diff --git a/examples/solving_initial_value_problems.ipynb b/examples/solving_initial_value_problems.ipynb index 9ff1a958a..6fd87dc9d 100644 --- a/examples/solving_initial_value_problems.ipynb +++ b/examples/solving_initial_value_problems.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:97c5464497923c38027b39772d5fd3274298becf3470be3a6c6eea6626287eec" + "signature": "sha256:b4dbdca98be50e477bddb995b524e3e3b20ec2c132d8a4fb06869c50fd65c49a" }, "nbformat": 3, "nbformat_minor": 0, @@ -32,7 +32,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 12 + "prompt_number": 1 }, { "cell_type": "markdown", @@ -103,8 +103,8 @@ "We begin with the Lotka-Volterra model, also known as the predator-prey model, which is a pair of first order, non-linear, differential equations frequently used to describe the dynamics of biological systems in which two species interact, one a predator and the other its prey. The model was proposed independently by Alfred J. Lotka in 1925 and Vito Volterra in 1926. \n", "\n", "\\begin{align}\n", - " \\frac{du}{dt} =& au - buv \\tag{2.1} \\\\\n", - " \\frac{dv}{dt} =& -cv + dbuv \\tag{2.2}\n", + " \\frac{du}{dt} =& au - buv \\tag{2.1.1} \\\\\n", + " \\frac{dv}{dt} =& -cv + dbuv \\tag{2.1.2}\n", "\\end{align}\n", "\n", "where $u$ is the number of preys (for example, rabbits), $v$ is the number of predators (for example, foxes) and $a, b, c, d$ are constant parameters defining the behavior of the population.\n", @@ -122,17 +122,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Defining an instance of the `IVP` class\n", + "### 2.1.1 Defining an instance of the `IVP` class\n", "\n", "First, we need to create an instance of the IVP class representing the Lotka-Volterra \"Predator-Prey\" model. To initialize an instance of the IVP class we need to define the following...\n", "\n", - "* ``f`` : Callable of the form ``f(t, y, *args)``. The function ``f`` is the right hand side of the system of equations defining the model. The independent variable, ``t``, should be a ``scalar``; ``y`` is an ``ndarray`` of dependent variables with ``y.shape == (n,)``. The function `f` should return a ``scalar``, ``ndarray`` or ``list`` (but not a ``tuple``).\n", - "* ``jac`` : Callable of the form ``jac(t, y, *args)``, optional(default=None). The Jacobian of the right hand side of the system of equations defining the ODE.\n", + "* ``f`` : Callable of the form ``f(t, y, *f_args)``. The function ``f`` is the right hand side of the system of equations defining the model. The independent variable, ``t``, should be a ``scalar``; ``y`` is an ``ndarray`` of dependent variables with ``y.shape == (n,)``. The function `f` should return a ``scalar``, ``ndarray`` or ``list`` (but not a ``tuple``).\n", + "* ``jac`` : Callable of the form ``jac(t, y, *jac_args)``, optional(default=None). The Jacobian of the right hand side of the system of equations defining the ODE.\n", "\n", - "$$ \\mathcal{J}_{i,j} = \\bigg[\\frac{\\partial f_i}{\\partial y_j}\\bigg] \\tag {2.3}$$\n", - "\n", - "* ``f_args`` : tuple, optional(default=None). Additional arguments that should be passed to the function `f`. Typically this will be a tuple of model parameters.\n", - "* ``jac_args`` : tuple, optional(default=None). Additional arguments that should be passed to the function `jac`. Typically this will be a tuple of model parameters.\n", + "$$ \\mathcal{J}_{i,j} = \\bigg[\\frac{\\partial f_i}{\\partial y_j}\\bigg] \\tag {2.1.3}$$\n", "\n", "Most all of this information can be found in the docstring for the `ivp.IVP` class." ] @@ -146,7 +143,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 3 + "prompt_number": 4 }, { "cell_type": "markdown", @@ -229,13 +226,13 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 4 + "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Since, from the docstring we see that the parameters `f_args`, and `jac_args` are optional, we can go ahead and create our instance of the `ivp.IVP` class representing the Lotka-Volterra model." + "We can go ahead and create our instance of the `ivp.IVP` class representing the Lotka-Volterra model using the above defined functions as follows..." ] }, { @@ -248,13 +245,15 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 5 + "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "In order to simulate the model, however, we will need to supply values for the model parameters $a,b,c,d$. Let's define some \"reasonable\" values..." + "### 2.1.2 Defining model parameters\n", + "\n", + "In order to simulate the model, however, we will need to supply values for the model parameters $a,b,c,d$. First, let's define some \"reasonable\" values." ] }, { @@ -267,64 +266,151 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 6 + "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "...and add them as attributes of the `lotka_volterra_ivp` instance." + "In order to add these parameter values to our model we need to pass them as arguments to the `set_f_params` and `set_jac_params` methods of the newly created instance of the `ivp.IVP` class. Check the doctrings of the methods for information on the appropriate syntax..." ] }, { "cell_type": "code", "collapsed": false, "input": [ - "lotka_volterra_ivp.f_args = lotka_volterra_params\n", - "lotka_volterra_ivp.jac_args = lotka_volterra_params" + "lotka_volterra_ivp.set_f_params?" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 7 + "prompt_number": 28 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "lotka_volterra_ivp.set_jac_params?" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 19 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From the docstring we see that both the `set_f_params` and the `set_jac_params` methods take an arbitrary number of positional arguments. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# this syntax is preferred!\n", + "lotka_volterra_ivp.set_f_params = lotka_volterra_params\n", + "\n", + "# this syntax works, but is not recommended!\n", + "lotka_volterra_ivp.set_jac_params = (1.0, 0.1, 1.5, 0.75)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 29 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "...and we can inspect that values of these attributes and see that the return results are the same." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "lotka_volterra_ivp.f_params" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 30, + "text": [ + "(1.0, 0.1, 1.5, 0.75)" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "lotka_volterra_ivp.jac_params" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 31, + "text": [ + "(1.0, 0.1, 1.5, 0.75)" + ] + } + ], + "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Some basic type checking is done in order to insure that the both the `f_args` and `jac_args` parameters are tuples. For example, the following will raise an `AttributeError`...." + "Alternatively, we could just directly set the `f_params` and `jac_params` attributes without needing to explicitly call either the `set_f_params` and `set_jac_params` methods!" ] }, { "cell_type": "code", "collapsed": false, "input": [ - "# dictionary is not a valid data type for parameters!\n", - "invalid_lotka_volterra_params = {'a': 1.0, 'b': 0.1, 'c': 1.5, 'd': 0.75}\n", - "lotka_volterra_ivp.f_args = invalid_lotka_volterra_params" + "# I generally prefer to set attributes directly...\n", + "lotka_volterra_ivp.f_params = lotka_volterra_params" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 33 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# ...result is the same\n", + "lotka_volterra_ivp.f_params" ], "language": "python", "metadata": {}, "outputs": [ { - "ename": "ValueError", - "evalue": "IVP.args must be a tuple, not a .", - "output_type": "pyerr", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0minvalid_lotka_volterra_params\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m'a'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'b'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m0.1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'c'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m1.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'd'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m0.75\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mlotka_volterra_ivp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf_args\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minvalid_lotka_volterra_params\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[0;32m/Users/drpugh/Research/python-dev/quant-econ/quantecon/ivp.py\u001b[0m in \u001b[0;36mf_args\u001b[0;34m(self, new_f_args)\u001b[0m\n\u001b[1;32m 86\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnew_f_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mtuple\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtypes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNoneType\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 87\u001b[0m \u001b[0mmesg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"IVP.args must be a tuple, not a {}.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 88\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmesg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnew_f_args\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__class__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 89\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mnew_f_args\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 90\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_f_params\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnew_f_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;31mValueError\u001b[0m: IVP.args must be a tuple, not a ." + "metadata": {}, + "output_type": "pyout", + "prompt_number": 34, + "text": [ + "(1.0, 0.1, 1.5, 0.75)" ] } ], - "prompt_number": 8 + "prompt_number": 34 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Using `ivp.IVP.solve` to integrate the ODE\n", + "### 2.1.3 Using `ivp.IVP.solve` to integrate the ODE\n", "\n", "In order to solve a system of ODEs, the `ivp.IVP.solve` method provides an interface into the ODE integration routines provided in the `scipy.integrate.ode` module. The method takes the following parameters...\n", "\n", @@ -356,7 +442,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 12 + "prompt_number": 26 }, { "cell_type": "markdown", @@ -380,7 +466,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 9 + "prompt_number": 35 }, { "cell_type": "markdown", @@ -419,11 +505,11 @@ "output_type": "display_data", "png": 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vbC5bVm1bpFaUNFVJvQAiIr1L7jtnz666NVIjvo2ThlXTJCIi0oVqmtyiniYR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\nlnuHguZkCoOOpKs937r8ooMJxFs5fBv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"text": [ - "" + "" ] } ], - "prompt_number": 23 + "prompt_number": 36 }, { "cell_type": "markdown", @@ -436,7 +522,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Using `ivp.IVP.interpolate` to interpolate the solution\n", + "### 2.1.4 Using `ivp.IVP.interpolate` to interpolate the solution\n", "\n", "The `IVP.interpolate` method provides an interface to the parametric [B-spline interpolation](http://en.wikipedia.org/wiki/B-spline) routines in `scipy.interpolate` in order to constuct a continuous approximation to the true solution. For more details on B-spline interpolation, including some additional economic applications, see chapter 6 of (Judd, 1998). The `ivp.IVP.interpolate` method takes the following parameters... \n", "\n", @@ -478,7 +564,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 14 + "prompt_number": 41 }, { "cell_type": "markdown", @@ -521,11 +607,11 @@ "output_type": "display_data", "png": 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Jql///llHN0WBSN0/B/iu35o17uQzgYT3Bg/OWD4l7vdOCRdqNIWNNWvgwAGp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"text": [ - "" + "" ] } ], - "prompt_number": 15 + "prompt_number": 42 }, { "cell_type": "markdown", @@ -538,12 +624,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Assessing accuracy using `ivp.IVP.compute_residual`\n", + "### 2.1.5 Assessing accuracy using `ivp.IVP.compute_residual`\n", "\n", "After computing a continuous approximation to the solution of our IVP, it is important to verify that the computed approximation is actually a \"good\" approximation. To assess the accuracy of our numerical solution we first define a residual function, $R(t)$, as the difference between the derivative of the B-spline approximation of the solution trajectory, $\\hat{\\textbf{y}}'(t)$, and the right-hand side of the original ODE evaluated along the approximated solution trajectory. \n", "\n", "\\begin{equation}\n", - " \\textbf{R}(t) = \\hat{\\textbf{y}}'(t) - f(t, \\hat{\\textbf{y}}(t)) \\tag{2.4}\n", + " \\textbf{R}(t) = \\hat{\\textbf{y}}'(t) - f(t, \\hat{\\textbf{y}}(t)) \\tag{2.1.4}\n", "\\end{equation}\n", "\n", "The idea is that if our numerical approximation of the true solution is \"good\", then this residual function should be roughly zero everywhere within the interval of approximation. The `ivp.IVP.compute_residual` method takes the following parameters...\n", @@ -570,7 +656,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 16 + "prompt_number": 38 }, { "cell_type": "markdown", @@ -585,7 +671,8 @@ "collapsed": false, "input": [ "# reset original parameters\n", - "lotka_volterra_ivp.args = lotka_volterra_params\n", + "lotka_volterra_ivp.f_params = lotka_volterra_params\n", + "lotka_volterra_ivp.jac_params = lotka_volterra_params\n", "\n", "# compute the residual\n", "residual = lotka_volterra_ivp.compute_residual(solution, ti, k=1)" @@ -593,7 +680,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 17 + "prompt_number": 43 }, { "cell_type": "markdown", @@ -640,11 +727,11 @@ "output_type": "display_data", "png": 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lxqqyYoUoor4+aevgoCF62iGq+6GiQqwk2qEFiZ5ee/t2QxDb2ycrQpCOUuOx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5AAAg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\nSZLUyYqeSnVV9BYDdwGzSH15xwOvA6cAt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"text": [ - "" + "" ] } ], - "prompt_number": 29 + "prompt_number": 44 }, { "cell_type": "markdown", @@ -669,20 +756,20 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 23 + "prompt_number": 45 }, { "cell_type": "code", "collapsed": false, "input": [ "# reset parameters\n", - "lotka_volterra_ivp.f_args = (1.0, 0.1, 2.0, 0.75)\n", - "lotka_volterra_ivp.jac_args = lotka_volterra_ivp.f_args " + "lotka_volterra_ivp.f_params = (1.0, 0.1, 2.0, 0.75)\n", + "lotka_volterra_ivp.jac_params = lotka_volterra_ivp.f_params " ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 19 + "prompt_number": 46 }, { "cell_type": "markdown", @@ -747,11 +834,11 @@ "output_type": "display_data", "png": 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kbt2qOnL66YrhDGFj9Fo1jyAr3AlowoTw1CiTgNnu/7OAJ4Hj3O/nIhH2FFAL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\nGRQJ5U70DIJDtoqe3HeMMmxgY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"text": [ - "" + "" ] } ], - "prompt_number": 21 + "prompt_number": 47 }, { "cell_type": "markdown", @@ -772,8 +859,8 @@ "def plot_lotka_volterra(a, b, c, d):\n", " \"\"\"Plots trajectories of the Lotka-Volterra system.\"\"\"\n", " # update the parameters and re-compute the solution\n", - " lotka_volterra_ivp.f_args = (a, b, c, d)\n", - " lotka_volterra_ivp.jac_args = (a, b, c, d)\n", + " lotka_volterra_ivp.f_params = (a, b, c, d)\n", + " lotka_volterra_ivp.jac_params = (a, b, c, d)\n", " tmp_solution = lotka_volterra_ivp.solve(t0, y0, h=1e-1, T=15, integrator='dopri5',\n", " atol=1e-12, rtol=1e-9)\n", " # extract the components of the solution\n", @@ -801,13 +888,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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7+SvkukEN9Wu4zYa+/cQdCpjELboqRsQvarPSEj6NiyqHCcKfl0T3QRPxi9ps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\npUurHdMP5fLauinnQrLUsV+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TV9Rb2d+6dXZgElDRuLijhMkTqjMoEFAy0Nj6q2kHHvP2GXNsMEB8gR6g1Lr+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\n9h9w36i99RdSe1PC5A+fhuRKcdG97+O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"text": [ - "" + "" ] } ], - "prompt_number": 24 + "prompt_number": 48 }, { "cell_type": "markdown", @@ -828,7 +915,7 @@ "The resulting dynamics are entirely deterministic giving a starting point $(x_0,y_0,z_0)$. Though it looks straightforward, for certain choices of the parameters, the trajectories become chaotic, and the\n", "resulting trajectories display some surprising properties.\n", "\n", - "### Incorporating SymPy\n", + "### 2.2.1 Incorporating SymPy\n", "While deriving the Jacobian matrix by hand is trivial for most simple 2D or 3D systems, it can quickly become tedious and error prone for larger systems (or even some highly non-linear 2D systems!). In addition to being an important input to most ODE integrators/solvers, Jacobians are also useful for assessing the stability properties of equilibria.\n", "\n", "An alternative approach for solving IVPs using the `ivp` module, which leverages the [SymPy](http://sympy.org/en/index.html) Python library to do the tedious computations involved in deriving the Jacobian, is as follows.\n", @@ -859,7 +946,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 25 + "prompt_number": 49 }, { "cell_type": "code", @@ -882,7 +969,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 26 + "prompt_number": 50 }, { "cell_type": "markdown", @@ -907,7 +994,7 @@ "metadata": {}, "output_type": "pyout", "png": "iVBORw0KGgoAAAANSUhEUgAAAIIAAABLCAMAAACLOq+zAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nZfGvVVqrP3IQNGlzv3QnAAAAAElFTkSuQmCC\n", - "prompt_number": 27, + "prompt_number": 51, "text": [ "\u23a1 \u03c3\u22c5(-x + y) \u23a4\n", "\u23a2 \u23a5\n", @@ -917,7 +1004,7 @@ ] } ], - "prompt_number": 27 + "prompt_number": 51 }, { "cell_type": "markdown", @@ -944,7 +1031,7 @@ "metadata": {}, "output_type": "pyout", "png": "iVBORw0KGgoAAAANSUhEUgAAAKAAAABLCAMAAADAknxeAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n", - "prompt_number": 28, + "prompt_number": 52, "text": [ "\u23a1 -\u03c3 \u03c3 0 \u23a4\n", "\u23a2 \u23a5\n", @@ -954,7 +1041,7 @@ ] } ], - "prompt_number": 28 + "prompt_number": 52 }, { "cell_type": "markdown", @@ -1002,7 +1089,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 29 + "prompt_number": 53 }, { "cell_type": "markdown", @@ -1073,7 +1160,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 30 + "prompt_number": 54 }, { "cell_type": "markdown", @@ -1092,7 +1179,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 31 + "prompt_number": 55 }, { "cell_type": "markdown", @@ -1105,21 +1192,24 @@ "cell_type": "code", "collapsed": false, "input": [ + "# create the instance\n", "lorenz_ivp = ivp.IVP(f=lorenz_system,\n", - " jac=lorenz_jacobian,\n", - " f_args=lorenz_params,\n", - " jac_args=lorenz_params)" + " jac=lorenz_jacobian)\n", + "\n", + "# specify the params\n", + "lorenz_ivp.f_params = lorenz_params\n", + "lorenz_ivp.jac_params = lorenz_params" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 32 + "prompt_number": 56 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Solving the Lorenz equations\n", + "### 2.2.2 Solving the Lorenz equations\n", "At this point I proceed in exactly the same fashion as in the previous Lotka-Volterra equations example: \n", "\n", "1. Solve the model using a discretized, finite-difference approximation.\n", @@ -1144,7 +1234,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 33 + "prompt_number": 57 }, { "cell_type": "markdown", @@ -1187,13 +1277,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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+IJs3bi5aexL7v+H1DTz/9PMcajtE35w+vB4vke0RPJUemiab9Mqxh48tWvvi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\nNz91M3/d81d2tu7MatbPUHK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Fd6g/MAvWroUFC+CDH1TRkYiIOIrSZzGjMX1mK5/XR2dP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\nUbbJQbMMazjakZwccvvUvsvKIho1SnNofKMc0dHsWWfOpIJ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Nnxk+g0snXeq6fD7+ZrW6qprWrlZ8Hh/L31jeewOb68e/0Ic4RRlC7kAEITcx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\n4m0dUblJKqfNbnm/SbqKu1SVe4nmnmk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buzniP8I3vvaN3u0vrH2B0IQQpQWlzInOIRjU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\n2luGfxB1I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"text": [ - "" + "" ] } ], - "prompt_number": 48 + "prompt_number": 59 }, { "cell_type": "markdown", @@ -1217,7 +1307,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 50 + "prompt_number": 60 }, { "cell_type": "markdown", @@ -1271,11 +1361,11 @@ "output_type": "display_data", "png": 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zv8GyUcuGtHJ1tW0ZHhjO3LS5PDvzWR6f/DiGYfDKyVd4/vDznK08OyRkHOqo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\nvZdISIBp04RxiFotfn77betj2VrLJ54QkaqXXrItrgC+/BJ2nK8lT0v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LE9Erb2/xuMnC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XByFPiFMdp8zmM4YWjFrIAYedB1Dh3aPNR+3WtmJMLRicaDuBrJAszJs0D/vP7cc7Je8gNyIX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HfGbt2UUImIiIhIyIQqwVoM4GEAIwFMAfCJ13XfAXAbABeABwCsCFFMjmtzL/+aGiYT/fvz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\nTPUbALEAvgJgs9916wE8G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"text": [ - "" + "" ] } ], - "prompt_number": 52 + "prompt_number": 61 }, { "cell_type": "markdown", @@ -1297,7 +1387,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 53 + "prompt_number": 62 }, { "cell_type": "markdown", @@ -1343,11 +1433,11 @@ "output_type": "display_data", "png": 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UaXOCJ3hw85dbk9kVjggHCwD7pbT/NjqPePqVs8HkXlYpM6vyAwDVa/e3O55c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\nORAREREvWnMgIiISYrTmQERER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"text": [ - "" + "" ] } ], - "prompt_number": 55 + "prompt_number": 63 }, { "cell_type": "code", @@ -1355,8 +1445,7 @@ "input": [], "language": "python", "metadata": {}, - "outputs": [], - "prompt_number": 25 + "outputs": [] } ], "metadata": {} diff --git a/quantecon/ivp.py b/quantecon/ivp.py index 5fb941c00..551448fe8 100644 --- a/quantecon/ivp.py +++ b/quantecon/ivp.py @@ -14,7 +14,7 @@ of the approximated solution. @author : David R. Pugh -@date : 2014-08-18 +@date : 2014-09-09 """ from __future__ import division @@ -25,7 +25,7 @@ class IVP(integrate.ode): - def __init__(self, f, jac=None, f_args=None, jac_args=None): + def __init__(self, f, jac=None): r""" Creates an instance of the IVP class. @@ -33,7 +33,7 @@ def __init__(self, f, jac=None, f_args=None, jac_args=None): ---------- f : callable ``f(t, y, *f_args)`` Right hand side of the system of equations defining the ODE. The - independent variable, `t`, is a ``scalar``; `y` is an ``ndarray`` + independent variable, ``t``, is a ``scalar``; ``y`` is an ``ndarray`` of dependent variables with ``y.shape == (n,)``. The function `f` should return a ``scalar``, ``ndarray`` or ``list`` (but not a ``tuple``). @@ -45,63 +45,8 @@ def __init__(self, f, jac=None, f_args=None, jac_args=None): \mathcal{J}_{i,j} = \bigg[\frac{\partial f_i}{\partial y_j}\bigg] - f_args : tuple, optional(default=None) - Additional arguments that should be passed to the function `f`. - jac_args : tuple, optional(default=None) - Additional arguments that should be passed to the function `jac`. - """ super(IVP, self).__init__(f, jac) - self.f_args = f_args - self.jac_args = jac_args - - @property - def f_args(self): - """ - Additional arguments passed to the user-supplied function `f`. - - :getter: Return the current arguments. - :setter: Set new values for the arguments. - :type: tuple - - """ - return self._f_args - - @property - def jac_args(self): - """ - Additional arguments passed to the user-supplied function `jac`. - - :getter: Return the current arguments. - :setter: Set new values for the arguments. - :type: tuple - - """ - return self._jac_args - - @f_args.setter - def f_args(self, new_f_args): - """Set new values for the parameters.""" - if not isinstance(new_f_args, (tuple, type(None))): - mesg = "IVP.args must be a tuple, not a {}." - raise AttributeError(mesg.format(new_f_args.__class__)) - elif new_f_args is not None: - self.set_f_params(*new_f_args) - self._f_args = new_f_args - else: - pass - - @jac_args.setter - def jac_args(self, new_jac_args): - """Set new values for the parameters.""" - if not isinstance(new_jac_args, (tuple, type(None))): - mesg = "IVP.args must be a tuple, not a {}." - raise AttributeError(mesg.format(new_jac_args.__class__)) - elif new_jac_args is not None: - self.set_jac_params(*new_jac_args) - self._jac_args = new_jac_args - else: - pass def _integrate_fixed_trajectory(self, h, T, step, relax): """Generates a solution trajectory of fixed length.""" @@ -134,7 +79,7 @@ def _integrate_variable_trajectory(self, h, g, tol, step, relax): current_step = np.hstack((self.t, self.y)) solution = np.vstack((solution, current_step)) - if g(self.t, self.y, *self.f_args) < tol: + if g(self.t, self.y, *self.f_params) < tol: break else: continue @@ -185,7 +130,7 @@ def compute_residual(self, traj, ti, k=3, ext=2): # rhs of ode evaluated along approximate solution T = ti.size - rhs_ode = np.vstack(self.f(ti[i], soln[i, 1:], *self.f_args) for i in range(T)) + rhs_ode = np.vstack(self.f(ti[i], soln[i, 1:], *self.f_params) for i in range(T)) rhs_ode = np.hstack((ti[:, np.newaxis], rhs_ode)) # should be roughly zero everywhere (if approximation is any good!) diff --git a/quantecon/tests/test_ivp.py b/quantecon/tests/test_ivp.py index 2a093e067..e3ef1f5af 100644 --- a/quantecon/tests/test_ivp.py +++ b/quantecon/tests/test_ivp.py @@ -2,7 +2,7 @@ Tests for ivp.py @author : David R. Pugh -@date : 2014-08-26 +@date : 2014-09-09 """ import nose @@ -11,11 +11,8 @@ from .. import ivp -# use the Solow Model with Cobb-Douglas production as test case -valid_params = (0.02, 0.02, 0.15, 0.33, 0.05) -invalid_params = {'g': 0.02, 'n': 0.02, 's': 0.15, 'alpha': 0.33, 'delta': 0.05} - +# use the Solow Model with Cobb-Douglas production as test case def solow_model(t, k, g, n, s, alpha, delta): """ Equation of motion for capital stock (per unit effective labor). @@ -148,6 +145,14 @@ def solow_analytic_solution(t, k0, g, n, s, alpha, delta): return analytic_traj +# create an instance of the IVP class +valid_params = (0.02, 0.02, 0.15, 0.33, 0.05) +model = ivp.IVP(f=solow_model, + jac=solow_jacobian) + +model.f_params = valid_params +model.jac_params = valid_params + # helper functions for conducting tests def _compute_fixed_length_solns(model, t0, k0): @@ -195,27 +200,16 @@ def _compute_variable_length_solns(model, t0, k0, g, tol): # testing functions -def test_validate_f_args(): - """Testing validation of f_args attribute.""" - with nose.tools.assert_raises(AttributeError): - model = ivp.IVP(f=solow_model, - f_args=invalid_params) - - -def test_validate_jac_args(): - """Testing validation of jac_args attribute.""" - with nose.tools.assert_raises(AttributeError): - model = ivp.IVP(f=solow_model, - jac=solow_jacobian, - jac_args=invalid_params) +def test_solve_args(): + """Testing arguments passed to the IVP.solve method.""" + # g and tol must be passed together! + with nose.tools.assert_raises(ValueError): + t0, k0 = 0, np.array([5.0]) + model.solve(t0, k0, g=_termination_condition) def test_solve_fixed_trajectory(): """Testing computation of fixed length solution trajectory.""" - model = ivp.IVP(f=solow_model, - jac=solow_jacobian, - f_args=valid_params, - jac_args=valid_params) # compute some fixed length trajectories t0, k0 = 0, np.array([5.0]) @@ -230,10 +224,6 @@ def test_solve_fixed_trajectory(): def test_solve_variable_trajectory(): """Testing computation of variable length solution trajectory.""" - model = ivp.IVP(f=solow_model, - jac=solow_jacobian, - f_args=valid_params, - jac_args=valid_params) # compute some variable length trajectories t0, k0, tol = 0, np.array([5.0]), 1e-3 @@ -255,10 +245,6 @@ def test_solve_variable_trajectory(): def test_interpolation(): """Testing parameteric B-spline interpolation methods.""" - model = ivp.IVP(f=solow_model, - jac=solow_jacobian, - f_args=valid_params, - jac_args=valid_params) # compute some fixed length trajectories t0, k0 = 0, np.array([5.0]) @@ -280,10 +266,6 @@ def test_interpolation(): def test_compute_residual(): """Testing computation of solution residual.""" - model = ivp.IVP(f=solow_model, - jac=solow_jacobian, - f_args=valid_params, - jac_args=valid_params) # compute some fixed length trajectories t0, k0 = 0, np.array([5.0])