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para.py
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para.py
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from __future__ import division
import numpy as np
from scipy.stats import lognorm, norm, uniform, gamma, truncnorm
from scipy.optimize import brentq, newton
from math import log, exp
import pandas
import pylab
import pickle
import multiprocessing as mp
def removekeys(d, keys):
r = dict(d)
for key in keys:
del r[key]
return r
class Para:
"Class for generating model parameters"
def __init__(self, charts=False, rebuild=False):
self.opt_lam = 0
if rebuild:
self.build_para(charts=charts)
else:
with open('para_dist.pkl', 'rU') as f:
para_dist = pickle.load(f)
f.close()
self.I_K_param = para_dist[0]
self.SD_I_param = para_dist[1]
self.rho_param = para_dist[2]
self.SA_K_param = para_dist[3]
self.evap_param = para_dist[4]
self.d_loss_param_a = para_dist[5]
self.d_loss_param_b = para_dist[6]
self.t_cost_param = para_dist[7]
self.Lambda_high_pa = para_dist[8]
self.theta_mu = para_dist[12]
self.theta_sig = para_dist[13]
self.q_bar_limits = para_dist[14]
self.rho_eps_param = para_dist[15]
self.sig_eta_param = para_dist[16]
self.prop_high = para_dist[17]
self.target_price = para_dist[18]
self.relative_risk_aversion = para_dist[19]
self.ch7_param = para_dist[20]
self.central_case()
self.solve_para()
self.set_property_rights()
### chapter 7 inflow share model
self.CS_c = -0.153007555
self.CS_b = 0.00930613
self.CSHL_c = -0.0891846
self.CSHL_b = 0.0047009
def build_para(self, charts=False):
home = '/home/nealbob'
folder = '/Dropbox/Thesis/STATS/chapter3/'
folder2 = '/Dropbox/Thesis/STATS/chapter2/'
folder7 = '/Dropbox/Thesis/STATS/chapter7/'
out = '/Dropbox/Thesis/IMG/chapter3/'
out7 = '/Dropbox/Thesis/IMG/chapter7/'
img_ext = '.pdf'
MDB_dams = pandas.read_csv(home + folder + 'MDB_dams.csv')
AUS_RIVERS = pandas.read_csv(home + folder + 'AUS_RIVERS.csv')
OMEGA = pandas.read_csv(home + folder7 + 'omega.csv')
#MDB_table = pandas.read_csv(home + folder + 'MDB_table.csv')
#open(home + folder + "MDB_table.tex", "w").write(MDB_table.to_latex(index=False, float_format=lambda x: '%10.1f' % x ))
################# WATER SUPPLY ################
#---------------# K - capacity
K = MDB_dams['K']
sample = (K > 50000)
K = K[sample] / 1000
bins = np.linspace(min(K), max(K), 18)
data = [K]
chart = {'OUTFILE' : (home + out + 'K' + img_ext),
'XLABEL' : 'Storage capacity (GL)',
'XMIN' : min(K),
'XMAX' : max(K),
'BINS' : bins}
if charts:
self.build_chart(chart, data, chart_type='hist')
#---------------# I_over_K - mean inflow over storage capacity
K = MDB_dams['K']
E_I = MDB_dams['mean_I']
sample = (K > 50000)
I_over_K = E_I[sample] / K[sample]
I_K_param = np.zeros(2)
I_K_param[0] = np.percentile(I_over_K, 10)
I_K_param[1] = np.percentile(I_over_K, 83)
x = np.linspace(0.2, 5, 500)
y = uniform.pdf(x, loc=I_K_param[0], scale=(I_K_param[1]-I_K_param[0]))
bins = np.linspace(min(I_over_K), 4, 18)
bins[17] = 15
data = [I_over_K, x, y]
data2 = [I_over_K]
chart = {'OUTFILE' : (home + out + 'I_over_K' + img_ext),
'XLABEL' : 'Mean annual inflow over storage capacity',
'XMIN' : 0,
'XMAX' : 4,
'BINS' : bins}
chart2 = {'OUTFILE' : (home + out + 'I_over_K_2' + img_ext),
'XLABEL' : 'Mean annual inflow over storage capacity',
'XMIN' : 0,
'XMAX' : 4,
'BINS' : bins}
if charts:
self.build_chart(chart, data, chart_type='hist')
self.build_chart(chart2, data2, chart_type='hist')
#---------------# SD_over_I - SD of inflow over mean inflow
sample = AUS_RIVERS['MAR'] < 700
SD_over_I = AUS_RIVERS['Cv'][sample]
bins = np.linspace(min(SD_over_I), max(SD_over_I), 13)
x = np.linspace(min(SD_over_I), max(SD_over_I), 500)
y = uniform.pdf(x, loc=0.43, scale=(1-0.4))
data = [SD_over_I, x, y]
data2 = [SD_over_I]
chart = {'OUTFILE' : (home + out + 'SD_over_I' + img_ext),
'XLABEL' : 'Standard deviation of annual inflow over mean',
'XMIN' : 0,
'XMAX' : max(SD_over_I),
'BINS' : bins}
chart2 = {'OUTFILE' : (home + out + 'SD_over_I_2' + img_ext),
'XLABEL' : 'Standard deviation of annual inflow over mean',
'XMIN' : 0,
'XMAX' : max(SD_over_I),
'BINS' : bins}
if charts:
self.build_chart(chart, data, chart_type='hist')
self.build_chart(chart2, data2, chart_type='hist')
#---------------# SA_over_K - surface area over capacity
SA = MDB_dams['sa']
sample = (K > 50000)
SA_over_K = SA[sample] / K[sample]
bins = np.linspace(min(SA_over_K), max(SA_over_K), 28)
SA_K_param = np.zeros(2)
SA_K_param[0] = np.percentile(SA_over_K, 10)
SA_K_param[1] = np.percentile(SA_over_K, 81.5)
x = np.linspace(min(SA_over_K), max(SA_over_K), 500)
y = uniform.pdf(x, loc=SA_K_param[0], scale=(SA_K_param[1] - SA_K_param[0]))
data = [SA_over_K, x, y]
data2 = [SA_over_K]
chart = {'OUTFILE' : (home + out + 'SA_over_K' + img_ext),
'XLABEL' : 'Storage surface area over storage capacity',
'XMIN' : min(SA_over_K),
'XMAX' : max(SA_over_K),
'BINS' : bins}
chart2 = {'OUTFILE' : (home + out + 'SA_over_K_2' + img_ext),
'XLABEL' : 'Storage surface area over storage capacity',
'XMIN' : min(SA_over_K),
'XMAX' : max(SA_over_K),
'BINS' : bins}
if charts:
self.build_chart(chart, data, chart_type='hist')
self.build_chart(chart2, data2, chart_type='hist')
#---------------# evap - net evaporation rate
evap = 0.75 * (MDB_dams['net_evap'] / 1000)
folder = '/Dropbox/Thesis/STATS/chapter3/'
evap = evap[sample]
folder = '/Dropbox/Thesis/STATS/chapter3/'
sample2 = evap > 0
evap = evap[sample2]
bins = np.linspace(min(evap), max(evap), 18)
evap_param = np.zeros(2)
evap_param[0] = np.percentile(evap, 15)
evap_param[1] = np.percentile(evap, 85)
x = np.linspace(min(evap), max(evap), 500)
y = uniform.pdf(x, loc=evap_param[0], scale=(evap_param[1]-evap_param[0]))
data = [evap, x, y]
data2 = [evap]
chart = {'OUTFILE' : (home + out + 'evap' + img_ext),
'XLABEL' : 'Average annual evaporation rate (meters)',
'XMIN' : min(evap),
'XMAX' : max(evap),
'BINS' : bins}
chart2 = {'OUTFILE' : (home + out + 'evap_2' + img_ext),
'XLABEL' : 'Average annual evaporation rate (meters)',
'XMIN' : min(evap),
'XMAX' : max(evap),
'BINS' : bins}
if charts:
self.build_chart(chart, data, chart_type='hist')
self.build_chart(chart2, data2, chart_type='hist')
#---------------# d_loss - delivery losses in irrigation areas
d_loss = np.zeros([5, 2])
Murray = pandas.read_csv(home + folder2 + 'Murray_loss.csv')
y = Murray['Loss']
N = len(y)
X = np.vstack([Murray['Pumped'], np.ones(N)]).T
d_loss[0,:] = np.linalg.lstsq(X, y)[0]
d_loss[0,1] = d_loss[0,1] / np.mean(Murray['Pumped'])
Shep = pandas.read_csv(home + folder2 + 'Shep_loss.csv')
y = Shep['Loss']
N = len(y)
X = np.vstack([Shep['Pumped'], np.ones(N)]).T
d_loss[1,:] = np.linalg.lstsq(X, y)[0]
d_loss[1,1] = d_loss[1,1] / (np.mean(Shep['Pumped']))
Jemm = pandas.read_csv(home + folder2 + 'Jemm_loss.csv')
y = Jemm['Loss']
N = len(y)
X = np.vstack([Jemm['Pumped'], np.ones(N)]).T
d_loss[2,:] = np.linalg.lstsq(X, y)[0]
d_loss[2,1] = d_loss[2,1] / (np.mean(Jemm['Pumped']))
Coll = pandas.read_csv(home + folder2 + 'Coll_loss.csv')
y = Coll['Loss']
N = len(y)
X = np.vstack([Coll['Pumped'], np.ones(N)]).T
d_loss[3,:] = np.linalg.lstsq(X, y)[0]
d_loss[3,1] = d_loss[3,1] / (np.mean(Coll['Pumped']))
MIA = pandas.read_csv(home + folder2 + 'MIA_loss.csv')
y = MIA['Loss']
N = len(y)
X = np.vstack([MIA['Pumped'], np.ones(N)]).T
d_loss[4,:] = np.linalg.lstsq(X, y)[0]
d_loss[4,1] = d_loss[4,1] / (np.mean(MIA['Pumped']))
#---------------# Inflow autocorrelation
rho_param = [0.2, 0.3]
################# WATER DEMAND ################
#---------------# Theta parameters (yield functions)
theta_mu = np.zeros([6, 2])
theta_mu[:,0] = np.array([154.7, 236.7, -35.8, 20.7, 14.9, -48.5])
#theta_mu[:,1] = np.array([-1785.4, 2545.3, -157.2, 1924.3, -537.5, -118.9])
theta_mu[:,1] = np.array([-1773.8, 2135.0, -133.3, 1597.1, -520.9, -100.8])
#clow = (41.5+14.9+231.7)*0.1
#chigh = (-76.5+2153.9-537.5)*0.1
theta_sig = np.zeros([6, 2])
#theta_sig[:,0] = np.array([0, 51.1, 16.8, 96.8, 38.8, 17.3])
#theta_sig[:,1] = np.array([0, 306.2, 22.3, 2370.1, 952.2, 151.4])
theta_sig[:,0] = np.array([0, 51.1, 16.8, 0, 0, 17.3])
theta_sig[:,1] = np.array([0, 306.2, 22.3, 0, 0, 151.4])
q_bar_limits = np.zeros([2,2])
q_bar_limits[:, 0] = np.array([0.5, 6.5])
q_bar_limits[:, 1] = np.array([5, 14])
w_ha = np.linspace(0,3,100)
profit_ha = theta_mu[0,0] + theta_mu[1,0]*w_ha + theta_mu[2,0] * w_ha**2 + theta_mu[3,0]*1 + theta_mu[4,0]*1**2 + theta_mu[5,0]*1*w_ha
data = [[w_ha, profit_ha]]
chart = {'OUTFILE' : (home + out + 'low_yield' + img_ext),
'XLABEL' : 'Water use per unit land (ML / HA)',
'XMIN' : min(w_ha),
'XMAX' : max(w_ha),
'YMIN' : 0,
'YMAX' : max(profit_ha)*1.05,
'YLABEL' : 'Profit per unit land (\$ / HA)'}
if charts:
self.build_chart(chart, data, chart_type='plot')
w_ha = np.linspace(0,9,100)
profit_ha = theta_mu[0,1] + theta_mu[1,1]*w_ha + theta_mu[2,1] * w_ha**2 + theta_mu[3,1]*1 + theta_mu[4,1]*1**2 + theta_mu[5,1]*1*w_ha
data = [[w_ha, profit_ha]]
chart = {'OUTFILE' : (home + out + 'high_yield' + img_ext),
'XLABEL' : 'Water use per unit land (ML / HA)',
'XMIN' : min(w_ha),
'XMAX' : max(w_ha),
'YMIN' : min(profit_ha)*1.5,
'YMAX' : max(profit_ha)*1.05,
'YLABEL' : 'Profit per unit land (\$ / HA)'}
if charts:
self.build_chart(chart, data, chart_type='plot')
#---------------# Epsilon parameters (yield functions)
rho_eps_param = np.array([0.3, 0.5])
sig_eta_param = np.array([0.1, 0.2])
################# Final Parameters ################
self.I_K_param = I_K_param
self.SD_I_param = np.array([0.4, 1])
self.rho_param = [0.2, 0.3]
self.SA_K_param = SA_K_param
self.evap_param = evap_param
self.d_loss_param_a = np.array([0, 0.15])
self.d_loss_param_b = np.array([0.15, 0.30])
self.theta_mu = theta_mu
self.theta_sig = theta_sig / 3
self.q_bar_limits = q_bar_limits
self.rho_eps_param = np.array([0.3, 0.5])
self.sig_eta_param = np.array([0.1, 0.2])
self.prop_high = np.array([0.05, 0.35])
self.target_price = 10 #np.array([50,200])
self.t_cost_param = np.array([10, 100])
self.Lambda_high_param = np.array([1, 2])
self.relative_risk_aversion = np.array([0, 3])
#### Summer-Winter model - chapter 7
self.ch7_param = {}
self.ch7_param['omega_mu'] = [0.55, 0.75]
self.ch7_param['omega_sig'] = [0.09, 0.12]
self.ch7_param['omega_ab'] = [0.3, 0.90]
self.ch7_param['delta_a'] = [0.02, 0.06]
self.ch7_param['omegadelta'] = [0.22, 0.36]
self.ch7_param['F_bar'] = [1, 1]
self.ch7_param['delta_b'] = [0.3, 0.6]
self.ch7_param['delta_Ea'] = [0, 0.1]
self.ch7_param['delta_Eb'] = [0.1, 0.3]
self.ch7_param['delta_R'] = [0, 0.2]
self.ch7_param['b_1'] = [0, 0.6]
self.ch7_param['b_value'] = [30, 130]
self.ch7_param['Bhat_alpha'] = [0.1, 0.5]
self.ch7_param['inflow_share'] = [0, 0.5]
self.ch7_param['capacity_share'] = [0, 0.5]
self.ch7_param['High'] = [1, 1]
self.ch7_param['e_sig'] = [0, 1]
para_dist = [self.I_K_param, self.SD_I_param, self.rho_param, self.SA_K_param, self.evap_param, self.d_loss_param_a, self.d_loss_param_b, self.t_cost_param, self.Lambda_high_param, [100, 100], [30, 70], [30, 70], self.theta_mu, self.theta_sig, self.q_bar_limits, self.rho_eps_param, self.sig_eta_param, self.prop_high, self.target_price, self.relative_risk_aversion, self.ch7_param]
with open('para_dist.pkl', 'wb') as f:
pickle.dump(para_dist, f)
f.close()
rows = ['$E[I_t]/K$', '$c_v$', '$\rho_I$' ,'$\alpha K^{2/3} / K $' , '$\delta_0$', '$\delta_{1a}$', '$\delta_{1b}$', '$\tau$', '$\Lambda_{high}$', '$n$', '$n_low$', '$n_high$', ]
cols = ['Min', 'Central case', 'Max']
n_rows = 12
data = []
for i in range(n_rows):
record = {}
record['Min'] = para_dist[i][0]
record['Central case'] = np.mean(para_dist[i])
record['Max'] = para_dist[i][1]
data.append(record)
tab = pandas.DataFrame(data)
tab.index = rows
tab_text = tab.to_latex(float_format = '{:,.2f}'.format, columns=['Min', 'Central case', 'Max' ], index=True)
with open(home + folder + "para_table.txt", "w") as f:
f.write(tab_text)
f.close()
def set_property_rights(self, scenario='CS'):
self.unbundled = False
if scenario == 'CS':
self.sr = 'CS'
self.ls = 1
self.HL = 0
self.opt_lam = 0
elif scenario == 'SWA':
self.sr = 'SWA'
self.ls = 1
self.HL = 0
self.opt_lam = 0
elif scenario == 'NS':
self.sr = 'NS'
self.ls = 0
self.HL = 0
self.opt_lam = 0
elif scenario == 'OA':
self.sr = 'OA'
self.ls = 0
self.HL = 0
self.opt_lam = 0
elif scenario == 'CS-SWA':
self.sr = 'CS-SWA'
self.ls = 1
self.HL = 0
self.opt_lam = 0
elif scenario == 'CS-SL':
self.sr = 'CS'
self.ls = 0
self.HL = 0
self.opt_lam = 0
elif scenario == 'SWA-SL':
self.sr = 'SWA'
self.ls = 0
self.HL = 0
self.opt_lam = 0
elif scenario == 'CS-SWA-SL':
self.sr = 'CS-SWA'
self.ls = 0
self.HL = 0
self.opt_lam = 0
elif scenario == 'RS':
self.sr = 'RS'
self.ls = 0
self.HL = 0
self.opt_lam = 0
elif scenario == 'RS-HL':
self.sr = 'RS'
self.ls = 0
self.HL = 1
self.opt_lam = 0
elif scenario == 'RS-O':
self.sr = 'RS'
self.ls = 0
self.HL = 0
self.opt_lam = 1
elif scenario == 'RS-HL-O':
self.sr = 'RS'
self.ls = 0
self.HL = 1
self.opt_lam = 1
elif scenario == 'CS-HL-O':
self.sr = 'CS'
self.ls = 1
self.HL = 1
self.opt_lam = 1
elif scenario == 'CS-HL':
self.sr = 'CS'
self.ls = 1
self.HL = 1
self.opt_lam = 0
elif scenario == 'CS-O':
self.sr = 'CS'
self.ls = 1
self.HL = 0
self.opt_lam = 1
elif scenario == 'CS-U':
self.sr = 'CS'
self.ls = 1
self.HL = 0
self.opt_lam = 1
self.unbundled = True
#if self.opt_lam == 1:
# if self.HL == 1:
# self.Lambda_high = self.prop * 1
# else:
# self.Lambda_high = self.prop * 1.5
#else:
# self.Lambda_high = self.prop
def aproximate_shares(self, nonoise=False):
home = '/home/nealbob'
model = '/Dropbox/Model/'
with open(home + model + 'sharemodel.pkl', 'rb') as f:
tree = pickle.load(f)
f.close()
temp = removekeys(self.para_list, ['sig_eta', 'rho_eps', 'delta0', 'LL'])
X = np.array([temp[p] for p in temp])
Y = tree.predict(X)
yRS = 0
if self.sr == 'RS':
if self.HL == 1:
y = Y[0,2]
else:
y = Y[0,0]
else:
if self.HL == 1:
y = Y[0,3]
yRS = Y[0,2]
else:
y = Y[0,1]
yRS = Y[0,0]
### for the CS-HL scenario chapter7
yhl = Y[0,3]
######################### !!!!
sig = 0.025
######################### !!!!
if nonoise:
self.Lambda_high = y
self.Lambda_high_RS = yRS
else:
self.Lambda_high = truncnorm((0.001 - y) / sig, (0.999 - y) / sig, loc=y, scale=sig).rvs()
self.Lambda_high_RS = truncnorm((0.001 - yRS) / sig, (0.999 - yRS) / sig, loc=yRS, scale=sig).rvs()
self.para_list['Lambda_high'] = self.Lambda_high
self.para_list['Lambda_high_RS'] = self.Lambda_high_RS
def aproximate_shares_ch7(self, nonoise=False):
home = '/home/nealbob'
model = '/Dropbox/Model/'
if self.HL == 1:
y = self.CSHL_c + self.CSHL_b * self.N_high
else:
y = self.CS_c + self.CS_b * self.N_high
yhl = self.CSHL_c + self.CSHL_b * self.N_high
self.yhl = yhl
self.Lambda_high_HL = truncnorm((0.001 - yhl) / 0.05, (0.999 - yhl) / 0.05, loc=yhl, scale=0.05).rvs()
if nonoise:
self.Lambda_high = y
else:
self.Lambda_high = truncnorm((0.001 - y) / 0.05, (0.999 - y) / 0.05, loc=y, scale=0.05).rvs()
self.y = y
self.para_list['Lambda_high'] = self.Lambda_high
print 'Lambda_high_hat: ' + str(y) + ', Lambda high: ' + str(self.Lambda_high)
def central_case(self, N=100, utility=False, printp=True, risk=0):
self.K = 1000000
self.beta = 0.945
I_K = np.mean(self.I_K_param)
SD_I = np.mean(self.SD_I_param)
self.I_m = I_K * self.K
self.I_sig = SD_I * self.I_m
SA_K = np.mean(self.SA_K_param)
self.I_bar = I_K * self.K
self.SD_I = self.I_bar * SD_I
self.rho_I = np.mean(self.rho_param)
self.delta0 = np.mean(self.evap_param)
m = (I_K * self.K) * (1-self.rho_I)
v = (((SD_I * (I_K*self.K))**2)*(1-self.rho_I**2))
# Log normal inflow shocks
#self.mu_I = log((m**2)/((v+m**2)**0.5))
#self.sig_I = (log(1 + (v/(m**2))))**0.5
# Gamma inflow shocks
self.theta_I = v / m
self.k_I = m**2 / v
#Summer Winter Model parameters - chapter 7
#################################################
self.ch7 = {}
for para in self.ch7_param:
self.ch7[para] = np.mean(self.ch7_param[para])
self.ch7['delta_Ea'] = self.ch7['delta_Ea'] * self.I_bar
self.ch7['delta_a'] = self.ch7['delta_a'] * self.I_bar
self.ch7['F_bar'] = self.ch7['F_bar'] * self.K
self.ch7['b_value'] = self.ch7['b_value'] * self.I_bar
self.ch7['High'] = False
##################################################
self.alpha = (SA_K*self.K) / (self.K**(2.0/3))
self.delta1a = np.mean(self.d_loss_param_a) * self.I_bar
self.delta1b = np.mean(self.d_loss_param_b)
self.theta = np.zeros([6,2])
self.theta = self.theta_mu
self.rho_eps = np.mean(self.rho_eps_param)
self.sig_eta = np.mean(self.sig_eta_param)
self.price = np.mean(self.target_price)
self.prop = np.mean(self.prop_high)
p = max(self.price, 0)
q_bar_low = (-1*(self.theta[1,0]+self.theta[5,0])) / (2*self.theta[2,0]) + p/(self.theta[2,0]*2)
q_bar_high = (-1*(self.theta[1,1]+self.theta[5,1])) / (2*self.theta[2,1]) + p/(self.theta[2,1]*2)
self.high_size = self.prop / (q_bar_high / q_bar_low)
self.N = N
self.N_low = int(N/2)
self.N_high = int(N/2)
self.L = newton(self.excessp, 2000, args=(self.price, ))
self.Land = self.L
self.t_cost = np.mean(self.t_cost_param)
p = max(self.max_price(self.L, self.price), 0)
q_bar_low = (-1* (self.theta[1,0]+self.theta[5,0])) / (2*self.theta[2,0]) + p/(self.theta[2,0]*2)
q_bar_high = (-1* (self.theta[1,1]+self.theta[5,1])) / (2*self.theta[2,1]) + p/(self.theta[2,1]*2)
self.prop = (self.N_high * q_bar_high * (self.high_size * self.L)) / ((self.N_high * q_bar_high * (self.high_size * self.L)) + self.N_low * q_bar_low * self.L)
if self.opt_lam == 1:
self.Lambda_high = self.prop * 1 #np.mean(self.Lambda_high_param)
else:
self.Lambda_high = self.prop * 2
if utility:
self.utility = 1
low_land = self.L
high_land = self.L * self.high_size
profit_bar_high = low_land * (self.theta[0, 0] + self.theta[1, 0]*q_bar_low + self.theta[2, 0]*(q_bar_low**2)+ self.theta[3, 0] + self.theta[4, 0] + self.theta[5, 0]*q_bar_low)
profit_bar_low = high_land * (self.theta[0, 1] + self.theta[1, 1]*q_bar_high + self.theta[2, 1]*(q_bar_high**2)+ self.theta[3, 1] + self.theta[4, 1] + self.theta[5, 1]*q_bar_high)
profit_bar = (profit_bar_low + profit_bar_high) / 2
self.risk_aversion_low = risk / profit_bar
self.risk_aversion_high = risk / profit_bar
else:
self.utility = 0
self.risk_aversion_low = 0
self.risk_aversion_high = 0
self.para_list = {'I_K': I_K, 'SD_I' : SD_I, 'Prop_high' : self.prop, 't_cost' : self.t_cost, 'L' : self.Land,'N_high' : self.N_high, 'rho_I' : self.rho_I, 'SA_K' : SA_K, 'alpha' : self.alpha, 'delta1a' : self.delta1a, 'delta1b' : self.delta1b, 'risk' : risk, 'rho_eps' : self.rho_eps, 'sig_eta' : self.sig_eta, 'delta0' : self.delta0, 'LL' : self.L}
if printp:
print '\n --- Main parameters --- \n'
print 'Inflow to capacity: ' + str(I_K)
print 'Coefficient of variation: ' + str(SD_I)
print 'Proportion of high demand: ' + str(self.prop)
print 'Target water price: ' + str(self.price)
print 'Transaction cost: ' + str(self.t_cost)
print 'High user inflow share: ' + str(self.Lambda_high)
print 'Land: ' + str(self.L)
print 'High Land: ' + str(self.high_size)
print 'Risk aversion: ' + str(risk)
def excessp(self, L, target_price):
p = self.max_price_max(L, target_price)
return p - target_price
def max_price(self, L, target_price):
#Q = self.K - self.delta1a*self.K - self.delta1b*self.K
W = min(self.I_bar, self.K)
Q = max(W - self.delta1a - self.delta1b*W, 0)
p = newton(self.excessD, target_price, args = (Q, L))
return p
def max_price_max(self, L, target_price):
Q = self.K - self.delta1a - self.delta1b*self.K
#Q = max(self.I_bar - self.delta1a*self.K - self.delta1b*self.I_bar, 0)
p = newton(self.excessD, target_price, args = (Q, L))
return p
def excessD(self, p, Q, L):
qsum = self.low_demand(p, L) + self.high_demand(p, L)
return qsum - Q
def low_demand(self, p, L):
qi = (-(self.theta[1,0] + self.theta[5,0])/(2*self.theta[2,0]) + p / (self.theta[2,0]*2) )
q = (qi * L * self.N_low)
return q
def high_demand(self, p, L):
qi = (-(self.theta[1,1] + self.theta[5,1])/(2*self.theta[2,1]) + p / (self.theta[2,1]*2) )
q = (qi * (self.high_size*L) * self.N_high)
return q
def randomize(self, N = 100, riskon=False):
ex = 10
self.L = 1000000
self.K = 1000000
self.beta = uniform.rvs(loc=0.93, scale =0.03)
I_K = uniform.rvs(loc=self.I_K_param[0], scale=(self.I_K_param[1] - self.I_K_param[0]))
SD_I = uniform.rvs(loc=self.SD_I_param[0], scale=(self.SD_I_param[1]-self.SD_I_param[0]))
SA_K = uniform.rvs(loc=self.SA_K_param[0], scale=(self.SA_K_param[1] - self.SA_K_param[0]))
self.I_bar = I_K * self.K
self.rho_I = uniform.rvs(loc=self.rho_param[0], scale=(self.rho_param[1]-self.rho_param[0]))
self.delta0 = uniform.rvs(loc=self.evap_param[0], scale=(self.evap_param[1] - self.evap_param[0]))
m = (I_K * self.K) * (1-self.rho_I)
v = (((SD_I * (I_K*self.K))**2)*(1-self.rho_I**2))
#print 'm ' + str(m)
#print 'v ' + str(m)
# Log normal inflow
#self.mu_I = log((m**2)/((v+m**2)**0.5))
#self.sig_I = (log(1 + (v/(m**2))))**0.5
# Gamma inflow
self.theta_I = v / m
self.k_I = m**2 / v
#print 'theta_I ' + str(self.theta_I)
#print 'k_I ' + str(self.k_I)
#Summer Winter Model parameters - chapter 7
#################################################
self.ch7 = {}
for para in self.ch7_param:
a = self.ch7_param[para][0]
b = self.ch7_param[para][1]
self.ch7[para] = uniform.rvs(loc=a, scale=(b - a))
self.ch7['delta_Ea'] = self.ch7['delta_Ea'] * self.I_bar
self.ch7['delta_a'] = self.ch7['delta_a'] * self.I_bar
self.ch7['F_bar'] = self.ch7['F_bar'] * self.I_bar
self.ch7['b_value'] = self.ch7['b_value'] * self.I_bar
self.ch7['High'] = False
##################################################
self.alpha = (SA_K*self.K) / (self.K**(2.0/3))
self.delta1a = uniform.rvs(loc=self.d_loss_param_a[0], scale=(self.d_loss_param_a[1]-self.d_loss_param_a[0])) * self.I_bar
self.delta1b = uniform.rvs(loc=self.d_loss_param_b[0], scale=(self.d_loss_param_b[1]-self.d_loss_param_b[0]))
self.theta = np.zeros([6, 2])
self.theta[0,:] = self.theta_mu[0,:]
constraint_binding = True
iters = 0
theta = np.zeros([6, 2])
while constraint_binding and iters < 10000:
iters += 1
for k in [3, 4]:
theta[k,0] = self.theta_mu[k,0]
theta[k,1] = self.theta_mu[k,1]
for k in [0, 1, 2, 5]:
theta[k,0] = norm.rvs(loc=self.theta_mu[k,0], scale=self.theta_sig[k,0])
theta[k,1] = norm.rvs(loc=self.theta_mu[k,1], scale=self.theta_sig[k,1])
if theta[1,0] > 0 and theta[1, 1] > 0:
if theta[2, 0] < 0 and theta[2, 1] < 0:
if theta[5, 0] < 0 and theta[5, 1] < 0:
qbarlow = -(theta[1,0]+theta[5,0]) / (2 * theta[2,0])
if qbarlow > self.q_bar_limits[0,0] and qbarlow < self.q_bar_limits[1,0]:
qbarhigh = -(theta[1,1]+theta[5,1]) / (2 * theta[2,1])
if qbarhigh > self.q_bar_limits[0,1] and qbarhigh < self.q_bar_limits[1,1]:
constraint_binding = False
self.theta = theta
if iters == 10000:
print 'Warning parameters not generated...'
self.theta = self.theta_mu
self.rho_eps = uniform.rvs(loc=self.rho_eps_param[0], scale=(self.rho_eps_param[1]-self.rho_eps_param[0]))
self.sig_eta = uniform.rvs(loc=self.sig_eta_param[0], scale=(self.sig_eta_param[1]-self.sig_eta_param[0]))
#self.price = uniform.rvs(loc=self.target_price[0], scale=(self.target_price[1]-self.target_price[0]))
self.N_low = int(uniform.rvs(loc=30, scale=40))
self.N_high = N - self.N_low
self.L_ratio = uniform.rvs(loc=0.75, scale=0.5)
self.L = self.L_ratio * I_K * (self.Land / (np.mean(self.I_K_param)))
p = max(self.max_price(self.L, self.price), 0)
q_bar_low = max((-1* (self.theta[1,0]+self.theta[5,0])) / (2*self.theta[2,0]) + p/(self.theta[2,0]*2),0)
q_bar_high = max((-1* (self.theta[1,1]+self.theta[5,1])) / (2*self.theta[2,1]) + p/(self.theta[2,0]*2),0)
self.prop = (self.N_high * q_bar_high * (self.high_size * self.L)) / ((self.N_high * q_bar_high * (self.high_size * self.L)) + self.N_low * q_bar_low * self.L)
low_land = self.L
high_land = self.L * self.high_size
profit_bar_high = low_land * (self.theta[0, 0] + self.theta[1, 0]*q_bar_low + self.theta[2, 0]*(q_bar_low**2)+ self.theta[3, 0] + self.theta[4, 0] + self.theta[5, 0]*q_bar_low)
profit_bar_low = high_land * (self.theta[0, 1] + self.theta[1, 1]*q_bar_high + self.theta[2, 1]*(q_bar_high**2)+ self.theta[3, 1] + self.theta[4, 1] + self.theta[5, 1]*q_bar_high)
profit_bar = (profit_bar_low + profit_bar_high) / 2
utility = np.random.rand(1) > 0.5
if riskon and utility[0]:
self.utility = 1
risk = uniform.rvs(loc=self.relative_risk_aversion[0], scale=self.relative_risk_aversion[1] - self.relative_risk_aversion[0])
self.risk_aversion_low = risk / profit_bar
self.risk_aversion_high = risk / profit_bar
else:
self.utility = 0
risk = 0
self.risk_aversion_low = 0
self.risk_aversion_high = 0
self.t_cost = (np.random.rand() * (self.t_cost_param[1]-self.t_cost_param[0]) + self.t_cost_param[0])
self.Lambda_high = max(min(self.prop, 0.95), 0) #* (np.random.rand() * (self.Lambda_high_param[1]-self.Lambda_high_param[0]) + self.Lambda_high_param[0]),0.95),0)
self.para_list = {'I_K' : I_K, 'SD_I' : SD_I, 'Prop_high' : self.prop, 't_cost' : self.t_cost, 'L' : self.Land,'N_high' : self.N_high, 'rho_I' : self.rho_I, 'SA_K' : SA_K, 'alpha' : self.alpha, 'delta1a' : self.delta1a, 'delta1b' : self.delta1b, 'risk' : risk, 'rho_eps' : self.rho_eps, 'sig_eta' : self.sig_eta, 'delta0' : self.delta0, 'LL' : self.L}
print '\n --- Main parameters --- \n'
print 'Inflow to capacity: ' + str(I_K)
print 'Coefficient of variation: ' + str(SD_I)
print 'Proportion of high demand:' + str(self.prop)
print 'Target water price: ' + str(p)
print 'Transaction cost: ' + str(self.t_cost)
print 'High user inflow share: ' + str(self.Lambda_high)
print 'Number of high users: ' + str(self.N_high)
print 'Land: ' + str(self.L)
print 'Risk aversion: ' + str(risk)
def check_random(self, num=2000, I = 1):
xlow = np.linspace(0,4, 200)
xhigh = np.linspace(0,10, 200)
ylow = np.zeros([200,num])
yhigh = np.zeros([200,num])
pylab.figure(0)
pylab.figure(1)
for i in range(num):
self.randomize()
ylow[:,i] = xlow * (self.theta[1,0]) + xlow * self.theta[5,0] * I + (xlow**2) * self.theta[2,0] + self.theta[0,0]+self.theta[3,0]+self.theta[4,0]
yhigh[:,i] = xhigh * (self.theta[1,1]) + xhigh * self.theta[5,1] * I + (xhigh**2) * self.theta[2,1] + self.theta[0,1]+self.theta[3,1]+self.theta[4,1]
ymeanlow = np.mean(ylow, axis=1)
ymeanhigh = np.mean(yhigh, axis=1)
yminlow = np.percentile(ylow, 10.0, axis=1)
yminhigh = np.percentile(yhigh, 10.0, axis=1)
ymaxlow = np.percentile(ylow, 90.0, axis=1)
ymaxhigh = np.percentile(yhigh, 90.0, axis=1)
ymulow = xlow * (self.theta_mu[1,0] + self.theta_mu[5,0]) + (xlow**2) * self.theta_mu[2,0] + self.theta_mu[0,0]+self.theta_mu[3,0]+self.theta_mu[4,0]
ymuhigh = xhigh * (self.theta_mu[1,1] + self.theta_mu[5,1]) + (xhigh**2) * self.theta_mu[2,1] + self.theta_mu[0,1]+self.theta_mu[3,1]+self.theta_mu[4,1]
pylab.figure(0)
pylab.plot(xlow, ymeanlow)
pylab.plot(xlow, ymulow)
pylab.plot(xlow, yminlow)
pylab.plot(xlow, ymaxlow)
pylab.plot(xlow, ylow[:,10])
pylab.ylim(0, 800)
pylab.figure(1)
pylab.plot(xhigh, ymeanhigh)
pylab.plot(xhigh, ymuhigh)
pylab.plot(xhigh, yminhigh)
pylab.plot(xhigh, ymaxhigh)
pylab.plot(xhigh, yhigh[:,10])
pylab.show()
def solve_para(self):
"""
Specify model solution parameters, sample sizes, iterations, exploration etc.
"""
self.CPU_CORES = 4 #mp.cpu_count()
# Evaluation simulation size (for generating model results)
self.T0 = 500000
#======================================================
# Planner SDP parameters
#======================================================
# SDP Tolerance level
self.SDP_TOL = 0.0012
# Max SDP Policy evaluations per policy improvement
self.SDP_ITER = 100
# SDP GRID points per dimension, S_t, I_t and I_t+1
self.SDP_GRID = 33
#======================================================
# Planner QV learning parameters
#======================================================
# Simulation sample size
self.T1 = 50000
# Sample grid parameters
self.sg_radius1 = 0.02
self.sg_points1 = 425
self.sg_points1_ch7 = 2500
self.sg_radius1_ch7 = 0.045
# Stage 2 search range
self.policy_delta = 0.16
self.QV_ITER1 = 40
self.QV_ITER2 = 10
#======================================================
# Optimal share search parameters
#======================================================
self.opt_lam_ITER = 12
#======================================================
# Decentralised model QV learning parameters
#======================================================
self.ITER1 = 40 # Initialization stage QV iterations
self.ITER2 = 80 # Main learning iterations
self.iters = 1 # QV iterations per learning iteration
#Proportion of users to update
self.update_rate = [6] * 5 + [6] * 5 + [5] * 10 + [4]*150 #+ [0.05] * 5
#self.update_rate = [12] * 5 + [10] * 150 #+ [0.05] * 5
self.update_rate_ch7 = [3] * 150 #+ [0.05] * 5
#Proportion of sample size to replace each iteration (< 1 implies rolling batch)
self.sample_rate = 0.125
# Number of exploring agents per class
#self.N_e = [5] * 4 + [4] * 4 + [3] * 4 + [2] * 150
self.N_e = [5] * 4 + [4] * 4 + [3] * 4 + [2] * 150
# Exploration range
#self.d = [0.25] * 4 + [0.2] * 4 + [0.15] * 4 + [0.085] * 150
self.d = [0.1] * 5 + [0.15] * 5 + [0.2] * 10 + [0.15] * 150# + [0.1] * 150
#self.d = [max(0.25 - 0.01 * i, 0.05) for i in range(150)]
self.envd = [0.3] * 4 + [0.2] * 4 + [0.15] * 6 + [0.1] * 6 + [0.1] * 100
# Total sample size, actual sim length = T1 / (2*N_e)
self.T2 = 500000
self.T2_ch7 = 800000
# State sample grid parameters
self.sg_radius2 = 0.045
self.sg_radius2_ch7 = 0.055
self.sg_samp2 = 0.4
self.sg_samp2_ch7 = 0.4
self.sg_prop2 = 0.85 #[0.80]*5 + [0.85]*5 + [0.9]*5 + [0.95]*5
self.sg_prop2_ch7 = 0.8
# Number of linear spline knots (for policy and value functions)
self.linT = 4
def test(self, prop = 0.1):
"Generate parameters for the test version of the model"
self.K = 50 # Storage capacity
self.S = 50 # Initial storage level
self.ITERS = 10
self.prop = prop
self.F = [0, 25, 50] # Inflow distribution coefficients
self.loss = [0]
self.N = 50 # Number of users
self.N_low = 25 # Number of low reliability users (rest are high)
self.rs = 'SWA' # Property rights system (CS, SWA, CPS, NS)
self.beta = 0.90 # Discount rate
self.u_para_low = [0, 1.2, -0.4] # Low reliability payoff function coefficients
self.u_para_high = [-0.5, 2.5, -1.4] # High reliability payoff function coefficients
self.e_para = [0.8, 1.2] # Maximum productivity level
self.t_cost = 0.3 # Spot market transaction cost per unit water