHXqFPv27WP//v1cuHDBvk2r1TJgwACGDh3K8OHD\nGTRo0A01fYKiQE6Oxl4jVR2msrPrjuIDcHFRCQhQ8Pe3BSl/fwU/P+X69AUvLER37pxtOXPG9ly/\nK6ZmV11dsYaEYB0yBGtICEpgoNRQiZtCc2uwHIFVwLjqFUajUQs8D0yuWvUtsAv4N/ASoAVeb3ZJ\nhRA3FYvFwvHjx9m3bx8xMTEU1BhN1rt3b2655RaGDx9OaGjoDVNLVVhIraa9lBQtqal1HycDl0fx\n2cKUrQO6v79Cz56tXCtVTVHQpqSgO3sW7dmztp/p6XXf5ulpC1RVi+rlJX2oxE2pWQHLZDLtNBqN\nE69YHQycM5lMZQBGo/G80WgMNplM8cBjLSynEOImUFFRwdGjR9m/fz8HDx6kqKjIvs3T05OIiAjG\njRtHcHBwp+2grqpQUKAhLU1LaqqWtLTLy6VL9V+Tm5tqr5EKCLCFKh+fFk7aeRWaS5fQnjljq506\nexbduXN1aqcwGLAGB2MdMMDW7DdwIGqvXtevUEJ0Iq3ZB8sNKDAajW9U/X4J6IWtc7sQQtSrtLSU\n2NhY9u3bx6FDhzDX+BL39fVl3LhxjBs3joCAgE4Vqqqb9tLStKSn116Ki+u/Dicn8Pe3TdBZHaT8\n/a1c98cclpSgO38ebXw8uoQEdPHxdTujA2rfvlgHDrQvSmCg9J8SogGtGbAuAK7Yaqs0wBogvxWP\nL4S4ARQWFpKWlkZqaiqxsbHExsZSWVlp396/f38iIiIIDw/Hz8+vHUvaNJWVkJFhC06pqZdDVEaG\nlhqXVYuzs61GysfHNmqveund+zo179VkNts6oleFKW1CAtqMjLrvc3S0105ZBw1CGTgQtWfP61w4\nIW4cLQlYV/5n4DwwoMbvwSaTKaEFxxdCdFLl5eXk5uaSlZVFeno66enpZGZmkp6eTmFhYa33ajQa\nQkJCCA8PJyIigr59+7ZTqRumqrYZzquDU3WgSkvTkpOjpWqqrTp69VLtIcrH53KgcnVtgyAFUFJi\n6zeVmIj2/Hl08fG2flNXFlivx9qvH0pQENb+/VEGDLA9duYmmb1eiOuhuaMInwKmAR5Go9HFZDIt\nMplMVqPR+Dzw36q3PddKZRRCdDDVz/LLysoiKyuL3NxcsrOz7aGq4IrHm9TUpUsXfH198fHxYcCA\nAYSHh+Pm5taGpW9YWRlkZWnJytKSmaklI0NjD1QNNetptbYpEKpDVM0w1WbTbqkqmosXbTVTSUlo\nz59Hm5yMNiur7nt1OpTAQKzBwSjBwbZA5e8vTX1CtDKNWt8433YSFRWljhw5sr2LIYSoUlBQQGpq\nqj1IZWZmkpWVRXZ2NuXl5Q3up9PpcHd3p2/fvnh7e9sDlbe3N25ubu3Wl6q6JionxzbNQXa2lsxM\njT1QFRQ0XC4nJ/DxUfD2VuyBytfX9rpNs4nVijYjA21iItqkJFvtVFISmitqBgHQ61H8/bEGBqL0\n62cLVQEB4OjYhgUW4sYVGxvLpEmT6v0PhzyLUAhBSUkJqamp9iU5OZnU1FQuXTFJZE0uLi54enri\n4eGBh4cH7u7ueHh40LdvX3r37o22neY6UhTIz7fVPGVna8nJsQWonBzb6/om4qym14Onp4Knpy04\neXurVT+v4/QHjdBcuoQ2JcW2JCejS05Gm5xMfZ271G7dbDVT/fujBASg9Otna+bTy3/mhWgP8i9P\niJuIoihkZmaSnJxMUlISKSkpJCcnk1vPiDGwNef5+fnh7e2Np6cnnp6eeHl54eHhQbdu3dq49Jcp\nCly4oCEnx1YDZWvOs9VCZWc33LkcbDVRHh4KffvaQpSXl4qnp4KHh62TebvkwpIStKmp6FJT0aam\n2gJVaiqaBppa1b59L9dKBQaiBAai9ukj800J0YFIwBLiBqOqKpcuXSI7O5ucnBxycnLIysoiJSWF\nlJSUWiP2qhkMBnx9ffH398fPz8/+s0+fPu3WnFdeDpmZ2qo+URpycy/XSOXmarFYGt7X1dVW82QL\nTioeHkrVouLi0vY1UXbl5WjT0+0BSpuaii4lBU1eXv3v79IFq78/ip+fbenXD2tAALRjuBVCNI0E\nLCE6KVVVycnJ4fz58yQkJJCWlmYPVY31j+rTpw8BAQEEBAQQGBhIQEAAnp6e6NphxNiVo/NqzhmV\nk1P/o2CqubqqVbVQalVNlGJv3nN2brtrqFdRkS1Ipafb+ktVv87OrjuCD8BgQPH1tfWX8vNDqQpV\nUlj3aUAAACAASURBVCslROclAUuITsBisZCdnU1SUpI9UCUmJlJcXFzv+7t161anX5Svry8BAQFt\n3rRXVAS5uVpyc221T3l5WnJzbc17ubkaSkvrDxA6na0pz8vLVvPUt6+tWc/TU8Xd/To9W+9aKAqa\n/HxbcEpLqxWmGmraQ6ezBanqEOXvj9XXF9XTU6ZEEOIGIwFLiA5CURR+/vlnMjMzycjIqPUzOzsb\nq9VaZx9XV1f69+9P//79CQwMtIeptgxRJSXVAao6NF1uxsvNbbxTOdj6RHl7154nysfHVhPVIWYO\nKClBm5lpW7KyLgeqjAyoqKh/H0dHFB8f2+LtbQtVPj4oXl4yHYIQNwkJWEK0EUVRyM3NtS95eXnk\n5eXZX+fn59fbPwpsk3G6u7vj7+9vD1RBQUFtMuVBzQCVm6slL+9ykMrN1VBUdPUA5e5uq31yd1er\nXtt+ursrdO/eAVrBSksvB6jMTDRZWZdfNzKSUnV1vRykqkOUtzdq7960T295IURHIQFLiFakKAr5\n+flkZmba54yq/pmVlVVvLVRNLi4ueHt74+XlhZeXFz4+PvZRe47XYe6imvNCVTfZ5eXZQlR1mLpa\nDZTBQFXz3eXQVP3aw6ODBKj/z96dx0dRH/4ff80eyea+E+5DARVFLPoF9AuicihCEO3XLdajLWq1\n4q/VL1AB64G2nl8PPFBrrXig7aoUFaUqp2IFqqioIIdCQ4AQkhCSbLI5duf3x2SXhNzJkgR4Px+P\neezszM7MZz8M7JvPfOYzYLVE5eRYwWnvXitEVbdMNXhJDyAigkDXrgS6dbNeg4GqRw91NheRBilg\nibSAaZoUFRXVukMvOAVbphoLUcnJyXTp0oW0tDTS09NJS0urNe8Kc8ci04SiIoP9+w/1fQpewguG\nqhrPVq5XZKTVApWaeqgfVM2WqISEDrwrr6bKSoz9+7Ht24ctJwej+tWWm4uRk4PRQH81wOpk3qWL\nFaK6dcMMhqlu3TCTk9UaJSItpoAlchifz8fu3bvrhKfga2N36IHVLyrYAhUcNyo4fyQC1MGDBnv3\nWoNp5uTYyMuzQlRenhWqGhsTCiAqilrBKS3NCk5paZ3oEh5Yj4MpLMTIyTkUonJzrRC1bx9Gfn79\nd+gFRUQQyMg4FJxqtErpkp6IhJsClhy3qqqq2LNnD1lZWaExooKPhWnsEVIxMTGhx8AE79TLyMgg\nIyOD9PT0sIaoQMBqgcrLM8jPNygosFqfcnJsoUBVVtb4PmJiTNLSTFJTA6SlBS/dmdWBqhMFKL8f\nIz8f2/79VktUzdfcXGz79jXcqRzAZsNMS7NCVJcumBkZ1nxGBmaXLpiJiZ3ki4rI8UABS455wQcT\n79y5k507d4ZGL8/OzqaqntEq7XZ7qNUpeOkuGKTS09PDdodesP9TXp4tdAkv2PpUUGCQl2cjP9+g\niW5bxMSYdO16aDDNjIxDYSo1tR0fONwUr7f+8JSXZ13GKyhovAUKMOPi6gSn0Hxamu7QE5FOQwFL\njgl+v5/8/Hzy8vLIy8sL3aEXbJ0qLi6ud7uMjAx69+5dawTz7t274wzDD3VlpfU4l7y82p3Hg0Fq\n//6m+z8BxMWZJCebpKaaJCdbwSn4aJeuXTtJC5TXiy0/H6N6shUUWPM1QpTh9Ta+D8PATE4mkJZm\ntUQd/pqRQcePICoi0jwKWNLpBceHysvLIz8/n/3799cJUwcOHCDQSOtHbGwsvXv3Do1gHgxU0a1s\n3qnZ+hQMT8HQFAxRBw4YjY5EDoeGMAi2NqWnm6SkWO9TUgIkJ5sdO6BmIIBx4IAVlgoKsOXl1Q5Q\n1cualRQjIgikp1thKTXVeq35PjVVLVAicsxQwJJOwTRNDhw4QHZ2Nrt37w697t69m7y8vCaHNwCr\nc3l6ejopKSmkpaWRmppKjx496NOnDykpKS0aL6qszApPeXlGKDgFX/Pzrdcm+rpjs0FKihm6Ay8Y\noIKX79LSrEe6dEjrk99vdRg/cMCaCguxHTiAUVAQClS2/Hxr+IJm1D0REVZISk7GTEkhkJJivaal\nYaamEkhPp3M0tYmItA8FLGk3Xq+3ziCb+/fvJycnh927d1PWSG/thIQEUlNTSU1NJSUlJTRfc1lz\nL+uZJhw4YJCTYw1VEOwDZYUpK0iVlDQdBKKiCN1pl5pqhkJT8DUlxWzfp5+YJpSWYhw4gK1meCoo\nOBSgqsOUcfAgTTavBXebkGBduqsOTTUDlJmSQiA52RoPSuFJRCREAUvCxuv11hnSIDi/f/9+vE30\nwYmNjaVHjx5079499Nq9e3cyMjKIiIhodjmCl+/y862wtG+fdbfdvn2HhjJo7GY0sK5UpaYGg5MV\nlmreiZea2k4PFK6sxCgqskJR8PXgwUNTUVFo3nbgAE02qwUZBmZiojUlJRFISgrNh8JUdWuULtuJ\niLScApY0i2maHDx4kH379pGXl1fnUS+5ublNBqjIyEjS09NJTU0N3ZGXmppKRkYG3bp1IyEhocnL\neOXlUFBgcOCAwYED1t12BQVGKEzl51vzTQWo+HiTjAxrqIK0tENBKtgSFR9/hAbPrKqqFYrqnWoG\nqqY6hh8uIoJAcrIVjhISDgWmmgEqKQkzIQEc+usvInKk6F9YCY1OnpubW6vzeH5+fmhq7Dl5QcEA\nFRwP6vDxoeLi4hoMUBUVsG+fUR2YDgWnmvMHDjT92Jag6GiTlBRrysgIVA9hcGgogza3PgUC4PVi\nFBfXnUpKrHBUz/smB606nN1uDU2QkGBNiYmH5hMSCCQkYMbHW1NysnXdUpfqREQ6nALWcaCqqip0\n993hDxgOzlc01eSDdQkv+FiX4PhQNV/j4+PrBCif79BI45s2WYEpP98KS/n5h+abemBwkN0Oyckm\nSUkBkpJMkpKsIQxSUoIdya2hDJoVoEwTyssxvF6rpaikBKO0NPTeKCmxQlFxsRWQqt8HQ1NTYzbV\ny2Y7FJji463AFHytJzgRG6sRxkVEjkIKWEcxn89HUVERRUVFHDx4MPRaUFDA/v37aw1h0NjI5GCN\nTh688+7wzuTB1+AI5cHn21mX4wx+/NHG+vVWK1NRkUFhocHBgwaFhc0b5wms4JSUdGhogkPTofdJ\nSYeN+WSa4PNZoai01ApI+7wYP3oPhaaaYameZc26Q64BZnQ0xMVZgSk4xcZagSk4H1weH48ZG2uN\n46TAJCJyzFPA6kRM06SwsJDdu3dz4MCBUHgqKiqiuLi41vuioqJmtToB2Gw2kpOTQwGqvocMx8TE\n4PNZd9fVDEibNxu1lgVbneoZAL1eDgckJloPBE5KsjqLJ8dVkBzjIzXaS4rLS3JkCQlGEXZfKUZZ\nGZSVWaHpQBnsqZ6vuby01Jr3+VrXilST04kZE2OFoZgYiImx3genmuEpPv5QoIqNVR8mERFpkH4h\n2pnf76e4uJiCggL27NkTGuspOJWWljZ7X06nk/j4+NCUkJBAfHx8KEylpKQRHZ2OYSTj9TopLDRC\n086dBl99FXxv4+BBo3ZrU8C0wosZsF4DAYzAofm4iApSYspIifKSFlVCamQRKc4ikuxFJBgHSTIK\nSaSQmKoijHIfxgEf5JRboagNrUZ1RERgRkeHAlGdgFTdatTQMlpwd6KIiEhzKWC1gmmalJeX4/V6\nKS0tpaSkBK/XG3rv9XopKSkJtToVFxeHLuE19MiWoJiYGHr06EFKSgrxMTHEx8YSFxWNyxGHw4jD\nYcZgC0Rj+KMo9zooKYaSYpPiIoPiXIPsEhubvTYKS5wcLHHi94MRKLGCkhkMTXVfjUAAF5Uk2Q+S\nZCsi0V5EsqOIJEcxiY5ikh1FJDqKSYkoItV5EJetAgKAt3pqCafTCkXR0eByWfNRUVD9akZHQ1RU\n3fmoKCsYBeejotSKJCIinVKn+3Uy8vOtGdOsf4JD4SC4TUOfNU38VVWU+nxUVVZSUVFBZUUFlZWV\nVJWXU1FeTmVlJWWlpZSWlVFWVoa3+rU0OO/zUerz4fX5KCsvp6T6NVCzDDXK1lhZCASwAzF2FzH2\nBFKcqcTb04ixJRNpJmM3EynfG0fBdzEUVEWT5Y+ixB+F1x9NgMM7gQeApi8RxtnKqkNSCYnVr8HQ\nVPM1yVFMtM13qH+T3Y4ZGQmRkZgulxWEoqIgsgdm5IlUuVyYkZHWsur5Wq/BbYLzkZHWuqgojask\nIiLHvE4XsN6bOBG/aeIHAqYZmvfX00m7ZuQoDQQo8fsprp6Kqqoo8fvxtrWPTjXTBJNI/LgImNE4\niMFpiyXSFoPTiMFuROMwYrATjWHEAFHYiMYkBr8ZS5UZQ6UZQ3kgGq8ZgRfIbfKoBtgMsBu47JXE\nOsuJiaggxllBrKuCuKhK4iIriYuuIi7GT3yMn9iYAHGxARLi/SQmgiPKYV0Gi4jAjEiAiDTMiAgr\n8Dgch4KP00lpZCSm02l93uHQ7f4iIiKt1OkC1vxcPyZ2TMMBpg0TGyZ2wG6NPh1sNMKoEQAMTJwE\nTCcBIjFxETAjCZhOTFw4bVHYbU5shh0DJ3abE8NwYDOcGDYHNpsLu+HCqJ4wXJhGJCaRBMxIqgIu\nqkwXhs2G3WbDYbNhGAZVhkEVhpX0DANqzhu26nlb9fvqyWZgs1vjNCXEmyQlBkhMNElMhsRkg8Rk\nSEq1kZBkEBtvEBNjEh3duithJtD4yFUiIiJyJHS6gLUveTlgYBhGdSYxmvWQXpvNht1ux2534LDb\nsdvtOBx2bDZ7kw0xJtDYTXE2IALrylZ0tElUlInLZc27XBAVZVZP4HKZ1Z+x5mNjrcnqf20SE2Nt\nY5XJABp7WF3znhUnIiIinUunC1innNIFu53qyXpYrs1mTYcHpeB7wwCHw8TqMmRiXQEziYwMEBnp\nx+m0WoBq7rPm5HRa20ZEWK9OpxWCgsuD4aldH9wrIiIiR61OF7Befrmlt6SJiIiIdC4aUlpEREQk\nzBSwRERERMJMAUtEREQkzBSwRERERMJMAUtEREQkzBSwRERERMJMAUtEREQkzBSwRERERMJMAUtE\nREQkzBSwRERERMJMAUtEREQkzBSwRERERMJMAUtEREQkzBSwRERERMJMAUtEREQkzNolYLnd7ofc\nbvej7XEsERERkY7WXi1YswCjnY4lIiIi0qGOSMByu93/53a7n3S73dEAHo8ncCSOIyIiItIZOZrz\nIbfbPRJ4BFjt8Xhm1lg+Brir+u1dHo9nBYDH45kR7oKKiIiIHC2a24IVCdxfc4Hb7bYBc4Fx1dPd\nbre7zmVAt9ttuN3uB4BzqgOZiIiIyDGtWS1YHo9nmdvtHnXY4v7AVo/HUwbgdrt/APoB2w7b1sTq\ngyUiIiJyXGhWwGpAMlDodrsfq35/EEjhsIDVUhs2bGjL5iIiIiIdri0BKx9IBG7CukNwPpDXlsKM\nHj1adxqKiIjIUa8ldxEeHn5+AAbUeN/f4/Fsb3uRRERERI5uzQpYbrf7NuBuINPtdj8H4PF4/Fid\n3D8CPqxeLyIiInLcM0zT7OgyiIiIiBxT9CxCERERkTBrSyf3VmlocNK2flYOaWEdLwBOAnzAAo/H\n89KRL+HRraGBdxv4rM7hVmhhHS9A53CLuN3uZ7HqzAb8yuPx/NjIZ3UOt0IL63gBOodbzO12/xE4\nBwgAv+5s53G7tmA1d3DSln5WDmlFvZnAzzwez/n6S91sdQberY/O4TZpVh1X0zncQh6P50aPx3M+\n1vnZYIDVOdx6za3jajqHW8Hj8fzB4/FcgBWcbmvocx11Hrf3JcLQ4KTVA5QGBydt62flkNbUm/7B\nbAGPx7MMKGjGR3UOt1IL6jhI53DrFAMVjazXOdx2TdVxkM7h1hsObG5kfYecx+19ibAlg5MekYFM\njwMtrbdi4DW3210A3KqhNsJK53D70DncelOBeY2s1zncdk3VMegcbjW32/0xkAqMbORjHXIet3fA\nasngpGEfyPQ40aJ683g8vwVwu91nAA8Dl7ZDGY8XOofbgc7h1nG73ZnAFo/H830jH9M53AbNrGOd\nw23g8XjOdbvdQ4GXgQkNfKxDzuP2vkTYksFJNZBp67S23nxA5ZEp0jGpOc35OofbpqWXTHQON5Pb\n7T4TGOXxeB5v4qM6h1upBXVck87h1smh8QajDjmP27UFy+Px+N1ud3BwUqgxOKnb7b4cKPV4PO81\n9VlpWEvquHrZ34CuWE3U09qxqEet6oF3xwNd3G53vMfjuaF6uc7hMGluHVcv0znccm8Au9xu90rg\nmxotKDqHw6dZdVy9TOdwK7jd7r9jXR6sAG6usbxTnMcaaFREREQkzDTQqIiIiEiYKWCJiIiIhJkC\nloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiI\nhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJ\niIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiY\nKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiI\niEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkC\nloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiI\nhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJ\niIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiYKWCJiIiIhJkCloiIiEiY\nKWCJiIiIhJmjPQ7idrvTgN8DScBNHo+noj2OKyIiItIR2qUFy+Px7Pd4PDOBrUBGexxTREREpKO0\n2yVCt9t9FXA2kN1exxQRERHpCIZpmq3a0O12jwQeAVZXt04Fl48B7qp+e5fH41lRY93lQK7H41nd\n+iKLiIiIdG5t6YMVCdwPnBNc4Ha7bcBcYEz1og/cbvdK4BTguuptZiIiIiJyDGt1wPJ4PMvcbveo\nwxb3B7Z6PJ4yALfb/QPQz+PxbAL+t6l9Ll++vHXNaSIiIiIdYPTo0UZ9y8N9F2EyUOh2ux+rfn8Q\nSAG2NXcHQ4YMCXORRERERMJvw4YNDa4Ld8DKBxKBmwADmA/khfkYIiIiIp1aW+8iPLxZ7AdgQI33\n/T0ez/Y2HkNERETkqNLqgOV2u28D7gYy3W73cwAej8eP1cn9I+DD6vUiIiIix5VWD9NwJCxfvtxU\nHywRERE5GmzYsKHdOrkfMXl5eVRU6Ak7Ise61NRUIiIiOroYIiJtclQErJKSEgzDoFu3bh1dFBE5\nggKBALt37yYjI0MhS0SOau32qJy2OHjwIMnJyR1dDBE5wmw2G927dycvTzcfi8jR7agIWIZhYBj1\nXuIUkWOMzXZU/LMkItIo/UsmIiIiEmYKWCIiIiJhpoB1lPr222/56KOPwrrPG264gREjRnDFFVe0\naT9Tpkzh008/DVOpGrd9+3buv//+etc988wzlJWVtUs5REREalLAOkpt3LiRZcuWhXWfzz33HA8+\n+GCb99Oefeb69evH7Nmz61333HPPKWCJiEiHOCqGaWhM7KRJYdtXyTvvtHib//znP9x66634fD5K\nS0uZPn06mZmZADzwwAPs2rWL3NxccnJyOOecc2oFGI/Hw1//+lcMw2DIkCH86U9/Cq3btWsXt99+\nO/v378c0TX7+859zzTXXAPCXv/yFP//5z3i9Xr755htGjRrFbbfdFtp28ODBTJ8+nVdeeQWfz8fC\nhQvp1asXAPfffz+ff/45eXl5dOnShZdeegmXyxXatjUDzxYUFHDDDTdQVFREnz59OHjwYK39NPY9\ne/bsyb333suSJUvYuXMnTz/9NMOGDau3bmfMmMHEiRMB8Pl8XHbZZRQVFdGzZ09ef/310D59Ph+X\nXnopubm5TJkyBYfDwfPPP0/37t355JNPeOKJJ3jjjTcAK6jOmDGDDz/8sMXfW0REpCFHfcDqaH/+\n858ZM2YMN910U511hmGQn5/P3/72NwAmTZrEhx9+yLhx49i8eTOvvPIKS5YsweFwcNttt/H3v/+d\nn/3sZ/j9fq688kruuusuRo8eXWe/1113HTExMXz99dc88MAD9R5369at9V5CvP7660MtPldddRXv\nvfceP/3pT9tUBw888ABDhgxh9uzZ7Nu3j3HjxoVasBr7ngDl5eWkpaXx5ptv8tprr/Hiiy+GAlZj\ndetyuXj//ff59NNPeeqpp+qsW7p0KWeccQZ///vfSUpKCq0bOXIkM2fOZM+ePXTr1o3XXnuNqVOn\ntun7i4iIHO6oD1itaXUKp0suuYQZM2aQlZXFxIkTGTFiRK31I0eOxG63A1bAWr9+PePGjePjjz8m\nOzubyy67DIDS0lISExMB2LZtGy6Xq95wFWSaZqOtTdOnT693eWJiImvWrGH79u14vV5ycnJa9H3r\ns3btWl555RUAMjIyGDhwYGhdY98TrDA0YcIEAHr16sXBgwdD65qqW2hdi9tVV13F3//+d6ZNm8ay\nZcuYO3dui/chIiLSmKM+YHW0oUOHsmrVKtatW8czzzzDkiVLarUq1QwAgUAgNDq10+nk4osvrnW5\nrKZAINDocVvTx8nr9ZKZmcn48eMZOnQoJ554YqsCyuHsdnuD+2nqezamqbptrZ///OdkZmZywgkn\nMHbsWCIjI9u8TxERkZrUyb2NAoEANpuNs88+m5tvvpnPP/88tM40TZYuXUpFRQUVFRW89dZbnHvu\nuQCMHj2at99+mx07dtT6PED//v0pLy/n3XffbfC4kZGR7N+/P1SG5ti+fTtOp5OZM2dyxhlnsHHj\nxrAErBEjRvDWW28B8OOPP7Jx48bQusa+Z1Maq9vmiIyMJDc3t84xk5OTGThwIHfddRe//OUvW7RP\nERGR5lALVhu9+eabvPDCC6HLgA899FBonWEY9O/fn6uuuoo9e/YwYcIEhg8fDkDv3r2ZN28eN9xw\nQ6gF6O6772b48OHY7XYWLlzInDlzePrpp7HZbFxyySXccMMNoX2fd955zJs3j4suuoi4uDheeukl\noqOjQ8etz6BBg+jZsycjR46ke/fujBgxIhTSapZ5/fr1TJgwgXvuuYczzzyzyTqYMWMG119/PWPG\njKFv37707ds3tK6x73m4w+8+bKxuG9qmpqlTp3LllVfSs2dPLr300tBNAgBut5u9e/dy0kknNfn9\nREREWsoIRwtGuCxfvtwcMmRIneXBDslHmwcffJCYmBhuvvnmji6KHGbWrFmcd955XHTRRR1dFKnH\n0fp3XkSOLxs2bGD06NH1/i9flwiPMD1DsXN56623GD9+PIDClYiIHDG6RHgE1RybSjqHn/70p20e\nlkJERKQpasESERERCTMFLBEREZEwU8ASERERCTMFLBEREZEwU8ASERERaYJpgs/X/M8rYB1hRUVF\n/PWvfz2ix+jZs2fY9/nll18yadKksO83nBqq2zVr1nDFFVeE5RhHom5bY/v27dx///2t3v5o+PMU\nEenMXnopgjlzoikqat7nFbCOsMLCQl544YUjeozjdayt46lu+/Xrx+zZszu6GCIix6VFi5wsWhTB\njh02fvzR3qxtNA5WG/3nP//h1ltvxefzUVpayvTp08nMzARg/fr1zJkzh6ysLC6++GKSk5N59dVX\nQ9vef//9fP755+Tl5dGlSxdeeuklXC4XYLWc3HvvvSxZsoSdO3fy9NNPM2zYMAC+/vprfve73xEX\nF8fw4cNrPWevuLiYWbNmsXfvXrKzs5k0aRJ/+MMfQuunTZvGCSecwMqVK/H5fPzmN78JjQv1+uuv\n88QTT9ClSxcGDx7c7Drw+Xz8/ve/Z/PmzZimyahRo7jjjjsAyMzMZPjw4SxatIg5c+awYMECBgwY\nwCOPPALA6tWruf/++zEMg/j4eB555BF69OgRqtuZM2dSXFxMIBDgjjvuYMSIEc2qW5/Pxx133MHX\nX39NSUkJb775JsnJyQB89dVX3HXXXfj9fpKSknj88cdJSUlpsm4bs2bNGu677z769OnD1q1bSUhI\n4C9/+QtJSUlNHjMrK4spU6YwceJEVqxYQUxMDG+//Xboe1x22WUUFRXRs2dPXn/99VrHnT9/PosW\nLcJms3Haaadx3333hc6hxv48G6vb4uJirrvuOkpKSigrKyMxMZFrrrmGyZMnA42fQ4sXL2bhwoWh\nbZ9//nn69+/PmjVrePTRR4mOjsbv93PBBRfw9NNP88Ybb9C/f/9m1bGISEdYtszBggWRAPz2tz7O\nOMPfrO2O+kflhPOyxzvvvNPibW6//Xa6d+/OTTfdVO/6Xbt2MWXKFD799NM66/Ly8khNTQXgqquu\n4tJLLw39UKWnp/Piiy8yYcIEXnvtNT7++GOeffZZAM455xwefPBBRo4cydq1a5k0aVLoocYABw4c\nICkpibKyMs466yyWL19Oly5dAOvHcdeuXSxcuJC4uLjQNnv27GHs2LGsXr2a1NRUHnvsMVauXNms\nOnn//fdZuHAhCxcurLNu0qRJ/OxnP6O4uJj33nuPV155hWHDhrFlyxby8/MZPXo0S5cupWvXrrz3\n3nvMnz+f9957D7BGWp8+fTpjx45l165dTJw4kVWrVoVCS0N1u2bNGm688UYWLVrEgAEDmDZtGsOH\nD+fqq6+moqKC0aNH88Ybb9ClSxfefvttli1bxpNPPtmsum3ImjVrmDZtGh9++CEZGRncc889VFVV\ncc899zR5zKysLIYNG8YzzzwTCjGH+/TTT3nqqadqBayVK1fy8MMP8/bbb+N0Opk9ezZxcXHMqII6\nQgAAIABJREFUmTOnyT/P+up29erVJCYmMn/+fIqKipg1axYPP/wwFRUV3H777aHjNnQOARQUFISC\n7DPPPMPWrVt57LHHWLNmDbfeeiuffPIJAwcO5KWXXmLp0qX069ePqVOn1vm+elSOiHQGa9faefDB\nKPx+uP76cjIzK2ut16NyjqBLLrmEv/3tb8yaNYs1a9bUWd9YgE1MTGTNmjUsWLAAr9dLTk5OaJ3L\n5WLChAkA9OrVi4MHDwLWZbHi4mJGjhwJwPDhw0MtFkF2u50PPviAV199lYiIiDoB4frrr6/zw7hh\nwwZGjRoVCnznn39+c6uAYcOGUVBQwA033MCiRYsoLy+vtf7UU08lISGBU089lcTERMrKygD497//\nzfDhw+natSsAEyZMYOfOnXi9XoqLi8nOzmbs2LGA1aI3bNgw/v3vf4f221jdDho0iAEDBgC162/b\ntm3s3r2bX//610yaNInnn3+ePXv2AM2r28YMHDiQjIwMwBoxfv369U0eM+iEE05oMFw19F1XrFjB\nFVdcgdPpBOC6665j+fLlQON/ng3VbbC80dHRofo6cOBA6DvVVN85BJCcnMw333zD3/72N7Zv386+\nfftC6/r164fL5SI+Pj50TpSWljb4nUVEOtK339p5+GErXP3sZxV1wlVTjvpLhK1pdQqnoUOHsmrV\nKtatW8czzzzDkiVLeOCBB5rczuv1kpmZyfjx4xk6dCgnnnhisy5H2WyNZ+LvvvuOG2+8kalTpzJo\n0CBSUlLq7Le+4zgcjlrLW9KymZKSwtKlS9myZQtvvPEG8+bNY/Xq1XU+d/g+DcMgEAjU+Vyw31N9\n5W5rnyi73U6vXr3qPW+aqtuWCAQCRERENHnMcByn5nywfpr682ysbq+++mrGjBnD2LFjOeOMM/jl\nL39Z57gNnR/Tpk0DYPLkyQwePLhOkBQRORr88IONP/7RRWUlXHRRJT//eUWL96EWrDYKBALYbDbO\nPvtsbr75Zj7//PNa6yMjIzlw4EDohzD4w7R9+3acTiczZ87kjDPOYOPGjc0KNfHx8aSnp7N27VoA\nPvjgg1qtAKtXr2bcuHH86le/Ij4+nqysrGbt96yzzuKzzz6jsLAQ0zRDfYCawzRNTNPkpJNO4pZb\nbiEnJwev19vkdv/1X//FunXryM7OBqz+OyeeeCLR0dHExcXRu3dvli5dCsDOnTtZt24dQ4cODW3f\nUN02pn///pSXl7NkyZJa5Yem67YpGzZsYNeuXQAsXLiQc889t8ljtsWYMWN4/fXXQy2Gzz//fKhV\nqrE/z6bq9pVXXmHs2LF89NFHPPzwwzgczf9/2NKlS3nkkUcYPXo0X3/9dVi+p4hIe9q922Du3ChK\nSw1GjKjixhvLac3/7Y/6FqyO9uabb/LCCy9gt1t3FTz00EO11mdkZHDOOecwatQo0tLSuP322znz\nzDMZNGgQPXv2ZOTIkXTv3p0RI0awf//+eo9hGEatlpt58+bx29/+loiICEaOHEl0dHRo3WWXXcZV\nV13FJ598Qv/+/Tn77LPrXCKsrxUoNTWVOXPmMGHCBJKSkjjrrLOa3Vq0detWbr75ZpxOJxUVFcyd\nO5eYmJh6v0dNycnJPPnkk1x77bUYhkFCQgLz588PrX/22WeZMWMG8+bNIxAI8Mwzz5CQkBBa31Dd\nHl5fNY9tt9tZuHAhs2bN4sknn8Rms3HppZfy61//usm6bYxhGJx00kncf//9bN26le7du3PnnXc2\n65j11U19+z/8M6NGjWLTpk1MmDABwzAYNGgQt9xyC9D0n2djddunTx8ef/zx0CXv+Ph4Zs6cyZln\nntlkeadPnx46p8ePH89XX31VZ5ua23aWuzRFRADy8w3uuiuawkKDn/zEz623+mjtxY2jvpO7SGew\nZs0ann766Tp3+R2N7rvvPvr164fb7QbgjjvuIDIystbdqEea/s6LSHsrKYFZs6LJyrJx0kl+7rmn\njKioxrdprJN7u7Rgud3uZOBOoCtwk8fjyW+P44q0l/pamI5WAwcO5KmnnuLll1/G7/dz+umnc9tt\nt3V0sUREjhjThHnzXGRl2ejZM8AddzQdrprSLgHL4/EUALe43e6JwGlA3R7QIkex//7v/+a///u/\nO7oYYTF58uRG72gUETnWLF7sZN06BzExJn/4Qxnx8W3fZ3t3cv8JsK6djykiIiJSr02bbLz8sjWQ\n6O9+56Nr1/B0nWp1C5bb7R4JPAKs9ng8M2ssHwPcVf32Lo/Hs6J6+cXAco/H04JHJYqIiIgcGQcP\nGqGxri69tILhw5s3SntztOUSYSRwP3BOcIHb7bYBc4Ex1Ys+cLvdK4F+wGzgE7fb7fN4PBvacFwR\nERGRNgkE4NFHXeTnGwwc6Ofqq5sY6yoQwLFuHabdjr/GkEENaXXA8ng8y9xu96jDFvcHtno8njIA\nt9v9A9DP4/FsA0a29lgiIiIi4eTxRPDll3bi401mzPDR4JB/Ph/OFStwvv02tr17CfToQelZZ9HU\n+A3h7uSeDBS63e7Hqt8fBFKAbWE+joiIiEirfPWVnddfj8AwYPp0H6mp9fe7cnzyCZF//jNG9ePD\nzPR0KsePt5q/2jlg5QOJwE2AAcwH8sJ8DBEREZFWyc83eOQRF6YJU6ZU8JOf1NPvqqgI17PP4qge\ncDnQvz8Vl15K1dlnQ/XA4k1p612Ehw/88wMwoMb7/h6PZ3sbj9Hp7dixg5SUFN58881ayx944AF+\n8pOfcPHFF3P++ecze/bsTv/okPfff58tW7bUWZ6ZmVlrVO7WevLJJ3nwwQfbvJ9wePDBB9m2rfWN\nq1OmTOHTTz8NY4lERORI8vvh4YddHDxoMHiwnylT6va7sn/3HTE332yFK5eL8ptuovT//o+qESOa\nHa6gDQHL7XbfBtwNZLrd7ucAPB6PH6uT+0fAh9Xrj3n/+Mc/mDx5MosXL6613DAMrrvuOt5//31W\nrlzJtm3bWLZsWQeVsnnee++9egNWuAbR7EyDcd52223079+/1dsfS4OLiogcD15+OYJNm+wkJZlM\nn173MTiOZcuI+sMfMAoL8Q8ciHfePCovuojWPIywLZ3cHwTqNEV4PJ4PscJVu5g0KTZs+3rnnZJW\nbbdkyRJee+01Jk+eTFFREfE1RigLtlgVFhZSUFBAjx49mrXPFStW8NBDD2Gz2fB6vSxcuJAePXqw\nZs0aHn30UaKjo/H7/VxwwQU8/fTTvPHGG/Tv35/S0lJmz57N999/j9/vx+1213rm3fz581m0aBE2\nm43TTjuN++67D5fLBcBvf/tbli9fzhdffMGzzz7L//t//4/x48eHtl27di0PPfQQ27dv57rrrgvt\n1+/3M3fuXD7//HOqqqq49tpr+dnPfhbabtasWfzrX/+ia9eupKam0qtXr2bVQWZmJsOGDWPdunXs\n37+f3/3ud1xxxRXNOua0adM44YQTWLlyJT6fj9/85jf89Kc/BeCFF17grbfeYtOmTSxevJgzzjgj\ntN1//vMfZs6cSXFxMYFAgDvuuIMRI0YAUFBQwA033EBRURF9+vTh4MGDtVokG6vbRYsW8dRTT4We\nWdm1a1defvllALKyspgyZQoTJ05kxYoVxMTEhB7OXFxczKxZs9i7dy/Z2dlMmjQp9MiazMxMhg8f\nzqJFi5gzZw4LFixgwIABPPLII82qXxGR48mHHzr4xz8isNvh97/3kZhY44pSIEDEyy8TsWgRAJWT\nJlH+q1+1qMXqcHrYcxtt27aNhIQEunTpwsSJE1m6dGnoh940TV588UXefPNNAoEAf/rTnzjllFOa\ntd977rmHJ598kkGDBtVZt2vXLj755BMGDhzITTfdxMUXXxx6uPOjjz5KYmIiH3zwAT6fj0mTJnHy\nySdz7rnnsnLlSpYsWcLSpUtxOp3Mnj2bRx99lDlz5gDwxBNPMG3aNC666CIyMzPrHHfPnj289tpr\nZGVlcfHFF4cC1ssvv4zNZuP999+nvLw89MPfu3dv3n77bTZv3syqVaswTZMrr7yS3r17N6sODMMg\nOjqad999l/379zNq1CguvPBCkpOTGz1m0OrVq3n99deJi4urtd9rr72Wa6+9lkmTJtVpgbrhhhuY\nPn06Y8eOZdeuXUycOJHVq1eTmJjIAw88wJAhQ5g9ezb79u1j3Lhxoe0bq1vTNLnzzjtZu3Zt6KHM\n7733Xq3j7tixg4EDB4b+LILi4uL44x//SFJSEmVlZZx11llcd911dOnSBcMw6NOnD9dffz0LFizg\nlVdeYdiwYQpYIiKH+eorO888Y/2H98Ybyzn11Br9rqqqcD3+OI6PPwa7nfIbbrBardroqA9YrW11\nCpfFixeTlZXFuHHj8Pl8fPvtt6GAZRgGU6dOZeLEiYwfP77Z4Qrgmmuu4ZZbbmHcuHFceumlDBhw\nqGtbv379cLlcxMfHc+qpp/Kvf/2LsrIywGr5euGFFwBwuVxceeWVLFu2jHPPPZfly5dzxRVX4HQ6\nAUKtUIf/qDfUTyzYAtSrVy+KiopCy1euXElWVhaTJk0CwOfzsXXrVnr37s3atWtxu93YqtthR4wY\ngdfrbXY9jB49GoC0tDTOOussNm7cyHnnndfoMYOuv/76OuGqMcXFxWRnZzN27FgAevbsybBhw1i/\nfj3jxo1j7dq1vPLKKwBkZGQwcODA0LaN1a1hGERERFBSUoJhGMTGxhIREVHr2CeccEKDj6ex2+18\n8MEHZGVlERERQW5uLl26dAHg1FNPZfPmzZx66qkkJiaGzgMREbFkZdl48EEXfj9cdlkFF15YeWhl\nRQWuhx/GsW4dREVRNmcO/sGDw3Lcoz5gdbR3332X5cuXk5iYCFjPpKt5mdA0TXr37s3VV1/NnXfe\nyfz585u136lTpzJlyhSWL1/O9ddfz/Tp00NhoimBQCA0b5pmKNwYhlFrXSAQqLcPUUP9ihoKXg6H\ng1mzZnFRPYnfbrfX2q6lnfwP3zYYTBo7ZmuPVd82Nevo8O9SU1N1O3fuXM4//3xOPvlknn322WaX\n57vvvuPGG29k6tSpDBo0iJSUlHrL0NlvnhAR6QiFhQb33BOF12tw9tlVXHNNjU7tPh9Rf/oT9q+/\nxoyNpezuuwkMGNDwzlqovZ9FeEz5/vvviY2NDYUrgPPPP5933323zmdvueUW/vWvf/HZZ581a99+\nv5/o6GgyMzO59NJL2bCh4cHvTdMM/cCOHj2aF198EYDS0lJeffVVxoyxBtYfM2YMr7/+OuXl5QA8\n//zzodaaIJfLxf79+4HaQa0xEyZM4IknnqCkpCRUnqCRI0eyePFiTNOkpKSE5cuXN2ufQcEbB7Kz\ns/nyyy85/fTTmzxma8XFxdG7d2+WLl0KwM6dO1m/fj1Dq0fsHTFiBG+99RYAP/74Ixs3bgxt21jd\nVlZW8sgjj7BmzRr+8Y9/cM4559Bcq1evZty4cfzqV78iPj6erKwshSkRkWYoL4c//clFbq5B//4B\nbr21Rqd2r5eou++2wlViImX33RfWcAVqwWqTxYsXc+GFF9ZaduGFF/Lkk09y5ZVXAodag6Kiorjn\nnnuYMWMGH3/8caizc0PuuOMOvvzySwKBAOnp6Tz++OOh/QX3WfM1OP+///u/zJ49m3HjxuH3+5ky\nZUqok/aoUaPYtGkTEyZMCPUFuuWWW2od9/LLL2fatGksXryYU045pdaQCg21bP30pz8lJyeHSZMm\nhTp1ezweYmNjufDCC1m1ahXnnXceqampdO/evUV33jmdTi655BLy8vJ4+OGHiY2NbfKYTZW3Mc8+\n+ywzZsxg3rx5BAIBnnnmGRISEgCYMWMG119/PWPGjKFv37707ds3tF1jdet0OklLS+Pyyy/H5XJh\nt9sZMmQIc+fObbKsl112GVdddVWoj93ZZ59Nbm5unc/pbkYRkUMCAXjsMRdbtthJSzP5wx/KqP6p\ngKIiou++G9v27ZipqZTecw9mM29AawmjM/1vePny5eaQIUPqLN+zZw/dunXrgBJJR5o0aRL33nsv\ng8N0Pbyj7N69m+nTp/PnP/+Z+Ph49uzZw8iRI/nmm2+Ijo7u6OJ1Svo7LyJt8dJLEbz1VgTR0SYP\nPlhG797WFRmjoICoO+/ElpVFoGtXyu69FzM9vdXH2bBhA6NHj673f7hqwRI5whITE4mIiMDtduN0\nOnE4HDz33HMKVyIiR8BHHzl46y1rOIbbbvMdCle5uUTdcYf1PMGePa1wlZx8xMqhgCWd1jvvvNPR\nRQiLmJiY0JhXIiJy5KxbZ2f+/EPDMQQfg2NkZxN9550YeXkETjyR0rlzocaYlUeCApaIiIgc9dau\ntfPgg1F1hmOw7dxJ1J13hkZnL7vjDoiJOeLlUcASERGRo9pnnzl46CFrrKvJkyv4xS+s4RhsW7cS\nNXcuRnEx/sGDKbv9dg71dj+yjoqAZbfbKS0tVZ8VkWOcaZoUFBTUGYhVRKQhn37q4P/+79BAor/4\nRQWGAfZvvyXq3nuhrIyqYcPwzZwJ7fhvy1ERsNLT08nNzaWwsLCjiyIiR5BpmiQkJNQabkNEpCFr\n1jh45BErXP3P/1Rw9dXV4WrDBqLuuw8qKqgaORLfrbeCo30jz1ERsAzDICMjo6OLISIiIp3Exx87\neOwxK1xdfnkFV11lhSvHqlW45s0Dv5/KsWMpnzaNQyOMtp+jImCJiIiIBK1ebYWrQACmTKngiisq\nMDBxLvoHkQsWAFAxeTIVv/oVdNBAzApYIiIictRYscLBE09Y4eqKK6xwRSBA5F//irN6eJ/yqVOp\nnDy5Q8upgCUiIiKdnmmCxxPBwoVWR/Wf/7yCKVMqoLIS12OP4VizBux2fLfeStW553ZwaRWwRERE\npJOrrIT58yNZvtyJzQbXXltOZmal9dDm++7D/s03EBVF2e234z/99I4uLqCAJSIiIp1YSQk88EAU\nGzfaiYyEGTPKGDbMbz365o9/xLZzJ2ZSEmV3302gb9+OLm6IApaIiIh0Srm5BvfcE0VWlo3ERJM7\n7iijf/8A9m+/xfXAAxhFRQR69KDsrrswGxltwO/3U1lZSUVFBVVVVVRWVoamqqoqqqqq8Pv9BAKB\n0PvgvGmaBAIBAoEApmni91uP3wkEAqSlpTV4TAUsERER6RRM06SsrIyysjK++66Kxx5Lo7DQS2pq\nCZmZX7F58wE2LlhH1fLllFZW4u3SheKMDMqfeYby8vJaU0VFReg1GIrC7e67725wnQKWiIiIhJXf\n76e4uJiioiKKiopC88XFxZSUlNSavF4vxcXFeL1eysrKCAQCFBWdxq5dvyAQKCUmZivR0X/llZe8\n2PbuxSgoACCQmopps8EXXzRZHsMwcDgcRERE4HQ6Q5PD4Qi92u12bDYbDoej1nu73Y5hGNhsNmw2\nW2jeaGL4BwUsERERaZRpmni9Xg4cOEBhYSEHDx6ksLCw1nxRUVHo1ev1tvI4NgoKMtm//0KcTgc9\ne25m6NDPiI8YSNzatcQaBlFdumC78EIizjyTqKgooqKiiIyMxOVyERERQWRkJBEREaH3EREROByO\nJgNRa2zYsKHBdQpYIiIix7GysjLy8/PJz88nLy+PgoKC0FRYWBiar6ysbPY+DcMgLi6O+Ph44uPj\niYuLC72PiYkhNja2zlRWFsdzz6WwebOT1FRrGAa3uxv2rT2IevhhDKcT89RTKZszh8BJJx3BGgkP\nBSwREZFjVGVlJfv37ycvL4/c3NzQazBM5efnU1pa2qx9uVwukpKSSEpKIiEhgcTExHpf4+PjiY2N\nxdaCx9OsW2fniSdcFBcbJCWZTJ/u4/TTKnH+YzGRr7wCfj/+AQPwzZ6NmZLS2upoVwpYIiIiR6lg\ngNq3bx+5ubnk5OSE5nNzcyksLGxyH06nk9TUVFJSUkJTUlISycnJoUCVnJxMVFRU2MtfUQELFkSy\nZIkTgDPP9HPLLT4SKcR17+PYq/tXVWZmUv7LX4LTGfYyHCkKWCIiIp1YaWkpOTk57N27t9aUk5ND\nfn4+pmk2uK3dbiclJYXU1FTS0tJIS0sjPT09tCwlJYW4uLgj0j+pKdnZBg8/HMWOHTbsdvjFL8qZ\nNKkS53ff4HrkEYyCAsy4OHy//S3+YcPavXxtpYAlIiLSwSorK9m3bx/Z2dns3r2b3bt3s2fPHvbs\n2dNoK5TNZiM1NZWMjIzQlJ6eTpcuXUhPTyc5OblFl+rag2nCsmUOnn/ehc8HXboEmDHDx4B+VUT8\n7W9EeDwQCOAfOBDf9OmYjYw11ZkpYImIiLQTr9dLdnY2WVlZ7N69m127drF792727dvX4FhNTqeT\nLl260LVr11pTRkYGaWlpOI+iy2Z79xo8/bSLjRvtAIwcWcVNN/mIPZCN67Z52LdsAcOg4vLLqfj5\nz8Fu7+ASt54CloiISJh5vV7+85//kJWVxa5du8jKyiI7O5v8/Px6P28YBunp6XTv3p0ePXrQvXt3\nunfvTrdu3UhJSel0rVAtFQjAO+84efXVSCoqID7e5Npryznv3Aoi3l5M5MKFUFmJmZKC73e/w3/G\nGR1d5DZTwBIREWmlyspKsrOz2blzZyhQ7dy5k7y8vHo/73Q66dGjBz169KBnz5707NmT7t2707Vr\nVyIjI9u59O1j504bTz0VydatVmvUuedWcf315SQW78I1+wns338PQOWYMZRPnQqxsR1Z3LBRwBIR\nEWmGwsJCduzYwY4dO9i5cyc7duwgOzu73kt7TqeTXr160bt371CQ6tmzJxkZGUd9a1RzVVbCG29E\n8MYbEfj9kJJi8pvf+Bh6ViXOt98m8tVXrVar5GR8N9+M/6yzOrrIYdUuAcvtdj8EODwez/+2x/FE\nRERayzRN9u3bx48//sgPP/zADz/8wI8//lhvZ3PDMOjWrRu9e/emd+/e9OnTh169etGtW7fjJkjV\n58sv7fzlL5Hs2mXVwfjxlVxzTTlxe7cT+ftnsW/dCkDlBRdQfu21EBfXkcU9ItqrBWsW8Eg7HUtE\nRKRZTNNkz549bN++vVagqu9RL1FRUfTt25c+ffqEXnv37o3L5eqAkndO2dkGCxZEsn69FS+6dw8w\nbVo5p/U5SOQrr+JcuhRM02q1uukm/EOHdnCJj5x2CVgejyfgdrvb41AiIiINKigoYOvWrWzbto1t\n27axfft2SkpK6nwuMTGRE044gRNPPJETTzyRvn37HleX91qquBg8HmvAUL8fXC5wu8uZlFlB9Kcr\niXxoAUZhIdjtVGRmUjFlCkRHd3Sxj6hWBSy32z0Sq0VqtcfjmVlj+Rjgruq3d3k8nhVtL6KIiEjL\nlZWVsX37drZu3Rqa6ruLLzExkQEDBtCvX79QqEpOTu6QwTePNn4/fPCBk9dei6CoyMAwYMyYSq6+\nuoKUop1E3v0s9u++sz47cCDlN95IoE+fji10O2ltC1YkcD9wTnCB2+22AXOBMdWLPgBWuN1uI/hZ\nt9s9xuPxLGtDeUVEROoIBAJkZWWxZcuWUJjatWsXgUCg1ueio6Pp168f/fv3Z8CAAfTv35+UlBSF\nqRYyTfjiCzsLFkSSlWW16p12mp9rry2nX3I+Ea+9hvOjjyAQwExIoPyXv6TqggvgOKrnVgUsj8ez\nzO12jzpscX9gq8fjKQNwu90/uN3u/h6PZxtWHywREZGwKCoqYsuWLXz//fds2bKFbdu2UVZWVusz\ndrudfv36MWDAgNB0vHc+byvThK++svPaaxFs2WINu5CRYTJ1ajnDzygh8p23iXjrLfD5wG6n8uKL\nKb/yymOyE3tTwtkHKxkodLvdj1W/PwikANvCeAwRETnOBAIBdu3axffff8/mzZvZsmULu3fvrvO5\n9PR0TjrppFDr1IknnnjMji3VEb75xs7ChRFs2mQFq4QEk8suq2DixeVEfbKCyN+8ilFQAEDVsGGU\n/+IXmD16dGSRO1Q4A1Y+kAjcBBjAfKD+kdZEREQa4PP52LZtG5s3b2bz5s18//33de7qi4iIoF+/\nfpx88smcfPLJnHTSSSQlJXVQiY9tmzbZWLgwkm++sYJVXJwVrC4eX0HsxnVEznwN286dAAT69aP8\nV7/CP2hQB5a4c2hLwDr8QuoPwIAa7/t7PJ7tbdi/iIgcBwoKCkJhatOmTezYsaPO4J2pqamccsop\noUDVt29fHA6NlX2kmKbVYvXmmxF89ZUVrGJiTCZPrmTihHLiv/+CyD+8hm279TNvpqZSfs01VJ17\nLugSLND6uwhvA8YDXdxud7zH47nB4/H43W73XOCj6o/dHaYyiojIMSJ4uW/Tpk2hULVv375an7HZ\nbJxwwgmccsopoSktLa2DSnx88fthzRoHixdH8MMPVlCKioJLLqlgUmY5Cdu/ImLua9ZDmQEzMZGK\nyy+n8sILISKiI4ve6RimaXZ0GUKWL19uDhkypKOLISIiYZSTk8PGjRv56quv2LhxI0VFRbXWR0VF\ncdJJJ4XC1IABA4g+xsdI6mzKyuCjj5y8804EubnWBaqEBJMJEyq5eHw5Sds3EPHGG9g3bQLATEig\n4rLLqBw/3hr06ji1YcMGRo8eXe+tkWpfFRGRsCoqKmLjxo18/fXXfP311+Tk5NRan5KSwsCBAxk4\ncCCnnHIKffr00Z19HSQ/3+C995wsXerE67VyQvfuASZPruS8kT5iPv+UiDvfwrZjBwBmXBwVl15K\n5YQJVtOWNEgBS0RE2sTr9fLtt9/yzTff8M0337Cj+sc4KCYmhtNPP53Bgwdz+umn0717d4071YGC\n/avef9/JunUOgt3dBg70M3lyBUPPKCNy1Qqct/4D29691jaJiVRccgmVF10EMTEdWPqjhwKWiIi0\nSGlpKVu2bOHrr7/m22+/Zfv27bUG9HQ6nZxyyikMHjyYwYMH069fP7VQdQJeL6xYYbVWZWdbfx52\nO5x9dhWTJ1cwsNsBnB98gHP+EuuxNkCgSxcqL7uMygsuUB+rFlLAEhGRRuXn59e5y68V7ho9AAAg\nAElEQVRmoLLb7QwcOJBBgwYxaNAgTj75ZCL0Y9xp/PijjaVLnaxa5aS83FqWnGxy4YWVjBtXSVrx\nDpzvvINz9WqorAQg0LcvFf/zP1Sdc46VwqTFFLBERKSWiooKPvvsMzZs2MCmTZvq3OUXHCH99NNP\nZ9CgQQwcOJAo9cfpVLxe+OQTJx9+6GT79kOth6ef7ufiiysZelYFkV/+m4jH3sW+cWNofdVZZ1GZ\nmYn/jDOOq8faHAkKWCIiAlh3+/3zn/9k2bJlte70c7lcoTv8Bg4cyIABA3Adx3eOdVamCZs321i2\nzMknnxxqrYqJMTn//CrGj6+kV1wBzo8+wvnXDzByc60PuFxUjh5NxYQJx/XI6+GmgCUichwLBAJs\n2LCB999/ny+++ILg0D19+/blggsu4LTTTqNPnz7YdZmo0yosNFi1ysFHHznZtetQa9Vpp/kZN66S\ns4dXEr31G5yv/xPHZ58R7NVupqdTMXEilWPGQGxsRxX/mKWAJSJyHMrJyeHTTz/ln//8Z+gSoMPh\nYMSIEYwfP56TTz5Zd/p1YiUl8NlnDj75xMnGjXaCXeISE01Gj65kzJhKesQcwLFiBc5bP8IWfHaj\nzUbVsGFUXnQR/p/8RKOuH0EKWCIixwHTNPnhhx9Yt24d69atY2f1s+PAekjy+PHjGTNmDAkJCR1X\nSGmUzwf//reDjz928MUXDqqqrOV2OwwdWsWYMZWcNdiH66vPcby4HMcXXxxqrUpOpnLcOCrHjcNM\nTe3Ab3H8UMASETlGVVVV8e2334ZCVV5eXmhdVFQUZ555JhdccAFDhgzRMAqdlM8HX37p4NNPHaxf\n78Dns5YbhtVh/dxzKxk+rJLEgp04ly/H8dQqjGD/Obvdaq0aPRr/f/2X7gZsZwpYIiLHkGBL1cqV\nK1m9enWtzupJSUkMGzaMYcOGcfrpp+N0OjuwpNIQr9dqqfrsM6ulqqLi0LqTTvIzcmQVI0ZUkVK+\nB+cnn+CYsxrbrl2hzwR69aJy9Giqzj8fMzGxA76BgAKWiMgxIT8/n1WrVrFixQp21fix7dGjB8OH\nD2fYsGH0799fLVWd1MGDBuvX2/nXv5x89ZU9NLo6WKFq+PAqzjmnim6uAhxr1uC4/+PQA5fBeoRN\n1YgRVI4ezf9n777jo6ry/4+/7p2ZZNInPZRQQ5FiAZbigogUC8X22xG/lt8uylpwd3WBr6Brwd0V\n1BXFAqjrWlh0HZHVFeWnK01RQREUFSlBIEAS0ttkJpmZe39/3MwkIT0MKfB5Ph73ce/cPjeX5M05\n556r9esnXSx0ABKwhBCikyouLuabb75h8+bNfPfdd4EnAKOjoxk/fjwTJkygb9++0li9g8rKUti+\n3cy2bWb27q1uqK6qxhOAY8Z4GT3aS2JYKeYvv8Sy/FNM339PYEWr1agCvOgio98qKZHsUCRgCSFE\nJ+H1etm7dy+7du1i165dHDx4MBCqzGYzI0eOZMKECQwfPhyzWX69dzS6DgcPqmzbZmb7djNHjlSX\nJppMMGyYEapGjfJiU4sxb9+OecWXmL/9lpot2r2jRuEdNw7vyJEg/ZF1WPIvUAghOihN0zh+/Dg/\n/PADO3fuZPfu3bhcrsByi8XC4MGDGT16NGPHjiU6Orodz1bUx+2G774zsWOHmR07zOTnV5cmhofr\njBjhY9QoL8OGeYksz8W8bRvmx7/EtGdPdUmVouAbOhTvRRfhGTMG5OfcKUjAEkKIDqKkpIT9+/ez\nf/9+9u3bx/79+3E6nbXW6d69OxdccAHDhg1j8ODB0qN6B5SVpQQC1Q8/mPyv9wOMdwCOGmVU/Q0Z\n4iPkxDGjpOqhLzHt31+9osmE74IL8F54Id5Ro6SxeickAUsIIdpBWVkZhw4d4uDBg/z888/s37+f\nzMzMOuvFx8czcOBAzj//fC644AKSkpLa4WxFYwoLFX780cQPP5jYvdvEsWPVVX+KYjRSHz7cx4gR\nXvr0qMSydw+mHTswv7QD9dix6h2FhOAdPhzv6NF4f/EL6V29k5OAJYQQp5m/ZOrQoUOkp6dz6NAh\nsrOz66wXEhJCWloaAwYMYMCAAfTv358E6RSyw8nJMQKVfzh+vPaTmREROhdcYASqYcN8xFJoBKo1\nOzB9+y1KeXlgXT0iAt8vfoF3zBi8F1wgbarOIBKwhBAiiDRN48iRI+zbt4+9e/eyb98+jvtfU1KD\nxWKhd+/e9O7dm7S0NPr27UuvXr2kcXoHlJur8P33/hIqMzk5tZ/KtFph4EAfgwf7GDLEx4B+HkKO\nHMT8zTeY/rID04EDRgv3KlpqKt5f/ALfiBH4Bg4E+ZmfkeSnKoQQp+jEiRN8+umn7N69m/3799dq\niA7VJVNpaWn06dOHvn370r17d3mBcgeVn28Eqt27jVCVnV23hGrQIB+DBhmBqm9fDUtBDqZvv8X8\nwbeYdu+u7k0dwGIxGqmPGIF3xAj0lJQ2/kaiPUjAEkKIVnA6nXzxxRds3LiRH3/8sdaypKQkBg4c\nyIABAxg4cCC9e/eWkqkO7MSJ6jZUP/5oIiurdqAKD9cZPNjH0KFGoOrTR0N1OTH98APmzd9ievrb\n6pcpV9GTkvBecAHeESPwnXeeVP2dheRfvBBCNJPP52PXrl1s3LiR7du346l6PCwkJITRo0dz4YUX\nMnDgQOLi4tr5TEVDdB2OH1fYs8fEDz+Y+fFHE7m5tav8wsJg8GAvgwf7OPdco4RKrXRj2rsX07Yf\nMP39B6MX9Rrdrevh4fiGDjWe/Dv/fPQuXaQ39bOcBCwhhGiE0+lk9+7dfP311+zYsYOioqLAsiFD\nhjBhwgQuvPBCIiIi2vEsRUPKy+HAARN795rYt09l3z4TpaW1g09EhFFC5W9D1aePhqnSVTtQ7d9f\nK1BhMuEbNAjfeefhPe88tAED5GXKohYJWEIIUYOu6xw9epQdO3bwzTffsGfPHnw1/rB2796dCRMm\nMH78eOkyoYPRNDh+XA0EqX37TGRkqIH+Ov1sNp1zzjHC1JAhPnr21FArXJh++gnTF99jeulHo2F6\nzUClqmhpaXiHDME3eDC+IUNAQrVohAQsIYQAPB4Pa9asYcOGDeTk5ATmq6rKoEGDGD58OCNGjKBX\nr17ybr8OoqQE9u0zsX+/EaYOHFBxOmv/bEwm6NdPY8AAHwMG+Bg40EdSko5aVIhp717UTT8ZwSo9\nvf5ANXQoviFD8A0aJIFKtIgELCHEWe/IkSMsXbqUQ4cOARATE8Pw4cMZPnw45513nryCpgMoKYGD\nB038/LNKerqJgwfVOk/3AcTH6/Tv76N/fx/nnGO0nwo1+1CPHDGq/P75E6a9e1FOnKi9ocmEr39/\nI0wNGYLvnHMkUIlTIgFLCHHW0jSN//znP6xatQqPx0NKSgp33nkn5557Lqpa94+3OP103egm4dAh\nlUOHjCB18KCpTt9TAKGhkJbmqyqd0ujf30d8vA6lpZj27cO0ax+mN34y2k+53bU3tlqNQHXOOfgG\nDJBAJYJOApYQ4qyUk5PDsmXL+P777wGYMmUKs2bNIjw8vJ3P7OxRUQEZGSqHD6scPmzi0CGVI0fU\nOo3QwQhTffoYDdD79vWRlqaRmqph8lWiHjqE6cAB1FXpxvjo0Trb68nJ+AYONALVwIFoPXtKo3Rx\nWknAEkKcVXRdZ/PmzbzwwguUl5djs9mYM2cOo0aNau9TO2P5fMYLkA8fNhqdHzmikpGhkpVVtwE6\nQFSUTq9eGr16VYep7t01VN2HmpGBmp6O6YP9mNLTUQ8frt12CsBsxtevnxGkBg7EN3Agemxsm3xX\nIfwkYAkhzmiappGXl0d2djZZWVns2LGD7du3AzBq1CjmzJmDzWZr57M8M2ia8Z6+I0dUjh5VOXLE\nCFRHj6p4vXXXN5kgNdUIUr17+6rGGnFxOoquoR4/jvrzz5g+PmCEqvR0qKysvRNFQUtNxdevH1q/\nfvjS0tD69AGLpW2+tBANOO0By263RwN/q/r4mMPhOHi6jymEOPvous7x48fZu3cvhw8fJisri+zs\nbLKzswMdgvpZrVZmz57NpEmT5InAVtA0yMtTAuHJH6aOHlXrNHXyS0rS6dnTR48eGj17GkP37pqR\ngyoqjEbohw6hfnXQqPI7fNioQzz52CkpaGlpRpDq3x9fnz4g1bqiA2qLEqyrgGeAA8ADwJ/a4JhC\niDOcy+XiwIED7N27N/BS5dLS0nrXtdlsdO3alZSUFLp27cr48eNJTk5u4zPufLxeyM5WOH7cH6SM\nEHXsWMNBymbT6dlTqwpSPlJTjelA+/GSEkyHD6N+exDTvw+h/vyz8ZqZk6v5AD0xEV+fPkagqiqd\nQp7oFJ1EWwSsblXHuQIIa4PjCSHOQJqmkZ6eHuhR/dChQ2gnNeCJjY1l4MCB9OvXj27dupGSkkJK\nSgphYfKrpzElJXDsmMrx47WHrCy1vtwDGEEqNVULBChj8FXnn8pK1KNHUY8cQd2egenIEdQjR1Dy\n8uruTFXRevRA693bCFR9++Lr1UvClOjUWhWw7Hb7OOBJYIvD4ZhfY/4k4KGqjw85HI6NQCbwHXAE\nmHdqpyuEOJtUVFTw3Xff8fXXX/PVV19RWFgYWGYymUhLSwu8VPmcc84hMTFRqvwaUFICWVkqmZlG\ncKqeVigra/iaJSbqdOtmBCgjUPno3l2rzj6ahpKZienoUdQPDhuBKiMDNTOTeluwh4Tg690brXdv\ntD59jOlevYzHBIU4g7S2BCsUWAxc6J9ht9tVYBEwqWrWR8BG4N/AEkAFlrb6TIUQZyRd1ykpKSE/\nP7/WcPjwYXbt2kVljUbN8fHxjBw5kpEjRzJ48GCsVms7nnnHomlG/1HZ2SrZ2QpZWWrVtBGiTu7h\nvCarFbp2NdpEdetWPe7aVSNwiTUNJS/PKJX6xAhRpqowxUlt3ACjVKp7d7TUVLRevdB69sTXowd6\n164gfYyJs0CrApbD4fjEbrePP2l2P2C/w+FwAdjt9oN2u72fw+E4ANx5iucphOikvF4veXl55OTk\ncOLECXJzcwPTeXl5FBQU1GmEXlNaWhojR47kF7/4BX369DmrS6jcbjhxojpAnTihcuKEEghS9T2p\n52e1QpcuRmjq0sUYunXT6NJFx2bTCVzWykrUzEzUY8dQvzpmjI8dM9pJ1dPoHECPj0fr1Qtfz55G\nVV/PnmipqRASEvyLIEQnEcw2WHFAkd1uf6rqczEQj9G4XQhxhtF1HafTSUFBQZ0hPz+fwsLCQIA6\nua3UySIiIoiPj681JCUlMWzYMOLj49voG7U/XYeSEoWsrOrQlJ1tTGdmqhQVNR4ubTadLl00UlJ0\nUlK0wNCli05MTI0QBVBSYgSnHcerQ9SxY6gnTtRftQfoNhtat25GgOrZMxCoiIwM4lUQ4swQzICV\nD9gwSqsUYDlQT2tGIURn4HK5OH78OFlZWeTl5VFYWEh+fn6tEFV5cp9E9VAUhfj4eJKTk0lKSiIp\nKSkwnZCQQHx8/FlT1adpUFSkkJOjkJur1hrn5Kjk5DT8dB4Y/UYlJ9cNUP7PdS6jy4WalYX6YxZq\nZiZKljFWMzNRiorqP4iqonXtalTvde9uBKqqsTQ6F6L5TiVgnfxfqYNA/xqf+zkcjvRT2L8Q4jRz\nu93k5eVx4sQJjh8/XmvIz89vcvuwsDDi4uICQ3x8PDabjfj4+MC8hIQELGdJp48ej9E/VM3wlJtr\nhKfcXONzY9V4AOHhOikpOsnJ/qq86jCVmKjXbb7kdhshamcWSlV4UquClFLjoYA6rNbaASo11Rh3\n6SKddAoRBK19ivBe4HIgxW63RzscjtscDofPbrcvAv5btdrDQTpHIUQL6bpOaWkphYWFgdKm/Px8\n8vLyao0b6jcKwGw207VrV7p27UpiYmKtEOWfPpve2+evvsvL8w+1w1NOjlGFp+uN7ycqSicpSScx\nUQuMk5ON8JSYqBEVRe2qPF1HKS5GOXECdW82ak6OURKVnW2EqIKChg9mNqN16WKUSHXpgl5zOiFB\nGpsLcRopelO/DdrQhg0b9GHDhrX3aQjRoXk8nkD7ppphyd/uyV+N11jDcT+TyURCQgKJiYl069aN\nbt260b17d7p160ZycjLqWfIHWNOgsNAITgUFKnl5Cvn5RojKz1eqBrXeh+VqMpkgLs4ISomJOklJ\n1cEpKUknIUGj3i65XC7UEyeMEJVdFaJqTDdab2g2G72bd+1qBCh/iOraVUKUEKfZzp07mThxYr2N\nI+VdhEJ0IOXl5RQUFARCU83SJ3+YKi4upjn/MQoPDw+UNMXGxpKQkBBo8+Sfjo6OPqNDlK5DaSkU\nFqoUFCgUFhpDQYHxuaDAqLYrLFQa7FCzpogInfh4Y0hKqg5N/pKo+Hgdk6meDSsrjS4O9uUYQSo7\n2xjn5KBmZ6OUlDT+PSIi0FNS0JKS0FJS0JOTjSDVpQt6UpKEKCE6IAlYQrQxp9NJZmYmmZmZZGVl\nBYbMzExKmvhDC6CqaqBtk39c8+m72NhY4uLizujey30+KCgwSpyKioyAVFSk1BoXFhrzm2rz5Gez\nGcEpIUELhKj4eI2EBJ24OGNcb1t8fxVebi7qwTwjNOXVGOfmNtyg3M9iQUtONoJTcjJaUpJRGpWU\nhJacLE/pCdEJScASIki8Xm+gzVN93Rb4p8vKyhrch8ViqROY/IM/TMXGxmKqt5ik8/P5jHZORUU1\ng5JRPWdU2xlVdkVFSkM9CdQRHq4TF6cTG+sfa4HphAQjRMXH6w23666oMMLTXiMsqbm5RmlUTo4x\nzs2tv6PNmkwmo6+oxEQjSJ1UGqXHxkoplBBnGAlYQjTB7XZTVFREQUEBxcXFtUJUzeni4uJm7S8k\nJIQuXbrQtWvXwNg/HRcXd8Z1pOn1QnFxdelSUZFCcbFR8lSz1Km4WKGkpOlG4mA0ArfZ9EDpks1m\nBCj/EBOjBaYb7AFC11FKSlDy81GO5qMWFBjTeXnV0wUFKI08CBDYVVQUekICWmJi9TgxES0hAT0p\nCT0uTgKUEGcZCVjirOXvKDM3N5e8vLzA2D8UFhZSWFhIeXl5s/anqio2m61Wu6eaT9z5hzOh3ZPH\nQ1VIqhuaalbT+UNTcykKREcbPYv7h9jYulV1cXE65sZ+e1VWouTnox6sCkr5+bVCk5qXZzx915z6\nQ5OpOjglJaEnJBjhqUaIqr/luhDibCYBS5xx3G534Im6oqIiiouLKS4urjVdXFxMfn4+7saezqpi\nNpsD7ZpsNhs2my0Qnvzz/cs6c3DyeKgTjgoLa5cylZQY04291+5kqlo3NNlsGjExRniqOT8mpoFG\n4mC8C6+kBKWwEOVYoTEuKkItrJqu+qwUFqI4nc06Nz0yEj0uzqi+i4+vnq4a6wkJ6NHRUvokhGgx\nCVii06jZPUHN17H42zf5q+uaW+IEYLVaSUxMDDxV55/29/tks9mIjIzslNV2Hg+1Spj8AclfqlRz\nKC5Wcbmav2+TyejPyaiOqw5NNUud/OPo6Ho6x/TTdSgvRyksRM0sQtlTVCss1QpPJSU061G/qhPU\n4+LqhqaEhOrpuDgarj8UQohTIwFLtCt/aCoqKqKkpCRQ0lRaWhooafKHqOZ2T2CxWGqVKsXExATG\n/mn/584UntxuAoGotLR2WKoZmvztnVpSygRGaIqOrhmO6gYmf5CKjGygUEfXweUynqorKUHZV2SM\nS0pQiotRi4uNZTWGJhuI19x9dDS6zYYeG4seG4sWG1vrsx4bi2az0fAJCiFE25CAJU4bXdcpKyuj\noKCA3NxccnJyyMnJITc3NzAUFBQ0KzRBdRunk5+uq9nWKTY2lqioqE4RmtxuajXwLi5Wa1XF+UOU\nf7oZr/2rpWYpkz8wxcQYJUr+ISpKD8yLiKgnk2gaOJ0opaXGkFWEsi94gQmA0FCjRCk2Fj0mpuHw\nFBMjr3ARQnQaErBEi2maRllZWa12Tf5SJv/g7yyzqZcB+/t0stlsREdHB0qZ/NPR0dG12jt15O4J\nPB7qlC7VbADuH4x5jb/Utz4WC4FQFB2t1wlLMTHGMn9JU1RUjao5XTe6G/AHJf9wuASlrMx4Uq60\n1AhOVZ+V0lKUsjKa3R+CX0iIEYyio9GqxnpMTPX4pEGq6YQQZyIJWGc5n89HeXl5YCgtLaWkpKTW\nUFxcHJj2V+X5mtkWxmq1Bvp1SkxMJCkpKTAkJiYSHx+PudHHwdpHVU1XrWDkD03FxWqddkylpUqL\n2jCBEZjqa/QdE1MdnvxhKjpaJzQUFK/HCD1OpxGEyspQnE5jyHJCurN2QKoxtLhkyX8tIiIgMhI9\nKkoCkxBCNFPH+8smWsXj8dQKQqWlpYGwVHPsdDoDg8vlatZTdPWJiIggNjY2UNJU82k6f6CKi4sj\nIiIiyN+0dXw+AiVL1WMoLlZrBKfaYaqlecRfJVez6s3/ZFzgKbkoHzGWMmLNpURoZajlRjiiZljK\ndKIccFYHKX8VndPZ6pAEgMVi9NfU2BAdjR4VBf7PkZE03h+CEEKI+shvzg7K336pqKgo0B+TvzG4\nvxSpZumSq6XFJ1VUVSUsLIzw8HDCw8OJiooiOjq6wcHfONzSjm1hqh48o6xMoazMCEwnByR/SPK3\nZ2ppg2+A0FCM0qRojZhILzHhlcSEuogJdWMLLSfGVGYMainRFBPhLUF1lYPbbYSiMhdKTrnR6Nvp\nRHG5oKLi1L68yWR0LRARYYSfiAhj2j/459UTnqRkSQgh2o4ErDag6zrl5eV1+mQqKyujrKyM0tLS\nwLT/c0lJCZ4WlFaYTKZa4ejkaf8QGRlJZGRkIFCFhYW1a4Pw+p6MKy2tDk4lJUpVkCIw3+ls4sW8\nmm60G6oxKLqPaGsl0dYKokIqiAlxEWMpJ9rsrApKpdjUEmIpIkYrwOYrIKyi2AhH+eXN7x6gKYqC\nHh5uhCB/UPJPR0ZCeHj1Z39gqrGeUU/Y8RvwCyHE2U4C1kk0TaOyspLKykq8Xi9ut7tWGyWn0xmY\ndrlceDyewLoejwePxxOYdjqdgQbgLQlLfmFhYcTGxgY6tvQP/gbhNRuCR0REtFtQ8pco+UuKyssV\nyssJTBvjqiBVrFBc4KO4EIqLocIF6BpoOormq5o2Ptea1jQUvTowhasVRKnlRJnKiVLKiFWLiKaY\nWL2QGLWUWHMp0aYybOYybCFlRJnKURUdPBhD8/qhrGaxoIeHG+EoLKz2dNVnwsNrT4eHo1utRjDy\nz7daJSAJIcRZoMMFrFdffRWz2YzZbMZkMqGqKmazGVVV8Xq9dQZ/qPH5fHWW+Xw+PB4PmqYFPnu9\n3lqf/etUVlYG9nM6hIaGBvpfqtkHU81SpaioKCIiIoiMjCQmJgbr6ajS0TSjHY/Hg1I1prIyMK1X\neHCWapSV6DhLq4eyMoUyp0pJmUpRqZniMgvFTjOFZaEUlYfg9SnVJUcnhSSlRkiC2l0yWBUvMeYy\nYkxOok1Oos3GOMpUTpTZSYzZmI40lRvzzeVEqi4saiM/J5MJ3WoFqxU9LAysXdCtVrz+eTXHYWHo\noaFV61nRQ0ON0qWaYSksTLoHEEII0SIdLmCtXbu2vU8Bi9lMiMWCxWIh1GIhPCyM8LAwIsLCCLda\nA+OwkBBCTCZjfZMJs6piVtXAdFhICHGRkdgiIgizWIz3nvl8KD6fEWx8PuOz1wsFBZCTU/3Z56te\n3+s1pr1eoyTH46merrnM58NXqVFWYaHUZabMbaHMZaaswkKZ20JpZQhOj5UyXxjlWihOXxiuqrFT\ns+LyWSnXwtBpbgmLBrgAF+FqBdEmJ5EmFxEmF+FmNxEmNxGqi0iTi3CTm2iTE5vFSYzVTUyEh5hw\nD2ERCkqIxQg7ISFGwPGPQ8PRQ2xGtVjVPD0sDF9oqBGWqsIRYWFGSVHVtIQhIYQQ7a3DBaxbfD58\nuo5X0/BqGpqu49M0fLqORVEwKwohVWOzomBRFExVY7OiYAZjHmBRVcxV02ZArVpuqhrMioJZ17Fo\nGiFACGDW9erQ0sqG46dC16FCD6HcF0qZL4wyLZwyX7gxHRiiKK2aV+qLqBqHU+oLx6WFNn0QRQFF\nBVUx2gT5p83G/IiQSiJDPUSEeoi0eogM8xEZ5iEyTCM6wostyktMtEZ0lI/YGKN7gdAIE4SGooda\nIST6pKAUih4SYgQli6VWFVnbX2EhhBDi9OtwAeuGYHckWbOX8Ob0GK4oRnfW/rHJhK6qxnTVoCkm\n3Hoo5XoYFUoolYTgxYIXM5W6BY8SggczlVVByaWF4vKFUq5Zq4ZQyn2huH3GuNwbgttnweUNodxr\nQdOrjq8ooFBjWgGLAiFK7Xn4g5KCaoLICJ3ICJ2ISJ3IaIiMUoiIVoiMVomIVjHaUuuEhemEhxs9\nePunw8Nb94YRb8s3EUIIIc5YHS5gHf/L8kAVlY4RGsDIRj5dxacpxuCrGteYpwN61Wej2Y+Cplev\n7/EqeDUFj0fB61Pw+BS8XhWPzxgqPSqVXhWPx3gticcDFRUKLpfRiWR5uTHtdjcvqzVKrRrqqc2y\nWIwAFBmpExFhBCBjXD0vKgoiI/WTBo2wsJoBqWZVnw74qgYhhBBCnE4dLmDd9KeB7X0KzWI099Gr\nar10LBZjbDYb/TKGhBjzwsJ0wsJOHhslRVZr3emwMOnXUQghhOjsOtyfcputdtFQoBYMI3iYTDom\nU6D2rmow5vnX9S8zavSM97H5g48/BFksYDYb24WEGPNDQmpP+8f+EOQPR2Fhxv6FEEIIIerT4QLW\n66+3tIMiIYQQQoiOpRXNmYUQQgghRGMkYAkhhBBCBJkELCGEEEKIIJOAJYQQQggRZBKwhBBCCCGC\nTAKWEEIIIUSQScASQgghhAgyCVhCCCGEEEHWJgHLbrc/brfbl7bFsYQQQggh2ltblWAtoPabh4UQ\nQgghzlinJWDZ7fa/2e32Z+12eziAw+HQTsdxhBBCCCE6oma9i9But48DngS2OBIILf0AACAASURB\nVByO+TXmTwIeqvr4kMPh2AjgcDjmBftEhRBCCCE6i+aWYIUCi2vOsNvtKrAImFI1PGy32+tUA9rt\ndsVuty8BLqwKZEIIIYQQZ7RmlWA5HI5P7Hb7+JNm9wP2OxwOF4Ddbj8IpAEHTtpWx2iDJYQQQghx\nVmhWwGpAHFBkt9ufqvpcDMRzUsBqqZ07d57K5kIIIYQQ7e5UAlY+YAPuxHhCcDmQdyonM3HiRHnS\nUAghhBCdXkueIjw5/BwE+tf43M/hcKSf+ikJIYQQQnRuzQpYdrv9XuBhYLrdbn8BwOFw+DAauf8X\n+LhquRBCCCHEWU/Rdb29z0EIIYQQ4owi7yIUQgghhAiyU2nk3ioNdU56quuKai28xq8CAwA38KrD\n4Xjt9J9h59ZQx7sNrCv3cCu08Bq/itzDLWK321diXDMV+I3D4fi5kXXlHm6FFl7jV5F7uMXsdvtf\ngAsBDfhtR7uP27QEq7mdk7Z0XVGtFddNB65zOBwT5B91s9XpeLc+cg+fkmZd4ypyD7eQw+G43eFw\nTMC4PxsMsHIPt15zr3EVuYdbweFw/MnhcFyCEZzubWi99rqP27qKMNA5aVUHpf7OSU91XVGtNddN\nfmG2gMPh+AQoaMaqcg+3UguusZ/cw61TClQ2slzu4VPX1DX2k3u49UYDPzWyvF3u47auImxJ56Sn\npSPTs0BLr1sp8Ibdbi8A7pGuNoJK7uG2Ifdw680CljWyXO7hU9fUNQa5h1vNbrd/CiQA4xpZrV3u\n47YOWC3pnDToHZmeJVp03RwOx+8B7Hb7+cATwNVtcI5nC7mH24Dcw61jt9unA/scDsfeRlaTe/gU\nNPMayz18ChwOx0V2u30k8DowtYHV2uU+busqwpZ0TiodmbZOa6+bG/CcnlM6IzWnOF/u4VPT0ioT\nuYebyW63DwfGOxyOp5tYVe7hVmrBNa5J7uHWyabxAqN2uY/btATL4XD47Ha7v3NSqNE5qd1u/xVQ\n7nA4PmhqXdGwllzjqnn/ArpgFFHPacNT7bSqOt69HEix2+3RDofjtqr5cg8HSXOvcdU8uYdb7m3g\nqN1u3wR8X6MERe7h4GnWNa6aJ/dwK9jt9rcwqgcrgbtqzO8Q97F0NCqEEEIIEWTS0agQQgghRJBJ\nwBJCCCGECDIJWEIIIYQQQSYBSwghhBAiyCRgCSGEEEIEmQQsIYQQQoggk4AlhBBCCBFkErCEEEII\nIYJMApYQQgghRJBJwBJCCCGECDIJWEIIIYQQQSYBSwghhBAiyCRgCSGEEEIEmQQsIYQQQoggk4Al\nhBBCCBFkErCEEEIIIYJMApYQQgghRJBJwBJCCCGECDIJWEIIIYQQQSYBSwghhBAiyCRgCSGEEEIE\nmQQsIYQQQoggk4AlhBBCCBFkErCEEEIIIYJMApYQQgghRJBJwBJCCCGECDIJWEIIIYQQQSYBSwgh\nhBAiyCRgCSGEEEIEmQQsIYQQQoggk4AlhBBCCBFkErCEEEIIIYJMApYQQgghRJBJwBJCCCGECDIJ\nWEIIIYQQQSYBSwghhBAiyCRgCSGEEEIEmQQsIYQQQoggk4AlhBBCCBFkErCEEEIIIYJMApYQQggh\nRJBJwBJCCCGECDIJWEIIIYQQQSYBSwghhBAiyCRgCSGEEEIEmQQsIYQQQoggk4AlhBBCCBFkErCE\nEEIIIYJMApYQQgghRJBJwBJCCCGECDIJWEIIIYQQQSYBSwghhBAiyCRgCSGEEEIEmQQsIYQQQogg\nk4AlhBBCCBFkErCEEEIIIYJMApYQQgghRJBJwBJCCCGECDIJWEIIIYQQQSYBSwghhBAiyCRgCSGE\nEEIEmQQsIYQQQoggk4AlhBBCCBFkErCEEEIIIYLM3BYHsdvtccCDQBfgTofDkd8WxxVCCCGEaA+K\nruttdjC73T4NKHU4HFva7KBCCCGEEG2srasILwC2t/ExhRBCCCHaVKurCO12+zjgSWCLw+GYX2P+\nJOChqo8PORyOjVXzrwA2OBwO9ymcrxBCCCFEh3cqbbBCgcXAhf4ZdrtdBRYBk6pmfWS32zcBacBC\n4DO73e52OBw7T+G4QgghhBAdWqsDlsPh+MRut48/aXY/YL/D4XAB2O32g0Caw+E4AIxrap8bNmxo\nuwZhQgghhBCnaOLEiUp984P9FGEcUGS325+q+lwMxAMHmruDYcOGBfmUhBBCCCFaRzl+HOuLL2La\ntQsArW9fyhcvBquVnTsbrpALdsDKB2zAnYACLAfygnwMIYQQQojTzrx1K9anngKPBz0igsqbbsJz\n2WWgNv2M4KkGrJOLxQ4C/Wt87udwONJP8RhCCCGEEG3K8uGHhL7wAug63gkTqJg1Cz0mptnbt7qb\nBrvdfi/wMDDdbre/AOBwOHwYjdz/C3xctVwIIYQQonPQdULeeIPQlStB16m4+Wbcd9/donAFbdzR\naFM2bNigSxssIYQQQrSXkNWrCXnrLVBV3HPm4J08ucF1d+7c2WaN3E+bvLw8Kisr2/s0hBCnWUJC\nAiEhIe19GkKIs5Bl/frqcHXvvXjHjGn1vjpFwCorK0NRFLp27drepyKEOI00TeP48eMkJydLyBJC\ntCnTtm1GmyvAfeedpxSuoO1fldMqxcXFxMXFtfdpCCFOM1VV6datG3l58vCxEKLtqHv3EvbEE6Bp\nVF5/Pd4pU059n0E4r9NOURQUpd4qTiHEGUZtxuPPQggRLEphIWGLF4PHg2fKFCpnzgzKfuU3mRBC\nCCHOTl4v1sceQyksxDdoEBW33w5BKtCRgCWEEEKIs1LoK69g2rMHPTYW9733gjl4TdMlYHVSP/zw\nA//973+Dus/bbruNsWPHcv3115/SfmbOnMnnn38epLNqXHp6OosXL6532YoVK3C5XG1yHkIIIToX\n85YtWN5/H0wmXAsWoMfGBnX/ErA6qd27d/PJJ58EdZ8vvPACjz322Cnvpy3bzKWlpbFw4cJ6l73w\nwgsSsIQQQtShHjqE9dlnAaiYPRvtnHOCfoxO0U1DYyJnzAjavsr+858Wb3PkyBHuuece3G435eXl\nzJ07l+nTpwOwZMkSjh49Sk5ODtnZ2Vx44YW1AozD4eAf//gHiqIwbNgw/vrXvwaWHT16lPvvv5/c\n3Fx0Xed//ud/uPnmmwH4+9//zosvvojT6eT7779n/Pjx3HvvvYFtzzvvPObOncuqVatwu92sXr2a\nHj16ALB48WJ27NhBXl4eKSkpvPbaa1it1sC2rel4tqCggNtuu42SkhJ69epFcXFxrf009j1TU1P5\n85//zLp16zh8+DDPP/88o0aNqvfazps3j2nTpgHgdru55pprKCkpITU1lTfffDOwT7fbzdVXX01O\nTg4zZ87EbDbz0ksv0a1bNz777DOeeeYZ3n77bcAIqvPmzePjjz9u8fcWQgjRCZWWYl2yBCor8Vxy\nCZ7LLz8th+n0Aau9vfjii0yaNIk777yzzjJFUcjPz+df//oXADNmzODjjz9mypQp/PTTT6xatYp1\n69ZhNpu59957eeutt7juuuvw+XzccMMNPPTQQ0ycOLHOfm+99VYiIiL47rvvWLJkSb3H3b9/f71V\niLNnzw6U+Nx444188MEHXHvttad0DZYsWcKwYcNYuHAhJ06cYMqUKYESrMa+J0BFRQWJiYmsWbOG\nN954g1deeSUQsBq7tlarlQ8//JDPP/+c5557rs6y9evXc/755/PWW28RW6PYd9y4ccyfP5/MzEy6\ndu3KG2+8waxZs07p+wshhOgkNA3rU0+hZmWh9elDxR13BK1R+8k6fcBqTalTMF155ZXMmzePjIwM\npk2bxtixY2stHzduHCaTCTAC1ldffcWUKVP49NNPOXbsGNdccw0A5eXl2Gw2AA4cOIDVaq03XPnp\nut5oadPcuXPrnW+z2di6dSvp6ek4nU6ys7Nb9H3rs23bNlatWgVAcnIygwYNCixr7HuCEYamTp0K\nQI8ePSguLg4sa+raQutK3G688Ubeeust5syZwyeffMKiRYtavA8hhBCdT8hbb2HesQM9KgrXggUQ\nGnrajtXpA1Z7GzlyJJs3b2b79u2sWLGCdevW1SpVqhkANE0L9E5tsVi44ooralWX1aRpWqPHbU0b\nJ6fTyfTp07n88ssZOXIkffv2bVVAOZnJZGpwP019z8Y0dW1b63/+53+YPn06ffr0YfLkyYSexn9g\nQgghOgbT118T8uaboCi4581DT0k5rceTRu6nSNM0VFVlzJgx3HXXXezYsSOwTNd11q9fT2VlJZWV\nlbzzzjtcdNFFAEycOJH33nuPQ4cO1VofoF+/flRUVPD+++83eNzQ0FByc3MD59Ac6enpWCwW5s+f\nz/nnn8/u3buDErDGjh3LO++8A8DPP//M7t27A8sa+55NaezaNkdoaCg5OTl1jhkXF8egQYN46KGH\n+PWvf92ifQohhOh8lMxMrEuXAlB54434LrjgtB9TSrBO0Zo1a3j55ZcD1YCPP/54YJmiKPTr148b\nb7yRzMxMpk6dyujRowHo2bMny5Yt47bbbguUAD388MOMHj0ak8nE6tWrue+++3j++edRVZUrr7yS\n2267LbDviy++mGXLlnHZZZcRFRXFa6+9Rnh4eOC49Rk6dCipqamMGzeObt26MXbs2EBIq3nOX331\nFVOnTuWRRx5h+PDhTV6DefPmMXv2bCZNmkTv3r3p3bt3YFlj3/NkJz992Ni1bWibmmbNmsUNN9xA\namoqV199deAhAQC73U5WVhYDBgxo8vsJIYToxNxuwhYvRnE68Y4aReUptjtuLiUYJRjBsmHDBn3Y\nsGF15vsbJHc2jz32GBEREdx1113tfSriJAsWLODiiy/msssua+9TEfXorP/mhRAdjK5jffJJzJ9+\nitatG+V/+xtERARt9zt37mTixIn1/i9fqghPM3mHYsfyzjvvcHnVI7kSroQQ4sxm+fe/MX/6KVit\nuBcuDGq4aopUEZ5GNfumEh3Dtddee8rdUgghhOj4TDt3Evr66wC477kHrao/yLYiJVhCCCGEOKMo\nmZlYn3gCNI3KmTPxjhnT5ucgAUsIIYQQZw6Xi7BHH61u1D5zZruchgQsIYQQQpwZNA3r00+jZmSg\npabivvtuUNsn6kjAEkIIIcQZIeTttzF/+SV6RASuNm7UfjIJWEIIIYTo9EzbtxOyerXRU/vcuejd\nu7fr+UjAOs1KSkr4xz/+cVqPkZqaGvR97tq1ixkzZgR9v8HU0LXdunUr119/fVCOcTqubWukp6ez\nePHiVm/fGX6eQgjRWurPPxNWs6f2ESOCfgyfD/bvb35skoB1mhUVFfHyyy+f1mOcrX1tnU3XNi0t\njYULF7b3aQghRIej5OYS9sgj4HLhvegiKv/P/wnavjUNdu82sXx5KL/+dQTz54eTn9+8vwvSD9Yp\nOnLkCPfccw9ut5vy8nLmzp3L9OnTAfjqq6+47777yMjI4IorriAuLo5//vOfgW0XL17Mjh07yMvL\nIyUlhddeew2r1QoYJSd//vOfWbduHYcPH+b5559n1KhRAHz33Xf84Q9/ICoqitGjR9d6z15paSkL\nFiwgKyuLY8eOMWPGDP70pz8Fls+ZM4c+ffqwadMm3G43d9xxR6BfqDfffJNnnnmGlJQUzjvvvGZf\nA7fbzf/+7//y008/oes648eP54EHHgBg+vTpjB49mrVr13Lffffx6quv0r9/f5588kkAtmzZwuLF\ni1EUhejoaJ588km6VxXrHjlyhPnz51NaWoqmaTzwwAOMHTu2WdfW7XbzwAMP8N1331FWVsaaNWuI\ni4sD4Ntvv+Whhx7C5/MRGxvL008/TXx8fJPXtjFbt27l0UcfpVevXuzfv5+YmBj+/ve/Exsb2+Qx\nMzIymDlzJtOmTWPjxo1ERETw3nvvBb7HNddcQ0lJCampqbz55pu1jrt8+XLWrl2LqqoMGTKERx99\nNHAPNfbzbOzalpaWcuutt1JWVobL5cJms3HzzTdz1VVXAY3fQ++++y6rV68ObPvSSy/Rr18/tm7d\nytKlSwkPD8fn83HJJZfw/PPP8/bbb9OvX79mXWMhhKijrIywRYtQCgrwDRmC+w9/gFP8j7GmwZ49\nJrZuNfPFF2aKiqr317WrRk6OQnx8038bOv2rcoJZ7fGf//ynxdvcf//9dOvWjTvvvLPe5UePHmXm\nzJl8/vnndZbl5eWRkJAAwI033sjVV18d+EOVlJTEK6+8wtSpU3njjTf49NNPWblyJQAXXnghjz32\nGOPGjWPbtm3MmDEj8FJjgMLCQmJjY3G5XIwYMYINGzaQUvXW8Dlz5nD06FFWr15NVFRUYJvMzEwm\nT57Mli1bSEhI4KmnnmLTpk3NuiYffvghq1evZvXq1XWWzZgxg+uuu47S0lI++OADVq1axahRo9i3\nbx/5+flMnDiR9evX06VLFz744AOWL1/OBx98ABg9rc+dO5fJkydz9OhRpk2bxubNmwOhpaFru3Xr\nVm6//XbWrl1L//79mTNnDqNHj+amm26isrKSiRMn8vbbb5OSksJ7773HJ598wrPPPtusa9uQrVu3\nMmfOHD7++GOSk5N55JFH8Hq9PPLII00eMyMjg1GjRrFixYpAiDnZ559/znPPPVcrYG3atIknnniC\n9957D4vFwsKFC4mKiuK+++5r8udZ37XdsmULNpuN5cuXU1JSwoIFC3jiiSeorKzk/vvvDxy3oXsI\noKCgIBBkV6xYwf79+3nqqafYunUr99xzD5999hmDBg3itddeY/369aSlpTFr1qw631delSOEaJLH\nQ9iiRZh270ZLTaV8yRI46XdSSxQUKLzzTghbt5opLKwOVV26aPzyl17GjvXSu7dWK7/Jq3JOoyuv\nvJJ//etfLFiwgK1bt9ZZ3liAtdlsbN26lVdffRWn00l2dnZgmdVqZerUqQD06NGD4uJiwKgWKy0t\nZdy4cQCMHj06UGLhZzKZ+Oijj/jnP/9JSEhInYAwe/bsOn8Yd+7cyfjx4wOBb8KECc29BIwaNYqC\nggJuu+021q5dS0VFRa3lgwcPJiYmhsGDB2Oz2XC5XAB8/fXXjB49mi5dugAwdepUDh8+jNPppLS0\nlGPHjjF58mTAKNEbNWoUX3/9dWC/jV3boUOH0r9/f6D29Ttw4ADHjx/nt7/9LTNmzOCll14iMzMT\naN61bcygQYNITk4GjB7jv/rqqyaP6denT58Gw1VD33Xjxo1cf/31WCwWAG699VY2bNgANP7zbOja\n+s83PDw8cL0KCwsD36mm+u4hgLi4OL7//nv+9a9/kZ6ezokTJwLL0tLSsFqtREdHB+6J8vLyBr+z\nEEI0SNexPvccpt270W02XA8+2Opw5fHA2rUW7rgjgvfft1BYqJCcrHPNNZUsXVrOypXl3HxzJX36\naC0qHOv0VYStKXUKppEjR7J582a2b9/OihUrWLduHUuWLGlyO6fTyfTp07n88ssZOXIkffv2bVZ1\nlNpEfx4//vgjt99+O7NmzWLo0KHEx8fX2W99xzGbzbXmt6RkMz4+nvXr17Nv3z7efvttli1bxpYt\nW+qsd/I+FUVB07Q66/nbPdV33qfaJspkMtGjR49675umrm1LaJpGSEhIk8cMxnFqTvuvT1M/z8au\n7U033cSkSZOYPHky559/Pr/+9a/rHLeh+2POnDkAXHXVVZx33nl1gqQQQgRDyOrVmDdtAqsV14MP\notfzH8Hm2LXLxEsvhXLsmPH7f+RIL3Z7Jf36tSxM1UdKsE6RpmmoqsqYMWO466672LFjR63loaGh\nFBYWBv4Q+v8wpaenY7FYmD9/Pueffz67d+9uVqiJjo4mKSmJbdu2AfDRRx/VKgXYsmULU6ZM4Te/\n+Q3R0dFkZGQ0a78jRozgyy+/pKioCF3XA22AmkPXdXRdZ8CAAdx9991kZ2fjdDqb3O4Xv/gF27dv\n59ixY4DRfqdv376Eh4cTFRVFz549Wb9+PQCHDx9m+/btjBw5MrB9Q9e2Mf369aOiooJ169bVOn9o\n+to2ZefOnRw9ehSA1atXc9FFFzV5zFMxadIk3nzzzUCJ4UsvvRQolWrs59nUtV21ahWTJ0/mv//9\nL0888QRmc/P/H7Z+/XqefPJJJk6cyHfffReU7ymEEDWZP/6YEIcDVBXX//4vWlpai/eRk6OweLGV\nhx4K49gxlS5dNB580MWf/uSmf/9TD1dwBpRgtbc1a9bw8ssvYzKZAHj88cdrLU9OTubCCy9k/Pjx\nJCYmcv/99zN8+HCGDh1Kamoq48aNo1u3bowdO5bc3Nx6j6EoSq2Sm2XLlvH73/+ekJAQxo0bR3h4\neGDZNddcw4033shnn31Gv379GDNmTJ0qwvpKgRISErjvvvuYOnUqsbGxjBgxotmlRfv37+euu+7C\nYrFQWVnJokWLiKinc7eT9xcXF8ezzz7LLbfcgqIoxMTEsHz58sDylStXMm/ePJYtW4amaaxYsYKY\nmJjA8oau7cnXq+axTSYTq1evZsGCBTz77LOoqsrVV1/Nb3/72yavbWMURWHAgAEsXryY/fv3061b\nNx588MFmHbO+a1Pf/k9eZ/z48ezZs4epU6eiKApDhw7l7rvvBpr+eTZ2bXv16sXTTz8dqPKOjo5m\n/vz5DB8+vMnznTt3buCevvzyy/n222/rbFNz247ylKYQonMwbduGdcUKACruuKPF3TFUVMC//x3C\n22+H4PFAaChcd10FV17poaq1RdB0+kbuQnQEW7du5fnnn6/zlF9n9Oijj5KWlobdbgfggQceIDQ0\ntNbTqKeb/JsXQpzM9N13hC1aBF4vlb/6FZU33dSi7dPTVZYutQaqA8eN8/Kb31SQkND6HNRYI3cp\nwRIiCOorYeqsBg0axHPPPcfrr7+Oz+fj3HPP5d57723v0xJCnMXUn34i7K9/Ba8Xz9SpVN54Y7O3\n1TR4550Q3ngjBJ8PunfXuOOOCoYO9Z3GM5aAJURQ/PKXv+SXv/xle59GUFx11VWNPtEohBBtSU1P\nNzoSdbvxXHIJFbNnN7uvqxMnFJ56ysqePUYznmnTPPzf/1tBaOjpPGODBCwhhBBCdEjq/v2EPfQQ\nitOJd/RoKn73O2jGE9+6Dps3m3nhhVDKyxVsNp0//MHN8OGnt9SqJglYQgghhOhw1L17CXv4YZTy\ncryjR+OePx+qHihrTGkprFxp5bPPjIgzapSX3/3OTXT06T7j2iRgCSGEEKJDUffsIXzRIuP9ghde\niHvePGhGlzF79qj87W9h5OUpWK0we7abSZO8Qel2oaUkYAkhhBCiwzD9+KPxtKDbjXfcONx//GOT\nJVe6Du+9Z+G110Lx+WDAAB/33OOma9f26ylBApYQQgghOgTT998bDdorKvCOH4/77rubDFdlZbBs\nmZXt241Ic/XVldx0U2VzCrxOKwlYQgghhGh3pl27jK4YKiuNpwV///smG7Snp6s8/riV7GyViAij\nIfvo0W3XkL0x8qqcIDh06BDx8fGsWbOm1vwlS5ZwwQUXcMUVVzBhwgQWLlzY4V8d8uGHH7Jv3746\n86dPn16rV+7WevbZZ3nsscdOeT/B8Nhjj3HgwIFWbz9z5kw+//zzIJ6REEKcncwbNxolV5WVeCZN\najJc6Tr8v/9n4d57w8nOVunTR2Pp0vIOE65AAlZQ/Pvf/+aqq67i3XffrTVfURRuvfVWPvzwQzZt\n2sSBAwf45JNP2uksm+eDDz6oN2AFqxPNjtQZ57333ku/fv1avf2Z1LmoEEK0C13HsmYN1qefBp+P\nymuuoeKuuxoNVy4XLF1qZfnyUDweuPRSD48/Xk6XLh2rAKPTVxHOmBEZtH395z9lrdpu3bp1vPHG\nG1x11VWUlJQQXeNZUH+JVVFREQUFBXTv3r1Z+9y4cSOPP/44qqridDpZvXo13bt3Z+vWrSxdupTw\n8HB8Ph+XXHIJzz//PG+//Tb9+vWjvLychQsXsnfvXnw+H3a7vdY775YvX87atWtRVZUhQ4bw6KOP\nYrVaAfj973/Phg0b+Oabb1i5ciW/+93vuPzyywPbbtu2jccff5z09HRuvfXWwH59Ph+LFi1ix44d\neL1ebrnlFq677rrAdgsWLOCLL76gS5cuJCQk0KNHj2Zdg+nTpzNq1Ci2b99Obm4uf/jDH7j++uub\ndcw5c+bQp08fNm3ahNvt5o477uDaa68F4OWXX+add95hz549vPvuu5x//vmB7Y4cOcL8+fMpLS1F\n0zQeeOABxo4dC0BBQQG33XYbJSUl9OrVi+Li4lolko1d27Vr1/Lcc88F3lnZpUsXXn/9dQAyMjKY\nOXMm06ZNY+PGjURERARezlxaWsqCBQvIysri2LFjzJgxI/DKmunTpzN69GjWrl3Lfffdx6uvvkr/\n/v158sknm3V9hRCiXWkaoS++iOXDD0FRqLjlFjwzZjS6SUaGymOPWTl6VMVqhTvvdHPxxd42OuGW\n6fQBq70dOHCAmJgYUlJSmDZtGuvXrw/8odd1nVdeeYU1a9agaRp//etfOeecc5q130ceeYRnn32W\noUOH1ll29OhRPvvsMwYNGsSdd97JFVdcEXi589KlS7HZbHz00Ue43W5mzJjBwIEDueiii9i0aRPr\n1q1j/fr1WCwWFi5cyNKlS7nvvvsAeOaZZ5gzZw6XXXYZ06dPr3PczMxM3njjDTIyMrjiiisCAev1\n119HVVU+/PBDKioqAn/4e/bsyXvvvcdPP/3E5s2b0XWdG264gZ49ezbrGiiKQnh4OO+//z65ubmM\nHz+eSy+9lLi4uEaP6bdlyxbefPNNoqKiau33lltu4ZZbbmHGjBl1SqBuu+025s6dy+TJkzl69CjT\npk1jy5Yt2Gw2lixZwrBhw1i4cCEnTpxgypQpge0bu7a6rvPggw+ybdu2wEuZP/jgg1rHPXToEIMG\nDQr8LPyioqL4y1/+QmxsLC6XixEjRnDrrbeSkpKCoij06tWL2bNn8+qrSgAjvAAAIABJREFUr7Jq\n1SpGjRolAUsI0fFVVGBduhTzl1+C2Yz7j3/EW/Wf2YZ88omZlSutVFZCaqrGvfe66dFDa6MTbrlO\nH7BaW+oULO+++y4ZGRlMmTIFt9vNDz/8EAhYiqIwa9Yspk2bxuWXX97scAVw8803c/fddzNlyhSu\nvvpq+vfvH1iWlpaG1WolOjqawYMH88UXX+ByuQCj5Ovll18GwGq1csMNN/DJJ59w0UUXsWHDBq6/\n/nosVa8M95dCnfxHvaF2Yv4SoB49elBSUhKYv2nTJjIyMphR9T8Pt9vN/v376dmzJ9u2bcNut6NW\nFfeOHTsWp9PZ7OswceJEABITExkxYgS7d+/m4osvbvSYfrNnz64TrhpTWlrKsWPHmDx5MgCpqamM\nGjWKr776iilTprBt2zZWrVoFQHJyMoMGDQps29i1VRSFkJAQysrKUBSFyMhIQkJCah27T58+Db6e\nxmQy8dFHH5GRkUFISAg5OTmkpKQAMHjwYH766ScGDx6MzWYL3AdCCNFhlZQQ9uijmPbsQY+IwH3/\n/fiGDGlwdbcbVq4MZeNG4/frJZd4uP32CqoqCDqsTh+w2tv777/Phg0bsNlsgPFOuprVhLqu07Nn\nT2666SYefPBBli9f3qz9zpo1i5kzZ7JhwwZmz57N3LlzA2GiKZpWneh1XQ+EG0VRai3TNK3eNkQN\ntStqKHiZzWYWLFjAZZddVmeZyWSqtV1LG/mfvK0/mDR2zNYeq75tal6jk79LTU1d20WLFjFhwgQG\nDhzIypUrm30+P/74I7fffjuzZs1i6NChxMfH13sOHf3hCSGEAFAzMrD+9a+oWVno8fG4Hn4YrZFa\njZpVgiEhcPvtRsehjfH5fLhcLlwuF263m/LyciorK6moqKCyshK3243H48HtdlNZWUllZSUejwev\n14vH4wlM+z9rmoamafh8vsC0f5g5c2aD59EmActutz8OmB0Oxx/b4nhtZe/evURGRgbCFcCECRN4\n//33ueGGG2qte/fddzNmzBi+/PJLxowZ0+S+fT4f4eHhTJ8+nYMHD7Jz584GA5au64E/sBMnTuSV\nV17hL3/5C+Xl5fzzn//k4YcfBmDSpEksXryYmTNnEhoayksvvRQorfGzWq3k5uYCRkhQm/HOp6lT\np/LMM88wduxYIiMj0XU9EC7GjRvHSy+9xA033IDT6WTDhg3N+v5+/jZSx44dY9euXZx77rlNHrO1\noqKi6NmzJ+vXr+fyyy/n8OHDfPXVV4Eqt7Fjx/LOO+8wd+5cfv75Z3bv3h3YtrFr6/F4ePLJJ9m6\ndSvx8fEtOqctW7YwZcoUfvOb37Bnzx4yMjIkTAkhOiXT9u2ELV0KLhda7964HngAPSGhznq6rlNe\nXs769T7+8Y8YXC4nNlspV1zxDXl5J/jHP8opKyujrKwMp9OJ0+mkvLw8EKoqKyvb4dvV1VYlWAuA\nM65hyLvvvsull15aa96ll17Ks88+GwhY/j/6YWFhPPLII8ybN49PP/000Ni5IQ888AC7du1C0zSS\nkpJ4+umnA/vz77Pm2D/9xz/+kYULFzJlyhR8Ph8zZ84MNNIeP348e/bsYerUqYG2QHfffXet4/7q\nV79izpw5vPvuu5xzzjm1ulRoKMBce+21ZGdnM2PGjECjbofDQWRkJJdeeimbN2/m4osvJiEhgW7d\nurUoCFksFq688kry8vJ44okniIyMbPKYTZ1vY1auXMm8efNYtmwZmqaxYsUKYmJiAJg3bx6zZ89m\n0qRJ9O7dm969ewe2a+zaWiwWEhMT+dWvfoXVasVkMjFs2DAWLVrU5Llec8013HjjjYE2dmPGjCEn\nJ6fOevI0oxCiw9I0lDffpGTVKg57veQPGkTO5MkUbdxIUVFRYCguLqa0tJTi4gqOHr2KwsLRQD42\n2w7Cw9/i3XebF5wURSEsLCwwWK1WrFYrISEhhIaGEhoaWmfaYrFgMpmwWCxYLBbMZnNgrKoqJpMJ\nVVXrDG63u+HzaKv/Ddvt9qccDsc9ja2zYcMGfdiwYXXmZ2Zm0rVr19N2bqJjmjFjBn/+858577zz\n2vtUTsnx48eZO3cuL774ItHR0WRmZjJu3Di+//57wsPD2/v0OiT5Ny9E56DrOmVlZeTl5ZGbm0te\nXh4FBQXVQ24uRV9/Tam/ZiQ5GT0pqcH9lZf35OjRm/B6k7FY4Nz/396dB8dx3nf+f3f3XLgB4j55\nggd4ArwpShRFOhZleyMpcttOnNI6ydpee5OKvXblV5X9leOqX1V2N+sjWa/WrvWutXG8csYby0ri\n2DIpSqIk3gTBE8TBEyDuc4ABBjPT3b8/eqaBAUAKAEEc5PdV1dU93T2D5qhFfPh9nn6eTW+zdu1N\n0tPTSE1NJSUlhZSUFFJTUxNeJyUlkZKSgs/nw+v1ztk/Oqurqzlw4MCkP2xGFSxd15/Erki96/f7\nvz5m/0HgG7GX3/D7/Udn8vlCPEoyMzPxeDzouu78i+gHP/iBhCshxIJnWRZ9fX20tbXR0dFBe3s7\nnZ2dCcs9qzgjI6h37qCEQqiaRvr69WStXElmZiaZmZmkp6eTmZlJVlYWaWmZfPDBMt58M4/ychfL\nl1v8+38fYtmyqT11vhDNtInQC/wlsCe+Q9d1FfgmcDC2603gqK7rSvxcXdcP+v3+hT3Splgw/vEf\n/3G+L2FWpKSkOGNeCSHEQhOJRGhvb6elpYXW1lba2tpob293lg/r0+Tz+cjNzSUnJ4ecnByys7PJ\n7eyk4Ne/JrukhCVlZXi/8Q2Ue4yB2NKi8J3v+Kir01BVeP75MJ/9bJhxD1svOjMKWH6//4iu6/vG\n7S4H6v1+/zCAruvXdV0v9/v9Ddh9sIQQQggxD0zTpLOzk6amJpqbm50w1draSldXV8JT0OOlpaWR\nl5dHXl4eBQUF5ObmkpubS15eHjk5OaSmpo42yYXDeH/0I9xvvQVuN9G9e+0Jm1NSJnyuZcHhwy5+\n+EMfoRBkZ1t85SshNm1aONPdPIjZ7OS+BOjTdf07sdf9QDYw88nehBBCCDFl0WiUlpYW7ty5Q3Nz\nsxOo7t69e89KlKqq5OfnU1hYSFFREQUFBRQUFJCfn09eXh4pk4SjySjNzST91V+h3rwJmsbIv/7X\n9sjsk/SH6u9X+N73vJw6ZceQJ5+M8sUvhpjG0IUL3mwGrG4gE/gSoACvAF2z8cGapjE0NCR9VoR4\nxFmWRU9Pz4SBWIUQiUzTpK2tjTt37nD79m1nfffuXQxj8gpQZmYmJSUllJaWUlxc7ISp/Px8Z5Dk\nmXK98w6+V16BUAizoIDQ17+OeY+5Xk+d0vhv/81HX59CSorFF784wr59C3O6mwfxIAFrfCS9Dqwe\n87rc7/c3PsDnO/Ly8ujo6KCvr282Pk4IsUBZlkVGRkbCcBtCPO6Ghoa4desWt27d4ubNm872yMjI\npOfn5+dTVlbmBKn4ejozW0xZMIj3f/5P3Efs7tXRvXsJffnLkzYJDg3BD3/o5cgRO8xt2GDwp38a\nIi/v0Rzbb6ZPEf4ZcAgo0HU93e/3f8Hv9xu6rn8TOBw77S9m6RpRFIX8/PzZ+jghhBBiQQoEAjQ2\nNnL9+nUaGxu5desWra2tk567ZMkSli5dytKlSyktLaWsrIyysjKSkpLm5Fq1ixfx/c3foHR0gNvN\nyOc/T+S3fmvSJsErVzS++10f7e0Kbjf8/u+P8K/+VYQpjGW9aM3ZOFhTca9xsIQQQohHTSAQoKGh\nwQlT169fd2bSGMvlclFaWsry5ctZtmwZK1asYNmyZc6UbHMuFML74x/j/qd/AsBcuZLQV76COclT\ngpEI/OQnHl5/3YNlwYoVJl/96sKepHk6Zn0cLCGEEEJMXTgc5vr16zQ0NFBfX099fT1tbW0TzvP5\nfKxYsYKVK1eycuVKVqxYQUlJCS7Xwvh1rdbW4vvrv0ZtaQFNI6zrhD/5SZjk+m7eVPn2t33cvq2i\nqvDSS2E+/ekwD9jda9FYGP/FhBBCiEeEZVl0dnZSW1tLbW0t9fX13Lx5c0Lnc6/Xy8qVK1m1apWz\nLi4untIcsHMuHMbz2mt4Xn8dTBOzrIzQn/4p5qpVk53Kz37m4f/+Xw+GAYWFJl/5Soi1ax+NqtVU\nScASQgghHkAkEuHGjRtcu3aN2tparl27Rk9PT8I5iqJQVlbG6tWrWbNmDatXr6asrOxD56VdCLSL\nF/G+8opdtVIUwi++SPj3fo/JSlEXLmj89//upaXFDomHDkX43OdGiE0Z+1iRgCWEEEJMQygUoq6u\njitXrnD58mXq6+snjDGVmprK2rVrWbduHWvWrGHVqlWLbqghpb8fz49+hPuoPeudWVpK6Mtfxqyo\nmHBuf7/Cj37k4ehRO3SVlpp8+cshKioer6rVWBKwhBBCiPsIBoNcvXqVK1eucOXKFRobGyc095WU\nlDiBat26dRQVFS3Mpr6psCxcb72F99VXUQIBcLsJf+pThF94YULVyrLgrbdcvPqql0DAfkLw058O\n8/zzj09fq3uRgCWEEEKMYRgGdXV11NTUUFNTQ0NDQ0KgUlWVVatWsX79etavX09FRcX8PdE3y9Sm\nJrzf/z7apUsAGJs2EfrSl7CKiiac29ys8MorPi5ftps5N282+Lf/NkRR0cIZnWA+ScASQgjx2Gtt\nbeX8+fOcP3+eS5cuMTQ05BzTNI1169Y5gWrt2rVTnj5m0RgcxPvaa7j/5V/AMLDS0xn5wz8k+vTT\nE8a1GhoCv9/DG2/YndgzMiz+8A/t0dgnGQLrsSUBSwghxGMnGAxy6dIlqqurqampmTBkQklJCZs3\nb2bLli1s3Lhx0fWfmjLTxH34MJ4f/9huDlRVIs8+y8hnPwvjqnKWBe+95+J//S8vPT0KigIf+UiE\nl18eGX+qQAKWEEKIx4BpmjQ0NHD+/Hlqamqoq6tLaPZLTU1ly5YtzpKXlzePVzs3tMuX8f6P/2FP\nzgwY69cz8m/+DeaKFRPOvX1b5Qc/8DrNgatXG3z+8yOsXv34dmL/MBKwhBBCPJJ6e3uprq52qlQD\nAwPOMU3TqKiooLKyki1btlBeXr54O6VPk9LcjPfHP8Z14gQAVk4OI3/wB0SfeGJCc2AwCK+95uWX\nv3RjGJCebvHyyyMcOBB9pKe5mQ0SsIQQQjwSotEodXV1VFdXc+7cOW7cuJFwvKCggMrKSiorK9m4\nceOj14/qQyi9vXheew334cNgGPbTgb/zO4RffJHxA1VFIvCb37j5+7/30NenoKrw3HMRfvd3pTlw\nqiRgCSGEWLRCoRDnz5/nxIkTnDlzhmAw6Bxzu91s2rSJqqoqqqqqKC4unscrnUdDQ3hefx3PL34B\nIyN2P6uDBwn/3u9hZWcnnGqacOyYi5/8xEt7u13NWrfO4AtfGGHFCmkOnA4JWEIIIRaVYDDI2bNn\nOX78ONXV1YyMjDjHSkpKqKqqYuvWrVRUVOD1eufxSudZOIz7zTfx+P0o/f0ARHfuJPz7vz9hYmbL\ngrNnNX78Yy+3btltf6WlJp/9bJhdu+TpwJmQgCWEEGLB6+/v5/Tp05w4cYKamhqi0ahzbPXq1eze\nvZtdu3Y9vlWqsSIR3L/5DZ6f/QwlNmWPsW4dIy+/POko7Fevqvzt33q5etXuwJ6TY/GZz4zwzDNR\nFsFMPguWBCwhhBALUkdHBydPnuTkyZNcvXoV07SbqFRVZcOGDU6oys3NnecrXSAiEdxHjtgVq+5u\nAMzlyxn5zGcwdu6c0IG9rk7lpz/1cu6cnaLS0y1eeinMc89F8Hjm/OofORKwhBBCLBjNzc2cOHGC\nEydO0NjY6OzXNI2qqip2797Nzp07yczMnMerXGAiEdxHj9rBqrMTAHPpUsK/+7tEd+5k/ON+DQ0q\nr73m4exZOwL4fPD882F++7fDPGb9/h8qCVhCCCHmjWVZNDQ0OJWq5uZm55jX62Xr1q3s3r2bbdu2\nPXZP/X2o4WHcv/41njfecJoCzbIywp/+NNE9eyYEq8ZGO1idOTMarJ57LsyLL4blycCHQAKWEEKI\nOWUYBleuXOHEiROcPHmS7lhzFtgDfu7YsYPdu3ezZcuWx7uT+r0EAnj++Z9x//M/owwOAmAuW0b4\nk5+0x7IaF6yuX1f56U89nDpl/8r3euFjHwvzwgsRMjJk3sCHRQKWEEKIhy4cDlNTU8OJEyc4ffp0\nwqCf2dnZ7Ny5k927d7N+/XpcLvnVNBmlowPPP/0T7jffhFAIsDuvh196CWPbtoQ+VpYFly5p/MM/\neDh/3u5j5fGMBqvMTAlWD5vcxUIIIR6K4eFhzp0754xRFYqFArCHU9i5cye7du16rEZRnwm1rg7P\nG2/YI6/HpvcxqqrsYLV+fUKwMgw4ccLFz3/uobHR/k59Pnj22TAvvijBai5JwBJCCDFrBgcHneEU\nqquriUQizrEVK1awe/dudu/eTdm4cZjEOKaJ69Qp3G+8gXb1qr1P04ju20f4t38bc9WqhNNDITh6\n1M0vfuGmrc0OVhkZFp/4RIRnn5U+VvNBApYQQogH0t/fz6lTpzh+/DgXLlxImER57dq1znAKhYWF\n83iVi0QggPvoUdz/8i+obW0AWCkpRD76USIf+xjWuCEpAgH45S89/PKXbgIBu5JVWGjywgsR9u+P\nIF3Y5o8ELCGEENPW3d3NiRMnOH78+IQxqjZu3OhUqrLHTcUiJqfW1+P+1a9wHztmTwQImAUFRD7x\nCSIHD0JSUsL5LS0Kb7zh4a233ITD9r7ycpPf+R175HVpcZ1/ErCEEEJ8KMuyaG5u5uTJk5w+fZq6\nujrnmKZpznAKO3fuJCMjYx6vdBEZGcF17BieX/0KdcyYX0ZVFeFDhzC2b5/wROC1ayqvv+7h5EkX\nVqw71bZtUV54IcKGDYZMabOASMASQggxKdM0uXbtGqdPn+bkyZO0tLQ4x9xuN1VVVezZs4ft27eT\nmpo6j1e6uCh37+J+803cR444wyxYaWlEDh4k8tGPYhUVJZxvmnD6tMYvfuFxprNxueDppyM8/3yE\nsjKZhHkhkoAlhBDCYVkWtbW1vP3225w6dYq+vj7nWHp6Otu2bWPXrl1s2bIFn883j1e6yIyM4Dp5\nEvfhw2gXLzq7jdWriRw6RHTvXsZ3mOruVjh82M2bb7rp7rZLUykpFocORfj4xyMsWSJPBC5kErCE\nEELQ0tLCO++8wzvvvENbrHM1QH5+Prt27WLnzp2sW7cOTWb/nTrLsvtWvfUWrvfeQwkG7f1uN5F9\n+4gcOoRZXp7wFtOE8+c1fv1rN2fPuuKjMlBUZHLoUISPfCRCcvIc/znEjEjAEkKIx1QgEOD999/n\n7bffTuhTlZ2dzb59+9i3bx/Lli1DkY4906L09eF65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- "text": [ - "" - ] - } - ], - "prompt_number": 4 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/finite_mc_solutions.ipynb b/solutions/finite_mc_solutions.ipynb deleted file mode 100644 index 2b06cd0df..000000000 --- a/solutions/finite_mc_solutions.ipynb +++ /dev/null @@ -1,305 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:ef11aa46317b28348e59461a81a9d8dc6f5fd73d218983f81faa0af0fbcb9f6a" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Finite Markov Chains" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/finite_markov.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import print_function, division # Omit for Python 3.x\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from quantecon import mc_compute_stationary, mc_sample_path\n" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "Compute the fraction of time that the worker spends unemployed,\n", - "and compare it to the stationary probability.\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "alpha = beta = 0.1\n", - "N = 10000\n", - "p = beta / (alpha + beta)\n", - "\n", - "P = ((1 - alpha, alpha), # Careful: P and p are distinct\n", - " (beta, 1 - beta))\n", - "P = np.array(P)\n", - "\n", - "fig, ax = plt.subplots(figsize=(9, 6))\n", - "ax.set_ylim(-0.25, 0.25)\n", - "ax.grid()\n", - "ax.hlines(0, 0, N, lw=2, alpha=0.6) # Horizonal line at zero\n", - "\n", - "for x0, col in ((0, 'blue'), (1, 'green')):\n", - " # == Generate time series for worker that starts at x0 == #\n", - " X = mc_sample_path(P, x0, N)\n", - " # == Compute fraction of time spent unemployed, for each n == #\n", - " X_bar = (X == 0).cumsum() / (1 + np.arange(N, dtype=float)) \n", - " # == Plot == #\n", - " ax.fill_between(range(N), np.zeros(N), X_bar - p, color=col, alpha=0.1)\n", - " ax.plot(X_bar - p, color=col, label=r'$X_0 = \\, {} $'.format(x0))\n", - " ax.plot(X_bar - p, 'k-', alpha=0.6) # Overlay in black--make lines clearer\n", - "\n", - "ax.legend(loc='upper right')\n", - "\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 3, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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VaP5cfj6ZoamkBR2gqhneMBGgTMEKtG/TnRXrFgKQv1BBQqPvpSqTkGhuhQm7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\nSMaHzSJ5mEcyMYvkERrMK1psgRYtbiIiwhugRUIIIYQwgYFFS2A74ub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- "text": [ - "" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First save the data into a file called `web_graph_data.txt` by executing the next cell" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%%file web_graph_data.txt\n", - "a -> d;\n", - "a -> f;\n", - "b -> j;\n", - "b -> k;\n", - "b -> m;\n", - "c -> c;\n", - "c -> g;\n", - "c -> j;\n", - "c -> m;\n", - "d -> f;\n", - "d -> h;\n", - "d -> k;\n", - "e -> d;\n", - "e -> h;\n", - "e -> l;\n", - "f -> a;\n", - "f -> b;\n", - "f -> j;\n", - "f -> l;\n", - "g -> b;\n", - "g -> j;\n", - "h -> d;\n", - "h -> g;\n", - "h -> l;\n", - "h -> m;\n", - "i -> g;\n", - "i -> h;\n", - "i -> n;\n", - "j -> e;\n", - "j -> i;\n", - "j -> k;\n", - "k -> n;\n", - "l -> m;\n", - "m -> g;\n", - "n -> c;\n", - "n -> j;\n", - "n -> m;\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Overwriting web_graph_data.txt\n" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\"\"\"\n", - "Return list of pages, ordered by rank\n", - "\"\"\"\n", - "import numpy as np\n", - "from operator import itemgetter\n", - "import re\n", - "\n", - "infile = 'web_graph_data.txt'\n", - "alphabet = 'abcdefghijklmnopqrstuvwxyz'\n", - "\n", - "n = 14 # Total number of web pages (nodes)\n", - "\n", - "# == Create a matrix Q indicating existence of links == #\n", - "# * Q[i, j] = 1 if there is a link from i to j\n", - "# * Q[i, j] = 0 otherwise\n", - "Q = np.zeros((n, n), dtype=int)\n", - "f = open(infile, 'r')\n", - "edges = f.readlines()\n", - "f.close()\n", - "for edge in edges:\n", - " from_node, to_node = re.findall('\\w', edge)\n", - " i, j = alphabet.index(from_node), alphabet.index(to_node)\n", - " Q[i, j] = 1\n", - "# == Create the corresponding Markov matrix P == #\n", - "P = np.empty((n, n))\n", - "for i in range(n):\n", - " P[i,:] = Q[i,:] / Q[i,:].sum()\n", - "# == Compute the stationary distribution r == #\n", - "r = mc_compute_stationary(P)[0]\n", - "ranked_pages = {alphabet[i] : r[i] for i in range(n)}\n", - "# == Print solution, sorted from highest to lowest rank == #\n", - "print('Rankings\\n ***')\n", - "for name, rank in sorted(ranked_pages.items(), key=itemgetter(1), reverse=1):\n", - " print('{0}: {1:.4}'.format(name, rank))\n", - "\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Rankings\n", - " ***\n", - "g: 0.1607\n", - "j: 0.1594\n", - "m: 0.1195\n", - "n: 0.1088\n", - "k: 0.09106\n", - "b: 0.08326\n", - "e: 0.05312\n", - "i: 0.05312\n", - "c: 0.04834\n", - "h: 0.0456\n", - "l: 0.03202\n", - "d: 0.03056\n", - "f: 0.01164\n", - "a: 0.002911\n" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 3" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "A solution from the [quantecon library](https://github.com/jstac/quant-econ/tree/master/quantecon) can be found [here](https://github.com/jstac/quant-econ/blob/master/quantecon/markov/approximation.py)\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 5 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 5 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/graph.txt b/solutions/graph.txt deleted file mode 100644 index ae50eb228..000000000 --- a/solutions/graph.txt +++ /dev/null @@ -1,100 +0,0 @@ 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node91 22.35 -node80, node92 121.87, node88 28.78, node98 264.34 -node81, node94 99.78, node89 39.52, node92 99.89 -node82, node91 47.44, node88 28.05, node93 11.99 -node83, node94 114.95, node86 8.75, node88 5.78 -node84, node89 19.14, node94 30.41, node98 121.05 -node85, node97 94.51, node87 2.66, node89 4.90 -node86, node97 85.09 -node87, node88 0.21, node91 11.14, node92 21.23 -node88, node93 1.31, node91 6.83, node98 6.12 -node89, node97 36.97, node99 82.12 -node90, node96 23.53, node94 10.47, node99 50.99 -node91, node97 22.17 -node92, node96 10.83, node97 11.24, node99 34.68 -node93, node94 0.19, node97 6.71, node99 32.77 -node94, node98 5.91, node96 2.03 -node95, node98 6.17, node99 0.27 -node96, node98 3.32, node97 0.43, node99 5.87 -node97, node98 0.30 -node98, node99 0.33 -node99, \ No newline at end of file diff --git a/solutions/ifp_solutions.ipynb b/solutions/ifp_solutions.ipynb deleted file mode 100644 index 67979ddd4..000000000 --- a/solutions/ifp_solutions.ipynb +++ /dev/null @@ -1,288 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:93efd2c39b0b56525d85fa0248677e2a0739e27ff07ee120a92797b0261694bc" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Optimal Savings" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/ifp.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from quantecon import compute_fixed_point\n", - "from quantecon.models import ConsumerProblem" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "cp = ConsumerProblem()\n", - "K = 80\n", - "\n", - "# Bellman iteration \n", - "V, c = cp.initialize()\n", - "print(\"Starting value function iteration\")\n", - "for i in range(K):\n", - " # print \"Current iterate = \" + str(i)\n", - " V = cp.bellman_operator(V) \n", - "c1 = cp.bellman_operator(V, return_policy=True) \n", - "\n", - "# Policy iteration \n", - "print(\"Starting policy function iteration\")\n", - "V, c2 = cp.initialize()\n", - "for i in range(K):\n", - " # print \"Current iterate = \" + str(i)\n", - " c2 = cp.coleman_operator(c2)\n", - "\n", - "fig, ax = plt.subplots(figsize=(10, 8))\n", - "ax.plot(cp.asset_grid, c1[:, 0], label='value function iteration')\n", - "ax.plot(cp.asset_grid, c2[:, 0], label='policy function iteration')\n", - "ax.set_xlabel('asset level')\n", - "ax.set_ylabel('consumption (low income)')\n", - "ax.legend(loc='upper left')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Starting value function iteration\n", - "Starting policy function iteration" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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HZAYu2zCXiIjIS2eMIeh0EGP/Gs/vx1aR6mRD3I/+zID3SxEwANzc7J1Q7OVl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\n5Ilt+9FC4eJAIiIs84aNGgUjvo3kRt4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DjydvzwAaAk0Io2mx9MEH8PzzsHAhrN2wlt6j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\nhaSxbtgzVmYK5VuMDSbmV/XsJIcSrnCqQ/h+epyw5mG2yue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- "text": [ - "" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "r_vals = np.linspace(0, 0.04, 4) \n", - "\n", - "fig, ax = plt.subplots(figsize=(10, 8))\n", - "for r_val in r_vals:\n", - " cp = ConsumerProblem(r=r_val)\n", - " v_init, c_init = cp.initialize()\n", - " c = compute_fixed_point(cp.coleman_operator, c_init, verbose=False)\n", - " ax.plot(cp.asset_grid, c[:, 0], label=r'$r = %.3f$' % r_val)\n", - "\n", - "ax.set_xlabel('asset level')\n", - "ax.set_ylabel('consumption (low income)')\n", - "ax.legend(loc='upper left')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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LVXWAL0/2n9jPpKhJTImZQq1KtXiyyZPM7T6XMsU1A0pyTsmYiEghsXevadQa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- "text": [ - "" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 3" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "from scipy import interp\n", - "from quantecon import mc_sample_path \n", - "\n", - "def compute_asset_series(cp, T=500000, verbose=False):\n", - " \"\"\"\n", - " Simulates a time series of length T for assets, given optimal savings\n", - " behavior. Parameter cp is an instance of consumerProblem\n", - " \"\"\"\n", - "\n", - " Pi, z_vals, R = cp.Pi, cp.z_vals, cp.R # Simplify names\n", - " v_init, c_init = cp.initialize()\n", - " c = compute_fixed_point(cp.coleman_operator, c_init, verbose=verbose)\n", - " cf = lambda a, i_z: interp(a, cp.asset_grid, c[:, i_z])\n", - " a = np.zeros(T+1)\n", - " z_seq = mc_sample_path(Pi, sample_size=T)\n", - " for t in range(T):\n", - " i_z = z_seq[t]\n", - " a[t+1] = R * a[t] + z_vals[i_z] - cf(a[t], i_z)\n", - " return a\n", - "\n", - "cp = ConsumerProblem(r=0.03, grid_max=4)\n", - "a = compute_asset_series(cp)\n", - "fig, ax = plt.subplots(figsize=(10, 8))\n", - "ax.hist(a, bins=20, alpha=0.5, normed=True)\n", - "ax.set_xlabel('assets')\n", - "ax.set_xlim(-0.05, 0.75)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 4" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The following code takes a few minutes to run" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "M = 25\n", - "r_vals = np.linspace(0, 0.04, M) \n", - "fig, ax = plt.subplots(figsize=(10,8))\n", - "\n", - "for b in (1, 3):\n", - " asset_mean = []\n", - " for r_val in r_vals:\n", - " cp = ConsumerProblem(r=r_val, b=b)\n", - " mean = np.mean(compute_asset_series(cp, T=250000))\n", - " asset_mean.append(mean)\n", - " ax.plot(asset_mean, r_vals, label=r'$b = %d$' % b)\n", - " print(\"Finished iteration b=%i\" % b)\n", - "\n", - "ax.set_yticks(np.arange(.0, 0.045, .01))\n", - "ax.set_xticks(np.arange(-3, 2, 1))\n", - "ax.set_xlabel('capital')\n", - "ax.set_ylabel('interest rate')\n", - "ax.grid(True)\n", - "ax.legend(loc='upper left')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Finished iteration b=1\n", - "Finished iteration b=3" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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77jzuPu7ugi3GJG3o1Vdh9Gj4xS9CRyIpG3J9Pc4xwD+J+sHuJ1q+4uKy791b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\nsgeJFoU9qOx4DnBjziIqUiX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- "text": [ - "" - ] - } - ], - "prompt_number": 6 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/jv_solutions.ipynb b/solutions/jv_solutions.ipynb deleted file mode 100644 index 8d22a3fcd..000000000 --- a/solutions/jv_solutions.ipynb +++ /dev/null @@ -1,222 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:508943d1ce2372490699818cedf35a0997172a9adcaf9c6de4b3eeb42efd275d" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: On-the-Job Search" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/jv.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "import random\n", - "from quantecon import compute_fixed_point\n", - "from quantecon.models import JvWorker" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here\u2019s code to produce the 45 degree diagram" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "wp = JvWorker(grid_size=25)\n", - "G, pi, F = wp.G, wp.pi, wp.F # Simplify names\n", - "\n", - "v_init = wp.x_grid * 0.5\n", - "print(\"Computing value function\")\n", - "V = compute_fixed_point(wp.bellman_operator, v_init, max_iter=40, verbose=False)\n", - "print(\"Computing policy functions\")\n", - "s_policy, phi_policy = wp.bellman_operator(V, return_policies=True)\n", - "\n", - "# Turn the policy function arrays into actual functions\n", - "s = lambda y: np.interp(y, wp.x_grid, s_policy)\n", - "phi = lambda y: np.interp(y, wp.x_grid, phi_policy)\n", - "\n", - "def h(x, b, U):\n", - " return (1 - b) * G(x, phi(x)) + b * max(G(x, phi(x)), U)\n", - "\n", - "plot_grid_max, plot_grid_size = 1.2, 100\n", - "plot_grid = np.linspace(0, plot_grid_max, plot_grid_size)\n", - "fig, ax = plt.subplots(figsize=(8,8))\n", - "ax.set_xlim(0, plot_grid_max)\n", - "ax.set_ylim(0, plot_grid_max)\n", - "ticks = (0.25, 0.5, 0.75, 1.0)\n", - "ax.set_xticks(ticks)\n", - "ax.set_yticks(ticks)\n", - "ax.set_xlabel(r'$x_t$', fontsize=16)\n", - "ax.set_ylabel(r'$x_{t+1}$', fontsize=16, rotation='horizontal')\n", - "\n", - "ax.plot(plot_grid, plot_grid, 'k--') # 45 degree line\n", - "for x in plot_grid:\n", - " for i in range(50):\n", - " b = 1 if random.uniform(0, 1) < pi(s(x)) else 0\n", - " U = wp.F.rvs(1)\n", - " y = h(x, b, U)\n", - " ax.plot(x, y, 'go', alpha=0.25)\n", - "\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Computing value function\n", - "Computing policy functions" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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1BkanRpHgE9hc30RzVzM2/BuS+1GaXy8vW2wwNuTMvSulKQxGAxpsDbjYf1Hy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\nT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UOG0alRVlgB2HEdeqkqALVGZTQwis1mI0OGGzduUNNWQyaTz/CvrKtEi2r89PM/nX+n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\n3kOGDA91PMSZs2eo+GRO5BVFIf2DNF/85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- "text": [ - "" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Looking at the dynamics, we can see that \n", - "\n", - "* If $x_t$ is below about 0.2 the dynamics are random, but $x_{t+1} > x_t$ is very likely\n", - "* As $x_t$ increases the dynamics become deterministic, and $x_t$ converges to a steady state value close to 1\n", - "\n", - "Referring back to the figure here\n", - "\n", - "http://quant-econ.net/py/jv.html#solving-for-policies\n", - "\n", - "we see that $x_t \\approx 1$ means that $s_t = s(x_t) \\approx 0$ and $\\phi_t = \\phi(x_t) \\approx 0.6$\n", - "\n" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The figure can be produced as follows" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "wp = JvWorker(grid_size=25)\n", - "\n", - "def xbar(phi):\n", - " return (wp.A * phi**wp.alpha)**(1 / (1 - wp.alpha))\n", - "\n", - "phi_grid = np.linspace(0, 1, 100)\n", - "fig, ax = plt.subplots(figsize=(9, 7))\n", - "ax.set_xlabel(r'$\\phi$', fontsize=16)\n", - "ax.plot(phi_grid, [xbar(phi) * (1 - phi) for phi in phi_grid], 'b-', label=r'$w^*(\\phi)$')\n", - "ax.legend(loc='upper left')\n", - "\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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Tp+qMnlSmgCJSBc8/7+XJJ/3sv3+MwYM1tSOSTtq1i3LssRHeeMPL8uUaRUlV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\nOrMm7pF1fvzRYMqUILm5NqNH69smIiI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- "text": [ - "" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Observe that the maximizer is around 0.6\n", - "\n", - "This this is similar to the long run value for $\\phi$ obtained\n", - "in exercise 1\n", - "\n", - "Hence the behaviour of the infinitely patent worker is similar to that of the\n", - "worker with $\\beta = 0.96$\n", - "\n", - "This seems reasonable, and helps us confirm that our dynamic programming\n", - "solutions are probably correct\n" - ] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/kalman_solutions.ipynb b/solutions/kalman_solutions.ipynb deleted file mode 100644 index 7aa4e305b..000000000 --- a/solutions/kalman_solutions.ipynb +++ /dev/null @@ -1,1626 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# quant-econ Solutions: The Kalman Filter" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/kalman.html" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from quantecon import Kalman\n", - "from quantecon import LinearStateSpace\n", - "from scipy.stats import norm" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise 1" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": [ - "iVBORw0KGgoAAAANSUhEUgAAAlQAAAHqCAYAAADCsNCxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", - 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"output_type": "display_data" - } - ], - "source": [ - "# == parameters == #\n", - "theta = 10 # Constant value of state x_t\n", - "A, C, G, H = 1, 0, 1, 1\n", - "ss = LinearStateSpace(A, C, G, H, mu_0=theta)\n", - "\n", - "# == set prior, initialize kalman filter == #\n", - "x_hat_0, Sigma_0 = 8, 1\n", - "kalman = Kalman(ss, x_hat_0, Sigma_0)\n", - "\n", - "# == draw observations of y from state space model == #\n", - "N = 5\n", - "x, y = ss.simulate(N)\n", - "y = y.flatten()\n", - "\n", - "# == set up plot == #\n", - "fig, ax = plt.subplots(figsize=(10,8))\n", - "xgrid = np.linspace(theta - 5, theta + 2, 200)\n", - "\n", - "for i in range(N):\n", - " # == record the current predicted mean and variance == #\n", - " m, v = [float(z) for z in (kalman.x_hat, kalman.Sigma)]\n", - " # == plot, update filter == #\n", - " ax.plot(xgrid, norm.pdf(xgrid, loc=m, scale=np.sqrt(v)), label=r'$t=%d$' % i)\n", - " kalman.update(y[i])\n", - "\n", - "ax.set_title(r'First %d densities when $\\theta = %.1f$' % (N, theta)) \n", - "ax.legend(loc='upper left')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise 2" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": [ - "iVBORw0KGgoAAAANSUhEUgAAAiAAAAGnCAYAAACO1OzhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", - "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm83HV97/HXh4RASEIgCYQtEJAgi4rKKqKCS6VYpde2\n", - "Ki6tVnDX9tpb0S7q1bZqe6u21VrEtep1qV4V3FCruLSKguyLsu+ELQlZIYHv/ePzG87k5CxzzpmZ\n", - "3yyv5+NxHjPzm9/M75sfy3nnu3y+UUpBkiSpm7aruwGSJGn4GEAkSVLXGUAkSVLXGUAkSVLXGUAk\n", - "SVLXGUAkSVLXTRpAIuITEbEyIi6b4Jx/johrIuKSiHhCe5soSZIGTSs9IJ8EThrvzYg4GTiwlLIC\n", - "eBXwkTa1TZIkDahJA0gp5SfAqglOeR7w6erc84FdImJpe5onSZIGUTvmgOwN3NL0+lZgnzZ8ryRJ\n", - 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- "T = 600\n", - "z = np.empty(T)\n", - "x, y = ss.simulate(T)\n", - "y = y.flatten()\n", - "\n", - "for t in range(T):\n", - " # Record the current predicted mean and variance, and plot their densities\n", - " m, v = [float(temp) for temp in (kalman.x_hat, kalman.Sigma)]\n", - " \n", - " f = lambda x: norm.pdf(x, loc=m, scale=np.sqrt(v))\n", - " integral, error = quad(f, theta - epsilon, theta + epsilon)\n", - " z[t] = 1 - integral\n", - " \n", - " kalman.update(y[t])\n", - "\n", - "fig, ax = plt.subplots(figsize=(9, 7))\n", - "ax.set_ylim(0, 1)\n", - "ax.set_xlim(0, T)\n", - "ax.plot(range(T), z) \n", - "ax.fill_between(range(T), np.zeros(T), z, color=\"blue\", alpha=0.2) " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise 3" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Eigenvalues of A:\n", - "[ 0.9+0.j -0.1+0.j]\n", - "Stationary prediction error variance:\n", - "[[ 0.40329109 0.1050718 ]\n", - " [ 0.1050718 0.41061711]]\n" - ] - }, - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": [ - "iVBORw0KGgoAAAANSUhEUgAAAhMAAAFwCAYAAAACK/lNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", - "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XecXFd9///Xe5tWWvXqLslyE7bBNtiADVh0CDaEFiAQ\n", - "QiAkIYSahBaS1YaW/PINJbRQElpIIZSEECCQYNkY0ww2tnHFVa6SLFl9Ja328/vjnDs7Wu3uzOzs\n", - "7hS9n4+HPTszd2bOjGbu/dzP+ZxzFBGYmZmZTVZHoxtgZmZmrc3BhJmZmdXFwYSZmZnVxcGEmZmZ\n", - "1cXBhJmZmdXFwYSZmZnVpWIwIekNkq6VdJ2kN8xEo8zMzKx1TBhMSDoD+F3gXOARwEWS1sxEw8zM\n", - "zKw1VMpMnAb8OCIGI+IgcCnwvOlvlpmZmbWKSsHEdcDjJS2WNAd4FnDc9DfLzMzMWkXXRHdGxI2S\n", - "/hr4DrAbuAoYnomGmZmZWWtQLWtzSHovcFdE/H3ZbV7cw8zMrM1EhKrddsLMBICk5RGxSdIJwHOB\n", - "R9fzgjb9JK2PiPWNbocl/vdoPv43aS7+92g+tSYKKgYTwJclLQEOAH8YETsm1TIzMzNrSxWDiYh4\n", - 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C, G, H, mu_0 = np.zeros(2))\n", - "\n", - "# === Define the prior density === #\n", - "Sigma = [[0.9, 0.3], \n", - " [0.3, 0.9]]\n", - "Sigma = np.array(Sigma)\n", - "x_hat = np.array([8, 8])\n", - "\n", - "# === Initialize the Kalman filter === #\n", - "kn = Kalman(ss, x_hat, Sigma)\n", - "\n", - "# == Print eigenvalues of A == #\n", - "print(\"Eigenvalues of A:\")\n", - "print(eigvals(A))\n", - "\n", - "# == Print stationary Sigma == #\n", - "S, K = kn.stationary_values()\n", - "print(\"Stationary prediction error variance:\")\n", - "print(S)\n", - "\n", - "# === Generate the plot === #\n", - "T = 50\n", - "x, y = ss.simulate(T)\n", - "\n", - "e1 = np.empty(T-1)\n", - "e2 = np.empty(T-1)\n", - "\n", - "for t in range(1, T):\n", - " kn.update(y[:,t])\n", - " e1[t-1] = np.sum((x[:,t] - kn.x_hat.flatten())**2)\n", - " e2[t-1] = np.sum((x[:,t] - np.dot(A, x[:,t-1]))**2)\n", - "\n", - "fig, ax = plt.subplots(figsize=(9,6))\n", - "ax.plot(range(1, T), e1, 'k-', lw=2, alpha=0.6, label='Kalman filter error') \n", - "ax.plot(range(1, T), e2, 'g-', lw=2, alpha=0.6, label='conditional expectation error') \n", - "ax.legend()\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/solutions/lakemodel_solutions.ipynb b/solutions/lakemodel_solutions.ipynb deleted file mode 100644 index 930a10e28..000000000 --- a/solutions/lakemodel_solutions.ipynb +++ /dev/null @@ -1,423 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Lake Model Solutions" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Excercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We begin by initializing the variables and import the necessary modules" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from quantecon.models import LakeModel\n", - "\n", - "alpha = 0.012\n", - "lamb = 0.2486\n", - "b = 0.001808\n", - "d = 0.0008333\n", - "g = b-d\n", - "N0 = 100.\n", - "e0 = 0.92\n", - "u0 = 1-e0\n", - "T = 50" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now construct the class containing the initial conditions of the problem" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Initial Steady State: [ 0.94737184 0.05262816]\n" - ] - } - ], - "source": [ - "LM0 = LakeModel(lamb,alpha,b,d)\n", - "x0 = LM0.find_steady_state()# initial conditions\n", - "\n", - "print(\"Initial Steady State: %s\" % x0)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "New legislation changes $\\lambda$ to $0.2$" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "LM1 = LakeModel(0.2,alpha,b,d)" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "New Steady State: [ 0.93540871 0.06459129]\n" - ] - } - ], - "source": [ - "xbar = LM1.find_steady_state() # new steady state\n", - "X_path = np.vstack(LM1.simulate_stock_path(x0*N0,T)) # simulate stocks\n", - "x_path = np.vstack(LM1.simulate_rate_path(x0,T)) # simulate rates\n", - "print(\"New Steady State: %s\" % xbar)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now plot stocks" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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MgJdeCuFq/nw46qh0qDrhBOjVK+6eiohIS1WSQesf/3BuuCGstbn6arjwQk39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\nXgAAAABJRU5ErkJggg==\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize=[10,9])\n", - "plt.subplot(3,1,1)\n", - "plt.plot(X_path[:,0])\n", - "plt.title(r'Employment')\n", - "plt.subplot(3,1,2)\n", - "plt.plot(X_path[:,1])\n", - "plt.title(r'Unemployment')\n", - "plt.subplot(3,1,3)\n", - "plt.plot(X_path.sum(1))\n", - "plt.title(r'Labor Force')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And how the rates evolve:" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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B+2ZmZmal5LcjW7DeevD978OvflXuSMzMzMy6UUsYwIIFsPnm8MQTsNlmJTutmZmZmVvC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\nTwObSxoKzAEOAcb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EnFmKrsOI+GtEfCoijitFXGZm7aFQEtam16vzjutJejPpjxGxPbAI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\ngO9GxMuSqoDVI+IUSb8F3o2IcySdCvS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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize=[10,6])\n", - "plt.subplot(2,1,1)\n", - "plt.plot(x_path[:,0])\n", - "plt.hlines(xbar[0],0,T,'r','--')\n", - "plt.title(r'Employment Rate')\n", - "plt.subplot(2,1,2)\n", - "plt.plot(x_path[:,1])\n", - "plt.hlines(xbar[1],0,T,'r','--')\n", - "plt.title(r'Unemployment Rate')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We see that it takes 20 periods for the economy to converge to it's new steady state levels" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This next exercise has the economy expriencing a boom in entrances to the labor market and then later returning to the original levels. For 20 periods the economy has a new entry rate into the labor market " - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "bhat = 0.003\n", - "T_hat = 20\n", - "LM1 = LakeModel(lamb,alpha,bhat,d)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We simulate for 20 periods at the new parameters" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "X_path1 = np.vstack(LM1.simulate_stock_path(x0*N0,T_hat)) # simulate stocks\n", - "x_path1 = np.vstack(LM1.simulate_rate_path(x0,T_hat)) # simulate rates" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now using the state after 20 periods for the new initial conditions we simulate for the additional 30 periods" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "X_path2 = np.vstack(LM0.simulate_stock_path(X_path1[-1,:2],T-T_hat+1)) # simulate stocks\n", - "x_path2 = np.vstack(LM0.simulate_rate_path(x_path1[-1,:2],T-T_hat+1)) # simulate rates" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally we combine these two paths and plot" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "x_path = np.vstack([x_path1,x_path2[1:]]) # note [1:] to avoid doubling period 20\n", - "X_path = np.vstack([X_path1,X_path2[1:]]) # note [1:] to avoid doubling period 20" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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fRUrh0L8gipvuX/HSvStuun/1S64tVwcD4919vbuXAmOA8xLf/Rn4f/koTkRE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\ntWZNGqFavNhV083MrHPKuqA9IlZKGtvs9HTSZs4AC4A8MDc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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize=[10,9])\n", - "plt.subplot(3,1,1)\n", - "plt.plot(X_path[:,0])\n", - "plt.title(r'Employment')\n", - "plt.subplot(3,1,2)\n", - "plt.plot(X_path[:,1])\n", - "plt.title(r'Unemployment')\n", - "plt.subplot(3,1,3)\n", - "plt.plot(X_path.sum(1))\n", - "plt.title(r'Labor Force')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And the rates:" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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icLbcl91vIGnC9IHZPX8jqWS1e506wU9/mmrQyrD116ykrr46NWnutVepIzEz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\npUve0ZiZtV3NPZXGDKBfNoqyC3A4cE9JnXuAY7K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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize=[10,6])\n", - "plt.subplot(2,1,1)\n", - "plt.plot(x_path[:,0])\n", - "plt.hlines(x0[0],0,T,'r','--')\n", - "plt.title(r'Employment Rate')\n", - "plt.subplot(2,1,2)\n", - "plt.plot(x_path[:,1])\n", - "plt.hlines(x0[1],0,T,'r','--')\n", - "plt.title(r'Unemployment Rate')" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.4.3" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/solutions/lln_clt_solutions.ipynb b/solutions/lln_clt_solutions.ipynb deleted file mode 100644 index f0374ffba..000000000 --- a/solutions/lln_clt_solutions.ipynb +++ /dev/null @@ -1,263 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:f143b3d9651965911f999068d8298ff7f16dc26102a931f2446fab57b788162b" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: LLN and CLT" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/lln_clt.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Standard imports" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here is one solution\n", - "\n", - "You might have to modify or delete the lines starting with `rc`, depending on your configuration" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\"\"\"\n", - "Illustrates the delta method, a consequence of the central limit theorem.\n", - "\"\"\"\n", - "\n", - "from scipy.stats import uniform, norm\n", - "from matplotlib import rc\n", - "\n", - "# == Specifying font, needs LaTeX integration == #\n", - "rc('font',**{'family':'serif','serif':['Palatino']})\n", - "rc('text', usetex=True)\n", - "\n", - "# == Set parameters == #\n", - "n = 250\n", - "replications = 100000\n", - "distribution = uniform(loc=0, scale=(np.pi / 2))\n", - "mu, s = distribution.mean(), distribution.std()\n", - "\n", - "g = np.sin\n", - "g_prime = np.cos\n", - "\n", - "# == Generate obs of sqrt{n} (g(\\bar X_n) - g(\\mu)) == #\n", - "data = distribution.rvs((replications, n)) \n", - "sample_means = data.mean(axis=1) # Compute mean of each row\n", - "error_obs = np.sqrt(n) * (g(sample_means) - g(mu))\n", - "\n", - "# == Plot == #\n", - "asymptotic_sd = g_prime(mu) * s\n", - "fig, ax = plt.subplots(figsize=(10, 6))\n", - "xmin = -3 * g_prime(mu) * s\n", - "xmax = -xmin\n", - "ax.set_xlim(xmin, xmax)\n", - "ax.hist(error_obs, bins=60, alpha=0.5, normed=True)\n", - "xgrid = np.linspace(xmin, xmax, 200)\n", - "lb = r\"$N(0, g'(\\mu)^2 \\sigma^2)$\"\n", - "ax.plot(xgrid, norm.pdf(xgrid, scale=asymptotic_sd), 'k-', lw=2, label=lb)\n", - "ax.legend()\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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HzTl2bDcxMVvp3n1h1pp5cXFX7i8ijku35EQkR0uXLuW5554DYNq0aXTo0MFwIvtSsmRF\nevb8Hnd3b7ZtW8KyZa+YjiQiBUSFSUSytXXrVrp27Up6ejohISE8++yzpiPZpfLla9OjxyJcXNz4\n9dcpREdPNx1JRAqACpOIXOH48eN07tyZkydP0q1bN8aNG2c6kl3z9Q3gwQczV4/64YfB7N37s+FE\nIpLfNIZJRC6Rnp5Oz5492blzJxUrVqJYsVr06fNGno+PidlMUXyArn79Xhw+vIlffplMeHhX7rvv\ncdORRCQfqTCJyCVGjBjBjz/+SPny5WnZsjs1a17b1aXVqx8qoGT2r337MI4c2cyuXUtZsWIuZ86M\no0SJEqZjiUg+0C05EcmyaNEiJkyYgNVqZf78+ZQqVcZ0JIfi4uJKly5z8fauQUJCPP/5z3+w2Wym\nY4lIPlBhEhEAduzYwdNPPw3AxIkTCQgIMBvIQXl4eNOjx2KsVlc+/vhj5syZYzqSiOQDFSYRITk5\nma5du3LixAm6dOnCCy+8YDqSQ7vpprto3rwjAP/5z3/YuHGj4UQicqNUmESEIUOGsGnTJmrVqsWc\nOXOwWCymIzm8GjXq07dvX1JSUrLKqIg4LhUmkSJuwYIFzJ49G3d3dxYsWICnp6fpSE5j6tSpNGjQ\ngF27djF48GDTcUTkBugpOZEi7MCBA/Tr1w+ASZMmUa9ePcOJnEdMTAwDBoTh69uCzZu38L///Y+4\nuNNUq3bnVY/TGnQi9kmFSaSIysjIoFevXhw/fpz7778/awkUyR8Xrz+XmnoX3303gHXrIvDzexsv\nr1tyPE5r0InYJ92SEymiJk+ezIoVK6hYsaLGLRUwf/9+1K79ICkpSSxe/CQZGemmI4nINVJhEimC\nYmNjGTlyJAAfffQRN910k+FEzs1isdCp02xKlfJh796fWbNmgulIInKNVJhEipgzZ87Qs2dPUlNT\nGTRoEPfff7/pSEVCyZIV6Nz5YwCiol7n4MH1ZgOJyDVRYRIpYoYOHcq2bdu44447mDBBVzoKU82a\nQTRt+gIZGWksWvQ4586dMh1JRPJIg75FioCQkPHExyezf/92li//EhcXKzVqtGTgwPFXPa6oLqRb\nkNq3f4s9eyI5cmQzP/30Ep06zTQdSUTyQIVJpAiIj0/Gx+cFFi2qC0C7duPx8xua63FFeSHdguLq\n6k6XLl8wc6Y/sbGzqFu3O9WrtzcdS0RyoVtyIkXE0qUvc/LkIapUaU6zZlr6xKSKFe+kVavXAfjm\nm766NSfiAFSYRIqAQ4d2sWHDh1itxXjwwQ9xcbGajlTktWgxDB+fBiQmxhEZOdJ0HBHJhQqTiJM7\ndeoUa9d+A0Dr1qFUqFDHcCIBsFrd6Nz5I1xcXPntt/fYt2+16UgichUqTCJObvjw4Zw+nYSPT0Pu\nvvtl03HkIj4+DWjRIhiw8fXXz5Cammw6kojkQIVJxImtWrWK999/H4vFhc6d52C1upmOJJdp1eo1\nypevw7Fj21m5crTpOCKSAxUmESeVnJzMM888A8Bdd92Dj08Dw4kkO66uxenc+SMsFhfWrp3I0aMH\nTUcSkWyoMIk4qVGjRrFjxw7q1q1LvXotTceRq6hSpSnNmr2IzZbB2rVfc+7cOdORROQyKkwiTmjD\nhg1MnjwZFxcX5syZg9WqKdfsXZs2b1C2bE2OHz/CpEmTTMcRkcuoMIk4mYyMDAYOHEhGRgaDBw+m\nSZMmpiNJHri5laBjxxkAjBkzhj179hhOJCIXU2EScTKzZ89m3bp13Hzzzbzxxhum48g1qFatLdWq\n3cXZs2cZPHgwNpvNdCQROU+FScSJHDlyhJCQEACmTJmCp6en4URyrRo37oCnpyffffcdS5YsMR1H\nRM5TYRJxIsOGDeP48eMEBgbSrVs303HkOnh4lGLcuHEADBkyhFOntGyKiD1QYRJxEj///DOffPIJ\nxYsX54MPPsBisZiOJNdp4MCB+Pv7s3//fsaMGWM6joiQ98JUvUBTiMgNSU1N5bnnngMgJCSEWrVq\nGU4kN8JqtTJ9+nQsFgtvv/02W7ZsMR1JpMjLrTBVA4YBO3PY/grQFwjPz1Aicm2mTJnCH3/8QY0a\nNbLGMIlja9SoEQMHDiQtLY3nnntOA8BFDMttcpY9wASgXzbbugK7gEVAGTKL06x8TSciudq7dy+j\nR2cuqfHBBx/g7u5uOJHciJiYGHr3DgXg3LnSuLuXZNWqVbRs+TA1a2Y/W7uPjwdhYcGFmFKk6LmR\n2ezaA9PPv94NBKLCJFLoXnrpJc6cOUO3bt0ICgoyHUduUHKyFV/f0Kz39913J4sXP8mGDWu4556P\ncXcvc8UxcXGhV3wmIvnrRgZ9VwcSz7/enQ9ZROQaLV++nEWLFlGiRAnefvtt03GkANx11+Pcemsr\nzpw5ysqVmldLxJQbKUyJQI3zr2vwb3kSkUKQlpbG888/D8CIESOoUqWK4URSECwWC/fe+y4Wiwu/\n/fYe//zzp+lIIkXS9d6SKwOsJ/MqUySZg8OX5rRzaGho1uuAgAACAgKu82tF5IKZM2eyZcsWfH19\nGTp0qOk4UoB8fBrg59eXmJgZ/PTTizz++A+aNkIkn0RFRREVFZXrfnkpTF3JLEbPArMBPyAE6M6/\nY5hswPKcTnBxYRKRGxMSMp69exNYvPg9AHx9mzBgQNhVj4mJ2YyvbyGEkwLTps0YtmyZy65dP7Fj\nx3fcdltH05FEnMLlF3IuPERzubwUpgVceusulsyyBDDg+uKJyPWKj09m164zpKQkU61aW1q1mpvr\n1YbVqx8qpHRSUEqWrEBAwGh++ukFfvrpRapXD8TVtbjpWCJFhmb6FnEwx48fITp6GhaLC0FB7+jW\nTBHSuPFzlC9fh4SEnaxbN9V0HJEiRYVJxIHYbDZ+++1HbLZ0GjUayE033WU6khQiq9WNoKApAPz8\n8xhOnYo3nEik6FBhEnEgX331FfHxe3B39yYgIPv77OLcatYM4rbbOnHu3EkiI0eYjiNSZKgwiTiI\ns2fPZj0N16bNGEqUKGc4kZgSFPQ2Li5ubNz4EQcPrjcdR6RIUGEScRBTp05lz549lClTgUaN+puO\nIwaVLVuTZs1eBOCnn17UOnMihUCFScQBHD16lHHjxgHQqFEQLi43sqqROINWrUZSokQF9u9fw759\nf5mOI+L0VJhEHMAbb7zBiRMnCAoKonLlGrkfIE6veHFPAgJCAYiJieDcuXNmA4k4ORUmETu3fft2\npk2bhouLC5MmTTIdR+yIn19fype/nZMnE5g2bZrpOCJOTYVJxM4FBweTlpZGnz59uPPOO03HETti\ntbrRvv0EIPMq5PHjxw0nEnFeKkwiduznn3/mq6++omTJkrzxhlaqlyvddltHfHx8SUhI4M033zQd\nR8RpqTCJ2KmMjIysaQSGDRtGpUqVDCcSe2SxWGjUKBD490lKEcl/Kkwidmru3LlER0dz8803ZxUn\nkeyUK3czTz75JOfOnWP48OGm44g4JRUmETt09uzZrB98Y8eOpWTJkoYTib0bO3Ys7u7uzJs3j19/\n/dV0HBGno8IkYofeffdd9u3bR7169ejVq5fpOOIAbrnlFl58MXMyy6FDh2oyS5F8psIkYmeOHTuW\nNXh30qRJWK1Ww4nEUYSEhFChQgXWrl3LV199ZTqOiFNRYRKxM2+99RYnTpygQ4cOBAYGmo4jDsTT\n05PXX38dgBEjRpCWlmY4kYjz0PoKInZk3759vP/++wCEhYUZTiOOIiYmht69QwFIT0+nVClv/vrr\nL1q3foRatfyyPcbHx4OwsOBCTCni2FSYROxIaGgoKSkpPProozRs2NB0HHEQyclWfH1Ds9536FCH\nRYseZ/PmWAIC5uHm5nHFMXFxoVd8JiI5U2ESMSgkZDzx8ckAJCb+w9dff4zF4kJKSoWsKwaXi4nZ\njK9v4WUUx3PnnY+ydu1E4uM38ttv79OixSumI4k4PBUmEYPi45OzrgzMnfsQNpuNRo0GUq/e1ByP\nWb36oUJKJ47KYnGhXbu3+Pzz+1i9+i38/fvi7l7GdCwRh6ZB3yJ2YP/+tWzbtgQ3txK0bv2a6Tji\nBGrUCMLXN4CzZ4+zevV403FEHJ4Kk4hhNpuNiIgQAJo1e5FSpXwMJxJnYLFYaNcu88GBdeve5eTJ\nQ4YTiTg2FSYRw3bs+J59+1bh4VGOu+/WWBPJP1WqNKVOnUdIS0smKmq06TgiDk2FScSgjIwMIiMz\nl0Bp2XIE7u5ehhOJs2nbdhwWiwsbNnzI0aPbTMcRcVgqTCIG7dmzmSNHNuPpWZXGjZ8zHUecUPny\nt9OgQR9stnRWrHjVdBwRh6XCJGJISkoKGzasAKBNmzdwdXU3nEicVUBAKK6u7mzduoCDB9ebjiPi\nkFSYRAyZPn06p08nUaFCXerVe9J0HHFinp6VadJkCACRkSFamFfkOqgwiRhw4sQJxo4dC0C7dm/i\n4qIFdqVg3XNPCO7uZdizZzm7dy8zHUfE4agwiRgwefJkjh49SsWKVbnttk6m40gR4OHhTYsWmdNX\nREToKpPItVJhEilkR44cYfLkyQD4+bXHYrEYTiRFRdOmgyld+mbi4zcQF/eH6TgiDkWFSaSQvfXW\nW5w+fZqOHTty0023mI4jRUjmTPKhAGzcGEVaWprZQCIORIVJpBAdOHCAadOmAWSNYRIpTA0a9KZs\n2ZqcOHGM//3vf6bjiDgMFSaRQjRmzBhSUlLo0aMH9evXNx1HiiCr1Y2AgMxZv0ePHk1KSorhRCKO\nQYVJpJDs2rWLOXPm4OLiwujRWqZCzLnzzkcpU6Yi+/btY9asWabjiDgEFSaRQhIaGkpaWhpPPfUU\ntWvXNh1HijCLxYWGDdsAMG7cOM6cOWM4kYj9U2ESKQR//PEHn3/+OW5ubrz++uum44hQtWptGjVq\nRHx8PO+//77pOCJ2T4VJpBC8/vrr2Gw2+vXrh6+vr+k4IlgslqwHD8aPH09SUpLhRCL2TYVJpIDF\nxMSwaNEiPDw8GDlypOk4Ilk6dOhAy5YtSUhIYMqUKabjiNg1FSaRAvbqq5krxA8aNIhKlSoZTiPy\nL4vFwrhx4wB4++23OXbsmOFEIvZLhUmkAK1evZoff/yR0qVLExwcbDqOyBVatmxJUFAQJ0+eZPz4\n8abjiNitvBSmV4C+QHg228LOb5sOeOVjLhGHZ7PZsm7BvfTSS5QrV85wIpHsXRjL9P777/P3338b\nTiNin3IrTF2BXcAsYD2Z5eiCvhdtiwEaFURAEUe1bNkyfv75Z8qWLctLL71kOo5Ijho1asTDDz9M\ncnJy1i06EblUboWpPbD7/OvdgP9F26KBYKAdUAaIzPd0Ig7q4qtLwcHBeHp6Gk4kcnVjxozBYrEw\nc+ZM4uLiTMcRsTu5FabqQOL517sv27YBiADGA4HolpxIliVLlhAdHY2Pjw+DBg0yHUckV3Xr1qVn\nz56kpqbyxhtvmI4jYndyK0yJQI3zr2vwb3kCGEbm2KVGQCwwPN/TiTig9PR0XnvtNQBGjhxJiRIl\nDCcSyZvQ0FCsViuffPIJ27ZtMx1HxK645rJ9PZlXmSKBasDS85+XIbMozb9oP++cThIaGpr1OiAg\ngICAgOsKK+II5s2bx5YtW7jlllvo27dv7geIGBATE0Pv3qFXfF69en127Ijl3nu70Lp110u2+fh4\nEBampz3FuURFRREVFZXrfrkVpolkXkUCsAHLAT8ghMzxS8FkDvguc37fbF1cmEScWWpqKqNGjQIy\nZ/cuXry44UQi2UtOtuLrG3rF597ez/DeezWJi/uDoKDP8fGpn7UtLu7K/UUc3eUXcnJaHD23wgQw\n4LL3sUD3HLaJFEkhIeOJj09m+/ZYdu7ciadnWVau3MuqVaFXPS4mZjNaKUXsiZdXVRo1Gsi6de+y\nYsVrPPbY16YjidiFvBQmEclFfHwyVaoMZ/HiWgC0b/8+1as/lutxq1c/VNDRRK7ZPfcMJzZ2Ftu3\nf8OBA79SpUoz05FEjNNM3yL5JCZmBidO7Kdixbu4884epuOIXLdSpW6iadPnAVi+/FXDaUTsgwqT\nSD5ITT3HqlWZE/61aTMGi0X/aolju/vuVyhe3Is9eyLZs2eF6Tgixum/6iL54K+/fuP06SNUrtyE\n2rUfNB3ZEBFeAAAgAElEQVRH5IZ5eHjTvPlQAJYvH4nNZjOcSMQsFSaRG5SUlMSWLWsAaNNmLBaL\nxXAikfzRrNkLlChRngMHfmHHju9NxxExSoVJ5Aa9/fbbnDt3lltvbU316u1NxxHJN8WLl6ZFixAA\nVqx4VVeZpEhTYRK5AUePHmXKlCkAtG2rq0vifBo3fo7SpW8mPn4je/duNR1HxBgVJpEbMGHCBE6e\nPEnlyjW55ZZ7TMcRyXdubh60bJn5pNzGjVGkp6cbTiRihgqTyHX6+++/ef/99wFo2LCN4TQiBcfP\n7xnKlPElKekon3/+uek4IkaoMIlcpzfffJPk5GQefvhhypW72XQckQJjtRajdetQIHOpq3PnzpkN\nJGKACpPIddi7dy8zZszAYrEwZswY03FECly9ek/g5VWePXv2MGfOHNNxRAqdCpPIdRgzZgypqan0\n7NmTunXrmo4jUuBcXKw0aBAAZP79T05ONhtIpJCpMIlcox07dvDxxx9jtVoJDQ01HUek0Nx66x00\naNCAQ4cOMW3aNNNxRAqVCpPINQoNDSU9PZ2nn36amjVrmo4jUmgsFgtjx44F4K233uLkyZOGE4kU\nHhUmkWuwZcsWvvzyS4oVK8Zrr71mOo5Iobv//vtp1qwZR48e5d133zUdR6TQqDCJXIPXX38dm81G\n//79ueWWW0zHESl0FouFceMyF5qeNGkSx48fN5xIpHC4mg4g4iiio6NZvHgxHh4ejBgxwnQckUIX\nExND796hAPj4VCM+fg+tWz+In1+7qx7n4+NBWFhwISQUKTgqTCJ59OqrmbMdDx48GB8fH8NpRApf\ncrIVX99QAB544F4+/LA5f/21gaCghZQsWTHH4+LiQgsnoEgB0i05kTxYtWoVP/30E6VLl2bYsGGm\n44gYV6VKM267rSOpqadZteot03FECpwKk0gubDZb1tWll156iXLlyhlOJGIf2rTJnLQ1OnoaJ04c\nMJxGpGCpMInkIiIigp9//pmyZcvy4osvmo4jYjd8fBpQt2530tNTWLlSM96Lc1NhErkKm83GyJEj\nARg2bBheXl6GE4nYl4CA0VgsLmzcOIeEhF2m44gUGA36FrlMSMh44uMzl33Yt28b69evx929JJs2\nJWU9IXS5mJjN+PoWXkYRe1G+/O3Ur9+LjRs/ZuXKUB5++FPTkUQKhAqTyGXi45Px9Q3FZsvgxx8b\nAhAQ8Ca1ag3J8ZjVqx8qrHgidqd161Fs2vQ5mzZ9TosWIVSsqPUVxfnolpxIDv74Yz6HD2/C07Mq\n/v79TccRsVtlyvji5/csYCMq6nXTcUQKhAqTSDYyMtKy/sPfuvXruLoWN5xIxL61avUqrq7u/Pnn\nIg4dijEdRyTfqTCJZOP33z/l2LHteHvXoH79p0zHEbF7pUvfTOPG/wFgxQqtsyjOR4VJ5DLp6ems\nXDkayHwCyGp1M5xIxDHcc08IxYqVYufOH9i3b43pOCL5SoVJ5DI7dsSSlLSXChXu4M47HzUdR8Rh\nlChRnmbNMucqW758JDabzXAikfyjwiRykeTkZDZt+hnInMXYxcVqOJGIY2nefCju7t7s3buS3bsj\nTMcRyTcqTCIX+e9//0ty8ikqVfLj9tsfNh1HxOG4u3vRokXmeou6yiTORIVJ5LykpCTefPNNANq0\nGYvFYjGcSMQxNWkymJIlb+LQofVs2/a16Tgi+UKFSeS8SZMmkZCQwE033UrNmveajiPisIoVK0nL\nliOAzCfmdJVJnIEKkwhw+PBh3n77bQD8/Nrp6pLIDfL374+nZ1WOHNnMnj1bTMcRuWEqTCLA2LFj\nOXPmDJ07d6Zixaqm44g4PFfX4rRunTn56++/R5GWlmY4kciNUWGSIm/37t3MmDEDi8XCuHHjTMcR\ncRr16z+Ft3cNTpxI4JNPPjEdR+SGqDBJkTdq1ChSU1Pp1asXdetq0VCR/GK1utGmzRsAhIaGkpyc\nbDiRyPVTYZIibfPmzXz++ee4ubkRGhpqOo6I07nzzkfx9r6JAwcO8MEHH5iOI3LdVJikSBs5MnOe\nmIEDB+Lr62s6jojTsVhc8PdvD8Cbb75JYmKi4UQi1yc/CpMf0DcfziNSqNasWcM333xDyZIlGTly\npOk4Ik7r5ptrEBAQwPHjxxk/frzpOCLXJS+F6RUyC1F4NtvaA/7ArPwMJVLQbDYbISEhAAwdOpSK\nFSsaTiTivCwWC2FhYQC8++67HDx40HAikWuXW2HqCuwisxCt59IrSWXOb1dZEofzww8/sHr1asqV\nK8fQoUNNxxFxek2bNqVLly4kJyczevRo03FErlluhak9sPv8691kXk26oPv536eTefXJK3+jiRSM\njIwMhg8fDmSOYfL09DScSKRoGDduHFarlTlz5rBt2zbTcUSuSW6FqTpwYYTe7su2+QM7gQHntw3P\n32giBWPu3Lls2rSJqlWrMnDgQNNxRIqM2rVr06dPH9LT0zVuUByOay7bE4EaQNz53y9+vMEbiD3/\nehnQLaeTXPy4dkBAAAEBAdccVCQ/nDt3jtdeew2A0aNH4+7ubjiRSNEyatQoPvvsMxYuXMi6deto\n2rSp6UhSxEVFRREVFZXrfrkVpvVkXmWKBKoBS89/Xub8Nn9gOZllKjqnk2h+G7EXs2fPZvfu3dSp\nU4cnn3zSdByRIqdy5co8//zzhIWFERwczIoVK7R2oxh1+YWcnMbY5XZLbiKZpagvYCOzHPkBM89v\nqwF0IXP80uwbzCxSoE6dOsUbb2TOOjxu3DhcXXP7/wURKQjBwcF4e3uzcuVKfvzxR9NxRPIkLz8x\nBlz2PpZ/B3xfvk3Ebk2cOJHDhw/TtGlTHnroIdNxRIqMmJgYevcOveSz6tUbEROzjMcff5pOnfpf\ncZXJx8eDsLDgQkwpcnX6X2wpEg4dOsSkSZMAmDx5sm4BiBSi5GQrvr6hl3xWpcpZduyoxfHjBzh5\n8jbq1Xv8ku1xcZfuL2KaCpM4tZCQ8cTHJ7N27decOXOGW265nVmzljFr1rIcj4mJ2YxWSREpWK6u\n7gQEvMHXX/dhxYpXueOOrri6FjcdSyRHKkzi1OLjkylRohs7d47BxcWVBx9cQrlyt131mNWrdbtO\npDDUr9+LX36ZxD//bCUmZgZNmw4xHUkkR1p8V5xeRMQwbLYM/P3751qWRKTwuLhYadv2TQB+/nkM\nZ88mGU4kkjMVJnFqf/+9hx07vqdYsdK0bv266TgicpnatR+katUWnDlzlDVrtDCv2C8VJnFaGRkZ\nREdnTh3WokUwJUtqgV0Re2OxWOjQYTIAv/46haSkfYYTiWRPhUmc1hdffEFCQjylS1emefMXTccR\nkRxUqdKUunV7kJZ2luXLXzUdRyRbKkzilM6ePZu1VlWbNmNwcythOJGIXE27dm9htRZj06ZP+fvv\n2NwPEClkKkzilKZOncq+ffvw9q5I/fq9TMcRkVx4e1ejSZPBACxdOhSbzWY4kcilVJjE6Rw7dow3\n38x88sbfPxAXF6vhRCKSFy1bjsTd3Zu4uCgOHNhhOo7IJVSYxOmMGTOGpKQkAgMDqVy5puk4IpJH\nHh7eWU+zxsQsIy0tzXAikX+pMIlT2bVrF//973+xWCxMnDjRdBwRuUaNGz+Ht3cNkpKO8uGHH5qO\nI5JFhUmcyvDhw0lNTaVXr17Ur1/fdBwRuUZWazHatw8D4PXXX+fkyZOGE4lkUmESp/Hrr78yf/58\n3N3dGTt2rOk4InKd6tTpQoUKVThy5AhhYWGm44gAWktOHMiFhXSzY7PZ+P77zMv3tWo14tVXZwNa\nSFfEEVksFho16sAPP8xh8uTJ9O3bF1/9iyyGqTCJw4iPT8bXNzTbbZs2fcbRowcpVcqHBx74nuLF\nSwNaSFfEUVWsWJXHHnuML7/8kuDgYObNm2c6khRxuiUnDu/cudNERIQA0Lbtm1llSUQc2/jx4/Hw\n8CA8PJxVq1aZjiNFnAqTOLw1ayZw8uRBKlXyp0GDp0zHEZF8UrVqVYYNGwbACy+8QEZGhuFEUpSp\nMIlDS0rax9q1EwC49953sFj0V1rEmbzyyitUrlyZ2NhYPvnkE9NxpAjTTxdxaBERwaSlnaVu3R7c\ncss9puOISD4rWbIk48ePB2DEiBGaZkCMUWESh7V//1q2bJmLq6s77duPNx1HRApIz549adasGfHx\n8VnLHokUNhUmcUg2WwY//vg8AM2bv0yZMrcaTiQiBcVisfDOO+8A8Pbbb7N7927DiaQoUmESh7Rp\n02ccOhRN6dI3c889wabjiEgBa9q0KU888QTnzp3LGgguUphUmMThpKSczJpGoF27MIoVK2U4kYgU\nhrfeeosSJUqwcOFCVqxYYTqOFDEqTOJwVq58g1On/qZy5abUq/e46TgiUkiqVKnC8OHDARg0aBCp\nqamGE0lRosIkDuWff7aybt07gIX7739f0wiIFDEvv/wyNWrUYOvWrbz33num40gRoqVRxGHYbDZ+\n+GEIGRlp+Pv35+abG5mOJCIFJCYmht69Q7Pd5uvbhF27dhESMpxffz1IiRKZs/v7+HgQFqYxjVIw\nVJjEYezdu5U9eyLx8ChL27bjTMcRkQKUnGzNce1IX1/Yv/8k27d/y7ZtR3j44ckAxMVlv79IftD9\nDHEIp0+fZv36pUDmenElSpQznEhETAoKegertTibNn3G3r1aZ04KngqTOIRx48Zx5swJKlXyw8/v\nWdNxRMSwsmVr0KJF5vQCP/wwiIyMNMOJxNmpMInd2759O5MmTQLg/vs/wMXFajiRiNiDe+4Jwcvr\nVg4f3kR09HTTccTJqTCJXbPZbDz//POkpqZSs2YDqlRpZjqSiNgJN7cSBAVNAWD58ldJTj5tOJE4\nMxUmsWtLlizhxx9/xMvLCz+/9qbjiIiduf32h6hRI4iUlCRiYyNMxxEnpsIkduvUqVMMGTIEgDFj\nxuDhUdJwIhGxNxaLhfvum4rVWoydOzeyapUGgEvBUGESuzVq1Cj279+Pv78/zz33nOk4ImKnypW7\njRYtMudf6t+/P+fOnTOcSJyRCpPYpQ0bNvDOO+/g4uLCjBkzsFo10FtEctay5QhKly7Ln3/+ycSJ\nE03HESekwiR2Jz09nf79+5ORkcHgwYPx9/c3HUlE7JyrqzvNmj0AwNixY9m5c6fhROJsVJjE7kyb\nNo3169dTuXJlxowZYzqOiDiIm2+uzhNPPMHZs2d57rnnsNlspiOJE9HSKFLoQkLGEx+fnO22M2dO\n8tVX7wNQq1YLBg+enLUtJmYzvr6FkVBEHNXkyZP57rvvWLZsGXPnzuWxxx4zHUmcRH4UpjJAO2Bh\nPpxLioD4+OQc14iaP787qannqF37QVq1movFYsnatnr1Q4WUUEQcVcWKFZkwYQJ9+/blxRdf5N57\n78Xb29t0LHECebkl9wrQFwjPYftwoEe+JZIia8eO79m6dT5ubiW57773LilLIiJ51adPH1q0aMHh\nw4cZPny46TjiJHIrTF2BXcAsYD2ZxelifoBG1skNO3fuNN9//x8A2rR5Ay+vWwwnEhFHdeHpWldX\nV2bMmMHatWtNRxInkFthag/sPv96N3D540r+QHR+h5KiZ/nykSQmxuHj04CmTYeYjiMiDq5u3boM\nG5a5OO8zzzzD2bNnDScSR5dbYaoOJJ5/vfuybe3JvE2n+yZyQ/bvX8u6dVOxWKw8+OAcXFz0LIKI\n3LjXXnuN2rVr89dff+mJW7lhuf1kSgRqAHHnf0+8aFu/87/KAI2Al4FJ2Z0kNDQ063VAQAABAQHX\nGVecTVraWZYs6QPYaNEimEqVGpqOJCJOwt3dnQ8//JCWLVsyfvx4unTpgp+fn+lYYmeioqKIiorK\ndb/cCtN6Mq8yRQLVgKXnPy8DdD//2g8IIYeyBJcWJpGLrVz5BseObaN8+dtp3fo103FExMm0aNGC\nwYMHM3XqVPr06cP69etxc3MzHUvsyOUXckaPHp3tfrkVponA9POvbcBy/i1I3cksUf2AhkADYOMN\nZJYi5u+/Y1mzZgJg4cEH5+Dq6m46kog4sJiYGHr3Dr3i89TUkpQqVYbff/+dJk2CqF+/VdY2Hx8P\nwsKCCzGlOKq8DBYZcNn7WP69urQnm+0iuUpPT2XJkj7YbOk0bfoCVas2Nx1JRBxccrI1xzneHn64\nHZ9+2p7Nm9dw993vU6HCHQDExWW/v8jltDSKGLFmzXgOH/4db+/qtG071nQcEXFy1au3w8+vL+np\n51iypA8ZGemmI4mDUWGSQnf8+BFWrnwDgE6dZlOsWEnDiUSkKAgMnEjp0pU5eHAd69a9azqOOBgV\nJilUqamprFmzhIyMVPz9+1OtWhvTkUSkiHB396Jjx8xhucuXv8rRo9sMJxJHosIkhWrcuHEcO3YI\nL69bCAycYDqOiBQxt93Wkfr1e5GWlszixU/q1pzkmQqTFJr169czdmzmeKWHHvqE4sU9DScSkaLo\n3nun4ulZlUOH1rN582rTccRBqDBJoThz5gxPPvkk6enp3HFHM3x9A0xHEpEiyt3di4ce+hiA339f\nSXS0VviS3KkwSaEICQlh27Zt3HHHHfj5tTMdR0SKuGrV2tK06QvYbDaefPJJkpOTTUcSO6fCJAVu\n2bJlvPfee7i6uvLZZ59htWqtOBExr127N/HyKs9ff/1FSEiI6Thi51SYpEAdP36cp59+GshcIqdh\nQ60VJyL2wc3Ng5YtH8HV1ZWpU6cSERFhOpLYMRUmKVCDBg3i4MGDNGvWjOBgLT8gIvalXLlKjBo1\nCoCnn36axMTEXI6QokqFSQrMl19+yRdffEGJEiX49NNPcXXVrTgRsT8hISE0a9aMAwcOMHDgQGw2\nm+lIYof0E0xuSEjIeOLjrxwseeJEAt9+OwOAevXaMHbsZ1nbYmI24+tbWAlFRK7O1dWV//3vfzRs\n2JC5c+cSGBhInz59TMcSO6PCJDckPj75isUu09PPMWdOC1JTz3HHHV3p0CEci8WStX316ocKOaWI\nyNXVqlWLadOm0atXLwYNGkTz5s2pU6eO6VhiR3RLTvJdZOQIDh2KxsvrVjp1mnVJWRIRsVdPPvkk\nvXr1Ijk5mR49emiqAbmECpPkqx07fuCXXyZjsVjp2nUu7u5lTEcSEcmzDz74gFq1arF582aGDh1q\nOo7YERUmyTcnTx7iq696AdC27ViqVGlmOJGIyLUpVaoU8+bNo1ixYkybNo1FixaZjiR2QoVJ8kVG\nRjqLFz/JmTNHqV69PS1aDDMdSUTkujRs2JCJEycC8Mwzz7B3717DicQeqDBJvli9Oow9e5ZTsmRF\nHn74UywW/dUSEcc1ePBgOnXqRGJiIo899hipqammI4lhekpObtju3ZFERb0OwMMPf0qpUj6GE4mI\n5E1MTAy9e4dmu61EidspUSKKX375hQYNWtG4cVDWNh8fD8LCNBlvUaLCJDfk9Okkvv/+UWy2DFq2\nHEmNGh1MRxIRybPkZOsVU6NcrESJznzySQBbt/7KHXe8SN263QGIi8v5GHFOum8i1y0lJYWoqPmc\nOXOUGjWCCAgYbTqSiEi+uuWWFnTo8DYAS5b04ciRPwwnElNUmOS6Pf/88xw9ehAvr1t55JHPcXGx\nmo4kIpLvmjQZxF13PU5q6mnCwx8hJeWE6UhigAqTXJePPvqIGTNm4OJipUePRZQoUc50JBGRAmGx\nWOjYcQYVK97FsWPb+eqr3lpvrghSYZJrFhMTw8CBAwFo1uwBKlXyM5xIRKRgFStWkh49FlG8uBd/\n/bWYLVvWmI4khUyFSa7JsWPH6NKlCykpKfTr149atRqajiQiUijKlq3JI49kLiS+YcNyIiMjDSeS\nwqTCJHmWmppK9+7d2bt3L40bN2bq1KmmI4mIFKrbbutIq1avYbPZ6N69O7t27TIdSQqJCpPkic1m\nY9CgQSxfvpybbrqJhQsXUrx4cdOxREQKXevWo6hSpRYJCQl07NiRxMRE05GkEKgwSZ68++67zJw5\nk+LFi7NkyRKqVq1qOpKIiBEuLlZatuzCnXfeyV9//UWPHj1IS0szHUsKmCaulCwhIeOJj0++4vMD\nB3awfPmXADRt2pFp035g2rQfAIiJ2Yyvb2GmFBExr1ix4nzzzTc0adKEpUuX8uKLL/Lee++ZjiUF\nSIVJssTHJ18x4+2RI1tYtepubDYbrVuPIiDg0u2rVz9UeAFFROyIr68vX331FW3atOH999+nTp06\nPPfcc6ZjSQHRLTnJ0enTR/jyy06cO3eSunV70Lr1KNORRETsyt13382HH34IwJAhQ1i2bJnhRFJQ\nVJgkW2lpZ5k37xESE+OoXLkJnTt/hMViMR1LRMTuPPHEE4wYMYL09HS6devG1q1bTUeSAqBbcnKF\njIx0Fi16nP371+DpWYUePb7Czc3DdCwREbsRExND796hWe9tNlduvbUOe/f+SZMmzbnvvmcoWdLz\nkmN8fDwICwsu5KSSX1SY5BI2m43vv/8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- "text": [ - "" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What happens when you replace $[0, \\pi / 2]$ with $[0, \\pi]$?\n", - "\n", - "In this case, the mean $\\mu$ of this distribution is $\\pi/2$, and since $g' = \\cos$, we have $g'(\\mu) = 0$\n", - "\n", - "Hence the conditions of the delta theorem are not satisfied\n" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First we want to verify the claim that\n", - "\n", - "$$\n", - " \\sqrt{n} \\mathbf Q ( \\bar{\\mathbf X}_n - \\boldsymbol \\mu )\n", - " \\stackrel{d}{\\to} \n", - " N(\\mathbf 0, \\mathbf I)\n", - "$$\n", - "\n", - "This is straightforward given the facts presented in the exercise\n", - "\n", - "Let\n", - "\n", - "$$\n", - " \\mathbf Y_n := \\sqrt{n} ( \\bar{\\mathbf X}_n - \\boldsymbol \\mu )\n", - " \\quad \\text{and} \\quad\n", - " \\mathbf Y \\sim N(\\mathbf 0, \\Sigma)\n", - "$$\n", - "\n", - "By the multivariate CLT and the continuous mapping theorem, we have\n", - "\n", - "$$\n", - " \\mathbf Q \\mathbf Y_n \n", - " \\stackrel{d}{\\to} \n", - " \\mathbf Q \\mathbf Y\n", - "$$\n", - "\n", - "Since linear combinations of normal random variables are normal, the vector\n", - "$\\mathbf Q \\mathbf Y$ is also normal\n", - "\n", - "Its mean is clearly $\\mathbf 0$, and its variance covariance matrix is\n", - "\n", - "$$\n", - " \\mathrm{Var}[\\mathbf Q \\mathbf Y]\n", - " = \\mathbf Q \\mathrm{Var}[\\mathbf Y] \\mathbf Q'\n", - " = \\mathbf Q \\Sigma \\mathbf Q'\n", - " = \\mathbf I\n", - "$$\n", - "\n", - "In conclusion, $\\mathbf Q \\mathbf Y_n \\stackrel{d}{\\to} \\mathbf Q \\mathbf Y \\sim N(\\mathbf 0, \\mathbf I)$, which is what we aimed to show\n", - "\n", - "Now we turn to the simulation exercise\n", - "\n", - "Our solution is as follows\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from scipy.stats import uniform, chi2\n", - "from scipy.linalg import inv, sqrtm\n", - "\n", - "# == Set parameters == #\n", - "n = 250\n", - "replications = 50000\n", - "dw = uniform(loc=-1, scale=2) # Uniform(-1, 1)\n", - "du = uniform(loc=-2, scale=4) # Uniform(-2, 2)\n", - "sw, su = dw.std(), du.std()\n", - "vw, vu = sw**2, su**2\n", - "Sigma = ((vw, vw), (vw, vw + vu))\n", - "Sigma = np.array(Sigma)\n", - "\n", - "# == Compute Sigma^{-1/2} == #\n", - "Q = inv(sqrtm(Sigma)) \n", - "\n", - "# == Generate observations of the normalized sample mean == #\n", - "error_obs = np.empty((2, replications))\n", - "for i in range(replications):\n", - " # == Generate one sequence of bivariate shocks == #\n", - " X = np.empty((2, n))\n", - " W = dw.rvs(n)\n", - " U = du.rvs(n)\n", - " # == Construct the n observations of the random vector == #\n", - " X[0, :] = W\n", - " X[1, :] = W + U\n", - " # == Construct the i-th observation of Y_n == #\n", - " error_obs[:, i] = np.sqrt(n) * X.mean(axis=1)\n", - "\n", - "# == Premultiply by Q and then take the squared norm == #\n", - "temp = np.dot(Q, error_obs)\n", - "chisq_obs = np.sum(temp**2, axis=0)\n", - "\n", - "# == Plot == #\n", - "fig, ax = plt.subplots(figsize=(10, 6))\n", - "xmax = 8\n", - "ax.set_xlim(0, xmax)\n", - "xgrid = np.linspace(0, xmax, 200)\n", - "lb = \"Chi-squared with 2 degrees of freedom\"\n", - "ax.plot(xgrid, chi2.pdf(xgrid, 2), 'k-', lw=2, label=lb)\n", - "ax.legend()\n", - "ax.hist(chisq_obs, bins=50, normed=True)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 4 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/lqcontrol_solutions.ipynb b/solutions/lqcontrol_solutions.ipynb deleted file mode 100644 index d0dc34921..000000000 --- a/solutions/lqcontrol_solutions.ipynb +++ /dev/null @@ -1,434 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:e48cf621b35f99f4171d6e351d4743b93d56b3b64a0395068394da284edb1648" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: LQ Control Problems" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/lqcontrol.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Common imports for the exercises" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import division\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from quantecon import LQ" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here\u2019s one solution\n", - "\n", - "We use some fancy plot commands to get a certain style \u2014 feel free to use simpler ones" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "The model is an LQ permanent income / life-cycle model with hump-shaped income\n", - "\n", - "$$ y_t = m_1 t + m_2 t^2 + \\sigma w_{t+1} $$\n", - "\n", - "where $\\{w_t\\}$ is iid $N(0, 1)$ and the coefficients $m_1$ and $m_2$ are chosen so that\n", - "$p(t) = m_1 t + m_2 t^2$ has an inverted U shape with\n", - "\n", - "* $p(0) = 0, p(T/2) = \\mu$, and \n", - "* $p(T) = 0$.\n", - "\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# == Model parameters == #\n", - "r = 0.05\n", - "beta = 1 / (1 + r)\n", - "T = 50\n", - "c_bar = 1.5\n", - "sigma = 0.15\n", - "mu = 2\n", - "q = 1e4\n", - "m1 = T * (mu / (T/2)**2)\n", - "m2 = - (mu / (T/2)**2)\n", - "\n", - "# == Formulate as an LQ problem == #\n", - "Q = 1\n", - "R = np.zeros((4, 4)) \n", - "Rf = np.zeros((4, 4))\n", - "Rf[0, 0] = q\n", - "A = [[1 + r, -c_bar, m1, m2], \n", - " [0, 1, 0, 0],\n", - " [0, 1, 1, 0],\n", - " [0, 1, 2, 1]]\n", - "B = [[-1],\n", - " [0],\n", - " [0],\n", - " [0]]\n", - "C = [[sigma],\n", - " [0],\n", - " [0],\n", - " [0]]\n", - "\n", - "# == Compute solutions and simulate == #\n", - "lq = LQ(Q, R, A, B, C, beta=beta, T=T, Rf=Rf)\n", - "x0 = (0, 1, 0, 0)\n", - "xp, up, wp = lq.compute_sequence(x0)\n", - "\n", - "# == Convert results back to assets, consumption and income == #\n", - "ap = xp[0, :] # Assets\n", - "c = up.flatten() + c_bar # Consumption\n", - "time = np.arange(1, T+1)\n", - "income = wp[0, 1:] + m1 * time + m2 * time**2 # Income\n", - "\n", - "\n", - "# == Plot results == #\n", - "n_rows = 2\n", - "fig, axes = plt.subplots(n_rows, 1, figsize=(12, 10))\n", - "\n", - "plt.subplots_adjust(hspace=0.5)\n", - "for i in range(n_rows):\n", - " axes[i].grid()\n", - " axes[i].set_xlabel(r'Time')\n", - "bbox = (0., 1.02, 1., .102)\n", - "legend_args = {'bbox_to_anchor' : bbox, 'loc' : 3, 'mode' : 'expand'}\n", - "p_args = {'lw' : 2, 'alpha' : 0.7}\n", - "\n", - "axes[0].plot(range(1, T+1), income, 'g-', label=\"non-financial income\", **p_args)\n", - "axes[0].plot(range(T), c, 'k-', label=\"consumption\", **p_args)\n", - "axes[0].legend(ncol=2, **legend_args)\n", - "\n", - "axes[1].plot(range(T+1), ap.flatten(), 'b-', label=\"assets\", **p_args)\n", - "axes[1].plot(range(T+1), np.zeros(T+1), 'k-')\n", - "axes[1].legend(ncol=1, **legend_args)\n", - "\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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IIRqdypJdIerUs88+a+wQRAMk9UKUR+qFKI/UC2EI9Tl/sPQhFkIIIYQQdaomfYilhVgY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\nA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- "text": [ - "" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is a permanent income / life-cycle model with polynomial growth in income\n", - "over working life followed by a fixed retirement income. The model is solved\n", - "by combining two LQ programming problems as described in the lecture." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# == Model parameters == #\n", - "r = 0.05\n", - "beta = 1 / (1 + r)\n", - "T = 60\n", - "K = 40\n", - "c_bar = 4\n", - "sigma = 0.35\n", - "mu = 4\n", - "q = 1e4\n", - "s = 1\n", - "m1 = 2 * mu / K\n", - "m2 = - mu / K**2\n", - "\n", - "# == Formulate LQ problem 1 (retirement) == #\n", - "Q = 1\n", - "R = np.zeros((4, 4)) \n", - "Rf = np.zeros((4, 4))\n", - "Rf[0, 0] = q\n", - "A = [[1 + r, s - c_bar, 0, 0], \n", - " [0, 1, 0, 0],\n", - " [0, 1, 1, 0],\n", - " [0, 1, 2, 1]]\n", - "B = [[-1],\n", - " [0],\n", - " [0],\n", - " [0]]\n", - "C = [[0],\n", - " [0],\n", - " [0],\n", - " [0]]\n", - "\n", - "# == Initialize LQ instance for retired agent == #\n", - "lq_retired = LQ(Q, R, A, B, C, beta=beta, T=T-K, Rf=Rf)\n", - "# == Iterate back to start of retirement, record final value function == #\n", - "for i in range(T-K):\n", - " lq_retired.update_values()\n", - "Rf2 = lq_retired.P\n", - "\n", - "# == Formulate LQ problem 2 (working life) == #\n", - "R = np.zeros((4, 4)) \n", - "A = [[1 + r, -c_bar, m1, m2], \n", - " [0, 1, 0, 0],\n", - " [0, 1, 1, 0],\n", - " [0, 1, 2, 1]]\n", - "B = [[-1],\n", - " [0],\n", - " [0],\n", - " [0]]\n", - "C = [[sigma],\n", - " [0],\n", - " [0],\n", - " [0]]\n", - "\n", - "# == Set up working life LQ instance with terminal Rf from lq_retired == #\n", - "lq_working = LQ(Q, R, A, B, C, beta=beta, T=K, Rf=Rf2)\n", - "\n", - "# == Simulate working state / control paths == #\n", - "x0 = (0, 1, 0, 0)\n", - "xp_w, up_w, wp_w = lq_working.compute_sequence(x0)\n", - "# == Simulate retirement paths (note the initial condition) == #\n", - "xp_r, up_r, wp_r = lq_retired.compute_sequence(xp_w[:, K]) \n", - "\n", - "# == Convert results back to assets, consumption and income == #\n", - "xp = np.column_stack((xp_w, xp_r[:, 1:]))\n", - "assets = xp[0, :] # Assets\n", - "\n", - "up = np.column_stack((up_w, up_r))\n", - "c = up.flatten() + c_bar # Consumption\n", - "\n", - "time = np.arange(1, K+1)\n", - "income_w = wp_w[0, 1:K+1] + m1 * time + m2 * time**2 # Income\n", - "income_r = np.ones(T-K) * s\n", - "income = np.concatenate((income_w, income_r))\n", - "\n", - "# == Plot results == #\n", - "n_rows = 2\n", - "fig, axes = plt.subplots(n_rows, 1, figsize=(12, 10))\n", - "\n", - "plt.subplots_adjust(hspace=0.5)\n", - "for i in range(n_rows):\n", - " axes[i].grid()\n", - " axes[i].set_xlabel(r'Time')\n", - "bbox = (0., 1.02, 1., .102)\n", - "legend_args = {'bbox_to_anchor' : bbox, 'loc' : 3, 'mode' : 'expand'}\n", - "p_args = {'lw' : 2, 'alpha' : 0.7}\n", - "\n", - "axes[0].plot(range(1, T+1), income, 'g-', label=\"non-financial income\", **p_args)\n", - "axes[0].plot(range(T), c, 'k-', label=\"consumption\", **p_args)\n", - "axes[0].legend(ncol=2, **legend_args)\n", - "\n", - "axes[1].plot(range(T+1), assets, 'b-', label=\"assets\", **p_args)\n", - "axes[1].plot(range(T+1), np.zeros(T+1), 'k-')\n", - "axes[1].legend(ncol=1, **legend_args)\n", - "\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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iya/KZ2v21naXuS9/H6crTxPuE86ImBHnvT60x1D+dvnfUKHi3YPvsv7E+naX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\n8xdfccpdTg4MGAB/+lP4FKR/f2jYEKZNg3vvhTPPDJNPp04NazDru+x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- "text": [ - "" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 3" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The first task is to find the matrices $A, B, C, Q, R$ that define the\n", - "LQ problem\n", - "\n", - "Recall that $x_t = (\\bar q_t \\;\\, q_t \\;\\, 1)'$, while $u_t = q_{t+1} - q_t$\n", - "\n", - "Letting $m_0 := (a_0 - c) / 2a_1$ and $m_1 := 1 / 2 a_1$, we can\n", - "write $\\bar q_t = m_0 + m_1 d_t$, and then, with some manipulation\n", - "\n", - "$$\n", - " \\bar q_{t+1} = m_0 (1 - \\rho) + \\rho \\bar q_t + m_1 \\sigma w_{t+1}\n", - "$$\n", - "\n", - "By our definition of $u_t$, the dynamics of $q_t$ are $q_{t+1} = q_t + u_t$\n", - "\n", - "Using these facts you should be able to build the correct $A, B, C$ matrices (and then\n", - "check them against those found in the solution code below)\n", - "\n", - "Suitable $R, Q$ matrices can be found by inspecting the objective\n", - "function, which we repeat here for convenience:\n", - " \n", - "$$\n", - " \\min\n", - " \\mathbb E \\,\n", - " \\left\\{ \n", - " \\sum_{t=0}^{\\infty} \\beta^t \n", - " a_1 ( q_t - \\bar q_t)^2 + \\gamma u_t^2\n", - " \\right\\}\n", - "$$\n", - "\n", - "Our solution code is\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# == Model parameters == #\n", - "a0 = 5\n", - "a1 = 0.5\n", - "sigma = 0.15\n", - "rho = 0.9\n", - "gamma = 1\n", - "beta = 0.95\n", - "c = 2\n", - "T = 120\n", - "\n", - "# == Useful constants == #\n", - "m0 = (a0 - c) / (2 * a1)\n", - "m1 = 1 / (2 * a1)\n", - "\n", - "# == Formulate LQ problem == #\n", - "Q = gamma\n", - "R = [[a1, -a1, 0],\n", - " [-a1, a1, 0],\n", - " [0, 0, 0]]\n", - "A = [[rho, 0, m0 * (1 - rho)],\n", - " [0, 1, 0],\n", - " [0, 0, 1]]\n", - "\n", - "B = [[0],\n", - " [1],\n", - " [0]]\n", - "C = [[m1 * sigma],\n", - " [0],\n", - " [0]]\n", - "\n", - "lq = LQ(Q, R, A, B, C=C, beta=beta)\n", - "\n", - "# == Simulate state / control paths == #\n", - "x0 = (m0, 2, 1)\n", - "xp, up, wp = lq.compute_sequence(x0, ts_length=150)\n", - "q_bar = xp[0, :] \n", - "q = xp[1, :]\n", - "\n", - "# == Plot simulation results == #\n", - "fig, ax = plt.subplots(figsize=(10, 6.5))\n", - "ax.set_xlabel('Time')\n", - "\n", - "# == Some fancy plotting stuff -- simplify if you prefer == #\n", - "bbox = (0., 1.01, 1., .101)\n", - "legend_args = {'bbox_to_anchor' : bbox, 'loc' : 3, 'mode' : 'expand'}\n", - "p_args = {'lw' : 2, 'alpha' : 0.6}\n", - "\n", - "time = range(len(q))\n", - "ax.set_xlim(0, max(time))\n", - "ax.plot(time, q_bar, 'k-', lw=2, alpha=0.6, label=r'$\\bar q_t$')\n", - "ax.plot(time, q, 'b-', lw=2, alpha=0.6, label=r'$q_t$')\n", - "ax.legend(ncol=2, **legend_args)\n", - "s = r'dynamics with $\\gamma = {}$'.format(gamma)\n", - "ax.text(max(time) * 0.6, 1 * q_bar.max(), s, fontsize=14)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - 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OirumpiZvb4jL5eKjjz6K6jmIsccwDJ566ik2b96M1Wrllltu4brrrvP2Eaal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\neX2iM1ku115ycq6lulrN9wlj145hoa6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JnsrKynA6neTm5vr1/3Xdp+rtUEFJxDcfdb6j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- "text": [ - "" - ] - } - ], - "prompt_number": 5 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/lqramsey_solutions.ipynb b/solutions/lqramsey_solutions.ipynb deleted file mode 100644 index 3ba4cac7b..000000000 --- a/solutions/lqramsey_solutions.ipynb +++ /dev/null @@ -1,115 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:8b871eeb53c0476bfcab412f6c1c759213122ffe4093af5762506c44a35b1d3e" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Optimal Taxation" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/lqramsey.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import sys\n", - "import os\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "# lqramsy.py lives in the examples folder. We need\n", - "# to append it to the path so we can import it below\n", - "sys.path.append(os.path.abspath(\"../examples\"))" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from numpy import array\n", - "from lqramsey import *\n", - "\n", - "# == Parameters == #\n", - "beta = 1 / 1.05 \n", - "rho, mg = .95, .35\n", - "A = array([[0, 0, 0, rho, mg*(1-rho)],\n", - " [1, 0, 0, 0, 0],\n", - " [0, 1, 0, 0, 0],\n", - " [0, 0, 1, 0, 0],\n", - " [0, 0, 0, 0, 1]])\n", - "C = np.zeros((5, 1))\n", - "C[0, 0] = np.sqrt(1 - rho**2) * mg / 8\n", - "Sg = array((1, 0, 0, 0, 0)).reshape(1, 5) \n", - "Sd = array((0, 0, 0, 0, 0)).reshape(1, 5) \n", - "Sb = array((0, 0, 0, 0, 2.135)).reshape(1, 5) # Chosen st. (Sc + Sg) * x0 = 1\n", - "Ss = array((0, 0, 0, 0, 0)).reshape(1, 5)\n", - "\n", - "economy = Economy(beta=beta, \n", - " Sg=Sg, \n", - " Sd=Sd, \n", - " Sb=Sb, \n", - " Ss=Ss, \n", - " discrete=False, \n", - " proc=(A, C))\n", - "\n", - "T = 50\n", - "path = compute_paths(T, economy)\n", - "gen_fig_1(path)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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s2nTmgrNbt0rZXbq4T8kBcc+KiBArSvmMhHZ7maujM2tOeYxG15QckCQBXl6S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\n6LFjsHatPbdyZWO3qYKm7qeCIzr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- "text": [ - "" - ] - } - ], - "prompt_number": 3 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/lss_solutions.ipynb b/solutions/lss_solutions.ipynb deleted file mode 100644 index 9ac2d36d0..000000000 --- a/solutions/lss_solutions.ipynb +++ /dev/null @@ -1,5297 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# quant-econ Solutions: The Linear State Space Model" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/linear_models.html" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from quantecon import LinearStateSpace" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise 1" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": [ - "iVBORw0KGgoAAAANSUhEUgAAAf4AAAExCAYAAACd0cBEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", - "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XmcXUWZ//HPk4QkJOz7YgQEFFCQNYKiBFdEBRFnEHcd\n", - "5TfjMuiPUWZTxNEXw6gjOjiIMyq4wagRAQdkRxhHwCBhRzbDTghLIAuELM/8UXW6b3dud9/b99Q5\n", - "1fd8369Xv27f7dzqJ+l+TtVTVcfcHREREWmGSXU3QERERKqjxC8iItIgSvwiIiINosQvIiLSIEr8\n", - "IiIiDaLELyIi0iCVJn4z+56ZLTSzm0d4/j1mdqOZ3WRmvzWzPVqeO8TM7jCzu8zs+OpaLSIi0j+q\n", - "7vF/HzhklOfvBV7j7nsA/wR8B8DMJgOnxvfuBhxtZrsmbquIiEjfqTTxu/vVwFOjPP87d3863r0W\n", - "eEH8fjZwt7svcPeVwNnA4UkbKyIi0odyrvH/BXBB/H5b4IGW5x6Mj4mIiEgXptTdgHbM7GDgw8Cr\n", - "4kPaV1hERKQE2SX+OKHvP4BD3L0oCzwEzGp52SxCr7/d+3WSICIijeLu1ulrs0r8ZvZC4BfAe939\n", - "7pan5gE7m9n2wMPAUcDRIx2nmwBI98zsDHf/YN3t6GeKcTUU5/QU4/S67fBWmvjN7CzgIGAzM3sA\n", - 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mu_0=np.ones(3))\n", - "x, y = ar.simulate(ts_length=50)\n", - "\n", - "fig, ax = plt.subplots(figsize=(8, 4.6))\n", - "y = y.flatten()\n", - "ax.plot(y, 'b-', lw=2, alpha=0.7)\n", - "ax.grid()\n", - "ax.set_xlabel('time')\n", - "ax.set_ylabel(r'$y_t$', fontsize=16)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise 2" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": [ - "iVBORw0KGgoAAAANSUhEUgAAAgQAAAExCAYAAAADXboVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", - "AAALEgAACxIB0t1+/AAAIABJREFUeJztvXn8ZEdV9/8+mZnMZJZksu/JQBZIQkgCJiIIBNkiYBBB\n", - "BEUWeQBZBRURHx5BQeFR4PHH+kPZIkoQzQ8eoiyiguwgyBKWQBIYmCRkMllmMntmJvX7o+p0V1fX\n", - "Xbr7dve93z7v1+v7un1v3+/t6q57qz51zqlT4pzDMAzDMIzF5qB5F8AwDMMwjPljgsAwDMMwDBME\n", - "hmEYhmGYIDAMwzAMAxMEhmEYhmFggsAwDMMwDFooCETk3SKyWUSuKnj/YhHZJiJfD3+vmHUZDcMw\n", - 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"text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "phi_1, phi_2, phi_3, phi_4 = 0.5, -0.2, 0, 0.5\n", - "sigma = 0.2\n", - "\n", - "A = [[phi_1, phi_2, phi_3, phi_4],\n", - " [1, 0, 0, 0],\n", - " [0, 1, 0, 0],\n", - " [0, 0, 1, 0]]\n", - "C = [[sigma], \n", - " [0], \n", - " [0], \n", - " [0]]\n", - "G = [1, 0, 0, 0]\n", - "\n", - "ar = LinearStateSpace(A, C, G, mu_0=np.ones(4))\n", - "x, y = ar.simulate(ts_length=200)\n", - "\n", - "fig, ax = plt.subplots(figsize=(8, 4.6))\n", - "y = y.flatten()\n", - "ax.plot(y, 'b-', lw=2, alpha=0.7)\n", - "ax.grid()\n", - "ax.set_xlabel('time')\n", - "ax.set_ylabel(r'$y_t$', fontsize=16)\n", - "plt.show()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise 3" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": [ - 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range(I):\n", - " x, y = ar.simulate(ts_length=T)\n", - " y = y.flatten()\n", - " ax.plot(y, 'c-', lw=0.8, alpha=0.5)\n", - " ensemble_mean = ensemble_mean + y\n", - "\n", - "ensemble_mean = ensemble_mean / I\n", - "ax.plot(ensemble_mean, color='b', lw=2, alpha=0.8, label=r'$\\bar y_t$')\n", - "\n", - "m = ar.moment_sequence()\n", - "population_means = []\n", - "for t in range(T):\n", - " mu_x, mu_y, Sigma_x, Sigma_y = next(m)\n", - " population_means.append(float(mu_y))\n", - "ax.plot(population_means, color='g', lw=2, alpha=0.8, label=r'$G\\mu_t$')\n", - "ax.legend(ncol=2)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise 4" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": [ - "iVBORw0KGgoAAAANSUhEUgAAAfsAAAE/CAYAAABB8mpwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", - 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"\n", - "ax.grid(alpha=0.4)\n", - "ax.set_ylim(ymin, ymax)\n", - "ax.set_ylabel(r'$y_t$', fontsize=16)\n", - "ax.vlines((T0, T1, T2), -1.5, 1.5)\n", - "\n", - "ax.set_xticks((T0, T1, T2))\n", - "ax.set_xticklabels((r\"$T$\", r\"$T'$\", r\"$T''$\"), fontsize=14)\n", - "\n", - "mu_x, mu_y, Sigma_x, Sigma_y = ar.stationary_distributions()\n", - "ar.mu_0 = mu_x\n", - "ar.Sigma_0 = Sigma_x\n", - "\n", - "for i in range(80):\n", - " rcolor = random.choice(('c', 'g', 'b'))\n", - " x, y = ar.simulate(ts_length=T4)\n", - " y = y.flatten()\n", - " ax.plot(y, color=rcolor, lw=0.8, alpha=0.5)\n", - " ax.plot((T0, T1, T2), (y[T0], y[T1], y[T2],), 'ko', alpha=0.5)\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/solutions/lucas_asset_solutions.ipynb b/solutions/lucas_asset_solutions.ipynb deleted file mode 100644 index 485119e30..000000000 --- a/solutions/lucas_asset_solutions.ipynb +++ /dev/null @@ -1,134 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:5f292f065c543bb774ce6339e9df65c4c0355185a80ee7706e978871fff5d702" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: The Lucas Asset Pricing Model" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/lucas_model.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's start with standard imports" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import division # Omit for Python 3.x\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from quantecon.models import LucasTree" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "fig, ax = plt.subplots(figsize=(10,7))\n", - "\n", - "ax.set_xlabel(r'$y$', fontsize=16)\n", - "ax.set_ylabel(r'price', fontsize=16)\n", - "\n", - "for beta in (.95, 0.98):\n", - " print(\"Comuting at beta = {}\".format(beta))\n", - " tree = LucasTree(gamma=2, beta=beta, alpha=0.90, sigma=0.1)\n", - " grid, price_vals = tree.grid, tree.compute_lt_price()\n", - " label = r'$\\beta = {}$'.format(beta)\n", - " ax.plot(grid, price_vals, lw=2, alpha=0.7, label=label)\n", - "\n", - "ax.legend(loc='upper left')\n", - "ax.set_xlim(min(grid), max(grid))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Comuting at beta = 0.95\n", - "Comuting at beta = 0.98" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - }, - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 4, - "text": [ - "(0.39945149497311855, 2.5034328637756031)" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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RN/QarnCpwhggGXgMiABOANWA5WgpU0RERC7zfez3/Hfzf92iHUZBZswcRVPKdQUCQRe+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\nkHXooLMrRSTvFMxEShDLslhzeA2fb/2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- "text": [ - "" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/mpe_solutions.ipynb b/solutions/mpe_solutions.ipynb deleted file mode 100644 index c0ef4f81d..000000000 --- a/solutions/mpe_solutions.ipynb +++ /dev/null @@ -1,448 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:fe34c3ed8ef6dc3c221131eb9cb17288d7b967994bfe193a90cb5a044cc5a030" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Markov Perfect Equilibria" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/markov_perf.html" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We begin with some standard imports" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "import quantecon as qe\n", - "import matplotlib.pyplot as plt\n", - "from numpy import dot" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First let's compute the duopoly MPE under the stated parameters \n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# == Parameters == #\n", - "a0 = 10.0\n", - "a1 = 2.0\n", - "beta = 0.96\n", - "gamma = 12.0\n", - "\n", - "# == In LQ form == #\n", - "\n", - "A = np.eye(3)\n", - "\n", - "B1 = np.array([[0.], [1.], [0.]])\n", - "B2 = np.array([[0.], [0.], [1.]])\n", - "\n", - "\n", - "R1 = [[0., -a0/2, 0.],\n", - " [-a0/2., a1, a1/2.],\n", - " [0, a1/2., 0.]]\n", - "\n", - "R2 = [[0., 0., -a0/2],\n", - " [0., 0., a1/2.],\n", - " [-a0/2, a1/2., a1]]\n", - "\n", - "Q1 = Q2 = gamma\n", - "\n", - "S1 = S2 = W1 = W2 = M1 = M2 = 0.0\n", - "\n", - "# == Solve using QE's nnash function == #\n", - "F1, F2, P1, P2 = qe.nnash(A, B1, B2, R1, R2, Q1, Q2, S1, S2, W1, W2, M1, M2,\n", - " beta=beta)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we evaluate the time path of industry output and prices given initial condition $q_{10} = q_{20} = 1$" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "AF = A - B1.dot(F1) - B2.dot(F2)\n", - "n = 20\n", - "x = np.empty((3, n))\n", - "x[:, 0] = 1, 1, 1 \n", - "for t in range(n-1):\n", - " x[:, t+1] = np.dot(AF, x[:, t])\n", - "q1 = x[1, :]\n", - "q2 = x[2, :]\n", - "q = q1 + q2 # Total output, MPE\n", - "p = a0 - a1 * q # Price, MPE" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next let's have a look at the monopoly solution\n", - "\n", - "For the state and control we take\n", - "\n", - "$$ \n", - " x_t = q_t - \\bar q \n", - " \\quad \\text{and} \\quad\n", - " u_t = q_{t+1} - q_t\n", - "$$\n", - "\n", - "To convert to an LQ problem we set\n", - "\n", - "$$\n", - " R = a_1\n", - " \\quad \\text{and} \\quad\n", - " Q = \\gamma \n", - "$$\n", - "\n", - "in the payoff function $x_t' R x_t + u_t' Q u_t$ and \n", - "\n", - "$$\n", - " A = B = 1\n", - "$$\n", - "\n", - "in the law of motion $x_{t+1} = A x_t + B u_t$\n", - "\n", - "We solve for the optimal policy $u_t = - Fx_t$ and track the resulting dynamics of $\\{q_t\\}$, starting at $q_0 = 2.0$\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "R = a1\n", - "Q = gamma\n", - "A = B = 1\n", - "lq_alt = qe.LQ(Q, R, A, B, beta=beta)\n", - "P, F, d = lq_alt.stationary_values()\n", - "q_bar = a0 / (2.0 * a1)\n", - "qm = np.empty(n)\n", - "qm[0] = 2\n", - "x0 = qm[0] - q_bar\n", - "x = x0\n", - "for i in range(1, n):\n", - " x = A * x - B * F * x\n", - " qm[i] = float(x) + q_bar\n", - "pm = a0 - a1 * qm" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's have a look at the different time paths" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "fig, axes = plt.subplots(2, 1, figsize=(9, 9))\n", - "\n", - "ax = axes[0]\n", - "ax.plot(qm, 'b-', lw=2, alpha=0.75, label='monopolist output')\n", - "ax.plot(q, 'g-', lw=2, alpha=0.75, label='MPE total output')\n", - "ax.set_ylabel(\"output\")\n", - "ax.set_xlabel(\"time\")\n", - "ax.set_ylim(2, 4)\n", - "ax.legend(loc='upper left', frameon=0)\n", - "\n", - "\n", - "ax = axes[1]\n", - "ax.plot(pm, 'b-', lw=2, alpha=0.75, label='monopolist price')\n", - "ax.plot(p, 'g-', lw=2, alpha=0.75, label='MPE price')\n", - "ax.set_ylabel(\"price\")\n", - "ax.set_xlabel(\"time\")\n", - "ax.legend(loc='upper right', frameon=0)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 5, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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Bx31r2Vbz2OrnBhzWV31Pa4aE2rbX3CbN39JbltIutJ2ny3CgwCIibmersHGq/JTTqcRW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\ngBpgtW+ZFeGaREREJM5EOrC0AD8CTgcmA98HxoRo9y5Q6lseiHBNEif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- "text": [ - "" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We treat the case $\\delta = 0.02$\n", - "\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "delta = 0.02\n", - "D = np.array([[-1, 0.5], [0.5, -1]])\n", - "b = np.array([25, 25])\n", - "c1 = c2 = np.array([1, -2, 1])\n", - "e1 = e2 = np.array([10, 10, 3])\n", - "\n", - "delta_1 = 1 - delta" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 6 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Recalling that the control and state are\n", - "\n", - "$$\n", - " u_{it} =\n", - " \\begin{bmatrix} \n", - " p_{it} \\\\\n", - " q_{it} \n", - " \\end{bmatrix}\n", - " \\quad \\text{and} \\quad\n", - " x_t =\n", - " \\begin{bmatrix}\n", - " I_{1t} \\\\\n", - " I_{2t} \\\\\n", - " 1\n", - " \\end{bmatrix}\n", - "$$\n", - "\n", - "we set up the matrices as follows:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# == Create matrices needed to compute the Nash feedback equilibrium == #\n", - "\n", - "A = np.array([[delta_1, 0, -delta_1*b[0]],\n", - " [0, delta_1, -delta_1*b[1]],\n", - " [0, 0, 1]])\n", - "\n", - "B1 = delta_1 * np.array([[1, -D[0, 0]],\n", - " [0, -D[1, 0]],\n", - " [0, 0]])\n", - "B2 = delta_1 * np.array([[0, -D[0, 1]],\n", - " [1, -D[1, 1]],\n", - " [0, 0]])\n", - "\n", - "R1 = -np.array([[0.5*c1[2], 0, 0.5*c1[1]],\n", - " [0, 0, 0],\n", - " [0.5*c1[1], 0, c1[0]]])\n", - "R2 = -np.array([[0, 0, 0],\n", - " [0, 0.5*c2[2], 0.5*c2[1]],\n", - " [0, 0.5*c2[1], c2[0]]])\n", - "\n", - "Q1 = np.array([[-0.5*e1[2], 0], [0, D[0, 0]]])\n", - "Q2 = np.array([[-0.5*e2[2], 0], [0, D[1, 1]]])\n", - "\n", - "S1 = np.zeros((2, 2))\n", - "S2 = np.copy(S1)\n", - "\n", - "W1 = np.array([[0, 0],\n", - " [0, 0],\n", - " [-0.5*e1[1], b[0]/2.]])\n", - "W2 = np.array([[0, 0],\n", - " [0, 0],\n", - " [-0.5*e2[1], b[1]/2.]])\n", - "\n", - "M1 = np.array([[0, 0], [0, D[0, 1] / 2.]])\n", - "M2 = np.copy(M1)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can now compute the equilibrium using `qe.nnash`" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "F1, F2, P1, P2 = qe.nnash(A, B1, B2, R1, R2, Q1, Q2, S1, S2, W1, W2, M1, M2)\n", - "\n", - "print(\"\\nFirm 1's feedback rule:\\n\")\n", - "print(F1)\n", - "\n", - "print(\"\\nFirm 2's feedback rule:\\n\")\n", - "print(F2)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Firm 1's feedback rule:\n", - "\n", - "[[ 2.43666582e-01 2.72360627e-02 -6.82788293e+00]\n", - " [ 3.92370734e-01 1.39696451e-01 -3.77341073e+01]]\n", - "\n", - "Firm 2's feedback rule:\n", - "\n", - "[[ 2.72360627e-02 2.43666582e-01 -6.82788293e+00]\n", - " [ 1.39696451e-01 3.92370734e-01 -3.77341073e+01]]\n" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let's look at the dynamics of inventories, and reproduce the graph corresponding to $\\delta = 0.02$" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "AF = A - B1.dot(F1) - B2.dot(F2)\n", - "n = 25\n", - "x = np.empty((3, n))\n", - "x[:, 0] = 2, 0, 1\n", - "for t in range(n-1):\n", - " x[:, t+1] = np.dot(AF, x[:, t])\n", - "I1 = x[0, :]\n", - "I2 = x[1, :]\n", - "fig, ax = plt.subplots(figsize=(9, 5))\n", - "ax.plot(I1, 'b-', lw=2, alpha=0.75, label='inventories, firm 1')\n", - "ax.plot(I2, 'g-', lw=2, alpha=0.75, label='inventories, firm 2')\n", - "ax.set_title(r'$\\delta = {}$'.format(delta))\n", - "ax.legend()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 9, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 9 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/numbers.txt b/solutions/numbers.txt deleted file mode 100644 index acd67b486..000000000 --- a/solutions/numbers.txt +++ /dev/null @@ -1,6 +0,0 @@ -prices -3 -8 - -7 -21 \ No newline at end of file diff --git a/solutions/numpy_solutions.ipynb b/solutions/numpy_solutions.ipynb deleted file mode 100644 index a30c69f12..000000000 --- a/solutions/numpy_solutions.ipynb +++ /dev/null @@ -1,353 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:5d40d5ac28199d1ce7bf6b873bf4f8ba1b3446df849b7677095b54f0e8b14ad0" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: NumPy" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/numpy.html" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Tell the notebook to display figures embedded in the browser:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Import numpy and some plotting functionality:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 5 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This code does the job" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def p(x, coef):\n", - " X = np.empty(len(coef))\n", - " X[0] = 1\n", - " X[1:] = x\n", - " y = np.cumprod(X) # y = [1, x, x**2,...]\n", - " return np.dot(coef, y)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 6 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's test it" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "coef = np.ones(3)\n", - "print(coef)\n", - "print(p(1, coef))\n", - "# For comparison\n", - "q = np.poly1d(coef)\n", - "print(q(1))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[ 1. 1. 1.]\n", - "3.0\n", - "3.0\n" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here's our first pass at a solution:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from numpy import cumsum\n", - "from numpy.random import uniform\n", - "\n", - "class discreteRV:\n", - " \"\"\"\n", - " Generates an array of draws from a discrete random variable with vector of\n", - " probabilities given by q. \n", - " \"\"\"\n", - "\n", - " def __init__(self, q):\n", - " \"\"\"\n", - " The argument q is a NumPy array, or array like, nonnegative and sums\n", - " to 1\n", - " \"\"\"\n", - " self.q = q\n", - " self.Q = cumsum(q)\n", - "\n", - " def draw(self, k=1):\n", - " \"\"\"\n", - " Returns k draws from q. For each such draw, the value i is returned\n", - " with probability q[i].\n", - " \"\"\"\n", - " return self.Q.searchsorted(uniform(0, 1, size=k)) " - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 8 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The logic is not obvious, but if you take your time and read it slowly, you will understand\n", - "\n", - "There is a problem here, however\n", - "\n", - "Suppose that `q` is altered after an instance of `discreteRV` is created, for example by" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "q = (0.1, 0.9)\n", - "d = discreteRV(q)\n", - "d.q = (0.5, 0.5)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 9 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The problem is that `Q` does not change accordingly, and `Q` is the data used in the `draw` method\n", - "\n", - "To deal with this, one option is to compute `Q` every time the draw method is called\n", - "\n", - "But this is inefficient relative to computing `Q` once off\n", - "\n", - "A better option is to use descriptors\n", - "\n", - "A solution from the [quantecon library](https://github.com/jstac/quant-econ/tree/master/quantecon) using descriptors that behaves as we desire can be found [here](https://github.com/jstac/quant-econ/blob/master/quantecon/discrete_rv.py)\n" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 3" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "An example solution is given below.\n", - "\n", - "In essence we've just taken [this code](https://github.com/jstac/quant-econ/blob/master/quantecon/ecdf.py) from \n", - "[QuantEcon](https://github.com/jstac/quant-econ/tree/master/quantecon) and added in a plot method" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\"\"\"\n", - "Modifies ecdf.py from QuantEcon to add in a plot method\n", - "\n", - "\"\"\"\n", - "\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "\n", - "class ECDF(object):\n", - " \"\"\"\n", - " One-dimensional empirical distribution function given a vector of\n", - " observations.\n", - "\n", - " Parameters\n", - " ----------\n", - " observations : array_like\n", - " An array of observations\n", - "\n", - " Attributes\n", - " ----------\n", - " observations : array_like\n", - " An array of observations\n", - "\n", - " \"\"\"\n", - "\n", - " def __init__(self, observations):\n", - " self.observations = np.asarray(observations)\n", - "\n", - " def __call__(self, x):\n", - " \"\"\"\n", - " Evaluates the ecdf at x\n", - "\n", - " Parameters\n", - " ----------\n", - " x : scalar(float)\n", - " The x at which the ecdf is evaluated\n", - "\n", - " Returns\n", - " -------\n", - " scalar(float)\n", - " Fraction of the sample less than x\n", - "\n", - " \"\"\"\n", - " return np.mean(self.observations <= x)\n", - "\n", - " def plot(self, a=None, b=None):\n", - " \"\"\"\n", - " Plot the ecdf on the interval [a, b].\n", - "\n", - " Parameters\n", - " ----------\n", - " a : scalar(float), optional(default=None)\n", - " Lower end point of the plot interval\n", - " b : scalar(float), optional(default=None)\n", - " Upper end point of the plot interval\n", - "\n", - " \"\"\"\n", - "\n", - " # === choose reasonable interval if [a, b] not specified === #\n", - " if a is None:\n", - " a = self.observations.min() - self.observations.std()\n", - " if b is None:\n", - " b = self.observations.max() + self.observations.std()\n", - "\n", - " # === generate plot === #\n", - " x_vals = np.linspace(a, b, num=100)\n", - " f = np.vectorize(self.__call__)\n", - " plt.plot(x_vals, f(x_vals))\n", - " plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 10 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here's an example of usage" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "X = np.random.randn(1000)\n", - "F = ECDF(X)\n", - "F.plot()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 11 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/odu_solutions.ipynb b/solutions/odu_solutions.ipynb deleted file mode 100644 index 924916dad..000000000 --- a/solutions/odu_solutions.ipynb +++ /dev/null @@ -1,667 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:3657e17830750f2d1264e69668c8c58421e2d2ede892e952f3999c1a6edf9559" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Search with Unknown Offer Distribution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/odu.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from quantecon import compute_fixed_point\n", - "from quantecon.models import SearchProblem" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "This code solves the \"Offer Distribution Unknown\" model by iterating on a guess of the\n", - "reservation wage function. You should find that the run time is much shorter than that of the value function approach in `odu_vfi.py`\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sp = SearchProblem(pi_grid_size=50)\n", - "\n", - "phi_init = np.ones(len(sp.pi_grid)) \n", - "w_bar = compute_fixed_point(sp.res_wage_operator, phi_init)\n", - "\n", - "fig, ax = plt.subplots(figsize=(9, 7))\n", - "ax.plot(sp.pi_grid, w_bar, linewidth=2, color='black')\n", - "ax.set_ylim(0, 2)\n", - "ax.grid(axis='x', linewidth=0.25, linestyle='--', color='0.25')\n", - "ax.grid(axis='y', linewidth=0.25, linestyle='--', color='0.25')\n", - "ax.fill_between(sp.pi_grid, 0, w_bar, color='blue', alpha=0.15)\n", - "ax.fill_between(sp.pi_grid, w_bar, 2, color='green', alpha=0.15)\n", - "ax.text(0.42, 1.2, 'reject')\n", - "ax.text(0.7, 1.8, 'accept')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Computed iterate 1 with error 0.426161\n", - "Computed iterate 2 with error 0.127050" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 3 with error 0.076090" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 4 with error 0.046400" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 5 with error 0.028295" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 6 with error 0.018182" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 7 with error 0.013566" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 8 with error 0.009611" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 9 with error 0.007113" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 10 with error 0.005174" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 11 with error 0.003732" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 12 with error 0.002657" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 13 with error 0.001876" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 14 with error 0.001348" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 15 with error 0.000965" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The next piece of code is not one of the exercises from quant-econ, it's just a fun simulation to see \n", - "what the effect of a change in the underlying distribution on the unemployment rate is.\n", - "\n", - "At a point in the simulation, the distribution becomes significantly worse. It takes a while for agents to learn this, and in the meantime they are too optimistic, and turn down too many jobs. As a result, the unemployment rate spikes.\n", - "\n", - "The code takes a few minutes to run." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from scipy import interp\n", - "# Set up model and compute the function w_bar\n", - "sp = SearchProblem(pi_grid_size=50, F_a=1, F_b=1)\n", - "pi_grid, f, g, F, G = sp.pi_grid, sp.f, sp.g, sp.F, sp.G\n", - "phi_init = np.ones(len(sp.pi_grid)) \n", - "w_bar_vals = compute_fixed_point(sp.res_wage_operator, phi_init)\n", - "w_bar = lambda x: interp(x, pi_grid, w_bar_vals)\n", - "\n", - "\n", - "class Agent(object):\n", - " \"\"\"\n", - " Holds the employment state and beliefs of an individual agent.\n", - " \"\"\"\n", - "\n", - " def __init__(self, pi=1e-3):\n", - " self.pi = pi\n", - " self.employed = 1\n", - "\n", - " def update(self, H):\n", - " \"Update self by drawing wage offer from distribution H.\"\n", - " if self.employed == 0:\n", - " w = H.rvs()\n", - " if w >= w_bar(self.pi):\n", - " self.employed = 1\n", - " else:\n", - " self.pi = 1.0 / (1 + ((1 - self.pi) * g(w)) / (self.pi * f(w)))\n", - "\n", - "\n", - "num_agents = 5000\n", - "separation_rate = 0.025 # Fraction of jobs that end in each period \n", - "separation_num = int(num_agents * separation_rate)\n", - "agent_indices = list(range(num_agents))\n", - "agents = [Agent() for i in range(num_agents)]\n", - "sim_length = 600\n", - "H = G # Start with distribution G\n", - "change_date = 200 # Change to F after this many periods\n", - "\n", - "unempl_rate = []\n", - "for i in range(sim_length):\n", - " if i % 20 == 0:\n", - " print(\"date =\", i)\n", - " if i == change_date:\n", - " H = F\n", - " # Randomly select separation_num agents and set employment status to 0\n", - " np.random.shuffle(agent_indices)\n", - " separation_list = agent_indices[:separation_num]\n", - " for agent_index in separation_list:\n", - " agents[agent_index].employed = 0\n", - " # Update agents\n", - " for agent in agents:\n", - " agent.update(H)\n", - " employed = [agent.employed for agent in agents]\n", - " unempl_rate.append(1 - np.mean(employed))\n", - "\n", - "fig, ax = plt.subplots(figsize=(9, 7))\n", - "ax.plot(unempl_rate, lw=2, alpha=0.8, label='unemployment rate')\n", - "ax.axvline(change_date, color=\"red\")\n", - "ax.legend()\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Computed iterate 1 with error 0.426161\n", - "Computed iterate 2 with error 0.127050" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 3 with error 0.076090" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 4 with error 0.046400" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 5 with error 0.028295" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 6 with error 0.018182" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 7 with error 0.013566" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 8 with error 0.009611" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 9 with error 0.007113" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 10 with error 0.005174" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 11 with error 0.003732" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 12 with error 0.002657" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 13 with error 0.001876" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 14 with error 0.001348" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 15 with error 0.000965" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "date = 0\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 20\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 40\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 60\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 80\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 100\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 120\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 140\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 160\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 180\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 200\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 220\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 240\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 260\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 280\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 300\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 320\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 340\n", - "date = " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 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P+jEzdHzwgQ4mXbo4BxO/X47x+4GZM+WiOWMG8P770oz04IPW97afC0XOrJTZ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\niYuTpqoLLpAKzsSJ1oqJEirgKImJMmfNgAHVC2B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- "text": [ - "" - ] - } - ], - "prompt_number": 4 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/oop_solutions.ipynb b/solutions/oop_solutions.ipynb deleted file mode 100644 index 9b5c34d99..000000000 --- a/solutions/oop_solutions.ipynb +++ /dev/null @@ -1,135 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:39099b5d6503621c4076c7a6bd2ec02bc59c2747a07ebb54a8b27f1175ed52d6" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Object Oriented Programming" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/python_oop.html" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "class ECDF(object):\n", - "\n", - " def __init__(self, observations):\n", - " self.observations = observations\n", - "\n", - " def __call__(self, x):\n", - " counter = 0.0\n", - " for obs in self.observations:\n", - " if obs <= x:\n", - " counter += 1\n", - " return counter / len(self.observations)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# == test == #\n", - "\n", - "from random import uniform\n", - "samples = [uniform(0, 1) for i in range(10)]\n", - "F = ECDF(samples)\n", - "\n", - "print(F(0.5)) # Evaluate ecdf at x = 0.5\n", - "\n", - "F.observations = [uniform(0, 1) for i in range(1000)]\n", - "\n", - "print(F(0.5))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "0.5\n", - "0.486\n" - ] - } - ], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "class Polynomial(object):\n", - "\n", - " def __init__(self, coefficients):\n", - " \"\"\"\n", - " Creates an instance of the Polynomial class representing \n", - "\n", - " p(x) = a_0 x^0 + ... + a_N x^N, \n", - " \n", - " where a_i = coefficients[i].\n", - " \"\"\"\n", - " self.coefficients = coefficients\n", - "\n", - " def __call__(self, x):\n", - " \"Evaluate the polynomial at x.\"\n", - " y = 0\n", - " for i, a in enumerate(self.coefficients):\n", - " y += a * x**i \n", - " return y\n", - "\n", - " def differentiate(self):\n", - " \"Reset self.coefficients to those of p' instead of p.\"\n", - " new_coefficients = []\n", - " for i, a in enumerate(self.coefficients):\n", - " new_coefficients.append(i * a)\n", - " # Remove the first element, which is zero\n", - " del new_coefficients[0] \n", - " # And reset coefficients data to new values\n", - " self.coefficients = new_coefficients\n" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 3 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/optgrowth_solutions.ipynb b/solutions/optgrowth_solutions.ipynb deleted file mode 100644 index a5258d251..000000000 --- a/solutions/optgrowth_solutions.ipynb +++ /dev/null @@ -1,731 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:89ab78e36bdc736c251923085e90e94893f9cca4f6d752519c6a21410f45c597" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Infinite Horizon Dynamic Programming" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/dp_intro.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from quantecon import compute_fixed_point\n", - "from quantecon.models import GrowthModel" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "alpha, beta = 0.65, 0.95\n", - "gm = GrowthModel() \n", - "true_sigma = (1 - alpha * beta) * gm.grid**alpha\n", - "w = 5 * gm.u(gm.grid) - 25 # Initial condition\n", - "\n", - "fig, ax = plt.subplots(3, 1, figsize=(8, 10))\n", - "\n", - "for i, n in enumerate((2, 4, 6)):\n", - " ax[i].set_ylim(0, 1)\n", - " ax[i].set_xlim(0, 2)\n", - " ax[i].set_yticks((0, 1))\n", - " ax[i].set_xticks((0, 2))\n", - "\n", - " v_star = compute_fixed_point(gm.bellman_operator, w, max_iter=n)\n", - " sigma = gm.compute_greedy(v_star)\n", - "\n", - " ax[i].plot(gm.grid, sigma, 'b-', lw=2, alpha=0.8, label='approximate optimal policy')\n", - " ax[i].plot(gm.grid, true_sigma, 'k-', lw=2, alpha=0.8, label='true optimal policy')\n", - " ax[i].legend(loc='upper left')\n", - " ax[i].set_title('{} value function iterations'.format(n))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Computed iterate 1 with error 4.296600\n", - "Computed iterate 2 with error 4.080228" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 1 with error 4.296600" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 2 with error 4.080228" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 3 with error 3.875034" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 4 with error 3.680327" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 1 with error 4.296600" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 2 with error 4.080228" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 3 with error 3.875034" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 4 with error 3.680327" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 5 with error 3.495502" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 6 with error 3.327466" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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o9+7dnYKn/TU+Ph4/P79WvoKuQwKsEEK0M3V1dZw4ccKpONf+evr0abf7RUdH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- "text": [ - "" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from scipy import interp\n", - "\n", - "gm = GrowthModel() \n", - "w = 5 * gm.u(gm.grid) - 25 # To be used as an initial condition\n", - "discount_factors = (0.9, 0.94, 0.98)\n", - "series_length = 25\n", - "\n", - "fig, ax = plt.subplots(figsize=(8,5))\n", - "ax.set_xlabel(\"time\")\n", - "ax.set_ylabel(\"capital\")\n", - "\n", - "for beta in discount_factors:\n", - "\n", - " # Compute the optimal policy given the discount factor\n", - " gm.beta = beta\n", - " v_star = compute_fixed_point(gm.bellman_operator, w, max_iter=20)\n", - " sigma = gm.compute_greedy(v_star)\n", - "\n", - " # Compute the corresponding time series for capital\n", - " k = np.empty(series_length)\n", - " k[0] = 0.1\n", - " sigma_function = lambda x: interp(x, gm.grid, sigma)\n", - " for t in range(1, series_length):\n", - " k[t] = gm.f(k[t-1]) - sigma_function(k[t-1])\n", - " ax.plot(k, 'o-', lw=2, alpha=0.75, label=r'$\\beta = {}$'.format(beta))\n", - "\n", - "ax.legend(loc='lower right')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Computed iterate 1 with error 5.999396\n", - "Computed iterate 2 with error 3.791226" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 3 with error 2.531863" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 4 with error 1.767013" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 5 with error 1.303066" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 6 with error 1.011176" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 7 with error 0.816201" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 8 with error 0.689199" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 9 with error 0.590297" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 10 with error 0.514201" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 11 with error 0.454587" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 12 with error 0.402620" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 13 with error 0.359115" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 14 with error 0.321714" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 15 with error 0.288297" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 16 with error 0.258360" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 17 with error 0.232150" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 18 with error 0.208786" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 19 with error 0.187838" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 20 with error 0.169022" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 1 with error 4.401010" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 2 with error 3.153136" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 3 with error 2.962891" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 4 with error 2.784289" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 5 with error 2.616550" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 6 with error 2.458976" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 7 with error 2.318565" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 8 with error 2.171183" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 9 with error 2.042677" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 10 with error 1.921553" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 11 with error 1.806962" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 12 with error 1.698904" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 13 with error 1.597220" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 14 with error 1.494743" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 15 with error 1.405415" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 16 with error 1.321367" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 17 with error 1.242295" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 18 with error 1.167909" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 19 with error 1.097938" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 20 with error 1.032124" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 1 with error 7.118648" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 2 with error 6.974372" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 3 with error 6.833300" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 4 with error 6.702746" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 5 with error 6.564332" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 6 with error 6.427286" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 7 with error 6.299795" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 8 with error 6.173511" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 9 with error 6.048887" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 10 with error 5.924557" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 11 with error 5.805184" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 12 with error 5.687164" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 13 with error 5.570272" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 14 with error 5.453828" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 15 with error 5.338835" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 16 with error 5.225067" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 17 with error 5.112733" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 18 with error 5.001816" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 19 with error 4.892653" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Computed iterate 20 with error 4.784860" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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thaVLkzh2LKFGaHbokExc3J24XOb7a3ut2N+0KYnCwoQa9W7TJpnBg+/0+Wez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\nJCamUVSUUHksMTGJWbPwKazre/3JNm3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- "text": [ - "" - ] - } - ], - "prompt_number": 4 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/pandas_solutions.ipynb b/solutions/pandas_solutions.ipynb deleted file mode 100644 index 09e3dd20a..000000000 --- a/solutions/pandas_solutions.ipynb +++ /dev/null @@ -1,143 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:64f4052833189e82a5e08a5f420c03f35541190523433e0cc861059c15e642b9" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Pandas" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/pandas.html" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Show the plot inline in the browser:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Run some imports:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "import pandas as pd\n", - "import datetime as dt\n", - "import pandas.io.data as web\n", - "import matplotlib.pyplot as plt" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now the main code" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "ticker_list = {'INTC': 'Intel',\n", - " 'MSFT': 'Microsoft',\n", - " 'IBM': 'IBM',\n", - " 'BHP': 'BHP',\n", - " 'RSH': 'RadioShack',\n", - " 'TM': 'Toyota',\n", - " 'AAPL': 'Apple',\n", - " 'AMZN': 'Amazon',\n", - " 'BA': 'Boeing',\n", - " 'QCOM': 'Qualcomm',\n", - " 'KO': 'Coca-Cola',\n", - " 'GOOG': 'Google',\n", - " 'SNE': 'Sony',\n", - " 'PTR': 'PetroChina'}\n", - "\n", - "start = dt.datetime(2013, 1, 1)\n", - "end = dt.datetime.today()\n", - "\n", - "price_change = {}\n", - "\n", - "for ticker in ticker_list:\n", - " prices = web.DataReader(ticker, 'yahoo', start, end)\n", - " closing_prices = prices['Close']\n", - " change = 100 * (closing_prices[-1] - closing_prices[0]) / closing_prices[0]\n", - " name = ticker_list[ticker]\n", - " price_change[name] = change\n", - "\n", - "pc = pd.Series(price_change)\n", - "pc.sort()\n", - "fig, ax = plt.subplots(figsize=(10,8))\n", - "pc.plot(kind='bar', ax=ax)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 3, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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i1Q7QItUOsIlUO0CLVDtAi1Q7QIs08R62Th5CkmZn+/ad3HTTjVPb37ZtR7J//w1T258k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\nrfT/f99aLw5PIb+hfBjDO2Q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- "text": [ - "" - ] - } - ], - "prompt_number": 3 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/pbe_solutions.ipynb b/solutions/pbe_solutions.ipynb deleted file mode 100644 index 59bf723b7..000000000 --- a/solutions/pbe_solutions.ipynb +++ /dev/null @@ -1,316 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:146d44fe94502737f63b15030f98115c70f0a5640993ee9a6d598a28f6c87000" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Python by Example" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/python_by_example.html" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def factorial(n):\n", - " k = 1\n", - " for i in range(n):\n", - " k = k * (i + 1)\n", - " return k\n", - "\n", - "factorial(4)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "24" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from random import uniform\n", - "\n", - "def binomial_rv(n, p):\n", - " count = 0\n", - " for i in range(n):\n", - " U = uniform(0, 1)\n", - " if U < p:\n", - " count = count + 1 # Or count += 1\n", - " return count\n", - "\n", - "binomial_rv(10, 0.5)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 2, - "text": [ - "6" - ] - } - ], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 3" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider the circle of diameter 1 embedded in the unit square\n", - "\n", - "Let $A$ be its area and let $r=1/2$ be its radius \n", - "\n", - "If we know $\\pi$ then we can compute $A$ via $A = \\pi r^2$\n", - "\n", - "But here the point is to compute $\\pi$, which we can do by $\\pi = A / r^2$\n", - "\n", - "Summary: If we can estimate the area of the unit circle, then dividing by $r^2 = (1/2)^2 = 1/4$\n", - "gives an estimate of $\\pi$\n", - "\n", - "We estimate the area by sampling bivariate uniforms and looking at the fraction that fall into the unit circle\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import division # Omit if using Python 3.x\n", - "from math import sqrt\n", - "\n", - "n = 100000\n", - "\n", - "count = 0\n", - "for i in range(n):\n", - " u, v = uniform(0, 1), uniform(0, 1)\n", - " d = sqrt((u - 0.5)**2 + (v - 0.5)**2)\n", - " if d < 0.5:\n", - " count += 1\n", - "\n", - "area_estimate = count / n\n", - "\n", - "print(area_estimate * 4) # dividing by radius**2" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "3.14008\n" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 4" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "payoff = 0\n", - "count = 0\n", - "\n", - "for i in range(10):\n", - " U = uniform(0, 1)\n", - " count = count + 1 if U < 0.5 else 0\n", - " if count == 3:\n", - " payoff = 1\n", - "\n", - "print(payoff)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "1\n" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 5" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The next line embeds all subsequent figures in the browser itself" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline " - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 5 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import matplotlib.pyplot as plt\n", - "from random import normalvariate\n", - "\n", - "alpha = 0.9\n", - "ts_length = 200\n", - "current_x = 0\n", - "\n", - "x_values = []\n", - "for i in range(ts_length + 1):\n", - " x_values.append(current_x)\n", - " current_x = alpha * current_x + normalvariate(0, 1)\n", - "plt.plot(x_values, 'b-')\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 6, - "text": [ - "[]" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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heMXdGpbJlXMPdW0Zt7BMMuzOPVFnqhdqayW+mChuD3ICfOc7Ep7Zt0+u2E1N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\nO4ryctGmRBSSc38RMGX1XwM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- "text": [ - "" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 6" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "alphas = [0.0, 0.8, 0.98]\n", - "ts_length = 200\n", - "\n", - "for alpha in alphas:\n", - " x_values = []\n", - " current_x = 0\n", - " for i in range(ts_length):\n", - " x_values.append(current_x)\n", - " current_x = alpha * current_x + normalvariate(0, 1)\n", - " plt.plot(x_values, label='alpha = ' + str(alpha))\n", - "plt.legend()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 7, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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2UDuFNYXkaAuM/mVrq/SvHzhg+fbO0aFGA/X1Xe2T9HRjfQhYRvqd7Z3fKvrJ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\n19tVfv/wU435eIzq80Of078NoFLddx+99uuvVao773Tteq2ltVWl8vF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- "text": [ - "" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/py_adv_feat_solutions.ipynb b/solutions/py_adv_feat_solutions.ipynb deleted file mode 100644 index 3530509bf..000000000 --- a/solutions/py_adv_feat_solutions.ipynb +++ /dev/null @@ -1,220 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:00d3c4a4e3d630d4fdd4d251547c405d48259d94e963483ef895180aa5e81cbe" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: More Language Features" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/python_advanced_features.html" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here's the standard solution" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def x(t):\n", - " if t == 0:\n", - " return 0\n", - " if t == 1:\n", - " return 1\n", - " else:\n", - " return x(t-1) + x(t-2)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's test it" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print([x(i) for i in range(10)])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]\n" - ] - } - ], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "One solution is as follows" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def column_iterator(target_file, column_number):\n", - " \"\"\"A generator function for CSV files.\n", - " When called with a file name target_file (string) and column number \n", - " column_number (integer), the generator function returns a generator \n", - " which steps through the elements of column column_number in file\n", - " target_file.\n", - " \"\"\"\n", - " f = open(target_file, 'r')\n", - " for line in f:\n", - " yield line.split(',')[column_number - 1]\n", - " f.close()\n", - "\n", - "dates = column_iterator('test_table.csv', 1) \n", - "\n", - "i = 1\n", - "for date in dates:\n", - " print(date)\n", - " if i == 10:\n", - " break\n", - " i += 1" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Date\n", - "2009-05-21\n", - "2009-05-20\n", - "2009-05-19\n", - "2009-05-18\n", - "2009-05-15\n", - "2009-05-14\n", - "2009-05-13\n", - "2009-05-12\n", - "2009-05-11\n" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 3" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's save the data first" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%%file numbers.txt\n", - "prices\n", - "3\n", - "8\n", - "\n", - "7\n", - "21" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Overwriting numbers.txt\n" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "f = open('numbers.txt')\n", - "\n", - "total = 0.0 \n", - "for line in f:\n", - " try:\n", - " total += float(line)\n", - " except ValueError:\n", - " pass\n", - "\n", - "f.close()\n", - "\n", - "print(total)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "39.0\n" - ] - } - ], - "prompt_number": 5 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/pyess_solutions.ipynb b/solutions/pyess_solutions.ipynb deleted file mode 100644 index cd3de969d..000000000 --- a/solutions/pyess_solutions.ipynb +++ /dev/null @@ -1,462 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:de49037570346c68172d121a401bf7fdc0293e786765a79b1e3ea6888656c8a3" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Python Essentials" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/python_essentials.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import division # Omit for Python 3.x" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "heading", - "level": 4, - "metadata": {}, - "source": [ - "Part 1 solution:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here's one possible solution" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "x_vals = [1, 2, 3]\n", - "y_vals = [1, 1, 1]\n", - "sum([x * y for x, y in zip(x_vals, y_vals)])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 2, - "text": [ - "6" - ] - } - ], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This also works" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sum(x * y for x, y in zip(x_vals, y_vals))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 3, - "text": [ - "6" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "heading", - "level": 4, - "metadata": {}, - "source": [ - "Part 2 solution:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "One solution is" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sum([x % 2 == 0 for x in range(100)])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 4, - "text": [ - "50" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This also works:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sum(x % 2 == 0 for x in range(100))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 5, - "text": [ - "50" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Some less natural alternatives that nonetheless help to illustrate the flexibility of list comprehensions are" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "len([x for x in range(100) if x % 2 == 0])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 6, - "text": [ - "50" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sum([1 for x in range(100) if x % 2 == 0])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 7, - "text": [ - "50" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "heading", - "level": 4, - "metadata": {}, - "source": [ - "Part 3 solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here's one possibility" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "pairs = ((2, 5), (4, 2), (9, 8), (12, 10))\n", - "sum([x % 2 == 0 and y % 2 == 0 for x, y in pairs])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 8, - "text": [ - "2" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def p(x, coeff):\n", - " return sum(a * x**i for i, a in enumerate(coeff))\n" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 9 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "p(1, (2, 4))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 10, - "text": [ - "6" - ] - } - ], - "prompt_number": 10 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 3" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here's one solution:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def f(string):\n", - " count = 0\n", - " for letter in string:\n", - " if letter == letter.upper() and letter.isalpha():\n", - " count += 1\n", - " return count\n", - "f('The Rain in Spain')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 11, - "text": [ - "3" - ] - } - ], - "prompt_number": 11 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 4" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here's a solution:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def f(seq_a, seq_b):\n", - " is_subset = True\n", - " for a in seq_a:\n", - " if a not in seq_b:\n", - " is_subset = False\n", - " return is_subset\n", - "\n", - "# == test == #\n", - "\n", - "print(f([1, 2], [1, 2, 3]))\n", - "print(f([1, 2, 3], [1, 2]))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "True\n", - "False\n" - ] - } - ], - "prompt_number": 12 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Of course if we use the `sets` data type then the solution is easier" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def f(seq_a, seq_b):\n", - " return set(seq_a).issubset(set(seq_b))" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 13 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 5" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def linapprox(f, a, b, n, x):\n", - " \"\"\"\n", - " Evaluates the piecewise linear interpolant of f at x on the interval \n", - " [a, b], with n evenly spaced grid points.\n", - "\n", - " Parameters \n", - " ===========\n", - " f : function\n", - " The function to approximate\n", - "\n", - " x, a, b : scalars (floats or integers) \n", - " Evaluation point and endpoints, with a <= x <= b\n", - "\n", - " n : integer\n", - " Number of grid points\n", - "\n", - " Returns\n", - " =========\n", - " A float. The interpolant evaluated at x\n", - "\n", - " \"\"\"\n", - " length_of_interval = b - a\n", - " num_subintervals = n - 1\n", - " step = length_of_interval / num_subintervals \n", - "\n", - " # === find first grid point larger than x === #\n", - " point = a\n", - " while point <= x:\n", - " point += step\n", - "\n", - " # === x must lie between the gridpoints (point - step) and point === #\n", - " u, v = point - step, point \n", - "\n", - " return f(u) + (x - u) * (f(v) - f(u)) / (v - u)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 14 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/ree_solutions.ipynb b/solutions/ree_solutions.ipynb deleted file mode 100644 index d58bf5a40..000000000 --- a/solutions/ree_solutions.ipynb +++ /dev/null @@ -1,490 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:74697b84bde6bdaa59ce401c9a3df13db7f91c9e4deccbfa69ccf0b066b7a4df" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Rational Expectations Equilibrium" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/rational_expectations.html" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The following solutions were put together by Chase Coleman, Spencer Lyon, Thomas Sargent and John Stachurski" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Common imports for the solutions" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import print_function\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We'll use the LQ class from quantecon" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from quantecon import LQ" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 3 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To map a problem into a [discounted optimal linear control problem](http://quant-econ.net/py/lqcontrol.html), we need to define\n", - "\n", - "* state vector $x_t$ and control vector $u_t$\n", - "\n", - "* matrices $A, B, Q, R$ that define preferences and the law of motion for the state\n", - "\n", - "For the state and control vectors we choose\n", - "\n", - "$$\n", - " x_t = \\begin{bmatrix} y_t \\\\ Y_t \\\\ 1 \\end{bmatrix},\n", - " \\qquad\n", - " u_t = y_{t+1} - y_{t}\n", - "$$\n", - "\n", - "For $, B, Q, R$ we set\n", - "\n", - "$$\n", - " A = \n", - " \\begin{bmatrix} \n", - " 1 & 0 & 0 \\\\\n", - " 0 & \\kappa_1 & \\kappa_0 \\\\ \n", - " 0 & 0 & 1 \n", - " \\end{bmatrix},\n", - " \\quad\n", - " B = \\begin{bmatrix} 1 \\\\ 0 \\\\ 0 \\end{bmatrix} ,\n", - " \\quad\n", - " R = \n", - " \\begin{bmatrix} \n", - " 0 & a_1/2 & -a_0/2 \\\\ \n", - " a_1/2 & 0 & 0 \\\\ \n", - " -a_0/2 & 0 & 0 \n", - " \\end{bmatrix},\n", - " \\quad\n", - " Q = \\gamma / 2\n", - "$$\n", - "\n", - "By multiplying out you can confirm that\n", - "\n", - "* $x_t' R x_t + u_t' Q u_t = - r_t$\n", - "\n", - "* $x_{t+1} = A x_t + B u_t$\n", - "\n", - "We'll use the module ``lqcontrol.py`` to solve the firm's problem at the stated parameter values\n", - "\n", - "This will return an LQ policy $F$ with the interpretation $u_t = - F x_t$, or\n", - "\n", - "$$\n", - " y_{t+1} - y_t = - F_0 y_t - F_1 Y_t - F_2\n", - "$$\n", - "\n", - "Matching parameters with $y_{t+1} = h_0 + h_1 y_t + h_2 Y_t$ leads to\n", - "\n", - "$$\n", - " h_0 = -F_2, \\quad h_1 = 1 - F_0, \\quad h_2 = -F_1\n", - "$$\n", - "\n", - "Here's our solution" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "# == Model parameters == #\n", - "\n", - "a0 = 100\n", - "a1 = 0.05\n", - "beta = 0.95\n", - "gamma = 10.0\n", - "\n", - "# == Beliefs == #\n", - "\n", - "kappa0 = 95.5\n", - "kappa1 = 0.95\n", - "\n", - "# == Formulate the LQ problem == #\n", - "\n", - "A = np.array([[1, 0, 0], [0, kappa1, kappa0], [0, 0, 1]])\n", - "B = np.array([1, 0, 0])\n", - "B.shape = 3, 1\n", - "R = np.array([[0, a1/2, -a0/2], [a1/2, 0, 0], [-a0/2, 0, 0]])\n", - "Q = 0.5 * gamma\n", - "\n", - "# == Solve for the optimal policy == #\n", - "\n", - "lq = LQ(Q, R, A, B, beta=beta)\n", - "P, F, d = lq.stationary_values()\n", - "F = F.flatten()\n", - "out1 = \"F = [{0:.3f}, {1:.3f}, {2:.3f}]\".format(F[0], F[1], F[2])\n", - "h0, h1, h2 = -F[2], 1 - F[0], -F[1]\n", - "out2 = \"(h0, h1, h2) = ({0:.3f}, {1:.3f}, {2:.3f})\".format(h0, h1, h2)\n", - "\n", - "print(out1)\n", - "print(out2)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "F = [0.000, 0.046, -96.949]\n", - "(h0, h1, h2) = (96.949, 1.000, -0.046)\n" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The implication is that\n", - "\n", - "$$\n", - " y_{t+1} = 96.949 + y_t - 0.046 \\, Y_t\n", - "$$\n", - "\n", - "\n", - "For the case $n > 1$, recall that $Y_t = n y_t$, which, combined with the previous equation, yields\n", - "\n", - "$$\n", - " Y_{t+1} \n", - " = n \\left( 96.949 + y_t - 0.046 \\, Y_t \\right) \n", - " = n 96.949 + (1 - n 0.046) Y_t \n", - "$$" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To determine whether a $\\kappa_0, \\kappa_1$ pair forms the\n", - "aggregate law of motion component of a rational expectations equilibrium, we\n", - "can proceed as follows:\n", - "\n", - "* Determine the corresponding firm law of motion $y_{t+1} = h_0 + h_1 y_t + h_2 Y_t$\n", - "\n", - "* Test whether the associated aggregate law :$Y_{t+1} = n h(Y_t/n, Y_t)$ evaluates to $Y_{t+1} = \\kappa_0 + \\kappa_1 Y_t$\n", - "\n", - "In the second step we can use $Y_t = n y_t = y_t$, so that $Y_{t+1} = n h(Y_t/n, Y_t)$ becomes\n", - "\n", - "$$\n", - " Y_{t+1} = h(Y_t, Y_t) = h_0 + (h_1 + h_2) Y_t\n", - "$$\n", - "\n", - "Hence to test the second step we can test $\\kappa_0 = h_0$ and $\\kappa_1 = h_1 + h_2$\n", - "\n", - "The following code implements this test\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "candidates = (\n", - " (94.0886298678, 0.923409232937),\n", - " (93.2119845412, 0.984323478873),\n", - " (95.0818452486, 0.952459076301)\n", - " )\n", - "\n", - "for kappa0, kappa1 in candidates:\n", - "\n", - " # == Form the associated law of motion == #\n", - " A = np.array([[1, 0, 0], [0, kappa1, kappa0], [0, 0, 1]])\n", - "\n", - " # == Solve the LQ problem for the firm == #\n", - " lq = LQ(Q, R, A, B, beta=beta)\n", - " P, F, d = lq.stationary_values()\n", - " F = F.flatten()\n", - " h0, h1, h2 = -F[2], 1 - F[0], -F[1]\n", - "\n", - " # == Test the equilibrium condition == #\n", - " if np.allclose((kappa0, kappa1), (h0, h1 + h2)):\n", - " print('Equilibrium pair =', kappa0, kappa1)\n", - " print('(h0, h1, h2) = ', h0, h1, h2)\n", - " break\n", - "\n", - "\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Equilibrium pair = 95.0818452486 0.952459076301\n", - "(h0, h1, h2) = 95.0818139011 1.0 -0.0475409397193\n" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The output tells us that the answer is pair (iii), which implies $(h_0, h_1, h_2) = (95.0819, 1.0000, -.0475)$\n", - "\n", - "(Notice we use `np.allclose` to test equality of floating point numbers, since exact equality is too strict)\n", - "\n", - "Regarding the iterative algorithm, one could loop from a given\n", - "$(\\kappa_0, \\kappa_1)$ pair to the associated firm law and then to a new $(\\kappa_0, \\kappa_1)$ pair\n", - "\n", - "This amounts to implementing the operator $\\Phi$ described in the lecture\n", - "\n", - "(There is in general no guarantee that this iterative process will converge to\n", - "a rational expectations equilibrium)\n" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 3" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We are asked to write the planner problem as an LQ problem \n", - "\n", - "For the state and control vectors we choose\n", - "\n", - "$$\n", - " x_t = \\begin{bmatrix} Y_t \\\\ 1 \\end{bmatrix},\n", - " \\quad\n", - " u_t = Y_{t+1} - Y_{t}\n", - "$$\n", - "\n", - "For the LQ matrices we set\n", - "\n", - "$$\n", - " A = \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix},\n", - " \\quad\n", - " B = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix},\n", - " \\quad\n", - " R = \\begin{bmatrix} a_1/2 & -a_0/2 \\\\ -a_0/2 & 0 \\end{bmatrix},\n", - " \\quad\n", - " Q = \\gamma / 2\n", - "$$\n", - "\n", - "By multiplying out you can confirm that\n", - "\n", - "* $x_t' R x_t + u_t' Q u_t = - s(Y_t, Y_{t+1})$\n", - "\n", - "* $x_{t+1} = A x_t + B u_t$\n", - "\n", - "By obtaining the optimal policy and using $u_t = - F x_t$ or\n", - "\n", - "$$\n", - " Y_{t+1} - Y_t = -F_0 Y_t - F_1 \n", - "$$\n", - "\n", - "we can obtain the implied aggregate law of motion via $\\kappa_0 = -F_1$\n", - "and $\\kappa_1 = 1-F_0$\n", - "\n", - "The Python code to solve this problem is below:\n", - "\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "# == Formulate the planner's LQ problem == #\n", - "\n", - "A = np.array([[1, 0], [0, 1]])\n", - "B = np.array([[1], [0]])\n", - "R = np.array([[a1 / 2, -a0 / 2], [-a0 / 2, 0]])\n", - "Q = gamma / 2\n", - "\n", - "# == Solve for the optimal policy == #\n", - "\n", - "lq = LQ(Q, R, A, B, beta=beta)\n", - "P, F, d = lq.stationary_values()\n", - "\n", - "# == Print the results == #\n", - "\n", - "F = F.flatten()\n", - "kappa0, kappa1 = -F[1], 1 - F[0]\n", - "print(kappa0, kappa1)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "95.0818452486 0.952459076301\n" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The output yields the same $(\\kappa_0, \\kappa_1)$ pair obtained as an equilibrium from the previous exercise\n" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 4" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The monopolist's LQ problem is almost identical to the planner's problem from\n", - "the previous exercise, except that\n", - "\n", - "$$\n", - " R = \\begin{bmatrix} \n", - " a_1 & -a_0/2 \\\\ \n", - " -a_0/2 & 0 \n", - " \\end{bmatrix} \n", - "$$\n", - "\n", - "The problem can be solved as follows\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "A = np.array([[1, 0], [0, 1]])\n", - "B = np.array([[1], [0]])\n", - "R = np.array([[a1, -a0 / 2], [-a0 / 2, 0]])\n", - "Q = gamma / 2\n", - "\n", - "lq = LQ(Q, R, A, B, beta=beta)\n", - "P, F, d = lq.stationary_values()\n", - "\n", - "F = F.flatten()\n", - "m0, m1 = -F[1], 1 - F[0]\n", - "print(m0, m1)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "73.472927865 0.926527070421\n" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We see that the law of motion for the monopolist is approximately $Y_{t+1} = 73.4729 + 0.9265 Y_t$\n", - "\n", - "In the rational expectations case the law of motion was approximately\n", - "$Y_{t+1} = 95.0818 + 0.9525 Y_t$\n", - "\n", - "One way to compare these two laws of motion is by their fixed points, which give long run equilibrium output in each case\n", - "\n", - "For laws of the form $Y_{t+1} = c_0 + c_1 Y_t$, the fixed point is $c_0 / (1 - c_1)$\n", - "\n", - "If you crunch the numbers, you will see that the monopolist adopts a lower long run\n", - "quantity than obtained by the competitive market, implying a higher market price\n", - "\n", - "This is analogous to the elementary static-case results\n" - ] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/schelling_solutions.ipynb b/solutions/schelling_solutions.ipynb deleted file mode 100644 index 1b6120ee2..000000000 --- a/solutions/schelling_solutions.ipynb +++ /dev/null @@ -1,212 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:5e1afd01c6098b2b6a7baba17451d4df9ed1533d55b3ed33ccdbcf380e3f1cd6" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Schelling's Segregation Model" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/schelling.html" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here's one solution that does the job we want. If you feel like a further exercise you can probably speed up some of the computations and then increase the number of agents. \n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from random import uniform, seed\n", - "from math import sqrt\n", - "import matplotlib.pyplot as plt\n", - "\n", - "seed(10) # for reproducible random numbers\n", - "\n", - "class Agent:\n", - "\n", - " def __init__(self, type):\n", - " self.type = type\n", - " self.draw_location()\n", - "\n", - " def draw_location(self):\n", - " self.location = uniform(0, 1), uniform(0, 1)\n", - "\n", - " def get_distance(self, other):\n", - " \"Computes euclidean distance between self and other agent.\"\n", - " a = (self.location[0] - other.location[0])**2\n", - " b = (self.location[1] - other.location[1])**2\n", - " return sqrt(a + b)\n", - "\n", - " def happy(self, agents):\n", - " \"True if sufficient number of nearest neighbors are of the same type.\"\n", - " distances = []\n", - " # distances is a list of pairs (d, agent), where d is distance from\n", - " # agent to self\n", - " for agent in agents:\n", - " if self != agent:\n", - " distance = self.get_distance(agent)\n", - " distances.append((distance, agent))\n", - " # == Sort from smallest to largest, according to distance == #\n", - " distances.sort()\n", - " # == Extract the neighboring agents == #\n", - " neighbors = [agent for d, agent in distances[:num_neighbors]]\n", - " # == Count how many neighbors have the same type as self == #\n", - " num_same_type = sum(self.type == agent.type for agent in neighbors)\n", - " return num_same_type >= require_same_type\n", - "\n", - " def update(self, agents):\n", - " \"If not happy, then randomly choose new locations until happy.\"\n", - " while not self.happy(agents):\n", - " self.draw_location()\n", - "\n", - " \n", - "def plot_distribution(agents, cycle_num):\n", - " \"Plot the distribution of agents after cycle_num rounds of the loop.\"\n", - " x_values_0, y_values_0 = [], []\n", - " x_values_1, y_values_1 = [], []\n", - " # == Obtain locations of each type == #\n", - " for agent in agents:\n", - " x, y = agent.location\n", - " if agent.type == 0:\n", - " x_values_0.append(x)\n", - " y_values_0.append(y)\n", - " else:\n", - " x_values_1.append(x)\n", - " y_values_1.append(y)\n", - " fig, ax = plt.subplots(figsize=(8, 8))\n", - " plot_args = {'markersize' : 8, 'alpha' : 0.6}\n", - " ax.set_axis_bgcolor('azure')\n", - " ax.plot(x_values_0, y_values_0, 'o', markerfacecolor='orange', **plot_args)\n", - " ax.plot(x_values_1, y_values_1, 'o', markerfacecolor='green', **plot_args)\n", - " ax.set_title('Cycle {}'.format(cycle_num - 1))\n", - " plt.show()\n", - "\n", - "# == Main == #\n", - "\n", - "num_of_type_0 = 250\n", - "num_of_type_1 = 250\n", - "num_neighbors = 10 # Number of agents regarded as neighbors\n", - "require_same_type = 7 # Want at least this many neighbors to be same type\n", - "\n", - "# == Create a list of agents == #\n", - "agents = [Agent(0) for i in range(num_of_type_0)]\n", - "agents.extend(Agent(1) for i in range(num_of_type_1))\n", - "\n", - "\n", - "count = 1\n", - "# == Loop until none wishes to move == #\n", - "while 1:\n", - " print('Entering loop ', count)\n", - " plot_distribution(agents, count)\n", - " count += 1\n", - " no_one_moved = True\n", - " for agent in agents:\n", - " old_location = agent.location\n", - " agent.update(agents)\n", - " if agent.location != old_location:\n", - " no_one_moved = False\n", - " if no_one_moved:\n", - " break\n", - " \n", - "print('Converged, terminating.')\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Entering loop 1\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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Pc5NcOBMKiwl/R2CX9B3ZwuzH//ko7mq4FvzE55pG2fQaVqTWwNBDTrJ2T2MxVDGrXXD5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+/ZNZbxJyVVsc62WfPtOJpTJIZUUVjZuakIqivztGb2Ep0J5Mav6V9AdIh3iR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9RmManUxKuLQq94qObEVa+Y66LciTIf7jzXHuvhFqqoqY8E8yMNZHqWOEv39l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- "text": [ - "" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Converged, terminating.\n" - ] - } - ], - "prompt_number": 2 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/scipy_solutions.ipynb b/solutions/scipy_solutions.ipynb deleted file mode 100644 index f8a0da152..000000000 --- a/solutions/scipy_solutions.ipynb +++ /dev/null @@ -1,112 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:da5a4e2755161c4b9d309d2697cd1a0f4c41ef40220265dd07daac825891c8ff" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: SciPy" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/scipy.html" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here's a reasonable solution:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def bisect(f, a, b, tol=10e-5):\n", - " \"\"\"\n", - " Implements the bisection root finding algorithm, assuming that f is a\n", - " real-valued function on [a, b] satisfying f(a) < 0 < f(b).\n", - " \"\"\"\n", - " lower, upper = a, b\n", - " if upper - lower < tol:\n", - " return 0.5 * (upper + lower)\n", - " else:\n", - " middle = 0.5 * (upper + lower)\n", - " print('Current mid point = {}'.format(middle))\n", - " if f(middle) > 0: # Implies root is between lower and middle\n", - " bisect(f, lower, middle)\n", - " else: # Implies root is between middle and upper\n", - " bisect(f, middle, upper)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can test it as follows" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "f = lambda x: np.sin(4 * (x - 0.25)) + x + x**20 - 1\n", - "\n", - "bisect(f, 0, 1)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Current mid point = 0.5\n", - "Current mid point = 0.25\n", - "Current mid point = 0.375\n", - "Current mid point = 0.4375\n", - "Current mid point = 0.40625\n", - "Current mid point = 0.421875\n", - "Current mid point = 0.4140625\n", - "Current mid point = 0.41015625\n", - "Current mid point = 0.408203125\n", - "Current mid point = 0.4091796875\n", - "Current mid point = 0.40869140625\n", - "Current mid point = 0.408447265625\n", - "Current mid point = 0.4083251953125\n", - "Current mid point = 0.40826416015625\n" - ] - } - ], - "prompt_number": 2 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/short_path_solutions.ipynb b/solutions/short_path_solutions.ipynb deleted file mode 100644 index 2dc6b8c52..000000000 --- a/solutions/short_path_solutions.ipynb +++ /dev/null @@ -1,285 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:f97b7eff16bd2ce0f5f813b45826fad4a21fd16ae441ee3fe59c2e4abdd0aa9f" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Shortest Paths" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/short_path.html" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If you Shift-Enter in the next cell you'll save the data we want to work with in the local directory --- then scroll down for the solution." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%%file graph.txt\n", - "node0, node1 0.04, node8 11.11, node14 72.21\n", - "node1, node46 1247.25, node6 20.59, node13 64.94\n", - "node2, node66 54.18, node31 166.80, node45 1561.45\n", - "node3, node20 133.65, node6 2.06, node11 42.43\n", - "node4, node75 3706.67, node5 0.73, node7 1.02\n", - "node5, node45 1382.97, node7 3.33, node11 34.54\n", - "node6, node31 63.17, node9 0.72, node10 13.10\n", - "node7, node50 478.14, node9 3.15, node10 5.85\n", - "node8, node69 577.91, node11 7.45, node12 3.18\n", - "node9, node70 2454.28, node13 4.42, node20 16.53\n", - "node10, node89 5352.79, node12 1.87, node16 25.16\n", - "node11, node94 4961.32, node18 37.55, node20 65.08\n", - "node12, node84 3914.62, node24 34.32, node28 170.04\n", - "node13, node60 2135.95, node38 236.33, node40 475.33\n", - "node14, node67 1878.96, node16 2.70, node24 38.65\n", - "node15, node91 3597.11, node17 1.01, node18 2.57\n", - "node16, node36 392.92, node19 3.49, node38 278.71\n", - "node17, node76 783.29, node22 24.78, node23 26.45\n", - "node18, node91 3363.17, node23 16.23, node28 55.84\n", - "node19, node26 20.09, node20 0.24, node28 70.54\n", - "node20, node98 3523.33, node24 9.81, node33 145.80\n", - "node21, node56 626.04, node28 36.65, node31 27.06\n", - "node22, node72 1447.22, node39 136.32, node40 124.22\n", - "node23, node52 336.73, node26 2.66, node33 22.37\n", - "node24, node66 875.19, node26 1.80, node28 14.25\n", - "node25, node70 1343.63, node32 36.58, node35 45.55\n", - "node26, node47 135.78, node27 0.01, node42 122.00\n", - "node27, node65 480.55, node35 48.10, node43 246.24\n", - "node28, node82 2538.18, node34 21.79, node36 15.52\n", - "node29, node64 635.52, node32 4.22, node33 12.61\n", - "node30, node98 2616.03, node33 5.61, node35 13.95\n", - "node31, node98 3350.98, node36 20.44, node44 125.88\n", - "node32, node97 2613.92, node34 3.33, node35 1.46\n", - "node33, node81 1854.73, node41 3.23, node47 111.54\n", - "node34, node73 1075.38, node42 51.52, node48 129.45\n", - "node35, node52 17.57, node41 2.09, node50 78.81\n", - "node36, node71 1171.60, node54 101.08, node57 260.46\n", - "node37, node75 269.97, node38 0.36, node46 80.49\n", - "node38, node93 2767.85, node40 1.79, node42 8.78\n", - "node39, node50 39.88, node40 0.95, node41 1.34\n", - "node40, node75 548.68, node47 28.57, node54 53.46\n", - "node41, node53 18.23, node46 0.28, node54 162.24\n", - "node42, node59 141.86, node47 10.08, node72 437.49\n", - "node43, node98 2984.83, node54 95.06, node60 116.23\n", - "node44, node91 807.39, node46 1.56, node47 2.14\n", - "node45, node58 79.93, node47 3.68, node49 15.51\n", - "node46, node52 22.68, node57 27.50, node67 65.48\n", - "node47, node50 2.82, node56 49.31, node61 172.64\n", - "node48, node99 2564.12, node59 34.52, node60 66.44\n", - "node49, node78 53.79, node50 0.51, node56 10.89\n", - "node50, node85 251.76, node53 1.38, node55 20.10\n", - "node51, node98 2110.67, node59 23.67, node60 73.79\n", - "node52, node94 1471.80, node64 102.41, node66 123.03\n", - "node53, node72 22.85, node56 4.33, node67 88.35\n", - "node54, node88 967.59, node59 24.30, node73 238.61\n", - "node55, node84 86.09, node57 2.13, node64 60.80\n", - "node56, node76 197.03, node57 0.02, node61 11.06\n", - "node57, node86 701.09, node58 0.46, node60 7.01\n", - "node58, node83 556.70, node64 29.85, node65 34.32\n", - "node59, node90 820.66, node60 0.72, node71 0.67\n", - "node60, node76 48.03, node65 4.76, node67 1.63\n", - "node61, node98 1057.59, node63 0.95, node64 4.88\n", - "node62, node91 132.23, node64 2.94, node76 38.43\n", - "node63, node66 4.43, node72 70.08, node75 56.34\n", - "node64, node80 47.73, node65 0.30, node76 11.98\n", - "node65, node94 594.93, node66 0.64, node73 33.23\n", - "node66, node98 395.63, node68 2.66, node73 37.53\n", - "node67, node82 153.53, node68 0.09, node70 0.98\n", - "node68, node94 232.10, node70 3.35, node71 1.66\n", - "node69, node99 247.80, node70 0.06, node73 8.99\n", - "node70, node76 27.18, node72 1.50, node73 8.37\n", - "node71, node89 104.50, node74 8.86, node91 284.64\n", - "node72, node76 15.32, node84 102.77, node92 133.06\n", - "node73, node83 52.22, node76 1.40, node90 243.00\n", - "node74, node81 1.07, node76 0.52, node78 8.08\n", - "node75, node92 68.53, node76 0.81, node77 1.19\n", - "node76, node85 13.18, node77 0.45, node78 2.36\n", - "node77, node80 8.94, node78 0.98, node86 64.32\n", - "node78, node98 355.90, node81 2.59\n", - "node79, node81 0.09, node85 1.45, node91 22.35\n", - "node80, node92 121.87, node88 28.78, node98 264.34\n", - "node81, node94 99.78, node89 39.52, node92 99.89\n", - "node82, node91 47.44, node88 28.05, node93 11.99\n", - "node83, node94 114.95, node86 8.75, node88 5.78\n", - "node84, node89 19.14, node94 30.41, node98 121.05\n", - "node85, node97 94.51, node87 2.66, node89 4.90\n", - "node86, node97 85.09\n", - "node87, node88 0.21, node91 11.14, node92 21.23\n", - "node88, node93 1.31, node91 6.83, node98 6.12\n", - "node89, node97 36.97, node99 82.12\n", - "node90, node96 23.53, node94 10.47, node99 50.99\n", - "node91, node97 22.17\n", - "node92, node96 10.83, node97 11.24, node99 34.68\n", - "node93, node94 0.19, node97 6.71, node99 32.77\n", - "node94, node98 5.91, node96 2.03\n", - "node95, node98 6.17, node99 0.27\n", - "node96, node98 3.32, node97 0.43, node99 5.87\n", - "node97, node98 0.30\n", - "node98, node99 0.33\n", - "node99, " - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Overwriting graph.txt\n" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here's our solution" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "def read_graph(in_file):\n", - " \"\"\" Read in the graph from the data file. The graph is stored\n", - " as a dictionary, where the keys are the nodes, and the values\n", - " are a list of pairs (d, c), where d is a node and c is a number.\n", - " If (d, c) is in the list for node n, then d can be reached from\n", - " n at cost c.\n", - " \"\"\"\n", - " graph = {}\n", - " infile = open(in_file)\n", - " for line in infile:\n", - " elements = line.split(',')\n", - " node = elements.pop(0).strip()\n", - " graph[node] = []\n", - " if node != 'node99':\n", - " for element in elements:\n", - " destination, cost = element.split()\n", - " graph[node].append((destination.strip(), float(cost)))\n", - " infile.close()\n", - " return graph\n", - "\n", - "def update_J(J, graph):\n", - " \"The Bellman operator.\"\n", - " next_J = {}\n", - " for node in graph:\n", - " if node == 'node99':\n", - " next_J[node] = 0\n", - " else:\n", - " next_J[node] = min(cost + J[dest] for dest, cost in graph[node])\n", - " return next_J\n", - "\n", - "def print_best_path(J, graph):\n", - " \"\"\" Given a cost-to-go function, computes the best path. At each node n, \n", - " the function prints the current location, looks at all nodes that can be \n", - " reached from n, and moves to the node m which minimizes c + J[m], where c \n", - " is the cost of moving to m.\n", - " \"\"\"\n", - " sum_costs = 0\n", - " current_location = 'node0'\n", - " while current_location != 'node99':\n", - " print(current_location)\n", - " running_min = 1e100 # Any big number\n", - " for destination, cost in graph[current_location]:\n", - " cost_of_path = cost + J[destination]\n", - " if cost_of_path < running_min:\n", - " running_min = cost_of_path\n", - " minimizer_cost = cost\n", - " minimizer_dest = destination\n", - " current_location = minimizer_dest\n", - " sum_costs += minimizer_cost\n", - "\n", - " print('node99\\n')\n", - " print('Cost: ', sum_costs)\n", - "\n", - "\n", - "## Main loop\n", - "\n", - "graph = read_graph('graph.txt')\n", - "M = 1e10\n", - "J = {}\n", - "for node in graph:\n", - " J[node] = M\n", - "J['node99'] = 0\n", - "\n", - "while 1:\n", - " next_J = update_J(J, graph)\n", - " if next_J == J:\n", - " break\n", - " else:\n", - " J = next_J\n", - "print_best_path(J, graph)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "node0\n", - "node8\n", - "node11\n", - "node18\n", - "node23\n", - "node33\n", - "node41\n", - "node53\n", - "node56\n", - "node57\n", - "node60\n", - "node67\n", - "node70\n", - "node73\n", - "node76\n", - "node85\n", - "node87\n", - "node88\n", - "node93\n", - "node94\n", - "node96\n", - "node97\n", - "node98\n", - "node99\n", - "\n", - "Cost: 160.55000000000007\n" - ] - } - ], - "prompt_number": 2 - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/speed_solutions.ipynb b/solutions/speed_solutions.ipynb deleted file mode 100644 index c31920a22..000000000 --- a/solutions/speed_solutions.ipynb +++ /dev/null @@ -1,352 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:728c30baab8bd9b2a010feb63e9e78bbf9dff69dade2e90e64e8118ed3ba9652" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Need for Speed" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/need_for_speed.html" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's start with some imports" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "from numba import jit" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We let \n", - "\n", - "* 0 represent \"low\"\n", - "* 1 represent \"high\"" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "p, q = 0.1, 0.2 # Prob of leaving low and high state respectively" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here's a pure Python version of the function" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def compute_series(n):\n", - " x = np.empty(n, dtype=int)\n", - " x[0] = 1 # Start in state 1\n", - " U = np.random.uniform(0, 1, size=n)\n", - " for t in range(1, n):\n", - " current_x = x[t-1]\n", - " if current_x == 0:\n", - " x[t] = U[t] < p\n", - " else:\n", - " x[t] = U[t] > q\n", - " return x" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's run this code and check that the fraction of time spent in the low state is about 0.666" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "n = 100000\n", - "x = compute_series(n)\n", - "print(np.mean(x == 0)) # Fraction of time x is in state 0" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "0.66725\n" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let's time it" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%timeit compute_series(n)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "1 loops, best of 3: 198 ms per loop\n" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next let's implement a Numba version, which is easy" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "compute_series_numba = jit(compute_series)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 6 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's check we still get the right numbers" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "x = compute_series_numba(n)\n", - "print(np.mean(x == 0))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "0.66283\n" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's see the time" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%timeit compute_series_numba(n)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "1000 loops, best of 3: 1.77 ms per loop\n" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is a nice speed improvement for one line of code\n", - "\n", - "Now let's implement a Cython version" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%load_ext cythonmagic" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 9 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%%cython\n", - "import numpy as np\n", - "from numpy cimport int_t, float_t\n", - "\n", - "def compute_series_cy(int n):\n", - " # == Create NumPy arrays first == #\n", - " x_np = np.empty(n, dtype=int)\n", - " U_np = np.random.uniform(0, 1, size=n)\n", - " # == Now create memoryviews of the arrays == #\n", - " cdef int_t [:] x = x_np\n", - " cdef float_t [:] U = U_np\n", - " # == Other variable declarations == #\n", - " cdef float p = 0.1\n", - " cdef float q = 0.2\n", - " cdef int t\n", - " # == Main loop == #\n", - " x[0] = 1 \n", - " for t in range(1, n):\n", - " current_x = x[t-1]\n", - " if current_x == 0:\n", - " x[t] = U[t] < p\n", - " else:\n", - " x[t] = U[t] > q\n", - " return np.asarray(x)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 10 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "compute_series_cy(10)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 11, - "text": [ - "array([1, 0, 0, 0, 0, 0, 0, 0, 0, 0])" - ] - } - ], - "prompt_number": 11 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "x = compute_series_cy(n)\n", - "print(np.mean(x == 0))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "0.66842\n" - ] - } - ], - "prompt_number": 12 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%timeit compute_series_cy(n)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "100 loops, best of 3: 3.39 ms per loop\n" - ] - } - ], - "prompt_number": 13 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The Cython implementation is fast, but not as fast as Numba" - ] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/solutions/statd_solutions.ipynb b/solutions/statd_solutions.ipynb deleted file mode 100644 index d631303ff..000000000 --- a/solutions/statd_solutions.ipynb +++ /dev/null @@ -1,263 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:eaaf9c03d6c37a8e46ed0c66d97861af8fafdbfef1ce39d7383cc2ab548ee7d5" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "quant-econ Solutions: Continuous State Markov Chains" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/stationary_densities.html" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "Look ahead estimation of a TAR stationary density, where the TAR model is\n", - "\n", - "$$ X_{t+1} = \\theta |X_t| + (1 - \\theta^2)^{1/2} \\xi_{t+1} $$\n", - "\n", - "and $\\xi_t \\sim N(0,1)$. Try running at n = 10, 100, 1000, 10000 to get an\n", - "idea of the speed of convergence." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from scipy.stats import norm, gaussian_kde\n", - "from quantecon import LAE\n", - "\n", - "phi = norm()\n", - "n = 500\n", - "theta = 0.8\n", - "# == Frequently used constants == #\n", - "d = np.sqrt(1 - theta**2) \n", - "delta = theta / d\n", - "\n", - "def psi_star(y):\n", - " \"True stationary density of the TAR Model\"\n", - " return 2 * norm.pdf(y) * norm.cdf(delta * y) \n", - "\n", - "def p(x, y):\n", - " \"Stochastic kernel for the TAR model.\"\n", - " return phi.pdf((y - theta * np.abs(x)) / d) / d\n", - "\n", - "Z = phi.rvs(n)\n", - "X = np.empty(n)\n", - "for t in range(n-1):\n", - " X[t+1] = theta * np.abs(X[t]) + d * Z[t]\n", - "psi_est = LAE(p, X)\n", - "k_est = gaussian_kde(X)\n", - "\n", - "fig, ax = plt.subplots(figsize=(10,7))\n", - "ys = np.linspace(-3, 3, 200)\n", - "ax.plot(ys, psi_star(ys), 'b-', lw=2, alpha=0.6, label='true')\n", - "ax.plot(ys, psi_est(ys), 'g-', lw=2, alpha=0.6, label='look ahead estimate')\n", - "ax.plot(ys, k_est(ys), 'k-', lw=2, alpha=0.6, label='kernel based estimate')\n", - "ax.legend(loc='upper left')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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pxdtvv01ubi5lZWX87ne/49ZbbwWgpqYGOzs7nJ2dKSsr47e//a3pvKKiIr76\n6itqa2uxsrJixIgRWLTdNvTggw/y0ksvkZaWBkBlZSWfffYZAEuXLuXYsWP8+9//pqWlhT/96U8U\nFBRc1Wfbvn07R48epbW1FUdHR6ysrEwxeHp6kpWV1eXn7qna2lp0Oh3u7u4YjUbWr19Pamqqab+n\npyfnzp2jubkZ0MqcDzzwAKtWraK4uBjQRuG2bJGlNYaqU6dOcfz4cRpogFEwwnoE1wRf0+15RiO8\n9x7k5mpNMVeu7L8Eqt099wQzd+5EWloaeeGFTZw5AzeMuwELvQX7zu0jpzKn+4sIIa6KJFE94Ozs\nzHfffcemTZtYs2YNU6ZM4b333uPhhx/G1dWVkJAQPvzwwy5HT7ra99hjj7Fs2TIWLVqEk5MTcXFx\nJCYm9uhcnU7HnXfeyaJFixgzZgwhISE8/fTTgDZfqb6+Hnd3d6ZPn86SJUtM1zIajfzhD3/A19cX\nNzc3du3axV/+8hcArr/+ep544gluu+02nJ2dmTBhAps3bwa0UZrPPvuM3/zmN7i7u5OZmcnMmTOv\n6rMVFBRw88034+zsTHh4uKlpZ/t5n3/+Oa6urqxatarTz33h99JZr6r21+Hh4fyf//N/iIuLw8vL\ni9TU1A4xz58/n4iICLy8vEwlwVdffZXg4GBiY2NxdnZm4cKFnDx58rKfUwxu7aNQ+tF6LG0sWTh6\nYY9aGnz+OaSmgoODVsKz73kXhF61evUyvLx0nD27k9deK8WiwYO5QXNRSvFV+lfmCUqIYUDWzhPi\nR5Kf4cEtPz+f5557jtrWWqwXWePi7MJL81/C1rLrngRHjsCf/6z1fXr8cW2tO3N69933+eCDRGxs\nprNgwT38YlUNz+18ioaWBv7vjP/LGNcx5g1QiEGmJ2vn9WQkajGQDmQAT3SyPx6oBA63PZ6+kiCF\nEMKcvv/+e+2JP1jZWTF/1PxuE6jycvjrX7XnN95o/gQK4IYbljF+vAVVVftJT89n01cOzB+tLQf1\n1QkZjRKiL3SXRFkAb6ElUuHA7cC4To7bAUS1PV7szQCFEKKvVFdXk5CQQFVjFbpROuyt7Jk3al6X\n5xiNsG4d1NbC+PFgxmUrOxg5ciTx8TMJCzNy7tx/2LEDXMoWYG9lz4mSE6SXpJs7RCGGnO6SqBgg\nE8gGmoFPgM7u+ZU1OoQQg86OHTtobm6meWQz9gZ75o+ej52VXZfnbNkCJ09qCwnfe6/WbmCgWLp0\nKS4uljhSDbx6AAAgAElEQVQ5JVFbm8fn/7BnqtsiAL4+8bWUnYXoZd0lUb7Ahfevn2vbdiEFTAeO\nABvRRqyEEGJAa25uZvv27dQ01WAxxgJbS9tuR6EKCuA//9Ge33eftqzLQOLi4sLMmTPx9FRYWGyg\nsRGyvpvHCGsHssqySCtOM3eIQgwp3SVRPflnSxLgD0wE/hf48scGJYQQfS0hIYHq6mrq7Otw9nFm\nVuCsLu/IUwo+/hhaWmDGDAgfoP9cXLx4MZaWFlhZHcLaOp9zZ2xwLdNGozZlbjJzdEIMLd0128xF\nS5Da+aONRl2o+oLnm4A/A65A2cUXe+6550zP4+PjiY+P73mkQgjRS5RS/PDDDzS2NKIL1WGht+h2\nFGrXLsjI0Mp4N93UT4FeBYPBwMyZM9mxYweenhs5e/Z+cnbNwTjvWzJKM8gozSDELcTcYQox4Gzf\nvp3t27df0TndVfMtgRPAfCAPSESbXH78gmM8gSK0UasY4J9AUCfXkhYHYkiSn+HBJysri9///vfk\nN+fjucyT2IBY7p98/2WPr6iA556D+npYsQKmTOm/WK9GWVkZTz/9NEopIiOfIznZk1q//2A38Rsi\nPcfzyLRHzB2iEANeT1ocdDcS1QI8DGxGu1PvfbQEqn1l4LXAT4GH2o6tA267kiANBkOvLvEhRH8z\nGLpfGkQMLNu3b6fF2ILR14jeQs/CMQu7PP6LL7QEKjISJk/upyB/BFdXV6ZPn86uXbvQ6zcwcuTP\nac6dR9HI70jVpZJTmUOAc4C5wxRi0OvJ2nmb2h4XunBRu7fbHlelrOySqp8QQvSZ6upqkpKSKKwr\nxC3MjTD3sC4TilOnICFBW87l1lsH1t14XVmyZAl79+4lOfkAd955LR995EFTxmwa3L9jU8YmVkav\n7P4iQoguybIvQohhZc+ePVpbA7dmbJ1sWTB6wWWPVQr++U/t+YIF4O7eT0H2Ajc3N+Li4jAajWRm\nbmTqVPCsXcDpLEuSCg5TWFNo7hCFGPQkiRJCDBtGo5GdO3dSVl+GU6gTI0eMZLzH+Msen5gIp0+D\nszMsXtyPgfaSJUuWoNfrSUhIYO7cYlxsXbDIj6W0RLH19FZzhyfEoCdJlBBi2EhNTaW0tJQqyyoM\n/gbig+IvOyezsRH+/W/t+Q03gG3XK8EMSO7u7sTGxmI0Gtm9eyPLl4Nv43yysmD3mX3UNtWaO0Qh\nBjVJooQQw8bu3bupb67HMsgSG0sbpvtPv+yxP/ygrZEXGAixsf0YZC9rH43av38/EREljPPzwb52\nPKfPNLHjzA5zhyfEoCZJlBBiWKisrOTo0aMU1BXgGeZJjG/MZZtr1tVpy7uANgo1WCaTd8bDw4OY\nmBiMRiNbt37HLbeAb+MCzp6Fb09odykKIa6OJFFCiGFh//79NLc00+LegrW9NfFB8Zc99vvvtQWG\nQ0MhLKz/Yuwr11xzDaBNqvfyqmbehDDsmv1IOVHJgdwDZo5OiMFLkighxJCnlGLPnj0U1RbhOtaV\nYNdg/J39Oz22uhq2ts25Xr58cI9CtfPx8WHixIk0Nzezbds2brpJR0DLAgoL4bOk76RZrBBXSZIo\nIcSQl5mZSWFhIeWqHNdAV+YEzbnssZs3Q0MDTJgAY8b0Y5B9rH00avv27Tg6NnDrrKlYKyf2peaS\nUZpp5uiEGJwkiRJCDHl79uyhpqkG+9H2ONg6EOUV1elxVVXQvnTW8uX9F19/GDNmDCEhIdTV1bFr\n1y6u+4klQbpZVFTC3/f9YO7whBiUJIkSQgxpDQ0NHDp0iIIabUL5NN9pWFlYdXrs999DczNMmgT+\nnVf7BrXFbc2uvv/+e6ysWrh37mz0WLDp8GHK6yvMHJ0Qg48kUUKIIe3QoUPUN9TT7NKMnYsdMwNm\ndnpcbS3saLvjf8mSfgywH0VERODr60tFRQUJCQlcu8AFf8soqmqMrN+209zhCTHoSBIlhBjS9u/f\nT0ldCYYQA6MMo/B18u30uO3btblQ4eEQFNSvIfYbnU5nGo3avHkzFhZG7p4dD8DnibtoapF2B0Jc\nCUmihBBDVmlpKSdPnqS4oRj3Me6XHYVqbDx/R95QHYVqFx0djbu7O4WFhSQnJ3PLgmA8bf0or6/i\nr1uSzB2eEIOKJFFCiCErMTGRuuY6LH0scbB3YKrP1E6P27lTK+eNGQMhIf0cZD/T6/UsXLgQaB+N\ngjtnzAXgH/u2I4NRQvScJFFCiCFJKcX+/fsprCnEI9SDaJ9obCxtLjmupUWbUA7aKNRQ6AvVnenT\np+Po6Eh2djYnTpzgZ3On4mRvS35jFt/syDN3eEIMGpJECSGGpDNnzpCfn0+FqsDgbyDWr/MF8A4d\ngooK8PGB8eP7OUgzsba2Zt68eYA2GmVnbcPSidoo3V+376a11ZzRCTF4SBIlhBiSEhISqGiowGm0\nEx6OHgS7Bl9yjFLnR6EWLBgeo1Dt4uPjsbGxIS0tjdzcXO6eMwt7e8hq2M/uvc3mDk+IQUGSKCHE\nkNPa2sqBAwcorC3EY6wHsX6x6DrJkDIyICcHnJwgJsYMgZqRvb09M2bMALS+UUGGAKaODaBZV8tf\ntyTLaJQQPSBJlBBiyElPT6eisoJ6m3ocRjpctpTXPgoVHw9WnfffHNLmzZuHTqcjMTGR6upqbo2b\niZ0dHK/dRWKiuaMTYuCTJEoIMeQcOHCA4rpi3ILdCHUPxd3e/ZJjCgvhyBEteZo92wxBDgAjR45k\n4sSJtLS0sH37dmL9YhgTaE2F5Qm+2FyErEssRNckiRJCDCnNzc0kJydTVFuEe7A7cf5xnR63bZv2\nZ2wsODr2Y4ADzIIFCwDYsWMHlliyZFI0tjZwpHwPKSlmDk6IAU6SKCHEkJKamkp5dTktji24uLsw\n2XvyJcc0NMD+/drztpvUhq3g4GCCgoKoqakhISGBOUEz8fWDQuu9bNjYKqNRQnRBkighxJBy8OBB\nimuL8QjxYJLXJGwtbS85Zt8+LZEKDdVaGwxnOp2O+fPnA9oE81Euo4gK9kFZVXHoXAoZGWYOUIgB\nTJIoIcSQ0djYSEpKCkV1RbiPcWeq76UdypU6v9DwnDn9HOAANWXKFAwGA/n5+aSlpRE/aiY+vlBg\ns5vNm80dnRADlyRRQoghIyUlhfKacixcLXBzdyN8ZPglx5w4Afn54OICkyaZIcgByMLCgrlztaVf\ntm7dSqxfLAF+llTZHOPgsVLOnjVzgEIMUJJECSGGjAMHDlBUW4RHiLbMi6Xe8pJj2kehZs0CC4t+\nDnAAmzVrlqn5ZkVxBdP8J+PppSi03mtanFkI0ZEkUUKIIaGhoYHU1FSK64q1Ul4niw2Xl0NyspY8\nzZxphiAHMHt7e6ZPnw5oc6NmBszE1wcKbfaQeMBIVZWZAxRiAJIkSggxJKSkpFBWV4athy1e7l6d\nLvOyezcYjVoZz8XFDEEOcBc23/Sy8iLAzQMH93KKSTON4AkhzpMkSggxJCQlJVFcW2yaUH7xMi9G\nI+zZoz0frs01u+Ph4WFqvrlz506m+0/H1w+KrPezYwc0y5J6QnQgSZQQYtBrbGzk6NGjFNcW4zba\njRjfSxfCO3ZMK+eNHKm1NhCdm9fWOGvXrl1Ee0fj5ASNhmTKq+tlKRghLiJJlBBi0EtNTaW4uhg7\nDzsCvQLxdfS95Jjdu7U/Z86ETtYiFm3Gjh2Lj48PlZWV5JzIIcw9FC/fZkqsk9i6FWm+KcQFJIkS\nQgx6hw4dMk0oj/aJvqSUV1kJKSnahPK2udPiMnQ6HXPaGmht376dOL84Ro6EKsf95OZqLSKEEBpJ\nooQQg1pTUxNHUo5QWldqSqIutnevNicqMhKcnMwQ5CATGxuLra0tJ0+exFN5Ymtpja3vSRr0JdLu\nQIgLSBIlhBjUjh07RlFVEXYj7RjjOwZvR+8O+5XqWMoT3bO1tWXatGkAJOxJIMo7Cm9vKLVLICUF\niorMHKAQA4QkUUKIQe3w4cMU12kTyqd4T7lk/4kTUFICrq4QfmkDc3EZ8fHxAOzfv58o9yisrMAi\ncD8KxbZt5o1NiIFCkighxKDV2tp6vpQ3uvNS3v792p9xcaCX33g95uPjw9ixY2loaKA8sxxnW2cc\nvYqotjjN3r1QV2fuCIUwP/mVIoQYtDIyMsgty8Xa2ZqxgWPxdPDssL+xEZKStOexsWYIcJBrH43a\nuWMnMT4xjLAHy6D9NDae77klxHAmSZQQYtA6cuQIJbUluI1y63QUKjlZS6TGjAEPDzMEOMhNmjQJ\nZ2dn8vPz8WxsS1B9D2CkhW3btMn6QgxnkkQJIQYlpRTJR5IprS/FbZQbk70nX3JMeylPRqGujoWF\nBbNmzQLg+MHj+Dv7Y+dUh3FkCmVlkJpq5gCFMDNJooQQg1Jubi5Z57LQ2+oJCwnDY0THoaaKCjh+\nHCwtYcql881FD82aNQu9Xs/hw4cZ7zQeHWA/VstOd+40b2xCmJskUUKIQSklJYWSuhJcg1w7HYVK\nSNDaG0RGwogRZghwiHBxcSEqKgqj0UjjqUb0Oj0NTqko62pSU7U7H4UYriSJEkIMSsnJbaW8IDei\nvKM67FOq41154sdpn2B+aP8hxrmNQ2/Risu4gygFu3aZNzYhzEmSKCHEoFNRUUHKiRRada2EhIZc\nslZeTg7k5YGDA0REmCnIISQkJARvb28qKytxq3YDwOirZal79kBLizmjE8J8JIkSQgw6KSkplNSX\nYPA3EO1/6Vp57aNQMTHaennix9HpdMxsa/defLwYW0tbqvTZuPgWUV0Nhw+bOUAhzESSKCHEoJOc\nnExpXSmuo1wvKeW1tkJiovZc7srrPbGxsVhaWpJ+PJ0Q+xB0gOv4AwDs2GHe2IQwF0mihBCDSkND\nAwdTDtLY2sio0FGMchnVYf+xY1BTAz4+EBBgpiCHIAcHB6KiolBKoTurjfxVOSZiY6vIyNDKp0IM\nN5JECSEGlbS0NAqrC3HycmLa6GmXLeXFxsJFu8SP1F7SO5t6FgcrB0oaCgiZfA6Q0SgxPEkSJYQY\nVJKTk02tDS4u5dXVwZEjWvI0bZqZAhzCQkNDGTlyJOXl5XjWaR3MbUZrtdP9+7Xu8EIMJ5JECSEG\nDaPRSEJSAnXNdfiH+jPWbWyH/QcPaneKjRsHLi5mCnIIu3CCeeNpLWM61XiA0aMVDQ3n56IJMVxI\nEiWEGDQyMzPJKcnB3sWe6WHT0es6/gqTZV76XlxcHHq9nrzMPBxwoLy+nNFTMwGtpKeUmQMUoh9J\nEiWEGDSOHDmilfI6uSuvtBSyssDaGiZNMlOAw4CzszPjx4/HaDTiVOwEQL3rARwc4OxZOH3azAEK\n0Y8kiRJCDApKKfYd3EdNUw0+IT6Mcx/XYf+hQ9qfkZFgY2OGAIeRuLY28NWnqlFKcaTwENPiWgHp\nYC6GF0mihBCDQkFBASdzTmJtZ830CdOxsrDqsP+A1rKI6GgzBDfMREZG4uDgQFVRFQ4NDtQ01eAR\ncRzQ5qU1NJg5QCH6iSRRQohBITU1lZK6EgyBBqJ9O2ZKRUXaUi+2tjB+vJkCHEYsLS2JiYlBp9Nh\nnWcNwKmGRMaOhaYmLZESYjiQJEoIMSgcTD5IVWMVI4NGEuHRcUG89r+0J00CK6tOTha9bvr06QBU\nZlVibDWSXJBMTFwTALt3mzMyIfqPJFFCiAGvsbGRxKOJoIO4qDhsLW077G9PoqZONUNww5S/vz/+\n/v4Ym4zYltrS2NKIpW8Kdnba5PJz58wdoRB9rydJ1GIgHcgAnujiuKlAC3BjL8QlhBAmJ0+epLi6\nGEcPR2JGxXTYl5cHubkwYgSEhZkpwGGqfYK57pzWGj656ICpyemePeaKSoj+010SZQG8hZZIhQO3\nA+Muc9yrwLeALLQghOhVySnJlDeUYwgwEOkZ2WFf+yhUVBRYWpohuGEsJiYGvV5PXV4dLfUtHC06\nypTYOgASEqC52cwBCtHHukuiYoBMIBtoBj4Blndy3CPA50BxbwYnhBAAuw7uwqiMRE6IxMnGybRd\nqfNJlNyV1/8cHR2JiIjAAgtsi21pNbZSbHGYgACorYXkZHNHKETf6i6J8gXOXvD6XNu2i49ZDvyl\n7bX0qxVC9Jri4mIyzmZgZWvFnIlzOuw7exYKC8HJCUJDzRTgMDetrX7XelbrE3Uw7yBtK8PIBHMx\n5HWXRPUkIfof4Ddtx+qQcp4QohelHkulrL4MF18Xonw6dilvH4WaPBn0cpuMWUycOBFbW1uaSppo\nrGwkvSSdsInVWFtDejoUS31CDGHdzSDIBfwveO2PNhp1oSloZT4Ad2AJWunv64sv9txzz5mex8fH\nEx8ff0XBCiGGn10Hd9HU2kTQ2CC8HbxN26WUNzBYW1szefJk9u7diypQGJ2NnKxMZsqUWezbp00w\nv/56c0cpRPe2b9/O9u3br+ic7pKog0AIEATkAbeiTS6/0OgLnq8H/kMnCRR0TKKEEKI7LS0tJCQn\nADA3Zi463fmB7tOntfXyDAYIDjZXhAK0kt7evXtpymnCeqw1B/MOcu0MLYnauxeWLZORQjHwXTy4\n89vf/rbbc7r7sW4BHgY2A2nAp8BxYGXbQwgh+kxWVhaFlYWMcBtBXEhch33to1BTpoBOJhGY1dix\nYzEYDFjUW1BbVMvJ0pN4+Ffh6QmVlZCaau4IhegbPfm3wSYgFAgGXm7btrbtcbH7gC96JzQhxHC3\n99Beaptr8RzlSYhriGm70SgNNgcSvV7P1KlTsdRbYp1vjVEZSS44LBPMxZAnA6xCiAFrx4EdgNal\n3EJvYdqemamNcLi7Q2CguaITF5rals025TahjIqDeQeJjQULCzh6VPvvJcRQI0mUEGJAqqio4MTp\nE1hYWjA/en6HfYcOaX9GR0spb6Dw9/fHw8MDu1Y7agtqySjLQFlXMmGCNnKYkGDuCIXofZJECSEG\npKSUJCobKnH1d2Wiz0TTdqXg8GHt+eTJZgpOXEKn0xEdHY2F3gKrQiuUUiTlJ9G2TjH79mn/7YQY\nSiSJEkIMSN/v/x6FYnzEeOyt7E3bT53SSkNubhAQYMYAxSWmTJkCQHNuM8ZWIwfzDjJ+PDg6amsc\nnjlj5gCF6GWSRAkhBhyj0ciBIwcAmD+tYykvKUn7MypKSnkDja+vL15eXtgZtZJeZlkm1c0VpkWJ\n9+0zb3xC9DZJooQQA07mqUwKyguwc7ZjTsT5pV6klDewXVjSsym0ASApP4m4tu4UiYmyKLEYWiSJ\nEkIMON/v/54WYwtjQsfgbu9u2p6TozXYdHaG0aO7uIAwm+i29vGN5xpNJT0/P630WlcHKSlmDlCI\nXiRJlBBiwNl9SGssNGPKjA7bpZQ38Hl7e+Pr64s99tTk1ZBVlkVZfZlpgvneveaNT4jeJEmUEGJA\nqampIT0zHb1ezzXTrjFtv7CUFxV1mZPFgNBe0rMutAa0kt7UqVrPqLQ0qKgwc4BC9BJJooQQA8qu\nQ7uob67HI8CDMM8w0/a8PCgsBAcHGDvWjAGKbrWX9JrzmjG2aCU9BweYOFF6RomhRZIoIcSAsjVh\nKwBTJk7psOBweylv0iRZzHag8/DwICAgAHudVtI7XX6a0rpS0wTzvXulZ5QYGuRXkRBiwFBKceiI\n1o58fkzH1gZyV97gMmXKFCx050t6h/IPEREBTk5QUADZ2eaNT4jeIEmUEGLAyMzOpLC0EFsHW+ZM\nON/aoLAQcnPBzg5CQ80YoOix9pJeU24Trc2tHMo7hIUFpp5RMsFcDAWSRAkhBoxNezehUISNC8Pe\n+nyX8vZRqIkTwdLSTMGJK+Lu7k5QUBAOFg7U5taSXZFNcW2x6S69AwekZ5QY/CSJEkIMGHuS9gAw\nM3pmh+3t86GklDe4REdHo9fpO5T0fHwgKAjq6yE52bzxCfFjSRIlhBgQ6hvqOXHyBDqdjiWxS0zb\nS0u1NddsbCA83IwBiivWvpZeU/75kh7QYYK5EIOZJFFCiAHhh4M/0NjciJefF6M8Rpm2t5fyJkwA\nKyszBSeuiqurK6NHj8bBwoG6vDpyKnMoqi1i6lStLHv8OJSXmztKIa6eJFFCiAGhvbVB9KToTlsb\nSClvcJo0aRJ6nR7bElsADuYdZMQIbX6bUtIzSgxukkQJIcxOKcXB5INAx9YGlZWQlaWNQI0fb67o\nxI8xadIkAJrymkxr6QEdloGRnlFisJIkSghhdhk5GRQVF2FrZ0v8pHjT9iNHtD/Dw7U5UWLw8fT0\nxMfHBzvsaCpqIrcql8KaQsLDtYWkCwvh1ClzRynE1ZEkSghhdpv2bgIgPDwcG6vz2VJ7EjVxojmi\nEr2lvaRnV2oHaHfp6fXne0bt22fG4IT4ESSJEkKYXXtrg1nRs0zbGhogPR10OoiMNFdkojeYSnq5\nTVrp9qKS3sGD0NRkruiEuHqSRAkhzKquoY709HQAlkw/39rg2DFoaYExY8DR0VzRid4QEBCAq6sr\nFk0WtJS2kFuVS0FNAd7eMGqU9IwSg5ckUUIIs/r+4Pc0Nzfj6+dLoGegaXv7X6ptgxhiENPpdKaS\n3oiyEQCX9IySkp4YjCSJEkKY1Q+JPwAQHRlt2tbaCkePas9lPtTQEBUVBUBzXrO20HS+lkRFR0vP\nKDF4SRIlhDAbpRSHjmh/mS6IXWDafvKkVuLx8QEPD3NFJ3pTcHAwDg4OtFa3Qg3kVuWSX50vPaPE\noCZJlBDCbNLPplNcWIytjS2zo2abtreX8mQUaujQ6/VERkai1+lxKHUAIClf66QaG6sds2+f9IwS\ng4skUUIIs9m8fzMA48PHY22lLVKr1PnWBjIfamhpv0uvNb8VwFTSi4gAJycoKIDsbHNFJ8SVkyRK\nCGE2ew5prQ1mRs80bcvJ0ebGuLhAYODlzhSDUXh4ODY2NtSV1GHRaGEq6VlYQEyMdoxMMBeDiSRR\nQgizqGms4UT6CXToOrQ2uLDB5gVL6IkhwMrKioiICPQ6PY5lWt+K9pJe+116Bw9qrS2EGAwkiRJC\nmMXWQ1tpbmzG19uXAO8A03ZpbTC0td+lpwq0yU/tjTf9/MDfH2prISXFbOEJcUUkiRJCmMW2xG0A\nTI2aatpWUgK5uWBnB2PHmisy0ZfGjx+PhYUFVXlVWButyavOI786H5CeUWLwkSRKCNHvlFIkpWhl\nnIXTFpq2t49CjR+v9Q4SQ4+9vT2hoaEopTBUGoDzE8xjYsDCAlJToarKnFEK0TOSRAkh+l3q2VRK\n80uxt7EnbmKcabssODw8mEp6+VpJr717uaOjlkAbjZCYaLbwhOgxSaKEEP1uc8JmlFJEhEZga2sL\nQE0NZGZqIxHjx5s5QNGnIttWlC4/W46t3pa86jzyqvOA8z2j9u83V3RC9JwkUUKIfrcvSZv0MnPq\n+dYGR49qIxChodqcKDF0ubi4EBAQQHNzM14NXsD50ajISBgxAs6e1R5CDGSSRAkh+lV5fTmZJzKx\n0FlwTew1pu1yV97w0j4aZVFkAZxvdWBpCVPb7jWQCeZioJMkSgjRr3448gNNdU34ePgQ4Ke1Nmhq\ngrQ0bb/Mhxoe2pOokuwS7K3sO5T02u/SS0zUFqMWYqCSJEoI0a9+SPwBgKmTpqJr66Z5/LiWSAUF\naZ3KxdAXEBCAi4sLlRWVBOq01vTtJb3AQPD2hupqOHbMnFEK0TVJooQQ/abF2ELyUa1ut2DaAtN2\nKeUNPzqdjgkTJgBgU2oDaK0OlFLodNIzSgwOkkQJIfrNsbxjlOWW4WDjwLRJ0wBtMnl7h2op5Q0v\n7SW9suwyRliPIL86n/warfHmtGmg12s/G7W15oxSiMuTJEoI0W+2JGzBaDQyLmQc9vb2AGRlae0N\nPDy0Eo4YPsLCwrCysiLnTA6hI0KB8yU9FxcIC9PW0Tt40JxRCnF5kkQJIfrN3qS9AMyccr61gSw4\nPHxZW1szbtw4AOzLtaT6YN5BlNKacEpJTwx0kkQJIfpFYU0h2SezsdJbsSBWmw+llMyHGu7aS3qV\nOZU4WDtQUFNgKulNmgS2tnD6NOTnmzNKITonSZQQol/sSttFQ3UDXq5ejAoaBWh/MRYXa8t9jB5t\n5gCFWbRPLj+RfoLxblqr+oN5Wv3O2hqio7XjpIO5GIgkiRJC9Iv21gbRk6JNrQ3aR6EiI7VJxGL4\ncXFxITAwkKamJlxrXQFtXlR7Se/CZWCMRnNFKUTn5NeWEKLPNbY0kpKagg4d82Pmm7a3z4eSUt7w\n1l7SqzpbZSrptTfeDA6GkSOhogLS080ZpRCXkiRKCNHnjuYfpexsGY42jkydpK3pUV4O2dlayaZt\nbrEYptpLesdSjzHJS8uoD+Vrd+lJzygxkEkSJYToc98lfoex1Ujo6FCcnJyA86NQERFgZWXG4ITZ\ntXcvLy8vx1f5Ap2X9JKToaHBXFEKcSlJooQQfUopxb4kbQhhTswc0/YLWxuI4e3C7uW152pNJb3c\n6lwA3Nxg7FhtaaBDh8wZqRAdSRIlhOhT56rOcTbjLNYW1sTHxANQVwcnTmiTydumw4hhrn1eVOrR\nVKK8owBIyk8y7ZeSnhiIJIkSQvSpXWm7aKhqwMfNh1GjtNYGx45Ba6s2aXjECDMHKAaEcePGYW1t\nTXZ2NiH2IUDHxpuTJ2vz5zIyoKTEnJEKcZ4kUUKIPvVDgtbaIGZSDPq2PgbSYFNczMrKytS9vDG/\nEQdrBwprCk0lPVtbiNIGqGQ0SgwYkkQJIfpMbVMtx1KPodfpWRi3ENDWQktN1fbLfChxofZ5UReW\n9NrX0oPzJb39+7Vu90KYmyRRQog+c/jsYSrzKnGxcyEqUvtL8cQJ7Q4rPz9wdzdzgGJAaU+ijh8/\nzsSRWoZ9KP/8XXqhoWAwaOW8jAyzhSmEiSRRQog+813idxiNRiLGRjCibfKTlPLE5VzYvdxYbLyk\npKfXn293ICU9MRD0JIlaDKQDGcATnexfDhwBDgOHgHm9Fp0QYtAyKiOJSYkAzJ02F9BKMNLaQHTl\nwtR5RxwAACAASURBVLv0JntPBjov6SUlQWNjv4cnRAfdJVEWwFtoiVQ4cDtwcW/h74GJQBRwL/Bu\n74YohBiMTpefJi8rDztLO2ZGzwS0DuWVleDqCv7+5o1PDEztSdTRo0fPJ1EXlPQ8PbXFqhsazo9q\nCmEu3SVRMUAmkA00A5+gjTxdqPaC5w6A3HwqhOCH5B9oqmvC39MfPz8/oOMoVNsaxEJ04O/vb+pe\nbldnh6ONI4U1hZyrOvf/2bvv6CrPK9H/39PUe68g0QRIoAIIJCx6Nca4jkuc4iQTp9/0zOTOnZvc\nmblT1szclTaxf8k4zUncG9im96qGBEJIgBqoo96lU97fH4900JGOsDDq2p+1WByd93nP2kqCsvU8\n+93bvkZ6Romp4uOSqEjg1qCvK/vfG+oR4CrwEfDNsQlNCDGdncw+CUDaijR0/RmT1EOJjzO4e/mV\ngisOu1EDVq5Uo4KKitQMRiEmy8clUaN9iPRd1DHfbuCP9xWREGLaa+lpobiwGIPOwJY1WwCoq4Oa\nGvDwgIULJzlAMaUNHOldunTJoS5q4EjPw0N1utc0uHBh0sIUAuPHXK8CBlcuRKN2o0Zyqv8zA4HG\noRd//OMf219v2LCBDRs2jDJMIcR0klmWSXtdO8FewSyLV7sKA0d5y5aBwTCJwYkpb3D38hBDCD6u\nPtR31nOr7RZzfOcA6kgvJ0cd6W3fLsfD4v4dP36c48eP39M9H5dEZQMLgRigGngKVVw+2HygFLVr\nldL/3rAEChyTKCHEzHX4/GE0TSNxaSKurq6AHOWJ0RvoXp6fn0/hlUJWRKzgWNkxsqqy7ElUfDz4\n+EBtLZSVqWJzIe7H0M2dn/zkJx97z8cd51mArwMHgELgNVTt0wv9fwAeBy6jWhz8FHj63sIWQswk\nFpuF3Hw1OHbTatXxpK0NSkvBaISlSyczOjFdDD7SWxWxCnCcpafXw+rVau3585MSohCj6hP1ERAH\nLAD+uf+9l/r/APwbkIBqcZABZI1xjEKIaaT4djH15fV4uXiRvjIdgEuXVP3KkiVqBpoQH2eguLyw\nsJAozygC3ANo6m6itLnUvmag8WZWFpjNkxGlmO2kY7kQYkwdyT2CucdMbFQsISEhgDTYFPfO19eX\nmJgYzGYzxcXFrIxYCajdqAFRUTBnDnR1qURdiIkmSZQQYkydzj4NYG+w2dsLV6+qwl9JosS9GHyk\nNziJsmk2+xrpGSUmkyRRQogxU99ZT2lRKSa9ic1rNgNw5Yo6apk3TxUCCzFag5OoaJ9oQjxDaOtt\n41rjNfuaVavU055XrqjaOyEmkiRRQogxc/rqaTobOwn1CyVuURwgR3nik4uKiiIgIIDW1lZu3brF\nqsg7BeYDvL0hIQFsNukZJSaeJFFCiDFz+OxhAFJTUjEajVitcPmyuiatDcS9Gty9PD8/336kl1uT\ni8Vmsa9bu1b9feaMeoBBiIkiSZQQYkz0WnrJy89Dh47ta7cDcOMGdHZCWJgaHCvEvRp8pBfhHUGk\nTySdfZ0UNRTZ1yQkqKPimhrVM0qIiSJJlBBiTOSU59BS3YKvuy+pyamANNgU9y8uLg5XV1du3bpF\nc3OzfTcqsyrTvsZguNPu4MyZyYhSzFaSRAkhxsT+s/tVl/KERNzc3NA0qYcS989kMrG0v0Pr4Kf0\n8mvzMVvvNIcaONLLzlZPhAoxESSJEkLcN03TOJ+t2kZvSVMDh2/dgsZG8PWF2NjJjE5Md4OP9EI8\nQ4jxi6HH0sPl+sv2NWFhMH8+9PSomXpCTARJooQQ962ssYzq0mpcDa5sTlOtDQaO8hITZTisuD/L\nli1Dp9NRXFxMb2+v08ab4FhgLsREkCRKCHHfPjzzIVaLlUULFuHv7w9IPZQYO97e3sTGxmI2myks\nLLQnUZfqLtFj6bGvW7ECXF3VAw11dZMVrZhNJIkSQty3E+dPALB+9XoA6uuhqgrc3SEubjIjEzPF\n4CM9f3d/FgQswGw1k1+bb1/j5gYrVX7F2bOTEaWYbSSJEkLcl+bOZooKi9Dr9Oxevxu4swu1bBkY\njZMYnJgxBpKogoICNE2zN97MqnaceT9wpHfunGrAKcR4kiRKCHFf9p3dh6XXQsycGOZEzgHkKE+M\nvYiICIKCgmhra6OsrIwV4SvQ6/Rcqb9Ce2+7fd28earIvLX1TqNXIcaLJFFCiPty5MwRANatWQeo\n//MqLQWTSTVBFGIs6HQ6hyM9b1dv4kPisWk2cmpyBq27sxslR3pivEkSJYT4xHr6esjvbwa1Z8Me\nQPWG0jRYskQV+QoxVgYnUQCpkaqp6+DGm6Aab+r1cOmSDCUW40uSKCHEJ3bg/AF6unsIjwhncexi\nQI7yxPhZuHAhbm5uVFVV0djYSGJoIi4GF0qaSmjoarCv8/GB5ctVTdT585MYsJjxJIkSQnxiB04f\nAGBtqjo/6e6GoiK1C9C/aSDEmDEajcTHxwNqN8rV6EpSmMrWh+5Gpaerv2UosRhPkkQJIT4Ri8VC\ndq5qdvjQ+ocAVchrtcKCBeDtPZnRiZlq6JHe6qjVgEqitEHZ0rJlqlt+ba2q0RNiPEgSJYT4RE7m\nnqS9o52A4ABSF8vAYTExEhIS0Ov1FBcX09PTw5KgJXi5eFHTXkNlW6V9nV4PaWnqtXQwF+NFkigh\nxCey99heAFavWo1Op8NshoICdU2SKDFevLy8mDdvHlarlcLCQgx6g72D+YWqCw5rB470srPVTD0h\nxpokUUKIe2Y2m8nMVjUoD21UR3lXr0JvL8yZA4GBkxmdmOlGOtLLqsrCpt3psBkaqo6We3tlKLEY\nH5JECSHu2bmcczS3N+MX5sfaJaqoXI7yxEQZSKIuX76MzWYj1i+WII8gWnpauNZ4zWGtDCUW40mS\nKCHEPdt7dC8aGitWrsDV6IrNpvpDASQnT25sYuYLCwsjODiYjo4OSktL0el0I/aMWrFCzdQrKVFF\n5kKMJUmihBD3pKuri8yLmeh0Oh5c/yAAN25ARwcEB0N4+CQHKGa8wd3LB5q9DiRRuTW5mK1m+1pX\n1ztDiWU3Sow1SaKEEPckKzuLxs5G/CL9SFugHn8aOMpLTlZjN4QYb0n958Z5eXlomka4dzhzfOfQ\nbe7mcr3j0LzBQ4ktlomOVMxkkkQJIe7Jh8c/xGqzEp8cj7+7P5om9VBi4i1YsABvb2/q6+uprq4G\nRh4DExsLkZHQ3n7n2FmIsSBJlBBi1Jqbm8kpyEFv0LNt7TYAKiuhsVE1Npw3b5IDFLOGXq8nMTER\nULtRAKsiV6HT6bhcd5kuc5d9rU4HGRnq9cmTEx6qmMEkiRJCjNq5c+do7GokMCaQVTGrALh4UV1L\nTJSjPDGxkvufYrjY/z9CPzc/FgctxmKzkF2d7bB29WpwcVFjierrJzxUMUNJEiWEGBVN0zhw7AA9\nlh7mJ85nru9cQI7yxORZvHgxbm5u3Lp1i4YGNYB4TdQaAM5XOk4e9vC4U2B+6tSEhilmMEmihBCj\ncuPGDYpvFePq6cqm1E3odDrq66GqCtzdIS5usiMUs43RaGTZsmXAnd2o5LBkXI2ulDSVUN/puOU0\ncKR39qwUmIuxIUmUEGJUzp49S2NXIyFxISRHqGOUgSLdZcvAaJzE4MSsNfRIz9XoSkp4CjB8Nyo2\nFqKiVDuOgR1UIe6HJFFCiI/V29vLmQtn6OjrYG7CXBYHLQbu1EPJUZ6YLAkJCZhMJkpLS2ltbQUg\nLUq13jh36xyaptnX6nSwbp16LQXmYixIEiWE+Fg5OTlUt1TjG+5LalwqRr2RtjYoLQWTCeLjJztC\nMVu5urqydOlSNE2zN95cFLiIAPcAmrqbuN503WF9aqoqMC8uhrq6yYhYzCSSRAkhPtbAUV7o4lCS\nwgaaHIKmweLFaqyGEJNloPHmwJGeTqezF5ifu3XOYa27O6xSD5Zy+vTExShmJkmihBB3VVNTQ2FR\nIR3WDkIXhZIQkgBAbq66vmLFJAYnBGogsV6vp7i4mK4u1R9qIInKrcml19LrsH7gSE8KzMX9kiRK\nCHFXJ0+epKm7ieBFwcSHx+Nucqe9XR2HGAyqP5QQk8nLy4tFixZhtVq5fFmNfAn1CmV+wHx6LD1c\nrL3osH7uXIiOVgXmFy86+0QhRkeSKCHEiHp7e1WDze5GwhPC7Ud5+flgs8GSJar/jhCTbeiRHozc\nM2pwgbn0jBL3Q5IoIcSIsrKy6OjqwOZnwyvIi8Qwte2Uk6Oup6RMYnBCDDKQRF25coW+vj4AVkas\nxGQwUdRQRHN3s8P61FRwdZUCc3F/JIkSQjilaRonTpygpbuF4CXBxPjF4OfmR2enGp2h18tRnpg6\n/P39iY2Npa+vjytXrgDgYfJgeehyNE3jQtUFh/VubiqRAjhxYqKjFTOFJFFCCKfKy8u5efMmHXQQ\nvCB42FFeXBx4eU1ykEIMMrTxJozcMwpg/Xr199mz0OtYey7EqEgSJYRw6sSJE2iahinGhN6otydR\n8lSemKoGjvQuXbqEpf+xu6XBS/Fx9aG2o5aK1gqH9dHRMH8+dHdDZuaEhytmAEmihBDDtLW1kZWV\nRXtfO/5x/oR6hRLmFUZXFxQWqqM86VIupprQ0FAiIyPp7u6mqKgIAIPeQGqkOrcb2jMKYMMG9ffx\n46rvmRD3QpIoIcQwJ06cwGKx4BXthbuvO4mhieh0Oi5dAqsVFi4Eb+/JjlKI4VauXAlAdna2/b20\naHWkl1mVidlqdlifkgI+PlBZCSUlExenmBkkiRJCODCbzfajPOMCNVVYjvLEdDGQRF28eBGzWSVM\nUT5RxPjF0GXuGtYzymiEBx5Qr48dm9BQxQwgSZQQwsGFCxdob2/HP9Qfq78VH1cfYv1j6emBK1dU\nj53++l0hppyQkBDmzJlDT08PBQUF9vfXzlkLwOmbw2e9rFunjqgvXoT+GcZCjIokUUIIO03TOHLk\nCAChy0PR6XQsD12OXqfn0iU1ImPhQnX8IcRUtap/ON7gI71VEatwMbhQ3FBMfWe9w3p/f1XjZ7XK\nPD1xbySJEkLYXb16lerqanx9fWkPbAeGH+VJg00x1a3oP2++dOkSvf29C9xN7qyIUO+fvXV22D0D\n7Q5OnlTJlBCjIUmUEMLu4MGDACSnJVPdWY27yZ0lwUvo7YWBkxE5yhNTXWBgIPPnz6evr49Lly7Z\n339gjip+OnvrLDbN5nBPXByEh0NLi+qFJsRoSBIlhACgoqKCq1ev4ubmhscCNRBveehyjHojBQVg\nNqueOn5+kxyoEKPg7Cm9+f7zCfMKo7WnlYL6Aof1Ot2d3ajjxycqSjHdSRIlhABg//79AKxbt47C\nlkIAVoSr4w+ZlSemmxUrVqDT6SgoKKC7uxsAnU531wLztDQ1Dqa4GKqrJzRcMU1JEiWEoLa2losX\nL2I0GklOS6a8pRw3oxtLg5fS2wuXL6t1kkSJ6cLX15dFixZhsVjIy8uzv78mag0GvYHLdZdp7XF8\nFM/NDVavVq9lnp4YDUmihBAcOHAATdNIS0ujpFt1HFwWugyTwcSlS9DXp47yAgImOVAh7oGzIz0f\nVx8SQxOxaTbOVY7cwfz8eejqmogoxXQmSZQQs1xzczMXLlxAr9ezbds2cmvUY3gp4WrbKStLret/\nalyIaSMlJQW9Xs/Vq1fp6Oiwvz/4SG/oUOKICFi8GHp61GBiIe5GkighZrn9+/djtVpJSUnB5G2i\ntLkUF4MLCSEJdHWpp/L0eulSLqYfLy8vlixZgtVq5eLFO53KlwYvxd/dn9udt7nedH3YfZs3q7+P\nHgWbbdhlIewkiRJiFmtpaeF0f3fBXbt22UdiLAtdhovBhYsXVc+cuDhpsCmmp4HGm1kDW6qAXqcn\nPTodcF5gvmwZhIZCYyMMKqcSYhhJooSYxQ4cOIDFYmHFihVERESQU60ewxs4yhsoJekvLRFi2klM\nTMRoNHLt2jVaB810WRu9Fp1OR25NLl1mx+InnQ42bVKv+xv4C+HUaJOoHUARcB34oZPrnwLygUvA\nGWD5mEQnhBg3LS0tnDp1ClC7UC09LZQ0l2AymEgISaC9HYqKwGCQBpti+vLw8CAhIQFN08gdaLsP\nBHoEsjhoMWarmQuVF4bdl5YGHh5w4waUl09gwGJaGU0SZQB+gUqklgLPAEuGrCkF1qGSp38A/r8x\njFEIMQ4OHjyI2WwmJSWFyMhI8mrz0DSN+OB43Ixu5OSoepD4ePD0nOxohfjkBp7Sy8zMdHh/3dx1\nAJyoODGswNzVFR5QDc5lN0qMaDRJVCpwAygHzMCrwJ4ha84BA/ukF4CoMYpPCDEOWltbOXnyJKB2\noQD7U3kD88XkqTwxUyxfvhxXV1dKS0upr78zfDgxNBFfN19q2mucFphv3KgeqsjJUeNghBhqNElU\nJHBr0NeV/e+N5AvAh/cTlBBifO3fvx+z2UxycjJRUVG09bZxvfE6Rr2RZSHLaG5WxxguLpCYONnR\nCnF/XF1dSenvFHv+/Hn7+wa9gYw5GQAcLz8+7L6AANVg1mqVUTDCudEkUdrHL7HbCHwe53VTQogp\noLm5mZMnT6LT6di9ezcAebV52DQbS4OX4m5ytxeUL1umjjWEmO7WrFkDwIULFxyO7jLmZqDX6cmr\nzRvWwRzutDs4eVI1nRViMOMo1lQB0YO+jkbtRg21HPg1qnaq2dkH/fjHP7a/3rBhAxsGWsMKISbM\nBx98gMViYdWqVURGqk1labApZrq4uDgCAgJoaGjgxo0bLFy4EAA/Nz+SwpLIrcnl9M3T7Fq0y+G+\nefMgNhbKylQX83XrJiN6MRGOHz/O8XvcchxNEpUNLARigGrgKVRx+WBzgLeB51D1U04NTqKEEBOv\noaGBs2fPotfr7btQHX0dFDcUY9AbSAxLpL4eKirUHLGEhEkOWIgxotPpSE1NZf/+/Zw/f96eRAGs\nj1lPbk0up26eYufCneh1joc0mzfDb36jCswzMlQLBDHzDN3c+clPfvKx94zmOM8CfB04ABQCrwFX\ngRf6/wD8PeAP/Aq4CGQO/xghxGTbt28fVquV1atXExoaCsDFmovYNBtLgpbgYfKw70IlJ4PJNInB\nCjHGBo70cnJyMJvN9vfjAuMI8wqjubuZ/Nr8YfelpIC/P9TWwpUrExaumAZG2yfqIyAOWAD8c/97\nL/X/AfgiEAgk9/9JHcMYhRBjoK6ujgsXLmAwGOxP5AFkVausaWXESjTtzlGeNNgUM014eDgxMTF0\nd3eTn38nWdLpdPZ2BycrTg67z2BQT+oBHDo0IaGKaUI6lgsxS+zduxebzUZ6ejrBwcEAtPS0cK3x\nGiaDieTwZKqroaYGvLxgydBucELMAAO7UefOnXN4Py06DReDC4W3C6nrqBt2X0aGOuIuKlLH3UKA\nJFFCzArV1dVkZ2djNBp58MEH7e9nV2ejaRrLQpbhZnRjoBdhcrL67VuImSY1NRWj0UhhYSHNzXee\ngfIweZAaqQ5RnO1GeXjcKSo/cGBCQhXTgCRRQswCe/fuRdM0MjIyCAgIsL+fWaWyptTIVDQNLvRP\nv1i9ejKiFGL8eXp6kpiYiM1mG7YbNXCkd/bWWfqsw/sZbN6sfrnIzYVBPTvFLCZJlBAz3M2bN8nN\nzcVkMrFz5077+3UddVS0VOBucichJIHiYmhuhqAgWLBgEgMWYpytXbsWgLNnzzr0jJrrN5dY/1i6\nzF1kV2cPu8/PD9asAU2DgwcnLFwxhUkSJcQM9/777wPq8V1fX1/7+wMF5clhyZgMJgYaOa9ZI49w\ni5ltyZIl+Pv7c/v2ba5fdxz3sn7uekB1MB86Tw9g2zb17+P8eWhrm5BwxRQmSZQQM1h5eTmXL1/G\nxcWF7du329/XNM3hKK+3Vx1RgBzliZlPr9eTnp4OwJkzZxyurYxYiZeLFxUtFZQ2lw67NywMkpLA\nbJbBxEKSKCFmtH379gGwceNGvL297e/fartFXUcdPq4+xAXFkZcHvb0wfz6EhExWtEJMnLS0NABy\nc3Pp7u62v28ymMiYq+bpHS497PTegd9HTpyAnp7xjVNMbZJECTFDlZWVcfnyZVxdXdm2bZvDtYFd\nqJURK9Hr9A5HeULMBsHBwcTFxdHX10fWQHO0fhtiNmDQG8irzaOhq2HYvbGxsGgRdHermXpi9pIk\nSogZavAulJeXl/19TdPsRbOrIlfR0qJ63xiN0mBTzC4PPPAAACdPnnSof/Jz82NlxEpsmo1jZcec\n3juwG3X4MFgs4x6qmKIkiRJiBiotLaWgoAA3Nze2bt3qcO1603Wau5sJ8ggi1i+WzEyw2WD5ctUL\nR4jZIiUlBS8vL27dukXFkA6aW+ZtAeD0zdP0WIaf2cXHQ1QUtLbeaQ0iZh9JooSYgUbahYI7R3mr\nIlcBOgZa5chRnphtjEajvTbq5JBzuTm+c1gUuIgeSw9nb50ddq9Od2c36uBB1fZAzD6SRAkxw5SW\nlnLlyhWnu1AWm4XcGvUYXmpkKpWVUF2txrzEx09GtEJMrowMVUSelZVFV1eXw7XN8zYDcKT0CDbN\nNuzelSshMFANJh54ulXMLpJECTHD7N27F4BNmzbh6enpcK3wdiGdfZ1E+kQS4R1h34VKTVU1UULM\nNqGhoSxevJi+vj4uDDmXWx66nGDPYBq6GsivzR92r14PO3ao1x98ILtRs5EkUULMICUlJRQWFuLu\n7s6WLVuGXc+qUk8hpUamYrPBwENJcpQnZrN1/UPxTp065VBgrtfp2RS7CYAjZc6bQqWng78/VFVB\nXt74xyqmFkmihJhB7rYL1WPpIa9W/ZRfGbGSwkLVcTk8HObMmfBQhZgyEhMT8fHxoaqqipKSEodr\n6dHpuJvcud54nYqWimH3Go0wME1JdqNmH0mihJghSkpKuHr16oi7UDnVOfRZ+1gUuIggjyCHgnIZ\n8yJmM6PRaG93cOyYY0sDN6MbD8xR1+62G+XnB7duQf7wUz8xg0kSJcQM8dFHHwFqF8rDSa+CgSeM\n0qLT6OpSP+x1OlUPJcRst27dOvR6Pbm5ubS0tDhc2xizEb1OT3Z1Ni09LcPuNZmkNmq2kiRKiBmg\nsrLSPiNv06ZNw67Xd9Zzo+kGrkZXVoSvIDNTzf5avBgCAiYhYCGmGH9/f5KTk7HZbMPaHQR6BJIc\nnozVZh2x+eYDD4CvL9y8CZcvT0TEYiqQJEqIGeDAgQOA6sA8tC8U3NmFWhG+AheDK6dP079+wkIU\nYsrbuHEjoArMLUPakG+dp9qFnKg4QZe5a9i9JtOdvlH79slu1GwhSZQQ01xDQwPZ2dkYDIZhfaEA\nbJqN85VqOF5adBoVFap2w8tLTaMXQigLFiwgKiqKtrY2srOzHa7F+scSFxRHt7mbE+UnnN6fkQE+\nPlBRAQUFExGxmGySRAkxzR08eBCbzUZqaioBTs7mihqKaO5uJtgzmIUBC+27UGlp0htKiMF0Op19\nN+rYsWMO7Q4Adi5Qj+EdKTtCn7Vv2P0uLjAw61t2o2YHSaKEmMba2to4e1Yd1W0fOEsYwl5QHpVG\nX5/O3htq7doJCVGIaSU1NRVPT0/Ky8spLS11uLY4aDExfjG097Zz5uYZp/evWwfe3lBeDoWFExCw\nmFSSRAkxjR05cgSz2UxSUhLh4eHDrneZu8irzUOn05EWnUZWFvT0wIIFqj+UEMKRi4sL69evB9Qu\n72A6nY4dC9RjeAdLDmKxWYbd7+p6Zzdq717ZjZrpJIkSYprq7u7mxAlVm7Fj4PnqIbKrszFbzSwO\nWkyAe4AUlAsxChs3bsRoNJKfn099fb3DtaSwJMK9w2nqbrJPABhq/XpVG1VWJn2jZjpJooSYpk6c\nOEF3dzdxcXHExsY6XTNwlJcenU5Vlfqh7u4OK1ZMZKRCTC8+Pj6sXr0aTdM4csSxwebg3aj9N/Y7\nHUzs6goPPqhev/su2IYvETOEJFFCTENms9n+w33nwMyJIWraayhrLsPd5E5SWJJ9F2r1alUAK4QY\n2UDX/7Nnz9LZ2elwbVXEKgI9AqntqLWPUhoqIwOCgqCmBobMNRYziCRRQkxDZ8+epa2tjTlz5rB4\n8WLna/p3oVZGrERnc+G86nIgR3lCjEJERAQJCQn09fXZj80HGPQGts1XhU/7b+wf9hQfqCdfd+9W\nr99/HyzDy6fEDCBJlBDTjM1msxe87ty5E52TwXc2zcaFKvXrb3p0Orm50NUFMTEQHT2R0QoxfQ30\nXTt69Ch9fY4tDdZGr8XH1YeKlgquNlx1en9qKkRGQlMTDGmCLmYISaKEmGby8/NpaGggODiYpBG6\nZRbUF9Da00qYVxixfrH2ozxpayDE6MXFxRETE0N7eztnzji2NDAZTGyetxlQu1HO6PXwyCPq9Qcf\nqCdjxcwiSZQQ08xALdTmzZvR653/Ex7oYZMWnUZ9vY5r11QdlAwbFmL0dDqd/cnXgwcPDhsFs37u\netxN7hQ3FHO98brTz1i2DObPh44OOHx43EMWE0ySKCGmkYqKCq5fv467uztpaWlO17T0tHCp7hIG\nvYH06HT7LtSqVeDmNoHBCjEDJCUlERERQVNTE5mZmQ7X3E3ubI5Vu1HvF7/vtDZKp4NHH1WvDx2C\n9vZxD1lMIEmihJhGjh49CqhBw24jZERnbp7BptlICkvCXe9Df0NzKSgX4hMYvBu1f/9+bEP6FWye\ntxlPF0+uNV6juLHY6WcsXAgJCeo4b7/zkz8xTUkSJcQ00draSlZWFnq93j7fayibZuPUzVMAZMzJ\nIDtbHSPMmQMjtJISQnyMVatWERQURF1dHbm5uQ7XPEwe9if13it6z+luFNypjTp+XBWai5lBkigh\npokTJ05gtVpJSkoiMDDQ6ZqC+gL7sOHFQYs5fly9v3GjOlYQQtw7vV5vn035wQcfDNuN2hizEW9X\nb0qbSymoL3D6GdHRqibRYlENOMXMIEmUENOA2Wy296rZvHnziOtOVqjnqDPmZFBRoaO8HDw9oJa8\nHwAAIABJREFUVT2UEOKTS09PJzAwkOrqarKzsx2uuRpd7V3MR6qNArUbZTKp5ptDZhuLaUqSKCGm\ngQsXLtDR0cHcuXOZP3++0zVN3U1cqb9iLyg/dky9v3at+sEthPjkjEYju3btAmDfvn3DdqPWz12P\nr5svN1tvjtjFPDAQ+huh8/rrMpx4JpAkSogpbvD8rs2bNzttrglqF8qm2UgOS4Y+b7Kz1RFe/0B6\nIcR9WrNmDcHBwdTV1XFhyCwXk8HEroUqyXq/+H2nM/UAduwAX181xzLL+fxiMY1IEiXEFFdUVER1\ndTW+vr6sGGFysNlq5lSFKijfGLuRM2dU7UVCgprfJYS4fwaDgYceeghQtVFWq9Xh+to5awn0CKS6\nvZrs6mxnH4Gb250i87ffht7ecQ1ZjDNJooSY4gZ2oTZs2IDRaHS6Jqcmh46+DqJ9o4nxme9QUC6E\nGDupqamEhYVx+/btYV3MjXqjfTdq37V9I+5GpaWpJ2abm1XvKDF9SRIlxBRWV1fH5cuXMZlMZGRk\njLjuePlxQD0ldPGijuZmCA+HpUsnKFAhZgm9Xs/DDz8MwN69e+kZMstlTdQaQjxDqOuo43zleaef\nodPBX/2Ven3ggEqmxPQkSZQQU9hAc83Vq1fj7e3tdE15SzllzWV4uniyMmKVfbTE5s3S1kCI8ZCS\nkkJsbCxtbW0cGrKVZNAb2B23G4C9xXsxW81OP2PhQlixAvr64J13xj1kMU4kiRJiiurq6uJsf7vx\nu7U1GNiFWhu9lsoKF3tbg9WrJyBIIWYhnU7H448/DqiZeq2trQ7XV0asJNo3mqbuJg6Xjjww77HH\n7rQ8KCsb15DFOJEkSogp6tSpU/T19bF06VIiIiKcrmnvbSerKgudTsf6mPX0l0+xbp0aOCyEGB8L\nFy4kKSmJvr4+9u7d63BNr9PzxNInANh/Yz9tvW1OPyMoSFoeTHeSRAkxBVmtVo71N3q62y7UiYoT\nWGwWlocuR9cdxMWLYDDAhg0TFKgQs9ijjz6KXq/nzJkzVFdXO1xbHLSYxLBEeiw9vF/8/oifMdDy\noLQUhtSpi2lAkighpqC8vDyam5sJCwsjPj7e6Rqz1cyJctXFfMu8LRw9CjabqrPw85vIaIWYncLC\nwli3bh02m41XX311WKfyx5Y8hl6n58zNM1S3Vzv9DDe3O0Xmb78N7e3jHbUYS5JECTEFDbQ12LRp\n04jNNTOrMmnrbSPaN5pIt4WcUm2i2LZtoqIUQjz88MN4eXlRXFxMTk6Ow7UwrzDWx6zHptl4s/DN\nET9jxQr1JG1nJ7z11nhHLMaSJFFCTDFlZWWUlJTg4eHBmjVrnK7RNM1esLpl3hZOntTR26t+EEdH\nT2S0Qsxunp6ePNLfPfPNN9+kd0j3zIcWPYS7yZ0r9Ve4Un/F6WfodPDss6rI/Nw5KC4e97DFGJEk\nSogpZmAXKiMjA1dXV6drrjZcpbq9Gl83XxKDV9LfCUF2oYSYBGvXrmXu3Lk0Nzfz0UcfOVzzcvGy\nN+B8s/DNERtwBgfDgw+q13/+s5o4IKY+SaKEmEKam5vJyclBr9ez8S7txo+UqkRrY8xGcrKMtLWp\nHajFiycqUiHEAL1ez9NPPw2olgdDi8w3xm4kyCOI6vZqTt88PeLnbNsGYWFQW6uacIqpT5IoIaaQ\n48ePY7PZSElJwd/f3+mayrZKCuoLcDG4kDFnHQcPqve3b5fmmkJMlnnz5pGRkYHVauWPf/wjNtud\nHSej3shjSx4DVAPOHkuP088wGuFTn1KvP/oI6uvHPWxxnySJEmKK6O3t5VR/dfjd2hocuKF+RX1g\nzgNcu+JJXR0EBqriVCHE5Hnsscfw9fWltLSUEydOOFxLCU9hfsB82nrb2Hdt34ifsWiRmq1nNsNf\n/iK9o6Y6SaKEmCIuXLhAZ2cnsbGxzJs3z+mahq4GsquzMegNbI7dwocfqve3bwe9/GsWYlJ5eHjw\n7LPPAvDOO+/Q2Nhov6bT6Xgq/il0Oh1Hy46O2PIA4PHH1dSBwkLIzh73sMV9kB+7QkwBmqbZC8q3\nDLQwduJQySFsmo3UyFSqSwK5dUs16ktPn6hIhRB3k5SUREpKCr29vbzyyisOvaPm+s1l3dx1WG1W\nXi0Y3ldqgLe3SqQAXn0V2pw3PBdTgCRRQkwBBQUF1NbW4u/vT3JystM17b3tnLmlWhpvnbfNYRfK\nZJqoSIUQH+eZZ57B09OTwsJCjh8/7nBtT9wevFy8KG4oJrt65G2m9HTVsqSjA/70JznWm6okiRJi\nCjjYXx2+efNmDAaD0zVHy45itppJDEukrSqCsjL1G+sDD0xkpEKIj+Pj48Nzzz0HwFtvvUVNTY39\nmqeLp73I/I3CN0YsMtfp4DOfAXd3yMuDrKzxj1vcO0mihJhk5eXlXLt2DXd3dzIyMpyu6TJ3caxc\nzdLbNm+7fRdqyxYYoZWUEGISpaSkkJaWhtls5uWXX8YyqPFTenQ68/zn0drTyrtF7474Gf7+8OST\n6vVf/gItLeMdtbhXo02idgBFwHXgh06uLwbOAT3Ad8cmNCFmh0OHDgGquaabm5vTNUfLjtJt7mZJ\n8BIst+dz7ZoqPJVBw0JMXU8//TRBQUHcvHmT9957z/6+TqfjU8s/hV6n53j5ccqay0b8jPR0WLYM\nurrglVfkWG+qGU0SZQB+gUqklgLPAEuGrGkEvgH8+5hGJ8QM19DQQG5uLgaDgU2bNjld023utjfX\nfHDBLt7vHwi/dasaXiqEmJrc3Nx4/vnn0ev1HDx4kPz8fPu1KJ8ots3fhqZpvHLpFaw2q9PP0Ong\nuefAwwMuX1ZjYcTUMZokKhW4AZQDZuBVYM+QNbeB7P7rQohROnz4MDabjdTU1BGbax4tO0qXuYu4\noDjMdQspKQEvLxgh5xJCTCELFizg0UcfBeB3v/sdDQ0N9mu7Fu0iyCOIyrZK+yxMZ/z8oL8hOq+/\nDs3N4xqyuAejSaIigVuDvq7sf08IcR86Ozs5c6b/abutW52u6bH0cKRs+C7Ujh1SCyXEdLF161aS\nkpLo6uripZdewmxW+w0uBhc+tVy1KN97bS/1nSO3KE9NhaQk6O6GP/xBjvWmitEkUfJflRDj4MSJ\nE/T19ZGQkEBkpPPfS46WHaWzr5OFgQvpqVpEeTn4+MD69RMbqxDik9PpdHz2s58lODiYmzdvOvSP\nWhq8lDVRazBbzfw+7/cj9o7S6dRIGC8v1YRzYOi4mFzGUaypAqIHfR2N2o26Zz/+8Y/trzds2MAG\nqYoVs5TZbObYMfW03Ui7UJ19nRwsUa0PHlzwEG+9pAbj7dwJLi4TE6cQYmx4eHjw5S9/mX/913/l\n/PnzREREsH37dgD+Kv6vuNpwlRtNNzhWfoxNsc7P6n18VH3Uiy/CW2/BggUwd+5Efhcz2/Hjx4f1\n9fo4oxlXagSKgc1ANZCJKi6/6mTtj4F24D+cXNNGyrCFmG1Onz7NH//4R+bMmcOPfvQjdE4mB79z\n9R3239jPkuAlrOFb/Pa3EBAA/+f/SHNNIaarvLw8fvWrX6HT6fjyl79MUlISAPm1+fxX1n/hYnDh\nf63/X4R4hoz4GX/5Cxw/DsHB8Hd/Jw+YjJf+n8t3zZNGc5xnAb4OHAAKgddQCdQL/X8AwlB1U98G\n/g64CXh9kqCFmOk0TbO3Ndi2bZvTBKq1p5WjZWq/ftf8Rxh4OnrPHkmghJjOkpKSePTRR9E0jZdf\nfpmKigoAEsMSSY1Mpc/axx/y/4BNs434GU88AdHRcPu2dDOfbKPtE/UREAcsAP65/72X+v8A1KKO\n+XwBf2AO0DF2YQoxc1y6dIna2loCAwNZsWKF0zUfXv+QPmsfSWFJlOfF0NQEkZGquFQIMb1t376d\ntLQ0ent7+fnPf059vSoofzrhaXxcfbjeeP2uT+uZTPDXf60eLsnMhLNnJypyMZR0LBdiAmmaxoED\nBwA1aFivH/5PsKGrgVM3T6HT6dg2dw8ffaTef+wxcLJcCDHN6HQ6nnvuOeLj42lvb+enP/0pra2t\neLp48tmkzwLwbtG7VLaNXH4cGgrPPqtev/oqVFdPRORiKPmRLMQEKioqoqSkBC8vL9auXet0zbtF\n72K1WVkduZq8UxF0dkJcHMTHT3CwQohxYzQaeeGFF4iJiaGhoYGf/exndHZ2khCSwPqY9VhtVl6+\n+DJm68jtF9esgbQ06OuDX/9a/S0mliRRQkwQTdPYt28foJ7Ic3XS6KmsuYysqixMBhPpgXs4olpE\n8fjj6hFnIcTM4erqyte//nXCwsKorKzkpz/9KV1dXTy+5HFCvUKpaqvinaJ37voZzzwDYWFqJ+q1\n16Q+aqJJEiXEBLl27Ro3btzA09PTaXsPTdN4o/ANALbM28LRDwKwWtXsLHmMWYiZydvbm29/+9sE\nBwdTUVHBz3/+czSLxueTP49Bb+BI6REu110e8X5XV1UfZTLB6dNw8uQEBi8kiRJionzwwQeAqoVy\nNmj4Yu1FSppK8Hb1Jta6g7w89QPykUcmOlIhxETy8/PjO9/5DoGBgZSWlvKzn/2MEJcQ9sSpCWu/\ny/sdLT0tI94fFQWf/rR6/dprcO3aREQtQJIoISbE9evXKS4uxsPDg40bNw67brFZePvq2wDsWrib\n995SSdbOneDrO6GhCiEmQUBAAN/5zncICAigpKSE//zP/yQtJI2lwUvp6Ovg5Ysv37XtwerVsG0b\nWK3w0kvQ2DiBwc9ikkQJMc40TeO9/kZPmzdvxt3dfdiaw6WHud15m3DvcGxlGVRVQVAQbNky0dEK\nISZLUFAQ3//+9wkNDeXWrVv8x3/8B4/EPIKPqw/FDcXsu7bvrvc/+igsXQodHfCrX0Fv7wQFPotJ\nEiXEOCsoKOD69et4eXmxxUlW1NzdzAfX1FHfrrlPsfd99c/yiSeksaYQs01AQADf+973iIqKora2\nlhd/+iKPRD+CXqfng2sfUFBfMOK9er2qjwoJgVu3ZFDxRJAkSohxZLPZeOcd9XTNzp07ndZCvVn4\nJn3WPlLCU7h0dAnd3bBsmZrYLoSYfXx8fPjud7/LvHnzaGpq4t2X3yXdNx2Aly++TGPXyGd1Hh7w\n1a+qUTDZ2dDflk6ME0mihBhHmZmZVFVVERAQwPr164ddL2ooIrs6GxeDC4mmJ8nMVLtPTz8tLQ2E\nmM08PDz41re+xZIlS2hrayP37VzCzeF09nXyYvaLd+0fFR4On/+8ev3uu5CXN0FBz0KSRAkxTiwW\nC++//z4ADz/8MKYhZ3MWm4XXCl4DYNu8nXz0dgAADz6o6qGEELObq6srX/va10hKSqKrq4vaw7VY\nqizcbL3JHy/9Ee0uZ3WJiWrWpqbBb34DJSUTGPgsIkmUEOPk2LFjNDY2EhERwerVq4ddP3DjANXt\n1YR6hWIp3kZtrWqat23bJAQrhJiSTCYTL7zwAuvWrUOzavRl9lF3qY7zt87fdb4eqKd7MzLAbIZf\n/hJqaiYo6FlEkighxkFra6u9O/njjz8+bEZebUctH17/EIAtIc9x6IARgOeeA6NxYmMVQkxter2e\nZ599lsceewwPkweGIgMlJ0t468pbXKm/MuJ9Op2ar5eYCJ2d8LOfQcvI7abEJyBJlBDj4J133qGn\np4fExEQSEhIcrmmaxiuXXsFis5AWtZbT7y3CaoUNG2DhwsmJVwgxtel0OrZv385f//VfE+YThumW\niYKPCvjV+V9R3T7y9GG9Hr74RZg/H5qaVCLV1TWBgc9wkkQJMcZKS0s5d+4cRqORJ554Ytj10zdP\nc73xOj6uPvjXPE5FBQQEqB4vQghxNytXrlQF5xFL0NfpyXwzk38/+u+09baNeI+LC3zta6pcoKpK\n9ZAyj1yXLu6BJFFCjCFN03jtNVUsvnXrVkJCQhyuN3Y18mbhmwBsCn2KQx96AuoYz0n3AyGEGGbh\nwoX8zd/8Delx6ehadRx75Rj//OE/02sZubumpyd885vg56fGwrz8MthGboAuRkmSKCHG0PHjxykv\nL8ff35+dO3c6XNM0jd/n/54eSw+JoSlkv78CsxkeeADi4ycpYCHEtBQaGsr//NH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- "text": [ - "" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here's one program that does the job" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from scipy.stats import lognorm, beta\n", - "\n", - "# == Define parameters == #\n", - "s = 0.2\n", - "delta = 0.1\n", - "a_sigma = 0.4 # A = exp(B) where B ~ N(0, a_sigma)\n", - "alpha = 0.4 # f(k) = k**alpha\n", - "\n", - "phi = lognorm(a_sigma) \n", - "\n", - "def p(x, y):\n", - " \"Stochastic kernel, vectorized in x. Both x and y must be positive.\"\n", - " d = s * x**alpha\n", - " return phi.pdf((y - (1 - delta) * x) / d) / d\n", - "\n", - "n = 1000 # Number of observations at each date t\n", - "T = 40 # Compute density of k_t at 1,...,T\n", - "\n", - "fig, axes = plt.subplots(2, 2, figsize=(11, 8))\n", - "axes = axes.flatten()\n", - "xmax = 6.5\n", - "\n", - "for i in range(4):\n", - " ax = axes[i] \n", - " ax.set_xlim(0, xmax)\n", - " psi_0 = beta(5, 5, scale=0.5, loc=i*2) # Initial distribution\n", - "\n", - " # == Generate matrix s.t. t-th column is n observations of k_t == #\n", - " k = np.empty((n, T))\n", - " A = phi.rvs((n, T))\n", - " k[:, 0] = psi_0.rvs(n)\n", - " for t in range(T-1):\n", - " k[:, t+1] = s * A[:,t] * k[:, t]**alpha + (1 - delta) * k[:, t]\n", - "\n", - " # == Generate T instances of lae using this data, one for each t == #\n", - " laes = [LAE(p, k[:, t]) for t in range(T)]\n", - "\n", - " ygrid = np.linspace(0.01, xmax, 150)\n", - " greys = [str(g) for g in np.linspace(0.0, 0.8, T)]\n", - " greys.reverse()\n", - " for psi, g in zip(laes, greys):\n", - " ax.plot(ygrid, psi(ygrid), color=g, lw=2, alpha=0.6)\n", - " ax.set_xlabel('capital')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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cSgTQtm1z4HptbLwD0qVmRIRfrVYjFAoZcQjXIoayz+LiIqFQiP7+flzXpVQq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- "text": [ - "" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise 3" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here's a possible solution.\n", - "\n", - "Note the way we use vectorized code to simulate the $k$ time series for one boxplot all at once." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "n = 20\n", - "k = 5000\n", - "J = 6\n", - "\n", - "theta = 0.9\n", - "d = np.sqrt(1 - theta**2) \n", - "delta = theta / d\n", - "\n", - "fig, axes = plt.subplots(J, 1, figsize=(10, 4*J))\n", - "initial_conditions = np.linspace(8, 0, J)\n", - "X = np.empty((k, n))\n", - "\n", - "for j in range(J):\n", - " \n", - " axes[j].set_ylim(-4, 8)\n", - " title = 'time series from t = ' + str(initial_conditions[j])\n", - " axes[j].set_title(title)\n", - " \n", - " Z = np.random.randn(k, n)\n", - " X[:,0] = initial_conditions[j]\n", - " for t in range(1, n):\n", - " X[:, t] = theta * np.abs(X[:, t-1]) + d * Z[:, t]\n", - " axes[j].boxplot(X)\n", - "\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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GB/qMVZZRd51ObqnuOZGCi+dokmyE3AqTh9CfzxBatnwLuetRLU0iUsfHN91K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\n333D9PHHwze+UXm4rJsDy2Nsbd8OBx8cplOMsbViRfwhHEateW5k+et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dtne0lbflpJOq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lW7zqw0KQtWttLwS7RaVrY0HykrablX7WLEs9JUyKHSlHsfqnE9OzD3X9aqlkNGGG8YY41SvNiV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\n04s+7t0LEydmPw/h1ltrL4KaFmm33hom7957GxeF9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-2009-05-01,8848.84,9017.32,8827.13,8977.37,154800,8977.37 -2009-04-30,8615.45,8844.77,8615.45,8828.26,174800,8828.26 -2009-04-28,8678.28,8808.64,8493.77,8493.77,169600,8493.77 -2009-04-27,8783.34,8840.53,8648.51,8726.34,152200,8726.34 -2009-04-24,8832.10,8852.83,8694.92,8707.99,212200,8707.99 -2009-04-23,8776.94,8860.55,8647.80,8847.01,186200,8847.01 -2009-04-22,8777.53,8802.90,8683.27,8727.30,195000,8727.30 -2009-04-21,8802.09,8802.09,8612.76,8711.33,175400,8711.33 -2009-04-20,8899.59,8933.80,8813.72,8924.75,167800,8924.75 -2009-04-17,8854.33,8953.34,8834.63,8907.58,184200,8907.58 -2009-04-16,8848.43,9030.00,8720.62,8755.26,173000,8755.26 -2009-04-15,8777.68,8800.52,8681.03,8742.96,158400,8742.96 -2009-04-14,8955.90,8961.73,8749.92,8842.68,181800,8842.68 -2009-04-13,8930.35,9024.45,8888.10,8924.43,167400,8924.43 -2009-04-10,9041.23,9068.80,8856.69,8964.11,228600,8964.11 -2009-04-09,8665.16,8920.86,8664.26,8916.06,192000,8916.06 -2009-04-08,8746.73,8765.64,8556.75,8595.01,168000,8595.01 -2009-04-07,8838.66,8884.45,8778.92,8832.85,150600,8832.85 -2009-04-06,8856.84,8992.06,8812.36,8857.93,173600,8857.93 -2009-04-03,8814.10,8884.63,8697.17,8749.84,217400,8749.84 -2009-04-02,8453.73,8741.67,8449.87,8719.78,213000,8719.78 -2009-04-01,8173.36,8351.91,8084.62,8351.91,157000,8351.91 -2009-03-31,8199.43,8383.74,8088.45,8109.53,178800,8109.53 -2009-03-30,8621.85,8651.06,8236.08,8236.08,164200,8236.08 -2009-03-27,8711.72,8843.18,8626.97,8626.97,157800,8626.97 -2009-03-26,8430.22,8640.28,8383.99,8636.33,135200,8636.33 -2009-03-25,8499.69,8553.01,8392.56,8479.99,162000,8479.99 -2009-03-24,8334.68,8504.41,8297.27,8488.30,195000,8488.30 -2009-03-23,7943.14,8229.13,7922.55,8215.53,178400,8215.53 -2009-03-19,8017.93,8034.09,7902.49,7945.96,138000,7945.96 -2009-03-18,8006.86,8054.35,7895.28,7972.17,176800,7972.17 -2009-03-17,7767.34,7967.03,7723.94,7949.13,171400,7949.13 -2009-03-16,7630.20,7754.75,7630.20,7704.15,150400,7704.15 -2009-03-13,7301.12,7571.45,7300.87,7569.28,217000,7569.28 -2009-03-12,7320.45,7345.02,7198.25,7198.25,153200,7198.25 -2009-03-11,7165.39,7393.81,7161.85,7376.12,155800,7376.12 -2009-03-10,7059.77,7100.77,7021.28,7054.98,133000,7054.98 -2009-03-09,7191.13,7241.02,7028.49,7086.03,132800,7086.03 -2009-03-06,7328.29,7328.29,7167.07,7173.10,159600,7173.10 -2009-03-05,7336.02,7532.87,7336.02,7433.49,185400,7433.49 -2009-03-04,7146.71,7320.65,7104.63,7290.96,159800,7290.96 -2009-03-03,7177.79,7288.14,7088.47,7229.72,146600,7229.72 -2009-03-02,7454.28,7454.28,7234.96,7280.15,125400,7280.15 -2009-02-27,7463.42,7589.77,7414.40,7568.42,140600,7568.42 -2009-02-26,7470.60,7599.81,7433.06,7457.93,143200,7457.93 -2009-02-25,7368.44,7471.03,7330.44,7461.22,165400,7461.22 -2009-02-24,7266.68,7270.90,7155.16,7268.56,146800,7268.56 -2009-02-23,7314.30,7417.18,7209.43,7376.16,164200,7376.16 -2009-02-20,7544.07,7554.70,7382.33,7416.38,140800,7416.38 -2009-02-19,7604.22,7642.69,7537.56,7557.65,138200,7557.65 -2009-02-18,7539.96,7565.79,7479.18,7534.44,149400,7534.44 -2009-02-17,7690.13,7710.43,7615.94,7645.51,120800,7645.51 -2009-02-16,7732.68,7804.24,7694.73,7750.17,110600,7750.17 -2009-02-13,7789.35,7887.74,7730.27,7779.40,149600,7779.40 -2009-02-12,7842.53,7862.52,7685.68,7705.36,146000,7705.36 -2009-02-10,8066.94,8124.79,7917.27,7945.94,138600,7945.94 -2009-02-09,8178.07,8257.71,7969.03,7969.03,140400,7969.03 -2009-02-06,8054.27,8169.04,8033.24,8076.62,147200,8076.62 -2009-02-05,7985.53,8093.96,7901.04,7949.65,169400,7949.65 -2009-02-04,7897.24,8084.97,7863.65,8038.94,156800,8038.94 -2009-02-03,7862.95,8084.41,7800.80,7825.51,181600,7825.51 -2009-02-02,7908.51,7955.75,7795.27,7873.98,159800,7873.98 -2009-01-30,8142.88,8142.88,7922.39,7994.05,148000,7994.05 -2009-01-29,8201.16,8305.38,8138.99,8251.24,160200,8251.24 -2009-01-28,8052.25,8171.63,7936.59,8106.29,140000,8106.29 -2009-01-27,7782.90,8115.15,7782.07,8061.07,152400,8061.07 -2009-01-26,7714.26,7807.16,7671.04,7682.14,115000,7682.14 -2009-01-23,7965.41,7965.41,7745.25,7745.25,119800,7745.25 -2009-01-22,7988.30,8051.74,7809.89,8051.74,142600,8051.74 -2009-01-21,7949.96,8009.22,7829.30,7901.64,147000,7901.64 -2009-01-20,8187.14,8190.42,7962.46,8065.79,128000,8065.79 -2009-01-19,8318.26,8351.68,8221.84,8256.85,102600,8256.85 -2009-01-16,8125.20,8283.91,8067.47,8230.15,140600,8230.15 -2009-01-15,8309.38,8309.38,7997.73,8023.31,158400,8023.31 -2009-01-14,8425.75,8516.07,8359.16,8438.45,132800,8438.45 -2009-01-13,8732.63,8732.93,8405.50,8413.91,135600,8413.91 -2009-01-09,8932.71,8956.85,8773.20,8836.80,137000,8836.80 -2009-01-08,9143.21,9148.83,8876.42,8876.42,150000,8876.42 -2009-01-07,9133.80,9325.35,9106.05,9239.24,205600,9239.24 -2009-01-06,9130.01,9171.03,9029.94,9080.84,154800,9080.84 -2009-01-05,8991.21,9127.38,8987.36,9043.12,85000,9043.12 -2008-12-30,8716.28,8859.56,8702.95,8859.56,60800,8859.56 -2008-12-29,8726.31,8763.67,8638.60,8747.17,83200,8747.17 -2008-12-26,8642.14,8740.76,8611.36,8739.52,75800,8739.52 -2008-12-25,8531.51,8599.50,8531.16,8599.50,61200,8599.50 -2008-12-24,8630.25,8631.83,8476.69,8517.10,100800,8517.10 -2008-12-22,8602.50,8751.18,8593.76,8723.78,109800,8723.78 -2008-12-19,8640.22,8743.22,8570.56,8588.52,138000,8588.52 -2008-12-18,8565.16,8728.36,8534.84,8667.23,138800,8667.23 -2008-12-17,8658.22,8741.24,8425.66,8612.52,148400,8612.52 -2008-12-16,8608.40,8634.26,8471.24,8568.02,132200,8568.02 -2008-12-15,8349.85,8700.17,8349.85,8664.66,129200,8664.66 -2008-12-12,8599.12,8610.73,8087.99,8235.87,185600,8235.87 -2008-12-11,8642.26,8720.55,8519.11,8720.55,162200,8720.55 -2008-12-10,8376.00,8704.92,8376.00,8660.24,155600,8660.24 -2008-12-09,8362.37,8499.60,8314.85,8395.87,150800,8395.87 -2008-12-08,7970.69,8358.27,7959.01,8329.05,139000,8329.05 -2008-12-05,7975.05,8024.33,7908.65,7917.51,139400,7917.51 -2008-12-04,8030.20,8107.69,7849.84,7924.24,148000,7924.24 -2008-12-03,7965.31,8056.38,7889.82,8004.10,121200,8004.10 -2008-12-02,8266.32,8266.32,7863.69,7863.69,136000,7863.69 -2008-12-01,8464.36,8464.36,8307.28,8397.22,107000,8397.22 -2008-11-28,8400.05,8518.13,8336.57,8512.27,145400,8512.27 -2008-11-27,8311.24,8458.68,8300.49,8373.39,116600,8373.39 -2008-11-26,8229.72,8317.83,8149.56,8213.22,118800,8213.22 -2008-11-25,8026.06,8356.83,8025.69,8323.93,155000,8323.93 -2008-11-21,7600.35,7994.68,7406.18,7910.79,185200,7910.79 -2008-11-20,8149.77,8149.79,7703.04,7703.04,154400,7703.04 -2008-11-19,8309.35,8370.09,8115.71,8273.22,143800,8273.22 -2008-11-18,8415.60,8440.41,8302.24,8328.41,144200,8328.41 -2008-11-17,8366.88,8767.98,8218.82,8522.58,146000,8522.58 -2008-11-14,8378.13,8689.85,8378.13,8462.39,155600,8462.39 -2008-11-13,8564.47,8564.47,8148.30,8238.64,166600,8238.64 -2008-11-12,8694.91,8782.48,8574.20,8695.51,153800,8695.51 -2008-11-11,8965.29,9056.31,8704.56,8809.30,153800,8809.30 -2008-11-10,8711.99,9106.29,8711.99,9081.43,155400,9081.43 -2008-11-07,8774.49,8868.10,8266.09,8583.00,206400,8583.00 -2008-11-06,9373.65,9380.30,8806.71,8899.14,176000,8899.14 -2008-11-05,9224.05,9521.24,9216.30,9521.24,208600,9521.24 -2008-11-04,8702.77,9142.29,8699.77,9114.60,164800,9114.60 -2008-10-31,8958.22,9012.31,8576.98,8576.98,206000,8576.98 -2008-10-30,8269.71,9030.85,8269.71,9029.76,220600,9029.76 -2008-10-29,7741.52,8211.90,7741.52,8211.90,222800,8211.90 -2008-10-28,7143.34,7626.42,6994.90,7621.92,240800,7621.92 -2008-10-27,7568.36,7878.97,7141.27,7162.90,237400,7162.90 -2008-10-24,8391.04,8391.04,7647.07,7649.08,194600,7649.08 -2008-10-23,8547.79,8547.79,8016.61,8460.98,216800,8460.98 -2008-10-22,9198.14,9198.14,8674.69,8674.69,160600,8674.69 -2008-10-21,9139.26,9358.51,9135.41,9306.25,154800,9306.25 -2008-10-20,8775.24,9038.45,8687.70,9005.59,165600,9005.59 -2008-10-17,8579.57,8763.71,8539.51,8693.82,171400,8693.82 -2008-10-16,9400.85,9400.85,8458.45,8458.45,186200,8458.45 -2008-10-15,9390.50,9601.30,9269.49,9547.47,185000,9547.47 -2008-10-14,8407.94,9455.62,8407.94,9447.57,169400,9447.57 -2008-10-10,9016.34,9016.34,8115.41,8276.43,247200,8276.43 -2008-10-09,9168.16,9443.45,9100.93,9157.49,213400,9157.49 -2008-10-08,10011.64,10011.64,9159.81,9203.32,205400,9203.32 -2008-10-07,10328.54,10363.14,9916.21,10155.90,210800,10155.90 -2008-10-06,10817.27,10839.50,10374.38,10473.09,185000,10473.09 -2008-10-03,11052.10,11099.73,10938.14,10938.14,174400,10938.14 -2008-10-02,11423.13,11452.39,11143.79,11154.76,156400,11154.76 -2008-10-01,11396.61,11456.64,11314.28,11368.26,142400,11368.26 -2008-09-30,11565.70,11565.70,11160.83,11259.86,165000,11259.86 -2008-09-29,11883.25,12062.67,11721.05,11743.61,122400,11743.61 -2008-09-26,12026.34,12082.64,11788.73,11893.16,131400,11893.16 -2008-09-25,11925.71,12025.41,11835.28,12006.53,113600,12006.53 -2008-09-24,12031.98,12115.03,11904.60,12115.03,152600,12115.03 -2008-09-22,12037.89,12263.95,12037.89,12090.59,150400,12090.59 -2008-09-19,11631.60,11920.86,11615.20,11920.86,184600,11920.86 -2008-09-18,11576.94,11577.88,11301.46,11489.30,163000,11489.30 -2008-09-17,11737.62,11880.03,11708.70,11749.79,158000,11749.79 -2008-09-16,12028.45,12028.45,11551.40,11609.72,184000,11609.72 -2008-09-12,12256.78,12277.57,12059.09,12214.76,194600,12214.76 -2008-09-11,12237.52,12259.02,12081.51,12102.50,131600,12102.50 -2008-09-10,12249.14,12404.67,12159.97,12346.63,155200,12346.63 -2008-09-09,12529.96,12529.96,12335.74,12400.65,119600,12400.65 -2008-09-08,12359.93,12671.76,12352.35,12624.46,135000,12624.46 -2008-09-05,12385.65,12385.65,12163.33,12212.23,155600,12212.23 -2008-09-04,12627.64,12660.57,12514.26,12557.66,145200,12557.66 -2008-09-03,12703.36,12767.50,12647.29,12689.59,129200,12689.59 -2008-09-02,12779.89,12920.52,12491.07,12609.47,126600,12609.47 -2008-09-01,12936.81,12940.55,12834.18,12834.18,87600,12834.18 -2008-08-29,12925.45,13079.37,12918.49,13072.87,120800,13072.87 -2008-08-28,12827.72,12847.46,12718.53,12768.25,89600,12768.25 -2008-08-27,12734.39,12783.63,12681.98,12752.96,87000,12752.96 -2008-08-26,12711.03,12801.21,12656.09,12778.71,87000,12778.71 -2008-08-25,12797.54,12949.33,12797.54,12878.66,86600,12878.66 -2008-08-22,12727.37,12732.69,12631.94,12666.04,87800,12666.04 -2008-08-21,12885.34,12885.34,12723.83,12752.21,105200,12752.21 -2008-08-20,12753.98,12923.66,12753.98,12851.69,110400,12851.69 -2008-08-19,13016.50,13016.50,12782.10,12865.05,103200,12865.05 -2008-08-18,12971.49,13270.37,12934.22,13165.45,114000,13165.45 -2008-08-15,12991.91,13029.58,12952.21,13019.41,94800,13019.41 -2008-08-14,12942.61,13090.68,12926.98,12956.80,116400,12956.80 -2008-08-13,13205.64,13205.64,12953.34,13023.05,125200,13023.05 -2008-08-12,13397.99,13420.10,13276.15,13303.60,125200,13303.60 -2008-08-11,13259.46,13468.81,13259.46,13430.91,113800,13430.91 -2008-08-08,13026.53,13259.73,12962.82,13168.41,162400,13168.41 -2008-08-07,13257.99,13257.99,13034.15,13124.99,136000,13124.99 -2008-08-06,13059.43,13295.51,13048.97,13254.89,156400,13254.89 -2008-08-05,12957.01,13049.58,12893.34,12914.66,144600,12914.66 -2008-08-04,13083.28,13113.94,12910.17,12933.18,142000,12933.18 -2008-08-01,13276.57,13294.17,13039.21,13094.59,135000,13094.59 -2008-07-31,13410.40,13467.67,13256.38,13376.81,137000,13376.81 -2008-07-30,13267.37,13372.28,13264.08,13367.79,109000,13367.79 -2008-07-29,13220.33,13220.33,13018.22,13159.45,106400,13159.45 -2008-07-28,13407.36,13468.94,13327.12,13353.78,93600,13353.78 -2008-07-25,13452.37,13469.83,13324.22,13334.76,109600,13334.76 -2008-07-24,13411.28,13603.31,13393.57,13603.31,126200,13603.31 -2008-07-23,13259.65,13388.63,13238.55,13312.93,127200,13312.93 -2008-07-22,12944.56,13184.96,12921.02,13184.96,112400,13184.96 -2008-07-18,12976.22,12999.64,12762.33,12803.70,113200,12803.70 -2008-07-17,12889.80,12929.74,12852.93,12887.95,111000,12887.95 -2008-07-16,12725.12,12815.40,12671.34,12760.80,122400,12760.80 -2008-07-15,12902.13,12902.13,12715.81,12754.56,118800,12754.56 -2008-07-14,13022.29,13185.90,12969.93,13010.16,123800,13010.16 -2008-07-11,13063.50,13164.10,12918.22,13039.69,146200,13039.69 -2008-07-10,12934.31,13139.85,12930.32,13067.21,120200,13067.21 -2008-07-09,13169.89,13284.65,13038.77,13052.13,123000,13052.13 -2008-07-08,13286.50,13294.97,12984.54,13033.10,121800,13033.10 -2008-07-07,13212.80,13409.30,13169.55,13360.04,107000,13360.04 -2008-07-04,13285.49,13288.55,13135.46,13237.89,117400,13237.89 -2008-07-03,13161.78,13326.95,13118.89,13265.40,154200,13265.40 -2008-07-02,13489.87,13489.87,13247.05,13286.37,136600,13286.37 -2008-07-01,13514.86,13576.41,13448.35,13463.20,121400,13463.20 -2008-06-30,13584.51,13598.48,13454.28,13481.38,123600,13481.38 -2008-06-27,13605.26,13605.56,13453.35,13544.36,127800,13544.36 -2008-06-26,13845.41,13950.56,13798.05,13822.32,114400,13822.32 -2008-06-25,13820.78,13833.23,13635.68,13829.92,123600,13829.92 -2008-06-24,13766.28,13877.49,13738.39,13849.56,100200,13849.56 -2008-06-23,13769.44,13920.75,13667.84,13857.47,117600,13857.47 -2008-06-20,14171.02,14190.00,13903.21,13942.08,129600,13942.08 -2008-06-19,14324.71,14324.71,14069.16,14130.17,130800,14130.17 -2008-06-18,14301.36,14469.99,14301.36,14452.82,110800,14452.82 -2008-06-17,14387.00,14387.00,14299.67,14348.37,110800,14348.37 -2008-06-16,14118.23,14369.09,14103.50,14354.37,120000,14354.37 -2008-06-13,14011.12,14041.34,13810.38,13973.73,230400,13973.73 -2008-06-12,14010.32,14010.32,13826.07,13888.60,133400,13888.60 -2008-06-11,14137.54,14194.48,13993.57,14183.48,131000,14183.48 -2008-06-10,14281.36,14308.89,13983.56,14021.17,120600,14021.17 -2008-06-09,14275.34,14278.84,14117.79,14181.38,122000,14181.38 -2008-06-06,14530.36,14601.27,14489.44,14489.44,150600,14489.44 -2008-06-05,14392.59,14392.59,14262.02,14341.12,152000,14341.12 -2008-06-04,14270.07,14435.57,14250.11,14435.57,168800,14435.57 -2008-06-03,14275.61,14289.47,14127.75,14209.17,152600,14209.17 -2008-06-02,14342.96,14461.03,14189.97,14440.14,000,14440.14 -2008-05-30,14195.66,14366.63,14192.17,14338.54,166600,14338.54 -2008-05-29,13832.65,14147.89,13832.65,14124.47,128800,14124.47 -2008-05-28,13937.14,13979.39,13665.57,13709.44,132400,13709.44 -2008-05-27,13750.82,13931.23,13750.82,13893.31,100200,13893.31 -2008-05-26,13875.98,13883.51,13670.92,13690.19,117800,13690.19 -2008-05-23,13945.10,14157.24,13925.38,14012.20,146400,14012.20 -2008-05-22,13772.65,13984.81,13658.02,13978.46,159200,13978.46 -2008-05-21,14002.52,14041.24,13847.18,13926.30,160200,13926.30 -2008-05-20,14220.12,14286.67,14121.92,14160.09,159800,14160.09 -2008-05-19,14294.52,14343.19,14219.08,14269.61,133800,14269.61 -2008-05-16,14363.62,14392.53,14194.91,14219.48,144200,14219.48 -2008-05-15,14167.02,14352.84,14167.02,14251.74,160200,14251.74 -2008-05-14,13961.96,14121.94,13877.40,14118.55,142400,14118.55 -2008-05-13,13814.39,13976.92,13734.50,13953.73,129200,13953.73 -2008-05-12,13565.91,13793.41,13540.68,13743.36,103000,13743.36 -2008-05-09,13941.30,13946.51,13639.99,13655.34,130400,13655.34 -2008-05-08,14008.19,14036.31,13930.28,13943.26,120400,13943.26 -2008-05-07,14147.57,14208.67,14022.79,14102.48,139800,14102.48 -2008-05-02,13944.26,14072.92,13944.26,14049.26,114000,14049.26 -2008-05-01,13802.59,13884.63,13727.07,13766.86,110800,13766.86 -2008-04-30,13802.94,13976.10,13766.24,13849.99,143200,13849.99 -2008-04-28,13907.97,14003.28,13745.61,13894.37,139400,13894.37 -2008-04-25,13614.53,13886.37,13614.53,13863.47,127200,13863.47 -2008-04-24,13613.83,13654.78,13497.16,13540.87,108800,13540.87 -2008-04-23,13455.56,13717.05,13449.04,13579.16,112200,13579.16 -2008-04-22,13587.51,13608.17,13519.12,13547.82,100800,13547.82 -2008-04-21,13639.85,13739.44,13639.77,13696.55,124600,13696.55 -2008-04-18,13426.26,13485.04,13323.74,13476.45,102400,13476.45 -2008-04-17,13315.83,13495.94,13313.06,13398.30,127200,13398.30 -2008-04-16,13130.66,13222.43,13112.07,13146.13,121200,13146.13 -2008-04-15,12952.65,13052.82,12875.92,12990.58,112400,12990.58 -2008-04-14,13132.67,13132.67,12858.63,12917.51,101000,12917.51 -2008-04-11,13061.77,13329.40,13040.35,13323.73,147600,13323.73 -2008-04-10,13029.81,13062.46,12898.49,12945.30,128000,12945.30 -2008-04-09,13295.16,13348.38,12998.54,13111.89,117200,13111.89 -2008-04-08,13373.96,13402.91,13225.76,13250.43,110600,13250.43 -2008-04-07,13240.56,13485.90,13228.86,13450.23,125200,13450.23 -2008-04-04,13286.35,13360.81,13220.00,13293.22,122000,13293.22 -2008-04-03,13190.16,13389.90,13137.10,13389.90,142600,13389.90 -2008-04-02,12836.41,13189.36,12836.41,13189.36,145000,13189.36 -2008-04-01,12539.80,12779.14,12521.84,12656.42,114600,12656.42 -2008-03-31,12709.28,12709.28,12430.63,12525.54,124000,12525.54 -2008-03-28,12594.34,12874.45,12507.68,12820.47,122600,12820.47 -2008-03-27,12618.42,12621.56,12475.88,12604.58,114200,12604.58 -2008-03-26,12648.97,12711.78,12591.01,12706.63,107400,12706.63 -2008-03-25,12639.74,12791.24,12572.77,12745.22,130200,12745.22 -2008-03-24,12473.06,12582.46,12438.20,12480.09,108400,12480.09 -2008-03-21,12331.64,12496.41,12308.03,12482.57,122000,12482.57 -2008-03-19,12142.33,12374.75,12142.33,12260.44,143800,12260.44 -2008-03-18,11828.99,11995.06,11793.60,11964.16,157800,11964.16 -2008-03-17,12089.03,12132.69,11691.00,11787.51,172600,11787.51 -2008-03-14,12509.81,12582.57,12167.09,12241.60,232000,12241.60 -2008-03-13,12741.26,12772.37,12351.72,12433.44,143400,12433.44 -2008-03-12,12841.88,13071.22,12799.42,12861.13,141000,12861.13 -2008-03-11,12392.31,12674.89,12352.79,12658.28,162200,12658.28 -2008-03-10,12716.84,12777.07,12527.07,12532.13,151200,12532.13 -2008-03-07,13024.61,13024.61,12744.52,12782.80,144200,12782.80 -2008-03-06,13068.89,13365.22,13050.55,13215.42,134200,13215.42 -2008-03-05,12973.03,13044.01,12919.81,12972.06,128800,12972.06 -2008-03-04,13080.29,13110.39,12883.07,12992.28,138600,12992.28 -2008-03-03,13412.87,13413.63,12992.18,12992.18,142400,12992.18 -2008-02-29,13735.44,13738.56,13533.25,13603.02,126600,13603.02 -2008-02-28,13877.88,13962.30,13794.71,13925.51,118400,13925.51 -2008-02-27,14007.32,14105.47,13956.44,14031.30,127400,14031.30 -2008-02-26,14036.89,14053.85,13803.46,13824.72,133800,13824.72 -2008-02-25,13612.31,13969.18,13612.31,13914.57,152000,13914.57 -2008-02-22,13530.19,13540.62,13378.72,13500.46,144200,13500.46 -2008-02-21,13462.72,13783.97,13439.59,13688.28,143000,13688.28 -2008-02-20,13729.75,13729.75,13310.37,13310.37,163600,13310.37 -2008-02-19,13761.76,13853.21,13691.88,13757.91,147400,13757.91 -2008-02-15,13508.53,13666.68,13356.39,13622.56,154800,13622.56 -2008-02-14,13254.59,13626.45,13251.86,13626.45,147200,13626.45 -2008-02-13,13162.95,13240.26,13036.62,13068.30,138800,13068.30 -2008-02-12,12998.87,13138.28,12923.42,13021.96,147600,13021.96 -2008-02-08,13143.08,13279.52,12997.88,13017.24,170600,13017.24 -2008-02-07,13077.25,13244.19,12972.55,13207.15,163000,13207.15 -2008-02-06,13548.53,13552.19,13099.24,13099.24,176800,13099.24 -2008-02-05,13806.17,13821.92,13665.64,13745.50,133600,13745.50 -2008-02-04,13642.60,13889.24,13642.60,13859.70,138200,13859.70 -2008-02-01,13517.74,13648.39,13444.08,13497.16,142600,13497.16 -2008-01-31,13227.48,13622.68,13154.77,13592.47,165200,13592.47 -2008-01-30,13500.52,13514.13,13271.13,13345.03,152400,13345.03 -2008-01-29,13246.69,13506.81,13224.66,13478.86,147000,13478.86 -2008-01-28,13482.84,13501.86,13087.91,13087.91,152800,13087.91 -2008-01-25,13258.77,13647.16,13248.89,13629.16,178800,13629.16 -2008-01-24,12952.50,13134.77,12952.50,13092.78,189600,13092.78 -2008-01-23,12756.31,13063.78,12619.78,12829.06,178000,12829.06 -2008-01-22,13125.23,13125.23,12572.68,12573.05,199000,12573.05 -2008-01-21,13701.43,13704.65,13320.51,13325.94,152600,13325.94 -2008-01-18,13577.50,13902.64,13365.32,13861.29,191000,13861.29 -2008-01-17,13596.38,13803.08,13472.45,13783.45,192800,13783.45 -2008-01-16,13796.73,13841.93,13500.59,13504.51,204600,13504.51 -2008-01-15,14134.91,14224.00,13915.15,13972.63,163800,13972.63 -2008-01-11,14419.43,14447.49,14096.54,14110.79,175400,14110.79 -2008-01-10,14546.32,14584.73,14388.11,14388.11,130200,14388.11 -2008-01-09,14364.71,14602.65,14271.57,14599.16,155400,14599.16 -2008-01-08,14429.30,14547.80,14365.86,14528.67,146800,14528.67 -2008-01-07,14549.38,14667.85,14438.61,14500.55,139800,14500.55 -2008-01-04,15155.73,15156.66,14542.58,14691.41,98800,14691.41 -2007-12-28,15413.37,15413.37,15240.96,15307.78,61200,15307.78 -2007-12-27,15616.41,15628.31,15535.51,15564.69,93000,15564.69 -2007-12-26,15613.96,15653.54,15559.47,15653.54,94000,15653.54 -2007-12-25,15441.33,15583.39,15441.33,15552.59,90600,15552.59 -2007-12-21,15044.35,15275.61,14998.01,15257.00,135400,15257.00 -2007-12-20,15151.37,15161.66,15017.97,15031.60,108600,15031.60 -2007-12-19,15165.09,15267.75,15030.51,15030.51,118200,15030.51 -2007-12-18,15099.20,15301.69,15004.41,15207.86,139800,15207.86 -2007-12-17,15433.30,15508.50,15219.07,15249.79,113200,15249.79 -2007-12-14,15547.19,15697.05,15433.77,15514.51,200200,15514.51 -2007-12-13,15818.48,15833.10,15532.53,15536.52,141000,15536.52 -2007-12-12,15828.65,15963.43,15700.15,15932.26,142800,15932.26 -2007-12-11,16003.09,16075.61,15972.45,16044.72,102800,16044.72 -2007-12-10,16007.33,16017.14,15826.25,15924.39,116200,15924.39 -2007-12-07,15992.24,16107.65,15948.54,15956.37,146000,15956.37 -2007-12-06,15782.40,15898.26,15740.94,15874.08,129200,15874.08 -2007-12-05,15418.95,15621.54,15365.39,15608.88,137000,15608.88 -2007-12-04,15613.89,15683.18,15446.47,15480.19,124200,15480.19 -2007-12-03,15747.47,15799.69,15577.69,15628.97,137600,15628.97 -2007-11-30,15520.53,15751.20,15520.53,15680.67,171200,15680.67 -2007-11-29,15339.61,15555.04,15339.61,15513.74,129800,15513.74 -2007-11-28,15271.14,15280.91,15089.35,15153.78,134200,15153.78 -2007-11-27,14953.93,15312.55,14801.87,15222.85,159200,15222.85 -2007-11-26,14921.57,15295.21,14912.83,15135.21,146000,15135.21 -2007-11-22,14726.62,15000.18,14669.85,14888.77,161200,14888.77 -2007-11-21,15113.83,15154.31,14770.22,14837.66,149000,14837.66 -2007-11-20,14868.98,15222.24,14751.27,15211.52,184600,15211.52 -2007-11-19,15177.17,15302.76,15040.10,15042.56,125400,15042.56 -2007-11-16,15238.73,15238.73,15030.02,15154.61,118800,15154.61 -2007-11-15,15536.35,15587.31,15396.30,15396.30,129800,15396.30 -2007-11-14,15311.38,15504.99,15287.26,15499.56,139000,15499.56 -2007-11-13,15148.16,15235.56,14988.77,15126.63,151000,15126.63 -2007-11-12,15377.37,15386.80,14998.51,15197.09,158600,15197.09 -2007-11-09,15675.48,15834.97,15566.12,15583.42,160400,15583.42 -2007-11-08,15889.03,15891.23,15626.06,15771.57,161200,15771.57 -2007-11-07,16325.18,16326.58,16081.03,16096.68,136000,16096.68 -2007-11-06,16152.58,16353.93,16144.40,16249.63,138800,16249.63 -2007-11-05,16458.14,16458.14,16211.79,16268.92,142800,16268.92 -2007-11-02,16647.40,16654.73,16484.54,16517.48,148200,16517.48 -2007-11-01,16812.90,16887.04,16795.55,16870.40,145000,16870.40 -2007-10-31,16620.59,16738.98,16552.54,16737.63,144800,16737.63 -2007-10-30,16655.31,16682.87,16492.56,16651.01,149200,16651.01 -2007-10-29,16613.30,16774.18,16613.30,16698.08,122000,16698.08 -2007-10-26,16358.61,16505.63,16348.86,16505.63,110200,16505.63 -2007-10-25,16368.02,16438.57,16199.02,16284.17,111600,16284.17 -2007-10-24,16518.00,16578.59,16330.33,16358.39,109200,16358.39 -2007-10-23,16486.71,16554.91,16416.92,16450.58,90400,16450.58 -2007-10-22,16563.57,16563.57,16264.70,16438.47,122000,16438.47 -2007-10-19,16965.00,16965.00,16711.57,16814.37,111600,16814.37 -2007-10-18,16974.69,17147.73,16974.69,17106.09,113800,17106.09 -2007-10-17,17114.20,17114.20,16795.74,16955.31,150600,16955.31 -2007-10-16,17267.07,17283.05,17104.20,17137.92,114400,17137.92 -2007-10-15,17399.67,17430.09,17292.13,17358.15,97000,17358.15 -2007-10-12,17417.94,17441.75,17280.60,17331.17,127000,17331.17 -2007-10-11,17188.81,17488.97,17154.75,17458.98,133000,17458.98 -2007-10-10,17231.14,17254.52,17146.39,17177.89,101800,17177.89 -2007-10-09,17166.17,17237.40,17133.52,17159.90,104600,17159.90 -2007-10-05,17070.61,17144.35,17032.75,17065.04,97200,17065.04 -2007-10-04,17085.32,17160.47,17043.76,17092.49,129200,17092.49 -2007-10-03,17066.14,17205.42,17017.77,17199.89,148200,17199.89 -2007-10-02,17027.92,17072.67,16986.38,17046.78,136000,17046.78 -2007-10-01,16773.10,16899.84,16685.80,16845.96,108600,16845.96 -2007-09-28,16903.64,16929.26,16755.21,16785.69,111600,16785.69 -2007-09-27,16551.94,16868.94,16551.94,16832.22,126800,16832.22 -2007-09-26,16388.51,16457.72,16388.51,16435.74,103800,16435.74 -2007-09-25,16317.19,16434.80,16240.26,16401.73,118000,16401.73 -2007-09-21,16284.43,16353.97,16245.94,16312.61,123000,16312.61 -2007-09-20,16474.66,16491.45,16344.28,16413.79,120800,16413.79 -2007-09-19,16038.12,16386.17,16038.12,16381.54,112200,16381.54 -2007-09-18,16037.49,16037.49,15780.90,15801.80,101000,15801.80 -2007-09-14,15895.05,16142.08,15877.09,16127.42,173000,16127.42 -2007-09-13,15886.76,15931.09,15802.36,15821.19,101600,15821.19 -2007-09-12,15978.78,16032.26,15731.32,15797.60,111000,15797.60 -2007-09-11,15787.86,15940.38,15610.65,15877.67,111000,15877.67 -2007-09-10,15906.52,15906.52,15651.83,15764.97,115400,15764.97 -2007-09-07,16179.78,16230.58,16027.93,16122.16,101000,16122.16 -2007-09-06,16003.88,16257.00,15840.05,16257.00,141200,16257.00 -2007-09-05,16506.11,16553.22,16154.90,16158.45,114200,16158.45 -2007-09-04,16445.73,16511.64,16392.21,16420.47,86600,16420.47 -2007-09-03,16511.07,16575.97,16452.74,16524.93,96600,16524.93 -2007-08-31,16270.99,16569.09,16266.23,16569.09,119400,16569.09 -2007-08-30,16182.09,16269.66,16091.28,16153.82,97200,16153.82 -2007-08-29,16068.10,16068.10,15830.28,16012.83,112000,16012.83 -2007-08-28,16214.09,16343.28,16192.84,16287.49,83800,16287.49 -2007-08-27,16429.01,16504.72,16263.95,16301.39,91600,16301.39 -2007-08-24,16286.01,16329.96,16188.08,16248.97,102800,16248.97 -2007-08-23,16093.82,16333.36,16093.82,16316.32,118200,16316.32 -2007-08-22,15866.60,15957.96,15787.96,15900.64,106400,15900.64 -2007-08-21,15773.86,16101.64,15754.51,15901.34,132600,15901.34 -2007-08-20,15477.26,15940.61,15477.26,15732.48,146600,15732.48 -2007-08-17,16035.38,16062.59,15262.10,15273.68,196800,15273.68 -2007-08-16,16296.40,16296.40,15859.46,16148.49,177000,16148.49 -2007-08-15,16659.07,16667.36,16433.30,16475.61,131400,16475.61 -2007-08-14,16824.63,16855.05,16747.94,16844.61,115400,16844.61 -2007-08-13,16791.80,16948.40,16725.55,16800.05,148200,16800.05 -2007-08-10,16923.21,16948.96,16651.71,16764.09,213200,16764.09 -2007-08-09,17170.36,17274.33,17148.95,17170.60,218800,17170.60 -2007-08-08,16930.39,17085.10,16911.68,17029.28,165000,17029.28 -2007-08-07,17009.63,17049.45,16863.46,16921.77,135000,16921.77 -2007-08-06,16781.14,16951.98,16675.39,16914.46,130600,16914.46 -2007-08-03,17019.80,17102.07,16913.27,16979.86,137200,16979.86 -2007-08-02,16956.33,16999.16,16652.80,16984.11,158000,16984.11 -2007-08-01,17169.20,17169.20,16845.54,16870.98,161400,16870.98 -2007-07-31,17318.01,17318.01,17195.29,17248.89,146400,17248.89 -2007-07-30,17138.53,17289.30,17042.66,17289.30,154000,17289.30 -2007-07-27,17454.59,17454.59,17196.16,17283.81,160400,17283.81 -2007-07-26,17807.23,17861.47,17678.98,17702.09,125200,17702.09 -2007-07-25,17810.97,17881.31,17733.96,17858.42,135200,17858.42 -2007-07-24,17998.76,18018.94,17906.11,18002.03,127400,18002.03 -2007-07-23,17995.71,18009.47,17892.75,17963.64,147200,17963.64 -2007-07-20,18148.60,18223.04,18124.74,18157.93,176600,18157.93 -2007-07-19,18095.95,18131.12,18037.33,18116.57,127600,18116.57 -2007-07-18,18136.06,18136.06,17964.28,18015.58,136600,18015.58 -2007-07-17,18269.36,18269.36,18167.82,18217.27,123400,18217.27 -2007-07-13,18161.02,18268.64,18150.99,18238.95,126200,18238.95 -2007-07-12,18105.89,18130.44,17919.17,17984.14,125600,17984.14 -2007-07-11,18116.66,18116.66,18028.87,18049.51,120600,18049.51 -2007-07-10,18244.69,18259.81,18204.04,18252.67,118800,18252.67 -2007-07-09,18226.07,18282.15,18213.59,18261.98,101200,18261.98 -2007-07-06,18184.64,18184.64,18086.01,18140.94,100600,18140.94 -2007-07-05,18191.89,18295.27,18191.89,18221.48,88800,18221.48 -2007-07-04,18158.77,18207.97,18143.58,18168.72,80400,18168.72 -2007-07-03,18206.49,18230.89,18146.74,18149.90,104800,18149.90 -2007-07-02,18139.04,18175.30,18062.49,18146.30,108600,18146.30 -2007-06-29,18010.50,18144.63,17973.50,18138.36,106000,18138.36 -2007-06-28,17915.63,17960.22,17893.37,17932.27,100000,17932.27 -2007-06-27,17981.77,17983.35,17848.05,17849.28,114200,17849.28 -2007-06-26,18098.33,18101.89,18008.60,18066.11,100400,18066.11 -2007-06-25,18107.68,18203.56,18079.85,18087.48,114400,18087.48 -2007-06-22,18177.89,18200.11,18092.36,18188.63,125600,18188.63 -2007-06-21,18117.30,18287.73,18107.81,18240.30,137200,18240.30 -2007-06-20,18173.07,18297.00,18141.95,18211.68,141400,18211.68 -2007-06-19,18131.59,18163.61,18103.56,18163.61,112000,18163.61 -2007-06-18,18127.41,18194.26,18112.93,18149.52,120600,18149.52 -2007-06-15,17945.84,18007.99,17930.34,17971.49,123800,17971.49 -2007-06-14,17834.78,17875.02,17815.30,17842.29,106800,17842.29 -2007-06-13,17631.87,17781.41,17591.93,17732.77,119200,17732.77 -2007-06-12,17845.22,17862.99,17735.56,17760.91,117200,17760.91 -2007-06-11,17899.02,17932.10,17801.63,17834.48,119600,17834.48 -2007-06-08,17904.68,17904.68,17696.51,17779.09,223600,17779.09 -2007-06-07,17879.01,18053.38,17866.52,18053.38,152400,18053.38 -2007-06-06,18001.20,18073.05,17991.19,18040.93,140800,18040.93 -2007-06-05,18019.79,18071.72,17950.45,18053.81,126200,18053.81 -2007-06-04,18067.90,18071.80,17973.42,17973.42,166600,17973.42 -2007-06-01,17949.92,18017.73,17943.68,17958.88,158600,17958.88 -2007-05-31,17715.77,17875.75,17701.57,17875.75,134200,17875.75 -2007-05-30,17664.37,17727.17,17484.30,17588.26,125800,17588.26 -2007-05-29,17524.82,17700.52,17521.64,17672.56,108000,17672.56 -2007-05-28,17544.98,17630.37,17544.67,17587.59,94200,17587.59 -2007-05-25,17529.27,17529.27,17370.18,17481.21,117800,17481.21 -2007-05-24,17680.45,17760.57,17606.56,17696.97,116400,17696.97 -2007-05-23,17763.15,17802.71,17699.12,17705.12,130600,17705.12 -2007-05-22,17578.31,17730.84,17545.26,17680.05,127800,17680.05 -2007-05-21,17455.55,17599.35,17411.51,17556.87,118400,17556.87 -2007-05-18,17563.53,17563.53,17320.81,17399.58,114800,17399.58 -2007-05-17,17586.33,17656.07,17482.44,17498.60,117000,17498.60 -2007-05-16,17487.00,17539.95,17430.70,17529.00,141000,17529.00 -2007-05-15,17577.14,17609.55,17491.59,17512.98,136000,17512.98 -2007-05-14,17682.74,17786.65,17673.86,17677.94,151400,17677.94 -2007-05-11,17616.02,17616.02,17455.28,17553.72,157600,17553.72 -2007-05-10,17793.49,17827.48,17712.89,17736.96,165400,17736.96 -2007-05-09,17616.58,17753.33,17616.58,17748.12,167000,17748.12 -2007-05-08,17651.47,17711.67,17587.92,17656.84,152400,17656.84 -2007-05-07,17564.17,17715.99,17558.24,17669.83,149400,17669.83 -2007-05-02,17310.75,17441.10,17227.09,17394.92,113400,17394.92 -2007-05-01,17396.30,17396.30,17203.03,17274.98,120200,17274.98 -2007-04-27,17377.04,17542.25,17299.37,17400.41,153800,17400.41 -2007-04-26,17359.84,17496.11,17321.05,17429.17,130000,17429.17 -2007-04-25,17379.52,17379.52,17221.55,17236.16,115200,17236.16 -2007-04-24,17363.84,17500.34,17305.78,17451.77,116000,17451.77 -2007-04-23,17589.61,17656.55,17413.64,17455.37,123600,17455.37 -2007-04-20,17471.56,17502.02,17404.62,17452.62,123400,17452.62 -2007-04-19,17530.00,17530.00,17219.73,17371.97,142600,17371.97 -2007-04-18,17557.40,17706.85,17538.34,17667.33,120000,17667.33 -2007-04-17,17750.67,17782.08,17452.12,17527.45,125200,17527.45 -2007-04-16,17507.18,17696.87,17507.18,17628.30,112000,17628.30 -2007-04-13,17629.02,17662.89,17327.37,17363.95,134000,17363.95 -2007-04-12,17601.65,17601.65,17455.18,17540.42,122200,17540.42 -2007-04-11,17699.39,17723.39,17618.19,17670.07,113800,17670.07 -2007-04-10,17631.02,17706.92,17613.15,17664.69,131400,17664.69 -2007-04-09,17606.03,17747.82,17606.03,17743.76,124600,17743.76 -2007-04-06,17502.90,17560.30,17422.55,17484.78,121000,17484.78 -2007-04-05,17507.46,17531.30,17430.38,17491.42,132800,17491.42 -2007-04-04,17400.68,17576.51,17394.14,17544.09,150400,17544.09 -2007-04-03,17154.78,17279.73,17095.92,17244.05,152000,17244.05 -2007-04-02,17346.25,17425.74,16999.05,17028.41,154000,17028.41 -2007-03-30,17318.85,17380.80,17267.10,17287.65,115200,17287.65 -2007-03-29,17119.95,17350.88,17036.22,17263.94,144600,17263.94 -2007-03-28,17328.12,17442.62,17141.65,17254.73,153000,17254.73 -2007-03-27,17357.26,17516.89,17315.91,17365.05,125800,17365.05 -2007-03-26,17517.92,17558.04,17425.00,17521.96,91800,17521.96 -2007-03-23,17519.51,17534.77,17407.97,17480.61,128400,17480.61 -2007-03-22,17383.62,17489.19,17379.40,17419.20,146400,17419.20 -2007-03-20,17155.35,17267.74,17146.53,17163.20,129400,17163.20 -2007-03-19,16713.99,17026.46,16713.99,17009.55,130800,17009.55 -2007-03-16,16779.48,16939.43,16643.76,16744.15,173200,16744.15 -2007-03-15,16803.99,16942.31,16760.68,16860.39,165000,16860.39 -2007-03-14,16936.19,16936.19,16628.85,16676.89,163600,16676.89 -2007-03-13,17268.71,17299.48,17153.20,17178.84,135200,17178.84 -2007-03-12,17312.14,17325.45,17206.94,17292.39,130000,17292.39 -2007-03-09,17224.67,17246.21,17100.74,17164.04,231600,17164.04 -2007-03-08,16729.79,17090.31,16685.95,17090.31,179200,17090.31 -2007-03-07,16982.30,16988.01,16731.77,16764.62,217400,16764.62 -2007-03-06,16654.85,16882.92,16649.10,16844.50,210000,16844.50 -2007-03-05,16992.44,16992.44,16532.91,16642.25,211000,16642.25 -2007-03-02,17351.40,17356.45,17160.43,17217.93,198000,17217.93 -2007-03-01,17542.23,17557.42,17261.60,17453.51,222400,17453.51 -2007-02-28,17843.61,17843.61,17382.79,17604.12,250200,17604.12 -2007-02-27,18239.30,18272.68,18073.22,18119.92,198000,18119.92 -2007-02-26,18219.75,18300.39,18145.42,18215.35,194800,18215.35 -2007-02-23,18113.56,18239.13,18046.42,18188.42,193400,18188.42 -2007-02-22,18033.23,18132.84,18024.48,18108.79,183200,18108.79 -2007-02-21,17896.60,17968.26,17850.09,17913.21,211200,17913.21 -2007-02-20,17919.33,17953.03,17828.95,17939.12,152200,17939.12 -2007-02-19,17835.13,17974.00,17810.05,17940.09,137000,17940.09 -2007-02-16,17828.78,17884.89,17793.35,17875.65,137600,17875.65 -2007-02-15,17891.24,17911.58,17815.17,17897.23,151400,17897.23 -2007-02-14,17662.29,17789.92,17648.81,17752.64,164800,17752.64 -2007-02-13,17481.77,17628.03,17440.43,17621.45,170000,17621.45 -2007-02-09,17339.56,17545.71,17274.89,17504.33,159600,17504.33 -2007-02-08,17368.35,17400.35,17212.78,17292.48,141800,17292.48 -2007-02-07,17367.91,17374.82,17199.66,17292.32,172200,17292.32 -2007-02-06,17384.50,17433.27,17345.10,17406.86,157000,17406.86 -2007-02-05,17531.41,17531.41,17294.98,17344.80,152400,17344.80 -2007-02-02,17569.16,17633.61,17532.64,17547.11,162000,17547.11 -2007-02-01,17377.03,17543.96,17361.01,17519.50,167800,17519.50 -2007-01-31,17493.83,17497.86,17275.84,17383.42,146000,17383.42 -2007-01-30,17510.00,17558.53,17452.63,17490.19,155000,17490.19 -2007-01-29,17393.19,17489.59,17319.37,17470.46,149200,17470.46 -2007-01-26,17368.05,17421.93,17300.84,17421.93,134400,17421.93 -2007-01-25,17604.60,17617.64,17427.54,17458.30,159000,17458.30 -2007-01-24,17505.31,17553.03,17498.36,17507.40,192200,17507.40 -2007-01-23,17350.31,17442.00,17321.29,17408.57,161200,17408.57 -2007-01-22,17429.90,17484.59,17401.32,17424.18,125600,17424.18 -2007-01-19,17340.38,17378.21,17242.77,17310.44,121400,17310.44 -2007-01-18,17248.14,17408.62,17220.42,17370.93,148800,17370.93 -2007-01-17,17153.25,17335.03,17002.67,17261.35,147000,17261.35 -2007-01-16,17190.90,17287.96,17175.85,17202.46,128400,17202.46 -2007-01-15,17160.25,17273.58,17144.44,17209.92,124400,17209.92 -2007-01-12,16979.73,17160.77,16941.39,17057.01,139400,17057.01 -2007-01-11,16958.57,17057.45,16758.46,16838.17,122000,16838.17 -2007-01-10,17192.42,17199.42,16847.57,16942.40,133400,16942.40 -2007-01-09,17018.89,17261.03,16983.97,17237.77,142400,17237.77 -2007-01-05,17315.54,17327.13,17011.10,17091.59,158600,17091.59 -2007-01-04,17322.50,17379.46,17315.76,17353.67,80200,17353.67 -2006-12-29,17228.49,17281.19,17225.83,17225.83,75400,17225.83 -2006-12-28,17290.11,17301.69,17163.75,17224.81,130600,17224.81 -2006-12-27,17207.12,17260.57,17207.12,17248.63,69200,17248.63 -2006-12-26,17070.32,17185.71,17056.59,17169.19,114000,17169.19 -2006-12-25,17104.80,17122.48,17056.69,17092.89,87000,17092.89 -2006-12-22,17011.42,17104.96,16992.77,17104.96,117000,17104.96 -2006-12-21,17040.93,17109.17,17010.04,17047.83,147200,17047.83 -2006-12-20,16829.58,17050.73,16829.58,17011.04,133200,17011.04 -2006-12-19,16883.86,16954.83,16754.21,16776.88,113000,16776.88 -2006-12-18,16962.65,16993.88,16930.55,16962.11,107400,16962.11 -2006-12-15,16927.94,16959.91,16858.35,16914.31,106200,16914.31 -2006-12-14,16714.34,16829.20,16714.34,16829.20,94600,16829.20 -2006-12-13,16609.25,16692.93,16589.73,16692.93,105400,16692.93 -2006-12-12,16621.69,16682.65,16583.78,16637.78,121200,16637.78 -2006-12-11,16487.30,16608.97,16470.40,16527.99,115000,16527.99 -2006-12-08,16429.80,16493.00,16387.80,16417.82,175600,16417.82 -2006-12-07,16461.91,16550.73,16416.30,16473.36,102200,16473.36 -2006-12-06,16309.80,16401.31,16254.45,16371.28,109800,16371.28 -2006-12-05,16370.56,16400.14,16239.28,16265.76,121400,16265.76 -2006-12-04,16263.98,16362.04,16185.92,16303.59,108600,16303.59 -2006-12-01,16313.02,16376.30,16242.01,16321.78,111800,16321.78 -2006-11-30,16183.30,16274.33,16152.85,16274.33,119200,16274.33 -2006-11-29,15948.69,16126.35,15945.07,16076.20,115200,16076.20 -2006-11-28,15711.72,15855.26,15653.69,15855.26,114000,15855.26 -2006-11-27,15615.56,15912.11,15615.56,15885.38,94800,15885.38 -2006-11-24,15784.26,15789.89,15639.19,15734.60,90600,15734.60 -2006-11-22,15680.53,15914.23,15675.48,15914.23,104200,15914.23 -2006-11-21,15766.43,15817.73,15696.22,15734.14,100200,15734.14 -2006-11-20,16004.34,16036.18,15725.94,15725.94,116200,15725.94 -2006-11-17,16182.31,16238.26,16067.27,16091.73,107000,16091.73 -2006-11-16,16292.48,16367.10,16143.70,16163.87,94400,16163.87 -2006-11-15,16348.74,16373.48,16243.47,16243.47,103200,16243.47 -2006-11-14,16178.81,16318.05,16176.02,16289.55,112800,16289.55 -2006-11-13,16016.42,16067.46,15913.86,16022.49,107600,16022.49 -2006-11-10,16133.91,16280.66,16104.74,16112.43,130000,16112.43 -2006-11-09,16218.86,16286.26,16094.49,16198.57,109400,16198.57 -2006-11-08,16404.05,16423.83,16199.43,16215.74,121600,16215.74 -2006-11-07,16509.79,16512.51,16378.72,16393.41,95800,16393.41 -2006-11-06,16278.78,16398.51,16204.13,16364.76,104200,16364.76 -2006-11-02,16281.95,16350.02,16209.14,16350.02,99000,16350.02 -2006-11-01,16338.72,16444.51,16246.24,16375.26,103800,16375.26 -2006-10-31,16389.45,16477.06,16314.29,16399.39,104400,16399.39 -2006-10-30,16544.50,16549.71,16329.89,16351.85,119000,16351.85 -2006-10-27,16879.33,16879.33,16643.91,16669.07,111800,16669.07 -2006-10-26,16794.41,16863.24,16772.31,16811.60,114400,16811.60 -2006-10-25,16837.80,16849.05,16697.01,16699.30,114600,16699.30 -2006-10-24,16853.73,16901.53,16759.98,16780.47,111400,16780.47 -2006-10-23,16641.32,16797.71,16598.53,16788.82,92400,16788.82 -2006-10-20,16556.09,16663.61,16552.36,16651.63,86400,16651.63 -2006-10-19,16673.26,16688.96,16506.22,16551.36,86400,16551.36 -2006-10-18,16519.91,16666.20,16466.74,16653.00,93600,16653.00 -2006-10-17,16704.86,16704.86,16561.26,16611.59,93600,16611.59 -2006-10-16,16663.22,16732.44,16648.43,16692.76,90200,16692.76 -2006-10-13,16494.49,16586.33,16493.64,16536.54,121600,16536.54 -2006-10-12,16386.37,16495.54,16343.49,16368.81,106400,16368.81 -2006-10-11,16497.27,16595.91,16399.74,16400.57,115400,16400.57 -2006-10-10,16325.48,16620.15,16325.48,16477.25,104400,16477.25 -2006-10-06,16444.71,16457.92,16360.64,16436.06,96800,16436.06 -2006-10-05,16291.79,16481.31,16286.64,16449.33,125800,16449.33 -2006-10-04,16288.92,16363.12,16028.32,16082.55,125000,16082.55 -2006-10-03,16198.55,16260.47,16148.89,16242.09,91000,16242.09 -2006-10-02,16169.00,16329.24,16157.98,16254.29,102600,16254.29 -2006-09-29,16097.08,16127.58,16007.37,16127.58,83400,16127.58 -2006-09-28,15970.39,16032.98,15911.22,16024.85,87000,16024.85 -2006-09-27,15692.98,15947.87,15681.44,15947.87,97600,15947.87 -2006-09-26,15594.48,15666.95,15517.90,15557.45,76400,15557.45 -2006-09-25,15550.56,15691.06,15513.87,15633.81,98200,15633.81 -2006-09-22,15706.85,15735.26,15580.19,15634.67,93000,15634.67 -2006-09-21,15820.11,15859.21,15674.84,15834.23,93400,15834.23 -2006-09-20,15757.97,15763.67,15622.28,15718.67,103000,15718.67 -2006-09-19,15948.47,16096.18,15867.05,15874.28,96600,15874.28 -2006-09-15,15872.29,15907.03,15763.90,15866.93,85400,15866.93 -2006-09-14,15831.72,15994.79,15801.88,15942.39,102000,15942.39 -2006-09-13,15889.50,15965.31,15730.67,15750.05,108600,15750.05 -2006-09-12,15843.80,15882.38,15675.37,15719.34,117000,15719.34 -2006-09-11,16053.13,16053.13,15772.07,15794.38,97800,15794.38 -2006-09-08,15907.97,16156.18,15831.75,16080.46,163000,16080.46 -2006-09-07,16141.94,16141.94,15944.03,16012.41,115600,16012.41 -2006-09-06,16350.27,16400.71,16245.16,16284.09,126000,16284.09 -2006-09-05,16357.29,16403.90,16280.68,16385.96,109400,16385.96 -2006-09-04,16280.18,16414.94,16280.18,16358.07,109000,16358.07 -2006-09-01,16072.81,16158.48,16029.56,16134.25,100200,16134.25 -2006-08-31,15884.61,16207.41,15882.26,16140.76,112200,16140.76 -2006-08-30,15929.90,15962.93,15769.16,15872.02,95600,15872.02 -2006-08-29,15881.92,15946.42,15811.73,15890.56,77400,15890.56 -2006-08-28,15953.08,16005.09,15745.01,15762.59,88000,15762.59 -2006-08-25,15955.76,16156.78,15874.63,15938.66,87000,15938.66 -2006-08-24,16088.54,16089.13,15910.62,15960.62,86800,15960.62 -2006-08-23,16161.82,16226.59,16118.12,16163.03,92600,16163.03 -2006-08-22,15994.99,16244.84,15994.99,16181.17,100400,16181.17 -2006-08-21,16104.50,16145.50,15936.61,15969.04,92000,15969.04 -2006-08-18,16052.58,16169.84,16022.12,16105.98,122400,16105.98 -2006-08-17,16142.56,16204.60,16008.44,16020.84,154600,16020.84 -2006-08-16,15970.60,16085.07,15962.98,16071.36,113400,16071.36 -2006-08-15,15831.69,15913.34,15807.72,15816.19,98400,15816.19 -2006-08-14,15550.96,15857.11,15549.67,15857.11,82800,15857.11 -2006-08-11,15622.24,15681.40,15555.60,15565.02,113600,15565.02 -2006-08-10,15585.09,15690.86,15536.15,15630.91,105800,15630.91 -2006-08-09,15417.02,15659.41,15240.30,15656.59,111400,15656.59 -2006-08-08,15234.39,15476.94,15189.10,15464.66,89200,15464.66 -2006-08-07,15494.47,15516.24,15154.06,15154.06,90000,15154.06 -2006-08-04,15502.56,15555.90,15435.33,15499.18,89200,15499.18 -2006-08-03,15527.27,15580.91,15441.67,15470.37,87000,15470.37 -2006-08-02,15341.53,15466.07,15287.81,15464.29,95600,15464.29 -2006-08-01,15387.52,15522.03,15365.71,15440.91,93000,15440.91 -2006-07-31,15462.39,15536.32,15433.20,15456.81,109400,15456.81 -2006-07-28,15217.44,15351.79,15150.53,15342.87,113000,15342.87 -2006-07-27,14883.50,15220.33,14839.49,15179.78,109600,15179.78 -2006-07-26,15065.57,15108.14,14882.67,14884.07,94600,14884.07 -2006-07-25,14970.60,15078.36,14948.36,15005.24,99400,15005.24 -2006-07-24,14700.58,14851.91,14560.67,14794.50,98400,14794.50 -2006-07-21,14825.16,14867.81,14784.24,14821.26,91200,14821.26 -2006-07-20,14713.56,14962.13,14705.43,14946.84,107000,14946.84 -2006-07-19,14503.83,14625.64,14456.43,14500.26,116200,14500.26 -2006-07-18,14714.18,14747.20,14437.24,14437.24,128000,14437.24 -2006-07-14,14914.01,14997.45,14815.90,14845.24,114200,14845.24 -2006-07-13,15127.74,15370.35,15053.61,15097.95,111800,15097.95 -2006-07-12,15405.42,15463.72,15169.15,15249.32,111400,15249.32 -2006-07-11,15485.26,15498.20,15333.59,15473.82,102000,15473.82 -2006-07-10,15149.91,15555.43,15079.74,15552.81,111200,15552.81 -2006-07-07,15428.32,15437.04,15276.15,15307.61,90400,15307.61 -2006-07-06,15455.18,15460.83,15278.18,15321.40,94600,15321.40 -2006-07-05,15504.17,15584.62,15479.93,15523.94,89600,15523.94 -2006-07-04,15677.04,15710.39,15617.81,15638.50,91000,15638.50 -2006-07-03,15573.35,15617.22,15513.29,15571.62,102600,15571.62 -2006-06-30,15333.10,15521.22,15333.10,15505.18,108800,15505.18 -2006-06-29,14981.70,15137.58,14975.78,15121.15,87600,15121.15 -2006-06-28,14998.01,14998.01,14824.80,14886.11,96400,14886.11 -2006-06-27,15165.63,15207.38,15095.11,15171.81,94000,15171.81 -2006-06-26,15080.23,15216.78,14987.77,15152.40,93200,15152.40 -2006-06-23,15001.77,15126.52,14865.57,15124.04,98200,15124.04 -2006-06-22,14812.17,15138.47,14812.17,15135.69,109000,15135.69 -2006-06-21,14712.86,14713.43,14482.96,14644.26,95000,14644.26 -2006-06-20,14811.11,14845.71,14621.87,14648.41,91800,14648.41 -2006-06-19,14815.86,14918.60,14772.14,14860.35,86400,14860.35 -2006-06-16,14679.35,14976.67,14679.35,14879.34,130200,14879.34 -2006-06-15,14453.33,14593.85,14417.70,14470.76,112600,14470.76 -2006-06-14,14084.52,14458.82,14045.53,14309.56,146000,14309.56 -2006-06-13,14650.59,14658.23,14218.60,14218.60,118600,14218.60 -2006-06-12,14685.46,14845.04,14580.87,14833.01,116000,14833.01 -2006-06-09,14530.50,14825.48,14389.31,14750.84,219200,14750.84 -2006-06-08,14990.04,14990.04,14496.96,14633.03,171400,14633.03 -2006-06-07,15285.05,15433.29,15095.15,15096.01,122200,15096.01 -2006-06-06,15500.92,15507.78,15340.93,15384.86,96200,15384.86 -2006-06-05,15719.31,15784.95,15622.75,15668.31,89600,15668.31 -2006-06-02,15600.28,15789.31,15266.97,15789.31,141200,15789.31 -2006-06-01,15603.25,15655.00,15417.51,15503.74,102600,15503.74 -2006-05-31,15660.87,15660.87,15442.53,15467.33,114400,15467.33 -2006-05-30,15920.79,15937.91,15814.83,15859.45,86400,15859.45 -2006-05-29,16111.54,16111.54,15885.07,15915.68,96800,15915.68 -2006-05-26,15827.87,15970.76,15819.32,15970.76,102000,15970.76 -2006-05-25,15809.33,15849.23,15644.62,15693.75,104600,15693.75 -2006-05-24,15676.64,15907.20,15508.51,15907.20,136200,15907.20 -2006-05-23,15722.05,15776.20,15582.86,15599.20,137200,15599.20 -2006-05-22,16254.56,16268.51,15837.26,15857.87,126400,15857.87 -2006-05-19,16041.18,16166.34,15925.69,16155.45,125000,16155.45 -2006-05-18,16089.25,16139.14,15914.39,16087.18,131800,16087.18 -2006-05-17,16259.02,16319.30,16033.66,16307.67,147800,16307.67 -2006-05-16,16508.89,16596.48,16116.73,16158.42,134600,16158.42 -2006-05-15,16395.88,16486.91,16317.20,16486.91,118800,16486.91 -2006-05-12,16655.98,16655.98,16422.49,16601.78,131600,16601.78 -2006-05-11,16887.37,17087.00,16840.85,16862.14,110200,16862.14 -2006-05-10,17161.47,17253.11,16883.39,16951.93,127600,16951.93 -2006-05-09,17253.81,17294.50,17178.95,17190.91,116600,17190.91 -2006-05-08,17334.19,17375.25,17248.59,17291.67,121000,17291.67 -2006-05-02,16920.13,17188.54,16900.33,17153.77,89200,17153.77 -2006-05-01,16929.83,16965.33,16868.69,16925.71,79600,16925.71 -2006-04-28,17039.37,17043.67,16750.50,16906.23,112400,16906.23 -2006-04-27,17118.92,17176.06,17094.72,17114.54,103600,17114.54 -2006-04-26,16993.23,17107.93,16944.54,17055.93,105200,17055.93 -2006-04-25,16929.36,17000.20,16787.44,16970.29,103400,16970.29 -2006-04-24,17245.62,17245.62,16892.15,16914.40,110600,16914.40 -2006-04-21,17332.35,17479.73,17258.49,17403.96,109000,17403.96 -2006-04-20,17391.94,17412.59,17283.97,17317.53,96200,17317.53 -2006-04-19,17405.92,17459.24,17350.12,17350.12,104600,17350.12 -2006-04-18,16971.76,17268.05,16945.30,17232.86,98400,17232.86 -2006-04-17,17233.73,17233.73,17000.36,17000.36,78200,17000.36 -2006-04-14,17319.33,17319.33,17149.08,17233.82,89600,17233.82 -2006-04-13,17232.28,17303.27,17068.96,17199.15,101200,17199.15 -2006-04-12,17297.18,17325.21,17162.00,17162.55,117400,17162.55 -2006-04-11,17460.68,17489.16,17295.42,17418.13,111600,17418.13 -2006-04-10,17455.03,17489.61,17385.25,17456.58,104000,17456.58 -2006-04-07,17498.88,17563.37,17418.94,17563.37,118000,17563.37 -2006-04-06,17365.57,17489.33,17347.01,17489.33,111400,17489.33 -2006-04-05,17340.14,17464.54,17187.35,17243.98,125800,17243.98 -2006-04-04,17295.58,17410.30,17266.39,17292.91,115400,17292.91 -2006-04-03,17127.61,17387.08,17105.50,17333.31,129600,17333.31 -2006-03-31,17088.76,17094.61,16995.77,17059.66,100600,17059.66 -2006-03-30,17011.13,17125.64,16974.47,17045.34,140400,17045.34 -2006-03-29,16670.38,16976.29,16613.72,16938.41,109000,16938.41 -2006-03-28,16550.47,16690.24,16463.95,16690.24,95600,16690.24 -2006-03-27,16599.92,16711.16,16599.92,16650.10,92600,16650.10 -2006-03-24,16501.50,16612.52,16462.47,16560.87,80800,16560.87 -2006-03-23,16605.48,16661.14,16464.47,16489.37,99000,16489.37 -2006-03-22,16578.50,16583.25,16477.26,16495.48,122600,16495.48 -2006-03-20,16299.35,16667.13,16299.35,16624.80,102200,16624.80 -2006-03-17,16172.74,16339.73,16106.38,16339.73,90600,16339.73 -2006-03-16,16354.71,16356.49,16032.55,16096.21,97400,16096.21 -2006-03-15,16342.52,16367.76,16291.77,16319.04,89600,16319.04 -2006-03-14,16401.11,16410.29,16238.36,16238.36,94600,16238.36 -2006-03-13,16264.59,16379.47,16242.16,16361.51,94800,16361.51 -2006-03-10,16007.41,16264.89,15982.02,16115.63,166800,16115.63 -2006-03-09,15645.30,16049.61,15645.30,16036.91,117800,16036.91 -2006-03-08,15657.79,15720.65,15553.14,15627.49,113400,15627.49 -2006-03-07,15864.57,15864.57,15678.12,15726.02,113000,15726.02 -2006-03-06,15668.63,15901.16,15609.80,15901.16,99800,15901.16 -2006-03-03,15835.43,15897.29,15658.64,15663.34,111200,15663.34 -2006-03-02,16068.76,16106.26,15879.71,15909.76,118200,15909.76 -2006-03-01,16026.82,16053.30,15910.65,15964.46,139200,15964.46 -2006-02-28,16218.62,16229.68,15953.32,16205.43,154400,16205.43 -2006-02-27,16156.15,16290.15,16123.29,16192.95,152600,16192.95 -2006-02-24,16034.67,16118.11,15947.04,16101.91,122800,16101.91 -2006-02-23,15908.87,16096.10,15892.51,16096.10,121400,16096.10 -2006-02-22,15882.64,15923.00,15679.91,15781.78,145600,15781.78 -2006-02-21,15602.83,15894.94,15573.71,15894.94,126800,15894.94 -2006-02-20,15620.58,15661.85,15389.58,15437.93,128800,15437.93 -2006-02-17,16078.51,16129.94,15702.67,15713.45,121600,15713.45 -2006-02-16,15901.38,16109.20,15842.00,16043.67,116200,16043.67 -2006-02-15,16302.94,16312.74,15932.83,15932.83,123200,15932.83 -2006-02-14,15845.19,16184.87,15691.86,16184.87,149200,16184.87 -2006-02-13,16191.93,16191.93,15877.66,15877.66,143800,15877.66 -2006-02-10,16525.50,16525.50,16090.93,16257.83,180200,16257.83 -2006-02-09,16444.74,16540.49,16351.43,16439.67,130800,16439.67 -2006-02-08,16609.96,16682.91,16272.68,16272.68,134400,16272.68 -2006-02-07,16768.16,16769.37,16681.04,16720.99,151400,16720.99 -2006-02-06,16736.23,16777.37,16578.19,16747.76,120200,16747.76 -2006-02-03,16596.21,16665.10,16567.87,16659.64,125000,16659.64 -2006-02-02,16632.60,16736.18,16611.53,16710.55,158600,16710.55 -2006-02-01,16594.90,16671.91,16480.09,16480.09,160400,16480.09 -2006-01-31,16603.90,16718.79,16561.31,16649.82,143200,16649.82 -2006-01-30,16615.91,16754.60,16538.72,16551.23,203400,16551.23 -2006-01-27,16079.94,16460.68,16079.92,16460.68,153800,16460.68 -2006-01-26,15783.70,15891.02,15764.89,15891.02,121800,15891.02 -2006-01-25,15725.76,15849.52,15651.00,15651.00,143800,15651.00 -2006-01-24,15470.91,15685.14,15470.39,15648.89,94600,15648.89 -2006-01-23,15497.61,15564.90,15312.71,15360.65,108400,15360.65 -2006-01-20,15847.17,15875.39,15597.77,15696.69,124000,15696.69 -2006-01-19,15396.60,15740.82,15396.60,15696.28,148000,15696.28 -2006-01-18,15725.64,15725.64,15059.52,15341.18,192400,15341.18 -2006-01-17,16152.07,16324.17,15805.95,15805.95,140200,15805.95 -2006-01-16,16360.04,16387.63,16221.59,16268.03,110000,16268.03 -2006-01-13,16454.32,16490.27,16383.23,16454.95,137400,16454.95 -2006-01-12,16426.69,16472.99,16310.45,16445.19,129800,16445.19 -2006-01-11,16164.92,16363.59,16005.24,16363.59,146200,16363.59 -2006-01-10,16487.05,16487.05,16124.35,16124.35,154600,16124.35 -2006-01-06,16408.31,16479.55,16320.43,16428.21,170400,16428.21 -2006-01-05,16441.27,16474.52,16368.51,16425.37,164600,16425.37 -2006-01-04,16294.65,16361.54,16250.76,16361.54,94200,16361.54 -2005-12-30,16412.75,16413.18,16111.43,16111.43,55600,16111.43 -2005-12-29,16247.54,16445.56,16246.67,16344.20,96200,16344.20 -2005-12-28,15920.67,16194.61,15911.23,16194.61,82000,16194.61 -2005-12-27,16033.94,16079.18,15962.73,15969.40,84400,15969.40 -2005-12-26,16027.66,16108.94,16026.18,16107.67,101800,16107.67 -2005-12-22,15975.99,15991.30,15759.73,15941.37,161800,15941.37 -2005-12-21,15713.07,16010.17,15711.91,15957.57,134800,15957.57 -2005-12-20,15388.71,15647.69,15365.39,15641.26,122200,15641.26 -2005-12-19,15252.15,15391.48,15196.00,15391.48,98200,15391.48 -2005-12-16,15222.00,15365.48,15095.56,15173.07,149000,15173.07 -2005-12-15,15376.27,15469.35,15254.44,15254.44,151400,15254.44 -2005-12-14,15817.93,15885.52,15447.15,15464.58,228800,15464.58 -2005-12-13,15754.31,15782.30,15666.09,15778.86,238400,15778.86 -2005-12-12,15549.65,15764.99,15548.46,15738.70,185600,15738.70 -2005-12-09,15127.80,15447.13,15117.15,15404.05,254400,15404.05 -2005-12-08,15470.65,15523.15,15183.36,15183.36,147800,15183.36 -2005-12-07,15520.34,15558.32,15467.75,15484.66,151200,15484.66 -2005-12-06,15518.67,15572.72,15423.38,15423.38,188600,15423.38 -2005-12-05,15413.52,15563.39,15379.64,15551.31,244600,15551.31 -2005-12-02,15272.62,15421.60,15245.36,15421.60,211800,15421.60 -2005-12-01,14914.75,15130.50,14880.18,15130.50,150800,15130.50 -2005-11-30,14981.34,15013.24,14872.15,14872.15,149000,14872.15 -2005-11-29,14900.64,14995.08,14868.03,14927.70,128200,14927.70 -2005-11-28,14847.58,14986.94,14821.75,14986.94,121400,14986.94 -2005-11-25,14693.87,14784.29,14613.18,14784.29,128000,14784.29 -2005-11-24,14816.71,14866.99,14721.60,14742.58,130400,14742.58 -2005-11-22,14726.04,14763.26,14650.06,14708.32,128400,14708.32 -2005-11-21,14719.28,14808.21,14590.56,14680.43,171000,14680.43 -2005-11-18,14542.78,14633.35,14542.78,14623.12,150800,14623.12 -2005-11-17,14192.78,14448.75,14169.47,14411.79,171600,14411.79 -2005-11-16,14035.74,14170.87,14015.62,14170.87,186800,14170.87 -2005-11-15,14069.87,14142.27,14043.45,14091.77,166600,14091.77 -2005-11-14,14218.72,14218.72,14105.45,14116.04,153600,14116.04 -2005-11-11,14170.33,14206.14,14133.89,14155.06,151200,14155.06 -2005-11-10,14058.29,14121.71,13981.99,14080.88,181400,14080.88 -2005-11-09,13989.31,14136.16,13951.40,14072.20,252400,14072.20 -2005-11-08,14067.78,14071.74,13982.85,14036.73,302000,14036.73 -2005-11-07,14084.11,14097.59,13982.75,14061.60,213800,14061.60 -2005-11-04,14040.63,14099.49,13978.96,14075.96,226800,14075.96 -2005-11-02,13865.10,13927.51,13807.81,13894.78,241000,13894.78 -2005-11-01,13718.21,13867.86,13706.33,13867.86,113800,13867.86 -2005-10-31,13459.99,13606.50,13456.07,13606.50,179000,13606.50 -2005-10-28,13344.93,13373.43,13272.84,13346.54,158200,13346.54 -2005-10-27,13440.72,13501.24,13387.66,13417.08,166000,13417.08 -2005-10-26,13291.46,13406.19,13285.60,13395.02,143400,13395.02 -2005-10-25,13227.92,13336.64,13219.05,13280.62,149200,13280.62 -2005-10-24,13232.41,13244.24,13083.04,13106.18,115800,13106.18 -2005-10-21,13065.96,13243.08,12996.29,13199.95,142800,13199.95 -2005-10-20,13221.91,13264.40,13175.93,13190.46,170400,13190.46 -2005-10-19,13297.65,13304.98,13073.46,13129.49,179200,13129.49 -2005-10-18,13376.19,13441.78,13321.97,13352.24,187600,13352.24 -2005-10-17,13486.18,13510.63,13341.64,13400.29,119400,13400.29 -2005-10-14,13581.32,13581.32,13361.96,13420.54,136400,13420.54 -2005-10-13,13388.02,13475.86,13266.98,13449.24,134600,13449.24 -2005-10-12,13565.87,13704.09,13463.74,13463.74,202200,13463.74 -2005-10-11,13280.33,13556.71,13241.84,13556.71,170600,13556.71 -2005-10-07,13279.30,13332.12,13221.33,13227.74,163000,13227.74 -2005-10-06,13554.56,13554.56,13285.83,13359.51,180200,13359.51 -2005-10-05,13761.81,13783.60,13655.94,13689.89,181200,13689.89 -2005-10-04,13597.38,13738.84,13593.01,13738.84,201600,13738.84 -2005-10-03,13566.20,13584.61,13454.67,13525.28,203400,13525.28 -2005-09-30,13677.45,13678.44,13539.15,13574.30,198400,13574.30 -2005-09-29,13515.73,13617.24,13440.90,13617.24,245800,13617.24 -2005-09-28,13307.53,13487.85,13306.52,13435.91,226600,13435.91 -2005-09-27,13370.09,13373.00,13282.30,13310.04,237400,13310.04 -2005-09-26,13229.27,13392.63,13229.27,13392.63,195000,13392.63 -2005-09-22,13120.89,13170.36,13090.28,13159.36,177800,13159.36 -2005-09-21,13181.71,13235.42,13108.65,13196.57,230600,13196.57 -2005-09-20,12991.63,13159.39,12991.63,13148.57,185200,13148.57 -2005-09-16,12992.18,12992.99,12888.74,12958.68,155200,12958.68 -2005-09-15,12817.78,12986.78,12806.71,12986.78,158800,12986.78 -2005-09-14,12847.62,12871.54,12830.88,12834.25,129000,12834.25 -2005-09-13,12896.22,12940.68,12847.19,12901.95,130600,12901.95 -2005-09-12,12841.02,12926.57,12813.97,12896.43,126200,12896.43 -2005-09-09,12561.84,12692.04,12556.43,12692.04,201400,12692.04 -2005-09-08,12601.02,12601.02,12498.40,12533.89,113600,12533.89 -2005-09-07,12682.85,12682.85,12574.90,12607.59,111400,12607.59 -2005-09-06,12686.68,12730.21,12581.28,12599.43,149200,12599.43 -2005-09-05,12616.30,12655.15,12580.37,12634.88,98800,12634.88 -2005-09-02,12571.88,12600.00,12544.37,12600.00,89800,12600.00 -2005-09-01,12501.43,12573.01,12501.43,12506.97,111200,12506.97 -2005-08-31,12428.60,12443.94,12393.68,12413.60,87200,12413.60 -2005-08-30,12411.41,12457.04,12396.10,12453.14,101000,12453.14 -2005-08-29,12386.76,12386.76,12274.81,12309.83,86400,12309.83 -2005-08-26,12458.08,12482.63,12385.03,12439.48,89800,12439.48 -2005-08-25,12443.21,12466.84,12401.34,12405.16,95800,12405.16 -2005-08-24,12421.53,12515.66,12416.51,12502.26,96200,12502.26 -2005-08-23,12511.81,12612.16,12472.93,12472.93,137600,12472.93 -2005-08-22,12330.70,12478.82,12330.70,12452.51,116200,12452.51 -2005-08-19,12276.80,12291.73,12219.52,12291.73,91000,12291.73 -2005-08-18,12322.80,12369.53,12292.82,12307.37,99800,12307.37 -2005-08-17,12286.83,12369.74,12270.85,12273.12,135000,12273.12 -2005-08-16,12324.76,12336.85,12277.41,12315.67,116600,12315.67 -2005-08-15,12254.53,12308.61,12236.61,12256.55,103600,12256.55 -2005-08-12,12276.24,12324.43,12228.13,12261.68,107800,12261.68 -2005-08-11,12178.08,12284.76,12167.48,12263.32,127400,12263.32 -2005-08-10,11996.29,12138.71,11991.69,12098.08,132800,12098.08 -2005-08-09,11797.33,11958.07,11797.33,11900.32,89800,11900.32 -2005-08-08,11670.71,11794.84,11614.71,11778.98,83800,11778.98 -2005-08-05,11842.16,11863.39,11724.61,11766.48,76600,11766.48 -2005-08-04,11945.14,11945.14,11823.20,11883.31,87600,11883.31 -2005-08-03,11987.98,12009.56,11950.31,11981.80,93600,11981.80 -2005-08-02,11954.23,11982.20,11920.88,11940.20,92800,11940.20 -2005-08-01,11907.42,11972.84,11906.04,11946.92,96200,11946.92 -2005-07-29,11900.56,11913.50,11826.86,11899.60,83800,11899.60 -2005-07-28,11881.86,11889.86,11853.62,11858.31,82000,11858.31 -2005-07-27,11770.57,11848.66,11770.57,11835.08,74400,11835.08 -2005-07-26,11762.69,11772.68,11719.02,11737.96,65600,11737.96 -2005-07-25,11721.70,11782.21,11718.66,11762.65,68000,11762.65 -2005-07-22,11751.92,11753.01,11650.37,11695.05,67000,11695.05 -2005-07-21,11808.53,11867.23,11786.73,11786.73,75800,11786.73 -2005-07-20,11780.73,11816.99,11761.21,11789.35,84800,11789.35 -2005-07-19,11761.61,11770.56,11731.99,11764.84,78800,11764.84 -2005-07-15,11825.67,11828.31,11758.68,11758.68,71000,11758.68 -2005-07-14,11715.46,11784.51,11715.46,11764.26,64600,11764.26 -2005-07-13,11705.83,11707.96,11659.65,11659.84,63000,11659.84 -2005-07-12,11737.32,11738.30,11672.94,11692.14,63200,11692.14 -2005-07-11,11676.97,11713.12,11668.77,11674.79,64200,11674.79 -2005-07-08,11563.84,11653.26,11563.84,11565.99,93000,11565.99 -2005-07-07,11586.12,11602.81,11567.51,11590.14,68200,11590.14 -2005-07-06,11648.04,11676.20,11603.53,11603.53,66800,11603.53 -2005-07-05,11645.23,11658.26,11606.76,11616.70,64800,11616.70 -2005-07-04,11664.22,11664.22,11629.16,11651.55,61200,11651.55 -2005-07-01,11573.37,11663.66,11540.93,11630.13,72000,11630.13 -2005-06-30,11573.78,11589.63,11542.45,11584.01,000,11584.01 -2005-06-29,11567.82,11594.57,11547.13,11577.44,66600,11577.44 -2005-06-28,11421.48,11519.48,11413.84,11513.83,70000,11513.83 -2005-06-27,11445.64,11445.64,11378.99,11414.28,58000,11414.28 -2005-06-24,11480.33,11537.03,11472.61,11537.03,64600,11537.03 -2005-06-23,11539.42,11576.75,11530.78,11576.75,61400,11576.75 -2005-06-22,11487.06,11560.60,11445.43,11547.28,70800,11547.28 -2005-06-21,11474.23,11511.23,11464.25,11488.74,57800,11488.74 -2005-06-20,11539.18,11539.18,11455.23,11483.35,80200,11483.35 -2005-06-17,11472.36,11514.03,11463.36,11514.03,91000,11514.03 -2005-06-16,11419.94,11462.52,11386.01,11416.38,91800,11416.38 -2005-06-15,11365.62,11429.93,11355.85,11415.88,82800,11415.88 -2005-06-14,11348.53,11363.48,11326.51,11335.92,64000,11335.92 -2005-06-13,11308.65,11371.82,11299.78,11311.51,65200,11311.51 -2005-06-10,11192.99,11331.37,11173.93,11304.23,145400,11304.23 -2005-06-09,11289.03,11294.43,11148.36,11160.88,67000,11160.88 -2005-06-08,11235.27,11322.43,11229.86,11281.03,73200,11281.03 -2005-06-07,11233.08,11258.28,11179.13,11217.45,59200,11217.45 -2005-06-06,11232.65,11270.62,11184.60,11270.62,60600,11270.62 -2005-06-03,11302.96,11317.94,11233.65,11300.05,67200,11300.05 -2005-06-02,11341.89,11374.69,11280.05,11280.05,82000,11280.05 -2005-06-01,11220.94,11329.67,11220.55,11329.67,76400,11329.67 -2005-05-31,11273.81,11297.33,11221.46,11276.59,80600,11276.59 -2005-05-30,11201.32,11302.52,11197.79,11266.33,78600,11266.33 -2005-05-27,11098.26,11192.33,11089.23,11192.33,69600,11192.33 -2005-05-26,11024.36,11047.37,10978.85,11027.94,79400,11027.94 -2005-05-25,11127.31,11127.90,10988.37,11014.43,83400,11014.43 -2005-05-24,11184.64,11199.23,11101.93,11133.65,75000,11133.65 -2005-05-23,11073.01,11163.54,11056.86,11158.65,66600,11158.65 -2005-05-20,11104.33,11110.45,11034.82,11037.29,70800,11037.29 -2005-05-19,10973.28,11102.43,10953.08,11077.16,87400,11077.16 -2005-05-18,10848.63,10891.69,10821.41,10835.41,77400,10835.41 -2005-05-17,11046.30,11066.76,10788.59,10825.39,86400,10825.39 -2005-05-16,11045.29,11048.85,10935.53,10947.22,68400,10947.22 -2005-05-13,11044.71,11103.08,11017.79,11049.11,79000,11049.11 -2005-05-12,11118.13,11135.50,11069.69,11077.94,70600,11077.94 -2005-05-11,11091.26,11120.70,11038.26,11120.70,71600,11120.70 -2005-05-10,11193.22,11211.36,11125.00,11159.46,85200,11159.46 -2005-05-09,11199.10,11199.10,11119.48,11171.32,81200,11171.32 -2005-05-06,11119.78,11192.17,11109.33,11192.17,75600,11192.17 -2005-05-02,10954.21,11035.95,10913.97,11002.11,59600,11002.11 -2005-04-28,10979.05,11008.90,10892.71,11008.90,105600,11008.90 -2005-04-27,10968.77,11022.44,10968.58,11005.42,82600,11005.42 -2005-04-26,11085.75,11085.75,11019.94,11035.83,65200,11035.83 -2005-04-25,11064.95,11114.45,11020.59,11073.77,58200,11073.77 -2005-04-22,11116.61,11134.99,11045.95,11045.95,82600,11045.95 -2005-04-21,10950.73,11001.31,10770.58,10984.39,102200,10984.39 -2005-04-20,11173.84,11199.38,11052.38,11088.58,85000,11088.58 -2005-04-19,11019.76,11082.84,10966.46,11065.86,100200,11065.86 -2005-04-18,11223.65,11223.65,10920.66,10938.44,130800,10938.44 -2005-04-15,11463.15,11463.15,11343.73,11370.69,95400,11370.69 -2005-04-14,11578.78,11580.55,11474.82,11563.17,81800,11563.17 -2005-04-13,11688.22,11718.78,11602.94,11637.52,72000,11637.52 -2005-04-12,11739.05,11764.01,11657.66,11670.30,62200,11670.30 -2005-04-11,11847.92,11847.92,11744.86,11745.64,65600,11745.64 -2005-04-08,11867.15,11911.90,11839.66,11874.75,90800,11874.75 -2005-04-07,11848.49,11848.49,11757.87,11810.99,83000,11810.99 -2005-04-06,11783.74,11841.25,11760.71,11827.16,72400,11827.16 -2005-04-05,11695.97,11786.65,11695.97,11774.31,80400,11774.31 -2005-04-04,11666.31,11701.19,11652.66,11667.54,79600,11667.54 -2005-04-01,11590.45,11723.63,11557.13,11723.63,79400,11723.63 -2005-03-31,11623.10,11668.95,11590.72,11668.95,73200,11668.95 -2005-03-30,11548.93,11608.45,11506.85,11565.88,94400,11565.88 -2005-03-29,11809.66,11809.66,11563.12,11599.82,83600,11599.82 -2005-03-28,11709.79,11816.72,11709.79,11792.30,57400,11792.30 -2005-03-25,11788.68,11802.70,11732.80,11761.10,66400,11761.10 -2005-03-24,11741.17,11819.37,11706.27,11745.97,88200,11745.97 -2005-03-23,11823.97,11823.97,11681.16,11739.12,94600,11739.12 -2005-03-22,11867.34,11889.13,11830.96,11841.97,89000,11841.97 -2005-03-18,11792.29,11922.54,11790.96,11879.81,80000,11879.81 -2005-03-17,11785.95,11808.04,11754.98,11775.50,86600,11775.50 -2005-03-16,11822.18,11873.18,11793.03,11873.18,72000,11873.18 -2005-03-15,11899.20,11912.81,11785.16,11821.09,87600,11821.09 -2005-03-14,11947.29,11955.29,11850.25,11850.25,84400,11850.25 -2005-03-11,11838.02,11964.21,11838.02,11923.89,177800,11923.89 -2005-03-10,11892.38,11959.18,11863.54,11864.91,99000,11864.91 -2005-03-09,11882.25,11966.69,11882.25,11966.69,105800,11966.69 -2005-03-08,11936.84,11936.84,11878.89,11886.91,86800,11886.91 -2005-03-07,11935.80,11975.46,11917.77,11925.36,103800,11925.36 -2005-03-04,11815.79,11881.98,11769.67,11873.05,99200,11873.05 -2005-03-03,11790.91,11856.46,11790.91,11856.46,98400,11856.46 -2005-03-02,11804.84,11831.69,11780.61,11813.71,100600,11813.71 -2005-03-01,11734.14,11780.53,11719.77,11780.53,103200,11780.53 -2005-02-28,11742.01,11754.90,11704.32,11740.60,93200,11740.60 -2005-02-25,11585.84,11677.20,11585.46,11658.25,74600,11658.25 -2005-02-24,11513.84,11557.86,11507.20,11531.15,65200,11531.15 -2005-02-23,11510.76,11510.76,11452.42,11500.18,75600,11500.18 -2005-02-22,11636.47,11651.51,11592.04,11597.71,69000,11597.71 -2005-02-21,11682.19,11690.49,11651.02,11651.02,70200,11651.02 -2005-02-18,11562.93,11660.12,11562.93,11660.12,75600,11660.12 -2005-02-17,11583.84,11638.18,11574.06,11582.72,73000,11582.72 -2005-02-16,11629.69,11684.91,11585.46,11601.68,82800,11601.68 -2005-02-15,11648.68,11676.26,11635.57,11646.49,75200,11646.49 -2005-02-14,11644.40,11677.57,11626.42,11632.20,110400,11632.20 -2005-02-10,11434.89,11553.73,11414.99,11553.56,112200,11553.56 -2005-02-09,11519.90,11538.13,11457.96,11473.35,111200,11473.35 -2005-02-08,11504.12,11519.03,11464.34,11490.43,105400,11490.43 -2005-02-07,11393.04,11531.25,11381.78,11499.86,72600,11499.86 -2005-02-04,11381.50,11383.05,11271.04,11360.40,89000,11360.40 -2005-02-03,11430.90,11444.18,11344.41,11389.35,102800,11389.35 -2005-02-02,11432.34,11447.28,11399.62,11407.14,103800,11407.14 -2005-02-01,11422.02,11422.02,11330.06,11384.40,104000,11384.40 -2005-01-31,11296.99,11467.50,11266.09,11387.59,88200,11387.59 -2005-01-28,11334.41,11340.28,11218.88,11320.58,87800,11320.58 -2005-01-27,11390.09,11390.09,11316.30,11341.31,85800,11341.31 -2005-01-26,11346.81,11379.57,11329.42,11376.57,108200,11376.57 -2005-01-25,11261.62,11276.91,11214.60,11276.91,81600,11276.91 -2005-01-24,11213.03,11303.21,11212.63,11289.49,75400,11289.49 -2005-01-21,11226.07,11290.14,11222.24,11238.37,74600,11238.37 -2005-01-20,11335.12,11335.12,11259.27,11284.77,86200,11284.77 -2005-01-19,11467.74,11486.93,11396.43,11405.34,89600,11405.34 -2005-01-18,11504.16,11509.40,11401.32,11423.26,106400,11423.26 -2005-01-17,11475.20,11535.86,11453.86,11487.10,100600,11487.10 -2005-01-14,11341.80,11491.18,11320.49,11438.39,111400,11438.39 -2005-01-13,11398.94,11424.68,11355.05,11358.22,69400,11358.22 -2005-01-12,11537.60,11548.89,11449.49,11453.39,85000,11453.39 -2005-01-11,11495.46,11580.69,11495.46,11539.99,87800,11539.99 -2005-01-07,11528.69,11528.69,11432.19,11433.24,72200,11433.24 -2005-01-06,11372.35,11492.26,11372.21,11492.26,87000,11492.26 -2005-01-05,11458.92,11461.10,11416.97,11437.52,77600,11437.52 -2005-01-04,11458.27,11547.02,11431.57,11517.75,41000,11517.75 -2004-12-30,11462.31,11489.28,11454.94,11488.76,29800,11488.76 -2004-12-29,11481.32,11500.95,11381.56,11381.56,60200,11381.56 -2004-12-28,11314.40,11424.13,11314.40,11424.13,64600,11424.13 -2004-12-27,11374.52,11383.10,11325.46,11362.35,46400,11362.35 -2004-12-24,11302.46,11369.98,11302.46,11365.48,72000,11365.48 -2004-12-22,11205.92,11240.18,11193.67,11209.44,79600,11209.44 -2004-12-21,11125.22,11186.71,11125.22,11125.92,67600,11125.92 -2004-12-20,11073.55,11129.13,11036.80,11103.42,59200,11103.42 -2004-12-17,10939.20,11130.82,10921.81,11078.32,68000,11078.32 -2004-12-16,10909.29,10980.21,10871.69,10924.37,63200,10924.37 -2004-12-15,10952.71,10999.92,10921.65,10956.46,69000,10956.46 -2004-12-14,10842.80,10941.70,10821.36,10915.58,68800,10915.58 -2004-12-13,10825.06,10854.76,10785.59,10789.25,62000,10789.25 -2004-12-10,10730.38,10828.67,10730.38,10756.80,147800,10756.80 -2004-12-09,10930.87,10930.87,10742.73,10776.63,73800,10776.63 -2004-12-08,10808.44,10948.97,10808.44,10941.37,65800,10941.37 -2004-12-07,10971.21,11001.68,10863.81,10873.63,58000,10873.63 -2004-12-06,11021.16,11026.86,10959.49,10981.96,74200,10981.96 -2004-12-03,11064.25,11107.10,11059.56,11074.89,76400,11074.89 -2004-12-02,10922.57,10995.38,10912.87,10973.07,67800,10973.07 -2004-12-01,10790.45,10800.33,10721.59,10784.25,64000,10784.25 -2004-11-30,10909.25,10923.56,10841.27,10899.25,67600,10899.25 -2004-11-29,10844.36,11013.30,10844.31,10977.89,74000,10977.89 -2004-11-26,10924.45,10927.44,10816.38,10833.75,67000,10833.75 -2004-11-25,10853.10,10900.34,10818.24,10900.34,62200,10900.34 -2004-11-24,10832.02,10915.20,10828.11,10872.33,60800,10872.33 -2004-11-22,10956.41,10956.41,10769.52,10849.39,67000,10849.39 -2004-11-19,11120.94,11158.45,11077.09,11082.84,61400,11082.84 -2004-11-18,11182.09,11235.32,11062.73,11082.42,73800,11082.42 -2004-11-17,11132.05,11192.33,11127.20,11131.29,69400,11131.29 -2004-11-16,11234.72,11268.81,11143.56,11161.75,76000,11161.75 -2004-11-15,11079.17,11231.14,11073.77,11227.57,87600,11227.57 -2004-11-12,10841.43,11026.93,10841.43,11019.98,80800,11019.98 -2004-11-11,11021.88,11048.29,10845.07,10846.92,68200,10846.92 -2004-11-10,10972.63,11030.22,10965.91,10994.96,63400,10994.96 -2004-11-09,10967.17,11040.44,10945.10,10964.87,62400,10964.87 -2004-11-08,11095.50,11096.45,10974.33,10983.83,59600,10983.83 -2004-11-05,11040.06,11089.60,11023.16,11061.77,75200,11061.77 -2004-11-04,10990.70,11005.20,10946.27,10946.27,88000,10946.27 -2004-11-02,10775.00,10895.70,10775.00,10887.81,75600,10887.81 -2004-11-01,10731.02,10735.19,10690.95,10734.71,60400,10734.71 -2004-10-29,10805.12,10805.12,10719.10,10771.42,89000,10771.42 -2004-10-28,10809.10,10895.09,10798.13,10853.12,93000,10853.12 -2004-10-27,10740.65,10777.43,10657.15,10691.95,70600,10691.95 -2004-10-26,10652.37,10683.94,10626.60,10672.46,62600,10672.46 -2004-10-25,10718.93,10718.93,10575.23,10659.15,72600,10659.15 -2004-10-22,10848.75,10892.27,10811.15,10857.13,78800,10857.13 -2004-10-21,10882.05,10901.34,10753.07,10789.23,78000,10789.23 -2004-10-20,10992.50,10992.50,10853.89,10882.18,88000,10882.18 -2004-10-19,11028.38,11106.82,11024.38,11064.86,65200,11064.86 -2004-10-18,11022.11,11022.11,10914.47,10965.62,59800,10965.62 -2004-10-15,10960.25,11015.45,10913.21,10982.95,83600,10982.95 -2004-10-14,11150.59,11150.59,11033.31,11034.29,99200,11034.29 -2004-10-13,11235.46,11306.87,11195.99,11195.99,63600,11195.99 -2004-10-12,11295.05,11320.79,11182.50,11201.81,74200,11201.81 -2004-10-08,11311.41,11370.34,11302.75,11349.35,80200,11349.35 -2004-10-07,11399.42,11410.40,11337.19,11354.59,80000,11354.59 -2004-10-06,11221.54,11408.10,11218.38,11385.38,93600,11385.38 -2004-10-05,11257.20,11304.72,11242.12,11281.83,78000,11281.83 -2004-10-04,11111.45,11282.65,11105.00,11279.63,94400,11279.63 -2004-10-01,10893.19,10987.18,10893.19,10985.17,84400,10985.17 -2004-09-30,10870.21,10928.19,10823.57,10823.57,73800,10823.57 -2004-09-29,10873.88,10873.89,10770.23,10786.10,66800,10786.10 -2004-09-28,10805.66,10821.84,10737.78,10815.57,66000,10815.57 -2004-09-27,10863.35,10888.04,10782.56,10859.32,56400,10859.32 -2004-09-24,10934.02,10934.02,10826.40,10895.16,75400,10895.16 -2004-09-22,11111.30,11135.46,10963.82,11019.41,73000,11019.41 -2004-09-21,11148.21,11151.11,11059.95,11080.87,78800,11080.87 -2004-09-17,11132.06,11145.49,11046.10,11082.49,75800,11082.49 -2004-09-16,11092.70,11177.66,11089.82,11139.36,76000,11139.36 -2004-09-15,11278.66,11285.80,11158.58,11158.58,96800,11158.58 -2004-09-14,11312.72,11352.42,11274.43,11295.58,92200,11295.58 -2004-09-13,11139.97,11257.85,11131.03,11253.11,86200,11253.11 -2004-09-10,11089.90,11089.96,10960.03,11083.23,168400,11083.23 -2004-09-09,11276.49,11330.33,11145.79,11170.96,104000,11170.96 -2004-09-08,11345.12,11357.85,11270.53,11279.19,89200,11279.19 -2004-09-07,11275.28,11312.06,11226.78,11298.94,3200,11298.94 -2004-09-06,11086.69,11270.36,11057.32,11244.37,94400,11244.37 -2004-09-03,11182.10,11186.82,11013.36,11022.49,75000,11022.49 -2004-09-02,11179.32,11190.51,11097.81,11152.75,62000,11152.75 -2004-09-01,11104.85,11169.43,11102.41,11127.35,66000,11127.35 -2004-08-31,11119.15,11154.28,11042.29,11081.79,66200,11081.79 -2004-08-30,11181.30,11226.30,11128.71,11184.53,61000,11184.53 -2004-08-27,11148.21,11209.59,11107.94,11209.59,58200,11209.59 -2004-08-26,11196.29,11225.95,11101.63,11129.33,105200,11129.33 -2004-08-25,10959.52,11143.75,10934.45,11130.02,84800,11130.02 -2004-08-24,10978.62,11016.12,10897.11,10985.33,60800,10985.33 -2004-08-23,10961.91,11007.64,10947.75,10960.97,61600,10960.97 -2004-08-20,10859.08,10938.94,10837.01,10889.14,67000,10889.14 -2004-08-19,10861.92,10908.74,10830.65,10903.53,63400,10903.53 -2004-08-18,10724.82,10774.26,10659.21,10774.26,51600,10774.26 -2004-08-17,10772.24,10802.64,10705.74,10725.97,52600,10725.97 -2004-08-16,10728.98,10730.53,10545.89,10687.81,59800,10687.81 -2004-08-13,10901.56,10903.61,10757.20,10757.20,65600,10757.20 -2004-08-12,11005.13,11091.64,11005.13,11028.07,54200,11028.07 -2004-08-11,11049.80,11076.38,10997.07,11049.46,66600,11049.46 -2004-08-10,10849.70,10972.07,10849.70,10953.55,67200,10953.55 -2004-08-09,10827.60,10916.46,10737.42,10908.70,70200,10908.70 -2004-08-06,10944.61,10974.45,10894.65,10972.57,78000,10972.57 -2004-08-05,11060.18,11104.69,10981.32,11060.89,74200,11060.89 -2004-08-04,11077.52,11084.98,10888.78,11010.02,78000,11010.02 -2004-08-03,11230.29,11258.88,11102.50,11140.57,70600,11140.57 -2004-08-02,11274.45,11279.71,11161.84,11222.24,64600,11222.24 -2004-07-30,11211.20,11325.99,11210.32,11325.78,71600,11325.78 -2004-07-29,11187.31,11189.28,11018.79,11116.84,67800,11116.84 -2004-07-28,11133.48,11236.03,11132.92,11204.37,66600,11204.37 -2004-07-27,11126.27,11180.80,11028.35,11031.54,69800,11031.54 -2004-07-26,11099.87,11159.55,11065.72,11159.55,52400,11159.55 -2004-07-23,11263.50,11264.25,11170.54,11187.33,61800,11187.33 -2004-07-22,11310.57,11310.57,11227.95,11285.04,51400,11285.04 -2004-07-21,11335.24,11433.86,11326.68,11433.86,60400,11433.86 -2004-07-20,11318.14,11318.14,11191.76,11258.37,64400,11258.37 -2004-07-16,11327.75,11475.12,11243.28,11436.00,79200,11436.00 -2004-07-15,11413.33,11440.02,11315.97,11409.14,75800,11409.14 -2004-07-14,11663.40,11664.00,11356.65,11356.65,91600,11356.65 -2004-07-13,11544.02,11608.62,11501.22,11608.62,65800,11608.62 -2004-07-12,11532.64,11598.90,11474.08,11582.28,62600,11582.28 -2004-07-09,11283.28,11449.45,11283.08,11423.53,68800,11423.53 -2004-07-08,11372.63,11411.31,11279.55,11322.23,61600,11322.23 -2004-07-07,11359.71,11429.24,11251.35,11384.86,70400,11384.86 -2004-07-06,11536.45,11606.60,11475.27,11475.27,56200,11475.27 -2004-07-05,11622.85,11648.85,11511.49,11541.71,52400,11541.71 -2004-07-02,11781.54,11781.54,11693.00,11721.49,57800,11721.49 -2004-07-01,11933.33,11988.12,11889.70,11896.01,64600,11896.01 -2004-06-30,11869.86,11887.95,11808.13,11858.87,68000,11858.87 -2004-06-29,11816.89,11885.50,11788.15,11860.81,83000,11860.81 -2004-06-28,11801.88,11884.06,11774.67,11884.06,67800,11884.06 -2004-06-25,11742.94,11780.40,11661.11,11780.40,77600,11780.40 -2004-06-24,11652.54,11744.15,11649.29,11744.15,84200,11744.15 -2004-06-23,11642.23,11678.84,11547.13,11580.56,83400,11580.56 -2004-06-22,11546.93,11581.27,11472.08,11581.27,70400,11581.27 -2004-06-21,11474.39,11729.13,11474.39,11600.16,68600,11600.16 -2004-06-18,11552.72,11555.20,11310.16,11382.08,61000,11382.08 -2004-06-17,11630.21,11649.33,11510.18,11607.90,61200,11607.90 -2004-06-16,11492.43,11673.48,11492.43,11641.72,79400,11641.72 -2004-06-15,11457.11,11482.92,11349.43,11387.70,72200,11387.70 -2004-06-14,11495.80,11622.80,11475.31,11491.66,68200,11491.66 -2004-06-11,11595.00,11637.73,11486.55,11526.82,134000,11526.82 -2004-06-10,11378.45,11624.71,11367.40,11575.97,81400,11575.97 -2004-06-09,11514.72,11521.06,11419.13,11449.74,73600,11449.74 -2004-06-08,11533.93,11542.59,11452.99,11521.93,79000,11521.93 -2004-06-07,11212.64,11485.63,11212.64,11439.92,80000,11439.92 -2004-06-04,11057.19,11128.05,11017.25,11128.05,69400,11128.05 -2004-06-03,11275.95,11358.51,10963.56,11027.05,97600,11027.05 -2004-06-02,11283.21,11283.21,11184.73,11242.34,69600,11242.34 -2004-06-01,11204.69,11338.47,11170.09,11296.76,75000,11296.76 -2004-05-31,11288.79,11297.15,11100.85,11236.37,76200,11236.37 -2004-05-28,11267.23,11345.40,11255.99,11309.57,97800,11309.57 -2004-05-27,11163.82,11219.46,11119.15,11166.03,66600,11166.03 -2004-05-26,11095.37,11213.79,11093.83,11152.09,71600,11152.09 -2004-05-25,11071.51,11071.51,10927.44,10962.93,68800,10962.93 -2004-05-24,11094.71,11170.27,11043.22,11101.64,83600,11101.64 -2004-05-21,10889.89,11076.43,10872.01,11070.25,77600,11070.25 -2004-05-20,10949.07,11045.66,10760.69,10862.04,98000,10862.04 -2004-05-19,10777.38,10993.08,10716.23,10967.74,99800,10967.74 -2004-05-18,10533.17,10711.09,10524.50,10711.09,94600,10711.09 -2004-05-17,10790.79,10790.79,10489.84,10505.05,102200,10505.05 -2004-05-14,10846.61,10939.09,10739.49,10849.63,107600,10849.63 -2004-05-13,11081.75,11081.75,10825.10,10825.10,96200,10825.10 -2004-05-12,11017.65,11157.34,10984.79,11153.58,111200,11153.58 -2004-05-11,10850.48,10970.47,10790.13,10907.18,123000,10907.18 -2004-05-10,11384.03,11392.79,10838.93,10884.70,126400,10884.70 -2004-05-07,11497.40,11582.07,11438.82,11438.82,102200,11438.82 -2004-05-06,11777.44,11785.26,11554.02,11571.34,93000,11571.34 -2004-04-30,11862.35,11862.35,11652.17,11761.79,115200,11761.79 -2004-04-28,12077.21,12085.39,11969.33,12004.29,108800,12004.29 -2004-04-27,12115.05,12115.05,12025.21,12044.88,93400,12044.88 -2004-04-26,12135.31,12195.66,12095.70,12163.89,107200,12163.89 -2004-04-23,12050.70,12120.66,12015.22,12120.66,126200,12120.66 -2004-04-22,12026.09,12074.14,11952.78,11980.10,98600,11980.10 -2004-04-21,11943.90,12001.27,11881.42,11944.30,107800,11944.30 -2004-04-20,11821.46,12037.95,11768.08,11952.26,111200,11952.26 -2004-04-19,11854.64,11861.17,11623.65,11764.21,113800,11764.21 -2004-04-16,11817.97,11864.41,11690.24,11824.56,109600,11824.56 -2004-04-15,12118.03,12189.98,11770.40,11800.40,188600,11800.40 -2004-04-14,12064.49,12134.27,12034.46,12098.18,169600,12098.18 -2004-04-13,12140.12,12170.96,12096.96,12127.82,125200,12127.82 -2004-04-12,11926.48,12085.07,11926.48,12042.70,83800,12042.70 -2004-04-09,12012.63,12012.63,11862.34,11897.51,105400,11897.51 -2004-04-08,12013.16,12119.31,11961.56,12092.59,109800,12092.59 -2004-04-07,12017.35,12097.70,12001.00,12019.62,119000,12019.62 -2004-04-06,12042.99,12095.64,11937.52,12079.70,144000,12079.70 -2004-04-05,11949.31,12003.92,11934.58,11958.32,104400,11958.32 -2004-04-02,11726.87,11843.93,11715.41,11815.95,89000,11815.95 -2004-04-01,11756.16,11813.70,11648.48,11683.42,100000,11683.42 -2004-03-31,11716.55,11783.83,11592.83,11715.39,72600,11715.39 -2004-03-30,11824.83,11869.00,11677.20,11693.68,70800,11693.68 -2004-03-29,11775.46,11843.34,11672.92,11718.24,82200,11718.24 -2004-03-26,11619.48,11782.18,11611.54,11770.65,107600,11770.65 -2004-03-25,11431.61,11530.91,11425.58,11530.91,123800,11530.91 -2004-03-24,11295.97,11384.69,11234.70,11364.99,122400,11364.99 -2004-03-23,11200.83,11327.62,11071.66,11281.09,93000,11281.09 -2004-03-22,11332.24,11351.71,11284.84,11318.51,74800,11318.51 -2004-03-19,11416.04,11487.73,11364.36,11418.51,73800,11418.51 -2004-03-18,11571.36,11647.71,11452.39,11484.28,121200,11484.28 -2004-03-17,11297.46,11478.35,11297.46,11436.86,92800,11436.86 -2004-03-16,11253.43,11311.07,11236.35,11242.29,97800,11242.29 -2004-03-15,11284.35,11348.40,11278.05,11317.90,97800,11317.90 -2004-03-12,11163.58,11191.45,11045.94,11162.75,169400,11162.75 -2004-03-11,11310.15,11354.96,11237.04,11297.04,118000,11297.04 -2004-03-10,11490.26,11492.57,11353.90,11433.24,98200,11433.24 -2004-03-09,11460.60,11532.04,11439.04,11532.04,90800,11532.04 -2004-03-08,11578.02,11643.37,11502.86,11502.86,129000,11502.86 -2004-03-05,11476.49,11537.29,11411.66,11537.29,121600,11537.29 -2004-03-04,11341.98,11480.84,11336.97,11401.79,141600,11401.79 -2004-03-03,11365.72,11430.01,11320.00,11351.92,119800,11351.92 -2004-03-02,11344.83,11386.48,11282.49,11361.51,103200,11361.51 -2004-03-01,11112.68,11329.00,11096.68,11271.12,106800,11271.12 -2004-02-27,10852.75,11069.28,10851.77,11041.92,86600,11041.92 -2004-02-26,10734.33,10815.29,10690.95,10815.29,53600,10815.29 -2004-02-25,10626.64,10727.47,10617.86,10658.73,55400,10658.73 -2004-02-24,10821.97,10856.56,10629.72,10644.13,61800,10644.13 -2004-02-23,10745.05,10893.43,10736.44,10868.96,65000,10868.96 -2004-02-20,10743.80,10765.79,10676.21,10720.69,55800,10720.69 -2004-02-19,10745.40,10813.06,10723.43,10753.80,63600,10753.80 -2004-02-18,10759.48,10798.15,10676.81,10676.81,67800,10676.81 -2004-02-17,10556.18,10721.31,10529.26,10701.13,81400,10701.13 -2004-02-16,10566.02,10617.70,10534.41,10548.72,66000,10548.72 -2004-02-13,10436.69,10572.62,10413.06,10557.69,70400,10557.69 -2004-02-12,10450.37,10557.01,10449.70,10459.26,70000,10459.26 -2004-02-10,10418.18,10460.40,10299.43,10365.40,61400,10365.40 -2004-02-09,10533.40,10595.94,10359.17,10402.61,67200,10402.61 -2004-02-06,10484.43,10502.35,10399.40,10460.92,57600,10460.92 -2004-02-05,10377.90,10478.41,10374.90,10464.60,67800,10464.60 -2004-02-04,10614.73,10627.26,10418.77,10447.25,82200,10447.25 -2004-02-03,10787.32,10800.78,10507.93,10641.92,80400,10641.92 -2004-02-02,10784.93,10861.97,10765.38,10776.73,67800,10776.73 -2004-01-30,10761.83,10838.40,10729.38,10783.61,62200,10783.61 -2004-01-29,10755.37,10786.21,10666.55,10779.44,68000,10779.44 -2004-01-28,10844.58,10901.45,10799.54,10852.47,64200,10852.47 -2004-01-27,11049.12,11075.30,10916.51,10928.03,63200,10928.03 -2004-01-26,11004.44,11013.37,10872.79,10972.60,74800,10972.60 -2004-01-23,11001.87,11139.39,10937.48,11069.01,77600,11069.01 -2004-01-22,11060.31,11115.13,10997.45,11000.70,75400,11000.70 -2004-01-21,11056.14,11163.62,11002.39,11002.39,83200,11002.39 -2004-01-20,11055.01,11193.64,10979.25,11103.10,88200,11103.10 -2004-01-19,10937.46,11044.31,10916.99,11036.33,90400,11036.33 -2004-01-16,10719.19,10857.20,10715.25,10857.20,72600,10857.20 -2004-01-15,10855.20,10881.77,10665.15,10665.15,85600,10665.15 -2004-01-14,10797.70,10883.24,10730.45,10863.00,89200,10863.00 -2004-01-13,10965.61,10965.61,10790.41,10849.68,80400,10849.68 -2004-01-09,10932.34,11008.56,10861.28,10965.05,95000,10965.05 -2004-01-08,10760.98,10888.61,10727.80,10837.65,80400,10837.65 -2004-01-07,10835.90,10852.06,10710.30,10757.82,64800,10757.82 -2004-01-06,10918.48,10945.30,10790.60,10813.99,76800,10813.99 -2004-01-05,10787.83,10862.35,10785.87,10825.17,44000,10825.17 -2003-12-30,10617.62,10681.28,10609.58,10676.64,39200,10676.64 -2003-12-29,10454.69,10574.94,10454.69,10500.62,52400,10500.62 -2003-12-26,10367.13,10417.41,10336.08,10417.41,55400,10417.41 -2003-12-25,10347.75,10367.68,10311.60,10365.35,44800,10365.35 -2003-12-24,10397.86,10400.25,10326.17,10371.27,54800,10371.27 -2003-12-22,10248.81,10386.44,10248.62,10372.51,54000,10372.51 -2003-12-19,10215.71,10305.81,10213.21,10284.54,62200,10284.54 -2003-12-18,10096.80,10173.68,10073.26,10104.00,57600,10104.00 -2003-12-17,10276.19,10280.08,10058.34,10092.64,62000,10092.64 -2003-12-16,10352.04,10352.04,10222.88,10271.60,58200,10271.60 -2003-12-15,10308.34,10490.77,10308.34,10490.77,76000,10490.77 -2003-12-12,10139.69,10228.22,10085.85,10169.66,98000,10169.66 -2003-12-11,9972.58,10088.11,9951.34,10075.14,59000,10075.14 -2003-12-10,10053.17,10053.17,9859.00,9910.56,60000,9910.56 -2003-12-09,10107.26,10158.65,10004.71,10124.28,60200,10124.28 -2003-12-08,10281.25,10293.74,10013.59,10045.34,60200,10045.34 -2003-12-05,10406.47,10456.78,10333.64,10373.46,57800,10373.46 -2003-12-04,10341.71,10449.54,10339.89,10429.99,68400,10429.99 -2003-12-03,10412.24,10485.47,10326.39,10326.39,58400,10326.39 -2003-12-02,10452.64,10552.35,10373.95,10410.15,68600,10410.15 -2003-12-01,10006.13,10439.00,9911.92,10403.27,66600,10403.27 -2003-11-28,10144.43,10144.43,10033.47,10100.57,47600,10100.57 -2003-11-27,10155.28,10173.60,10075.23,10163.38,51000,10163.38 -2003-11-26,9965.54,10161.79,9965.54,10144.83,58800,10144.83 -2003-11-25,9976.13,10064.45,9959.51,9960.20,64400,9960.20 -2003-11-21,9804.44,9888.93,9758.34,9852.83,68600,9852.83 -2003-11-20,9722.07,9883.89,9653.76,9865.70,74600,9865.70 -2003-11-19,9804.09,9804.70,9614.60,9614.60,71200,9614.60 -2003-11-18,9790.92,9906.88,9678.78,9897.05,80600,9897.05 -2003-11-17,10077.88,10077.88,9756.50,9786.83,75800,9786.83 -2003-11-14,10338.20,10354.84,10164.12,10167.06,79800,10167.06 -2003-11-13,10345.21,10431.41,10277.54,10337.67,63800,10337.67 -2003-11-12,10252.57,10328.91,10155.64,10226.22,69600,10226.22 -2003-11-11,10407.80,10407.80,10112.10,10207.04,90600,10207.04 -2003-11-10,10592.35,10617.98,10481.07,10504.54,63800,10504.54 -2003-11-07,10583.12,10641.50,10479.25,10628.98,67600,10628.98 -2003-11-06,10825.14,10825.14,10537.13,10552.30,87600,10552.30 -2003-11-05,10816.23,10837.54,10668.39,10837.54,79400,10837.54 -2003-11-04,10693.66,10869.35,10693.66,10847.97,78000,10847.97 -2003-10-31,10708.04,10774.11,10521.40,10559.59,64200,10559.59 -2003-10-30,10702.94,10761.62,10638.89,10695.56,74600,10695.56 -2003-10-29,10653.54,10791.75,10653.54,10739.22,81800,10739.22 -2003-10-28,10490.29,10592.05,10456.85,10561.01,61200,10561.01 -2003-10-27,10360.86,10483.34,10349.76,10454.12,59200,10454.12 -2003-10-24,10402.67,10480.53,10186.77,10335.70,80200,10335.70 -2003-10-23,10754.01,10754.01,10304.29,10335.16,97000,10335.16 -2003-10-22,11060.55,11060.85,10883.77,10889.62,82600,10889.62 -2003-10-21,11234.31,11238.63,10996.54,11031.52,105800,11031.52 -2003-10-20,10988.48,11210.94,10875.27,11161.71,109400,11161.71 -2003-10-17,11057.22,11112.29,10977.90,11037.89,96000,11037.89 -2003-10-16,10917.47,11025.15,10831.76,11025.15,114200,11025.15 -2003-10-15,10997.61,10997.61,10856.42,10899.95,107800,10899.95 -2003-10-14,10873.30,11031.73,10863.06,10966.43,96400,10966.43 -2003-10-10,10569.72,10852.42,10569.72,10786.04,104000,10786.04 -2003-10-09,10550.41,10598.96,10485.60,10531.44,66400,10531.44 -2003-10-08,10757.62,10797.80,10511.42,10542.20,75000,10542.20 -2003-10-07,10761.71,10820.33,10697.83,10820.33,66200,10820.33 -2003-10-06,10813.56,10905.19,10719.91,10740.14,106400,10740.14 -2003-10-03,10618.08,10726.92,10583.51,10709.29,114600,10709.29 -2003-10-02,10476.58,10620.62,10465.89,10593.53,116800,10593.53 -2003-10-01,10232.57,10361.24,10173.54,10361.24,80800,10361.24 -2003-09-30,10294.75,10420.76,10219.05,10219.05,59400,10219.05 -2003-09-29,10303.26,10309.17,10148.36,10229.57,59600,10229.57 -2003-09-26,10217.23,10366.21,10213.75,10318.44,73800,10318.44 -2003-09-25,10350.03,10371.69,10225.48,10310.04,84200,10310.04 -2003-09-24,10526.89,10672.54,10367.17,10502.29,116000,10502.29 -2003-09-22,10858.09,10858.09,10412.20,10475.10,121400,10475.10 -2003-09-19,11123.73,11160.19,10938.42,10938.42,115600,10938.42 -2003-09-18,10936.53,11067.62,10869.69,11033.32,87400,11033.32 -2003-09-17,11008.63,11099.06,10964.99,10990.11,115800,10990.11 -2003-09-16,10786.33,10887.03,10758.33,10887.03,93000,10887.03 -2003-09-12,10656.93,10751.43,10613.70,10712.81,126200,10712.81 -2003-09-11,10742.49,10749.01,10540.28,10546.33,71200,10546.33 -2003-09-10,10872.43,10938.30,10839.21,10856.32,89600,10856.32 -2003-09-09,10766.47,10927.62,10765.04,10922.04,93400,10922.04 -2003-09-08,10584.36,10725.54,10562.78,10683.76,61800,10683.76 -2003-09-05,10700.83,10707.75,10592.93,10650.77,73800,10650.77 -2003-09-04,10751.53,10783.68,10646.95,10646.95,90600,10646.95 -2003-09-03,10782.10,10813.59,10601.48,10715.69,94000,10715.69 -2003-09-02,10668.58,10748.76,10616.61,10690.08,103000,10690.08 -2003-09-01,10399.53,10670.18,10381.98,10670.18,100400,10670.18 -2003-08-29,10315.26,10362.85,10282.51,10343.55,85800,10343.55 -2003-08-28,10326.58,10356.42,10189.80,10225.22,85000,10225.22 -2003-08-27,10349.64,10415.53,10272.96,10308.99,101600,10308.99 -2003-08-26,10208.56,10356.76,10171.17,10332.57,86400,10332.57 -2003-08-25,10264.61,10331.27,10205.25,10276.64,62400,10276.64 -2003-08-22,10374.22,10378.13,10262.27,10281.17,90600,10281.17 -2003-08-21,10245.96,10377.39,10202.72,10362.69,108600,10362.69 -2003-08-20,10201.21,10334.29,10164.42,10292.06,107400,10292.06 -2003-08-19,10143.31,10241.94,10131.21,10174.10,117800,10174.10 -2003-08-18,9933.55,10048.92,9933.55,10032.97,85000,10032.97 -2003-08-15,9945.30,10038.09,9854.27,9863.47,95400,9863.47 -2003-08-14,9730.63,9924.69,9678.99,9913.47,94800,9913.47 -2003-08-13,9637.93,9762.16,9637.93,9752.75,78400,9752.75 -2003-08-12,9547.58,9620.21,9517.14,9564.81,60400,9564.81 -2003-08-11,9349.05,9498.15,9332.47,9487.80,50000,9487.80 -2003-08-08,9256.69,9367.64,9251.73,9327.53,74000,9327.53 -2003-08-07,9324.58,9334.56,9224.05,9265.56,64600,9265.56 -2003-08-06,9296.65,9375.43,9287.39,9323.91,68200,9323.91 -2003-08-05,9456.82,9459.16,9304.71,9382.58,78000,9382.58 -2003-08-04,9538.94,9538.94,9452.79,9452.79,60800,9452.79 -2003-08-01,9646.66,9652.19,9520.14,9611.67,80600,9611.67 -2003-07-31,9616.33,9646.21,9507.39,9563.21,73400,9563.21 -2003-07-30,9811.60,9821.28,9632.66,9632.66,79200,9632.66 -2003-07-29,9895.71,9932.18,9822.72,9834.31,76400,9834.31 -2003-07-28,9750.20,9846.19,9737.15,9839.91,67600,9839.91 -2003-07-25,9652.44,9692.40,9569.87,9648.01,69400,9648.01 -2003-07-24,9635.06,9718.38,9606.10,9671.00,75200,9671.00 -2003-07-23,9574.55,9631.26,9565.68,9615.34,88000,9615.34 -2003-07-22,9501.59,9541.05,9406.49,9485.97,56000,9485.97 -2003-07-18,9468.12,9591.62,9460.28,9527.73,67000,9527.73 -2003-07-17,9659.30,9659.30,9495.99,9498.86,67800,9498.86 -2003-07-16,9806.57,9823.59,9639.31,9735.97,69200,9735.97 -2003-07-15,9839.21,9909.65,9741.39,9751.00,82000,9751.00 -2003-07-14,9713.96,9798.44,9660.54,9755.63,64600,9755.63 -2003-07-11,9849.15,9851.68,9600.96,9635.35,95400,9635.35 -2003-07-10,9959.42,10070.11,9926.04,9955.62,101000,9955.62 -2003-07-09,9894.79,9990.95,9813.29,9990.95,89200,9990.95 -2003-07-08,9899.87,10027.60,9856.04,9898.72,117600,9898.72 -2003-07-07,9589.19,9839.90,9589.19,9795.16,97200,9795.16 -2003-07-04,9530.57,9637.66,9483.01,9547.73,78800,9547.73 -2003-07-03,9702.69,9896.64,9503.14,9624.80,145800,9624.80 -2003-07-02,9353.77,9592.24,9353.77,9592.24,126000,9592.24 -2003-07-01,9097.61,9285.53,9078.74,9278.49,107200,9278.49 -2003-06-30,9119.59,9140.71,9076.62,9083.11,97400,9083.11 -2003-06-27,9014.59,9132.95,9014.59,9104.06,91800,9104.06 -2003-06-26,8931.42,8941.46,8846.75,8923.41,68400,8923.41 -2003-06-25,8899.81,8977.69,8899.81,8932.26,73600,8932.26 -2003-06-24,9060.43,9074.66,8895.82,8919.26,74800,8919.26 -2003-06-23,9112.56,9172.53,9074.37,9137.14,95200,9137.14 -2003-06-20,9034.12,9122.90,9032.29,9120.39,81400,9120.39 -2003-06-19,9118.18,9140.76,9001.95,9110.51,69600,9110.51 -2003-06-18,9089.70,9188.95,9081.31,9092.97,75000,9092.97 -2003-06-17,8944.35,9062.38,8944.35,9033.00,77800,9033.00 -2003-06-16,8923.79,8924.46,8809.47,8839.83,53200,8839.83 -2003-06-13,8941.79,9020.89,8891.18,8980.64,126000,8980.64 -2003-06-12,8979.86,9002.29,8893.31,8918.60,78600,8918.60 -2003-06-11,8834.46,9007.29,8834.46,8890.30,98600,8890.30 -2003-06-10,8752.64,8807.26,8716.62,8789.09,69800,8789.09 -2003-06-09,8790.03,8882.51,8747.67,8822.73,94000,8822.73 -2003-06-06,8685.40,8814.04,8633.30,8785.87,92400,8785.87 -2003-06-05,8651.97,8685.55,8606.95,8657.23,89600,8657.23 -2003-06-04,8617.73,8671.56,8557.86,8557.86,67800,8557.86 -2003-06-03,8547.65,8605.54,8492.24,8564.49,65000,8564.49 -2003-06-02,8490.22,8602.22,8488.89,8547.17,77000,8547.17 -2003-05-30,8389.25,8461.73,8379.76,8424.51,77200,8424.51 -2003-05-29,8275.05,8383.93,8264.39,8375.36,62000,8375.36 -2003-05-28,8216.48,8311.84,8216.48,8234.18,48800,8234.18 -2003-05-27,8195.85,8205.58,8106.90,8120.24,46200,8120.24 -2003-05-26,8192.12,8262.81,8192.12,8227.32,47600,8227.32 -2003-05-23,8120.45,8219.87,8110.30,8184.76,64200,8184.76 -2003-05-22,8008.01,8072.76,7998.27,8051.66,61400,8051.66 -2003-05-21,8060.90,8120.91,7983.08,8018.51,59400,8018.51 -2003-05-20,7986.81,8100.84,7962.37,8059.48,58800,8059.48 -2003-05-19,8091.39,8098.74,7974.17,8039.13,63600,8039.13 -2003-05-16,8127.13,8151.50,8087.24,8117.29,54000,8117.29 -2003-05-15,8217.66,8217.66,8080.53,8123.40,67200,8123.40 -2003-05-14,8210.30,8271.47,8187.94,8244.91,55600,8244.91 -2003-05-13,8253.67,8339.07,8190.26,8190.26,63400,8190.26 -2003-05-12,8193.73,8236.83,8152.38,8221.12,58600,8221.12 -2003-05-09,8083.60,8152.16,8009.37,8152.16,65000,8152.16 -2003-05-08,8072.67,8072.67,8019.33,8031.55,53600,8031.55 -2003-05-07,8126.86,8156.00,8061.81,8109.77,57600,8109.77 -2003-05-06,7995.49,8133.34,7995.49,8083.56,61400,8083.56 -2003-05-02,7862.62,7907.19,7792.20,7907.19,53400,7907.19 -2003-05-01,7804.03,7896.16,7745.69,7863.29,55800,7863.29 -2003-04-30,7694.93,7831.42,7694.93,7831.42,63200,7831.42 -2003-04-28,7679.11,7685.36,7603.76,7607.88,46000,7607.88 -2003-04-25,7806.21,7806.21,7660.62,7699.50,52200,7699.50 -2003-04-24,7844.14,7937.86,7806.13,7854.57,51400,7854.57 -2003-04-23,7829.01,7895.60,7756.75,7793.38,52000,7793.38 -2003-04-22,7946.95,7946.95,7747.86,7790.46,47800,7790.46 -2003-04-21,7889.42,7996.54,7852.95,7969.08,49400,7969.08 -2003-04-18,7866.07,7899.35,7863.92,7874.51,47600,7874.51 -2003-04-17,7828.67,7851.09,7807.96,7821.90,48400,7821.90 -2003-04-16,7898.41,7934.69,7856.94,7879.49,63400,7879.49 -2003-04-15,7805.17,7906.19,7805.17,7838.83,60800,7838.83 -2003-04-14,7830.94,7885.52,7693.46,7752.10,64600,7752.10 -2003-04-11,7960.89,7974.22,7807.99,7816.49,65400,7816.49 -2003-04-10,8028.80,8031.00,7941.05,7980.12,51400,7980.12 -2003-04-09,8091.26,8159.50,8024.81,8057.61,57600,8057.61 -2003-04-08,8200.25,8200.25,8071.39,8131.41,50400,8131.41 -2003-04-07,8123.94,8249.98,8077.46,8249.98,51000,8249.98 -2003-04-04,7999.90,8101.37,7966.39,8074.12,51200,8074.12 -2003-04-03,8160.66,8178.24,7999.12,8017.75,53400,8017.75 -2003-04-02,8052.95,8069.85,7917.54,8069.85,51800,8069.85 -2003-04-01,7907.13,8019.47,7866.67,7986.72,54400,7986.72 -2003-03-31,8240.10,8240.10,7950.96,7972.71,45600,7972.71 -2003-03-28,8360.72,8360.72,8247.98,8280.16,43800,8280.16 -2003-03-27,8351.94,8381.93,8323.74,8368.67,43800,8368.67 -2003-03-26,8257.34,8375.79,8257.34,8351.92,39400,8351.92 -2003-03-25,8351.54,8377.17,8231.95,8238.76,48200,8238.76 -2003-03-24,8300.32,8451.05,8299.64,8435.07,58000,8435.07 -2003-03-20,8127.77,8287.09,8121.91,8195.05,54600,8195.05 -2003-03-19,7956.44,8051.04,7824.82,8051.04,48400,8051.04 -2003-03-18,7975.25,8081.17,7954.46,7954.46,56000,7954.46 -2003-03-17,8010.39,8018.32,7870.78,7871.64,41200,7871.64 -2003-03-14,7912.34,8038.46,7912.34,8002.69,1037455600,8002.69 -2003-03-13,7968.78,8003.18,7868.56,7868.56,408692800,7868.56 -2003-03-12,7908.23,7998.01,7888.31,7943.04,505407600,7943.04 -2003-03-11,7970.86,8062.12,7862.43,7862.43,678628400,7862.43 -2003-03-10,8097.27,8112.87,7975.36,8042.26,539741000,8042.26 -2003-03-07,8296.54,8336.30,8144.12,8144.12,564456800,8144.12 -2003-03-06,8461.71,8509.43,8369.15,8369.15,593320600,8369.15 -2003-03-05,8401.72,8493.61,8370.59,8472.62,569636600,8472.62 -2003-03-04,8474.84,8499.77,8414.51,8480.22,468741800,8480.22 -2003-03-03,8397.15,8490.40,8357.42,8490.40,465136400,8490.40 -2003-02-28,8429.98,8448.78,8332.41,8363.04,496882000,8363.04 -2003-02-27,8344.08,8377.61,8266.97,8359.38,502866000,8359.38 -2003-02-26,8327.46,8429.17,8327.46,8356.81,408184400,8356.81 -2003-02-25,8475.55,8481.23,8324.70,8360.49,495549600,8360.49 -2003-02-24,8503.98,8606.58,8489.03,8564.95,374840800,8564.95 -2003-02-21,8652.68,8685.42,8506.83,8513.54,456682200,8513.54 -2003-02-20,8626.44,8650.92,8575.66,8650.92,441357000,8650.92 -2003-02-19,8756.61,8772.95,8667.17,8678.44,540626400,8678.44 -2003-02-18,8775.38,8794.40,8674.38,8692.97,611585200,8692.97 -2003-02-17,8765.69,8821.31,8731.96,8771.89,628536200,8771.89 -2003-02-14,8627.00,8771.63,8613.73,8701.92,714486200,8701.92 -2003-02-13,8644.85,8672.99,8550.48,8599.66,540752800,8599.66 -2003-02-12,8514.78,8676.53,8514.78,8664.17,658504600,8664.17 -2003-02-10,8427.30,8502.36,8427.30,8484.93,376913800,8484.93 -2003-02-07,8482.74,8517.45,8422.67,8448.16,383372800,8448.16 -2003-02-06,8562.28,8595.23,8451.20,8484.19,484900600,8484.19 -2003-02-05,8425.19,8574.42,8423.93,8549.85,553701000,8549.85 -2003-02-04,8555.73,8579.41,8484.90,8484.90,596242200,8484.90 -2003-02-03,8285.55,8511.87,8253.76,8500.79,506553400,8500.79 -2003-01-31,8291.95,8348.07,8237.03,8339.94,583234200,8339.94 -2003-01-30,8364.90,8407.15,8312.41,8316.81,536095600,8316.81 -2003-01-29,8529.67,8529.67,8304.05,8331.08,540654000,8331.08 -2003-01-28,8531.53,8582.93,8511.14,8525.39,508021200,8525.39 -2003-01-27,8656.50,8690.13,8588.63,8609.47,504887600,8609.47 -2003-01-24,8779.44,8825.67,8701.32,8731.65,773407200,8731.65 -2003-01-23,8648.60,8794.97,8562.19,8790.92,796891800,8790.92 -2003-01-22,8680.57,8708.54,8568.66,8611.04,696631200,8611.04 -2003-01-21,8562.11,8755.35,8528.81,8708.58,641889600,8708.58 -2003-01-20,8639.04,8657.79,8495.00,8558.82,645672800,8558.82 -2003-01-17,8566.81,8732.85,8562.13,8690.25,648807800,8690.25 -2003-01-16,8572.66,8619.84,8536.11,8609.17,591225600,8609.17 -2003-01-15,8564.17,8612.13,8475.04,8611.75,597795400,8611.75 -2003-01-14,8512.82,8569.80,8451.70,8553.06,462942600,8553.06 -2003-01-10,8563.38,8569.85,8378.18,8470.45,495221600,8470.45 -2003-01-09,8440.32,8498.03,8400.59,8497.93,394982400,8497.93 -2003-01-08,8614.41,8614.41,8491.49,8517.80,380133400,8517.80 -2003-01-07,8810.74,8829.06,8654.52,8656.50,480549800,8656.50 -2003-01-06,8669.89,8761.78,8669.89,8713.33,232615000,8713.33 -2002-12-30,8617.65,8617.65,8543.70,8578.95,168062800,8578.95 -2002-12-27,8686.50,8714.05,8630.82,8714.05,326003800,8714.05 -2002-12-26,8575.58,8706.48,8572.72,8700.10,292922400,8700.10 -2002-12-25,8502.11,8527.73,8455.63,8501.14,328678000,8501.14 -2002-12-24,8434.26,8556.58,8389.49,8512.37,510317800,8512.37 -2002-12-20,8408.38,8421.91,8305.80,8406.88,493461400,8406.88 -2002-12-19,8312.30,8411.76,8256.52,8387.57,483763400,8387.57 -2002-12-18,8468.43,8489.53,8310.42,8344.01,437482000,8344.01 -2002-12-17,8525.15,8583.68,8487.20,8510.73,464156000,8510.73 -2002-12-16,8499.09,8570.43,8416.20,8450.94,445362800,8450.94 -2002-12-13,8694.23,8694.23,8496.29,8516.07,885691800,8516.07 -2002-12-12,8742.63,8754.81,8682.98,8708.69,363620600,8708.69 -2002-12-11,8855.87,8876.03,8725.32,8727.66,470391200,8727.66 -2002-12-10,8756.10,8869.26,8753.50,8804.52,481268200,8804.52 -2002-12-09,8836.68,8942.21,8798.56,8828.05,439849200,8828.05 -2002-12-06,8897.67,8907.15,8805.04,8863.26,489670400,8863.26 -2002-12-05,8968.63,9035.42,8907.35,8917.57,492858600,8917.57 -2002-12-04,9126.63,9126.63,8960.62,9006.73,528189000,9006.73 -2002-12-03,9244.17,9320.11,9183.58,9205.11,536443000,9205.11 -2002-12-02,9208.61,9251.82,9112.46,9174.47,477585200,9174.47 -2002-11-29,9171.76,9294.10,9125.35,9215.56,651403400,9215.56 -2002-11-28,8968.49,9185.68,8967.64,9176.78,657135600,9176.78 -2002-11-27,8761.17,8927.04,8761.17,8875.88,472613800,8875.88 -2002-11-26,8943.57,8983.24,8749.88,8823.99,520090600,8823.99 -2002-11-25,8818.40,8956.48,8751.62,8944.44,656192800,8944.44 -2002-11-22,8758.22,8819.60,8715.94,8772.56,682103600,8772.56 -2002-11-21,8537.97,8683.30,8530.93,8668.06,733791400,8668.06 -2002-11-20,8383.56,8533.01,8355.41,8459.62,687147600,8459.62 -2002-11-19,8329.63,8413.59,8246.53,8365.26,650037600,8365.26 -2002-11-18,8477.66,8479.78,8292.35,8346.01,550172000,8346.01 -2002-11-15,8402.26,8517.25,8399.68,8503.59,525206200,8503.59 -2002-11-14,8428.59,8501.36,8303.39,8303.39,517190000,8303.39 -2002-11-13,8505.93,8505.93,8389.36,8438.52,473855800,8438.52 -2002-11-12,8402.56,8526.88,8380.46,8464.77,498522400,8464.77 -2002-11-11,8619.74,8619.74,8430.50,8460.37,459883600,8460.37 -2002-11-08,8824.46,8824.46,8657.18,8690.77,464859000,8690.77 -2002-11-07,8911.67,8955.70,8854.44,8920.44,523936200,8920.44 -2002-11-06,8955.83,9100.68,8914.09,8953.29,523289800,8953.29 -2002-11-05,8790.66,8995.51,8790.57,8937.56,528042800,8937.56 -2002-11-01,8651.67,8698.19,8571.43,8685.72,416409200,8685.72 -2002-10-31,8830.71,8830.71,8576.70,8640.48,483240000,8640.48 -2002-10-30,8631.41,8842.78,8615.30,8756.59,444388200,8756.59 -2002-10-29,8715.74,8785.44,8678.25,8708.76,390968400,8708.76 -2002-10-28,8680.06,8757.51,8557.93,8757.51,366290400,8757.51 -2002-10-25,8612.57,8758.75,8612.57,8726.29,404263000,8726.29 -2002-10-24,8724.70,8735.62,8549.48,8614.30,448206200,8614.30 -2002-10-23,8623.87,8758.67,8499.49,8714.52,515509600,8714.52 -2002-10-22,8969.51,8969.51,8689.39,8689.39,444839200,8689.39 -2002-10-21,9108.51,9116.52,8948.33,8978.41,360508800,8978.41 -2002-10-18,9055.93,9134.80,9055.93,9086.13,475214800,9086.13 -2002-10-17,8894.13,9038.43,8894.13,8959.88,361571000,8959.88 -2002-10-16,8934.07,8974.79,8826.42,8884.87,485844600,8884.87 -2002-10-15,8641.66,8871.44,8641.66,8836.73,466605600,8836.73 -2002-10-11,8512.57,8611.40,8483.49,8529.61,564830200,8529.61 -2002-10-10,8468.03,8487.59,8197.22,8439.62,619958000,8439.62 -2002-10-09,8649.06,8651.66,8498.46,8539.34,538685200,8539.34 -2002-10-08,8712.22,8798.94,8674.48,8708.90,543959400,8708.90 -2002-10-07,8920.74,8920.74,8650.36,8688.00,608972800,8688.00 -2002-10-04,8899.77,9027.55,8860.65,9027.55,621473800,9027.55 -2002-10-03,9057.98,9087.96,8927.57,8936.43,574866000,8936.43 -2002-10-02,9252.29,9293.86,9049.33,9049.33,415330400,9049.33 -2002-10-01,9289.53,9289.53,9143.28,9162.26,442816800,9162.26 -2002-09-30,9421.25,9470.71,9315.25,9383.29,407879400,9383.29 -2002-09-27,9415.74,9572.37,9415.74,9530.44,582292200,9530.44 -2002-09-26,9264.97,9386.96,9264.97,9320.92,415439200,9320.92 -2002-09-25,9212.63,9349.24,9106.45,9165.41,437237000,9165.41 -2002-09-24,9396.42,9396.42,9188.29,9321.64,546891800,9321.64 -2002-09-20,9566.16,9672.82,9448.32,9481.08,478701200,9481.08 -2002-09-19,9606.78,9884.60,9606.78,9669.62,827962000,9669.62 -2002-09-18,9431.88,9521.58,9257.86,9472.06,547574400,9472.06 -2002-09-17,9349.38,9577.42,9349.38,9543.94,486859200,9543.94 -2002-09-13,9298.90,9305.69,9156.79,9241.93,1118312800,9241.93 -2002-09-12,9359.13,9440.54,9251.46,9415.23,398403600,9415.23 -2002-09-11,9384.18,9432.44,9353.18,9400.08,404387600,9400.08 -2002-09-10,9354.89,9455.85,9274.46,9309.31,455690200,9309.31 -2002-09-09,9221.50,9353.44,9221.50,9306.26,417316000,9306.26 -2002-09-06,9108.60,9150.45,8969.26,9129.07,510023400,9129.07 -2002-09-05,9147.66,9290.40,9075.70,9222.12,517238400,9222.12 -2002-09-04,9122.70,9159.06,8995.20,9075.09,624809200,9075.09 -2002-09-03,9449.20,9472.56,9217.04,9217.04,510067400,9217.04 -2002-09-02,9564.90,9565.08,9487.89,9521.63,326847800,9521.63 -2002-08-30,9646.78,9677.57,9524.78,9619.30,366890800,9619.30 -2002-08-29,9681.41,9697.55,9558.68,9620.14,390558800,9620.14 -2002-08-28,9921.08,9953.40,9745.31,9766.73,387014200,9766.73 -2002-08-27,10001.44,10067.25,9899.24,9907.30,384928800,9907.30 -2002-08-26,9811.84,10162.30,9797.04,10067.74,512197600,10067.74 -2002-08-23,9894.80,9979.88,9863.84,9867.45,544396800,9867.45 -2002-08-22,9650.54,9851.89,9551.14,9814.02,529763000,9814.02 -2002-08-21,9540.71,9706.69,9523.86,9642.61,412661600,9642.61 -2002-08-20,9696.43,9743.10,9585.67,9620.69,415972400,9620.69 -2002-08-19,9773.38,9773.38,9499.51,9599.10,383241400,9599.10 -2002-08-16,9859.17,9883.65,9727.88,9788.13,341109400,9788.13 -2002-08-15,9740.20,9851.68,9740.20,9795.57,404492400,9795.57 -2002-08-14,9642.03,9681.84,9618.87,9638.41,355714000,9638.41 -2002-08-13,9671.33,9795.95,9644.14,9688.61,332842800,9688.61 -2002-08-12,9931.82,9931.82,9747.82,9747.82,346130000,9747.82 -2002-08-09,9871.77,10043.30,9856.86,9999.79,531142800,9999.79 -2002-08-08,9844.70,9941.01,9740.43,9799.57,473644200,9799.57 -2002-08-07,9637.24,9875.33,9636.54,9834.40,539977600,9834.40 -2002-08-06,9622.52,9623.16,9439.41,9501.02,630054400,9501.02 -2002-08-05,9637.31,9775.93,9636.92,9704.93,557791200,9704.93 -2002-08-02,9716.71,9791.94,9633.83,9709.66,539051000,9709.66 -2002-08-01,9912.59,9912.59,9738.23,9793.51,493524600,9793.51 -2002-07-31,9964.75,9965.02,9831.59,9877.94,480490400,9877.94 -2002-07-30,9801.09,10013.99,9791.45,10003.72,544350600,10003.72 -2002-07-29,9654.13,9852.80,9636.69,9666.67,498883000,9666.67 -2002-07-26,9868.33,9868.33,9547.85,9591.03,578064000,9591.03 -2002-07-25,10079.98,10166.68,9911.13,9929.91,514695200,9929.91 -2002-07-24,10134.88,10142.90,9901.09,9947.72,538825600,9947.72 -2002-07-23,10102.46,10268.05,10003.81,10215.63,495785200,10215.63 -2002-07-22,10076.30,10295.71,9982.24,10189.01,447048200,10189.01 -2002-07-19,10421.53,10421.53,10174.68,10202.36,435193400,10202.36 -2002-07-18,10366.95,10513.99,10340.31,10498.26,514417200,10498.26 -2002-07-17,10256.39,10328.01,10113.61,10296.02,528231600,10296.02 -2002-07-16,10313.21,10503.04,10250.42,10250.42,503632200,10250.42 -2002-07-15,10548.21,10548.21,10373.29,10375.15,374059000,10375.15 -2002-07-12,10608.63,10694.41,10570.00,10601.45,530861200,10601.45 -2002-07-11,10647.59,10647.59,10457.07,10485.74,455178000,10485.74 -2002-07-10,10865.93,10975.72,10752.66,10752.66,448201800,10752.66 -2002-07-09,10836.19,10960.25,10770.99,10960.25,480981600,10960.25 -2002-07-08,10969.21,11050.69,10760.10,10769.20,558547800,10769.20 -2002-07-05,10701.37,10885.83,10701.37,10826.09,502188000,10826.09 -2002-07-04,10752.34,10791.22,10625.92,10632.81,493688400,10632.81 -2002-07-03,10521.64,10862.69,10495.67,10812.30,594448800,10812.30 -2002-07-02,10516.66,10622.32,10371.26,10622.32,449126600,10622.32 -2002-07-01,10655.00,10677.10,10541.22,10595.44,438658400,10595.44 -2002-06-28,10390.53,10621.84,10366.47,10621.84,489978400,10621.84 -2002-06-27,10182.12,10335.97,10176.18,10261.60,424463800,10261.60 -2002-06-26,10376.29,10376.29,10060.72,10074.56,513651000,10074.56 -2002-06-25,10463.97,10580.49,10404.22,10496.67,522084600,10496.67 -2002-06-24,10255.99,10490.87,10169.07,10471.32,526313200,10471.32 -2002-06-21,10489.78,10489.78,10327.91,10354.35,457947200,10354.35 -2002-06-20,10467.22,10629.44,10325.55,10612.98,601852000,10612.98 -2002-06-19,10757.03,10771.60,10448.70,10476.18,579618400,10476.18 -2002-06-18,10799.43,10884.26,10747.68,10839.93,481418000,10839.93 -2002-06-17,10858.05,10888.04,10577.89,10664.11,564320000,10664.11 -2002-06-14,11121.89,11127.16,10911.07,10920.63,1128034000,10920.63 -2002-06-13,11366.06,11396.28,11132.59,11144.84,464889200,11144.84 -2002-06-12,11392.32,11405.29,11261.93,11327.06,427608000,11327.06 -2002-06-11,11390.41,11514.53,11390.41,11449.44,395610200,11449.44 -2002-06-10,11470.92,11522.04,11370.21,11370.21,387837600,11370.21 -2002-06-07,11467.03,11467.03,11365.61,11438.53,000,11438.53 -2002-06-06,11700.13,11743.89,11540.32,11574.94,000,11574.94 -2002-06-05,11703.82,11769.40,11654.12,11663.87,000,11663.87 -2002-06-04,11854.51,11874.30,11624.39,11653.07,000,11653.07 -2002-06-03,11804.04,11905.16,11796.45,11901.39,000,11901.39 -2002-05-31,11780.49,11911.91,11743.99,11763.70,000,11763.70 -2002-05-30,11804.46,11812.59,11680.58,11770.03,000,11770.03 -2002-05-29,11837.27,11887.73,11796.59,11853.00,000,11853.00 -2002-05-28,11941.97,11950.28,11889.56,11936.08,000,11936.08 -2002-05-27,11975.33,12081.43,11952.68,11976.35,000,11976.35 -2002-05-24,12013.35,12023.42,11842.80,11976.28,000,11976.28 -2002-05-23,12001.28,12019.86,11936.87,11979.85,000,11979.85 -2002-05-22,11767.57,11963.23,11767.00,11961.98,000,11961.98 -2002-05-21,11803.74,11824.73,11765.21,11801.16,000,11801.16 -2002-05-20,11887.80,11942.91,11836.22,11856.54,000,11856.54 -2002-05-17,11820.33,11926.90,11817.65,11847.32,000,11847.32 -2002-05-16,11671.42,11747.35,11579.12,11738.69,000,11738.69 -2002-05-15,11486.06,11693.91,11486.06,11642.97,000,11642.97 -2002-05-14,11451.60,11507.66,11336.81,11356.19,000,11356.19 -2002-05-13,11473.93,11473.93,11309.48,11336.95,000,11336.95 -2002-05-10,11534.73,11587.43,11523.84,11531.11,000,11531.11 -2002-05-09,11633.80,11727.52,11620.52,11633.30,000,11633.30 -2002-05-08,11356.54,11581.41,11356.54,11520.75,000,11520.75 -2002-05-07,11500.13,11508.58,11250.86,11316.04,000,11316.04 -2002-05-02,11609.69,11609.69,11518.57,11551.01,000,11551.01 -2002-05-01,11540.09,11591.49,11528.29,11552.79,000,11552.79 -2002-04-30,11532.57,11548.78,11440.66,11492.54,000,11492.54 -2002-04-26,11681.80,11685.08,11464.59,11541.39,000,11541.39 -2002-04-25,11691.73,11708.01,11583.07,11648.72,000,11648.72 -2002-04-24,11749.32,11808.25,11663.71,11672.88,000,11672.88 -2002-04-23,11633.18,11812.99,11576.71,11736.83,000,11736.83 -2002-04-22,11555.08,11765.05,11555.08,11721.64,000,11721.64 -2002-04-19,11488.50,11525.88,11386.72,11512.01,000,11512.01 -2002-04-18,11499.78,11635.98,11485.09,11575.73,000,11575.73 -2002-04-17,11422.75,11544.83,11403.79,11543.71,000,11543.71 -2002-04-16,11160.91,11346.66,11141.27,11346.66,000,11346.66 -2002-04-15,11013.67,11138.70,10941.81,11137.30,000,11137.30 -2002-04-12,11069.84,11122.77,10896.12,10962.98,000,10962.98 -2002-04-11,11291.38,11320.67,11147.27,11147.27,000,11147.27 -2002-04-10,11089.13,11293.17,11052.70,11218.58,000,11218.58 -2002-04-09,11337.49,11363.20,11113.08,11114.49,000,11114.49 -2002-04-08,11321.28,11430.03,11265.18,11352.89,000,11352.89 -2002-04-05,11366.40,11412.99,11301.95,11335.49,000,11335.49 -2002-04-04,11430.25,11537.13,11336.20,11379.20,000,11379.20 -2002-04-03,11103.72,11476.94,11042.25,11400.71,000,11400.71 -2002-04-02,11142.83,11217.24,11049.85,11204.49,000,11204.49 -2002-04-01,11106.07,11148.50,11007.63,11028.70,000,11028.70 -2002-03-29,11350.35,11389.60,11024.94,11024.94,000,11024.94 -2002-03-28,11313.56,11348.22,11240.99,11333.11,000,11333.11 -2002-03-27,11251.70,11421.01,11190.39,11323.68,000,11323.68 -2002-03-26,11214.25,11524.23,11165.00,11207.92,000,11207.92 -2002-03-25,11339.06,11378.78,11166.92,11261.09,000,11261.09 -2002-03-22,11460.95,11519.68,11326.22,11345.08,000,11345.08 -2002-03-20,11833.97,11833.97,11503.79,11526.78,000,11526.78 -2002-03-19,11597.86,11792.82,11597.86,11792.82,000,11792.82 -2002-03-18,11745.81,11789.46,11477.68,11498.38,000,11498.38 -2002-03-15,11594.87,11709.44,11537.89,11648.01,000,11648.01 -2002-03-14,11471.83,11568.82,11347.25,11568.82,000,11568.82 -2002-03-13,11548.24,11774.18,11415.31,11415.31,000,11415.31 -2002-03-12,11863.71,11912.29,11607.33,11607.33,000,11607.33 -2002-03-11,11941.92,12034.04,11772.86,11919.30,000,11919.30 -2002-03-08,11710.20,12010.25,11634.31,11885.79,000,11885.79 -2002-03-07,11473.63,11690.36,11472.88,11648.34,000,11648.34 -2002-03-06,11375.87,11648.38,11358.53,11358.53,000,11358.53 -2002-03-05,11529.21,11602.75,11348.45,11348.45,000,11348.45 -2002-03-04,10942.50,11450.22,10941.36,11450.22,000,11450.22 -2002-03-01,10641.36,10813.45,10540.31,10812.00,000,10812.00 -2002-02-28,10634.93,10798.67,10587.83,10587.83,000,10587.83 -2002-02-27,10268.87,10573.09,10268.87,10573.09,000,10573.09 -2002-02-26,10405.46,10458.87,10183.52,10202.63,000,10202.63 -2002-02-25,10394.73,10446.28,10289.83,10296.47,000,10296.47 -2002-02-22,10219.85,10418.64,10165.72,10356.78,000,10356.78 -2002-02-21,9913.85,10295.42,9895.45,10295.42,000,10295.42 -2002-02-20,9783.16,9901.24,9773.95,9834.13,000,9834.13 -2002-02-19,10113.69,10129.34,9847.16,9847.16,000,9847.16 -2002-02-18,10021.55,10119.21,9980.89,10093.25,000,10093.25 -2002-02-15,10098.23,10152.00,10025.55,10048.10,000,10048.10 -2002-02-14,10014.18,10235.38,10014.18,10081.09,000,10081.09 -2002-02-13,9901.89,10039.25,9865.75,9968.35,000,9968.35 -2002-02-12,9816.96,9949.73,9816.96,9877.99,000,9877.99 -2002-02-08,9564.75,9753.75,9538.45,9686.06,000,9686.06 -2002-02-07,9481.09,9634.79,9458.70,9583.27,000,9583.27 -2002-02-06,9494.62,9602.52,9420.85,9420.85,000,9420.85 -2002-02-05,9577.17,9683.93,9473.46,9475.60,000,9475.60 -2002-02-04,9808.82,9808.82,9623.99,9631.93,000,9631.93 -2002-02-01,10026.96,10032.25,9735.05,9791.43,000,9791.43 -2002-01-31,9962.35,10012.15,9896.84,9997.80,000,9997.80 -2002-01-30,9921.73,9938.33,9843.12,9919.48,000,9919.48 -2002-01-29,10191.75,10191.75,10026.03,10026.03,000,10026.03 -2002-01-28,10190.28,10303.74,10156.19,10220.85,000,10220.85 -2002-01-25,10133.59,10149.87,10017.48,10144.14,000,10144.14 -2002-01-24,10089.25,10240.39,10012.80,10074.05,000,10074.05 -2002-01-23,10063.92,10154.82,10040.91,10040.91,000,10040.91 -2002-01-22,10225.52,10280.30,10050.98,10050.98,000,10050.98 -2002-01-21,10252.43,10393.56,10169.80,10280.25,000,10280.25 -2002-01-18,10165.16,10296.79,10151.43,10293.32,000,10293.32 -2002-01-17,10184.95,10257.45,10074.45,10128.18,000,10128.18 -2002-01-16,10172.16,10269.03,10096.34,10177.58,000,10177.58 -2002-01-15,10359.44,10359.44,10208.05,10208.05,000,10208.05 -2002-01-11,10536.25,10571.50,10441.59,10441.59,000,10441.59 -2002-01-10,10652.17,10710.48,10494.35,10538.43,000,10538.43 -2002-01-09,10661.25,10747.60,10638.43,10663.98,000,10663.98 -2002-01-08,10841.97,10843.26,10662.25,10695.60,000,10695.60 -2002-01-07,10803.45,10979.92,10803.45,10942.36,000,10942.36 -2002-01-04,10631.00,10871.49,10617.08,10871.49,000,10871.49 -2001-12-28,10498.80,10571.75,10427.62,10542.62,000,10542.62 -2001-12-27,10213.32,10457.61,10176.31,10457.61,000,10457.61 -2001-12-26,10273.05,10300.63,10170.90,10192.57,000,10192.57 -2001-12-25,10359.22,10359.22,10178.87,10254.81,000,10254.81 -2001-12-21,10394.73,10418.59,10253.72,10335.45,000,10335.45 -2001-12-20,10485.80,10501.98,10346.40,10434.52,000,10434.52 -2001-12-19,10393.04,10500.44,10347.18,10471.93,000,10471.93 -2001-12-18,10422.16,10582.07,10330.58,10432.17,000,10432.17 -2001-12-17,10482.40,10484.38,10302.97,10323.35,000,10323.35 -2001-12-14,10465.23,10603.71,10379.59,10511.65,000,10511.65 -2001-12-13,10721.61,10731.81,10433.45,10433.45,000,10433.45 -2001-12-12,10490.07,10821.13,10490.07,10801.52,000,10801.52 -2001-12-11,10523.86,10606.92,10467.61,10473.91,000,10473.91 -2001-12-10,10736.12,10738.39,10571.01,10571.01,000,10571.01 -2001-12-07,10833.30,10918.19,10762.97,10796.89,000,10796.89 -2001-12-06,10830.86,11052.51,10813.79,10857.28,000,10857.28 -2001-12-05,10549.39,10724.64,10523.22,10713.81,000,10713.81 -2001-12-04,10414.94,10478.47,10326.52,10452.65,000,10452.65 -2001-12-03,10694.65,10695.04,10370.62,10370.62,000,10370.62 -2001-11-30,10659.87,10697.90,10550.66,10697.44,000,10697.44 -2001-11-29,10607.45,10668.73,10512.66,10655.96,000,10655.96 -2001-11-28,10862.24,10900.31,10624.81,10624.81,000,10624.81 -2001-11-27,11012.85,11186.75,10948.89,10948.89,000,10948.89 -2001-11-26,10797.12,11067.92,10797.12,11064.30,000,11064.30 -2001-11-22,10617.44,10702.34,10529.21,10696.82,000,10696.82 -2001-11-21,10530.29,10789.18,10490.60,10661.08,000,10661.08 -2001-11-20,10779.58,10779.58,10555.44,10575.62,000,10575.62 -2001-11-19,10643.33,10849.19,10618.69,10727.94,000,10727.94 -2001-11-16,10488.70,10850.48,10454.20,10649.09,000,10649.09 -2001-11-15,10159.38,10489.89,10142.42,10489.89,000,10489.89 -2001-11-14,10120.16,10231.16,10076.59,10086.76,000,10086.76 -2001-11-13,10035.65,10057.74,9955.09,10030.56,000,10030.56 -2001-11-12,10225.59,10260.70,10081.56,10081.56,000,10081.56 -2001-11-09,10412.62,10412.62,10213.01,10215.71,000,10215.71 -2001-11-08,10345.49,10431.79,10269.97,10431.79,000,10431.79 -2001-11-07,10607.35,10632.49,10284.98,10284.98,000,10284.98 -2001-11-06,10518.02,10633.72,10494.89,10633.72,000,10633.72 -2001-11-05,10427.35,10447.54,10345.28,10447.54,000,10447.54 -2001-11-02,10460.61,10538.45,10322.28,10383.78,000,10383.78 -2001-11-01,10430.59,10498.39,10318.17,10347.28,000,10347.28 -2001-10-31,10443.65,10478.51,10366.34,10366.34,000,10366.34 -2001-10-30,10522.82,10538.79,10416.44,10512.82,000,10512.82 -2001-10-29,10779.19,10798.08,10612.31,10612.31,000,10612.31 -2001-10-26,10951.88,11020.50,10774.29,10795.16,000,10795.16 -2001-10-25,10847.10,11052.01,10838.60,10880.10,000,10880.10 -2001-10-24,10811.68,10960.91,10771.63,10802.15,000,10802.15 -2001-10-23,10685.35,10861.56,10649.59,10861.56,000,10861.56 -2001-10-19,10472.44,10595.97,10437.80,10538.79,000,10538.79 -2001-10-18,10654.53,10668.69,10474.85,10474.85,000,10474.85 -2001-10-17,10672.00,10790.03,10563.52,10755.45,000,10755.45 -2001-10-16,10433.90,10694.06,10412.25,10637.82,000,10637.82 -2001-10-15,10545.25,10545.25,10447.99,10452.54,000,10452.54 -2001-10-12,10474.35,10632.35,10421.57,10632.35,000,10632.35 -2001-10-11,10074.51,10347.01,10052.08,10347.01,000,10347.01 -2001-10-10,9995.43,10030.22,9934.00,9964.88,000,9964.88 -2001-10-09,10143.39,10143.39,10011.77,10011.77,000,10011.77 -2001-10-05,10165.45,10261.86,10039.51,10205.87,000,10205.87 -2001-10-04,10038.61,10215.89,10038.61,10205.48,000,10205.48 -2001-10-03,10194.73,10221.82,9924.23,9924.23,000,9924.23 -2001-10-02,9937.81,10136.56,9871.94,10136.56,000,10136.56 -2001-10-01,9766.75,9972.28,9604.09,9972.28,000,9972.28 -2001-09-28,9783.80,9933.69,9737.42,9774.68,000,9774.68 -2001-09-27,9601.07,9727.30,9585.81,9696.53,000,9696.53 -2001-09-26,9687.51,9697.12,9551.73,9641.70,000,9641.70 -2001-09-25,9637.60,9867.86,9593.07,9693.97,000,9693.97 -2001-09-21,9658.19,9658.19,9382.95,9554.99,000,9554.99 -2001-09-20,9837.17,9842.16,9688.12,9785.16,000,9785.16 -2001-09-19,9682.52,10061.10,9681.79,9939.60,000,9939.60 -2001-09-18,9623.98,9945.80,9623.98,9679.88,000,9679.88 -2001-09-17,9881.06,9881.06,9447.76,9504.41,000,9504.41 -2001-09-14,9625.26,10009.45,9580.34,10008.89,000,10008.89 -2001-09-13,9663.93,9682.63,9476.87,9613.09,000,9613.09 -2001-09-12,10140.42,10140.42,9600.84,9610.10,000,9610.10 -2001-09-11,10244.55,10344.58,10207.03,10292.95,000,10292.95 -2001-09-10,10395.10,10457.09,10195.69,10195.69,000,10195.69 -2001-09-07,10541.86,10566.65,10405.80,10516.79,000,10516.79 -2001-09-06,10575.26,10812.89,10509.68,10650.33,000,10650.33 -2001-09-05,10679.53,10679.53,10452.98,10598.79,000,10598.79 -2001-09-04,10413.71,10772.59,10325.83,10772.59,000,10772.59 -2001-09-03,10729.60,10758.90,10409.68,10409.68,000,10409.68 -2001-08-31,10811.37,10860.70,10684.16,10713.51,000,10713.51 -2001-08-30,10918.54,10969.06,10807.75,10938.45,000,10938.45 -2001-08-29,11087.15,11142.31,10973.27,10979.76,000,10979.76 -2001-08-28,11255.68,11267.95,11049.86,11189.40,000,11189.40 -2001-08-27,11273.96,11366.18,11273.96,11275.01,000,11275.01 -2001-08-24,11190.54,11230.14,11075.42,11166.31,000,11166.31 -2001-08-23,11414.99,11414.99,11104.18,11126.92,000,11126.92 -2001-08-22,11220.25,11504.06,11202.67,11396.43,000,11396.43 -2001-08-21,11317.13,11370.61,11159.27,11280.38,000,11280.38 -2001-08-20,11347.24,11358.09,11239.45,11257.94,000,11257.94 -2001-08-17,11537.69,11581.25,11412.36,11445.54,000,11445.54 -2001-08-16,11645.30,11645.30,11450.77,11515.02,000,11515.02 -2001-08-15,11812.00,11823.92,11648.86,11755.40,000,11755.40 -2001-08-14,11587.04,11936.75,11587.04,11917.95,000,11917.95 -2001-08-13,11697.12,11697.12,11417.70,11477.56,000,11477.56 -2001-08-10,11683.22,11870.91,11683.22,11735.06,000,11735.06 -2001-08-09,12036.99,12043.05,11754.56,11754.56,000,11754.56 -2001-08-08,12265.24,12293.39,12129.37,12163.67,000,12163.67 -2001-08-07,12154.72,12388.61,12079.55,12319.46,000,12319.46 -2001-08-06,12170.11,12327.23,12095.11,12243.90,000,12243.90 -2001-08-03,12336.51,12365.88,12241.27,12241.97,000,12241.97 -2001-08-02,12072.11,12407.37,12060.50,12399.20,000,12399.20 -2001-08-01,11920.64,11972.25,11817.76,11959.33,000,11959.33 -2001-07-31,11656.65,11877.84,11656.65,11860.77,000,11860.77 -2001-07-30,11846.00,11868.14,11539.16,11579.27,000,11579.27 -2001-07-27,11862.41,11948.20,11706.47,11798.08,000,11798.08 -2001-07-26,11914.34,11962.73,11822.77,11858.56,000,11858.56 -2001-07-25,11823.10,12054.30,11760.97,11891.61,000,11891.61 -2001-07-24,11608.86,11883.25,11562.38,11883.25,000,11883.25 -2001-07-23,11902.23,11902.23,11531.68,11609.63,000,11609.63 -2001-07-19,11898.11,11980.25,11863.12,11908.39,000,11908.39 -2001-07-18,12121.41,12135.31,11847.73,11892.58,000,11892.58 -2001-07-17,12215.47,12224.71,12102.94,12128.57,000,12128.57 -2001-07-16,12408.39,12408.39,12263.45,12343.37,000,12343.37 -2001-07-13,12417.56,12444.56,12294.04,12355.15,000,12355.15 -2001-07-12,12133.05,12407.95,12133.05,12407.95,000,12407.95 -2001-07-11,12178.25,12178.25,12005.11,12005.11,000,12005.11 -2001-07-10,12247.94,12382.29,12143.94,12300.41,000,12300.41 -2001-07-09,12191.31,12239.68,12029.20,12239.68,000,12239.68 -2001-07-06,12499.30,12499.30,12289.61,12306.08,000,12306.08 -2001-07-05,12563.44,12676.83,12515.51,12607.30,000,12607.30 -2001-07-04,12801.46,12801.46,12584.99,12629.02,000,12629.02 -2001-07-03,12855.50,12922.15,12747.05,12817.41,000,12817.41 -2001-07-02,12929.66,12929.66,12629.51,12751.18,000,12751.18 -2001-06-29,12843.95,12985.21,12819.46,12969.05,000,12969.05 -2001-06-28,12853.65,12876.56,12567.26,12679.88,000,12679.88 -2001-06-27,12936.52,12987.85,12828.98,12828.98,000,12828.98 -2001-06-26,12856.15,13026.80,12837.80,12978.82,000,12978.82 -2001-06-25,13052.96,13073.49,12823.45,12896.47,000,12896.47 -2001-06-22,13041.89,13079.11,12940.58,13044.61,000,13044.61 -2001-06-21,12776.76,13005.46,12727.55,12962.43,000,12962.43 -2001-06-20,12575.35,12762.09,12512.13,12674.64,000,12674.64 -2001-06-19,12734.13,12912.92,12511.66,12574.26,000,12574.26 -2001-06-18,12766.38,12787.23,12656.58,12697.79,000,12697.79 -2001-06-15,12722.38,12797.87,12578.78,12790.38,000,12790.38 -2001-06-14,12826.18,12935.07,12804.03,12846.66,000,12846.66 -2001-06-13,12883.51,12970.12,12803.42,12823.45,000,12823.45 -2001-06-12,13111.64,13164.19,12840.10,12840.10,000,12840.10 -2001-06-11,13413.10,13447.39,13224.99,13226.48,000,13226.48 -2001-06-08,13324.25,13510.70,13320.37,13430.22,000,13430.22 -2001-06-07,13122.58,13300.50,13050.17,13277.51,000,13277.51 -2001-06-06,13289.59,13313.14,13127.62,13174.84,000,13174.84 -2001-06-05,13232.52,13256.40,12984.07,13182.00,000,13182.00 -2001-06-04,13294.21,13312.35,13213.65,13312.35,000,13312.35 -2001-06-01,13365.08,13394.40,13244.90,13261.84,000,13261.84 -2001-05-31,13394.75,13419.94,13216.57,13262.14,000,13262.14 -2001-05-30,13680.77,13680.77,13468.73,13493.35,000,13493.35 -2001-05-29,13697.61,13836.40,13697.61,13773.89,000,13773.89 -2001-05-28,13732.10,13820.42,13701.83,13737.77,000,13737.77 -2001-05-25,13869.53,13958.35,13758.66,13765.92,000,13765.92 -2001-05-24,13914.32,13941.44,13801.46,13895.79,000,13895.79 -2001-05-23,14012.19,14205.09,13990.32,14067.70,000,14067.70 -2001-05-22,14271.70,14345.42,14091.19,14091.19,000,14091.19 -2001-05-21,13938.78,14214.21,13938.78,14176.83,000,14176.83 -2001-05-18,13931.62,14067.73,13877.77,13877.77,000,13877.77 -2001-05-17,13845.49,13975.12,13725.25,13910.67,000,13910.67 -2001-05-16,14050.63,14050.63,13694.27,13694.27,000,13694.27 -2001-05-15,13829.30,14103.06,13806.05,14054.03,000,14054.03 -2001-05-14,14041.79,14041.79,13828.70,13873.02,000,13873.02 -2001-05-11,14055.09,14178.32,14043.92,14043.92,000,14043.92 -2001-05-10,14035.50,14197.09,14015.70,14017.79,000,14017.79 -2001-05-09,14235.30,14235.30,13957.81,14084.85,000,14084.85 -2001-05-08,14420.17,14420.17,14227.37,14289.05,000,14289.05 -2001-05-07,14384.14,14556.11,14184.85,14529.41,000,14529.41 -2001-05-02,14441.39,14444.84,14296.54,14421.64,000,14421.64 -2001-05-01,14096.32,14425.46,14096.32,14425.46,000,14425.46 -2001-04-27,14036.26,14065.48,13795.05,13934.32,000,13934.32 -2001-04-26,13968.93,14084.55,13957.63,13973.03,000,13973.03 -2001-04-25,13799.29,13920.67,13769.58,13827.50,000,13827.50 -2001-04-24,13628.10,13762.95,13403.27,13743.18,000,13743.18 -2001-04-23,13837.19,14051.97,13639.11,13715.60,000,13715.60 -2001-04-20,13855.03,13999.58,13686.66,13765.67,000,13765.67 -2001-04-19,13789.47,14099.49,13789.47,13868.28,000,13868.28 -2001-04-18,13170.09,13705.86,13170.09,13641.79,000,13641.79 -2001-04-17,13179.33,13203.61,13019.60,13067.09,000,13067.09 -2001-04-16,13338.92,13451.02,13217.64,13254.89,000,13254.89 -2001-04-13,13454.87,13578.64,13291.20,13385.72,000,13385.72 -2001-04-12,13205.06,13452.60,13126.21,13352.44,000,13352.44 -2001-04-11,12784.64,13208.65,12724.47,13174.93,000,13174.93 -2001-04-10,12847.89,12893.85,12579.56,12620.27,000,12620.27 -2001-04-09,13304.36,13304.36,12841.76,12841.76,000,12841.76 -2001-04-06,13517.70,13674.58,13284.79,13383.76,000,13383.76 -2001-04-05,13344.20,13555.46,13323.16,13381.38,000,13381.38 -2001-04-04,13043.18,13242.78,12874.76,13242.78,000,13242.78 -2001-04-03,12970.67,13357.96,12970.67,13124.47,000,13124.47 -2001-04-02,13057.65,13089.47,12781.34,12937.86,000,12937.86 -2001-03-30,13203.00,13457.90,12992.45,12999.70,000,12999.70 -2001-03-29,13620.07,13620.07,13072.36,13072.36,000,13072.36 -2001-03-28,13726.48,13867.58,13567.71,13765.51,000,13765.51 -2001-03-27,13766.90,13829.47,13536.53,13638.33,000,13638.33 -2001-03-26,13309.72,13862.31,13296.98,13862.31,000,13862.31 -2001-03-23,12866.02,13242.72,12866.02,13214.54,000,13214.54 -2001-03-22,12982.53,13237.33,12853.97,12853.97,000,12853.97 -2001-03-21,12184.32,13103.94,12100.97,13103.94,000,13103.94 -2001-03-19,12183.98,12544.68,12143.67,12190.97,000,12190.97 -2001-03-16,12169.65,12374.45,12071.49,12232.98,000,12232.98 -2001-03-15,11685.64,12152.83,11433.88,12152.83,000,12152.83 -2001-03-14,11912.61,12004.38,11793.27,11843.59,000,11843.59 -2001-03-13,12044.78,12044.78,11710.33,11819.70,000,11819.70 -2001-03-12,12509.67,12509.67,12171.37,12171.37,000,12171.37 -2001-03-09,12549.19,12667.21,12500.51,12627.90,000,12627.90 -2001-03-08,12694.22,12756.97,12584.10,12650.56,000,12650.56 -2001-03-07,12748.56,12824.19,12539.75,12723.89,000,12723.89 -2001-03-06,12402.89,12687.74,12351.14,12687.74,000,12687.74 -2001-03-05,12285.46,12389.09,12133.90,12322.16,000,12322.16 -2001-03-02,12594.46,12594.46,12261.80,12261.80,000,12261.80 -2001-03-01,12811.52,12844.35,12528.50,12681.66,000,12681.66 -2001-02-28,12987.50,13040.31,12784.17,12883.54,000,12883.54 -2001-02-27,13232.86,13262.22,13041.33,13059.86,000,13059.86 -2001-02-26,13255.29,13315.86,13170.99,13201.14,000,13201.14 -2001-02-23,13054.46,13272.81,13048.54,13246.00,000,13246.00 -2001-02-22,13041.72,13125.34,12861.33,13073.36,000,13073.36 -2001-02-21,13181.50,13185.23,13084.55,13100.08,000,13100.08 -2001-02-20,13092.36,13248.36,13073.24,13248.36,000,13248.36 -2001-02-19,13060.20,13137.10,12950.74,13119.59,000,13119.59 -2001-02-16,13348.72,13349.08,13166.46,13175.49,000,13175.49 -2001-02-15,13273.91,13416.55,13273.67,13327.39,000,13327.39 -2001-02-14,13179.27,13405.52,13119.34,13284.06,000,13284.06 -2001-02-13,13431.72,13461.11,13247.95,13274.70,000,13274.70 -2001-02-09,13140.61,13460.39,13135.02,13422.83,000,13422.83 -2001-02-08,13336.34,13336.34,12966.83,13138.23,000,13138.23 -2001-02-07,13273.93,13373.78,13268.61,13366.01,000,13366.01 -2001-02-06,13316.25,13379.44,13240.37,13269.85,000,13269.85 -2001-02-05,13588.64,13588.64,13367.91,13385.52,000,13385.52 -2001-02-02,13764.69,13862.29,13703.63,13703.63,000,13703.63 -2001-02-01,13740.92,13779.55,13667.93,13779.55,000,13779.55 -2001-01-31,13855.74,13855.74,13726.51,13843.55,000,13843.55 -2001-01-30,13885.27,13910.71,13713.55,13826.65,000,13826.65 -2001-01-29,13724.26,13908.40,13721.86,13845.28,000,13845.28 -2001-01-26,13726.98,13750.23,13626.05,13696.06,000,13696.06 -2001-01-25,13879.83,13879.83,13730.17,13803.38,000,13803.38 -2001-01-24,14020.61,14034.11,13857.83,13893.58,000,13893.58 -2001-01-23,13966.64,14060.23,13913.10,13984.66,000,13984.66 -2001-01-22,14010.07,14039.40,13841.03,14032.42,000,14032.42 -2001-01-19,13956.34,14186.62,13947.92,13989.12,000,13989.12 -2001-01-18,13734.79,13931.91,13723.21,13873.92,000,13873.92 -2001-01-17,13593.83,13688.90,13476.55,13667.63,000,13667.63 -2001-01-16,13561.73,13598.20,13442.09,13584.45,000,13584.45 -2001-01-15,13450.28,13573.55,13441.52,13506.23,000,13506.23 -2001-01-12,13246.20,13451.95,13246.20,13347.74,000,13347.74 -2001-01-11,13433.09,13436.61,13123.81,13201.07,000,13201.07 -2001-01-10,13593.16,13593.16,13349.15,13432.65,000,13432.65 -2001-01-09,13732.85,13732.85,13460.82,13610.51,000,13610.51 -2001-01-05,13763.22,13947.06,13725.46,13867.61,000,13867.61 -2001-01-04,13898.09,13990.57,13667.68,13691.49,000,13691.49 -2000-12-29,13899.49,13966.82,13781.12,13785.69,000,13785.69 -2000-12-28,13966.95,13990.27,13866.18,13946.96,000,13946.96 -2000-12-27,13935.26,13981.49,13797.74,13981.49,000,13981.49 -2000-12-26,13878.52,14019.73,13794.43,14007.85,000,14007.85 -2000-12-22,13469.99,13517.23,13338.11,13427.08,000,13427.08 -2000-12-21,13768.03,13780.71,13182.51,13423.21,000,13423.21 -2000-12-20,14052.62,14082.64,13801.98,13914.43,000,13914.43 -2000-12-19,14461.64,14461.64,14132.37,14132.37,000,14132.37 -2000-12-18,14462.35,14566.21,14384.60,14483.90,000,14483.90 -2000-12-15,14832.39,14832.39,14552.29,14552.29,000,14552.29 -2000-12-14,15097.00,15117.69,14883.35,14927.19,000,14927.19 -2000-12-13,15086.25,15273.40,14989.85,15168.68,000,15168.68 -2000-12-12,15097.29,15270.89,15071.70,15114.64,000,15114.64 -2000-12-11,14775.93,15051.34,14775.93,15015.70,000,15015.70 -2000-12-08,14663.86,14769.44,14622.83,14696.51,000,14696.51 -2000-12-07,14825.62,14834.42,14720.36,14720.36,000,14720.36 -2000-12-06,14842.95,15109.64,14842.95,14889.37,000,14889.37 -2000-12-05,15068.97,15068.97,14695.05,14695.05,000,14695.05 -2000-12-04,14922.67,15067.19,14899.09,14954.73,000,14954.73 -2000-12-01,14600.53,14984.37,14596.39,14835.33,000,14835.33 -2000-11-30,14449.74,14683.50,14385.16,14648.51,000,14648.51 -2000-11-29,14606.36,14606.36,14438.56,14507.64,000,14507.64 -2000-11-28,14664.88,14788.41,14573.27,14658.87,000,14658.87 -2000-11-27,14422.25,14746.88,14412.43,14720.39,000,14720.39 -2000-11-24,14247.31,14430.11,14229.65,14315.35,000,14315.35 -2000-11-22,14420.04,14464.00,14172.64,14301.31,000,14301.31 -2000-11-21,14413.13,14414.59,14211.03,14408.46,000,14408.46 -2000-11-20,14510.39,14577.73,14450.63,14531.65,000,14531.65 -2000-11-17,14510.22,14601.17,14420.36,14544.30,000,14544.30 -2000-11-16,14852.24,14857.48,14551.66,14587.03,000,14587.03 -2000-11-15,14812.39,14958.33,14769.26,14799.14,000,14799.14 -2000-11-14,14680.54,14685.02,14549.73,14660.04,000,14660.04 -2000-11-13,14824.71,14824.71,14461.16,14664.64,000,14664.64 -2000-11-10,14952.18,15015.19,14873.52,14988.54,000,14988.54 -2000-11-09,15270.16,15270.16,14997.91,15060.05,000,15060.05 -2000-11-08,15256.16,15602.39,15219.11,15399.64,000,15399.64 -2000-11-07,15356.94,15422.15,15259.78,15340.33,000,15340.33 -2000-11-06,14904.29,15371.44,14887.36,15371.44,000,15371.44 -2000-11-02,14857.36,14961.69,14767.96,14837.78,000,14837.78 -2000-11-01,14557.45,14888.03,14557.45,14872.39,000,14872.39 -2000-10-31,14475.98,14566.05,14333.16,14539.60,000,14539.60 -2000-10-30,14607.02,14715.66,14425.22,14464.56,000,14464.56 -2000-10-27,14852.79,14989.41,14582.20,14582.20,000,14582.20 -2000-10-26,14787.38,14858.43,14577.20,14858.43,000,14858.43 -2000-10-25,15108.46,15108.46,14840.47,14840.47,000,14840.47 -2000-10-24,15100.08,15229.46,15066.60,15148.19,000,15148.19 -2000-10-23,15197.93,15224.81,15035.24,15097.96,000,15097.96 -2000-10-20,14842.81,15314.97,14842.81,15198.73,000,15198.73 -2000-10-19,14901.11,15027.13,14707.88,14811.08,000,14811.08 -2000-10-18,15324.35,15324.35,14832.97,14872.48,000,14872.48 -2000-10-17,15526.99,15545.06,15340.22,15340.22,000,15340.22 -2000-10-16,15366.81,15688.17,15366.81,15512.32,000,15512.32 -2000-10-13,15516.15,15516.15,15101.64,15330.31,000,15330.31 -2000-10-12,15491.80,15580.32,15392.74,15550.64,000,15550.64 -2000-10-11,15795.15,15795.15,15424.71,15513.57,000,15513.57 -2000-10-10,15958.12,15958.12,15792.36,15827.72,000,15827.72 -2000-10-06,16084.05,16084.05,15884.65,15994.24,000,15994.24 -2000-10-05,16157.20,16192.78,16052.12,16099.26,000,16099.26 -2000-10-04,15906.18,16153.67,15808.66,16149.08,000,16149.08 -2000-10-03,15905.25,15956.45,15779.54,15912.09,000,15912.09 -2000-10-02,15735.71,15902.51,15514.04,15902.51,000,15902.51 -2000-09-29,15663.71,15898.07,15663.71,15747.26,000,15747.26 -2000-09-28,15642.84,15888.35,15625.87,15626.96,000,15626.96 -2000-09-27,15907.19,15907.19,15621.88,15639.95,000,15639.95 -2000-09-26,15992.86,16038.07,15905.37,15928.62,000,15928.62 -2000-09-25,15850.56,16144.19,15850.56,15992.90,000,15992.90 -2000-09-22,16268.94,16270.42,15785.63,15818.25,000,15818.25 -2000-09-21,16422.49,16460.49,16290.79,16311.05,000,16311.05 -2000-09-20,16146.04,16523.27,16146.04,16458.31,000,16458.31 -2000-09-19,16013.33,16124.19,15774.72,16124.19,000,16124.19 -2000-09-18,16174.92,16174.92,15965.71,16061.16,000,16061.16 -2000-09-14,16208.33,16311.04,16144.11,16213.28,000,16213.28 -2000-09-13,16080.57,16306.40,16080.57,16190.52,000,16190.52 -2000-09-12,16111.97,16133.19,15885.32,16040.23,000,16040.23 -2000-09-11,16467.69,16477.53,16089.00,16130.90,000,16130.90 -2000-09-08,16370.23,16540.92,16239.26,16501.55,000,16501.55 -2000-09-07,16394.39,16397.10,16243.18,16300.46,000,16300.46 -2000-09-06,16433.85,16531.81,16364.95,16399.87,000,16399.87 -2000-09-05,16677.79,16712.33,16401.28,16452.27,000,16452.27 -2000-09-04,16764.33,16883.31,16661.48,16688.21,000,16688.21 -2000-09-01,16915.04,17018.52,16700.36,16739.78,000,16739.78 -2000-08-31,16918.03,17056.54,16769.49,16861.26,000,16861.26 -2000-08-30,17131.36,17131.36,16895.36,16901.67,000,16901.67 -2000-08-29,17165.91,17210.80,17004.01,17141.75,000,17141.75 -2000-08-28,16895.55,17209.16,16840.51,17181.12,000,17181.12 -2000-08-25,16718.54,16926.22,16603.69,16911.33,000,16911.33 -2000-08-24,16433.36,16778.02,16433.36,16670.82,000,16670.82 -2000-08-23,16446.47,16544.80,16351.42,16436.65,000,16436.65 -2000-08-22,16075.52,16454.74,15985.20,16454.74,000,16454.74 -2000-08-21,16249.94,16257.34,15945.92,16040.18,000,16040.18 -2000-08-18,16156.64,16280.49,16118.89,16280.49,000,16280.49 -2000-08-17,16356.14,16356.14,16079.74,16161.03,000,16161.03 -2000-08-16,16300.49,16409.13,16249.94,16356.03,000,16356.03 -2000-08-15,16181.50,16309.50,16131.48,16298.29,000,16298.29 -2000-08-14,16109.95,16227.35,16055.07,16153.91,000,16153.91 -2000-08-11,16008.06,16125.66,15888.56,16117.50,000,16117.50 -2000-08-10,16050.87,16053.61,15946.60,15975.65,000,15975.65 -2000-08-09,15873.42,16034.60,15778.86,16034.60,000,16034.60 -2000-08-08,16044.81,16073.20,15755.22,15820.11,000,15820.11 -2000-08-07,15666.81,16039.40,15666.81,16002.71,000,16002.71 -2000-08-04,15799.99,15897.25,15557.33,15667.36,000,15667.36 -2000-08-03,16185.72,16185.72,15725.98,15814.44,000,15814.44 -2000-08-02,16118.80,16211.55,16054.66,16206.19,000,16206.19 -2000-08-01,15784.60,16099.67,15773.72,16099.67,000,16099.67 -2000-07-31,15821.31,15854.66,15394.71,15727.49,000,15727.49 -2000-07-28,16134.19,16134.19,15815.53,15838.57,000,15838.57 -2000-07-27,16457.70,16457.70,16027.34,16182.01,000,16182.01 -2000-07-26,16553.57,16563.71,16400.22,16502.61,000,16502.61 -2000-07-25,16506.15,16573.59,16341.52,16573.59,000,16573.59 -2000-07-24,16767.20,16767.20,16370.50,16547.12,000,16547.12 -2000-07-21,17025.66,17098.74,16800.59,16811.49,000,16811.49 -2000-07-19,16905.34,17015.47,16703.01,16983.57,000,16983.57 -2000-07-18,17261.08,17349.59,16834.02,16945.07,000,16945.07 -2000-07-17,17188.98,17476.86,17150.17,17286.83,000,17286.83 -2000-07-14,17136.70,17176.20,17019.50,17142.90,000,17142.90 -2000-07-13,17348.34,17348.34,17009.65,17036.90,000,17036.90 -2000-07-12,17519.04,17541.98,17210.18,17342.13,000,17342.13 -2000-07-11,17567.50,17573.69,17436.58,17504.36,000,17504.36 -2000-07-10,17421.56,17594.66,17421.56,17572.68,000,17572.68 -2000-07-07,17290.46,17483.47,17290.46,17398.24,000,17398.24 -2000-07-06,17402.71,17402.71,17154.58,17282.37,000,17282.37 -2000-07-05,17473.76,17576.28,17364.70,17435.95,000,17435.95 -2000-07-04,17655.57,17661.11,17434.07,17470.15,000,17470.15 -2000-07-03,17451.65,17636.67,17451.65,17614.66,000,17614.66 -2000-06-30,17482.09,17510.07,17305.81,17411.05,000,17411.05 -2000-06-29,17448.35,17511.32,17383.01,17475.90,000,17475.90 -2000-06-28,17289.31,17421.07,17230.04,17370.17,000,17370.17 -2000-06-27,16969.48,17285.47,16969.48,17279.06,000,17279.06 -2000-06-26,16927.27,16975.07,16761.59,16925.40,000,16925.40 -2000-06-23,17055.67,17214.47,16899.00,16963.21,000,16963.21 -2000-06-22,17228.85,17364.26,17092.44,17106.01,000,17106.01 -2000-06-21,16922.25,17212.38,16854.21,17210.08,000,17210.08 -2000-06-20,16645.99,16907.55,16645.99,16907.55,000,16907.55 -2000-06-19,16382.11,16627.54,16359.96,16591.35,000,16591.35 -2000-06-16,16358.71,16480.08,16289.92,16318.31,000,16318.31 -2000-06-15,16635.24,16635.24,16334.96,16338.70,000,16338.70 -2000-06-14,16920.21,16920.21,16477.98,16654.42,000,16654.42 -2000-06-13,16950.93,16950.93,16768.86,16914.95,000,16914.95 -2000-06-12,16876.68,17018.64,16791.87,16980.61,000,16980.61 -2000-06-09,17004.72,17004.72,16785.77,16861.91,000,16861.91 -2000-06-08,17177.45,17250.83,16979.30,17004.34,000,17004.34 -2000-06-07,17134.14,17206.98,17019.25,17144.96,000,17144.96 -2000-06-06,17163.39,17207.15,17064.92,17170.08,000,17170.08 -2000-06-05,16842.04,17261.87,16842.04,17201.79,000,17201.79 -2000-06-02,16682.25,16941.42,16682.25,16800.06,000,16800.06 -2000-06-01,16320.08,16694.30,16320.08,16694.30,000,16694.30 -2000-05-31,16274.14,16538.67,16224.06,16332.45,000,16332.45 -2000-05-30,16275.96,16485.54,16210.04,16228.90,000,16228.90 -2000-05-29,16028.76,16245.44,16028.76,16245.44,000,16245.44 -2000-05-26,16219.02,16219.02,15870.25,16008.14,000,16008.14 -2000-05-25,16090.36,16374.06,16090.36,16247.82,000,16247.82 -2000-05-24,16237.88,16261.33,15876.34,16044.44,000,16044.44 -2000-05-23,16345.26,16493.70,16169.93,16318.73,000,16318.73 -2000-05-22,16802.66,16802.66,16174.40,16386.01,000,16386.01 -2000-05-19,16960.29,16960.29,16572.05,16858.17,000,16858.17 -2000-05-18,17365.09,17365.09,16971.82,17031.63,000,17031.63 -2000-05-17,17588.81,17691.39,17348.88,17404.03,000,17404.03 -2000-05-16,17342.84,17558.51,17283.52,17551.25,000,17551.25 -2000-05-15,17396.45,17396.45,17192.71,17313.69,000,17313.69 -2000-05-12,16963.87,17362.20,16963.87,17357.86,000,17357.86 -2000-05-11,17605.65,17605.65,16779.42,16882.46,000,16882.46 -2000-05-10,17799.21,17803.44,17393.59,17701.47,000,17701.47 -2000-05-09,18152.37,18152.37,17804.04,17844.54,000,17844.54 -2000-05-08,18465.71,18475.45,18189.80,18199.96,000,18199.96 -2000-05-02,18497.52,18586.16,18428.92,18439.36,000,18439.36 -2000-05-01,17979.25,18403.08,17979.25,18403.08,000,18403.08 -2000-04-28,18035.54,18137.01,17926.43,17973.70,000,17973.70 -2000-04-27,18122.70,18245.44,18012.41,18019.17,000,18019.17 -2000-04-26,18326.90,18439.18,17948.36,18134.31,000,18134.31 -2000-04-25,18433.30,18630.30,18176.83,18272.33,000,18272.33 -2000-04-24,18247.48,18987.34,18247.48,18480.15,000,18480.15 -2000-04-21,19050.68,19269.06,18091.10,18252.68,000,18252.68 -2000-04-20,19041.53,19382.44,18959.32,18959.32,000,18959.32 -2000-04-19,18998.06,19192.63,18794.48,19086.62,000,19086.62 -2000-04-18,19089.00,19330.40,18547.38,18969.52,000,18969.52 -2000-04-17,20341.50,20341.50,18603.87,19008.64,000,19008.64 -2000-04-14,20456.48,20604.37,20330.89,20434.68,000,20434.68 -2000-04-13,20736.40,20736.40,20385.16,20526.42,000,20526.42 -2000-04-12,20475.96,20833.21,20436.74,20833.21,000,20833.21 -2000-04-11,20544.40,20656.87,20516.94,20522.52,000,20522.52 -2000-04-10,20368.81,20640.11,20368.81,20619.06,000,20619.06 -2000-04-07,20269.59,20463.67,20252.81,20252.81,000,20252.81 -2000-04-06,20476.23,20556.97,20171.62,20223.61,000,20223.61 -2000-04-05,20546.60,20654.63,20311.79,20462.77,000,20462.77 -2000-04-04,20747.82,20747.82,20536.33,20594.93,000,20594.93 -2000-04-03,20327.79,20726.99,20271.92,20726.99,000,20726.99 -2000-03-31,20371.07,20550.10,20259.35,20337.32,000,20337.32 -2000-03-30,20706.45,20809.79,20439.44,20441.50,000,20441.50 -2000-03-29,20406.56,20809.18,20406.56,20706.65,000,20706.65 -2000-03-28,20273.68,20388.18,20014.08,20374.34,000,20374.34 -2000-03-27,19976.14,20295.69,19880.11,20281.03,000,20281.03 -2000-03-24,19752.16,20012.41,19697.57,19958.08,000,19958.08 -2000-03-23,19749.51,19762.30,19568.77,19704.60,000,19704.60 -2000-03-22,19612.23,19734.43,19602.88,19733.59,000,19733.59 -2000-03-21,19598.53,19602.36,19455.11,19602.36,000,19602.36 -2000-03-17,19335.60,19573.48,19335.60,19566.32,000,19566.32 -2000-03-16,19095.63,19313.18,18892.26,19253.23,000,19253.23 -2000-03-15,19120.06,19120.06,18765.88,19078.60,000,19078.60 -2000-03-14,19139.57,19335.22,18956.25,19141.84,000,19141.84 -2000-03-13,19731.50,19760.35,19060.08,19189.93,000,19189.93 -2000-03-10,19734.84,19982.44,19686.50,19750.40,000,19750.40 -2000-03-09,19751.72,19885.54,19614.82,19662.33,000,19662.33 -2000-03-08,19856.37,19856.37,19692.04,19766.80,000,19766.80 -2000-03-07,19802.54,19944.24,19704.23,19944.24,000,19944.24 -2000-03-06,20041.48,20160.03,19742.58,19796.35,000,19796.35 -2000-03-03,20023.04,20034.60,19859.42,19927.54,000,19927.54 -2000-03-02,20097.59,20202.96,19903.29,20065.11,000,20065.11 -2000-03-01,20030.08,20165.51,20007.64,20081.67,000,20081.67 -2000-02-29,19761.52,19978.75,19747.02,19959.52,000,19959.52 -2000-02-28,19783.44,19904.86,19713.86,19720.10,000,19720.10 -2000-02-25,19623.38,19817.88,19539.00,19817.88,000,19817.88 -2000-02-24,19616.26,19698.95,19558.04,19571.44,000,19571.44 -2000-02-23,19439.17,19527.79,19373.04,19519.55,000,19519.55 -2000-02-22,19553.62,19712.37,19353.40,19390.58,000,19390.58 -2000-02-21,19736.15,19763.51,19543.75,19543.75,000,19543.75 -2000-02-18,19852.18,19862.94,19670.05,19789.03,000,19789.03 -2000-02-17,19646.37,19803.69,19518.08,19791.40,000,19791.40 -2000-02-16,19418.56,19612.60,19300.14,19599.18,000,19599.18 -2000-02-15,19587.82,19689.16,19331.05,19367.83,000,19367.83 -2000-02-14,19698.57,19748.42,19556.46,19556.46,000,19556.46 -2000-02-10,19915.53,19915.56,19710.02,19710.02,000,19710.02 -2000-02-09,19930.41,20046.14,19925.64,20007.77,000,20007.77 -2000-02-08,19955.30,19983.44,19834.81,19868.88,000,19868.88 -2000-02-07,19832.76,19948.60,19780.56,19945.43,000,19945.43 -2000-02-04,19866.19,20011.91,19752.12,19763.13,000,19763.13 -2000-02-03,19648.35,19878.83,19648.35,19786.42,000,19786.42 -2000-02-02,19522.33,19860.26,19522.33,19578.91,000,19578.91 -2000-02-01,19536.68,19553.68,19266.96,19423.38,000,19423.38 -2000-01-31,19375.11,19539.70,19224.47,19539.70,000,19539.70 -2000-01-28,19261.01,19595.83,19237.49,19434.78,000,19434.78 -2000-01-27,19125.62,19238.08,18971.68,19209.72,000,19209.72 -2000-01-26,18982.84,19145.90,18982.84,19111.19,000,19111.19 -2000-01-25,19004.39,19131.19,18815.37,18895.53,000,18895.53 -2000-01-24,18878.46,19124.57,18877.13,19056.71,000,19056.71 -2000-01-21,18994.89,18994.89,18713.17,18878.09,000,18878.09 -2000-01-20,18930.26,19167.03,18921.11,19008.01,000,19008.01 -2000-01-19,19181.87,19181.87,18897.75,18897.75,000,18897.75 -2000-01-18,19412.47,19412.47,19145.17,19196.57,000,19196.57 -2000-01-17,19025.62,19442.58,19025.62,19437.23,000,19437.23 -2000-01-14,18882.99,19058.02,18733.83,18956.55,000,18956.55 -2000-01-13,18667.18,18845.03,18667.18,18833.29,000,18833.29 -2000-01-12,18780.17,18811.87,18626.92,18677.42,000,18677.42 -2000-01-11,18246.10,18887.56,18246.10,18850.92,000,18850.92 -2000-01-07,18194.05,18285.73,18068.10,18193.41,000,18193.41 -2000-01-06,18574.01,18582.74,18168.27,18168.27,000,18168.27 -2000-01-05,19003.51,19003.51,18221.82,18542.55,000,18542.55 -2000-01-04,18937.45,19187.61,18937.45,19002.86,000,19002.86 -1999-12-30,18793.55,18960.33,18722.51,18934.34,000,18934.34 -1999-12-29,18777.85,18886.04,18729.08,18810.58,000,18810.58 -1999-12-28,18545.41,18816.70,18480.79,18783.52,000,18783.52 -1999-12-27,18596.49,18666.62,18472.60,18546.90,000,18546.90 -1999-12-24,18496.46,18777.04,18496.46,18584.95,000,18584.95 -1999-12-22,18164.34,18461.93,18164.34,18461.93,000,18461.93 -1999-12-21,18166.28,18168.10,18024.64,18080.38,000,18080.38 -1999-12-20,18137.94,18272.25,18060.35,18175.49,000,18175.49 -1999-12-17,18126.11,18255.92,18095.12,18095.12,000,18095.12 -1999-12-16,18126.54,18187.50,18006.32,18111.31,000,18111.31 -1999-12-15,18145.35,18302.83,18030.72,18138.36,000,18138.36 -1999-12-14,18204.52,18210.18,18039.61,18165.55,000,18165.55 -1999-12-13,18284.98,18284.98,18150.71,18205.08,000,18205.08 -1999-12-10,18264.54,18416.07,18212.99,18271.85,000,18271.85 -1999-12-09,18405.76,18405.76,18081.78,18260.72,000,18260.72 -1999-12-08,18556.63,18604.91,18383.89,18401.20,000,18401.20 -1999-12-07,18512.98,18657.44,18466.40,18593.96,000,18593.96 -1999-12-06,18380.70,18664.49,18380.70,18507.20,000,18507.20 -1999-12-03,18528.09,18610.77,18349.61,18368.14,000,18368.14 -1999-12-02,18535.88,18684.20,18339.85,18514.41,000,18514.41 -1999-12-01,18563.26,18718.92,18465.82,18495.95,000,18495.95 -1999-11-30,18853.44,18864.86,18477.72,18558.23,000,18558.23 -1999-11-29,18883.41,18909.89,18722.89,18850.27,000,18850.27 -1999-11-26,18776.98,19002.25,18675.05,18914.50,000,18914.50 -1999-11-25,18914.64,19020.90,18649.31,18721.78,000,18721.78 -1999-11-24,18796.02,19036.08,18664.02,18896.21,000,18896.21 -1999-11-22,18607.05,18848.73,18607.05,18822.12,000,18822.12 -1999-11-19,18576.42,18837.01,18570.84,18570.84,000,18570.84 -1999-11-18,18299.95,18686.87,18292.30,18532.81,000,18532.81 -1999-11-17,18218.72,18509.70,18071.25,18274.82,000,18274.82 -1999-11-16,18214.89,18289.41,18090.92,18155.14,000,18155.14 -1999-11-15,18295.50,18519.52,18198.09,18198.09,000,18198.09 -1999-11-12,18358.28,18483.50,18245.70,18258.55,000,18258.55 -1999-11-11,18551.86,18659.55,18310.26,18327.28,000,18327.28 -1999-11-10,18258.37,18622.78,18214.79,18567.87,000,18567.87 -1999-11-09,18259.41,18498.05,18259.41,18292.16,000,18292.16 -1999-11-08,18381.24,18481.52,18179.78,18240.98,000,18240.98 -1999-11-05,18340.18,18491.31,18173.97,18354.90,000,18354.90 -1999-11-04,18067.36,18377.73,18067.36,18348.13,000,18348.13 -1999-11-02,17976.91,18058.42,17857.11,17991.96,000,17991.96 -1999-11-01,17982.39,18119.94,17952.96,17996.92,000,17996.92 -1999-10-29,17467.89,17947.57,17467.89,17942.08,000,17942.08 -1999-10-28,17403.27,17525.88,17403.27,17413.71,000,17413.71 -1999-10-27,17655.78,17655.78,17360.83,17382.36,000,17382.36 -1999-10-26,17656.43,17751.83,17578.73,17671.79,000,17671.79 -1999-10-25,17494.93,17787.73,17494.93,17648.79,000,17648.79 -1999-10-22,17458.98,17607.66,17432.19,17438.80,000,17438.80 -1999-10-21,17543.83,17605.41,17325.77,17448.27,000,17448.27 -1999-10-20,17297.66,17560.25,17297.66,17534.71,000,17534.71 -1999-10-19,17325.04,17377.28,17178.47,17254.17,000,17254.17 -1999-10-18,17568.92,17568.92,17194.03,17275.33,000,17275.33 -1999-10-15,17779.78,17808.44,17511.11,17601.57,000,17601.57 -1999-10-14,17765.75,17941.51,17702.24,17780.26,000,17780.26 -1999-10-13,18030.40,18030.91,17754.49,17754.49,000,17754.49 -1999-10-12,18098.20,18221.69,18084.49,18090.81,000,18090.81 -1999-10-08,18164.67,18164.67,17915.15,18062.18,000,18062.18 -1999-10-07,17985.96,18228.39,17985.96,18136.55,000,18136.55 -1999-10-06,17822.64,17926.13,17734.30,17896.42,000,17896.42 -1999-10-05,17819.00,17985.47,17775.95,17784.15,000,17784.15 -1999-10-04,17747.56,17888.86,17675.28,17763.71,000,17763.71 -1999-10-01,17589.73,17886.39,17510.29,17712.56,000,17712.56 -1999-09-30,17307.22,17771.21,17307.22,17605.46,000,17605.46 -1999-09-29,17313.32,17313.32,17071.02,17282.28,000,17282.28 -1999-09-28,16892.46,17388.70,16892.46,17325.70,000,17325.70 -1999-09-27,16888.02,17039.42,16820.93,16821.06,000,16821.06 -1999-09-24,17290.01,17290.01,16652.04,16871.73,000,16871.73 -1999-09-22,17842.87,17842.87,17248.92,17325.76,000,17325.76 -1999-09-21,17585.78,17932.79,17558.74,17932.79,000,17932.79 -1999-09-20,17418.23,17662.82,17418.23,17575.26,000,17575.26 -1999-09-17,17273.99,17391.15,17118.31,17342.27,000,17342.27 -1999-09-16,17703.97,17703.97,17058.13,17291.59,000,17291.59 -1999-09-14,17880.99,17880.99,17610.31,17777.22,000,17777.22 -1999-09-13,17735.60,17988.59,17735.60,17909.29,000,17909.29 -1999-09-10,17648.89,17831.60,17589.05,17711.02,000,17711.02 -1999-09-09,17707.09,17859.71,17677.28,17677.56,000,17677.56 -1999-09-08,17710.02,17710.02,17509.73,17641.38,000,17641.38 -1999-09-07,17777.92,17858.13,17651.94,17707.50,000,17707.50 -1999-09-06,17664.06,17839.71,17664.06,17756.51,000,17756.51 -1999-09-03,17632.10,17716.74,17559.40,17629.99,000,17629.99 -1999-09-02,17795.40,17800.80,17630.32,17631.25,000,17631.25 -1999-09-01,17479.57,17819.60,17479.57,17802.48,000,17802.48 -1999-08-31,17886.20,17886.20,17425.49,17436.56,000,17436.56 -1999-08-30,17642.05,17925.07,17642.05,17918.97,000,17918.97 -1999-08-27,17710.97,17816.67,17567.86,17599.37,000,17599.37 -1999-08-26,17863.91,17995.49,17666.29,17666.29,000,17666.29 -1999-08-25,18099.23,18164.99,17795.08,17855.16,000,17855.16 -1999-08-24,18266.22,18397.93,18095.41,18095.41,000,18095.41 -1999-08-23,18133.20,18384.86,18133.20,18233.55,000,18233.55 -1999-08-20,17907.52,18123.29,17907.52,18098.11,000,18098.11 -1999-08-19,17843.11,17923.30,17665.97,17879.74,000,17879.74 -1999-08-18,17873.31,18082.47,17827.89,17892.26,000,17892.26 -1999-08-17,17842.97,17916.08,17766.69,17860.09,000,17860.09 -1999-08-16,17499.12,17937.21,17499.12,17826.03,000,17826.03 -1999-08-13,17430.05,17493.95,17284.70,17435.17,000,17435.17 -1999-08-12,17280.79,17476.68,17280.79,17422.97,000,17422.97 -1999-08-11,17185.70,17361.82,17097.41,17211.16,000,17211.16 -1999-08-10,17188.87,17203.39,17040.72,17202.09,000,17202.09 -1999-08-09,17105.93,17313.97,17095.50,17190.45,000,17190.45 -1999-08-06,17345.53,17345.53,17046.12,17084.24,000,17084.24 -1999-08-05,17638.93,17638.93,17210.04,17358.19,000,17358.19 -1999-08-04,17913.62,17913.62,17631.81,17685.38,000,17685.38 -1999-08-03,17824.68,17969.93,17597.74,17969.93,000,17969.93 -1999-08-02,17827.24,17909.89,17726.05,17825.70,000,17825.70 -1999-07-30,17857.91,17959.28,17677.14,17861.86,000,17861.86 -1999-07-29,17633.34,17957.37,17633.34,17869.92,000,17869.92 -1999-07-28,17508.66,17729.68,17508.66,17579.91,000,17579.91 -1999-07-27,17484.36,17613.24,17367.08,17462.72,000,17462.72 -1999-07-26,17568.32,17663.22,17491.34,17491.34,000,17491.34 -1999-07-23,17657.17,17657.17,17414.36,17534.44,000,17534.44 -1999-07-22,18221.07,18221.07,17665.04,17730.34,000,17730.34 -1999-07-21,18458.58,18458.58,18182.91,18257.52,000,18257.52 -1999-07-19,18288.37,18532.58,18288.37,18532.58,000,18532.58 -1999-07-16,18438.05,18623.15,18248.30,18248.30,000,18248.30 -1999-07-15,18402.63,18459.51,18269.52,18431.86,000,18431.86 -1999-07-14,18188.36,18455.60,18165.92,18357.86,000,18357.86 -1999-07-13,18231.83,18343.25,18172.25,18181.09,000,18181.09 -1999-07-12,17921.58,18274.18,17843.39,18274.18,000,18274.18 -1999-07-09,17965.70,17989.20,17813.46,17937.73,000,17937.73 -1999-07-08,17999.30,18045.56,17887.18,17967.65,000,17967.65 -1999-07-07,18075.21,18158.38,17949.73,17958.90,000,17958.90 -1999-07-06,18131.76,18159.55,17960.72,18050.73,000,18050.73 -1999-07-05,18001.16,18243.14,18001.16,18135.06,000,18135.06 -1999-07-02,17945.45,18066.28,17875.17,17932.47,000,17932.47 -1999-07-01,17607.60,17972.03,17607.60,17860.75,000,17860.75 -1999-06-30,17832.59,17958.34,17529.74,17529.74,000,17529.74 -1999-06-29,17675.84,17825.79,17649.31,17782.79,000,17782.79 -1999-06-28,17501.12,17688.03,17501.12,17610.58,000,17610.58 -1999-06-25,17597.78,17673.51,17430.42,17436.52,000,17436.52 -1999-06-24,17590.01,17700.46,17528.90,17628.32,000,17628.32 -1999-06-23,17742.53,17843.53,17580.05,17586.75,000,17586.75 -1999-06-22,17780.74,17828.21,17662.94,17777.62,000,17777.62 -1999-06-21,17485.90,17747.04,17485.90,17738.85,000,17738.85 -1999-06-18,17504.33,17650.38,17431.26,17431.26,000,17431.26 -1999-06-17,17268.45,17550.13,17268.45,17470.45,000,17470.45 -1999-06-16,17284.98,17346.23,17144.19,17210.18,000,17210.18 -1999-06-15,17216.28,17339.57,16990.55,17282.00,000,17282.00 -1999-06-14,17193.61,17384.90,17168.57,17188.82,000,17188.82 -1999-06-11,17084.57,17483.38,17070.60,17198.55,000,17198.55 -1999-06-10,16627.80,17130.36,16627.80,17102.62,000,17102.62 -1999-06-09,16499.16,16713.26,16450.76,16622.50,000,16622.50 -1999-06-08,16497.95,16571.12,16469.84,16562.92,000,16562.92 -1999-06-07,16318.44,16576.51,16318.44,16475.89,000,16475.89 -1999-06-04,16237.27,16368.15,16169.88,16300.75,000,16300.75 -1999-06-03,16418.92,16418.92,16127.90,16227.50,000,16227.50 -1999-06-02,16404.12,16458.34,16304.99,16417.99,000,16417.99 -1999-06-01,16090.15,16408.50,16026.95,16408.50,000,16408.50 -1999-05-31,15979.20,16111.65,15901.80,16111.65,000,16111.65 -1999-05-28,16118.26,16118.26,15886.62,15972.68,000,15972.68 -1999-05-27,16287.02,16330.77,16012.19,16177.19,000,16177.19 -1999-05-26,16172.72,16334.87,16070.88,16230.52,000,16230.52 -1999-05-25,16305.50,16305.50,16175.98,16214.23,000,16214.23 -1999-05-24,16261.15,16409.76,16157.22,16390.49,000,16390.49 -1999-05-21,16220.38,16303.83,16138.88,16292.98,000,16292.98 -1999-05-20,16150.42,16297.31,15946.66,16199.99,000,16199.99 -1999-05-19,16354.60,16354.60,16111.98,16128.18,000,16128.18 -1999-05-18,16440.38,16582.19,16291.12,16378.62,000,16378.62 -1999-05-17,16750.91,16750.91,16420.97,16421.02,000,16421.02 -1999-05-14,16899.84,16960.77,16750.67,16810.39,000,16810.39 -1999-05-13,16952.85,16958.02,16792.98,16851.25,000,16851.25 -1999-05-12,16782.56,17104.49,16782.56,16947.36,000,16947.36 -1999-05-11,17003.44,17003.44,16736.90,16743.18,000,16743.18 -1999-05-10,16983.29,17078.98,16931.63,16977.01,000,16977.01 -1999-05-07,17281.53,17281.53,16929.68,16946.52,000,16946.52 -1999-05-06,16762.78,17300.61,16762.78,17300.61,000,17300.61 -1999-04-30,16919.58,16953.13,16701.53,16701.53,000,16701.53 -1999-04-28,17013.87,17149.91,16881.60,16942.24,000,16942.24 -1999-04-27,16992.13,17069.72,16934.52,16957.27,000,16957.27 -1999-04-26,16919.76,17143.49,16915.15,16918.51,000,16918.51 -1999-04-23,16715.86,16923.25,16715.86,16923.25,000,16923.25 -1999-04-22,16563.72,16665.88,16484.08,16665.88,000,16665.88 -1999-04-21,16724.43,16736.06,16454.34,16495.02,000,16495.02 -1999-04-20,16587.17,16749.05,16526.53,16697.11,000,16697.11 -1999-04-19,16858.28,16858.28,16583.64,16674.21,000,16674.21 -1999-04-16,16754.31,16979.06,16754.31,16851.58,000,16851.58 -1999-04-15,16758.59,16844.97,16589.36,16727.08,000,16727.08 -1999-04-14,16698.18,16799.17,16436.19,16764.68,000,16764.68 -1999-04-13,16617.05,16855.67,16617.05,16715.16,000,16715.16 -1999-04-12,16797.08,16797.08,16507.40,16507.40,000,16507.40 -1999-04-09,16933.40,17166.06,16827.93,16855.63,000,16855.63 -1999-04-08,16552.50,16866.66,16483.52,16846.69,000,16846.69 -1999-04-07,16429.86,16563.20,16341.25,16554.50,000,16554.50 -1999-04-06,16360.98,16484.27,16084.71,16479.71,000,16479.71 -1999-04-05,16320.07,16634.79,16231.13,16334.78,000,16334.78 -1999-04-02,16351.72,16453.50,16243.46,16290.19,000,16290.19 -1999-04-01,15868.05,16449.97,15813.41,16327.56,000,16327.56 -1999-03-31,15865.77,16027.27,15651.35,15836.59,000,15836.59 -1999-03-30,16091.92,16184.54,15805.69,15859.12,000,15859.12 -1999-03-29,16031.32,16185.80,16002.28,16008.84,000,16008.84 -1999-03-26,16030.53,16181.09,15905.66,16016.99,000,16016.99 -1999-03-25,15591.41,16061.02,15591.41,15986.04,000,15986.04 -1999-03-24,15947.57,15947.57,15515.47,15515.47,000,15515.47 -1999-03-23,16401.96,16437.23,15988.41,16019.10,000,16019.10 -1999-03-19,15804.71,16421.81,15804.17,16378.78,000,16378.78 -1999-03-18,16238.91,16303.12,15717.92,15717.92,000,15717.92 -1999-03-17,16088.09,16269.20,15977.87,16268.11,000,16268.11 -1999-03-16,15749.55,16082.07,15591.62,16072.82,000,16072.82 -1999-03-15,15526.51,15790.24,15404.10,15779.60,000,15779.60 -1999-03-12,15588.89,15709.01,15408.38,15488.86,000,15488.86 -1999-03-11,15485.43,15840.23,15417.03,15502.14,000,15502.14 -1999-03-10,15134.05,15484.63,15134.05,15480.00,000,15480.00 -1999-03-09,14842.17,15096.70,14842.17,15096.70,000,15096.70 -1999-03-08,14925.59,15116.10,14779.05,14779.05,000,14779.05 -1999-03-05,14256.02,14895.39,14256.02,14894.00,000,14894.00 -1999-03-04,14202.20,14224.73,14121.02,14183.45,000,14183.45 -1999-03-03,13956.18,14170.46,13927.73,14170.36,000,14170.36 -1999-03-02,14260.55,14306.01,13921.06,13921.06,000,13921.06 -1999-03-01,14362.86,14468.86,14221.60,14221.75,000,14221.75 -1999-02-26,14456.33,14494.58,14363.31,14367.54,000,14367.54 -1999-02-25,14386.09,14470.45,14363.81,14470.45,000,14470.45 -1999-02-24,14483.59,14534.82,14326.15,14355.45,000,14355.45 -1999-02-23,14284.27,14500.65,14284.27,14500.65,000,14500.65 -1999-02-22,14149.67,14314.32,14096.70,14256.67,000,14256.67 -1999-02-19,14144.00,14179.77,14045.17,14098.04,000,14098.04 -1999-02-18,14155.89,14168.57,14041.93,14146.79,000,14146.79 -1999-02-17,14277.81,14407.33,14146.64,14158.67,000,14158.67 -1999-02-16,14095.25,14358.68,14095.25,14232.64,000,14232.64 -1999-02-15,14008.36,14101.22,14003.23,14054.72,000,14054.72 -1999-02-12,13925.24,14062.92,13925.24,13973.69,000,13973.69 -1999-02-10,13852.62,13971.15,13795.61,13952.40,000,13952.40 -1999-02-09,14008.56,14015.57,13885.79,13902.66,000,13902.66 -1999-02-08,13886.64,14024.92,13770.89,13992.49,000,13992.49 -1999-02-05,14049.69,14049.69,13769.25,13898.08,000,13898.08 -1999-02-04,14176.13,14255.67,13925.14,14086.85,000,14086.85 -1999-02-03,14250.55,14250.55,14089.09,14161.31,000,14161.31 -1999-02-02,14459.81,14459.81,14285.96,14349.83,000,14349.83 -1999-02-01,14544.12,14641.41,14356.30,14465.18,000,14465.18 -1999-01-29,14413.90,14628.88,14413.90,14499.25,000,14499.25 -1999-01-28,14472.05,14522.33,14331.77,14342.32,000,14342.32 -1999-01-27,14416.24,14526.21,14370.52,14450.06,000,14450.06 -1999-01-26,14251.29,14501.44,14251.29,14382.01,000,14382.01 -1999-01-25,14141.56,14251.09,14076.35,14208.81,000,14208.81 -1999-01-22,14235.67,14407.23,14154.40,14154.40,000,14154.40 -1999-01-21,14048.85,14331.23,14009.45,14245.42,000,14245.42 -1999-01-20,13794.92,14028.05,13738.96,14028.05,000,14028.05 -1999-01-19,13840.58,13883.01,13756.96,13770.44,000,13770.44 -1999-01-18,13762.34,13964.19,13754.58,13805.06,000,13805.06 -1999-01-14,13369.08,13738.86,13369.08,13738.86,000,13738.86 -1999-01-13,13353.81,13444.34,13313.77,13403.60,000,13403.60 -1999-01-12,13313.47,13535.66,13212.30,13360.97,000,13360.97 -1999-01-11,13354.41,13452.89,13224.63,13368.48,000,13368.48 -1999-01-08,13507.06,13507.06,13328.34,13391.81,000,13391.81 -1999-01-07,13576.00,13854.16,13516.41,13536.56,000,13536.56 -1999-01-06,13281.69,13475.63,13216.18,13468.46,000,13468.46 -1999-01-05,13437.03,13437.03,13122.61,13232.74,000,13232.74 -1999-01-04,13779.05,13779.05,13415.89,13415.89,000,13415.89 -1998-12-30,13832.32,13913.55,13812.87,13842.17,000,13842.17 -1998-12-29,13780.44,13846.90,13664.79,13846.90,000,13846.90 -1998-12-28,13876.54,13894.55,13703.29,13709.06,000,13709.06 -1998-12-24,13810.58,13815.21,13657.03,13706.73,000,13706.73 -1998-12-22,14183.74,14185.54,13722.10,13779.45,000,13779.45 -1998-12-21,14158.82,14158.82,14038.70,14152.95,000,14152.95 -1998-12-18,14161.46,14269.50,14078.14,14194.29,000,14194.29 -1998-12-17,14064.22,14169.32,13917.33,14126.99,000,14126.99 -1998-12-16,14092.32,14157.53,14016.81,14096.30,000,14096.30 -1998-12-15,14084.96,14192.60,13965.28,14011.19,000,14011.19 -1998-12-14,14349.18,14349.18,14103.86,14111.62,000,14111.62 -1998-12-11,14729.95,14729.95,14382.06,14405.64,000,14405.64 -1998-12-10,14890.92,15007.01,14807.40,14807.80,000,14807.80 -1998-12-09,14751.79,14931.90,14700.66,14931.90,000,14931.90 -1998-12-08,14775.02,14916.09,14775.02,14808.20,000,14808.20 -1998-12-07,14703.64,14748.91,14650.42,14723.49,000,14723.49 -1998-12-04,14641.41,14654.20,14536.01,14639.97,000,14639.97 -1998-12-03,14875.60,14875.60,14589.63,14697.08,000,14697.08 -1998-12-02,14863.71,15011.09,14781.78,14986.62,000,14986.62 -1998-12-01,14821.53,14931.16,14763.88,14835.41,000,14835.41 -1998-11-30,15107.09,15139.87,14883.11,14883.70,000,14883.70 -1998-11-27,15188.77,15320.23,15069.39,15069.39,000,15069.39 -1998-11-26,15101.62,15219.81,15043.72,15207.77,000,15207.77 -1998-11-25,15108.04,15124.60,14942.10,15073.47,000,15073.47 -1998-11-24,14904.20,15164.64,14904.20,15164.64,000,15164.64 -1998-11-20,14461.20,14779.94,14461.20,14779.94,000,14779.94 -1998-11-19,14557.10,14642.96,14354.41,14354.46,000,14354.46 -1998-11-18,14396.09,14701.45,14383.36,14599.23,000,14599.23 -1998-11-17,14475.88,14480.50,14276.81,14413.00,000,14413.00 -1998-11-16,14339.43,14450.56,14205.13,14428.27,000,14428.27 -1998-11-13,14119.38,14268.21,13984.68,14268.21,000,14268.21 -1998-11-12,14364.85,14418.08,14075.06,14075.06,000,14075.06 -1998-11-11,14137.63,14428.02,14065.51,14428.02,000,14428.02 -1998-11-10,14154.00,14270.05,14099.23,14108.09,000,14108.09 -1998-11-09,14172.80,14362.66,14063.27,14194.54,000,14194.54 -1998-11-06,14308.99,14308.99,14121.97,14121.97,000,14121.97 -1998-11-05,14624.45,14625.15,14180.71,14341.37,000,14341.37 -1998-11-04,14095.65,14527.81,14095.65,14527.81,000,14527.81 -1998-11-02,13648.28,13952.75,13648.28,13952.75,000,13952.75 -1998-10-30,13732.19,13835.56,13454.64,13564.51,000,13564.51 -1998-10-29,13566.80,13727.02,13432.10,13668.72,000,13668.72 -1998-10-28,13804.32,13920.81,13516.07,13516.07,000,13516.07 -1998-10-27,13855.05,14054.86,13762.44,13820.68,000,13820.68 -1998-10-26,14054.86,14054.86,13806.36,13843.46,000,13843.46 -1998-10-23,14327.65,14523.48,14042.63,14144.70,000,14144.70 -1998-10-22,14287.75,14742.44,14245.77,14295.56,000,14295.56 -1998-10-21,13921.36,14366.89,13921.36,14216.33,000,14216.33 -1998-10-20,13569.14,13808.84,13483.24,13808.05,000,13808.05 -1998-10-19,13263.18,13786.36,13263.18,13567.20,000,13567.20 -1998-10-16,13109.33,13309.99,13109.33,13280.54,000,13280.54 -1998-10-15,13113.36,13184.64,12892.96,12995.37,000,12995.37 -1998-10-14,13264.62,13454.04,13057.05,13070.73,000,13070.73 -1998-10-13,13538.80,13591.82,13241.20,13242.79,000,13242.79 -1998-10-12,12977.82,13572.87,12977.82,13555.01,000,13555.01 -1998-10-09,12923.45,13301.53,12787.90,12879.97,000,12879.97 -1998-10-08,13749.01,13749.01,12987.91,13026.06,000,13026.06 -1998-10-07,13095.90,13825.61,13095.90,13825.61,000,13825.61 -1998-10-06,12936.38,13216.28,12927.78,13021.64,000,13021.64 -1998-10-05,13185.98,13185.98,12910.27,12948.12,000,12948.12 -1998-10-02,13141.56,13320.23,12973.24,13223.69,000,13223.69 -1998-10-01,13377.24,13558.45,13018.75,13197.12,000,13197.12 -1998-09-30,13878.69,13966.77,13406.39,13406.39,000,13406.39 -1998-09-29,13937.82,13952.35,13553.02,13821.43,000,13821.43 -1998-09-28,13760.74,14121.47,13687.03,13909.37,000,13909.37 -1998-09-25,14057.85,14057.85,13678.47,13723.84,000,13723.84 -1998-09-24,13896.79,14297.50,13896.79,14205.78,000,14205.78 -1998-09-22,13640.56,13871.48,13521.13,13789.81,000,13789.81 -1998-09-21,13875.77,13875.77,13580.72,13597.30,000,13597.30 -1998-09-18,13799.75,14006.09,13697.75,13983.12,000,13983.12 -1998-09-17,14213.49,14279.77,13784.07,13859.14,000,13859.14 -1998-09-16,14229.32,14375.57,14176.02,14197.70,000,14197.70 -1998-09-14,13979.32,14329.92,13844.31,14227.37,000,14227.37 -1998-09-11,14551.25,14551.25,13725.62,13916.98,000,13916.98 -1998-09-10,14805.29,14902.00,14530.92,14666.03,000,14666.03 -1998-09-09,14968.18,15099.85,14629.62,14755.54,000,14755.54 -1998-09-08,14766.93,15294.26,14766.93,14913.49,000,14913.49 -1998-09-07,13984.47,14790.06,13912.69,14790.06,000,14790.06 -1998-09-04,14158.34,14185.86,14042.91,14042.91,000,14042.91 -1998-09-03,14362.54,14368.28,14207.84,14261.24,000,14261.24 -1998-09-02,14361.04,14589.41,14287.16,14376.62,000,14376.62 -1998-09-01,13979.82,14369.83,13664.74,14369.63,000,14369.63 -1998-08-31,13955.79,14224.18,13845.15,14107.89,000,14107.89 -1998-08-28,14289.21,14289.21,13792.76,13915.63,000,13915.63 -1998-08-27,14794.41,14794.41,14378.67,14413.79,000,14413.79 -1998-08-26,15113.04,15113.04,14866.03,14866.03,000,14866.03 -1998-08-25,15070.23,15226.97,15070.23,15072.93,000,15072.93 -1998-08-24,15145.25,15145.25,14859.34,14988.36,000,14988.36 -1998-08-21,15277.12,15416.88,15226.62,15298.20,000,15298.20 -1998-08-20,15445.75,15445.75,15236.26,15391.41,000,15391.41 -1998-08-19,15164.24,15416.48,15161.84,15406.34,000,15406.34 -1998-08-18,14896.70,15102.90,14845.75,15063.79,000,15063.79 -1998-08-17,15130.77,15137.66,14655.69,14794.66,000,14794.66 -1998-08-14,15305.09,15355.09,15049.45,15123.93,000,15123.93 -1998-08-13,15412.99,15476.32,15239.71,15382.02,000,15382.02 -1998-08-12,15287.31,15534.07,15269.83,15378.97,000,15378.97 -1998-08-11,15571.23,15630.07,15310.59,15406.99,000,15406.99 -1998-08-10,15800.35,15800.35,15595.70,15626.42,000,15626.42 -1998-08-07,15924.53,16037.26,15797.30,15829.17,000,15829.17 -1998-08-06,16048.15,16075.72,15834.77,15876.22,000,15876.22 -1998-08-05,16015.13,16019.33,15817.03,15992.16,000,15992.16 -1998-08-04,16061.44,16180.92,16004.25,16023.58,000,16023.58 -1998-08-03,16303.60,16303.60,16104.55,16165.08,000,16165.08 -1998-07-31,16286.61,16399.90,16286.61,16378.97,000,16378.97 -1998-07-30,16190.71,16311.54,16190.71,16201.60,000,16201.60 -1998-07-29,16074.18,16282.32,16047.25,16158.09,000,16158.09 -1998-07-28,16018.88,16180.27,15958.19,16114.54,000,16114.54 -1998-07-27,16281.97,16281.97,15944.26,15944.36,000,15944.36 -1998-07-24,16120.88,16418.38,16091.41,16361.89,000,16361.89 -1998-07-23,16268.48,16320.53,16158.44,16188.01,000,16188.01 -1998-07-22,16460.69,16460.69,16286.56,16293.06,000,16293.06 -1998-07-21,16619.78,16698.15,16407.74,16556.69,000,16556.69 -1998-07-17,16732.07,16732.07,16569.78,16570.78,000,16570.78 -1998-07-16,16605.24,16756.89,16498.25,16731.92,000,16731.92 -1998-07-15,16599.55,16614.14,16435.46,16614.14,000,16614.14 -1998-07-14,16379.92,16489.41,16331.37,16488.91,000,16488.91 -1998-07-13,15993.16,16360.39,15804.35,16360.39,000,16360.39 -1998-07-10,16464.79,16531.47,16066.03,16090.06,000,16090.06 -1998-07-09,16492.51,16492.51,16370.08,16446.95,000,16446.95 -1998-07-08,16528.12,16635.86,16497.30,16530.97,000,16530.97 -1998-07-07,16354.35,16531.22,16354.35,16416.28,000,16416.28 -1998-07-06,16433.67,16488.51,16350.45,16350.45,000,16350.45 -1998-07-03,16354.60,16625.42,16289.66,16511.24,000,16511.24 -1998-07-02,16433.47,16743.36,16432.62,16471.58,000,16471.58 -1998-07-01,15852.10,16362.89,15739.76,16362.89,000,16362.89 -1998-06-30,15471.43,15830.47,15462.24,15830.27,000,15830.27 -1998-06-29,15254.80,15424.53,15230.77,15365.73,000,15365.73 -1998-06-26,15123.03,15233.97,14977.67,15210.04,000,15210.04 -1998-06-25,15161.04,15205.04,15075.37,15132.22,000,15132.22 -1998-06-24,15129.02,15210.49,15000.15,15123.18,000,15123.18 -1998-06-23,15320.48,15320.48,15054.60,15054.60,000,15054.60 -1998-06-22,15285.01,15413.79,15246.25,15309.09,000,15309.09 -1998-06-19,15312.29,15351.45,15194.01,15267.98,000,15267.98 -1998-06-18,14825.17,15398.20,14825.17,15361.54,000,15361.54 -1998-06-17,14790.81,14899.85,14673.28,14715.38,000,14715.38 -1998-06-16,14743.21,14917.58,14614.74,14720.38,000,14720.38 -1998-06-15,14964.34,14964.34,14789.31,14825.17,000,14825.17 -1998-06-12,14978.32,15060.69,14784.52,15022.33,000,15022.33 -1998-06-11,15285.01,15285.01,15002.55,15014.04,000,15014.04 -1998-06-10,15520.38,15520.38,15298.80,15339.26,000,15339.26 -1998-06-09,15320.33,15530.17,15316.43,15530.17,000,15530.17 -1998-06-08,15283.52,15357.89,15254.00,15294.71,000,15294.71 -1998-06-05,15436.41,15440.86,15276.02,15323.43,000,15323.43 -1998-06-04,15314.24,15522.78,15292.91,15426.47,000,15426.47 -1998-06-03,15525.62,15525.62,15256.09,15347.00,000,15347.00 -1998-06-02,15404.15,15554.45,15353.20,15554.45,000,15554.45 -1998-06-01,15670.73,15702.05,15321.03,15321.03,000,15321.03 -1998-05-29,15740.41,15790.31,15604.70,15670.78,000,15670.78 -1998-05-28,15639.01,15891.71,15639.01,15796.55,000,15796.55 -1998-05-27,15824.53,15824.53,15549.90,15664.29,000,15664.29 -1998-05-26,15792.36,15942.16,15788.91,15884.82,000,15884.82 -1998-05-25,15784.42,15812.54,15733.12,15783.12,000,15783.12 -1998-05-22,15892.61,15915.23,15736.16,15801.65,000,15801.65 -1998-05-21,15695.25,15972.88,15695.25,15845.25,000,15845.25 -1998-05-20,15578.87,15788.01,15578.87,15652.95,000,15652.95 -1998-05-19,15397.95,15582.87,15309.19,15551.65,000,15551.65 -1998-05-18,15277.17,15405.00,15069.68,15384.47,000,15384.47 -1998-05-15,15270.63,15412.84,15213.29,15242.86,000,15242.86 -1998-05-14,15322.83,15448.45,15294.51,15307.69,000,15307.69 -1998-05-13,15281.77,15343.81,15162.89,15343.81,000,15343.81 -1998-05-12,15441.71,15446.20,15306.92,15322.48,000,15322.48 -1998-05-11,15213.34,15433.87,15213.34,15381.90,000,15381.90 -1998-05-08,15105.77,15209.81,15096.72,15149.00,000,15149.00 -1998-05-07,15187.79,15244.10,15020.05,15143.03,000,15143.03 -1998-05-06,15536.96,15536.96,15129.07,15243.84,000,15243.84 -1998-05-01,15656.14,15665.78,15463.60,15601.10,000,15601.10 -1998-04-30,15493.42,15647.65,15483.18,15641.26,000,15641.26 -1998-04-28,15526.47,15625.37,15334.47,15395.43,000,15395.43 -1998-04-27,15969.00,15969.00,15645.00,15650.00,000,15650.00 -1998-04-24,15836.00,16201.00,15834.00,16011.00,000,16011.00 -1998-04-23,15753.00,15906.00,15651.00,15762.00,000,15762.00 -1998-04-22,15832.00,15832.00,15601.00,15762.00,000,15762.00 -1998-04-21,15784.00,15927.00,15583.00,15826.00,000,15826.00 -1998-04-20,15706.00,15730.00,15599.00,15697.00,000,15697.00 -1998-04-17,15839.00,15854.00,15465.00,15704.00,000,15704.00 -1998-04-16,16372.00,16417.00,15875.00,15884.00,000,15884.00 -1998-04-15,16322.00,16404.00,16292.00,16299.00,000,16299.00 -1998-04-14,16309.00,16414.00,16188.00,16277.00,000,16277.00 -1998-04-13,16374.00,16401.00,16277.00,16318.00,000,16318.00 -1998-04-10,16500.00,16520.00,16266.00,16481.00,000,16481.00 -1998-04-09,16433.00,16624.00,16271.00,16537.00,000,16537.00 -1998-04-08,15988.00,16475.00,15962.00,16377.00,000,16377.00 -1998-04-07,15667.00,15979.00,15602.00,15979.00,000,15979.00 -1998-04-06,15568.00,15768.00,15488.00,15706.00,000,15706.00 -1998-04-03,15747.00,15955.00,15465.00,15518.00,000,15518.00 -1998-04-02,16215.00,16215.00,15634.00,15703.00,000,15703.00 -1998-04-01,16433.00,16441.00,16148.00,16242.00,000,16242.00 -1998-03-31,16295.00,16585.00,16178.00,16527.00,000,16527.00 -1998-03-30,16840.00,17010.00,16239.00,16263.00,000,16263.00 -1998-03-27,16974.00,17076.00,16737.00,16739.00,000,16739.00 -1998-03-26,16685.00,17112.00,16669.00,16981.00,000,16981.00 -1998-03-25,16659.00,16939.00,16575.00,16658.00,000,16658.00 -1998-03-24,16769.00,16769.00,16551.00,16606.00,000,16606.00 -1998-03-23,16884.00,17046.00,16764.00,16869.00,000,16869.00 -1998-03-20,16615.00,16879.00,16470.00,16830.00,000,16830.00 -1998-03-19,16612.00,16769.00,16560.00,16679.00,000,16679.00 -1998-03-18,17012.00,17022.00,16500.00,16620.00,000,16620.00 -1998-03-17,16893.00,17062.00,16844.00,16997.00,000,16997.00 -1998-03-16,17063.00,17063.00,16792.00,16861.00,000,16861.00 -1998-03-13,16564.00,17129.00,16555.00,17060.00,000,17060.00 -1998-03-12,16750.00,16750.00,16575.00,16575.00,000,16575.00 -1998-03-11,16949.00,16949.00,16746.00,16756.00,000,16756.00 -1998-03-10,17000.00,17063.00,16901.00,16983.00,000,16983.00 -1998-03-09,17205.00,17352.00,16976.00,16977.00,000,16977.00 -1998-03-06,16864.00,17191.00,16864.00,17132.00,000,17132.00 -1998-03-05,17011.00,17011.00,16845.00,16849.00,000,16849.00 -1998-03-04,17124.00,17213.00,17026.00,17096.00,000,17096.00 -1998-03-03,17237.00,17326.00,17063.00,17168.00,000,17168.00 -1998-03-02,16901.00,17276.00,16901.00,17264.00,000,17264.00 -1998-02-27,16561.00,16832.00,16561.00,16832.00,000,16832.00 -1998-02-26,16369.00,16549.00,16278.00,16502.00,000,16502.00 -1998-02-25,16156.00,16361.00,15932.00,16361.00,000,16361.00 -1998-02-24,16634.00,16634.00,16167.00,16198.00,000,16198.00 -1998-02-23,16717.00,16717.00,16610.00,16610.00,000,16610.00 -1998-02-20,16628.00,16799.00,16502.00,16756.00,000,16756.00 -1998-02-19,16582.00,16866.00,16548.00,16616.00,000,16616.00 -1998-02-18,16787.00,16854.00,16593.00,16614.00,000,16614.00 -1998-02-17,16738.00,16791.00,16588.00,16791.00,000,16791.00 -1998-02-16,16750.00,16776.00,16589.00,16776.00,000,16776.00 -1998-02-13,17161.00,17161.00,16711.00,16791.00,000,16791.00 -1998-02-12,17247.00,17252.00,17069.00,17175.00,000,17175.00 -1998-02-10,17215.00,17256.00,17162.00,17205.00,000,17205.00 -1998-02-09,17102.00,17224.00,17053.00,17205.00,000,17205.00 -1998-02-06,17022.00,17134.00,16981.00,17040.00,000,17040.00 -1998-02-05,16803.00,17051.00,16771.00,17003.00,000,17003.00 -1998-02-04,17050.00,17074.00,16796.00,16883.00,000,16883.00 -1998-02-03,16904.00,17144.00,16904.00,17023.00,000,17023.00 -1998-02-02,16685.00,16909.00,16641.00,16777.00,000,16777.00 -1998-01-30,17011.00,17011.00,16628.00,16628.00,000,16628.00 -1998-01-29,17045.00,17107.00,16926.00,17015.00,000,17015.00 -1998-01-28,17061.00,17259.00,16974.00,16974.00,000,16974.00 -1998-01-27,17101.00,17158.00,16908.00,16982.00,000,16982.00 -1998-01-26,16835.00,17353.00,16835.00,17073.00,000,17073.00 -1998-01-23,16402.00,16797.00,16402.00,16789.00,000,16789.00 -1998-01-22,16624.00,16712.00,16397.00,16406.00,000,16406.00 -1998-01-21,16459.00,16752.00,16459.00,16684.00,000,16684.00 -1998-01-20,16220.00,16430.00,16077.00,16367.00,000,16367.00 -1998-01-19,16155.00,16461.00,16155.00,16262.00,000,16262.00 -1998-01-16,15193.00,16063.00,15193.00,16046.00,000,16046.00 -1998-01-14,14866.00,15149.00,14866.00,15122.00,000,15122.00 -1998-01-13,14758.00,14901.00,14546.00,14756.00,000,14756.00 -1998-01-12,14877.00,14909.00,14629.00,14664.00,000,14664.00 -1998-01-09,14941.00,15066.00,14724.00,14995.00,000,14995.00 -1998-01-08,15061.00,15608.00,15019.00,15019.00,000,15019.00 -1998-01-07,14898.00,15038.00,14848.00,15028.00,000,15028.00 -1998-01-06,15008.00,15067.00,14714.00,14896.00,000,14896.00 -1998-01-05,15269.00,15307.00,14957.00,14957.00,000,14957.00 -1997-12-30,14838.00,15259.00,14838.00,15259.00,000,15259.00 -1997-12-29,14830.00,14853.00,14582.00,14775.00,000,14775.00 -1997-12-26,15312.00,15364.00,14779.00,14803.00,000,14803.00 -1997-12-25,14940.00,15730.00,14940.00,15300.00,000,15300.00 -1997-12-24,14792.00,15013.00,14682.00,14925.00,000,14925.00 -1997-12-22,15280.00,15280.00,14569.00,14799.00,000,14799.00 -1997-12-19,16105.00,16105.00,15171.00,15315.00,000,15315.00 -1997-12-18,16456.00,16456.00,16100.00,16162.00,000,16162.00 -1997-12-17,16014.00,16817.00,15795.00,16541.00,000,16541.00 -1997-12-16,15954.00,16130.00,15803.00,15985.00,000,15985.00 -1997-12-15,15866.00,15909.00,15643.00,15909.00,000,15909.00 -1997-12-12,16050.00,16153.00,15738.00,15904.00,000,15904.00 -1997-12-11,16397.00,16397.00,16025.00,16050.00,000,16050.00 -1997-12-10,16676.00,16676.00,16409.00,16478.00,000,16478.00 -1997-12-09,16185.00,16687.00,16185.00,16687.00,000,16687.00 -1997-12-08,16439.00,16516.00,16110.00,16132.00,000,16132.00 -1997-12-05,16351.00,16597.00,16348.00,16424.00,000,16424.00 -1997-12-04,16567.00,16589.00,16249.00,16307.00,000,16307.00 -1997-12-03,16861.00,16861.00,16583.00,16586.00,000,16586.00 -1997-12-02,17010.00,17074.00,16848.00,16910.00,000,16910.00 -1997-12-01,16594.00,17118.00,16486.00,17008.00,000,17008.00 -1997-11-28,16648.00,16785.00,16591.00,16633.00,000,16633.00 -1997-11-27,16117.00,16630.00,16117.00,16603.00,000,16603.00 -1997-11-26,15926.00,16379.00,15926.00,16046.00,000,16046.00 -1997-11-25,16608.00,16608.00,15774.00,15868.00,000,15868.00 -1997-11-21,16420.00,16809.00,16420.00,16722.00,000,16722.00 -1997-11-20,15875.00,16545.00,15831.00,16308.00,000,16308.00 -1997-11-19,16600.00,16600.00,15746.00,15842.00,000,15842.00 -1997-11-18,16242.00,17006.00,16090.00,16727.00,000,16727.00 -1997-11-17,15154.00,16283.00,15154.00,16283.00,000,16283.00 -1997-11-14,15355.00,15372.00,14966.00,15083.00,000,15083.00 -1997-11-13,15355.00,15603.00,15083.00,15427.00,000,15427.00 -1997-11-12,15820.00,15864.00,15359.00,15434.00,000,15434.00 -1997-11-11,15720.00,15867.00,15648.00,15867.00,000,15867.00 -1997-11-10,15722.00,15912.00,15565.00,15697.00,000,15697.00 -1997-11-07,16464.00,16464.00,15824.00,15836.00,000,15836.00 -1997-11-06,16466.00,16634.00,16422.00,16534.00,000,16534.00 -1997-11-05,16519.00,16525.00,16290.00,16448.00,000,16448.00 -1997-11-04,16494.00,16641.00,16400.00,16500.00,000,16500.00 -1997-10-31,16254.00,16635.00,16082.00,16459.00,000,16459.00 -1997-10-30,16828.00,16828.00,16302.00,16365.00,000,16365.00 -1997-10-29,16386.00,16920.00,16386.00,16857.00,000,16857.00 -1997-10-28,17019.00,17019.00,16218.00,16313.00,000,16313.00 -1997-10-27,17262.00,17262.00,16906.00,17039.00,000,17039.00 -1997-10-24,17040.00,17494.00,16864.00,17364.00,000,17364.00 -1997-10-23,17647.00,17647.00,17152.00,17152.00,000,17152.00 -1997-10-22,17267.00,17694.00,17267.00,17688.00,000,17688.00 -1997-10-21,17369.00,17555.00,17210.00,17210.00,000,17210.00 -1997-10-20,17391.00,17455.00,17231.00,17295.00,000,17295.00 -1997-10-17,17591.00,17591.00,17384.00,17478.00,000,17478.00 -1997-10-16,17335.00,17764.00,17184.00,17707.00,000,17707.00 -1997-10-15,17342.00,17427.00,17186.00,17331.00,000,17331.00 -1997-10-14,17220.00,17419.00,16968.00,17306.00,000,17306.00 -1997-10-13,17318.00,17318.00,17152.00,17205.00,000,17205.00 -1997-10-09,17624.00,17628.00,17331.00,17377.00,000,17377.00 -1997-10-08,17531.00,17718.00,17531.00,17619.00,000,17619.00 -1997-10-07,17843.00,17890.00,17479.00,17511.00,000,17511.00 -1997-10-06,17646.00,17854.00,17636.00,17825.00,000,17825.00 -1997-10-03,17468.00,17686.00,17402.00,17647.00,000,17647.00 -1997-10-02,17876.00,17876.00,17415.00,17455.00,000,17455.00 -1997-10-01,17820.00,17937.00,17522.00,17842.00,000,17842.00 -1997-09-30,18023.00,18054.00,17850.00,17888.00,000,17888.00 -1997-09-29,17992.00,17992.00,17681.00,17987.00,000,17987.00 -1997-09-26,18308.00,18354.00,17933.00,17995.00,000,17995.00 -1997-09-25,18370.00,18440.00,18184.00,18342.00,000,18342.00 -1997-09-24,18251.00,18420.00,18139.00,18420.00,000,18420.00 -1997-09-22,18077.00,18304.00,17960.00,18201.00,000,18201.00 -1997-09-19,17937.00,18076.00,17763.00,18058.00,000,18058.00 -1997-09-18,17682.00,17982.00,17661.00,17930.00,000,17930.00 -1997-09-17,18032.00,18176.00,17564.00,17683.00,000,17683.00 -1997-09-16,18005.00,18037.00,17873.00,17975.00,000,17975.00 -1997-09-12,18216.00,18216.00,17803.00,17966.00,000,17966.00 -1997-09-11,18626.00,18626.00,18189.00,18282.00,000,18282.00 -1997-09-10,18649.00,18724.00,18575.00,18705.00,000,18705.00 -1997-09-09,18637.00,18733.00,18514.00,18696.00,000,18696.00 -1997-09-08,18661.00,18775.00,18634.00,18634.00,000,18634.00 -1997-09-05,18577.00,18671.00,18455.00,18650.00,000,18650.00 -1997-09-04,18706.00,18713.00,18573.00,18615.00,000,18615.00 -1997-09-03,18349.00,18749.00,18349.00,18735.00,000,18735.00 -1997-09-02,18027.00,18245.00,17968.00,18233.00,000,18233.00 -1997-09-01,18215.00,18271.00,17885.00,17974.00,000,17974.00 -1997-08-29,18329.00,18329.00,17974.00,18229.00,000,18229.00 -1997-08-28,18473.00,18586.00,18386.00,18451.00,000,18451.00 -1997-08-27,18755.00,18755.00,18432.00,18442.00,000,18442.00 -1997-08-26,18666.00,18867.00,18538.00,18815.00,000,18815.00 -1997-08-25,18683.00,18741.00,18550.00,18656.00,000,18656.00 -1997-08-22,19074.00,19074.00,18576.00,18650.00,000,18650.00 -1997-08-21,19320.00,19394.00,19125.00,19157.00,000,19157.00 -1997-08-20,18953.00,19252.00,18906.00,19252.00,000,19252.00 -1997-08-19,19122.00,19246.00,18803.00,18961.00,000,18961.00 -1997-08-18,19213.00,19213.00,18835.00,19041.00,000,19041.00 -1997-08-15,19313.00,19466.00,19313.00,19326.00,000,19326.00 -1997-08-14,19056.00,19269.00,18989.00,19222.00,000,19222.00 -1997-08-13,19041.00,19154.00,18802.00,19009.00,000,19009.00 -1997-08-12,18946.00,19257.00,18917.00,19099.00,000,19099.00 -1997-08-11,19462.00,19462.00,18824.00,18824.00,000,18824.00 -1997-08-08,19395.00,19642.00,19256.00,19604.00,000,19604.00 -1997-08-07,19719.00,19772.00,19366.00,19476.00,000,19476.00 -1997-08-06,19537.00,19704.00,19233.00,19702.00,000,19702.00 -1997-08-05,19645.00,19768.00,19362.00,19514.00,000,19514.00 -1997-08-04,19839.00,19930.00,19457.00,19668.00,000,19668.00 -1997-08-01,20345.00,20399.00,19798.00,19804.00,000,19804.00 -1997-07-31,20241.00,20333.00,20041.00,20331.00,000,20331.00 -1997-07-30,20414.00,20419.00,20171.00,20213.00,000,20213.00 -1997-07-29,20628.00,20699.00,20403.00,20403.00,000,20403.00 -1997-07-28,20420.00,20601.00,20420.00,20575.00,000,20575.00 -1997-07-25,20330.00,20390.00,20304.00,20390.00,000,20390.00 -1997-07-24,20164.00,20290.00,20164.00,20286.00,000,20286.00 -1997-07-23,20244.00,20324.00,19999.00,20131.00,000,20131.00 -1997-07-22,20247.00,20280.00,20056.00,20157.00,000,20157.00 -1997-07-18,20444.00,20545.00,20248.00,20249.00,000,20249.00 -1997-07-17,20412.00,20585.00,20309.00,20519.00,000,20519.00 -1997-07-16,20139.00,20436.00,20139.00,20359.00,000,20359.00 -1997-07-15,20237.00,20243.00,20037.00,20069.00,000,20069.00 -1997-07-14,19909.00,20229.00,19909.00,20229.00,000,20229.00 -1997-07-11,19788.00,19893.00,19643.00,19875.00,000,19875.00 -1997-07-10,19710.00,19821.00,19609.00,19755.00,000,19755.00 -1997-07-09,19921.00,19964.00,19496.00,19697.00,000,19697.00 -1997-07-08,19732.00,19927.00,19732.00,19854.00,000,19854.00 -1997-07-07,19932.00,19932.00,19678.00,19705.00,000,19705.00 -1997-07-04,20123.00,20123.00,19907.00,19968.00,000,19968.00 -1997-07-03,20239.00,20252.00,20080.00,20121.00,000,20121.00 -1997-07-02,20204.00,20247.00,19976.00,20196.00,000,20196.00 -1997-07-01,20562.00,20562.00,20143.00,20176.00,000,20176.00 -1997-06-30,20586.00,20684.00,20493.00,20605.00,000,20605.00 -1997-06-27,20629.00,20743.00,20524.00,20524.00,000,20524.00 -1997-06-26,20715.00,20911.00,20625.00,20625.00,000,20625.00 -1997-06-25,20419.00,20736.00,20419.00,20679.00,000,20679.00 -1997-06-24,20383.00,20383.00,20215.00,20342.00,000,20342.00 -1997-06-23,20429.00,20462.00,20380.00,20436.00,000,20436.00 -1997-06-20,20536.00,20576.00,20357.00,20386.00,000,20386.00 -1997-06-19,20491.00,20591.00,20400.00,20508.00,000,20508.00 -1997-06-18,20598.00,20620.00,20429.00,20498.00,000,20498.00 -1997-06-17,20692.00,20721.00,20559.00,20594.00,000,20594.00 -1997-06-16,20595.00,20778.00,20549.00,20681.00,000,20681.00 -1997-06-13,20668.00,20815.00,20452.00,20528.00,000,20528.00 -1997-06-12,20340.00,20697.00,20340.00,20564.00,000,20564.00 -1997-06-11,20527.00,20634.00,20282.00,20290.00,000,20290.00 -1997-06-10,20228.00,20582.00,20228.00,20533.00,000,20533.00 -1997-06-09,20474.00,20519.00,20224.00,20224.00,000,20224.00 -1997-06-06,20474.00,20541.00,20363.00,20486.00,000,20486.00 -1997-06-05,20596.00,20606.00,20423.00,20488.00,000,20488.00 -1997-06-04,20592.00,20708.00,20512.00,20612.00,000,20612.00 -1997-06-03,20444.00,20672.00,20432.00,20563.00,000,20563.00 -1997-06-02,20084.00,20452.00,20041.00,20452.00,000,20452.00 -1997-05-30,20331.00,20390.00,20029.00,20069.00,000,20069.00 -1997-05-29,20367.00,20367.00,20125.00,20312.00,000,20312.00 -1997-05-28,19928.00,20352.00,19928.00,20351.00,000,20351.00 -1997-05-27,20068.00,20149.00,19848.00,19890.00,000,19890.00 -1997-05-26,20037.00,20155.00,19989.00,20044.00,000,20044.00 -1997-05-23,19932.00,20067.00,19907.00,20009.00,000,20009.00 -1997-05-22,19849.00,19939.00,19687.00,19877.00,000,19877.00 -1997-05-21,20322.00,20322.00,19764.00,19842.00,000,19842.00 -1997-05-20,20511.00,20612.00,20245.00,20333.00,000,20333.00 -1997-05-19,20290.00,20562.00,20206.00,20490.00,000,20490.00 -1997-05-16,20081.00,20348.00,20081.00,20325.00,000,20325.00 -1997-05-15,20162.00,20162.00,19855.00,20056.00,000,20056.00 -1997-05-14,20132.00,20210.00,20030.00,20210.00,000,20210.00 -1997-05-13,20207.00,20452.00,20120.00,20129.00,000,20129.00 -1997-05-12,19731.00,20148.00,19560.00,20144.00,000,20144.00 -1997-05-09,20097.00,20145.00,19757.00,19803.00,000,19803.00 -1997-05-08,19974.00,20107.00,19925.00,20062.00,000,20062.00 -1997-05-07,20147.00,20237.00,19952.00,20049.00,000,20049.00 -1997-05-06,19617.00,20223.00,19617.00,20181.00,000,20181.00 -1997-05-02,19244.00,19516.00,19188.00,19515.00,000,19515.00 -1997-05-01,19232.00,19588.00,19222.00,19275.00,000,19275.00 -1997-04-30,18764.00,19195.00,18764.00,19151.00,000,19151.00 -1997-04-28,18617.00,18684.00,18545.00,18670.00,000,18670.00 -1997-04-25,18648.00,18849.00,18571.00,18613.00,000,18613.00 -1997-04-24,18737.00,18983.00,18665.00,18698.00,000,18698.00 -1997-04-23,18618.00,18842.00,18618.00,18735.00,000,18735.00 -1997-04-22,18528.00,18732.00,18490.00,18544.00,000,18544.00 -1997-04-21,18400.00,18561.00,18400.00,18552.00,000,18552.00 -1997-04-18,18129.00,18370.00,18073.00,18352.00,000,18352.00 -1997-04-17,18016.00,18100.00,17970.00,18093.00,000,18093.00 -1997-04-16,17985.00,18094.00,17959.00,18031.00,000,18031.00 -1997-04-15,17712.00,18001.00,17712.00,17934.00,000,17934.00 -1997-04-14,17761.00,17827.00,17547.00,17692.00,000,17692.00 -1997-04-11,17493.00,17869.00,17448.00,17847.00,000,17847.00 -1997-04-10,17756.00,17934.00,17479.00,17486.00,000,17486.00 -1997-04-09,18007.00,18007.00,17703.00,17703.00,000,17703.00 -1997-04-08,17745.00,18035.00,17626.00,18022.00,000,18022.00 -1997-04-07,17902.00,17991.00,17664.00,17716.00,000,17716.00 -1997-04-04,18136.00,18136.00,17766.00,17861.00,000,17861.00 -1997-04-03,18022.00,18182.00,17973.00,18129.00,000,18129.00 -1997-04-02,17875.00,18048.00,17707.00,18037.00,000,18037.00 -1997-04-01,17935.00,17935.00,17529.00,17870.00,000,17870.00 -1997-03-31,18158.00,18205.00,17793.00,18003.00,000,18003.00 -1997-03-28,18184.00,18234.00,18058.00,18190.00,000,18190.00 -1997-03-27,18520.00,18594.00,18003.00,18210.00,000,18210.00 -1997-03-26,18461.00,18528.00,18189.00,18472.00,000,18472.00 -1997-03-25,18117.00,18549.00,18117.00,18440.00,000,18440.00 -1997-03-24,18683.00,18750.00,18044.00,18044.00,000,18044.00 -1997-03-21,18500.00,18634.00,18423.00,18633.00,000,18633.00 -1997-03-19,18490.00,18555.00,18379.00,18494.00,000,18494.00 -1997-03-18,18073.00,18445.00,18073.00,18445.00,000,18445.00 -1997-03-17,17962.00,18084.00,17864.00,18054.00,000,18054.00 -1997-03-14,17854.00,17940.00,17617.00,17924.00,000,17924.00 -1997-03-13,18144.00,18144.00,17900.00,17900.00,000,17900.00 -1997-03-12,18281.00,18326.00,18010.00,18183.00,000,18183.00 -1997-03-11,18130.00,18268.00,18089.00,18268.00,000,18268.00 -1997-03-10,18196.00,18196.00,17936.00,18114.00,000,18114.00 -1997-03-07,18001.00,18199.00,17837.00,18199.00,000,18199.00 -1997-03-06,18342.00,18435.00,17977.00,18041.00,000,18041.00 -1997-03-05,18618.00,18657.00,18208.00,18274.00,000,18274.00 -1997-03-04,18500.00,18689.00,18497.00,18565.00,000,18565.00 -1997-03-03,18517.00,18517.00,18346.00,18429.00,000,18429.00 -1997-02-28,19007.00,19007.00,18540.00,18557.00,000,18557.00 -1997-02-27,18936.00,19025.00,18855.00,19022.00,000,19022.00 -1997-02-26,19128.00,19217.00,18895.00,18991.00,000,18991.00 -1997-02-25,18854.00,19098.00,18776.00,19070.00,000,19070.00 -1997-02-24,19066.00,19229.00,18860.00,18897.00,000,18897.00 -1997-02-21,19031.00,19173.00,18965.00,19035.00,000,19035.00 -1997-02-20,18687.00,19101.00,18687.00,19052.00,000,19052.00 -1997-02-19,18483.00,18674.00,18329.00,18599.00,000,18599.00 -1997-02-18,18708.00,18728.00,18471.00,18471.00,000,18471.00 -1997-02-17,18731.00,18854.00,18654.00,18751.00,000,18751.00 -1997-02-14,18729.00,18881.00,18609.00,18722.00,000,18722.00 -1997-02-13,18505.00,18855.00,18505.00,18688.00,000,18688.00 -1997-02-12,18240.00,18521.00,18240.00,18410.00,000,18410.00 -1997-02-11,18158.00,18629.00,18158.00,18314.00,000,18314.00 -1997-02-10,17882.00,18268.00,17843.00,18181.00,000,18181.00 -1997-02-07,18072.00,18267.00,17792.00,17867.00,000,17867.00 -1997-02-06,18200.00,18257.00,17875.00,18038.00,000,18038.00 -1997-02-05,18303.00,18307.00,17901.00,18186.00,000,18186.00 -1997-02-04,18158.00,18629.00,18158.00,18314.00,000,18314.00 -1997-02-03,18308.00,18308.00,18077.00,18086.00,000,18086.00 -1997-01-31,17949.00,18610.00,17949.00,18330.00,000,18330.00 -1997-01-30,18305.00,18366.00,17782.00,17864.00,000,17864.00 -1997-01-29,17843.00,18335.00,17665.00,18335.00,000,18335.00 -1997-01-28,17301.00,17797.00,17195.00,17797.00,000,17797.00 -1997-01-27,17658.00,17665.00,17280.00,17335.00,000,17335.00 -1997-01-24,17894.00,17894.00,17541.00,17689.00,000,17689.00 -1997-01-23,17982.00,18129.00,17878.00,17909.00,000,17909.00 -1997-01-22,17441.00,18066.00,17441.00,18014.00,000,18014.00 -1997-01-21,17441.00,17572.00,17283.00,17358.00,000,17358.00 -1997-01-20,18104.00,18109.00,17237.00,17480.00,000,17480.00 -1997-01-17,18097.00,18447.00,17970.00,18090.00,000,18090.00 -1997-01-16,18126.00,18318.00,17971.00,18144.00,000,18144.00 -1997-01-14,18061.00,18182.00,17546.00,18093.00,000,18093.00 -1997-01-13,17338.00,18152.00,17020.00,18119.00,000,18119.00 -1997-01-10,18056.00,18058.00,17124.00,17304.00,000,17304.00 -1997-01-09,18632.00,18726.00,18072.00,18074.00,000,18074.00 -1997-01-08,18911.00,18998.00,18556.00,18680.00,000,18680.00 -1997-01-07,19444.00,19444.00,18896.00,18896.00,000,18896.00 -1997-01-06,19364.00,19501.00,19204.00,19446.00,000,19446.00 -1996-12-30,19391.00,19392.00,19109.00,19361.00,000,19361.00 -1996-12-27,19332.00,19424.00,19161.00,19369.00,000,19369.00 -1996-12-26,19543.00,19543.00,18820.00,19292.00,000,19292.00 -1996-12-25,19212.00,19556.00,19212.00,19549.00,000,19549.00 -1996-12-24,19698.00,19700.00,19162.00,19162.00,000,19162.00 -1996-12-20,19642.00,19823.00,19556.00,19690.00,000,19690.00 -1996-12-19,20070.00,20099.00,19560.00,19571.00,000,19571.00 -1996-12-18,20416.00,20416.00,20093.00,20093.00,000,20093.00 -1996-12-17,20370.00,20501.00,20231.00,20413.00,000,20413.00 -1996-12-16,20410.00,20472.00,20291.00,20422.00,000,20422.00 -1996-12-13,20452.00,20452.00,19952.00,20341.00,000,20341.00 -1996-12-12,20475.00,20504.00,20321.00,20501.00,000,20501.00 -1996-12-11,20756.00,20756.00,20467.00,20568.00,000,20568.00 -1996-12-10,20676.00,20854.00,20676.00,20822.00,000,20822.00 -1996-12-09,20397.00,20670.00,20397.00,20604.00,000,20604.00 -1996-12-06,20979.00,21002.00,20172.00,20277.00,000,20277.00 -1996-12-05,20672.00,20977.00,20669.00,20944.00,000,20944.00 -1996-12-04,20577.00,20677.00,20525.00,20660.00,000,20660.00 -1996-12-03,20682.00,20763.00,20479.00,20631.00,000,20631.00 -1996-12-02,21035.00,21068.00,20675.00,20675.00,000,20675.00 -1996-11-29,21014.00,21155.00,20978.00,21020.00,000,21020.00 -1996-11-28,21290.00,21290.00,21036.00,21036.00,000,21036.00 -1996-11-27,21398.00,21461.00,21259.00,21345.00,000,21345.00 -1996-11-26,21359.00,21460.00,21254.00,21418.00,000,21418.00 -1996-11-25,21276.00,21369.00,21197.00,21294.00,000,21294.00 -1996-11-22,21118.00,21216.00,21021.00,21216.00,000,21216.00 -1996-11-21,21169.00,21301.00,21105.00,21143.00,000,21143.00 -1996-11-20,20997.00,21218.00,20997.00,21190.00,000,21190.00 -1996-11-19,20792.00,20956.00,20733.00,20956.00,000,20956.00 -1996-11-18,20932.00,20940.00,20773.00,20796.00,000,20796.00 -1996-11-15,21058.00,21160.00,20920.00,20930.00,000,20930.00 -1996-11-14,21020.00,21084.00,20936.00,21031.00,000,21031.00 -1996-11-13,21201.00,21229.00,20923.00,20979.00,000,20979.00 -1996-11-12,21098.00,21251.00,21098.00,21206.00,000,21206.00 -1996-11-11,21153.00,21263.00,21033.00,21065.00,000,21065.00 -1996-11-08,20770.00,21227.00,20770.00,21201.00,000,21201.00 -1996-11-07,21064.00,21142.00,20757.00,20771.00,000,20771.00 -1996-11-06,20645.00,21095.00,20645.00,20992.00,000,20992.00 -1996-11-05,20655.00,20690.00,20494.00,20592.00,000,20592.00 -1996-11-01,20498.00,20695.00,20388.00,20633.00,000,20633.00 -1996-10-31,20676.00,20739.00,20450.00,20467.00,000,20467.00 -1996-10-30,20980.00,21001.00,20633.00,20682.00,000,20682.00 -1996-10-29,20920.00,21055.00,20920.00,20958.00,000,20958.00 -1996-10-28,20740.00,20904.00,20738.00,20885.00,000,20885.00 -1996-10-25,20943.00,20943.00,20700.00,20740.00,000,20740.00 -1996-10-24,21050.00,21115.00,20856.00,21003.00,000,21003.00 -1996-10-23,21046.00,21090.00,20791.00,21082.00,000,21082.00 -1996-10-22,21246.00,21246.00,21023.00,21124.00,000,21124.00 -1996-10-21,21607.00,21607.00,21300.00,21303.00,000,21303.00 -1996-10-18,21465.00,21789.00,21458.00,21612.00,000,21612.00 -1996-10-17,21403.00,21463.00,21330.00,21424.00,000,21424.00 -1996-10-16,21458.00,21478.00,21364.00,21397.00,000,21397.00 -1996-10-15,21095.00,21430.00,21095.00,21430.00,000,21430.00 -1996-10-14,20997.00,21058.00,20905.00,21029.00,000,21029.00 -1996-10-11,20891.00,21008.00,20806.00,20968.00,000,20968.00 -1996-10-09,20980.00,20983.00,20814.00,20871.00,000,20871.00 -1996-10-08,21100.00,21206.00,20969.00,21039.00,000,21039.00 -1996-10-07,21157.00,21161.00,21032.00,21161.00,000,21161.00 -1996-10-04,21267.00,21267.00,21060.00,21148.00,000,21148.00 -1996-10-03,21523.00,21548.00,21298.00,21332.00,000,21332.00 -1996-10-02,21469.00,21510.00,21413.00,21499.00,000,21499.00 -1996-10-01,21533.00,21564.00,21430.00,21463.00,000,21463.00 -1996-09-30,21538.00,21590.00,21494.00,21556.00,000,21556.00 -1996-09-27,21437.00,21604.00,21423.00,21547.00,000,21547.00 -1996-09-26,21369.00,21580.00,21369.00,21461.00,000,21461.00 -1996-09-25,21159.00,21351.00,21150.00,21351.00,000,21351.00 -1996-09-24,21105.00,21248.00,21041.00,21172.00,000,21172.00 -1996-09-20,21310.00,21310.00,21112.00,21112.00,000,21112.00 -1996-09-19,21109.00,21333.00,21023.00,21323.00,000,21323.00 -1996-09-18,21304.00,21312.00,21095.00,21157.00,000,21157.00 -1996-09-17,20929.00,21366.00,20929.00,21311.00,000,21311.00 -1996-09-13,20473.00,20924.00,20473.00,20843.00,000,20843.00 -1996-09-12,20514.00,20530.00,20375.00,20444.00,000,20444.00 -1996-09-11,20541.00,20580.00,20425.00,20571.00,000,20571.00 -1996-09-10,20269.00,20561.00,20269.00,20560.00,000,20560.00 -1996-09-09,20232.00,20373.00,20159.00,20202.00,000,20202.00 -1996-09-06,20367.00,20367.00,20123.00,20153.00,000,20153.00 -1996-09-05,20215.00,20487.00,20215.00,20380.00,000,20380.00 -1996-09-04,20218.00,20307.00,20066.00,20202.00,000,20202.00 -1996-09-03,20082.00,20290.00,19920.00,20198.00,000,20198.00 -1996-09-02,20187.00,20230.00,20082.00,20107.00,000,20107.00 -1996-08-30,20481.00,20481.00,20092.00,20167.00,000,20167.00 -1996-08-29,20687.00,20707.00,20504.00,20553.00,000,20553.00 -1996-08-28,20904.00,21040.00,20661.00,20710.00,000,20710.00 -1996-08-27,20862.00,21022.00,20828.00,20910.00,000,20910.00 -1996-08-26,21213.00,21213.00,20880.00,20884.00,000,20884.00 -1996-08-23,21378.00,21398.00,21188.00,21229.00,000,21229.00 -1996-08-22,21252.00,21386.00,21240.00,21363.00,000,21363.00 -1996-08-21,21215.00,21391.00,21215.00,21275.00,000,21275.00 -1996-08-20,21141.00,21163.00,20971.00,21127.00,000,21127.00 -1996-08-19,20848.00,21153.00,20848.00,21106.00,000,21106.00 -1996-08-16,20967.00,20967.00,20824.00,20834.00,000,20834.00 -1996-08-15,21008.00,21106.00,20913.00,20968.00,000,20968.00 -1996-08-14,20805.00,20981.00,20729.00,20981.00,000,20981.00 -1996-08-13,20653.00,20865.00,20643.00,20865.00,000,20865.00 -1996-08-12,20516.00,20667.00,20449.00,20667.00,000,20667.00 -1996-08-09,20735.00,20735.00,20492.00,20551.00,000,20551.00 -1996-08-08,20531.00,20772.00,20531.00,20731.00,000,20731.00 -1996-08-07,20717.00,20828.00,20453.00,20478.00,000,20478.00 -1996-08-06,20993.00,20993.00,20742.00,20745.00,000,20745.00 -1996-08-05,21020.00,21188.00,21020.00,21077.00,000,21077.00 -1996-08-02,21041.00,21149.00,20940.00,20940.00,000,20940.00 -1996-08-01,20665.00,21092.00,20525.00,20985.00,000,20985.00 -1996-07-31,20863.00,20863.00,20653.00,20693.00,000,20693.00 -1996-07-30,20907.00,20911.00,20790.00,20880.00,000,20880.00 -1996-07-29,21188.00,21285.00,20964.00,20968.00,000,20968.00 -1996-07-26,20938.00,21125.00,20877.00,21125.00,000,21125.00 -1996-07-25,20708.00,20979.00,20638.00,20884.00,000,20884.00 -1996-07-24,21114.00,21114.00,20628.00,20631.00,000,20631.00 -1996-07-23,20957.00,21164.00,20833.00,21164.00,000,21164.00 -1996-07-22,21476.00,21476.00,21006.00,21006.00,000,21006.00 -1996-07-19,21612.00,21702.00,21465.00,21476.00,000,21476.00 -1996-07-18,21432.00,21574.00,21428.00,21566.00,000,21566.00 -1996-07-17,21468.00,21567.00,21282.00,21413.00,000,21413.00 -1996-07-16,21637.00,21637.00,21363.00,21406.00,000,21406.00 -1996-07-15,21622.00,21753.00,21549.00,21753.00,000,21753.00 -1996-07-12,21807.00,21807.00,21558.00,21656.00,000,21656.00 -1996-07-11,21768.00,21900.00,21717.00,21893.00,000,21893.00 -1996-07-10,21955.00,22042.00,21758.00,21779.00,000,21779.00 -1996-07-09,21917.00,21977.00,21844.00,21920.00,000,21920.00 -1996-07-08,22148.00,22148.00,21802.00,21925.00,000,21925.00 -1996-07-05,22267.00,22374.00,22218.00,22232.00,000,22232.00 -1996-07-04,22354.00,22354.00,22204.00,22293.00,000,22293.00 -1996-07-03,22334.00,22390.00,22248.00,22379.00,000,22379.00 -1996-07-02,22467.00,22485.00,22270.00,22348.00,000,22348.00 -1996-07-01,22568.00,22600.00,22416.00,22456.00,000,22456.00 -1996-06-28,22545.00,22613.00,22461.00,22531.00,000,22531.00 -1996-06-27,22652.00,22657.00,22439.00,22502.00,000,22502.00 -1996-06-26,22590.00,22757.00,22573.00,22667.00,000,22667.00 -1996-06-25,22599.00,22659.00,22517.00,22597.00,000,22597.00 -1996-06-24,22566.00,22702.00,22504.00,22603.00,000,22603.00 -1996-06-21,22496.00,22599.00,22404.00,22531.00,000,22531.00 -1996-06-20,22361.00,22437.00,22133.00,22437.00,000,22437.00 -1996-06-19,22274.00,22504.00,22225.00,22367.00,000,22367.00 -1996-06-18,22306.00,22430.00,22264.00,22332.00,000,22332.00 -1996-06-17,22339.00,22519.00,22245.00,22245.00,000,22245.00 -1996-06-14,22127.00,22481.00,22127.00,22289.00,000,22289.00 -1996-06-13,22104.00,22205.00,22042.00,22082.00,000,22082.00 -1996-06-12,21883.00,22131.00,21883.00,22105.00,000,22105.00 -1996-06-11,21677.00,21863.00,21594.00,21818.00,000,21818.00 -1996-06-10,21730.00,21733.00,21641.00,21719.00,000,21719.00 -1996-06-07,21800.00,21800.00,21672.00,21752.00,000,21752.00 -1996-06-06,21912.00,22033.00,21804.00,21804.00,000,21804.00 -1996-06-05,21887.00,21986.00,21784.00,21881.00,000,21881.00 -1996-06-04,21641.00,21867.00,21641.00,21858.00,000,21858.00 -1996-06-03,21971.00,21972.00,21589.00,21589.00,000,21589.00 -1996-05-31,21905.00,22052.00,21887.00,21956.00,000,21956.00 -1996-05-30,21991.00,21991.00,21836.00,21886.00,000,21886.00 -1996-05-29,21953.00,22145.00,21877.00,22022.00,000,22022.00 -1996-05-28,21754.00,21993.00,21754.00,21945.00,000,21945.00 -1996-05-27,21840.00,21863.00,21557.00,21700.00,000,21700.00 -1996-05-24,21692.00,21805.00,21621.00,21798.00,000,21798.00 -1996-05-23,21934.00,22015.00,21632.00,21724.00,000,21724.00 -1996-05-22,22093.00,22196.00,21840.00,21958.00,000,21958.00 -1996-05-21,22001.00,22196.00,21893.00,22092.00,000,22092.00 -1996-05-20,21977.00,22311.00,21977.00,21979.00,000,21979.00 -1996-05-17,22102.00,22132.00,21815.00,21917.00,000,21917.00 -1996-05-16,22082.00,22251.00,22082.00,22147.00,000,22147.00 -1996-05-15,21371.00,22061.00,21371.00,22056.00,000,22056.00 -1996-05-14,21208.00,21311.00,21174.00,21301.00,000,21301.00 -1996-05-13,21459.00,21504.00,21171.00,21172.00,000,21172.00 -1996-05-10,21406.00,21477.00,21321.00,21420.00,000,21420.00 -1996-05-09,21742.00,21744.00,21298.00,21412.00,000,21412.00 -1996-05-08,21480.00,21729.00,21432.00,21729.00,000,21729.00 -1996-05-07,21624.00,21624.00,21431.00,21495.00,000,21495.00 -1996-05-02,21775.00,21783.00,21517.00,21662.00,000,21662.00 -1996-05-01,22031.00,22087.00,21773.00,21815.00,000,21815.00 -1996-04-30,22141.00,22163.00,21953.00,22041.00,000,22041.00 -1996-04-26,22250.00,22348.00,22231.00,22235.00,000,22235.00 -1996-04-25,22302.00,22345.00,22209.00,22230.00,000,22230.00 -1996-04-24,22151.00,22330.00,22151.00,22282.00,000,22282.00 -1996-04-23,22154.00,22217.00,22105.00,22120.00,000,22120.00 -1996-04-22,21913.00,22124.00,21913.00,22124.00,000,22124.00 -1996-04-19,21815.00,21931.00,21680.00,21884.00,000,21884.00 -1996-04-18,21764.00,21843.00,21695.00,21813.00,000,21813.00 -1996-04-17,21906.00,22008.00,21802.00,21816.00,000,21816.00 -1996-04-16,21927.00,22078.00,21866.00,21868.00,000,21868.00 -1996-04-15,21705.00,21923.00,21705.00,21883.00,000,21883.00 -1996-04-12,21698.00,21800.00,21579.00,21660.00,000,21660.00 -1996-04-11,21760.00,21782.00,21649.00,21694.00,000,21694.00 -1996-04-10,21774.00,21871.00,21773.00,21792.00,000,21792.00 -1996-04-09,21508.00,21818.00,21508.00,21744.00,000,21744.00 -1996-04-08,21636.00,21636.00,21398.00,21424.00,000,21424.00 -1996-04-05,21505.00,21728.00,21497.00,21696.00,000,21696.00 -1996-04-04,21452.00,21569.00,21397.00,21471.00,000,21471.00 -1996-04-03,21636.00,21755.00,21350.00,21465.00,000,21465.00 -1996-04-02,21569.00,21641.00,21465.00,21600.00,000,21600.00 -1996-04-01,21451.00,21758.00,21451.00,21560.00,000,21560.00 -1996-03-29,21301.00,21486.00,21250.00,21407.00,000,21407.00 -1996-03-28,21322.00,21433.00,21199.00,21296.00,000,21296.00 -1996-03-27,21047.00,21330.00,20992.00,21330.00,000,21330.00 -1996-03-26,20943.00,21290.00,20943.00,21015.00,000,21015.00 -1996-03-25,20746.00,20947.00,20746.00,20915.00,000,20915.00 -1996-03-22,20763.00,20811.00,20600.00,20701.00,000,20701.00 -1996-03-21,20471.00,20746.00,20471.00,20728.00,000,20728.00 -1996-03-19,20333.00,20615.00,20333.00,20443.00,000,20443.00 -1996-03-18,20243.00,20352.00,20224.00,20285.00,000,20285.00 -1996-03-15,19960.00,20247.00,19960.00,20191.00,000,20191.00 -1996-03-14,19735.00,19924.00,19709.00,19924.00,000,19924.00 -1996-03-13,19932.00,19932.00,19628.00,19735.00,000,19735.00 -1996-03-12,19882.00,20008.00,19854.00,19950.00,000,19950.00 -1996-03-11,20056.00,20056.00,19748.00,19796.00,000,19796.00 -1996-03-08,19919.00,20165.00,19823.00,20156.00,000,20156.00 -1996-03-07,20201.00,20201.00,19917.00,19957.00,000,19957.00 -1996-03-06,20167.00,20301.00,19946.00,20241.00,000,20241.00 -1996-03-05,20070.00,20304.00,20070.00,20184.00,000,20184.00 -1996-03-04,20166.00,20222.00,20062.00,20064.00,000,20064.00 -1996-03-01,20094.00,20250.00,19936.00,20169.00,000,20169.00 -1996-02-29,19974.00,20129.00,19903.00,20125.00,000,20125.00 -1996-02-28,20053.00,20211.00,19879.00,19920.00,000,19920.00 -1996-02-27,20427.00,20427.00,19977.00,20000.00,000,20000.00 -1996-02-26,20294.00,20480.00,20294.00,20480.00,000,20480.00 -1996-02-23,20393.00,20500.00,20267.00,20300.00,000,20300.00 -1996-02-22,20390.00,20437.00,20311.00,20341.00,000,20341.00 -1996-02-21,20655.00,20655.00,20322.00,20372.00,000,20372.00 -1996-02-20,20649.00,20668.00,20410.00,20656.00,000,20656.00 -1996-02-19,20760.00,20760.00,20632.00,20721.00,000,20721.00 -1996-02-16,20835.00,20835.00,20581.00,20803.00,000,20803.00 -1996-02-15,20921.00,21010.00,20751.00,20886.00,000,20886.00 -1996-02-14,20800.00,21042.00,20800.00,20944.00,000,20944.00 -1996-02-13,20964.00,21056.00,20783.00,20784.00,000,20784.00 -1996-02-09,21136.00,21157.00,20892.00,20935.00,000,20935.00 -1996-02-08,20956.00,21150.00,20911.00,21118.00,000,21118.00 -1996-02-07,20742.00,21039.00,20642.00,20943.00,000,20943.00 -1996-02-06,20606.00,20768.00,20556.00,20751.00,000,20751.00 -1996-02-05,20882.00,20882.00,20624.00,20653.00,000,20653.00 -1996-02-02,20947.00,21069.00,20874.00,20904.00,000,20904.00 -1996-02-01,20806.00,20943.00,20761.00,20935.00,000,20935.00 -1996-01-31,20787.00,21022.00,20787.00,20813.00,000,20813.00 -1996-01-30,20602.00,20797.00,20602.00,20722.00,000,20722.00 -1996-01-29,20658.00,20689.00,20532.00,20589.00,000,20589.00 -1996-01-26,20398.00,20693.00,20258.00,20664.00,000,20664.00 -1996-01-25,20359.00,20458.00,20289.00,20415.00,000,20415.00 -1996-01-24,20071.00,20313.00,19985.00,20313.00,000,20313.00 -1996-01-23,20209.00,20364.00,20041.00,20081.00,000,20081.00 -1996-01-22,20381.00,20392.00,20089.00,20197.00,000,20197.00 -1996-01-19,20376.00,20377.00,20156.00,20366.00,000,20366.00 -1996-01-18,20537.00,20537.00,20298.00,20370.00,000,20370.00 -1996-01-17,20656.00,20754.00,20570.00,20570.00,000,20570.00 -1996-01-16,20304.00,20567.00,20303.00,20567.00,000,20567.00 -1996-01-12,20423.00,20542.00,20208.00,20287.00,000,20287.00 -1996-01-11,20548.00,20548.00,20260.00,20378.00,000,20378.00 -1996-01-10,20592.00,20676.00,20459.00,20612.00,000,20612.00 -1996-01-09,20565.00,20653.00,20454.00,20652.00,000,20652.00 -1996-01-08,20617.00,20667.00,20471.00,20564.00,000,20564.00 -1996-01-05,20578.00,20670.00,20456.00,20669.00,000,20669.00 -1996-01-04,19946.00,20648.00,19946.00,20618.00,000,20618.00 -1995-12-29,19882.00,19940.00,19822.00,19868.00,000,19868.00 -1995-12-28,19990.00,20024.00,19868.00,19873.00,000,19873.00 -1995-12-27,19931.00,20012.00,19925.00,20012.00,000,20012.00 -1995-12-26,19792.00,19905.00,19691.00,19905.00,000,19905.00 -1995-12-25,19772.00,19831.00,19725.00,19775.00,000,19775.00 -1995-12-22,19728.00,19809.00,19670.00,19744.00,000,19744.00 -1995-12-21,19441.00,19658.00,19433.00,19653.00,000,19653.00 -1995-12-20,19201.00,19538.00,19201.00,19449.00,000,19449.00 -1995-12-19,19242.00,19242.00,19077.00,19140.00,000,19140.00 -1995-12-18,19365.00,19418.00,19299.00,19311.00,000,19311.00 -1995-12-15,19493.00,19500.00,19293.00,19347.00,000,19347.00 -1995-12-14,19318.00,19548.00,19268.00,19499.00,000,19499.00 -1995-12-13,19357.00,19439.00,19276.00,19283.00,000,19283.00 -1995-12-12,19236.00,19390.00,19234.00,19313.00,000,19313.00 -1995-12-11,19315.00,19378.00,19162.00,19227.00,000,19227.00 -1995-12-08,19421.00,19454.00,19159.00,19287.00,000,19287.00 -1995-12-07,19084.00,19443.00,19084.00,19412.00,000,19412.00 -1995-12-06,18893.00,19118.00,18889.00,19068.00,000,19068.00 -1995-12-05,18914.00,18978.00,18823.00,18880.00,000,18880.00 -1995-12-04,18889.00,19062.00,18889.00,18897.00,000,18897.00 -1995-12-01,18752.00,18986.00,18696.00,18833.00,000,18833.00 -1995-11-30,18578.00,18847.00,18578.00,18744.00,000,18744.00 -1995-11-29,18675.00,18738.00,18470.00,18534.00,000,18534.00 -1995-11-28,18560.00,18745.00,18540.00,18688.00,000,18688.00 -1995-11-27,18231.00,18690.00,18231.00,18543.00,000,18543.00 -1995-11-24,18246.00,18256.00,18147.00,18215.00,000,18215.00 -1995-11-22,18372.00,18372.00,18213.00,18240.00,000,18240.00 -1995-11-21,18376.00,18460.00,18251.00,18384.00,000,18384.00 -1995-11-20,18189.00,18445.00,18189.00,18384.00,000,18384.00 -1995-11-17,18008.00,18175.00,17987.00,18151.00,000,18151.00 -1995-11-16,17697.00,17942.00,17686.00,17940.00,000,17940.00 -1995-11-15,17805.00,17883.00,17655.00,17683.00,000,17683.00 -1995-11-14,17829.00,17889.00,17766.00,17803.00,000,17803.00 -1995-11-13,17856.00,17891.00,17692.00,17789.00,000,17789.00 -1995-11-10,17831.00,17893.00,17737.00,17844.00,000,17844.00 -1995-11-09,17877.00,18128.00,17821.00,17821.00,000,17821.00 -1995-11-08,17984.00,17984.00,17851.00,17863.00,000,17863.00 -1995-11-07,18034.00,18074.00,17936.00,18021.00,000,18021.00 -1995-11-06,18006.00,18252.00,17971.00,18037.00,000,18037.00 -1995-11-02,17533.00,18040.00,17533.00,18029.00,000,18029.00 -1995-11-01,17623.00,17623.00,17409.00,17474.00,000,17474.00 -1995-10-31,17502.00,17684.00,17358.00,17655.00,000,17655.00 -1995-10-30,17380.00,17516.00,17365.00,17509.00,000,17509.00 -1995-10-27,17699.00,17699.00,17337.00,17337.00,000,17337.00 -1995-10-26,17971.00,17976.00,17682.00,17727.00,000,17727.00 -1995-10-25,18017.00,18049.00,17945.00,17971.00,000,17971.00 -1995-10-24,18122.00,18261.00,18014.00,18014.00,000,18014.00 -1995-10-23,18122.00,18173.00,18025.00,18156.00,000,18156.00 -1995-10-20,17985.00,18219.00,17973.00,18157.00,000,18157.00 -1995-10-19,17908.00,18050.00,17908.00,17955.00,000,17955.00 -1995-10-18,17911.00,17918.00,17746.00,17896.00,000,17896.00 -1995-10-17,18006.00,18072.00,17841.00,17917.00,000,17917.00 -1995-10-16,17915.00,18141.00,17915.00,18016.00,000,18016.00 -1995-10-13,17924.00,17976.00,17777.00,17881.00,000,17881.00 -1995-10-12,17909.00,18052.00,17841.00,17971.00,000,17971.00 -1995-10-11,18156.00,18156.00,17891.00,17891.00,000,17891.00 -1995-10-09,18504.00,18504.00,18169.00,18176.00,000,18176.00 -1995-10-06,18201.00,18547.00,18183.00,18506.00,000,18506.00 -1995-10-05,18143.00,18267.00,18101.00,18220.00,000,18220.00 -1995-10-04,18167.00,18347.00,18056.00,18145.00,000,18145.00 -1995-10-03,17770.00,18160.00,17737.00,18143.00,000,18143.00 -1995-10-02,17921.00,17950.00,17684.00,17740.00,000,17740.00 -1995-09-29,18046.00,18139.00,17883.00,17913.00,000,17913.00 -1995-09-28,18219.00,18295.00,18023.00,18023.00,000,18023.00 -1995-09-27,17928.00,18262.00,17765.00,18262.00,000,18262.00 -1995-09-26,17595.00,17922.00,17595.00,17922.00,000,17922.00 -1995-09-25,17734.00,17855.00,17566.00,17566.00,000,17566.00 -1995-09-22,17958.00,17958.00,17666.00,17714.00,000,17714.00 -1995-09-21,18143.00,18143.00,17949.00,18035.00,000,18035.00 -1995-09-20,18561.00,18639.00,18142.00,18199.00,000,18199.00 -1995-09-19,18275.00,18481.00,18230.00,18474.00,000,18474.00 -1995-09-18,18781.00,18848.00,18319.00,18319.00,000,18319.00 -1995-09-14,18680.00,18791.00,18604.00,18759.00,000,18759.00 -1995-09-13,18470.00,18654.00,18421.00,18614.00,000,18614.00 -1995-09-12,18527.00,18674.00,18442.00,18472.00,000,18472.00 -1995-09-11,18271.00,18570.00,18195.00,18486.00,000,18486.00 -1995-09-08,17643.00,18501.00,17643.00,18280.00,000,18280.00 -1995-09-07,17656.00,17714.00,17512.00,17621.00,000,17621.00 -1995-09-06,17807.00,17899.00,17620.00,17620.00,000,17620.00 -1995-09-05,17731.00,17844.00,17503.00,17794.00,000,17794.00 -1995-09-04,18116.00,18116.00,17638.00,17749.00,000,17749.00 -1995-09-01,18053.00,18153.00,17909.00,18121.00,000,18121.00 -1995-08-31,17972.00,18160.00,17894.00,18117.00,000,18117.00 -1995-08-30,18171.00,18242.00,17956.00,17984.00,000,17984.00 -1995-08-29,17892.00,18185.00,17825.00,18135.00,000,18135.00 -1995-08-28,17742.00,17897.00,17581.00,17847.00,000,17847.00 -1995-08-25,17920.00,17920.00,17689.00,17771.00,000,17771.00 -1995-08-24,17700.00,17945.00,17600.00,17922.00,000,17922.00 -1995-08-23,17874.00,17933.00,17666.00,17732.00,000,17732.00 -1995-08-22,17858.00,18029.00,17818.00,17878.00,000,17878.00 -1995-08-21,18000.00,18000.00,17723.00,17871.00,000,17871.00 -1995-08-18,18095.00,18095.00,17913.00,18032.00,000,18032.00 -1995-08-17,18116.00,18268.00,18020.00,18150.00,000,18150.00 -1995-08-16,17522.00,18300.00,17522.00,18159.00,000,18159.00 -1995-08-15,16915.00,17453.00,16869.00,17453.00,000,17453.00 -1995-08-14,16819.00,17004.00,16819.00,16917.00,000,16917.00 -1995-08-11,16757.00,16856.00,16701.00,16792.00,000,16792.00 -1995-08-10,16771.00,16788.00,16546.00,16729.00,000,16729.00 -1995-08-09,16833.00,16931.00,16714.00,16789.00,000,16789.00 -1995-08-08,16645.00,16854.00,16512.00,16839.00,000,16839.00 -1995-08-07,16805.00,16873.00,16507.00,16615.00,000,16615.00 -1995-08-04,16881.00,16956.00,16642.00,16741.00,000,16741.00 -1995-08-03,16799.00,17160.00,16799.00,16894.00,000,16894.00 -1995-08-02,16319.00,16796.00,16274.00,16721.00,000,16721.00 -1995-08-01,16645.00,16645.00,16325.00,16359.00,000,16359.00 -1995-07-31,16652.00,16919.00,16594.00,16678.00,000,16678.00 -1995-07-28,16612.00,16726.00,16434.00,16649.00,000,16649.00 -1995-07-27,16367.00,16695.00,16308.00,16625.00,000,16625.00 -1995-07-26,16165.00,16387.00,16158.00,16387.00,000,16387.00 -1995-07-25,16572.00,16572.00,16148.00,16148.00,000,16148.00 -1995-07-24,16611.00,16644.00,16374.00,16592.00,000,16592.00 -1995-07-21,16509.00,16613.00,16482.00,16589.00,000,16589.00 -1995-07-20,16365.00,16453.00,16182.00,16453.00,000,16453.00 -1995-07-19,16518.00,16518.00,16240.00,16422.00,000,16422.00 -1995-07-18,16890.00,17018.00,16574.00,16574.00,000,16574.00 -1995-07-17,16574.00,16942.00,16574.00,16842.00,000,16842.00 -1995-07-14,16534.00,16591.00,16425.00,16518.00,000,16518.00 -1995-07-13,16632.00,16769.00,16436.00,16506.00,000,16506.00 -1995-07-12,16603.00,16834.00,16512.00,16606.00,000,16606.00 -1995-07-11,16217.00,16589.00,15955.00,16588.00,000,16588.00 -1995-07-10,16285.00,16703.00,16243.00,16243.00,000,16243.00 -1995-07-07,15309.00,16389.00,15309.00,16213.00,000,16213.00 -1995-07-06,14872.00,15257.00,14760.00,15257.00,000,15257.00 -1995-07-05,14759.00,14888.00,14675.00,14830.00,000,14830.00 -1995-07-04,14498.00,14769.00,14472.00,14756.00,000,14756.00 -1995-07-03,14519.00,14519.00,14296.00,14485.00,000,14485.00 -1995-06-30,14511.00,14624.00,14452.00,14517.00,000,14517.00 -1995-06-29,14678.00,14905.00,14445.00,14507.00,000,14507.00 -1995-06-28,14708.00,14755.00,14537.00,14618.00,000,14618.00 -1995-06-27,15155.00,15163.00,14745.00,14759.00,000,14759.00 -1995-06-26,15320.00,15378.00,15145.00,15145.00,000,15145.00 -1995-06-23,14987.00,15265.00,14987.00,15265.00,000,15265.00 -1995-06-22,14940.00,14954.00,14793.00,14926.00,000,14926.00 -1995-06-21,14685.00,14983.00,14665.00,14951.00,000,14951.00 -1995-06-20,14770.00,14866.00,14528.00,14666.00,000,14666.00 -1995-06-19,14705.00,14849.00,14700.00,14700.00,000,14700.00 -1995-06-16,14931.00,15021.00,14656.00,14703.00,000,14703.00 -1995-06-15,14667.00,14867.00,14376.00,14867.00,000,14867.00 -1995-06-14,14624.00,14801.00,14624.00,14660.00,000,14660.00 -1995-06-13,14818.00,14932.00,14582.00,14600.00,000,14600.00 -1995-06-12,15030.00,15030.00,14742.00,14813.00,000,14813.00 -1995-06-09,15415.00,15415.00,14978.00,15044.00,000,15044.00 -1995-06-08,15630.00,15630.00,15356.00,15442.00,000,15442.00 -1995-06-07,15643.00,15734.00,15557.00,15680.00,000,15680.00 -1995-06-06,15875.00,15923.00,15608.00,15661.00,000,15661.00 -1995-06-05,15854.00,15921.00,15740.00,15897.00,000,15897.00 -1995-06-02,15626.00,16016.00,15626.00,15849.00,000,15849.00 -1995-06-01,15481.00,15648.00,15420.00,15595.00,000,15595.00 -1995-05-31,15746.00,15746.00,15292.00,15437.00,000,15437.00 -1995-05-30,15573.00,15824.00,15573.00,15763.00,000,15763.00 -1995-05-29,15608.00,15608.00,15420.00,15574.00,000,15574.00 -1995-05-26,15540.00,15713.00,15406.00,15694.00,000,15694.00 -1995-05-25,16009.00,16033.00,15559.00,15579.00,000,15579.00 -1995-05-24,15885.00,16006.00,15808.00,15971.00,000,15971.00 -1995-05-23,15793.00,15916.00,15744.00,15916.00,000,15916.00 -1995-05-22,16102.00,16102.00,15712.00,15789.00,000,15789.00 -1995-05-19,16267.00,16267.00,16043.00,16141.00,000,16141.00 -1995-05-18,16501.00,16527.00,16205.00,16313.00,000,16313.00 -1995-05-17,16403.00,16516.00,16359.00,16471.00,000,16471.00 -1995-05-16,16606.00,16606.00,16385.00,16389.00,000,16389.00 -1995-05-15,16457.00,16636.00,16363.00,16610.00,000,16610.00 -1995-05-12,16506.00,16684.00,16387.00,16421.00,000,16421.00 -1995-05-11,16843.00,16873.00,16462.00,16462.00,000,16462.00 -1995-05-10,16908.00,16956.00,16800.00,16826.00,000,16826.00 -1995-05-09,17121.00,17167.00,16937.00,16958.00,000,16958.00 -1995-05-08,17111.00,17190.00,17072.00,17104.00,000,17104.00 -1995-05-02,16820.00,17116.00,16734.00,17089.00,000,17089.00 -1995-05-01,16820.00,16839.00,16708.00,16811.00,000,16811.00 -1995-04-28,16867.00,16869.00,16740.00,16807.00,000,16807.00 -1995-04-27,16902.00,16989.00,16809.00,16884.00,000,16884.00 -1995-04-26,16859.00,16932.00,16713.00,16826.00,000,16826.00 -1995-04-25,16837.00,17110.00,16837.00,16910.00,000,16910.00 -1995-04-24,16944.00,16981.00,16779.00,16804.00,000,16804.00 -1995-04-21,16700.00,16968.00,16700.00,16968.00,000,16968.00 -1995-04-20,16430.00,16665.00,16430.00,16643.00,000,16643.00 -1995-04-19,16181.00,16424.00,15977.00,16376.00,000,16376.00 -1995-04-18,16274.00,16323.00,16153.00,16225.00,000,16225.00 -1995-04-17,16046.00,16305.00,15893.00,16304.00,000,16304.00 -1995-04-14,16406.00,16530.00,16048.00,16048.00,000,16048.00 -1995-04-13,16336.00,16564.00,16275.00,16439.00,000,16439.00 -1995-04-12,16270.00,16434.00,16234.00,16345.00,000,16345.00 -1995-04-11,16205.00,16365.00,16109.00,16269.00,000,16269.00 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-1991-01-23,23173.00,23173.00,22952.00,23050.00,000,23050.00 -1991-01-22,23372.00,23497.00,23202.00,23254.00,000,23254.00 -1991-01-21,23755.00,23755.00,23352.00,23352.00,000,23352.00 -1991-01-18,23479.00,24050.00,23323.00,23808.00,000,23808.00 -1991-01-17,22403.00,23447.00,22100.00,23447.00,000,23447.00 -1991-01-16,23140.00,23140.00,22382.00,22443.00,000,22443.00 -1991-01-14,23198.00,23239.00,22911.00,23213.00,000,23213.00 -1991-01-11,23078.00,23241.00,22856.00,23241.00,000,23241.00 -1991-01-10,22925.00,23185.00,22712.00,23047.00,000,23047.00 -1991-01-09,22847.00,23099.00,22662.00,22969.00,000,22969.00 -1991-01-08,23708.00,23708.00,22859.00,22898.00,000,22898.00 -1991-01-07,24037.00,24037.00,23736.00,23737.00,000,23737.00 -1991-01-04,23827.00,24110.00,23796.00,24069.00,000,24069.00 -1990-12-28,23954.00,24055.00,23771.00,23849.00,000,23849.00 -1990-12-27,23938.00,24264.00,23866.00,23941.00,000,23941.00 -1990-12-26,23785.00,23976.00,23695.00,23888.00,000,23888.00 -1990-12-25,24090.00,24090.00,23768.00,23768.00,000,23768.00 -1990-12-21,24495.00,24495.00,23964.00,24120.00,000,24120.00 -1990-12-20,24853.00,24853.00,24516.00,24525.00,000,24525.00 -1990-12-19,24473.00,25064.00,24473.00,24877.00,000,24877.00 -1990-12-18,24094.00,24424.00,24094.00,24424.00,000,24424.00 -1990-12-17,24327.00,24327.00,24017.00,24088.00,000,24088.00 -1990-12-14,24637.00,24637.00,24174.00,24350.00,000,24350.00 -1990-12-13,24036.00,24643.00,24036.00,24643.00,000,24643.00 -1990-12-12,23956.00,24326.00,23893.00,23999.00,000,23999.00 -1990-12-11,23760.00,24006.00,23434.00,23957.00,000,23957.00 -1990-12-10,23565.00,23862.00,23351.00,23785.00,000,23785.00 -1990-12-07,22592.00,23538.00,22592.00,23522.00,000,23522.00 -1990-12-06,22239.00,22609.00,22239.00,22553.00,000,22553.00 -1990-12-05,21902.00,22251.00,21627.00,22194.00,000,22194.00 -1990-12-04,22679.00,22679.00,21862.00,21863.00,000,21863.00 -1990-12-03,22457.00,23034.00,22457.00,22726.00,000,22726.00 -1990-11-30,22684.00,22684.00,21934.00,22455.00,000,22455.00 -1990-11-29,23031.00,23031.00,22266.00,22713.00,000,22713.00 -1990-11-28,23610.00,23767.00,23046.00,23054.00,000,23054.00 -1990-11-27,23737.00,23737.00,23533.00,23624.00,000,23624.00 -1990-11-26,23417.00,23766.00,23417.00,23698.00,000,23698.00 -1990-11-22,22821.00,23400.00,22821.00,23400.00,000,23400.00 -1990-11-21,23158.00,23158.00,22615.00,22817.00,000,22817.00 -1990-11-20,23479.00,23479.00,23203.00,23205.00,000,23205.00 -1990-11-19,23193.00,23518.00,23177.00,23518.00,000,23518.00 -1990-11-16,23455.00,23455.00,22874.00,23172.00,000,23172.00 -1990-11-15,23931.00,23960.00,23453.00,23487.00,000,23487.00 -1990-11-14,23941.00,24046.00,23630.00,23937.00,000,23937.00 -1990-11-13,22939.00,23974.00,22939.00,23974.00,000,23974.00 -1990-11-09,22947.00,22947.00,22482.00,22932.00,000,22932.00 -1990-11-08,23444.00,23444.00,22834.00,22970.00,000,22970.00 -1990-11-07,23938.00,23938.00,23401.00,23500.00,000,23500.00 -1990-11-06,24416.00,24645.00,23868.00,23966.00,000,23966.00 -1990-11-05,24232.00,24575.00,24232.00,24385.00,000,24385.00 -1990-11-02,24244.00,24385.00,23672.00,24195.00,000,24195.00 -1990-11-01,25160.00,25160.00,24205.00,24295.00,000,24295.00 -1990-10-31,25253.00,25445.00,25145.00,25194.00,000,25194.00 -1990-10-30,25329.00,25329.00,24885.00,25242.00,000,25242.00 -1990-10-29,25004.00,25393.00,25004.00,25329.00,000,25329.00 -1990-10-26,25323.00,25323.00,24866.00,25006.00,000,25006.00 -1990-10-25,24908.00,25486.00,24908.00,25353.00,000,25353.00 -1990-10-24,25271.00,25271.00,24677.00,24877.00,000,24877.00 -1990-10-23,25099.00,25433.00,25084.00,25298.00,000,25298.00 -1990-10-22,24490.00,25232.00,24490.00,25071.00,000,25071.00 -1990-10-19,24364.00,25003.00,24364.00,24481.00,000,24481.00 -1990-10-18,23858.00,24367.00,23763.00,24367.00,000,24367.00 -1990-10-17,23615.00,24054.00,23551.00,23859.00,000,23859.00 -1990-10-16,23143.00,23819.00,23143.00,23606.00,000,23606.00 -1990-10-15,22404.00,23109.00,22404.00,23109.00,000,23109.00 -1990-10-12,22557.00,22557.00,22132.00,22390.00,000,22390.00 -1990-10-11,23480.00,23480.00,22521.00,22586.00,000,22586.00 -1990-10-09,23643.00,23971.00,23362.00,23495.00,000,23495.00 -1990-10-08,22858.00,23630.00,22858.00,23630.00,000,23630.00 -1990-10-05,22308.00,23140.00,22308.00,22828.00,000,22828.00 -1990-10-04,22829.00,22829.00,22260.00,22278.00,000,22278.00 -1990-10-03,22898.00,23463.00,22578.00,22849.00,000,22849.00 -1990-10-02,20222.00,22899.00,20222.00,22898.00,000,22898.00 -1990-10-01,20986.00,21076.00,19782.00,20222.00,000,20222.00 -1990-09-28,21756.00,21756.00,20671.00,20984.00,000,20984.00 -1990-09-27,22232.00,22312.00,21532.00,21772.00,000,21772.00 -1990-09-26,23371.00,23518.00,22251.00,22251.00,000,22251.00 -1990-09-25,23762.00,23762.00,23219.00,23359.00,000,23359.00 -1990-09-21,23570.00,23782.00,23050.00,23778.00,000,23778.00 -1990-09-20,23734.00,23836.00,23432.00,23603.00,000,23603.00 -1990-09-19,23879.00,24131.00,23726.00,23726.00,000,23726.00 -1990-09-18,24331.00,24331.00,23308.00,23885.00,000,23885.00 -1990-09-17,24889.00,24889.00,24286.00,24366.00,000,24366.00 -1990-09-14,25064.00,25064.00,24834.00,24897.00,000,24897.00 -1990-09-13,25254.00,25488.00,25012.00,25075.00,000,25075.00 -1990-09-12,24601.00,25288.00,24464.00,25216.00,000,25216.00 -1990-09-11,25064.00,25064.00,24471.00,24605.00,000,24605.00 -1990-09-10,23997.00,25081.00,23997.00,25081.00,000,25081.00 -1990-09-07,23787.00,24045.00,23406.00,23962.00,000,23962.00 -1990-09-06,24096.00,24268.00,23620.00,23812.00,000,23812.00 -1990-09-05,24888.00,24888.00,23641.00,24078.00,000,24078.00 -1990-09-04,25429.00,25460.00,24803.00,24908.00,000,24908.00 -1990-09-03,26014.00,26163.00,25418.00,25420.00,000,25420.00 -1990-08-31,25646.00,26183.00,25561.00,25978.00,000,25978.00 -1990-08-30,24916.00,25673.00,24751.00,25670.00,000,25670.00 -1990-08-29,25701.00,25701.00,24855.00,24895.00,000,24895.00 -1990-08-28,25146.00,25914.00,25146.00,25711.00,000,25711.00 -1990-08-27,24183.00,25142.00,24183.00,25142.00,000,25142.00 -1990-08-24,23731.00,24485.00,23547.00,24166.00,000,24166.00 -1990-08-23,25199.00,25199.00,23649.00,23738.00,000,23738.00 -1990-08-22,26254.00,26254.00,24845.00,25211.00,000,25211.00 -1990-08-21,26549.00,26956.00,26298.00,26298.00,000,26298.00 -1990-08-20,26760.00,26924.00,26456.00,26490.00,000,26490.00 -1990-08-17,27527.00,27527.00,26652.00,26787.00,000,26787.00 -1990-08-16,28097.00,28097.00,27436.00,27549.00,000,27549.00 -1990-08-15,26717.00,28159.00,26717.00,28112.00,000,28112.00 -1990-08-14,26194.00,26789.00,25949.00,26673.00,000,26673.00 -1990-08-13,27282.00,27282.00,25914.00,26176.00,000,26176.00 -1990-08-10,27646.00,27919.00,27168.00,27330.00,000,27330.00 -1990-08-09,28502.00,28502.00,27616.00,27616.00,000,27616.00 -1990-08-08,27657.00,28522.00,27573.00,28509.00,000,28509.00 -1990-08-07,28599.00,28599.00,27241.00,27653.00,000,27653.00 -1990-08-06,29486.00,29486.00,28273.00,28600.00,000,28600.00 -1990-08-03,30222.00,30222.00,29516.00,29516.00,000,29516.00 -1990-08-02,30800.00,30800.00,29929.00,30245.00,000,30245.00 -1990-08-01,31086.00,31372.00,30657.00,30838.00,000,30838.00 -1990-07-31,30504.00,31041.00,30504.00,31036.00,000,31036.00 -1990-07-30,30846.00,30846.00,30297.00,30443.00,000,30443.00 -1990-07-27,31341.00,31341.00,30378.00,30863.00,000,30863.00 -1990-07-26,31706.00,31795.00,31328.00,31370.00,000,31370.00 -1990-07-25,31739.00,31846.00,31651.00,31701.00,000,31701.00 -1990-07-24,31834.00,31924.00,31504.00,31702.00,000,31702.00 -1990-07-23,32421.00,32421.00,31782.00,31895.00,000,31895.00 -1990-07-20,33023.00,33023.00,32417.00,32422.00,000,32422.00 -1990-07-19,33051.00,33078.00,32848.00,33056.00,000,33056.00 -1990-07-18,33174.00,33187.00,32972.00,33048.00,000,33048.00 -1990-07-17,33065.00,33178.00,32969.00,33172.00,000,33172.00 -1990-07-16,32678.00,33022.00,32678.00,33022.00,000,33022.00 -1990-07-13,32617.00,32768.00,32524.00,32644.00,000,32644.00 -1990-07-12,32331.00,32578.00,32266.00,32575.00,000,32575.00 -1990-07-11,32151.00,32457.00,32144.00,32294.00,000,32294.00 -1990-07-10,32553.00,32553.00,32152.00,32152.00,000,32152.00 -1990-07-09,32458.00,32609.00,32418.00,32538.00,000,32538.00 -1990-07-06,32346.00,32482.00,32272.00,32445.00,000,32445.00 -1990-07-05,32449.00,32591.00,32352.00,32352.00,000,32352.00 -1990-07-04,32414.00,32627.00,32399.00,32446.00,000,32446.00 -1990-07-03,32180.00,32415.00,32134.00,32415.00,000,32415.00 -1990-07-02,31924.00,32160.00,31766.00,32160.00,000,32160.00 -1990-06-29,32145.00,32343.00,31934.00,31940.00,000,31940.00 -1990-06-28,32324.00,32339.00,31931.00,32106.00,000,32106.00 -1990-06-27,31600.00,32313.00,31600.00,32313.00,000,32313.00 -1990-06-26,31119.00,31573.00,31086.00,31572.00,000,31572.00 -1990-06-25,31638.00,31638.00,31124.00,31124.00,000,31124.00 -1990-06-22,32040.00,32040.00,31645.00,31695.00,000,31695.00 -1990-06-21,32100.00,32317.00,31923.00,32087.00,000,32087.00 -1990-06-20,32045.00,32182.00,32006.00,32088.00,000,32088.00 -1990-06-19,32324.00,32324.00,31914.00,32040.00,000,32040.00 -1990-06-18,32530.00,32634.00,32306.00,32377.00,000,32377.00 -1990-06-15,32659.00,32714.00,32537.00,32538.00,000,32538.00 -1990-06-14,32409.00,32756.00,32409.00,32668.00,000,32668.00 -1990-06-13,32349.00,32466.00,32191.00,32372.00,000,32372.00 -1990-06-12,32490.00,32594.00,32285.00,32322.00,000,32322.00 -1990-06-11,32964.00,32964.00,32488.00,32540.00,000,32540.00 -1990-06-08,33212.00,33345.00,32951.00,32993.00,000,32993.00 -1990-06-07,32939.00,33217.00,32937.00,33193.00,000,33193.00 -1990-06-06,32914.00,33052.00,32839.00,32954.00,000,32954.00 -1990-06-05,32945.00,33054.00,32856.00,32922.00,000,32922.00 -1990-06-04,32911.00,33082.00,32898.00,32925.00,000,32925.00 -1990-06-01,33110.00,33110.00,32831.00,32891.00,000,32891.00 -1990-05-31,32961.00,33228.00,32877.00,33131.00,000,33131.00 -1990-05-30,32805.00,33002.00,32465.00,32926.00,000,32926.00 -1990-05-29,33191.00,33204.00,32777.00,32818.00,000,32818.00 -1990-05-28,32839.00,33224.00,32839.00,33192.00,000,33192.00 -1990-05-25,32340.00,32839.00,32340.00,32794.00,000,32794.00 -1990-05-24,32184.00,32329.00,32070.00,32312.00,000,32312.00 -1990-05-23,31990.00,32317.00,31990.00,32177.00,000,32177.00 -1990-05-22,31721.00,31938.00,31600.00,31938.00,000,31938.00 -1990-05-21,31987.00,31987.00,31605.00,31765.00,000,31765.00 -1990-05-18,32093.00,32203.00,31870.00,32014.00,000,32014.00 -1990-05-17,31970.00,32179.00,31882.00,32062.00,000,32062.00 -1990-05-16,31983.00,32083.00,31906.00,31968.00,000,31968.00 -1990-05-15,32046.00,32323.00,31889.00,31997.00,000,31997.00 -1990-05-14,31542.00,32071.00,31542.00,32043.00,000,32043.00 -1990-05-11,31013.00,31513.00,31013.00,31512.00,000,31512.00 -1990-05-10,30957.00,31261.00,30957.00,30980.00,000,30980.00 -1990-05-09,30980.00,31111.00,30835.00,30946.00,000,30946.00 -1990-05-08,30950.00,31040.00,30730.00,30971.00,000,30971.00 -1990-05-07,30212.00,30957.00,30212.00,30956.00,000,30956.00 -1990-05-02,29736.00,30174.00,29736.00,30174.00,000,30174.00 -1990-05-01,29594.00,29691.00,29519.00,29690.00,000,29690.00 -1990-04-27,29437.00,29637.00,29437.00,29585.00,000,29585.00 -1990-04-26,29574.00,29680.00,29425.00,29425.00,000,29425.00 -1990-04-25,29507.00,29711.00,29433.00,29564.00,000,29564.00 -1990-04-24,29630.00,29630.00,29285.00,29501.00,000,29501.00 -1990-04-23,29834.00,29953.00,29521.00,29679.00,000,29679.00 -1990-04-20,29968.00,30200.00,29625.00,29835.00,000,29835.00 -1990-04-19,29296.00,30034.00,29296.00,29945.00,000,29945.00 -1990-04-18,28427.00,29250.00,28427.00,29249.00,000,29249.00 -1990-04-17,28407.00,28861.00,28336.00,28462.00,000,28462.00 -1990-04-16,29153.00,29153.00,28396.00,28463.00,000,28463.00 -1990-04-13,29586.00,29586.00,28954.00,29214.00,000,29214.00 -1990-04-12,29457.00,29688.00,29128.00,29623.00,000,29623.00 -1990-04-11,29654.00,30003.00,29340.00,29440.00,000,29440.00 -1990-04-10,30383.00,30383.00,29625.00,29625.00,000,29625.00 -1990-04-09,29298.00,30524.00,29298.00,30398.00,000,30398.00 -1990-04-06,28274.00,29279.00,28274.00,29279.00,000,29279.00 -1990-04-05,28423.00,28423.00,27251.00,28249.00,000,28249.00 -1990-04-04,28789.00,29143.00,28090.00,28443.00,000,28443.00 -1990-04-03,28005.00,28791.00,27678.00,28760.00,000,28760.00 -1990-04-02,29980.00,29980.00,28002.00,28002.00,000,28002.00 -1990-03-30,31002.00,31002.00,29828.00,29980.00,000,29980.00 -1990-03-29,31238.00,31438.00,30877.00,31026.00,000,31026.00 -1990-03-28,31800.00,31800.00,31107.00,31264.00,000,31264.00 -1990-03-27,31834.00,32164.00,31368.00,31826.00,000,31826.00 -1990-03-26,30378.00,31840.00,30378.00,31840.00,000,31840.00 -1990-03-23,29851.00,30372.00,29597.00,30372.00,000,30372.00 -1990-03-22,30776.00,30776.00,28830.00,29843.00,000,29843.00 -1990-03-20,31242.00,31551.00,30570.00,30807.00,000,30807.00 -1990-03-19,32609.00,32721.00,31198.00,31263.00,000,31263.00 -1990-03-16,32659.00,32918.00,32472.00,32616.00,000,32616.00 -1990-03-15,32365.00,32720.00,32365.00,32672.00,000,32672.00 -1990-03-14,32578.00,32762.00,32280.00,32352.00,000,32352.00 -1990-03-13,33318.00,33318.00,32621.00,32621.00,000,32621.00 -1990-03-12,33985.00,34006.00,33366.00,33368.00,000,33368.00 -1990-03-09,33724.00,34320.00,33724.00,33993.00,000,33993.00 -1990-03-08,33273.00,33939.00,32971.00,33691.00,000,33691.00 -1990-03-07,33798.00,33807.00,33180.00,33362.00,000,33362.00 -1990-03-06,33857.00,33989.00,33730.00,33791.00,000,33791.00 -1990-03-05,34072.00,34118.00,33752.00,33845.00,000,33845.00 -1990-03-02,33855.00,34092.00,33771.00,34058.00,000,34058.00 -1990-03-01,34587.00,34588.00,33830.00,33830.00,000,33830.00 -1990-02-28,33950.00,34756.00,33950.00,34592.00,000,34592.00 -1990-02-27,33346.00,34001.00,32793.00,33898.00,000,33898.00 -1990-02-26,34863.00,34863.00,32443.00,33322.00,000,33322.00 -1990-02-23,35803.00,35803.00,34841.00,34891.00,000,34891.00 -1990-02-22,35767.00,36148.00,35088.00,35827.00,000,35827.00 -1990-02-21,36866.00,36866.00,35695.00,35734.00,000,35734.00 -1990-02-20,37158.00,37158.00,36868.00,36896.00,000,36896.00 -1990-02-19,37496.00,37611.00,37097.00,37223.00,000,37223.00 -1990-02-16,37523.00,37674.00,37405.00,37460.00,000,37460.00 -1990-02-15,37186.00,37585.00,37186.00,37472.00,000,37472.00 -1990-02-14,37125.00,37183.00,37018.00,37156.00,000,37156.00 -1990-02-13,37320.00,37351.00,37094.00,37107.00,000,37107.00 -1990-02-09,37509.00,37509.00,37193.00,37288.00,000,37288.00 -1990-02-08,37346.00,37516.00,37181.00,37516.00,000,37516.00 -1990-02-07,37684.00,37693.00,37256.00,37302.00,000,37302.00 -1990-02-06,37680.00,37887.00,37643.00,37667.00,000,37667.00 -1990-02-05,37677.00,37732.00,37583.00,37631.00,000,37631.00 -1990-02-02,37256.00,37665.00,37256.00,37650.00,000,37650.00 -1990-02-01,37242.00,37332.00,37125.00,37206.00,000,37206.00 -1990-01-31,37201.00,37208.00,36957.00,37189.00,000,37189.00 -1990-01-30,37210.00,37336.00,37192.00,37216.00,000,37216.00 -1990-01-29,36913.00,37225.00,36913.00,37174.00,000,37174.00 -1990-01-26,36978.00,37088.00,36846.00,36874.00,000,36874.00 -1990-01-25,36822.00,37082.00,36766.00,36969.00,000,36969.00 -1990-01-24,37396.00,37463.00,36683.00,36779.00,000,36779.00 -1990-01-23,37213.00,37379.00,37018.00,37378.00,000,37378.00 -1990-01-22,36853.00,37257.00,36851.00,37257.00,000,37257.00 -1990-01-19,36704.00,36840.00,36365.00,36837.00,000,36837.00 -1990-01-18,36834.00,37003.00,36521.00,36729.00,000,36729.00 -1990-01-17,36894.00,37285.00,36821.00,36821.00,000,36821.00 -1990-01-16,37469.00,37469.00,36658.00,36850.00,000,36850.00 -1990-01-12,38130.00,38130.00,37517.00,37517.00,000,37517.00 -1990-01-11,37706.00,38170.00,37604.00,38170.00,000,38170.00 -1990-01-10,37928.00,37928.00,37460.00,37697.00,000,37697.00 -1990-01-09,38281.00,38297.00,37730.00,37951.00,000,37951.00 -1990-01-08,38332.00,38564.00,38121.00,38295.00,000,38295.00 -1990-01-05,38717.00,38787.00,38091.00,38275.00,000,38275.00 -1990-01-04,38922.00,38951.00,38705.00,38713.00,000,38713.00 -1989-12-29,38913.00,38957.00,38828.00,38916.00,000,38916.00 -1989-12-28,38835.00,38920.00,38678.00,38877.00,000,38877.00 -1989-12-27,38709.00,38884.00,38709.00,38802.00,000,38802.00 -1989-12-26,38470.00,38786.00,38470.00,38681.00,000,38681.00 -1989-12-25,38060.00,38467.00,37905.00,38424.00,000,38424.00 -1989-12-22,38268.00,38428.00,37863.00,38040.00,000,38040.00 -1989-12-21,38523.00,38540.00,38196.00,38215.00,000,38215.00 -1989-12-20,38442.00,38572.00,38311.00,38512.00,000,38512.00 -1989-12-19,38560.00,38560.00,38250.00,38439.00,000,38439.00 -1989-12-18,38304.00,38586.00,38304.00,38586.00,000,38586.00 -1989-12-15,38181.00,38273.00,38063.00,38271.00,000,38271.00 -1989-12-14,38058.00,38202.00,37994.00,38181.00,000,38181.00 -1989-12-13,37831.00,38062.00,37831.00,38062.00,000,38062.00 -1989-12-12,37764.00,37900.00,37676.00,37804.00,000,37804.00 -1989-12-11,37714.00,37840.00,37688.00,37753.00,000,37753.00 -1989-12-08,37864.00,37880.00,37625.00,37724.00,000,37724.00 -1989-12-07,37656.00,37858.00,37550.00,37858.00,000,37858.00 -1989-12-06,37453.00,37654.00,37299.00,37654.00,000,37654.00 -1989-12-05,37327.00,37548.00,37327.00,37494.00,000,37494.00 -1989-12-04,37135.00,37313.00,37124.00,37304.00,000,37304.00 -1989-12-01,37284.00,37333.00,37059.00,37133.00,000,37133.00 -1989-11-30,37034.00,37269.00,37019.00,37269.00,000,37269.00 -1989-11-29,36989.00,37129.00,36936.00,37021.00,000,37021.00 -1989-11-28,36893.00,36987.00,36826.00,36985.00,000,36985.00 -1989-11-27,36488.00,36883.00,36488.00,36882.00,000,36882.00 -1989-11-24,36305.00,36486.00,36305.00,36484.00,000,36484.00 -1989-11-22,36098.00,36388.00,36098.00,36287.00,000,36287.00 -1989-11-21,35920.00,36060.00,35920.00,36060.00,000,36060.00 -1989-11-20,35963.00,35975.00,35882.00,35894.00,000,35894.00 -1989-11-17,35903.00,36025.00,35900.00,35964.00,000,35964.00 -1989-11-16,35855.00,35953.00,35833.00,35876.00,000,35876.00 -1989-11-15,35806.00,35977.00,35805.00,35852.00,000,35852.00 -1989-11-14,35726.00,35776.00,35697.00,35769.00,000,35769.00 -1989-11-13,35714.00,35800.00,35678.00,35750.00,000,35750.00 -1989-11-10,35679.00,35742.00,35595.00,35663.00,000,35663.00 -1989-11-09,35626.00,35690.00,35467.00,35657.00,000,35657.00 -1989-11-08,35319.00,35629.00,35319.00,35596.00,000,35596.00 -1989-11-07,35371.00,35371.00,35099.00,35270.00,000,35270.00 -1989-11-06,35495.00,35573.00,35411.00,35434.00,000,35434.00 -1989-11-02,35546.00,35556.00,35361.00,35495.00,000,35495.00 -1989-11-01,35545.00,35640.00,35453.00,35564.00,000,35564.00 -1989-10-31,35413.00,35583.00,35413.00,35549.00,000,35549.00 -1989-10-30,35523.00,35523.00,35336.00,35417.00,000,35417.00 -1989-10-27,35694.00,35743.00,35375.00,35527.00,000,35527.00 -1989-10-26,35452.00,35697.00,35452.00,35678.00,000,35678.00 -1989-10-25,35536.00,35645.00,35442.00,35442.00,000,35442.00 -1989-10-24,35609.00,35651.00,35449.00,35527.00,000,35527.00 -1989-10-23,35514.00,35670.00,35514.00,35586.00,000,35586.00 -1989-10-20,35419.00,35611.00,35419.00,35486.00,000,35486.00 -1989-10-19,35129.00,35392.00,35129.00,35374.00,000,35374.00 -1989-10-18,35005.00,35152.00,34992.00,35108.00,000,35108.00 -1989-10-17,34508.00,35184.00,34508.00,34996.00,000,34996.00 -1989-10-16,35076.00,35076.00,34461.00,34469.00,000,34469.00 -1989-10-13,34844.00,35119.00,34844.00,35116.00,000,35116.00 -1989-10-12,35220.00,35220.00,34795.00,34795.00,000,34795.00 -1989-10-11,35381.00,35399.00,35006.00,35240.00,000,35240.00 -1989-10-09,35229.00,35405.00,35229.00,35376.00,000,35376.00 -1989-10-06,35508.00,35508.00,35051.00,35209.00,000,35209.00 -1989-10-05,35382.00,35537.00,35382.00,35523.00,000,35523.00 -1989-10-04,35390.00,35419.00,35338.00,35383.00,000,35383.00 -1989-10-03,35603.00,35603.00,35293.00,35366.00,000,35366.00 -1989-10-02,35672.00,35771.00,35613.00,35623.00,000,35623.00 -1989-09-29,35704.00,35778.00,35537.00,35637.00,000,35637.00 -1989-09-28,35398.00,35690.00,35398.00,35690.00,000,35690.00 -1989-09-27,35475.00,35654.00,35308.00,35371.00,000,35371.00 -1989-09-26,34978.00,35445.00,34975.00,35445.00,000,35445.00 -1989-09-25,34836.00,34990.00,34834.00,34961.00,000,34961.00 -1989-09-22,34783.00,34865.00,34733.00,34772.00,000,34772.00 -1989-09-21,34537.00,34759.00,34537.00,34745.00,000,34745.00 -1989-09-20,34499.00,34560.00,34448.00,34471.00,000,34471.00 -1989-09-19,34477.00,34581.00,34368.00,34471.00,000,34471.00 -1989-09-18,34394.00,34525.00,34385.00,34473.00,000,34473.00 -1989-09-14,34292.00,34410.00,34262.00,34402.00,000,34402.00 -1989-09-13,34345.00,34345.00,34186.00,34287.00,000,34287.00 -1989-09-12,34105.00,34333.00,34091.00,34333.00,000,34333.00 -1989-09-11,34129.00,34165.00,33955.00,34114.00,000,34114.00 -1989-09-08,34159.00,34316.00,34107.00,34116.00,000,34116.00 -1989-09-07,34228.00,34300.00,34111.00,34153.00,000,34153.00 -1989-09-06,34434.00,34436.00,34118.00,34271.00,000,34271.00 -1989-09-05,34513.00,34635.00,34338.00,34442.00,000,34442.00 -1989-09-04,34355.00,34559.00,34306.00,34484.00,000,34484.00 -1989-09-01,34439.00,34491.00,34220.00,34348.00,000,34348.00 -1989-08-31,34483.00,34516.00,34244.00,34431.00,000,34431.00 -1989-08-30,34700.00,34759.00,34423.00,34472.00,000,34472.00 -1989-08-29,34612.00,34688.00,34506.00,34688.00,000,34688.00 -1989-08-28,34740.00,34749.00,34493.00,34607.00,000,34607.00 -1989-08-25,34792.00,34892.00,34639.00,34740.00,000,34740.00 -1989-08-24,34903.00,34958.00,34663.00,34787.00,000,34787.00 -1989-08-23,35111.00,35179.00,34849.00,34893.00,000,34893.00 -1989-08-22,35115.00,35158.00,35011.00,35114.00,000,35114.00 -1989-08-21,35097.00,35191.00,35068.00,35141.00,000,35141.00 -1989-08-18,35104.00,35126.00,34951.00,35063.00,000,35063.00 -1989-08-17,35122.00,35192.00,34986.00,35090.00,000,35090.00 -1989-08-16,34819.00,35086.00,34819.00,35084.00,000,35084.00 -1989-08-15,34660.00,34813.00,34632.00,34811.00,000,34811.00 -1989-08-14,34693.00,34725.00,34590.00,34672.00,000,34672.00 -1989-08-11,34729.00,34832.00,34625.00,34713.00,000,34713.00 -1989-08-10,34843.00,34911.00,34709.00,34720.00,000,34720.00 -1989-08-09,34764.00,34861.00,34737.00,34859.00,000,34859.00 -1989-08-08,34616.00,34761.00,34531.00,34759.00,000,34759.00 -1989-08-07,34737.00,34759.00,34556.00,34630.00,000,34630.00 -1989-08-04,34747.00,34747.00,34660.00,34742.00,000,34742.00 -1989-08-03,34889.00,34930.00,34699.00,34780.00,000,34780.00 -1989-08-02,34894.00,35016.00,34851.00,34899.00,000,34899.00 -1989-08-01,34950.00,34964.00,34767.00,34898.00,000,34898.00 -1989-07-31,34723.00,34955.00,34723.00,34954.00,000,34954.00 -1989-07-28,34824.00,34946.00,34686.00,34706.00,000,34706.00 -1989-07-27,34539.00,34788.00,34539.00,34785.00,000,34785.00 -1989-07-26,34586.00,34771.00,34511.00,34516.00,000,34516.00 -1989-07-25,34156.00,34543.00,34156.00,34539.00,000,34539.00 -1989-07-24,33912.00,34095.00,33867.00,34093.00,000,34093.00 -1989-07-21,33689.00,33971.00,33619.00,33899.00,000,33899.00 -1989-07-20,33598.00,33701.00,33584.00,33665.00,000,33665.00 -1989-07-19,33344.00,33558.00,33344.00,33557.00,000,33557.00 -1989-07-18,33459.00,33465.00,33309.00,33344.00,000,33344.00 -1989-07-17,33585.00,33594.00,33415.00,33456.00,000,33456.00 -1989-07-14,33666.00,33699.00,33539.00,33575.00,000,33575.00 -1989-07-13,33733.00,33778.00,33628.00,33631.00,000,33631.00 -1989-07-12,33767.00,33816.00,33693.00,33702.00,000,33702.00 -1989-07-11,33689.00,33799.00,33665.00,33747.00,000,33747.00 -1989-07-10,33719.00,33843.00,33629.00,33676.00,000,33676.00 -1989-07-07,33480.00,33714.00,33480.00,33704.00,000,33704.00 -1989-07-06,33348.00,33516.00,33348.00,33423.00,000,33423.00 -1989-07-05,33221.00,33358.00,33221.00,33310.00,000,33310.00 -1989-07-04,33268.00,33280.00,33181.00,33190.00,000,33190.00 -1989-07-03,32895.00,33236.00,32697.00,33236.00,000,33236.00 -1989-06-30,32919.00,32950.00,32642.00,32949.00,000,32949.00 -1989-06-29,33198.00,33223.00,32923.00,32956.00,000,32956.00 -1989-06-28,33431.00,33431.00,32952.00,33246.00,000,33246.00 -1989-06-27,33622.00,33646.00,33445.00,33469.00,000,33469.00 -1989-06-26,33565.00,33693.00,33525.00,33626.00,000,33626.00 -1989-06-23,33398.00,33702.00,33398.00,33531.00,000,33531.00 -1989-06-22,33341.00,33427.00,33262.00,33325.00,000,33325.00 -1989-06-21,33241.00,33377.00,33177.00,33345.00,000,33345.00 -1989-06-20,33014.00,33283.00,33008.00,33233.00,000,33233.00 -1989-06-19,33039.00,33051.00,32858.00,33013.00,000,33013.00 -1989-06-16,32951.00,33195.00,32606.00,33055.00,000,33055.00 -1989-06-15,33467.00,33525.00,32913.00,32913.00,000,32913.00 -1989-06-14,33235.00,33408.00,33018.00,33403.00,000,33403.00 -1989-06-13,33464.00,33556.00,33135.00,33214.00,000,33214.00 -1989-06-12,33615.00,33615.00,33315.00,33398.00,000,33398.00 -1989-06-09,33756.00,33812.00,33581.00,33640.00,000,33640.00 -1989-06-08,33657.00,33838.00,33657.00,33718.00,000,33718.00 -1989-06-07,33497.00,33677.00,33399.00,33627.00,000,33627.00 -1989-06-06,33433.00,33574.00,33248.00,33452.00,000,33452.00 -1989-06-05,33650.00,33809.00,33408.00,33457.00,000,33457.00 -1989-06-02,33986.00,34065.00,33628.00,33667.00,000,33667.00 -1989-06-01,34294.00,34328.00,33932.00,33981.00,000,33981.00 -1989-05-31,34071.00,34269.00,34005.00,34267.00,000,34267.00 -1989-05-30,34142.00,34162.00,33990.00,34077.00,000,34077.00 -1989-05-29,34214.00,34338.00,34102.00,34161.00,000,34161.00 -1989-05-26,34054.00,34192.00,34024.00,34192.00,000,34192.00 -1989-05-25,33889.00,34006.00,33859.00,34005.00,000,34005.00 -1989-05-24,33809.00,33934.00,33707.00,33852.00,000,33852.00 -1989-05-23,34043.00,34043.00,33582.00,33817.00,000,33817.00 -1989-05-22,34007.00,34124.00,34003.00,34068.00,000,34068.00 -1989-05-19,33858.00,34007.00,33804.00,34001.00,000,34001.00 -1989-05-18,33983.00,33999.00,33768.00,33856.00,000,33856.00 -1989-05-17,33957.00,34040.00,33947.00,33992.00,000,33992.00 -1989-05-16,33796.00,33931.00,33740.00,33926.00,000,33926.00 -1989-05-15,33864.00,33864.00,33612.00,33716.00,000,33716.00 -1989-05-12,34078.00,34094.00,33839.00,33866.00,000,33866.00 -1989-05-11,34008.00,34082.00,33971.00,34081.00,000,34081.00 -1989-05-10,34047.00,34154.00,33988.00,33992.00,000,33992.00 -1989-05-09,34147.00,34175.00,33948.00,34032.00,000,34032.00 -1989-05-08,33980.00,34171.00,33980.00,34135.00,000,34135.00 -1989-05-02,33821.00,33978.00,33821.00,33955.00,000,33955.00 -1989-05-01,33722.00,33881.00,33722.00,33793.00,000,33793.00 -1989-04-28,33552.00,33738.00,33552.00,33713.00,000,33713.00 -1989-04-27,33458.00,33565.00,33425.00,33501.00,000,33501.00 -1989-04-26,33257.00,33446.00,33158.00,33435.00,000,33435.00 -1989-04-25,32854.00,33318.00,32854.00,33245.00,000,33245.00 -1989-04-24,33037.00,33115.00,32704.00,32806.00,000,32806.00 -1989-04-21,33153.00,33153.00,32781.00,33030.00,000,33030.00 -1989-04-20,33368.00,33397.00,33048.00,33185.00,000,33185.00 -1989-04-19,33320.00,33414.00,33286.00,33364.00,000,33364.00 -1989-04-18,33308.00,33362.00,33217.00,33322.00,000,33322.00 -1989-04-17,33189.00,33402.00,33189.00,33308.00,000,33308.00 -1989-04-14,33061.00,33151.00,32925.00,33150.00,000,33150.00 -1989-04-13,33268.00,33336.00,32951.00,33064.00,000,33064.00 -1989-04-12,33259.00,33435.00,33137.00,33256.00,000,33256.00 -1989-04-11,32998.00,33307.00,32940.00,33250.00,000,33250.00 -1989-04-10,33192.00,33224.00,32910.00,32999.00,000,32999.00 -1989-04-07,33027.00,33218.00,33025.00,33185.00,000,33185.00 -1989-04-06,33334.00,33334.00,32839.00,32996.00,000,32996.00 -1989-04-05,33338.00,33413.00,33240.00,33361.00,000,33361.00 -1989-04-04,33066.00,33340.00,33066.00,33312.00,000,33312.00 -1989-04-03,32863.00,33077.00,32847.00,33042.00,000,33042.00 -1989-03-31,32835.00,32964.00,32678.00,32839.00,000,32839.00 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-1984-01-09,9954.00,9954.00,9954.00,9954.00,000,9954.00 -1984-01-06,9961.00,9961.00,9961.00,9961.00,000,9961.00 -1984-01-05,9947.00,9947.00,9947.00,9947.00,000,9947.00 -1984-01-04,9927.00,9927.00,9927.00,9927.00,000,9927.00 diff --git a/solutions/uncertainty_traps_solutions.ipynb b/solutions/uncertainty_traps_solutions.ipynb deleted file mode 100644 index 2f6e43a3d..000000000 --- a/solutions/uncertainty_traps_solutions.ipynb +++ /dev/null @@ -1,312 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# quant-econ Solutions: Uncertainty Traps" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Solutions for http://quant-econ.net/py/uncertainty_traps.html" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "from __future__ import division\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "import quantecon as qe\n", - "import seaborn as sns\n", - "import itertools" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Exercise 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This exercise asked you to validate the laws of motion for $\\gamma$ and $\\mu$ given in the lecture, based on the stated result about Bayesian updating in a scalar Gaussian setting. The stated result tells us that after observing average output $X$ of the $M$ firms, our posterior beliefs will be\n", - "\n", - "$$\n", - " N(\\mu_0, 1/\\gamma_0)\n", - "$$\n", - "\n", - "where\n", - "\n", - "$$\n", - " \\mu_0 = \\frac{\\mu \\gamma + M X \\gamma_x}{\\gamma + M \\gamma_x}\n", - " \\quad \\text{and} \\quad\n", - " \\gamma_0 = \\gamma + M \\gamma_x\n", - "$$\n", - "\n", - "If we take a random variable $\\theta$ with this distribution and then evaluate the distribution of $\\rho \\theta + \\sigma_\\theta w$ where $w$ is independent and standard normal, we get the expressions for $\\mu'$ and $\\gamma'$ given in the lecture." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Exercise 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First let's replicate the plot that illustrates the law of motion for precision, which is\n", - "\n", - "$$\n", - " \\gamma_{t+1} = \n", - " \\left(\n", - " \\frac{\\rho^2}{\\gamma_t + M \\gamma_x} + \\sigma_\\theta^2\n", - " \\right)^{-1}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here $M$ is the number of active firms. The next figure plots $\\gamma_{t+1}$ against $\\gamma_t$ on a 45 degree diagram for different values of $M$" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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5EMfqXhQre1FsHMTO9N902QyYGHBgUum/6XebO+IF+S7E80VsK9Wb7UQGR5m6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aCqsYaNOZ+SUXocgABXfxZEzSTSa4CZK7uRNYSdnIIqPkg/S4G2FoARkX4kJ0bg7e5s5sqEEKL7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\nds0XuwmLDDzADQORo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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "palette = itertools.cycle(sns.color_palette())\n", - "econ = qe.models.UncertaintyTrapEcon()\n", - "rho, sig_theta, gx = econ.rho, econ.sig_theta, econ.gx # simplify names\n", - "g = np.linspace(1e-10, 3, 200) # gamma grid\n", - "fig, ax = plt.subplots(figsize=(9, 9))\n", - "ax.plot(g, g, 'k-') # 45 degree line\n", - "for M in range(7):\n", - " g_next = 1 / (rho**2 / (g + M * gx) + sig_theta**2)\n", - " label_string = r\"$M = {}$\".format(M)\n", - " ax.plot(g, g_next, lw=2, label=label_string, color=next(palette))\n", - "ax.legend(loc='lower right', fontsize=14)\n", - "ax.set_xlabel(r'$\\gamma$', fontsize=16)\n", - "ax.set_ylabel(r\"$\\gamma'$\", fontsize=16)\n", - "ax.grid()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The points where the curves hit the 45 degree lines are the long run steady states corresponding to each $M$, if that value of $M$ was to remain fixed. As the number of firms falls, so does the long run steady state of precision." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next let's generate time series for beliefs and the aggregates -- that is, the number\n", - "of active firms and average output." - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "sim_length=2000\n", - "\n", - "mu_vec = np.empty(sim_length)\n", - "theta_vec = np.empty(sim_length)\n", - "gamma_vec = np.empty(sim_length)\n", - "X_vec = np.empty(sim_length)\n", - "M_vec = np.empty(sim_length)\n", - "\n", - "mu_vec[0] = econ.mu\n", - "gamma_vec[0] = econ.gamma\n", - "theta_vec[0] = 0\n", - "\n", - "w_shocks = np.random.randn(sim_length)\n", - "\n", - "for t in range(sim_length-1):\n", - " X, M = econ.gen_aggregates()\n", - " X_vec[t] = X\n", - " M_vec[t] = M\n", - "\n", - " econ.update_beliefs(X, M)\n", - " econ.update_theta(w_shocks[t])\n", - "\n", - " mu_vec[t+1] = econ.mu\n", - " gamma_vec[t+1] = econ.gamma\n", - " theta_vec[t+1] = econ.theta\n", - "\n", - "# Record final values of aggregates\n", - "X, M = econ.gen_aggregates()\n", - "X_vec[-1] = X\n", - "M_vec[-1] = M" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First let's see how well $\\mu$ tracks $\\theta$ in these simulations" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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f2IfYfNzz9WbRVTEmPoHD070vYEA9AoC5chqF8+Yz0hc0VknOScJZt8TKaL9p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NUxmPa2nRpe65Lb88VxQtf1XBufKwVA1/WXdF3/IP/ldwHcB77mPUfTtF8G8N8B+BVd17fQwmO9\nE4HJXwD4DQDQNO0sgJuuFBHtcZqmfVPTtN/P/3kawBSA/xv51xzA1wH8AMDPADysadpovsboCQCv\nduApU/OcuVkAfoTqr/WTsNas/wLAb+bv+1UAL7XtGVOznCteTdP+naZp9+W/tOek8TXvIZqmjcLa\nXfkVXdc38je37FjvSEt6TdP+EMAzsLYN/S1d1znwr0fk34x/AmAC1hLOP4CV3v2XAGIArsDaKmZo\nmvZ1AH8XVtr3j3Rd/1cdedLUEE3THgPwTwFMA8jB2i76ZVjbAqu+1pqmKQD+GYBjAFIAfkvXdWbN\nupjPa74G4PdhXUnvANiG9Zqv8jXvHZqm/aewXufP8jdJAL8F67UM/FjnrBwiIiLqGt1Q/EpEREQE\ngIEJERERdREGJkRERNQ1GJgQERFR12BgQkRERF2DgQkRERF1DQYmRERE1DUYmBAREVHX+P8BolHf\ntv8BhnAAAAAASUVORK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(figsize=(9, 6))\n", - "ax.plot(range(sim_length), theta_vec, alpha=0.6, lw=2, label=r\"$\\theta$\")\n", - "ax.plot(range(sim_length), mu_vec, alpha=0.6, lw=2, label=r\"$\\mu$\")\n", - "ax.legend(fontsize=16)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let's plot the whole thing together" - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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tLLBrjuJ2zI4P0VjmWDPHFbkxs4DTV6cNTUjMAWOhsJ1XOyeJUo/v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\nlSvP8OubG9X6sXSy8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phPGGO2iXMTTZY7NxdyD98r6R8kDTVq3GyHiYCOCrd7gGY5JumD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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, axes = plt.subplots(4, 1, figsize=(12, 20))\n", - "# Add some spacing\n", - "fig.subplots_adjust(hspace=0.3)\n", - "\n", - "series = (theta_vec, mu_vec, gamma_vec, M_vec)\n", - "names = r'$\\theta$', r'$\\mu$', r'$\\gamma$', r'$M$'\n", - "\n", - "for ax, vals, name in zip(axes, series, names):\n", - " # determine suitable y limits\n", - " s_max, s_min = max(vals), min(vals)\n", - " s_range = s_max - s_min\n", - " y_max = s_max + s_range * 0.1\n", - " y_min = s_min - s_range * 0.1\n", - " ax.set_ylim(y_min, y_max)\n", - " # Plot series\n", - " ax.plot(range(sim_length), vals, alpha=0.6, lw=2)\n", - " ax.set_title(\"time series for {}\".format(name), fontsize=16)\n", - " ax.grid()\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "If you run the code above you'll get different plots, of course. Try experimenting with different parameters to see the effects on the time series. (It would also be interesting to experiment with non-Gaussian distributions for the shocks, but this is a big exercise since it takes us outside the world of the standard Kalman filter.)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.10" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/solutions/web_graph_data.txt b/solutions/web_graph_data.txt deleted file mode 100644 index acb184273..000000000 --- a/solutions/web_graph_data.txt +++ /dev/null @@ -1,37 +0,0 @@ -a -> d; -a -> f; -b -> j; -b -> k; -b -> m; -c -> c; -c -> g; -c -> j; -c -> m; -d -> f; -d -> h; -d -> k; -e -> d; -e -> h; -e -> l; -f -> a; -f -> b; -f -> j; -f -> l; -g -> b; -g -> j; -h -> d; -h -> g; -h -> l; -h -> m; -i -> g; -i -> h; -i -> n; -j -> e; -j -> i; -j -> k; -k -> n; -l -> m; -m -> g; -n -> c; -n -> j; -n -> m; \ No newline at end of file