{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "# Solving initial value problems (IVPs) in `quantecon`\n", "\n", "## David R. Pugh\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import sympy as sp\n", "\n", "# comment out if you don't want plots rendered in notebook\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1. Introduction\n", "This notebook demonstrates how to solve initial value problems (IVPs) using the [`quantecon`](http://jstac.github.io/quant-econ/) Python library. Before demonstrating how one might solve an IVP using `quantecon`, I provide formal definitions for ordinary differential equations (ODEs) and initial value problems (IVPs), as well as a short discussion of finite-difference methods that will be used to solve IVPs.\n", "\n", "## Ordinary differential equations (ODE)\n", "An [ordinary differential equation (ODE)](http://en.wikipedia.org/wiki/Ordinary_differential_equation) is in equation of the form\n", "\n", "\\begin{equation}\n", "\\textbf{y}'= \\textbf{f}(t ,\\textbf{y}) \\tag{1.1}\n", "\\end{equation}\n", "\n", "where $\\textbf{f}:[t_0,\\infty) \\times \\mathbb{R}^n\\rightarrow\\mathbb{R}^n$. In the case where $n=1$, then equation 1.1 reduces to a single ODE; when $n>1$, equation 1.1 defines a system of ODEs. ODEs are one of the most basic examples of functional equations: a solution to equation 1.1 is a function $\\textbf{y}(t): D \\subset \\mathbb{R}\\rightarrow\\mathbb{R}^n$. There are potentially an infinite number of solutions to the ODE defined in equation 1.1. In order to reduce the number of potentially solutions, we need to impose a bit more structure on the problem. \n", "\n", "## Initial value problems (IVPs)\n", "An [initial value problem (IVP)](http://en.wikipedia.org/wiki/Initial_value_problem) has the form\n", "\n", "\\begin{equation}\n", "\\textbf{y}'= \\textbf{f}(t ,\\textbf{y}),\\ t \\ge t_0,\\ \\textbf{y}(t_0) = \\textbf{y}_0 \\tag{1.2}\n", "\\end{equation}\n", "\n", "where $\\textbf{f}:[t_0,\\infty) \\times \\mathbb{R}^n\\rightarrow\\mathbb{R}^n$ and the initial condition $\\textbf{y}_0 \\in \\mathbb{R}^n$ is a given vector. Alternatively, I could also specify an initial value problem by imposing a terminal condition of the form $\\textbf{y}(T) = \\textbf{y}_T$. The key point is that the solution $\\textbf{y}(t)$ is pinned down at one $t\\in[t_0, T]$. \n", "\n", "The solution to the IVP defined by equation 1.2 is the function $\\textbf{y}(t): [t_0,T] \\subset \\mathbb{R}\\rightarrow\\mathbb{R}^n$ that satisfies the initial condition $\\textbf{y}(t_0) = \\textbf{y}_0$. So long as the function $\\textbf{f}$ is [reasonably well-behaved](http://en.wikipedia.org/wiki/Ordinary_differential_equation#Existence_and_uniqueness_of_solutions), the solution $\\textbf{y}(t)$ exists and is unique.\n", "\n", "## Finite-difference methods\n", "[Finite-difference methods](http://en.wikipedia.org/wiki/Finite_difference_method) are perhaps the most commonly used class of numerical methods for approximating solutions to IVPs. The basic idea behind all finite-difference methods is to construct a difference equation \n", "\n", "\\begin{equation}\n", "\\frac{\\textbf{y}(t_i + h) - \\textbf{y}_i}{h} \\approx \\textbf{y}'(t_i) = \\textbf{f}(t_i ,\\textbf{y}(t_i)) \\tag{1.3}\n", "\\end{equation}\n", "\n", "which is \"similar\" to the differential equation at some grid of values $t_0 < \\dots < t_N$. Finite-difference methods then \"solve\" the original differential equation by finding for each $n=0,\\dots,N$ a value $\\textbf{y}_n$ that approximates the value of the solution $\\textbf{y}(t_n)$.\n", "\n", "It is important to note that finite-difference methods only approximate the solution $\\textbf{y}$ at the $N$ grid points. In order to approximate $\\textbf{y}$ between grid points one must resort to some form of [interpolation](http://en.wikipedia.org/wiki/Interpolation). \n", "\n", "The literature on finite-difference methods for solving IVPs is vast and there are many excellent reference texts. Those interested in a more in-depth treatment of these topics, including formal proofs of convergence, order, and stability of the numerical methods used in this notebook, should consult (Hairer, 1993), (Butcher, 2008), (Iserles, 2009). Chapter 10 of (Judd, 1998) covers a subset of these more formal texts with a specific focus on economic applications. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2. Examples\n", "The remainder of this notebook demonstrates the usage and functionality of the `quantecon.ivp` module by way of example. To get started, we need to import the `quantecon.ivp module`..." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from quantecon import ivp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.1 Lotka-Volterra \"Predator-Prey\" model\n", "\n", "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{2.1.1} \\\\\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", "\n", "Parameter definitions are as follows:\n", "* $a$: the natural growing rate of prey in the absence of predators.\n", "* $b$: the natural dying rate of prey due to predation.\n", "* $c$: the natural dying rate of predators, in teh absence of prey.\n", "* $d$: the factor describing how many caught prey is necessary to create a new predator.\n", "\n", "I will use $\\textbf{y}=[u, v]$ to describe the state of both populations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 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, *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", "$$ \\mathcal{J}_{i,j} = \\bigg[\\frac{\\partial f_i}{\\partial y_j}\\bigg] \\tag {2.1.3}$$\n", "\n", "Most all of this information can be found in the docstring for the `ivp.IVP` class." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ivp.IVP?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the docstring we see that we are required to define a function describing the right-hand side of the system of differential equations that we wish to solve. While, optional, it is always a good idea to also define a function describing the Jacobian matrix of partial derivatives.\n", "\n", "For the Lotka-Volterra model, these two functions would look as follows..." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def lotka_volterra_system(t, y, a, b, c, d):\n", " \"\"\"\n", " Return the Lotka-Voltera system.\n", "\n", " Parameters\n", " ----------\n", " t : float\n", " Time\n", " y : ndarray (float, shape=(2,))\n", " Endogenous variables of the Lotka-Volterra system. Ordering is\n", " `y = [u, v]` where `u` is the number of prey and `v` is the number of\n", " predators.\n", " a : float\n", " Natural growth rate of prey in the absence of predators.\n", " b : float\n", " Natural death rate of prey due to predation.\n", " c : float\n", " Natural death rate of predators, due to absence of prey.\n", " d : float\n", " Factor describing how many caught prey is necessary to create a new\n", " predator.\n", "\n", " Returns\n", " -------\n", " jac : ndarray (float, shape=(2,2))\n", " Jacobian of the Lotka-Volterra system of ODEs.\n", "\n", " \"\"\"\n", " f = np.array([ a * y[0] - b * y[0] * y[1] ,\n", " -c * y[1] + d * b * y[0] * y[1] ])\n", " return f\n", "\n", "\n", "def lotka_volterra_jacobian(t, y, a, b, c, d):\n", " \"\"\"\n", " Return the Lotka-Voltera Jacobian matrix.\n", "\n", " Parameters\n", " ----------\n", " t : float\n", " Time\n", " y : ndarray (float, shape=(2,))\n", " Endogenous variables of the Lotka-Volterra system. Ordering is\n", " `y = [u, v]` where `u` is the number of prey and `v` is the number of\n", " predators.\n", " a : float\n", " Natural growth rate of prey in the absence of predators.\n", " b : float\n", " Natural death rate of prey due to predation.\n", " c : float\n", " Natural death rate of predators, due to absence of prey.\n", " d : float\n", " Factor describing how many caught prey is necessary to create a new\n", " predator.\n", "\n", " Returns\n", " -------\n", " jac : ndarray (float, shape=(2,2))\n", " Jacobian of the Lotka-Volterra system of ODEs.\n", "\n", " \"\"\"\n", " jac = np.array([[a - b * y[1], -b * y[0]],\n", " [b * d * y[1], -c + b * d * y[0]]])\n", " return jac" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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..." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "lotka_volterra_ivp = ivp.IVP(f=lotka_volterra_system,\n", " jac=lotka_volterra_jacobian)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 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." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# ordering is (a, b, c, d)\n", "lotka_volterra_params = (1.0, 0.1, 1.5, 0.75)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "lotka_volterra_ivp.set_f_params?" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "lotka_volterra_ivp.set_jac_params?" ] }, { "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", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lotka_volterra_ivp.set_f_params(*lotka_volterra_params)\n", "lotka_volterra_ivp.set_jac_params(*lotka_volterra_params)" ] }, { "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", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(1.0, 0.1, 1.5, 0.75)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lotka_volterra_ivp.f_params" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(1.0, 0.1, 1.5, 0.75)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lotka_volterra_ivp.jac_params" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# I generally prefer to set attributes directly...\n", "lotka_volterra_ivp.f_params = lotka_volterra_params" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(1.0, 0.1, 1.5, 0.75)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# ...result is the same\n", "lotka_volterra_ivp.f_params" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 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", "* `t0` : float. Initial condition for the independent variable.\n", "* `y0` : array_like (float, shape=(n,)). Initial condition for the dependent variables.\n", "* `h` : float, optional(default=1.0). Step-size for computing the solution. Can be positive or negative depending on the desired direction of integration.\n", "* `T` : int, optional(default=None). Terminal value for the independent variable. One of either `T` or `g` must be specified.\n", "* `g` : Callable of the form ``g(t, y, args)``, optional(default=None). Provides a stopping condition for the integration. If specified user must also specify a stopping tolerance, `tol`.\n", "* `tol` : float, optional (default=None). Stopping tolerance for the integration. Only required if `g` is also specifed.\n", "* `integrator` : str, optional(default='dopri5') Must be one of 'vode', 'lsoda', 'dopri5', or 'dop853'\n", "* `step` : bool, optional(default=False) Allows access to internal steps for those solvers that use adaptive step size routines. Currently only 'vode', 'zvode', and 'lsoda' support `step=True`.\n", "* `relax` : bool, optional(default=False) Currently only 'vode', 'zvode', and 'lsoda' support `relax=True`.\n", "* `**kwargs` : dict, optional(default=None). Dictionary of integrator specific keyword arguments. See the Notes section of the docstring for `scipy.integrate.ode` for a complete description of solver specific keyword arguments.\n", "\n", "... and returns:\n", "\n", "* `solution`: array_like (float). Simulated solution trajectory.\n", "\n", "The above information can be found in the doctring of the `ivp.IVP.solve` method." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# remember...always read the docs!\n", "ivp.IVP.solve?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example usage\n", "Using `dopri5`, an embedded Runge-Kutta method of order 4(5) with adaptive step size control due to [Dormand and Prince](http://en.wikipedia.org/wiki/Dormand%E2%80%93Prince_method), integrate the model forward from an initial condition of 10 rabbits and 5 foxes for 15 years." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# define the initial condition...\n", "t0, y0 = 0, np.array([10, 5])\n", "\n", "# ...and integrate!\n", "solution = lotka_volterra_ivp.solve(t0, y0, h=1e-1, T=15, integrator='dopri5',\n", " atol=1e-12, rtol=1e-9)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Plotting the solution\n", "\n", "Once we have computed the solution, we can plot it using the excellent [`matplotlib`](http://matplotlib.org/) Python library." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SGeVAiYyKEc4hkSFSQ71wyoGKk3qgRESkOOopkhEx9BwoM3uwmV1iZpeb2VVm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\n4BxgH2ASeIW73znsssVgbGys7CIMVMr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# extract the components of the solution trajectory\n", "t = solution[:, 0]\n", "rabbits = solution[:, 1]\n", "foxes = solution[:, 2]\n", "\n", "# create the plot\n", "fig = plt.figure(figsize=(8, 6))\n", "plt.plot(t, rabbits, 'r.', label='Rabbits')\n", "plt.plot(t, foxes , 'b.', label='Foxes')\n", "plt.grid()\n", "plt.legend(loc=0, frameon=False, bbox_to_anchor=(1, 1))\n", "plt.xlabel('Time', fontsize=15)\n", "plt.ylabel('Population', fontsize=15)\n", "plt.title('Evolution of fox and rabbit populations', fontsize=20)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we have plotted the time paths of rabbit and fox populations as sequences of points rather than smooth curves. This is done to visually emphasize the fact that finite-difference methods used to approximate the solution return a discrete approximation to the true continuous solution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 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", "* `traj` : array_like (float)\n", " Solution trajectory providing the data points for constructing the\n", " B-spline representation.\n", "* `ti` : array_like (float)\n", " Array of values for the independent variable at which to\n", " interpolate the value of the B-spline.\n", "* `k` : int, optional(default=3)\n", " Degree of the desired B-spline. Degree must satisfy\n", " :math:`1 \\le k \\le 5`.\n", "* `der` : int, optional(default=0)\n", " The order of derivative of the spline to compute (must be less\n", " than or equal to `k`).\n", "* `ext` : int, optional(default=2) Controls the value of returned elements\n", " for outside the original knot sequence provided by traj. For\n", " extrapolation, set `ext=0`; `ext=1` returns zero; `ext=2` raises a\n", " `ValueError`.\n", "\n", "... and returns:\n", "\n", "* `interp_traj`: ndarray (float). The interpolated trajectory.\n", "\n", "#### Example usage\n", "Approximate the solution to the Lotka-Volterra model at 1000 evenly spaced points using a 5th order B-spline interpolation and no extrapolation." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# define the desired interpolation points...\n", "ti = np.linspace(t0, solution[-1, 0], 1000)\n", "\n", "# ...and interpolate!\n", "interp_solution = lotka_volterra_ivp.interpolate(solution, ti, k=5, ext=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Plotting the interpolated solution\n", "\n", "We can now plot the interpolated solution using `matplotlib` as follows..." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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NsIV+O+xghn1Ggnxr+v6VQeL6PfaYDfuGYY89YOVKWLSoyUMT189pcbgBVQtU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# extract the components of the solution\n", "ti = interp_solution[:, 0]\n", "rabbits = interp_solution[:, 1]\n", "foxes = interp_solution[:, 2]\n", "\n", "# make the plot\n", "fig = plt.figure(figsize=(8, 6))\n", "\n", "plt.plot(ti, rabbits, 'r-', label='Rabbits')\n", "plt.plot(ti, foxes , 'b-', label='Foxes')\n", "\n", "plt.xlabel('Time', fontsize=15)\n", "plt.ylabel('Population', fontsize=15)\n", "plt.title('Evolution of fox and rabbit populations', fontsize=20)\n", "\n", "plt.legend(loc='best', frameon=False, bbox_to_anchor=(1,1))\n", "plt.grid()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we have plotted the time paths of rabbit and fox populations as smooth curves. This is done to visually emphasize the fact that the B-spline interpolation methods used to approximate the solution return a continuous approximation to the true continuous solution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 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{2.1.4}\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", "\n", "* `traj` : array_like (float). Solution trajectory providing the data points for constructing the B-spline representation.\n", "* `ti` : array_like (float). Array of values for the independent variable at which to interpolate the value of the B-spline.\n", "* `k` : int, optional(default=3). Degree of the desired B-spline. Degree must satisfy $1 \\le k \\le 5$.\n", "* `ext` : int, optional(default=2). Controls the value of returned elements for outside the original knot sequence provided by `traj`. For extrapolation, set `ext=0`; `ext=1` returns zero; `ext=2` raises a `ValueError`.\n", "\n", "... and returns:\n", "\n", "* `residual` : array (float) Difference between the derivative of the B-spline approximation of the solution trajectory and the right-hand side of the ODE evaluated along the approximated solution trajectory.\n", "\n", "Remember to check the docstring for more information!" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# life will be easier if you read the docs!\n", "lotka_volterra_ivp.compute_residual?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example usage\n", "Compute the residual to the Lotka-Volterra model at 1000 evenly spaced points using a 1st order B-spline interpolation (which is equivalent to linear interpolation!)." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# reset original parameters\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)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Plotting the residual\n", "\n", "In your introductory econometrics/statistics course, your professor likely implored you to \"always plot your residuals!\" This maxim of data analysis is no less true in numerical analysis. However, while patterns in residuals are generally a \"bad\" thing in econometrics/statistics (as they suggest model mispecification, or other related problems), patterns in a residual function, $\\textbf{R}(t)$, in numerical analysis are generally OK (and in certain cases actually desireable!). \n", "\n", "In this context, what is important is that overall size of the residuals is \"small\"." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ZGXsm6mB3tx5kxRS8dClPtm1tbv+YOXM06RNtD8Dlksjiqirero2IScm3vqVT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0eCS/DFiLFcqGvOr7WeAfBapdStAD4L4M6GnlUTYCsDYc24jHrVnHo7rCizvqX47LnA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\n+ZWcG5ifVIqu9sbNzCuAK8Y4fnyvApIkS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# extract the raw residuals\n", "rabbits_residual = residual[:, 1]\n", "foxes_residual = residual[:, 2]\n", "\n", "# typically, normalize residual by the level of the variable\n", "norm_rabbits_residual = np.abs(rabbits_residual) / rabbits\n", "norm_foxes_residual = np.abs(foxes_residual) / foxes\n", "\n", "# create the plot\n", "fig = plt.figure(figsize=(8, 6))\n", "plt.plot(ti, norm_rabbits_residual, 'r-', label='Rabbits')\n", "plt.plot(ti, norm_foxes_residual**2 / foxes, 'b-', label='Foxes')\n", "plt.axhline(np.finfo('float').eps, linestyle='dashed', color='k', label='Machine eps')\n", "plt.xlabel('Time', fontsize=15)\n", "plt.ylim(1e-16, 1)\n", "plt.ylabel('Residuals (normalized)', fontsize=15)\n", "plt.yscale('log')\n", "plt.title('Lotka-Volterra residuals', fontsize=20)\n", "plt.grid()\n", "plt.legend(loc='best', frameon=False, bbox_to_anchor=(1,1))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Understanding determinants of accuracy\n", "We can use [IPython widgets](https://github.com/ipython/ipywidgets) to investigate the determinants of accuracy of our approximated solution. Good candidates for exploration are... \n", "\n", "* `h`: the step size used in computing the initial finite difference solution. \n", "* `atol`: the absolute tolerance for the solver.\n", "* `rtol`: the relative tolerance for the solver.\n", "* `k`: the degree of the B-spline used in the interpolation of that finite difference solution." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from ipywidgets import interact\n", "from ipywidgets.widgets import FloatText, FloatSlider, IntSlider, Text" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# reset parameters\n", "lotka_volterra_ivp.f_params = (1.0, 0.1, 2.0, 0.75)\n", "lotka_volterra_ivp.jac_params = lotka_volterra_ivp.f_params " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can make use of the `@interact` decorator and the various IPython widgets to create an interactive visualization of the residual plot for the Lotka-Volterra \"Predator-Prey\" model." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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k5gLXXutAAwOgWpGWLCmftmqVxF6WBbA6RPXqcn4PH5as3GAz0W+5RTLQz5xx\npn0+cMSFu2mTWPMWLxYXv1mqVJHrZuZM+V1rJvfqJVnCOHFCTFgVZdUDxB2iN0dv3iz39lDz8MPi\n/g7ATz/Jpe1iCQYwjJlrAugGoDuAv1Vuk859zl+xFxsr4yYqLp172vyCaWdHm1p13ToT98pnnpEY\nNW2ZB188+SRQqxaouo28/CFDkHzFFRKHp6N/f4mVBgC8846UuQhFkL2e6GgJkF60qHzaqlXSIBsE\njKtp1EjE7qFDziWdXH99kIMMByY1VcINbccNqbFiUZHisjVTs4cIePNNyQ756COv2b17Kw/vTz8V\nYVAl+FuEqf4NGSIxsyqrVyNkAwY3aCDxr3v3Aq1bB7Wp5O3b5STaHfPXJGVij1nG7tW+SJmhsFBe\nCqdMkWwBk5Sdu9q1gb//XT4aysTet9/KOaxZ01q7gmXAAEnIAKRE0L59cj5MYvu3N2UK8PLLARdz\nxZ5tCACY+TiAJRDRByK6mojWE1EOER0gogkG691DREeUz+O6+dFENJOIThHRH0RUFkhDRPuI6DIi\nGgLgWQC3ElEuEW1Q5t9FRHuUdfcQ0e0h6ntIOH/FHuCRxXl9zqf4I7Mljh71v0phoYSFBXx5TEwE\nHnpIMmn9sWyZxEZNmwayK8RGjQI2btQFXEkbDx0CMtftEzPSjTfa274dBg0qvwkDEhAeqjfuatVE\nYO7dazowOyDXXSfB6iYz7qxy8qQYg+rXD2Ij//gHAIBj46yJ+KpVgXffBSZM8Irf69ULWL3yrDy8\nb7stiMZZpH9/EXgqqanAhReGZl/160stxWPHnEmRHD7cd803h9i0Cegat1cst336SBzdjTf6r1Go\n5fXXJRto5Ej7jRgzRiz0mhfYspeDb74RMVnR9OkDrF0rf2/fLuI9TIrZlZTIO25Z1QYXyxBREwBD\nAexSJp0GMIqZ4wEMAzCeiEboVksC0BrAEABPE5G2/MMIALMA1ALwFYD5ROSRMcjMSwC8DGAWM8cx\nc3ciqgFgCoAhisWxH4CNzvU09JzfYq9FC3H9AaiesgbDrjgT0JiTkiJB0tWrm9j++PFyEzTIZAMg\nd4MHH5QHb61ato1uSYMHy4Nf5zauWlWeDWveXSsPhmCrNVvBw6wIEXs2EyeSzARcx8c7K/ZatBCX\n89atzmxPR2qqXEdEJvunJyVFyqEAUF6CrdG9u7hzdYlEvXsDq389I5kjDRta364BpvrXujVw6pQE\n+AOSBRWLWUXsAAAgAElEQVSsi9UXqmXv+HHJvA6CpKQkMd0Y1jlyhtJSYPPGs+j61BCx4B89Ku1v\n00Z+Z0Zla7QcPSoZaG++aXnfHueuWjV5sfz447JJPXsCa9cySn9d4XwyjRkuuEB+TKWlIvYsviDY\n+u2ZZPt2+QkFkch+PjOfiE4BOAggHcBEAGDm5cy8Vfl7C4CZAPRyeiIzFyrzpwPQWuDWMfM8Zi4B\n8CaA6gDMZmmVAOhMRNWZOZ2Zt9vsW6Vwfou9li1F7OXmAllZuOGOGpgzx/8qply4KvXri2tDXx5A\nZfZscXuMkBeToDysI0fK679u2IyLLgI2/HgCuOmmIDZug44dpS1FReJ6snEjtkRCgog9EzGXphk4\nUGLXQoDqwgUgFqZ580TAmYFZYoYmTsR//xtE4vADD8iLBpdnM7ZpA2TlVEHmJfqX5RBDJNfM9u3S\nnlCKvfr15QTUqGHyrS0A3bvLfUQpheQ0B3/eibjCE6j19dTyagHR0VIP7/rrRYBpzqEXb78tGdU+\nRgOyxB13AHPnln2tVw9IiC7CrhZXygtXRVOzpqipAweAgwedG5nHAYIt+VmpELEjH/tcq1jQLgXQ\nAUAdaRb1JqKlRHSciLIBjFPnKTCAw5rvBwBozfeHyhaUTIzDuvmGMHM+gFsB3AfgGBF9T0RO5MZX\nGOe32GveXG4SyoNl8FVVsHq1cYk4lXXrgB49LOzj1ls9bo4evPMO8PTTZSrPrthLTk6Wt+7/+z+J\ntdLQo20u1qc3FuFSkVSrJtaa7dtFzERF2RZipuJqVMteRYu9PXvEfW4xhkq17GHWLCR36CBWumHD\n5BwWFflfedkyseyMHYs77giimk1SkljT1ILUkBC9jhGp2NLsapsb9cZ0XFT79tKW48clMSNUJpHa\ntcViG5QPXUhOTpa29u3rFUbhCPn5SL3rFXkxMCpG/uKLkmzi6y21sFAscX/9q63de527Ll3kmtm3\nr2xSzzr78EdTh+shWqFlS7mPHzokxaEtEFSdvQCsXRtcyc9KhZkc+dhHjdn7FcBnAN5Qpn8BYD6A\nxsycAGAqvF0b2ougGSSj12seSdxUEwBHjI6A1wTmn5h5MIAGAFIBeAc9hzHnt9irV08eLIcOAc2a\nISZGfpzaUDM9mzZZim8Wy96aNd5v/du3i1Bwsu7czTd7xQ51P7sW6yN7iU+3omnbVuJ7PMxYISIU\nYq9/f0m9NiIjQ7KhL7lECha3aiVue39vChpSU4H2JdvEQvfmm3Ledu6UQL5Alpp//xt44ongzykR\ncM01ntdMVhY6nd2ALcWV8NLarp0cg1Ba9QApQHn4sLNiUh+2oKW0VJKVJk4UM6zJawQA8MILSG2Y\nhPaX+nCpR0aKhW/SJONrZuFCySx3ahQSg8zpLsXrsbm6fRMWsyTRfv21GJoXL7Y4CFHTpnIPP3jQ\nstgLJee0ZS+8mAzgSiWZIhZAFjMXE1EvAPogVALwDyKKJqKOAO6GuHpVLiKi65Q4vb8CKASwGt6k\nA2ihCEIQUT0iGqHE7hVDYgdDP8ySg5zfYq9uXQlw1gRqX3GF78ETmKVaiyXdEhMjgkA/avjcuWL1\n05SWsB2zp8ad9Oolb9zp6WXz2u1ZjPSSOj7DBkNKy5bSniNHgroJm47ZKy0V15xTtGwp8ZZ6oV5U\nJA+8jh3ForBypbjx8vMlMcVH0WItqdtL0H7qY8C0aUi65x6ZGB0tpXS2b/ft+j96VKK+nSp0PGyY\nCAKVzZvRuUkWtmxz7tZgOi6qaVNnS+j4IiZGfvcBhkQ0Q1nfunUzdsMXFkrR4r/9TWJ0v/9eLJi+\nXiK07NwJTJuG1C43+S+mPHSobFt/jwGAL78MKinD8NwlJXkUc++S+xtSMq1nwefliU5t1ky80bNm\nSR7Zq6/KpfDKKyYr2jRtKuI9PV3iMS0Qqpi9M2ekL926hWTzf3Y83lqYOQPA5wD+AeB+AJOIKAfA\n3yHJFvp1fwGwG8BPAP7FzNoaWt9C3LFZAP4PwA1K/J5+v7MhwvEkEf2h/P0YxAqYAWAgxKV7zlAJ\n5p4wQrXsHT1aFoyelOTb43H0qDwfLBsE1Ld+bTbs4sVl2ZQqQVe5qFpVOvDzz2ViIGL1SnRtW4CN\nG6MqrLB8GS1blsdgORTs7xM1XsjJJJQqVcqH19Km1L30ksQ//etf5Qq9Vi0ZgWXcOODOO0XM+1Dv\nJSXA3t2laDOyuVjWtFSrBrz3ntRpvOUWb+vdrFlS+86p4agGDJCsW3VQ5pQUdOpE+GaL9U2VlsoA\nBsnJ8lupWlUe5AMHyk8g4MtMo0ay4okTQSdO+MVBsVdGly7GYu/ZZ+XArF1bfm0uXChxusuW+S+0\n+OqrwEMPIXV5DIbf6mffRDI83qxZnq7e4mK5F0ydaqtLPrnoovJkj+JidD6xDJsRa2kTKSniiOjc\nWQ6HfiSZnTvlPjxvnuS4NWvmZ2ONG8sKmZnOWvaDYMcOaXOstcPiAoCZvUYLZ2ZtbTHDuChmPgBA\nzaz92GC+38K32v0ycyaAAbpFkvytH+6c35a9xESpN3boUJllr0cPCefRjQwEwIZVT0Xv4snOFn+w\nLo4uqJg9lQEDPK0GO3age+8obS3UiqNJE3l4B1niwlRcjXpXdboIr/4hfvq0xFpOnux9wohk3u7d\n8uD1wbH1x5BYmoHo118AYNC/AQPkeBnFes6ZIxZhp4iPl6eSmnWckoJOlyRgyxZrwzuvWCGH6rHH\nRMz26SMP8sxMYOTIZPTrB6xfH2AjDRvKtXLihFjdQ0VMjHTOAStw2blr3lwsutrYzdRU4IsvZCg4\n7UvIsGFi0rr9dt/j6p44Ief/wQfL4zv9ceONUhdSO17runXyUhJEhrrhb+/CC+UaV+raNW9UjJxT\nhKwsc9tMSRHD+N//LkLOaMjAdu0kuuDmm8Uxst1f3mNiIpCVJRdbosmC9AqhitnbsSO0+WguLlY5\nv8VeRIRkce7eXXaTqFFDbqwbDSro2BZ7PXvKHU5VkH/8IapSZ51xxFhz0UXlT9WMDKC0FJ0urh6q\nCiL+qVOn3E0easueWlvL6fIyXbqIMFf56isR6b6y/qKiJPDoued8Psj3T5mPFg0K/ScIjBkjLjgt\np0/Lhel0sk3nzh5ir17/toiMRMCakyrTp4unctIkGWDhpZek+Q88ALzxhswfP17CVz/80M+GGjYs\nt+w5VULHCPXFwEmXP5EcR+2LwXvvyYEwsjbddZdYLw0KWwOQcz98OPKqJSIjI4BlC5CY0fr1y2vO\nAWI5HDTIak8CExUlDdq3D9i5E1U6tMMFFwQQZAonTojWffvtwINtEEm9+UmTpKrLwYM+FkxIEKGX\nkxOaEXpsYPtZ4eISIs5vsQfIjT89HYiLK5vUu7dnfVcVU2/YRtSoIS5NNesxJcVw7CO7xec94k46\nd0aZWWbnTqBdO1zYkbBtm71tp6SIO6VzZxGjERFiDLrsMok195s4WqeOCM6sLMtv3FpMxdWESuy1\na+c5Csp33wWOlxs4UFxLs2d7zysuxoEFW9CiR/nxMOzftddK7bZTp8qnrVwp2UFOihRATBDqBaIM\nIaad5I9Fi8RC89tvEndlZJ2+/PIkjB4toYavvSYfQ2rWlBeio0dDb9nT/h8EHueuQwdJLgHEwjZj\nBjB2rPGKRMALL4g71Khw9xdfAHfeiZ07pRxORIT3IgaN8RzJY9UqMYsFgc/fXtu20lflptiuXXnX\n/fHAA2LQtGKcHj1a7kFXXQVj62FCgsTOxsZaTloKVcyeK/Zcwg1X7EVHS9yeRux1724cfhNU3Lj2\n6ZmSYui70DTBPrVry5PhxImyG7H61m3FLXfqlLx5Dxki99Lp02WTZ85I0uvDD0v2XKdOfoaQrVtX\nxN6pUw51zg+qyHNa7LVqVV5moqREVI0Zy9oDD3iVwQEALF2K/TU7o3nnADXJEhKknIf24P7yC0IS\neKk+qfPy5FO3Llq39irZ6EVGBnDPPTJkqpnk2TZtRIt8+KGP2oBE8sA+cCC0sVeqyHNaNLdsKT8O\nQF646tTxX/etb185zz/95Dld/e0mJWHXLjk9pujb19Oyt327Q4MvG6DWKFUqGaiJ1P749Vd5iX7h\nBeu7e+wxecG8+26D+1hCgvxGw6h6sSv2XMINV+xFR4v5XxNJ68slcfCgCXeKLzp0kDsAIAH/BmLP\nrmXPK+6kbVu58yqWvbp15YU3Lc3c9o4eFc9zTIwYeiZMkJI0sbGiI2vXltHEfvhB3DF33inlvrxu\nwrVqybHNzAxqzExTcTWqZc/pmL2mTeXAFRfLA7xePXP12YYPlyebOiKEyqJF2F+/j0d9W5/901tq\nUlIsFnk0iVq6Qq1TRoTWrct1iy+ef15qdQ/QhzHr0PavcWMJyP/b33y8JMTFyTFzWohpcVDseZw7\n7YvB8uWBXwqIJDlm3jzP6T//LOc+MtLaC2a3bigLzi0qkvMZ7Ni/vq7Nhg3LRyGpX7/sluOPiRNF\n6NmtY/3mm5Ks/fbbuhkJCWIRtpENEYqYvdLSILxALi4hwhV76g3fQOzpxUtQYk8t4FxS4vON27Ex\nxFu0kBv9gQNlVfMvvNBcTE1OjljzRo8GPvggsKdr6FCJA587V1wtHscsIkIe3ocOhX6A9FBZ9iIj\nReAdOyZu1P79za1Xo4YcSG1ZEwBYvBgHqrYyN5iBdtxPQE6gzSHn/KKWrjh8WJJqgICWvaNHxdM4\nQT8MuQk6dJDQx1GjPKoECXFxYtlyKtvYiFDE7AFyc1ADy379NbAKBiQr9/vvPV25P/8sGQwQ45np\nQSHatRM1lJ8vltoWLUI3RKJuyLlAbtwtW+TyvT2IoeOjoiTv6cUXdaMYqnF6Tr/o2eTwYWlSqG95\nLi5WcMWe+lDRiL06daTqhtYoc/q0vDza9i41by4PAtVlbKCieve2t2mvuBPtjVixQqn1jQPx4INA\nv35ieTFLgwZipfn9d6kv7EH16lIhNYg7X6XG7AFyDNPT5XXdSordpZd6jqpw+DCQlYWDWXEeZQd9\n9q9bN0kOKS2Vi+/IkaAtNYY0aiT9S0sri5ULJPamThWjlJk8CqP+XXaZ5Cj85S+6FwTV3e/EMGa+\nUK/FAweC3pRH3xo0KFevmzebs8K2bSv3ns2by6etXy81MyFiz/QoZxERcp/Zu9exFwOf16Z6j0lP\nB+rVKwvh8xUqMm2a5KoE+/Ns1Uqsg/feq0k8Vu+lNoqMhyJmz3XhuoQjrtgzEHtE3q5cjYfLHs2a\nycNFYz3R89hjgUfKMoVawkIz0HurVoHdcsuWSQmNN9+03s9atSRYf/58ie8rQ727hzpmL5RiT32w\nWR3Z4ZJLPMXexo1Ajx5ISyNzycm1akk2zMGD4iNr2TI01ovISNnPnj1liTSq2DN6eJeWSszd/fcH\nt9vnnxet4HG9qNdJKC17gIx+0sfs+OcmqV9frpOzZ8Wda1aY9+8vyRSArJuaWmb51xjnzdGmjZy4\nnTtD60dU+3r8OFC3LuLiRJ9nZHgvWloqJVacqhg0bpzo2vffVyYENai48+zcGdoBYFxc7OCKPVUc\n6B4u+oDjoFy4gAiG48fFOuND7BHZ0ypecSc6FwsQWOwxA888A7z8sv0kxcRESVZ9+mlx7QIoLz9i\nKp3QGFNxNeqBC4UYUi17e/cGfIAfP66puNKxo0xQTcSbNqHgwotQWOhZIcJv/1TVFSoXrkpCgvRP\nEXsJCXIojR7ea9eKJuvUydymffUvMlIshH/7m2aQkooSewsXOjIKiUffYmPFJbB1q/zuzPahZ89y\nd/2uXRLYGBMDZotuXKA8ceLoUZ/3GSv4vDbj4qSu4KlTZRezGvqpZ+1aOTRO5YpUqSLXzfPP64ak\ntpKBphCKmD3LAt3FpQJwxZ7qC9C9HaojN6kEPexiXJy44vbtC6rAsCnUt+6TJ8v8bIHE3ooVUtbg\nlluC2/UFF0i94VGjlPEtTY135AChduOqLisfwzEdPy61wNq2lWO9Zg1E4HbtWp7avXEj0pr3RoMG\nFowRqtg7cCC0Q4jpxB5QXhNbz9y5UlfPCS66SJI8nn1WmVARbtxQUr++JElYEVqdOnnUOVSTtzIy\n5LK2FAGhvpikp5tLJLJLbKyIvaKisnPlS+z9/LPE9jrJhReKpfB5v2MiVA6WBbqLB0S0n4jyiegU\nEeUq/1sbB8/FC1fs6cc9VWjc2FPspacHWReYSB6kGleZU3jFnai1A6tVK7N0BRJ7770n1UKCHrIN\nEoTdsaMU1/Wo6G8TU3E1obTsJSTIkzc31/DcnTkjZfE6dxZ9PXmyCJjcXHjGA2zahGN1OnvpRb/9\na9FChF5aWmgLUxuIPXX0Mj1Ll0ruiVkCnb8XXxQBuWMHyoe9O0fEnlff4uMlONbKcG8dO0pZJmb5\nXzGB+Yn48E39+vLmkZZmeZxYI3yeO3XIuerVy24azZoZi71ffvEcbdApJkyQRB+1fKkdy14oYvYO\nHHDFXpAwgGHMXJOZ45T/TdaScPGFK/Z81CNp0kRutionTzpQ+qt2bbHsxQeosRYssbFyw9f4Y2vX\nFveiUVHS/HzHvFoARNdOnizZvHuLgzGHWkBVqU6oVT1xcSLS1cwdHf/5j5zS11+XGPEbbpDKGW+8\ngfKSOyUlwIEDSItsak2zqQ/vY8cceXj7JD5elJ3Gv2wk9k6fFj3Ss6dzu65VSzK5J05E+TUbivNY\nEcTGimgOIPYKCzXu/sREsQKfPCkuBEUp2NL39eqVJ9uE8nqJiZFrWpPRbGTZKy6WxC0ziclWqVtX\nrpsy654NsRcKXLHnCF6+DyIaQURbiCiTiJYSUQdleisiOklE3ZTvjYjoOBENVL7XJKKPiegoER0i\noklE4lshotZElExE2co6X1VkJyuSc/SO6iAnThhO1lv2MjIcEnt79zou9rziTlSxp4kZIio3EulZ\nskTcaU6OUNW4sSScPF0wMehtmYqrCWWQdlycWGsM3GK5ucArr4i41eqTxx+XJIaSxoq5Iy0NSExE\n2slIr2ew3/7Vq1duqQm1ZQ8od4fDWOytXi1Fx60Y3sycv4ceApKTgZRTLcxvOAzw6ltcnF+xd+YM\n8OijIlQSEpQXAqC8bMvhw2XxIrZGGVTduDbGiTXC57lTLemaWFwjsbd1q0x32JlRxkMPiZt4B+wl\nozgds1dQIEOfh3p0yPMNImoH4EsADwOoC2AxgO+JqCoz7wXwFIAZRBQNYDqA6cysFin9DMAZAK0A\ndAdwJYAxyrxJAJYwcwKAJgD+U0FdqnBcsbdsmYxVqyMklr3ExJCIPS9iYyUFTldHrFEjeYDoWbBA\niiQ7zSOPAL+W9MVmmIzkD4ZQi72DBw0r9H/+uVjx9KUWunaV5+6y9AvlCahk+Fh+gKtiT5NsExIM\napU1auT5wgOIlaZfP+d3Hxsr46C+vDLJ+Y1XJKplz+DNiVnKzezaJXFdW7fK0Liff47y0kyHDpX5\nbm0Z52rVEvP96dOhz4AHPKxpRmJvyxbD+vGOERcn1r1J+EdYWPbU2O5z1TAdRsxXLHiZRDQXwC0A\nFjDzUmYuAfAGgGgA/QCAmacB2A1gNYD6AP4OAERUD8BQAH9l5kJmzgAwGcBtyn6KATQnosbMfIaZ\nV1ZgHyuUc/6SJKJriehDIvqKiK60vIGuXcWspSMxUVwteXny3RGxV726vNo7PFi3V9yJjxEC1HHm\n9fz6a2hG4YqJAR6vMlluxEGg79/Zs/L27HFvd0DslbnV9MTFia/bILty6lSJdTTi6quBpTubeBQs\nNnqA+40bUt24ubmhrdKq9k2T4GJk2du61XwWrorZuKgxY4Afd7XAYTS2toNKxDBeNiPDcDSHzz4T\nF/g338i9pHlzKRL81FNAQf0Woqw1bwO2xF6NGlIZndmRZKWA507zI9R7QwApH2j1erHKgw8CSzAE\newutJ745HbOnMcye0xCBnfgE0YRrmTlR+dwAoBGAMr8UMzOAQ4DHzeJjAB0B/IeZi5VpzQFEAjim\nCMcsAB9ArIMA8CREB60hos1EdHcQbQ5rznmxx8zfMvNYAPdB1L8jEHnevBwRe+rNN9SWPVXs6Xxt\navk9LWlp4skO1Q35fn4X/8PlTtSvxdatwI03iuZp2lQehM88I9UfghF7paXiDqpeXUTv6dO6BVSR\npRN7O3fKc91X8PnAgcDydTXE0pKeDtSpg4wMi+7yWrXEJXf6tK3hoEyjWvQ0lr3Gjb3FXigrwMTH\nA3f034/3cV9odlARxMaKANL99nJzJeP4o488L6Nu3aSY+qeHr5Af4unTZfcHW27cGjVkO6G8VrRo\nRv5QjdBatmwJvdiLiwPuwTS8fSKI4TkcItTRFhUFM8iJTxBN0K97FCLctDQFcAQAiCgGYrGbBmAi\nEakWlUMACgHUVoRjLWZOYOYu0k8+zsxjmbkxgPEA3iOiVkG0O2wJG7FHRNOIKJ2IUnTTryKiHUS0\nk4ie9rOJvwN418k2qeXqAI8qJvZRxZ7DFhqvuBMfNe2MLDUrVkhN11C5HWL4NEbhv/jwQ/vbSE5O\nxuzZIsQGDpSHYG6utD0tTcbt3RvbxXbWwMSJMlBFRoZ40J58UreAj3Igc+cC11/v+9j16QNs2EAo\nqFm/bKD27Gxvw67fuKHoaAkEys0N7QPcIJtZbwkuKZHMR6ujA1iJi3rwzVb4KOFJKdtzDmAYswd4\nXSuffCK/M6NLdOxYYNbO7uLbrVmz7IKybdkD7BfL1BHw3GnEnho9onpDABF7nTs70hS/PIh38HnW\nNcjJsbae0zF7oc6LOY/5GsAwIhpERFWJ6AmIiFPdrm8DWKMYfhYBmAoAShbvjwDeIqI4Elppkjdu\nIiLVOpgNoFT5/OkIG7EHCar0KOhARFUAvKNM7wjgdk0GzigielPJvHkVwCJm3uhkg2rXFqPK2bPy\nrA3a++qjgHPIKPW8Zo0sexs3GnqxHWU8PsC0afZL7q1ZI5a3//1P4gBVw2ibNsCnnwIPPwxccVsd\nnFi4xvK2d+2SSvwzZ8r5ffddYM4cTTkHwGeh3x9+AIYP973t2FgZxGBTjb5lZU2MxJ5fqleXWmYO\nueV8YiD26tYVAax66g4ckBeeUIaCtesUhR69ozB3buj2EVJUQa4Re6WlwJQpwBNPGK9y2WXA+qP1\nkZV63CMu1JZwUPfr9Li/RkRHSzyFApGnda+oSPpQEQWGm+IwhsSuxLRpod+XP1yx5whe7l9m3gng\nDogeOAFgGIBrmPksEY0AMBiAOqbPYwC6E5Fq6r0TQBSAbQAyAcwGoJ6lngBWE9EpAPMBPMzM+0PR\nqcombMQeM/8GQF8YpBeAXcx8QPHBzwRwrbL8f5n5MQA3ArgcwE1ENNbJNiUmitjLypIHdNDWL/VB\n6vBD22fciW7sNSPL3rZt1oZ7tUOHiN1o106yfq2Sng689VYSvv7ad6D3gw9KXbu777Yeo/3GGxJz\np9a5jo8XYfmvf2kWMrDWFBZKXk///v6336kTsK1ql7L6ijk53mLPb9yQetGFepB3A7FXrZp8cnPl\nu90xP63GRd15JzBjhvX9VAaGMXuAx7WyfLkY7HyNfR0dDSR1PoklqS08Lg5b1XbUcIYgRqzR4vfc\nTZwopnYNauUXQEJgGjasuGSFh2p/iQ8+sHYPcDpmzxV7wcPMrZh5qcH0b5m5o+KKHcTMO5Tp3zFz\nU2bOVr7nMXM7Zv5K+Z7LzPcry9Ri5ouY+Wtl3tPM3ESp5ddWSfT4UxI2Ys8HjSE+d5XD8AzIBDP/\nh5l7KiczCGehN6rYcyReDyh/oGrKW4QUXWqckWWvIsQeIiJw663A119bX/Wf/5QizbpnihcvvSRe\nsHnzzG87K0vaNH685/Rx48S6V+aOMoiB/P13EXKBrFwdOwLbuIN9y56KQw9vnxjE7AFy3atDph0+\nHOSQgSa57jo5vj5KYIY3BmJvxozANSwHXlyAlVkdyix7RUXysR3xURHjxT71lFRM1lCnTvkQZraK\nQgdB3xqbEBkpCWeVhSv2XMKVqpXdgIqiW7du6NatG1q0aIGEhAR069at7K1OjdvQf09MTEJmJvDT\nT8moWhUA/C8f8Lsi9pLXrAFiYqyv7+P75MmTvftTrRqSlBqC6vJ9+yYhLQ1YtiwZREC/fknYvx84\ndiwZJ0/a37/f7ytWIHnTJjSsn4wFC5JQWAj8/ru59evWTcK8ecCjj05GcnLg8zVlShLuuw+Ij09G\nRETg7e/bl4RBg4AdO5KxY0f5/G3bktGuHfDdd0m4/XYgeflyIDoaSYobNzk5GZ9/DgwYELj/rVsD\nC/IykJyXh4Fx8cjJATZs8Gyf4fnTbg8AmJWrz+Hzo37fu1e2HxnpMb9OHeDHH5PRoQNw7FgSGjZ0\n6Pr0s/yaNcno3RuYOTMJjz4aov469F0b85WUlATExcn52roVSZdcgpISYPbsZEydCvi7f0TFHcEa\n9ALik5GcnKx4E5JAZKN9AFBQ4Mj14tW/AMvXqgWsXJmMmBjg6NEkNGlSgecDjDFjgBdfTMazz4am\nf4G+p6UBhw4lIzm58q7HTz/9FGlpaSgsLISLSxnMHDYfSLZNiuZ7HwA/aL4/A+BpG9tlO7z/PvPY\nscwLFjAPHWprE55MmMAMMBcWOrCxcpYtW+Y9cccO5nXrvCbHxTFnZ8vfW7Ywt2vnaFP8cumlzN9+\na375O+9kfvVVH/0zoLSUuW9f5lmzzG1/6FDmL780njdtGvMtt2gmNGrE/OKLZV+vv5555szA+1i7\nlrlb4gFmgHN+WMmxsd7LBOwfwFyrVuCdBcOMGbKfQ4c8Jg8ezLxokfw9bhzzu+9a37TZ86fl++/l\negl3vPr2ww9yHDdvZmbmVauYO3YMvJ2sVds5Fqe45LaRzMycmsrcpo3NRgHMPXrYXNkTq+fuwQeZ\np0yRv197jfnxxx1pRmAA5o4d+cQJ5vh45qwsc6vZuTb9UacOc3q6o5sMCuXZV+nPdvdT+Z9wc+MS\nPO5jqiwAACAASURBVFOu1wJoQ0TNiSgKUgjxu4pqTHy8lKzKy3MoEbKqYkiNqoCYvfbtgR49vCbX\nrl3uZtm/H2jd2tGm+OXaa4FFi8wte/Ik8N13UnvNsH8GEMmoHe+/H3jZvDxx91xzjfH8K66QMWDL\nclzi4jwSNDZulLIZgWjZEth3WtK4swuqGbpwTfUv1K5/9ZrUXZtqKANgsxQI7MVFXX45sH59+bVq\nh127xCXfqZPEez7yiBS9dRKvvuncuIsXS73FQCTUIsQjBwcLpXB2dnaQFZocKvZm9dypNZ2Binfj\nAuJGvvJK8yEjdq5NXxQXy3lzJOTHxcVhwkbsEdGXkDTqdkR0kIjuZqmU/RAkdXorgJnMvL2i2hQb\nK2Wv8vIcq2QgVEQ8jQ+0D++jR8sTEyqCwYMlSYNNBFBPny7i0OqNc/hwKfewd6//5X77TYb98hVz\n16yZPLg2b1YmxMWVPcCzsyXjsE2bwO1JTASKSiKRhxrIKTIWe6YI9WgIqsjTxezFxyt1DGFf7Nkh\nOlqyVBcvtrf+7Nky0kfjxhIzN326JKhedBEwf76zbfVAJ/aWLZMXh4BERKADdiD1tIQkGyXyWMLM\nxRkCEhMrV+wBEuM7a1bF7/fkyfJhjl1cwo2wEXvMPJKZGzFzNWZuxszTlemLmbk9S6bMqxXZpthY\nEXqnTzsk9kpDU75HG3cSCK1l7+jRii0AeuGFUn5l9+7Ay37+uVj1AGv9q1YNuOWWwDf7ZcuAQYP8\nLzNokCb+XCP2UlLEUmTmpk4E1I/JRTrqIzu/mqG1xlT/Qjl6BuAzQaNmzeDFnpXzp2XECLHuWuXH\nH8vHTP3nP8UCe9FFMobx4sWSkGPWwhwIr75pMrfPnBHrZJ8+JjYUEYGW2If9+eWWPdtib/lyyZR1\nAKvnTq0BDojYa1yRg6Eob5FDh8pxV7OC/WH32jQiK8twREUXl7AgbMReOBIT47Blz4xJK8ToxV5F\nWvaIREAFypbbtUsGAbA7Buu118p4v/5ITg4s9i66SNy1AET1KG7c1FRro0g0iD2tiL1I+w/wUIs9\nH5a9mjXFylRaKg/Pisw0HDxYRLmVn01Ghow/O3OmjISo5+KLpRj26NHe47g6gsayt2mThEmYOnWK\n2NuXJ2IvJycIN+6AARU3goaOhASUFTbOyAjtcM4efPSRFDOE/EyHDZNh6SqSoAS6i0uIccWeH0Lm\nxnUYK3EnlenGBUTArVjhf5l586T8RhXl6rQaV3PppeLKVZKRvSguFvfsxRf73063bsCGDcqXSZPE\nZAApmWcl1rF+XD7S0ADZeVH2Y/ZC7Q/zYdlT3biZmfJ7sBM6aDcuqkkTEUrbtplf54UXgBtu8D/W\nc79+Uoj7/vt9L2MWfzF7K1cCffua3FDVqmiB/difp8R3holwsHru1HsmUMGWrjFjPPzlt95qzpXr\nZMyea9lzCWdcsecHrdhz5EU5DCx7NWuWF8k9dqxyxN7Klf6X+emnMl1li2rVpC6fLw/Ntm0yCH2g\nc9qpk1jxzpyBjPmkPH337AFatTLfnvpx+WLZy7Np2UtNlaE9Qonqk67ieUtQ3bjHjwP164e2CUZc\neqlXKTefHD4MfPGFuG4D8fTT8kKwfLm19pSWiu4fMUJGdvEiOhp4/HGgalVro9NERKAhjiEtX8x5\nQcfsVRLqPbOkRO4zoR4G3BeDB8sLXUXWagwXge7iHyKaTkQv+JmfS0QtKq5FFYMr9vyg3rgci9kL\nkdizEneijcGqDMtep05SWV+1LuopKpKCutoiynbiavr3921BXL/eMFHZixo1JJtWb1nau9eaZa9W\nzBlkIwE5+ZGGLr2A/WvXLvQJGj5Q3bjBuBWDiYuyIvY+/FCC8824DqOigAkTxBJohYkTJd7v6qtF\n8H37bbLnAkQyLAtEbHTqZHLDERGoj3SkF8gFEnQ2rkNYPXexsSLycnLkkq2sZIVq1cTQFyjBx43Z\nCz+IaD8RFRJRom76BiIqJaKQlnZn5jj+Ew6Z5oo9Pzjuxg1RgoYVVLF39qzE1FS0taZqVTGSpaQY\nz1+9WuLhgn1D7t/ftwXRrNgDpIKNNqGE2bplL77GWeQgHvlFEWEdDmCEer0EFUMWBAMHitgL9J50\n5oyEbd13n/ltjxwJbN1q3k28Zw/w3nvAt99Kksfw4fK3ESUlwPbt1sReA6QhLV9E/blqJYqLk3tm\nVpaEjFQm11wDLFxYcfs7V89ZGMIA9gFQx7YFEXUCEA2DcXNdzOGKPT9ERcmLelaWQ+OKh8iyZyXu\nJC6uPAYrPr689F9F0rWrb7G3ciVwySWe0+zE1Vx8sTzI8/O9523bJsOYmaFFC2DfvvLvqkXSyoMs\nIaYY2UhAwZkq2lJ9ZTgZN2QbH+WAYmLkGAYj9oLpX4sW0rRA9fG+/14MoGbPKyC/73vuAT7+2Nzy\nr7wiWb6q5fDOO4ENG5IMl927V5YzbZCNiEAtZCH/bBQKC8PHjWs3Zi8zs/KtXEOHSkb2mTO+l3Fj\n9sKW/wIYrfk+GsBn2gWI6GoiWk9EOUR0gIgm6OZfQkQriChLmX+nZnYiES0golNEtIqIWmrWKyWi\nVsrf04noHT/LdiCiH4noJBFtJ6KbfXWIiGoS0cdEdJSIDhHRJCK58RLRaCL6jYj+Q0TZRLSNiC7T\nrHsXEe1R2rCHiG73tR9fuGIvANHR8sbmSE3bMInZO3Wqct9Cu3TxLfbWrbMQ5+SH6GhxtW43qMq4\naxfQtq257bRs6Sn2Dh2SGnxWSiXGx5YgB/EoKIrQDpkaXvjoUHQ0UFAg10yoE4KNIJLrYf16/8vN\nnh14/FkjRo6UAryBjO75+TJe8rhx5dP69hUReviw9/Jbt1oTnqhaFQSgdnQ+Tp4MHzeuVVQ3bm5u\n5VwvWurVE8u802Plzp0r5Z1Wr/ac7lr2HOV3AHFE1J6IqgC4FcAMeA66cBrAKGaOBzAMwHgiGgEA\nRNQcwCIAUwDUAdANwEbNurcCmAAgAcAeAC9p5ukf1IbLElENSA3gGco+bgPwLhF18NGnzwCcAdAK\nQHcAVwIYo5nfG8AuALUBTAQwl4gSlP1MATCEmWsC6KfriylcsReAyEi50Tsy6MXYscC//+3Ahjyx\nE7N3Lok9u3E1HTvKQ1dLQYEkGzQzGfXRooWMNKJiJ1FBFXuFPix7TsYN2aZtW0PftCr2KitmDxCX\nuz+xV1gI/PCDZHBb5cILxUobKGnou++AXr08S89UrQp065aMJUu8l9+zx2JdYyW4LaF6YdAxkk5i\n9dyp3pDMTIe8IUESyJVrtX/LlkkWd8+ecr3l5ZXPcy17jqNa964EsB3AUe1MZl7OzFuVv7cAmAng\nUmX27QB+YuavmbmEmbOYWfvUmcfM65i5FMAXEDGoon/z9bXsNQD2MfPnLGwCMBeAl3WPiOoBGArg\nr8xcyMwZACZD46oGkM7Mbyvt/RpAKkTEAkAJgM5EVJ2Z0+0MLuGKvQBERckPWleRwh7Nm8t4XpWI\nmo1bmQ8TVYTpDZ2ZmVIupV07Z/ejZc8eEXBm3dd6y97x49ZrhyXElfh144YFdevKwdGhFXuVZanp\n0UNeAnzxyy8SB2q3ptvw4SIW/bFwoZR00dOxI7B2rff0/fvl2jGNIvbiqxchO1teMM+1+E6VuDip\nyRgO7b/qKimy7QQlJRIT+vHHwJNPAr17Sz1HlT+TZY+IJhIRG3wmWljecFkLzAAwEsBdAD432Gdv\nIlpKRMeJKBvAOIiFDQCaQqxwvtDmaecD8FebwdeyzQH0IaJM5ZOltNeoGmlzAJEAjmmW/UDTXgA4\nolvnAIBGzJwPsS7ep6z/PRG199NeQ1yxF4DISAfFXoiwEneiulkq88YUHy9v/foK95s3y0NbV/3D\ndlyNkdiz4sIFyi17qjBNT7cuKuJrsrhxC8M4Zs8HTrhxg+1f167Apk2+5y9danJIMh9ccYWU+/EF\ns8R+XXml97zbb0/CH394T9+3z57YS6hehJwcOebh8GJg59xVry4vbuEg9rp3Fzf78ePG86307+uv\nZezdYYqt5eabJVZU5c9k2WPmicxMBp+JFpY3XNZCGw5CEjWGQixmer4AMB9AY2ZOADAV5Va5QwBC\nPWbgIQDJzJyofGoxc01mfsDHsoUAamuWTWDmLppl9OPNNINizWTmn5h5MERIpgL4yGpjXbEXgKgo\necsOZ7FnherVURYAXpluotatvcev3blTYmycwkjs7d5tTezFxspDS31Y2LHsRVdnFCAaBYXh8QC3\ngir2Cgoqzy3XvLk8SNX6kHqWLpVxdO3Sr5/EdqpjuurZtk2Og1EGdteuMr+oyHP6vn3yomAaJWYy\nPlose4WFCN/4zgBERTmY1BYkVavKgCJOREpMnQr89a/l4a0DBwKrVpW/CP6ZLHthxF8AXMbMBQbz\nYgFkMXMxEfWCWNVUvgBwORHdREQRRJRIRAZj6gTFAgDtiOgOIqpKRJFEdLFRzB4zp0Hi+94iojgS\nWhGRpsgY6hHRQ8q2bgbQAcAiIqpHRCOU2L1iSKxiidXGumIvAKplz5GYvRBhJe4kOloeJJUdAN6q\nlbfY82V1sxvz1aKF1PQr0fwsjhwBmja1tp369YMTe9UjS1CI6igsJMMHeFjE7PlAvV6CER/B9q9K\nFXHtp6Z6z8vNFaHWq5f97VerJnGihkWSIfUatXUftaxZk4w2baRAswqzDTeuQrhZ9uycu6io8LHs\nATIs4rJlxvPM9m/PHhH1w4eXT2vSRISfmqBTWUlMf0LKAnyYeR8zrzeaB+B+AJOIKAfA3wHM0qx3\nCMDVAJ4AkAlgAwCtFc3U/v0uxHwawGBIYsZR5fMqAF9q4U5l3jalTbPh6fJdDaAtgAwAkwDcyMxZ\nEJ32GMTNmwFgIMSla4lKKLxxbhEVJTXp/kyWvYICeUhWUp1eACL29CFiu3ZJdqRTREVJ8H1aWvmA\n7MeOSayNFYIWe1GlKET1sHmAW6FKFbn2c3Iq19LUoQOwY4f3EHcbNojrP9hs+Z49JfZuyBDveevX\n+88Qb99erl11mRMn5Dzb+X0lVC9AVpb8Rs9Vy161avIyaaUWZSgZNEiscsEwZw5w002eL/1EUhM0\nNVVeIMN9WM1zBWY2vHKYuQRAhOb7XBi7d9X5KwD0MZh+t+77LxCXqfo9wsKyuyCJGgFh5lyIQPU1\nUCMz88MAHtZNTAOQZGYf/nAtewHwMT58WGEl7kR14xZWskvRyI3ry7IXTMxX06aeA94fOwY0bGht\nG/XqeYo9q9m40VElfsVeOMfsAdLmrCz74sOJ/nXoYGzZs1Ig2x+q2DPC3z6SkpLQurXni8vhw9at\nxyqxUcXIzhb3Y2WNPqHFzrkLJzcuIK729HTjsbLN9m/BAk+rnkqbNhIaUloqrvxz7WXO5fzBFXsB\n8DE+/DmLaqnMy6vcG1PLlp5ir7RUvlsqV2ECvdhLS7Mu9urXL08msWPZqxZ57lr2gHKx50itSZu0\nby+WPT1O1WW8+GJjsVdcLC7arn6iffQhCSdOSHKzHapHng1KWIcDqtgLFytXlSri5v/9d3vrZ2YC\nGzeKhVCPKvTz8+V3YqX+potLReKKvQCcC5Y9K3E1RPIgycqqXOHRpImMzaty4oQ8HGINEuCDifky\nsuw1MEqM90OdOtI+ZhF7Vh/kVSMYVVCK3Fzjh3g4x+wB5YXFKytmD5D4ywMHvKdv2CAZl05sXx35\nQcvOnXKtGl2XgPRNb6W280KgUr1qCTIzw+elwG7MXnZ2+Fj2ACmAvWqV93Qz/fvhBxF6Rtd/48Zy\nHzuXS+W4VD7M/Bkz+4gMdgZX7AVAFXnhnKBhFVXsVab1oGFDuUmqmWx2LG5m0Iq906clWcNqEHVC\ngsSsFRXJ+pZv6kSojkLk5ob3S4MvwuF60Yt2QM7F7t3i4g0WIkkC2bXLc/ru3YHrPurjT4Ox7EVX\nFTduuIg9O0RFSUxwZVqC9fTpY9+y9+OPUq/PCNXqn58fXuLWxUWPK/YCcC5Y9qzG1ahuucp8oMTE\nyLHNyZHvaWm+LW5Oxeyp+7DqaklIEEtFMENAVUchioqM47DCPWavalVx+1dmzF7DhsDJk57jnB46\nJKLKqeu4fXux5GnZs0dcdb5ISkpC06bywFfLrwTlxq0aXm5cuzF74VauqndvcdOfPes53Uz/fvtN\nyrcYoYo9NznDJdxxxV4A/mwxe0B4WGqAcuse4F/sBUPjxuK6Vfdhx3qoWvaCKa1QHYUA/r+9ew+X\no6zyPf5dJOQGhA1BLgmQHUBAEGgQY5xBny3gIeAoKgNyiwIq4wUQvIDjDcQ5DnhBODDiQZAIIyKo\njDCSIwpuGGBGUAz3hCCQcEuQQIgEkkCyzh9VlXR29qWrq2pX1du/z/P0k13VvbvXSvfuXv2+q96q\nRtN9WknMZb5eRoyIXh9PN60x/+ij+fZ49re8SyuPMXJk9KG/MF5nP2vPXpWmcdsxalRUlLd6lprh\nsPnm0XtB33U3h7JwYTS1v9tu/V+vkT2pCxV7Q6jDyF7avpoqjOxB1NeUHCE3WLGXpedrwoRoRCh5\njLRH0sK6I3ttLVczfvygxV7Ve/aSmNudlssrv75TuXkXe+2M7CW55VbsjVxViS9iiXZ79qBaxR5E\nB/L0PcfyUPndcUe06Hbfs/ok3vCGqBh8+WUVe1JtKvaGEPLIXtnF3hZbwPPPRz8XNbLX/Bgvvhh9\nw09r002jYq/tkb2DDmLMzpOBgT80qqwKI3uwfrE3b16+xd4b39h/sdfKY2y99dojtrP27L30UrX6\n3dJKYq9asbf33tFRtWncfjvst9/A148YEf1dJAeYiVRVDT96hlfS31XlD+m0fTVjxkRLSpT94d1q\nsZel52uzzaJCbdWq9k9n1NUVFYptF3tmjBkfDXfUsWcva7GXV359i71WC7FWTZ687v2vXg0LFgx+\n2rMkt+aRvXaO2E6M2TBqKqvKdH+7PXtQnRwSjUZ09HazofJLRvYGM3589NyX/eVZZDAVLmGqIcR1\nk5JRyrLfnIZjZG/kyGjqdcmS9ou9TTaJpmmynHUkKZSq9gHYiqqM7E2cuLb/EqKfJ07M7/4nTIh6\nr155JdpevDj6IG/lSPzmtRizTuNCtb9cDqWq07h77w333hsV8a14/fVojcWhlvbZZJPotVLn0VgJ\nX43fUiSRtq8m+SAp+8O71WIva8/XhAnR47Rb7I0dm/0Uc0mBXeeevXaXH8orvze8Yd2zICxa1F4P\n5kDMoib+5FynrayXl+S22WbR6G+yYHk7rzOIpnGhOl8KQurZmzAhasl4/PG1+wbLb86caI3Fof7m\nN9kk6tsLqdVHwqNibwghjuxVpdjbfPO1B08sXhy9GRdh002jKdh2i73Ro6Np7yxN2Mn/eZ1HbMou\nQJqLvWSB63YXLx5I2mIv0XwQz8Ybt/++MWZkNI1b59dJVYs96H8qdyCzZ7e2YHcyshfSWqwSnhq/\npQyPOhxhlbavJvkgKfvNePz46MMRoqVNNt20/9tl7fnaZJPocdot9syynzJssA//qvfsZZVXfs3F\n3ssvR/+nA53Zol1bbbX2MVo5D3KSWzKyl2X0F2DMhtE0btmFdSJLz17Z7y/92WuvaCo3MVh+f/5z\nVBwOZfz4qNjTyJ5UmYq9IZx9Nlx4YdlR5Ksqo0zjx0cjbsujVUkKG2lMir0s6+SNG5dtbcI6jxAn\nZzkpW/NSPYsW5T+qlzxG0nuX5jGSA4GyFnsbbqCevSLtths8/HBrt007sqdiT6qsxm8pw+MNb4CT\nTio7isG127NX9gdKUuy99NLgI25Ze76SYi/L+SuTkb0iir2q9+xllVd+zWsmtjLq1o4tt4zuO3mM\nVnv2kiO2sxZ7IzaIKuuqjOyF1LMH8KY3rVvsDZSfe+sje0nPnqZxpcpU7HWgqiwnk/TSDTaFm4fm\nYq/dafmsxV6dVWVkb8yY6EjK5cvzPzgjkbbYS+Q1jTtii82A8v82s0haHapSsDbbZZdoyZ6+p03r\n65lnomK1lRUCRo2K2go0sidVVuO3FEm027NX9gdK88jeYMVe1p6vpDcwS7E3blz07V09e+nllZ/Z\n2lPXFTWN29wX2EpBmeSWx/I8PP00Iz56HFCdQim0nr2xY6Pleh57LNoeKL+5c2HXXVu7zw03jN5b\nNLInVaZirwPVrdjLKhnZW7ZMI3vtqMrIHkSvk5deKm4aNykmId3I3rhx0Qd+pmJv4kQ2GBn9UZb9\nt5lFlYs9WH8qtz9z5qQr9pYt08ieVFuN31LWMrNxZna3mR1SdixlqGvP3rhxsGJF1Ng+2FGVefbs\nZRnZU89ee/LML1nipKilepL7h2gkd6jT6yW5jR0bvZaXLs12hHAyoleVkb3QevZg3WJvoPzmzo2m\nfFtRh/OniwRR7AFnAD8rO4i6qEqxlyxp8sILxZ7NY+zYqNBbvrz9x9HIXjVkPk9xC/efjOwtXdr6\niHNer+WkyCv7bzOLOhV7A0k7sgeaxpVqq8xbipldZmaLzOy+Pvunm9kcM3vEzM7o5/cOBB4C/grU\neIGL9tW1Zw+i4unFFwf/gMza8zVqFGtOLt9uzmPGRE3dndizl7XYyzO/5sWLiyj2mkf2li4dekq2\nObdk9DfLabOq9LcJ4fXsQTRiN3du9PNgPXutjuwlxZ5G9qTKqvTneDlwIXBFssPMNgAuAg4AngHu\nNrNfufscM5sB7AOMB14CdgdeAX493IHXTVWOxoWoiCp6ZG/06OhDuN1lVyD7+WHrvM5elSQHQrRS\niLUjGdl7/fVoJDjNayYp9jbbrP3HD+F1UvVib8cd1x6g0Z9XXolO39jd3dr9aWRP6qACH/cRd78d\neLHP7qnAPHef7+6vAVcDh8a3v9LdT3P3j7r7Z4GfAD8c1qAroq49e9DayF7Wnq9Ro6LRmixnQ8la\n7A2m6j17WUf28sxv3Li15ykuYmRvww2j5/jZZ1s77VlzbnmM7CWqMnXeznNX5aVXIFpOZdmy6DXU\nX37z5kUFYavFqnr2pA5Sffcysz2ICrCtgTHAC8AjwJ3u3rdQy8Mk4Mmm7afix1+Pu1/R335ZX/IB\nVoVRhKTYK+LIykQyspdHL1UR07jSulyOeh3CxhtHxV7aYjLPYq/Oqj6yZwZTpgw8uvfII7Dzzq3f\nn6ZxpQ6G/HM0sx2ATwLHAFsBq4ElwAqgCxgHrDazW4FLgZ+5++rCIm5To9Gg0WjQ3d1NV1cXjUZj\nTb9G8u2urtvJvlZv/9xz0bZZ+fGPHQuPPdYbN8Lnk1/f7Tlzelm8GCZNaj/eaKHdHkaPbu/3ozM/\nFJNf0dtLlvTGUbb3+3nmN3YsPPhg9HyMH19Mvma9/Pa3sMkmQ9++p6dnzfa4cT28+CLMn99Lb2+W\nv+denn0W2v3/znO7Ob9Wf/+BB6LtkSPLj3+g7fHj4bHHevjAB9bP7+abe+NCtbX7+8tfou1Ro8rP\nr7e3l5kzZ7Jw4UKWJ+ehFAFw9wEvRMXbq8BvgU8AewIj+txmC+Bg4HyiUbi5wH6D3e8gjzcZuK9p\nexrw/5q2vwic0cb9uqx1zDHuVfkvecc73PfZx/2884p7jFtucR8/3r3RaP8+Tjgh+j976KH2fv8f\n/qE6/+dpve1t1Yn9X//V/fTT3bu63BcvLuYxdt/d/ZJLorzTOOgg94kT3S+9NNvjg/uMGdnuo0x/\n/GOUw6pVZUcysFNPdf/Od/q/7lOfcr/ggtbv64oronyvuy6f2PIUf/al/izWJbzLUF1brwK7uvu7\n3f0H7n6fu6/qUyw+7+6z3P3UuFj7GtH0azuMdY+ovRvYycwmm9ko4Ejg+jbvO1jJN7s6Go6evdGj\nox6dLNNKWdc/q/M6e17Bnr1ly7IdcDPUYzz/fGs9ns25JcvzhDSN285zN2pU9HrfoAI9wQPZYYfo\ntGn95ffEE60fnAFrp62Tf0WqaNA/R3c/2d3nt3pn7r7a3X/m7qnXvDOzq4A7gZ3NbIGZHR8XlicD\nNwEPAle7+xArJMlQsn545ykp9opcv27UKFi1Kluxl3xwFVHsVV2VXi/jxkVH4772WnEfru0uoD1y\nZFSIhlTstWPUqOr26yUGOyJ3/vx0xZ569qQOKvMn6e5HD7B/FjBrmMOplebeqLoZMyY6UrbIdfaS\nD98yR/YGU+fnrxV55jd2bPR6SUaPipBmhK45t+T1lccXl6oU2O08d3Uo9pKRvb75uUcje5Mnt35f\nSZHXiQuuS30M+idpZj9Kc2fufkK2cKTTJG+QRa+zB9Wdxq26qhQeMDxHvLY7spf1iO1QjBpV3WVX\nEt3dsGBBNOLfHOvixVH8ac7VnRR7XV25hiiSq6G6Kvboc3kPcBxwCLBv/O9x8f43FxWkDK7qPV+D\nST5QB5uSy5pfct9ZPoCKHNmr8/PXirx79oar2GvlMZpzy7PYq0qB3c5zN3Zs9QveMWNgiy3gF7/o\nXWd/2n49WPv+omJPqmyonr23JhfgbOBloiNtt3b3Pd19a+AdwN+Afyk+XAlNMqJX5EhAHiN76tmr\nhnZH3dp5jLQFS/L6qnqhU7TNN4c77yw7iqF1dxMvcbNWO8WeRvakDtIcL3UO8BV3X+fP2N3vIDoC\n99w8A5PW1bnnK/mAHOzIvaz5Jd+8qzqNW+fnrxV55jdqVLSgcpEF1dix0Sn8Wikom3MLcWSv3ecu\nzaLEZenuhs0261lnXzvFXvK3vfHGOQQlUpA0xd4OROee7c8rQHfmaGRYVOWDBIbn1G3q2cumSq+X\nkSOjZVeKnsZdskQje6GbMiUq7pq1U+wtWxb9W+e/cQlfmo/Ye4CzzGyb5p1mNhE4C/hTjnFJCnXu\n+Wql2MtjnT0odxp3MFV//qq0zt6IEbByZbEF1ejR8NJL7ffshbQER9Vfm1l0d8Odd/aus6+dYm/l\nylzCESlUmo+/E4nWu3vCzP4EPAdsCbwFWAwcm394ErrhGNlLiryqLr0irRuO0bPkOW73aNyqlESE\nvQAAIABJREFULzsike5uWLhw3X1pl10BmD4dbr45r6hEitHyR6y7PwjsCJxGdEq00fG/pwE7uvsD\nhUQoQ6pzz1crxV7W/Myi4qCq07hVf/6yjuzlmd9wLG+S5jH6W2cvj5G9qkydV/21mcWUKfDSSz1r\ntttZYw+i53v//XMNTSR3qT7+3H058P2CYpEONBwje5B9odcip3GldRrZk7xstx08/TS8/nr0nC1e\nHBVuOqpWQpT6I9bMDjazr5rZJWa2fbzvnXHvnpSgzn01w9GzB1FxUOY6ezo3bj6qNrLXX89eHsVe\nVUb2qv7azCJaPLmXp56Kttvp1xOpi5aLPTPbysz+ANwAfAT4KLBFfPXxwFfzD0+KUJUPEqjfyF67\ncdb5SL0qvV7yPCXZQNotKPOcxpXhsc02a4/ITXtOXJE6SfPRdSGwMbBrfGn++PodcECOcUkKde6r\nGY6ePcjes5e14Nlqq4Gvq/rzd9JJ8PGPt//7ndKzF+LIXtVfm1k1Gj08/nj082OPqdiTcKUp9qYT\nLar8KND3regpYFJuUUnHGK6RvazFXlbf/jZrpovq5uMfh0suKTuKSPIcDnZ6vazaXUIlj6O+ZXh1\nd68d2fvLX2CnncqMRqQ4aT9iXx9g/xbAqxljkTal7aup0pTicPXsZZ3GzWrMGJg0wNehkPuioJie\nvSKnStMUbUWts1eVkb3QX5srVvSuKfYefVTFnoQrTbH3X8ApZtbcop68JZ0A3JJbVNIx6jKyV5UP\n3043HH1x7U7HJl+iin4tS3623po107gq9iRkad6WzgDeCjwAfIOo0Pu4md0KvB34Sv7hSSvq3Fcz\nXD17ZY/sDabOz18riujZq0qx15xbiF8IQn9tvv/9PTzxBKxYAc8+C9tvX3ZEIsVIs6jyA8C+wB+B\n44BVwAeJ+vXe5u6PFBGg5K9KH0rDObKnNfLqr8oje1X6u5LWbLdddBaNefOin3UktYQq1Uesuz/q\n7jPcfaK7j3L3rd39GHefV1SAMrQ699UkRV7R69CVfYDGYOr8/LUiz/yG8wCNVr4cNOeWZ7FXlcIx\n9Nfm7bf3ssMO8POfw667lh2NSHHSrLP3NTP70ADXTTKzr+UXlnSKuqyzV5UP305XtWncZnqN1NPU\nqfC978G0aWVHIlKcNB+xZwFXmdmlZtb3e/W2wJm5RSWp1Lmvpi7r7BWpzs9fK/LMbzhOW1eFnr2q\nFI6d8No84ghYuhQOPbTsaESKk3Y85cvA+4D/MrNtC4hHOkxdRvakWop8vbS7Xl6eBVqR09Syrve8\nBxYsgD32KDsSkeKkfcu8heiI3A2BP5nZu/IPSdKqc1/NcJ4bt6rTuHV+/lpRRH5FrhWZZmSviJ69\ne+6BCy/M576y6oTXpll0cIZIyFJ/P3b3+cDfATcBvzGzz+UelXSM4RrZ23VXmDy52MeQ4VPk66Xs\nnr2994bNN8/nvkREANoa63D35cAMM/sT8C3g/lyjklTS9tVUpR8Ihq9n7/Ofz3wXhemEvqi8VWVk\nT+vs1Vvo+Ykk0nw/ng+saN7h7ucDBwFailLaMlwje1mF+EFeZyGP7ImI5C3NospT3P3efvb/HtgR\n2CHPwKR1de6rGa6evazUs9e+uvbslbnOXlXotSkShlyOT3T3pcDSPO5LOktdRvakWjSyJyLSukHf\nzszsLuA4d3/IzO4mOh/ugNx9ap7BSWvq3HcyXD17Vab80qvK0ivq2au30PMTSQz1dvYg8GrTzwG+\nnUmZ6jKyF+IHeZ1pZE9EpHWDvmW6+/Hu/nj883Hx9oCX4QlZ+qpz30ldevaKpPzSq8rRuM25vfe9\ncOCBxcRUFr02RcJQ8fEUCV1dRvZ09o1qqUqx12zaNPjtb/OPR0QkK/NB5h7M7Ftp7szdT88cUUpm\nZsA3gPHA3e5+ZT+38cHy7DRHHgk/+1k1pp2uvRaOOAL+9jfYeOOyoxnYsmXw5z/DfvuVHYmYwcUX\nwyc+Ucz933cf7LUXvPoqjBlTzGOIDAczw90L/GokdTHUd9fDU9yXA8Ne7AGHAtsCzwNPlfD4kkFd\nRvY22kiFXpVUcWRPRKSqhurZm5LikmmdPTO7zMwWmdl9ffZPN7M5ZvaImZ3Rz6/uAtzh7p8HPpUl\nhrqqc9+JevaUX1rTp8MBB+R6l+tod529ECk/kTBUaTzlcqKzcaxhZhsAF8X7dweOMrNd4+tmmNl5\nwDPAi/GvrBq+cCUPdRnZk+qYNQt22qn4xyly9FBEZDgN2rPX7y+Y7QfsDKzXzeLu388UjNlk4AZ3\n3zPengac6e4Hx9tfjB7Gz236nbHAhcAyYI67X9zP/apnr8mHPgTXXFONnr0bboD3vQ9ee03TZlIN\nc+bAm95Ujb8PkSzUsyeJlj9ezWwr4GZgN6L+vOQF1PyWmKnY68ck4Mmm7aeAdRZudvdXgY/l/Lgy\nTDSyJ1WjIk9EQpNmLOW7wEvAdkQF2NuARcCxwIeB9+QeXY4ajQaNRoPu7m66urpoNBprVk9P+jbq\nun3++eenyue553rj/5Xy44+mynq59VZ417vyya9u28qvWtt/+EO03crfR3PPV1Xiz3Nb+dVru7e3\nl5kzZ7Jw4UKWL1+OSKLlaVwzexL4DPAfwOvANHe/K77uK8A73P2gQe6ilcfobxr3LHefHm+vN43b\n4v0GPY3b29u75g+/tdvDddfBBRcUFlLLZs2CQw4ZfDQlbX51o/yq5cEH4c1vbm2Er265paX86k3T\nuJJIU+z9DXiPu99mZkuAY939P+Pr9gd+5e6bZArGrJuo2Nsj3h4BzAUOAJ4F7gKOcveHU95v0MVe\nnbVS7IkMp+XL4dRT4Qc/KDsSkWxU7EkiTafU40Q9dBCdJ/eYpuveC7yQJRAzuwq4E9jZzBaY2fHu\nvgo4Gbgpfsyr0xZ6Um064lGqZswYFXoiEpY0xd6vgXfHP/8LcJiZPWVmjwOnEB0R2zZ3P9rdJ7r7\naHff3t0vj/fPcvdd3P2N7n5OlscIVXPfSd20UuzVOb9WKL/6Cjk3UH4ioWj5AA13/+emn2eZ2d8D\n7wfGAr9191kFxCciIiIiGaReZ6+O1LNXXb/5TXRGBD09IiL5Us+eJFIvY2tmY4CJ9L+o8kN5BCUi\nIiIi+Wi5Z8/MtjWzG4nOVDEPuL/p8kD8r5Qg9L4T5VdvIecXcm6g/ERCkWZk70pgB+Ak4FFgZSER\niYiIiEhu0q6zd4y7X19sSPlTz151qWdPRKQY6tmTRJqlVx4CxhUViIiIiIjkL02xdzJwRrzkilRI\n6H0nyq/eQs4v5NxA+YmEIk3P3myi05XdZmYrgb/1vYG7b5lXYCIiIiKSXZqevSuAw4HrGeAADXf/\neq7R5UQ9e9Wlnj0RkWKoZ08SaUb2PgCc5u46a6SIiIhITaTp2fsrsKCoQKR9ofedKL96Czm/kHMD\n5ScSijTF3tnA581s46KCEREREZF8penZuxaYBmwE/BFY0ucm7u4fyje8fKhnr7puvRV6etSzJyKS\nN/XsSSJNz94biA7MANgw3hbJ5J3vhHvvLTsKERGRcLU8jevuPe7+rsEuRQYqA6tz34kZ7Lnn4Lep\nc36tUH71FXJuoPxEQtFSsWdmY8zsETObXnRAIiIiIpKfND17zwHHuvtNxYaUP/XsiYhIp1HPniTS\nHI37E+D4ogIRERERkfylKfYWAO80s7vN7Gwz+7SZfarp8smigpTBhd53ovzqLeT8Qs4NlJ9IKNIc\njfvd+N9tgLf0c70DF2eOSERERERy03LPXp2pZ09ERDqNevYkkWYaV0RERERqJlWxZ2ZdZnaGmd1g\nZnfE/55uZl1FBShDC73vRPnVW8j5hZwbKD+RULRc7JnZjsD9ROfI3YjogI2N4u374utFREREpELS\nrLN3PTAFmO7uTzftnwTcCDzh7ocWEmVG6tkTEZFOo549SaQp9pYCH3H36/q57jDgcncfn3N8uVCx\nJyIinUbFniTS9Ow5MGKQ+1E1VZLQ+06UX72FnF/IuYHyEwlFmmLv98A3zGxy8854+2zg5jwDExER\nEZHs0kzjdgO3ANsC9wCLgC2JFlh+EjjA3Z8oIsisNI0rIiKdRtO4kki1qLKZjQJOAN5KdCaNZ4E/\nADPdfWUhEeZAxZ6IiHQaFXuSSLXOnruvdPcfuPtH3f2Q+N9Lyiz0zGw7M7vOzC41szPKiqNMofed\nKL96Czm/kHMD5ScSijTnxl3DzEYAo/vud/dXMkeU3h7Ate5+lZn9tITHFxEREamsND1744FvAh8k\n6tVbb2jY3Qc6WreV+78M+Adgkbvv2bR/OnA+0SjkZe5+bp/f2xz4ObAauNLdf9zPfWsaV0REOoqm\ncSWRptj7KVExdinwELDe1G1/hVbLgZjtB7wMXJEUe2a2AfAIcADwDHA3cKS7zzGzGcA+wAvA7939\ndjO71t0P7+e+VeyJiEhHUbEniTQ9ewcBp7n7ae7+Q3f/cd9LlkDc/XbgxT67pwLz3H2+u78GXA0c\nGt/+Snc/Dfgl8Bkzuxh4PEsMdRV634nyq7eQ8ws5N1B+IqFI07O3DHiqqEAGMIloWZfEU0QF4Bru\n/iCw3mheX41Gg0ajQXd3N11dXTQaDXp6eoC1f/B13Z49e3al4lF+yq+T8tO2tquy3dvby8yZM1m4\ncCHLly9HJJFmGvdUYH/g/e6+upBgogWab2iaxj0MOMjdT4y3jwWmuvspKe9X07giItJRNI0riTQj\ne5OAvYC5ZvZ7YEmf693d81765Glg+6btbeN9IiIiItKCND17/0h0xOtI4N1EU6d9L1kZ6x7lezew\nk5lNjhd0PhK4PofHCUoyjB8q5VdvIecXcm6g/ERC0fLInrtPKTIQM7sK6AEmmNkC4Ex3v9zMTgZu\nYu3SKw8XGYeIiIhISFKdLq2u1LMnIiKdRj17khh0GtfMZsRny2iZme1kZu/IFpaIiIiI5GGonr3P\nAn8xs2+Y2V4D3cjMJpjZMWZ2AzAb2CbPIGVwofedKL96Czm/kHMD5ScSikF79tx9bzP7EHAy8GUz\nexl4GHgeWAF0AVOIjph9Efh34BPuriNmRURERCogzTp7OwIHEp2ibGtgDNGpyuYCdwC98VkuKkc9\neyIi0mnUsycJHaAhIiISIBV7kkizzp5UVOh9J8qv3kLOL+TcQPmJhELFnoiIiEjANI0rIiISIE3j\nSkIjeyIiIiIBU7EXgND7TpRfvYWcX8i5gfITCUXL58Y1s5HACHdf0bTvfwG7Abe5+z0FxCciIiIi\nGaRZZ+8XwEvufkK8fQpwPtHiyiOAD7r7fxYVaBbq2RMRkU6jnj1JpJnGnQbc2LT9BeC77j4WuBT4\ncp6BiYiIiEh2aYq9CcBCADPbA5gI/CC+7lqi6VwpQeh9J8qv3kLOL+TcQPmJhCJNsbcI6I5/ng7M\nd/e/xNtjgdU5xiUiIiIiOUjTs/cd4CjgKuB44CJ3Pyu+7svAoe4+taA4M1HPnoiIdBr17Emi5aNx\ngS8CS4G3AhcD32y67i3Az3KMS0RERERy0PI0rru/7u5nu/t73f2r7r6y6boPuvt3iwlRhhJ634ny\nq7eQ8ws5N1B+IqHQosoiIiIiARu0Z8/M/gq03Ozm7lvmEVTe1LMnIiKdRj17khiqZ+/fSFHsiYiI\niEi1tHw0bp2FPrLX29tLT09P2WEURvnVW8j5hZwbKL+608ieJNSzJyIiIhKwVCN7ZvZ24KPAzsCY\nvtdrnT0REZFq0MieJFoe2TOzdwO3AdsC+wF/BV4G9iI6ldoDRQQoIiIiIu1LM417NnAB8J54+6vu\nvj/RKN9rQG++oUmrQl8rSvnVW8j5hZwbKD+RUKQp9nYDZhGdA9eBjQDcfT5wFvDlvIMTERERkWzS\nnBt3ETDD3W8ys6eAr7j7zPi6Q4Br3X2jwiLNQD17IiLSadSzJ4k058a9F3gTcBNwM/DPZvY0sJJo\nivf+/MMTERERkSzSTOOeD7we//wlYBnwG+D3wJbAp/MNTVoVet+J8qu3kPMLOTdQfiKhaHlkz91v\nbPr5aTN7C7ATMBaY4+4rC4hPRERERDKo1Rk0zGwK0YEg4939iHjfOOD7wArgVne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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "@interact(h=FloatText(value=1e0), atol=FloatText(value=1e-3),\n", " rtol=FloatText(value=1e-3), k=IntSlider(min=1, value=3, max=5), \n", " integrator=Text(value='lsoda'))\n", "def plot_lotka_volterra_residuals(h, atol, rtol, k, integrator):\n", " \"\"\"Plots residuals of the Lotka-Volterra system.\"\"\"\n", " # re-compute the solution \n", " tmp_solution = lotka_volterra_ivp.solve(t0, y0, h=h, T=15, integrator=integrator,\n", " atol=atol, rtol=rtol)\n", "\n", " # re-compute the interpolated solution and residual\n", " tmp_ti = np.linspace(t0, tmp_solution[-1, 0], 1000)\n", " tmp_interp_solution = lotka_volterra_ivp.interpolate(tmp_solution, tmp_ti, k=k)\n", " tmp_residual = lotka_volterra_ivp.compute_residual(tmp_solution, tmp_ti, k=k)\n", " \n", " # extract the components of the solution\n", " tmp_rabbits = tmp_interp_solution[:, 1]\n", " tmp_foxes = tmp_interp_solution[:, 2]\n", "\n", " # extract the raw residuals\n", " tmp_rabbits_residual = tmp_residual[:, 1]\n", " tmp_foxes_residual = tmp_residual[:, 2]\n", "\n", " # typically, normalize residual by the level of the variable\n", " tmp_norm_rabbits_residual = np.abs(tmp_rabbits_residual) / tmp_rabbits\n", " tmp_norm_foxes_residual = np.abs(tmp_foxes_residual) / tmp_foxes\n", "\n", " # create the plot\n", " fig = plt.figure(figsize=(8, 6))\n", "\n", " plt.plot(tmp_ti, tmp_norm_rabbits_residual, 'r-', label='Rabbits')\n", " plt.plot(tmp_ti, tmp_norm_foxes_residual**2 / foxes, 'b-', label='Foxes')\n", " plt.axhline(np.finfo('float').eps, linestyle='dashed', color='k', label='Machine eps')\n", "\n", " plt.xlabel('Time', fontsize=15)\n", " plt.ylim(1e-16, 1)\n", " plt.ylabel('Residuals (normalized)', fontsize=15)\n", " plt.yscale('log')\n", " plt.title('Lotka-Volterra residuals', fontsize=20)\n", "\n", " plt.grid()\n", " plt.legend(loc='best', frameon=False, bbox_to_anchor=(1,1))\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sensitivity to parameters\n", "Once we have computed and plotted an approximate solution (and verified that the approximation is a good one by plotting the residual function!), we can try and learn something about the dependence of the solution on model parameters." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kV/oxkqZRo38jakDFaeQ5UO7+U3ffxN3nuPte7r63u3/P3W939+e5+27u/oKi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\nujHxdYmjSGNi65Pia7aO8fW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "@interact(a=FloatSlider(min=0.0, max=5.0, step=0.5, value=1.5),\n", " b=FloatSlider(min=0.0, max=1.0, step=0.01, value=0.5), \n", " c=FloatSlider(min=0.0, max=5.0, step=0.5, value=3.5),\n", " d=FloatSlider(min=0.0, max=1.0, step=0.01, value=0.5))\n", "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_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", " tmp_t = tmp_solution[:, 0]\n", " tmp_rabbits = tmp_solution[:, 1]\n", " tmp_foxes = tmp_solution[:, 2]\n", "\n", " # create the plot!\n", " fig = plt.figure(figsize=(8, 6))\n", " \n", " plt.plot(tmp_t, tmp_rabbits, 'r.', label='Rabbits')\n", " plt.plot(tmp_t, tmp_foxes , 'b.', label='Foxes')\n", " \n", " plt.xlabel('Time', fontsize=15)\n", " plt.ylabel('Population', fontsize=15)\n", " plt.title('Evolution of fox and rabbit populations', fontsize=20)\n", "\n", " plt.legend(loc='best', frameon=False, bbox_to_anchor=(1,1))\n", " plt.grid()\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.2 The Lorenz equations\n", "\n", "The [Lorenz equations](Lorenz Equations`:http://en.wikipedia.org/wiki/Lorenz_system) are a system of three coupled, first-order, non-linear differential equations which describe the trajectory of a particle through time. The system was originally derived by as a model of atmospheric convection, but the deceptive simplicity of the equations have made them an often-used example in fields beyond atmospheric physics.\n", "\n", "The equations describe the evolution of the spatial variables x, y, and z, given the governing parameters $\\sigma, \\beta, \\rho$, through the specification of the time-derivatives of the spatial variables:\n", "\n", "\\begin{align}\n", " \\frac{dx}{dt} =& \\sigma(y − x) \\tag{2.2.1} \\\\\n", " \\frac{dy}{dt} =& x(\\rho − z) − y \\tag{2.2.2} \\\\\n", " \\frac{dz}{dt} =& xy − \\beta z \\tag{2.2.3}\n", "\\end{align}\n", "\n", "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", "### 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", "\n", "1. Define the IVP using SymPy.\n", "2. Use SymPy routines for computing the Jacobian.\n", "3. Wrap the symbolic expressions as callable NumPy functions. \n", "4. Use these functions to create an instance of the `ivp.IVP` class.\n", "\n", "The remainder of this notebook implements each of these steps to solve and analyze the Lorenz equations defined above." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Step 1: Defining the Lorenz equations using SymPy\n", "We begin by defining a `sp.Matrix` instance containing the three Lorenz equations..." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# enables sympy LaTex printing...\n", "sp.init_printing()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# declare endogenous variables\n", "t, x, y, z = sp.var('t, x, y, z')\n", "\n", "# declare model parameters\n", "beta, rho, sigma = sp.var('beta, rho, sigma')\n", "\n", "# define symbolic model equations\n", "_x_dot = sigma * (y - x)\n", "_y_dot = x * (rho - z) - y\n", "_z_dot = x * y - beta * z\n", "\n", "# define symbolic system and compute the jacobian\n", "_lorenz_system = sp.Matrix([[_x_dot], [_y_dot], [_z_dot]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take a check out our newly defined `_lorenz_system` and make sure it looks as expected..." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIIAAABLCAMAAACLOq+zAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAo1xBWAAAAE3RSTlMA\nMquZdlQQQOkwRO/duyJmzYlsD8NxXgAAAAlwSFlzAAAOxAAADsQBlSsOGwAABPdJREFUaAXtWmuX\noyAMxYrsLL7X//9fl/AyIVGxnenunDN8aBGScA0BcktVs/nyUG8vQxhZqWZrtSvd2xGoGcZ9bACh\nqRh9miuELkTmSRCYayFMo6B9u+khYKiGsAjKtxEos3CdWghzy3WPWjp91KPUyvtqIQw3nHAGwfQM\nXiWEaWCaxw1nENRiS8UDCKbt/ZJN7tepUugbt6Ymq6l7CwhGt+D9qTeg3DJLMoRmaG03jFP2/iiv\nSLMqNQ9aDSTKCgir6sD72q09V2Yi6lukRWl62KYAXSqDvG+t7sXWzaguYwUFCmHqVAvDjmFVd2xK\nRS94FWWd7VT6MINmGXJZ3H4GAgvaMNYFytD7r7jhO5keJmILa6FBLxasixA273aN8EYICRH+jqZR\nE/WCCu+StuA6CFPYsBcUOAcT4cZNpk8geKfquBoterGgI3nB+BloQgQHsYNw7EyIMr1PmZMvvTDC\nlPgP910ZjqMLvmnAC3hFHgmg4NNunRrd3BYnWAmhddFiw+S6RekWES2SF5RxhzcE+164+6DPPLR2\nq34uVmwJwTxW3W5x0UAU0yJCoCL+6dUNOiwycC4zXgvhzjFlyC6hHm5XMFucVrqPeji1ENRI7bJ3\nOW4Y3DyN8YB85bBWz6csVus2BYD0ItVeKMP++K1Pel5L3E4Mv9hV74UXBzpW/4EAvvkGXii2/+MZ\n3XvEsN+7We3CC0/tBhJfYQPvDRcQniIw0ha4j8hq5xDunAzItHAQoN6yeg7hzvmILAt8BfWW1VMI\nwsla6svPnK/Icr6VQCiJCSIwttWPdNbI5uzgctwmZC+cr2Adym3IvsCIyZ4xQuJmOR1Ehs3oDkRI\n0aDwBDG0h0/KbQgERkxy3jxDrjOltAOby3XI8/IS5nwlyzkpym0IBLCCiYnK7KEH/0KyCqXkM74R\nPpox5ZuZLEiyTghzGw/h18fvbIYQkwQh8CqdMtAsTCt2/70sQ6AS6cnbywTkzwdhI7ndS6eJaH3O\nufDMM9mE725HoOSEO0sTbkMmghGTFI4DsAiKLptLlc4zjQjjPBwDrUncBkPgxCQSGLO5QDeQhR6X\nZpjXWSf6w/kK0STcBkPgxCT6s9smlIESY/nB+WDu847E+UoWhArhNhgCkQoPYYNONEQQkJtqdtXd\nKNkdmcFwTPklxPpOGi6OKcJtLrMmyPsj1z8Zsui6Oqwxt3Gq517w+93FCivGd48SX8FSmNtcQ3iG\nwHxy4obBf1X9YiK+alhs9wcCeOMbemGa7wY8nnaxftML7gLLjOc5pDjMWeM9CDOMbtEvvmema/tu\nQQgE8zAxLH/sq8RwC0L4zeqB0iMyytsg2P7ot7c3QLDN1OplCGkyZi7RFyUExIwK9kKcd2citDLr\n2vZ+QRDmIkPAzKhgL09DCD9ga3+zA67IzEWGgJhRyV4qIXAWEqLRpmuVnbko6TYGX9mU7KUSAhGD\nBxu2pDndbbCFUcaC08nMiLIXYvtGLMSLhLgmMXOJFjmEnXtQ9vIshHC7N4U1SZiLDIEwI3IzQxDc\nOSk9t2oCW6HMRYRAmRFlLwRD/UTYZl71Gi9rKHMRIVBmRNnLkxDYnRKxAw88FqjIzl5Ie70XriEU\ntzF4nIK94K76WDDxXoVoVz8U7IXoVXsh7gpEuf6hYC9EsRoC0frUh/8Gwj//a5U716HgC+JP9fSx\nMf/XKq3VX8A9NJYz5/mxAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left[\\begin{matrix}\\sigma \\left(- x + y\\right)\\\\x \\left(\\rho - z\\right) - y\\\\- \\beta z + x y\\end{matrix}\\right]$$" ], "text/plain": [ "⎡ σ⋅(-x + y) ⎤\n", "⎢ ⎥\n", "⎢x⋅(ρ - z) - y⎥\n", "⎢ ⎥\n", "⎣ -β⋅z + x⋅y ⎦" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "_lorenz_system" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Step 2: Computing the Jacobian using SymPy\n", "Once we have defined our model as a SymPy matrix, computing the Jacobian is trivial..." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKAAAABLCAMAAADAknxeAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\ngg==\n", "text/latex": [ "$$\\left[\\begin{matrix}- \\sigma & \\sigma & 0\\\\\\rho - z & -1 & - x\\\\y & x & - \\beta\\end{matrix}\\right]$$" ], "text/plain": [ "⎡ -σ σ 0 ⎤\n", "⎢ ⎥\n", "⎢ρ - z -1 -x⎥\n", "⎢ ⎥\n", "⎣ y x -β⎦" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "_lorenz_jacobian = _lorenz_system.jacobian([x, y, z])\n", "_lorenz_jacobian" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Step 3: Wrap the SymPy expression to create vectorized NumPy functions\n", "Now we wrap the SymPy matrices defining the model and the Jacobian to create vectorized NumPy functions. It is crucial that the interface for our wrapped functions matches the interface required by the `f` and `jac` parameters which we will pass to the `ivp.IVP` constructor to create an instance of the `ivp.IVP` class representing the Lorenz equations.\n", "\n", "Recall from the `ivp.IVP` docstring that... \n", "\n", " f : callable `f(t, y, *f_args)`\n", " Right hand side of the system of equations defining the ODE. The\n", " independent variable, `t`, is a `scalar`; `y` is an `ndarray`\n", " of dependent variables with `y.shape == (n,)`. The function `f`\n", " should return a `scalar`, `ndarray` or `list` (but not a\n", " `tuple`).\n", " jac : callable `jac(t, y, *jac_args)`, optional(default=None)\n", " Jacobian of the right hand side of the system of equations defining\n", " the ODE.\n", "\n", " .. :math:\n", "\n", " \\mathcal{J}_{i,j} = \\bigg[\\frac{\\partial f_i}{\\partial y_j}\\bigg]\n", " \n", "Thus our wrapped functions need to take a float `t` as the first argument, and array `y` as a second argument, followed by some arbitrary number of model parameters. We can handle all of this as follows..." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# in order to pass an array as an argument, we need to apply a change of variables\n", "X = sp.DeferredVector('X')\n", "change_of_vars = {'x': X[0], 'y': X[1], 'z': X[2]}\n", "_transformed_lorenz_system = _lorenz_system.subs(change_of_vars)\n", "_transformed_lorenz_jacobian = _transformed_lorenz_system.jacobian([X[0], X[1], X[2]])\n", "\n", "# wrap the symbolic expressions as callable numpy funcs\n", "_args = (t, X, beta, rho, sigma)\n", "_f = sp.lambdify(_args, _transformed_lorenz_system,\n", " modules=[{'ImmutableMatrix': np.array}, \"numpy\"])\n", "_jac = sp.lambdify(_args, _transformed_lorenz_jacobian,\n", " modules=[{'ImmutableMatrix': np.array}, \"numpy\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Step 4: Use these functions to create an instance of the `IVP` class\n", "First we define functions describing the right-hand side of the ODE and the Jacobian which we need to initialize the `ivp.IVP` class..." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def lorenz_system(t, X, beta, rho, sigma):\n", " \"\"\"\n", " Return the Lorenz system.\n", "\n", " Parameters\n", " ----------\n", " t : float\n", " Time\n", " X : ndarray (float, shape=(3,))\n", " Endogenous variables of the Lorenz system.\n", " beta : float\n", " Model parameter. Should satisfy :math:`0 < \\beta`.\n", " rho : float\n", " Model parameter. Should satisfy :math:`0 < \\rho`.\n", " sigma : float\n", " Model parameter. Should satisfy :math:`0 < \\sigma`.\n", "\n", "\n", " Returns\n", " -------\n", " rhs_ode : ndarray (float, shape=(3,))\n", " Right hand side of the Lorenz system of ODEs.\n", "\n", " \"\"\"\n", " rhs_ode = _f(t, X, beta, rho, sigma).ravel()\n", " return rhs_ode\n", "\n", "\n", "def lorenz_jacobian(t, X, beta, rho, sigma):\n", " \"\"\"\n", " Return the Jacobian of the Lorenz system.\n", "\n", " Parameters\n", " ----------\n", " t : float\n", " Time\n", " X : ndarray (float, shape=(3,))\n", " Endogenous variables of the Lorenz system.\n", " beta : float\n", " Model parameter. Should satisfy :math:`0 < \\beta`.\n", " rho : float\n", " Model parameter. Should satisfy :math:`0 < \\rho`.\n", " sigma : float\n", " Model parameter. Should satisfy :math:`0 < \\sigma`.\n", "\n", " Returns\n", " -------\n", " jac : ndarray (float, shape=(3,3))\n", " Jacobian of the Lorenz system of ODEs.\n", "\n", " \"\"\"\n", " jac = _jac(t, X, beta, rho, sigma)\n", " return jac" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... next we define a tuple of model parameters..." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# parameters with ordering (beta, rho, sigma)\n", "lorenz_params = (2.66, 28.0, 10.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... finally, we are ready to create the instance of the `ivp.IVP` class representing the Lorenz equations." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# create the instance\n", "lorenz_ivp = ivp.IVP(f=lorenz_system,\n", " jac=lorenz_jacobian)\n", "\n", "# specify the params\n", "lorenz_ivp.f_params = lorenz_params\n", "lorenz_ivp.jac_params = lorenz_params" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 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", "2. Use the discretized approximation in conjunction with parametric B-spline interpolation to construct a continuous approximation of the true solution.\n", "3. Compute and analyze the residual of the approximate solution.\n", "\n", "#### Step 1. Solve the model using a discretized, finite-difference approximation\n", "Using `dop853`, an embedded Runge-Kutta method of order 7(8) with adaptive step size control due to [Dormand and Prince](http://en.wikipedia.org/wiki/Dormand%E2%80%93Prince_method), integrate the Lorenz equations forward from an initial condition of $X_0 = (1.0, 1.0, 1.0)$ from $t=0$, to $T=100$." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# declare and initial condition\n", "t0, X0 = 0.0, np.array([1.0, 1.0, 1.0])\n", "\n", "# solve!\n", "solution = lorenz_ivp.solve(t0, X0, h=1e-2, T=100, integrator='dop853',\n", " atol=1e-12, rtol=1e-9)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Plotting the solution time paths\n", "We can use IPython widgets to construct a \"poor man's\" animation of the evolution of the Lorenz equations. " ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KGasyxqmMcSpnrNSEyZQkSVIL1kwNgTVTkqRJYs1UL3umJEmSWjCZ0shYi1DO\nWJUxTmWMUzljpSZMpiRJklqwZmoIrJmSJE0Sa6Z62TMlSZLUgsmURsZahHLGqoxxKmOcyhkrNWEy\nJUmS1II1U0NgzZQkaZJYM9XLnilJkqQWTKY0MtYilDNWZYxTGeNUzlipCZMpSZKkFqyZGgJrpiRJ\nk8SaqV72TEmSJLVgMqWRsRahnLEqY5zKGKdyxkpNmExJkiS1YM3UEFgzJUmaJNZM9SrumYqI/SLi\nXRHx9xFxTkTsGBEnRMTJEfHJiNirbWMiYq+IeF9EfDYijuxb9hcRcVbbY3Tt7+UR8YOI+HZE7FvP\n+5uIeNSwjiFJksZfUTIVEQ8HjsnMv8jM1wM/By4HLgXOA44CnjuE9rwBeB1wAXB837IXD2H/AETE\nU4EXAe8DPgecGBFfBn6WmdcM6zjqZS1COWNVxjiVMU7ljJWaWFa43p9TJTod9wN+nJmXR8QK4O+B\nj7dpSEQ8BfhSZt4TEWuA67uW7QA8Gvhgm2N0uR14RmZurvf/x8ARmXnykPYvSZImRFHNVETsnpm3\ndE3fCpyemX81zfoPB3bOzK8WNyRiZ+AnwIOA7wHPy8zz6mV/AJwLPLrTc9TkGNMc92XAaqqet81N\nnoc1U5KkSWLNVK+i23x9idQ+wEOAS2bY5Hjgd+bSkMz8QWbeDfwJ1W3EL3QtfipwR98tuDkfo19E\nvAF4XGYe3Z9IDesYkiRpvDUZGuFg4E7gN701A4rPDwG+2LBNzwQuqROrjgOALw3xGETEW4EHZOar\nu+YtH+Yx1MtahHLGqoxxKmOcyhkrNTFrMhUR942IUzqfeKNKpr6Tmf9ZLw/g9fXvz4mI99f7Pbou\n9O7e1yMj4j6zHHJP4Lqube4H7EdV7D6UY0TESQDdtynrHrcTS44hSZLUMWvNVEQ8D/g0cCTw7fr3\njZl5QL38TcCFmXlFPX0MsH9mvqpvP6uBi4F/zsw/nuF4XwC+l5nH1tP/E3glsCozr2p7jIg4AjgW\n+D/AY6jqs3an6oVanZnrZzrGNPu0ZkqSNDGsmepV8mm+y4DTgcfVjycBH4iIDwJ3Aed1EqnagfTW\nO3VsAH5Y72MmrwU+EhHvpbqd+LvATzqJVJtjRMT9qT7Fd1g9fTzwRuBq4NBOIjXLMSRJkn5j6COg\nR8SNwP7Aj4CdMvNHfcvfnJlvK9xXAN8HPpeZL5+PYzR9Hn3r2jNV4NJLL2X16tUL3YwlwViVMU5l\njFM5Y1X8vozlAAAUgklEQVTGnqleQ/1uvojYCbgrM+8AjgbuO2C1aeuZIuKsiJjqmvVcYAfgb5oe\nIyLWRMS1EXF93RM16LjvjYgbImIqIlZ1jgE8HlgPXDndtpIkabINtWcqIrYCPglcCNyamRf1LV9N\n1cvzL9Ns/0PgzMx8bUQ8BPgycEJmfrrJMep1rwcOourhuhJ4QWZe27X+ocBxmfnsiHgScCrw+/Ux\nDqYakf3Tg7bt2oc9U5KkiWHPVK/SEdCL1GM1vXDQsojYGjgkM/9yhl0cCzwxIt4J7EqVvFzZ4hhP\nBG7IzJvr5WcDRwDdCdERwBn1vq+oR1t/ENVXzeyUmWfOsK0kSZpwQ73NN5PM3DRLIkVm/ktmnpCZ\nb6gH0rxypvULjrEbcEvX9K31PArWKdlWc+D4LeWMVRnjVMY4lTNWamKoPVNjolG35dq1a1m5ciUA\ny5cvZ9WqVb8pYuy8OCd9umOxtGcxT09NTS2q9ji9tKc9n8qnp6amFlV7Fst05/d169ahexv6p/kW\nk4jYH3hLZq6pp08AMjNP6VrnH6hGXP+nevpaqmER9ppt2659WDMlSZoY1kz1GtltvgVyJfDwiNgz\nIrYFXgCc17fOecCL4TfJ18bM3FC4rSRJmnBjnUxl5ibgOOACqoE5z87MayLi2Ih4Rb3O54Gb6nGl\nTgNePdO2C/A0xkZ3d7FmZqzKGKcyxqmcsVITY18zlZnnA3v3zTutb/q40m0lSZK6jXXN1KhYMyVJ\nmiTWTPUa69t8kiRJ881kSiNjLUI5Y1XGOJUxTuWMlZowmZIkSWrBmqkhsGZKkjRJrJnqZc+UJElS\nCyZTGhlrEcoZqzLGqYxxKmes1ITJlCRJUgvWTA2BNVOSpElizVQve6YkSZJaMJnSyFiLUM5YlTFO\nZYxTOWOlJkymJEmSWrBmagismZIkTRJrpnrZMyVJktSCyZRGxlqEcsaqjHEqY5zKGSs1YTIlSZLU\ngjVTQ2DNlCRpklgz1cueKUmSpBZMpjQy1iKUM1ZljFMZ41TOWKkJkylJkqQWrJkaAmumJEmTxJqp\nXvZMSZIktWAypZGxFqGcsSpjnMoYp3LGSk2YTEmSJLVgzdQQWDMlSZok1kz1smdKkiSpBZMpjYy1\nCOWMVRnjVMY4lTNWasJkSpIkqQVrpobAmilJ0iSxZqqXPVOSJEktmExpZKxFKGesyhinMsapnLFS\nEyZTkiRJLVgzNQTWTEmSJok1U73smZIkSWrBZEojYy1COWNVxjiVMU7ljJWaMJmSJElqwZqpIbBm\nSpI0SayZ6mXPlCRJUgsmUxoZaxHKGasyxqmMcSpnrNSEyZQkSVIL1kwNgTVTkqRJYs1UL3umJEmS\nWjCZ0shYi1DOWJUxTmWMUzljpSZMpiRJklqwZmoIrJmSJE0Sa6Z62TMlSZLUwtgmUxGxY0RcEBHX\nRcQXI2KHadZbExHXRsT1EXF81/y/jYhrImIqIv45Ih4wutaPJ2sRyhmrMsapjHEqZ6zUxNgmU8AJ\nwEWZuTdwMfDG/hUiYivg/cCzgH2BIyNin3rxBcC+mbkKuGHQ9pIkSWNbMxUR1wIHZuaGiNgVuDQz\n9+lbZ3/gpMw8tJ4+AcjMPKVvvecC/yUzj57mWNZMSZImhjVTvca5Z2rnzNwAkJm3AzsPWGc34Jau\n6Vvref1eCnxh6C2UJElL3pJOpiLiwoj4Ttfjqvrn4QNWb9R1FBF/CdydmWe2a62sRShnrMoYpzLG\nqZyxUhPLFroBbWTmIdMti4gNEbFL122+HwxYbT2wR9f0inpeZx9rgcOAZ8zWlrVr17Jy5UoAli9f\nzqpVq1i9ejWw5cU56dMdi6U9i3l6ampqUbXH6aU97flUPj01NbWo2rNYpju/r1u3Dt3bONdMnQL8\nODNPqT+lt2NmntC3ztbAdcBBwG3A14AjM/OaiFgD/D1wQGb+aJZjWTMlSZoY1kz1GudkaifgfwG7\nAzcDz8/MjRHxYODDmfmcer01wKlUtzw/mpkn1/NvALYFOonU5Zn56mmOZTIlSZoYJlO9lnTN1Ewy\n88eZeXBm7p2Zz8zMjfX82zqJVD19fr3OIzqJVD3/EZm5Z2buVz8GJlIq191drJkZqzLGqYxxKmes\n1MTYJlOSJEmjMLa3+UbJ23ySpEnibb5e9kxJkiS1YDKlkbEWoZyxKmOcyhincsZKTZhMSZIktWDN\n1BBYMyVJmiTWTPWyZ0qSJKkFkymNjLUI5YxVGeNUxjiVM1ZqwmRKkiSpBWumhsCaKUnSJLFmqpc9\nU5IkSS2YTGlkrEUoZ6zKGKcyxqmcsVITJlOSJEktWDM1BNZMSZImiTVTveyZkiRJasFkSiNjLUI5\nY1XGOJUxTuWMlZowmZIkSWrBmqkhsGZKkjRJrJnqZc+UJElSCyZTGhlrEcoZqzLGqYxxKmes1ITJ\nlCRJUgvWTA2BNVOSpElizVQve6YkSZJaMJnSyFiLUM5YlTFOZYxTOWOlJkymJEmSWrBmagismZIk\nTRJrpnrZMyVJktSCyZRGxlqEcsaqjHEqY5zKGSs1YTIlSZLUgjVTQ2DNlCRpklgz1cueKUmSpBZM\npjQy1iKUM1ZljFMZ41TOWKkJkylJkqQWrJkaAmumJEmTxJqpXvZMSZIktWAypZGxFqGcsSpjnMoY\np3LGSk2YTEmSJLVgzdQQWDMlSZok1kz1smdKkiSpBZMpjYy1COWMVRnjVMY4lTNWasJkSpIkqQVr\npobAmilJ0iSxZqqXPVOSJEktmExpZKxFKGesyhinMsapnLFSEyZTkiRJLVgzNQTWTEmSJok1U73s\nmZIkSWphbJOpiNgxIi6IiOsi4osRscM0662JiGsj4vqIOH7A8tdHxOaI2Gn+Wz3erEUoZ6zKGKcy\nxqmcsVITY5tMAScAF2Xm3sDFwBv7V4iIrYD3A88C9gWOjIh9upavAA4Bbh5JiyVJ0pIztjVTEXEt\ncGBmboiIXYFLM3OfvnX2B07KzEPr6ROAzMxT6ulPA28DzgMel5k/nuZY1kxJkiaGNVO9xrlnaufM\n3ACQmbcDOw9YZzfglq7pW+t5RMThwC2ZedV8N1SSJC1dSzqZiogLI+I7XY+r6p+HD1i9uOsoIrYD\nTgRO6p7dtr2TzlqEcsaqjHEqY5zKGSs1sWyhG9BGZh4y3bKI2BARu3Td5vvBgNXWA3t0Ta+o5z0M\nWAl8OyKinv+NiHhiZg7aD2vXrmXlypUALF++nFWrVrF69Wpgy4tz0qc7Fkt7FvP01NTUomqP00t7\n2vOpfHpqampRtWexTHd+X7duHbq3ca6ZOgX4cWaeUn9Kb8fMPKFvna2B64CDgNuArwFHZuY1fevd\nBOyXmT+Z5ljWTEmSJoY1U72W9G2+WZwCHBIRnWTpZICIeHBEfBYgMzcBxwEXAFcDZ/cnUrXE23yS\nJGmAsU2mMvPHmXlwZu6dmc/MzI31/Nsy8zld651fr/OIzDx5mn09dLpP8qlcd3exZmasyhinMsap\nnLFSE2ObTEmSJI3C2NZMjZI1U5KkSWLNVC97piRJklowmdLIWItQzliVMU5ljFM5Y6UmTKYkSZJa\nsGZqCKyZkiRNEmumetkzJUmS1ILJlEbGWoRyxqqMcSpjnMoZKzVhMiVJktSCNVNDYM2UJGmSWDPV\ny54pSZKkFkymNDLWIpQzVmWMUxnjVM5YqQmTKUmSpBasmRoCa6YkSZPEmqle9kxJkiS1YDKlkbEW\noZyxKmOcyhincsZKTZhMSZIktWDN1BBYMyVJmiTWTPWyZ0qSJKkFkymNjLUI5YxVGeNUxjiVM1Zq\nwmRKkiSpBWumhsCaKUnSJLFmqpc9U5IkSS2YTGlkrEUoZ6zKGKcyxqmcsVITJlOSJEktWDM1BNZM\nSZImiTVTveyZkiRJasFkSiNjLUI5Y1XGOJUxTuWMlZowmZIkSWrBmqkhsGZKkjRJrJnqZc+UJElS\nCyZTGhlrEcoZqzLGqYxxKmes1ITJlCRJUgvWTA2BNVOSpElizVQve6YkSZJaMJnSyFiLUM5YlTFO\nZYxTOWOlJkymJEmSWrBmagismZIkTRJrpnrZMyVJktSCyZRGxlqEcsaqjHEqY5zKGSs1YTIlSZLU\ngjVTQ2DNlCRpklgz1cueKUmSpBZMpjQy1iKUM1ZljFMZ41TOWKkJkylJkqQWrJkaAmumJEmTxJqp\nXvZMSZIktTC2yVRE7BgRF0TEdRHxxYjYYZr11kTEtRFxfUQc37fsv0bENRFxVUScPJqWjy9rEcoZ\nqzLGqYxxKmes1MTYJlPACcBFmbk3cDHwxv4VImIr4P3As4B9gSMjYp962WrgD4DfzczfBf5uRO0e\nW1NTUwvdhCXDWJUxTmWMUzljpSbGOZk6AvhE/fsngOcOWOeJwA2ZeXNm3g2cXW8H8Crg5My8ByAz\n75jn9o69jRs3LnQTlgxjVcY4lTFO5YyVmhjnZGrnzNwAkJm3AzsPWGc34Jau6VvreQCPBA6IiMsj\n4pKIePy8tlaSJC1Jyxa6AW1ExIXALt2zgATeNGD1uX7cbhmwY2buHxFPAP4X8NBGDRUA69atW+gm\nLBnGqoxxKmOcyhkrNTG2QyNExDXA6szcEBG7Apdk5qP61tkfeEtmrqmnTwAyM0+JiC9Q3ea7rF52\nI/CkzPzRgGONZxAlSZqGQyNssaR7pmZxHrAWOAU4BvjMgHWuBB4eEXsCtwEvAI6sl50LPAO4LCIe\nCWwzKJECTyhJkibZOPdM7UR1a2534Gbg+Zm5MSIeDHw4M59Tr7cGOJWqfuyjmXlyPX8b4GPAKuBO\n4PWdXipJkqSOsU2mJEmSRmGcP803VA4CWmYYcaqXvz4iNtc9jGOnbZwi4m/rc2kqIv45Ih4wutaP\nxmznSL3OeyPihjoOq+ay7bhoGqeIWBERF0fE1fU16TWjbflotTmf6mVbRcQ3I+K80bR44bR87e0Q\nEZ+ur09XR8STRtfyBZSZPgoeVLVX/73+/Xiq4vT+dbYCbgT2BLYBpoB96mWrgQuAZfX0Axf6OS3G\nONXLVwDnAzcBOy30c1qMcQIOBraqfz8ZeMdCP6chx2fGc6Re51Dgc/XvTwIuL912XB4t47QrsKr+\n/f7Adcbp3nHqWv464B+B8xb6+SzmWAEfB15S/74MeMBCP6dRPOyZKucgoGXaxgng3cAb5rWVC69V\nnDLzoszcXK93OVUCOk5mO0eop88AyMwrgB0iYpfCbcdF4zhl5u2ZOVXP/wVwDVvG2Rs3bc4nImIF\ncBjwkdE1ecE0jlXdQ/60zDy9XnZPZv5shG1fMCZT5RwEtEyrOEXE4cAtmXnVfDd0gbU9n7q9FPjC\n0Fu4sEqe+3TrlMZtHDSJ0/r+dSJiJdWHba4YegsXh7Zx6rzBm4Qi4zax2gu4IyJOr2+JfigitpvX\n1i4S4zw0wpw5CGiZ+YpT/aI7ETikb99L0jyfT51j/CVwd2ae2WT7MbNkz5WFFBH3B84BXlv3UKlL\nRDwb2JCZU1F9Z6vn2fSWAfsBf5aZX4+I91B9T+5JC9us+Wcy1SUzD5luWURsqLvGO4OA/mDAauuB\nPbqmV9TzoMru/6U+zpV1cfVv5zRjVy1m8xinhwErgW9HRNTzvxERT8zMQftZ1Ob5fCIi1lLdenjG\ncFq8qMz43LvW2X3AOtsWbDsu2sSJiFhGlUh9MjMHjcU3LtrE6Y+AwyPiMGA7YPuIOCMzXzyP7V1I\nrc4pqjsLX69/P4eqJnTseZuvXGcQUCgYBDQitqUaBLTzyY/OIKDELIOALnGN45SZ/56Zu2bmQzNz\nL6oE9LFLMZEq0Op8imp8tDcAh2fmnfPf3JGb6bXUcR7wYvjNtxlsrG+dlmw7LtrECaqx9P4jM08d\nVYMXSOM4ZeaJmblHZj603u7iMU6koF2sNgC31P/jAA4C/mNE7V5YC10Bv1QewE7ARVSfeLkAWF7P\nfzDw2a711tTr3ACc0DV/G+CTwFXA14EDF/o5LcY49e3ru4zvp/nank83UA1G+8368YGFfk7zEKN7\nPXfgWOAVXeu8n+qTR98G9pvL+TUujwZxemw97ynAJqpPa32rPo/WLPTzWURx2m/APg5kzD/N1zZW\nwO9RJWRTVHdjdljo5zOKh4N2SpIkteBtPkmSpBZMpiRJklowmZIkSWrBZEqSJKkFkylJkqQWTKYk\nSZJaMJmStKhExKURsXn2NSVpcTCZkjQv6q9MmsujM6p0AiZTkpYMv5tP0nx5y4B5rwMeAJwKbOxb\nNlX/PBr4rflrliQNlyOgSxqZiLiJ6ktU98rM7y10eyRpGLzNJ2lRGVQzFREH1rcC3xwRj4uI8yNi\nY0T8OCLOiYgV9XoPjYizI+IHEfGriLg4Ih4zzXG2i4g3RsS3IuIXEfHziPhqRLxgFM9T0vgwmZK0\n2GT9GOSJwJepaqo+BFwBPA+4MCL2rqcfAnwC+CzVF9NeEBE9tw0jYgfgX4G3A/cAHwU+DjwQODMi\n3jbcpyRpnFkzJWkpORR4YWae3ZkRER8BXgp8FXhnZp7ctexNwFuBlwHv69rPqVTfbv/fM/Pvu9bf\nFvgMcGJEnJOZ35nPJyNpPNgzJWkp+XJ3IlX7RP1zI3BK37IzgABWdWZExE7AC4GvdydSAJl5F3A8\n1bXxqCG2W9IYs2dK0lLyjQHzvl//nMp7f6Jmff1zRde8JwBbAxkRJw3Y37b1z0c1bqWkiWIyJWkp\n+emAefdMtywzN0UEwDZds3+7/vmE+jFIAvdr2EZJE8bbfJImTSfpendmbj3D4+AFbaWkJcNkStKk\n+RrVpwGfttANkTQeTKYkTZTM/CHwKeDxEfGmiLjXdbAer2rlqNsmaWmyZkrSJDoOeDjVsAlHR8RX\ngA1UY1Q9Cng8cCSwbqEaKGnpMJmSNGol32E1aJ2ZBvOc07LM/HlEHAi8gmoIhOcB96VKqG4A/hy4\nsKCdkuR380mSJLVhzZQkSVILJlOSJEktmExJkiS1YDIlSZLUgsmUJElSCyZTkiRJLZhMSZIktWAy\nJUmS1ILJlCRJUgsmU5IkSS38f3IZJDxnnbUBAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "@interact(T=IntSlider(min=0, value=0, max=solution.shape[0], step=5))\n", "def plot_lorenz(T):\n", " \"\"\"Plots the first T points in the solution trajectory of the Lorenz equations.\"\"\" \n", " # extract the components of the solution trajectory\n", " t = solution[:T, 0]\n", " x_vals = solution[:T, 1]\n", " y_vals = solution[:T, 2]\n", " z_vals = solution[:T, 3]\n", "\n", " # create the plot\n", " fig = plt.figure(figsize=(8, 6))\n", " plt.plot(t, x_vals, 'r.', label='$x_t$', alpha=0.5)\n", " plt.plot(t, y_vals , 'b.', label='$y_t$', alpha=0.5)\n", " plt.plot(t, z_vals , 'g.', label='$z_t$', alpha=0.5)\n", "\n", " plt.grid()\n", " plt.xlabel('Time', fontsize=20)\n", " plt.ylabel('$x_t, y_t, z_t$', fontsize=20, rotation='horizontal')\n", " plt.title('Time paths of the $x,y,z$ coordinates', fontsize=25)\n", " plt.legend(frameon=False, bbox_to_anchor=(1.15,1))\n", " \n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Step 2: Construct a continuous approximation to the solution.\n", "\n", "Let's construct a continuous approximation to the solution of the Lorenz equations at 10000 evenly spaced points using a 5th order B-spline interpolation." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# define the desired interpolation points...\n", "ti = np.linspace(t0, solution[-1, 0], 1e4)\n", "\n", "# ...and interpolate!\n", "interp_solution = lorenz_ivp.interpolate(solution, ti, k=5, ext=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Plotting 2D projections of the solution in phase space\n", "The underlying structure of the Lorenz system becomes more apparent when I plot the interpolated solution trajectories in phase space. We can plot 2D projections of the time paths of the solution in phase space..." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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5msiqyOJkyUlOlp6kzlXHxMSJTEiYwPj48USG9s8bC2MMVY1VZJZnsj9/P7lV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SMoSESMvLxEKqFanc7s2SIVccUK0bj4448hLMw4cqW4xAwrB4eBHQRlMrG9vl6knA7WYNp8P7m6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6IJRgXBP/yBoWmrV7PPksG8eezR1BtERABPPOG5PS8PePXV7p/3kUcYohfo1NSwOuG+fQzL\nvPJKhhUKfkNyJgRBMAuZTwRBMAvJwVKR4mKKG0NcVVdTXEVHu3uvgN4TVwDwzW96394TcZWY2H4Y\nYKBQXMyS78ePAxMnAvfey9BCQRAEQRAEQegG0gerF/Cppr+38ECA286fd26fPdsU2wzc+mBNncr8\npbY0NvbsQ8rLgSefBF56Cdi4kflMRUWeOVTt2dgbvREcDvYc27wZeOYZ4PXXKQK/8Q1g2bJuiSsV\nejioYKPgHRXGTmw0DxXsVMFGwRNVxk0FO8VG81DFTl8RD1Zfc+oUMGeOc90QWMOHAwcPOrf3Zlnw\n667zvv3NN7t/zpQU5i8ZfamKi1kZcccOVgtMSuI+AwdySUmhF6+9Br/dxWZjcYziYn63p07xc8aM\nYf+rwYN9qyooCIIgCIIgCB0gOVh9SXMz86++8x0WdrDbgV//mp6jRYuATz7pfRvi44HHH/fc3tAA\n/PKX3T/vqlUs0uENqxUoLQUuXnS+XrzIXldJSeyHFRfHJTaW3jWjx1VYGM/hWqa9sRGor3cuNTU8\nX0kJxVxCAgXciBHA6NEs3S4EHJIzIQiCWch8IgiCWUgOlmoUFNCDYoiG8+cpPhIS3MXViBEs5d4b\n3Hyz9+2/+U33zxkZCYwb1/77oaHs+WX0/TJoaqK3qarKuZw7RwHV0MBX1ybDuk6hFRHBRsPGEh1N\nIXXVVQz/k6bAgiAIgiAIgp/wWw6Wpmm3app2WNM0u6Zp09q89wNN005qmnZU07Ql/rKpt+hyPKm3\n/KuQEIYHutIL1exac7DaNjIGgPz8LudJeWXhwu6F+oWHU3RlZwNz5sASEcFKimvXAuvXsxDHd7/r\nXL73Pb4+9hhw333AmjXATTexqfHkyUBaml/ElQrxwyrYKHhHhbETG81DBTtVsFHwRJVxU8FOsdE8\nVLHTV/xZ5OIQgJUAPnPdqGnaOACrAYwDcB2AZzXtMkmK8SawgoM9Rc+lS71nQ1shZLcDf/lLz845\ndWrPjhcEQRAEQRAERfF7DpamaVsA/Ieu61+2rD8BQNd1/Zct6xsB/ETX9V1eju0/Mc5NTQzDe+IJ\nipzmZuBXv+LfEyeyH1Nvk5rKQhQGug789Kc9O+fixQzNEwQfkZwJQRDMQuYTQRDMojvzSSCUaU8H\ncM5l/ULLtv5NcTELLxgepOJilhCPi3MXV5Mn954N0dHu62+/3fNzzpjR83MIgiAIgiAIgqKYmqCi\nadpmAKmumwDoAH6o6/r7ZnzGunXrkJmZCQCIj4/HlClTkJOTA8AZx9nX68a2DvcvKoKlrAywWLh+\n4QIsp08DYWHIaTmHJT8fGDDAfR1ATsv192Tdkp/PXKshQ5CzYAHw3HOw7NjRs/PHxgI7dpj2fT71\n1FMBOb7dGu8+Xm9ra1/bA3B8c3NzW3/PfUG/mU/6eD0Q/33JfNJ764E43jKfdL6em5uLx1uqBgeC\nPe2tB+K/LxXnExnvvp1PAjFE8EMAP1Y5RNBisbQOUru8+y6LWRj5Sm+/DRw+DNxyC/DOO879Jk8G\nDhww38b8fAqj8HCGK5rBd7/r6RXrAV36HgMAFexUwUYJ6fGOCmMnNpqHCnaqYKPMJ56oMG6AGnaK\njeahgp3dmU/6SmB9R9f1fS3r2QBeAzALDA3cDGC0t5lKhQmsyzzzDMVUWhrX//d/2bPpmmuAzZv7\n1rbuMHMmsGxZX1shKIzcEAmCYBYynwiCYBYBnYOladoKTdPOAZgN4N8txSyg6/oRAH8HcATABwAe\n7vezVHMzUFkJDBzI9fp6iqvoaODzz537Ge+rwJVX9rUFgiAIgiAIgtDn+E1g6br+T13Xh+i6Hqnr\n+iBd169zee8Xuq6P0nV9nK7rm/xlU2/hGk/qlZISiqfgYK4XFvJ10CD3cL3Ro3vFPgDOPlhmMHky\nEB9v3vla6PR7DBBUsFMFGwXvqDB2YqN5qGCnCjYKnqgybirYKTaahyp2+orfBJbgQlERMHiwc/3C\nBb6mprrvFxbmP5t6gpRlFwRBEARBEAQAfZCD1RP6TYzzP/8JDBkCXHEF119/HTh5ErjpJr5nMGIE\ncPp039jYVbKygNtv72srhH6A5EwIgmAWMp8IgmAWAZ2DJbhQVMRwQIDNfQsLGS5YUeG+X2+Iq6Qk\nZ+8tMxDvlSAIgiAIgiC0IgKrF+gwntRmA8rL2WQYAKqrWfRC04D9+537tQ0XNIuaGiA01JwcrOHD\ngYyMnp+nHVSJy1XBThVsFLyjwtiJjeahgp0q2Ch4osq4qWCn2GgeqtjpKyKw/E1JCb1IIS09nouK\n+HdyMsWWwahRvfP5zc3m9L0KDhbvlSAIgiAIgiC0QXKw/M3evQwJXL6c69u3A1u2ABMmuHuw5s0D\nvviib2zsChkZwH330fMmCCYgOROCIJiFzCeCIJiF5GCpQFGRs7kwwHBBq9UzJNBu969dvhASAlx9\ntYgrQRAEQRAEQWiDCKxeoMN40vJyhgMaGIUt4uLc9yspMd0uV3qUg5WS0nshjC6oEpergp0q2Ch4\nR4WxExvNQwU7VbBR8ESVcVPBTrHRPFSx01dEYPmbykr3przl5XxtaHDf79Qp/9nkC1FR4r0SBEEQ\nBEEQhHaQHCx/4nAA//3fwA9+wDA7hwP42c8oVrKzga++6msLOyctDVi/XgSWYDqSMyEIglnIfCII\ngllIDlagU1NDD5BRQbCqiq8JCe7iavJk/9vWFQYMEO+VIAiCIAiCIHSACKxeoN140qoq7+GBAwa4\n75ee3it2ueJzDlZwMBAZCWRl9Yo93lAlLlcFO1WwUfCOCmMnNpqHCnaqYKPgiSrjpoKdYqN5qGKn\nr4jA8ieVle7FLCoqKFzaFrgIROLjxXslCIIgCIIgCJ0gOVj+5PPP2eh38WKub9rEvlizZrn3vFq6\nFPjoo76x0RsJCQxrfPhhEVhCryE5E4IgmIXMJ4IgmIXkYAU6bUMEDQ9W2xBBM3pgRUX1/BwGYWHi\nvRIEQRAEQRCELiACqxdoN57UW4hgSAgQEeG+n8PRcyPq6zt8u8s5WEOHUvBlZ/fcJh9RJS5XBTtV\nsFHwjgpjJzaahwp2qmCj4Ikq46aCnWKjeahip6+E9LUBlxVte2DV1gK6Ti+WK2YILLNobqb3Kki0\nuCAIgiAIgiB0huRg+QtdZw+s732PIXcA8POfM+zuxhuBd9917jtvnntOVl8xbhxw6RLw0EMSHij0\nOpIzIQiCWch8IgiCWUgOViBTV0dhZYgrm42LrvPVle7kYMXG9tzGtlRUAAsWiLgSBEEQBEEQhC4i\nAqsX8BpP2jY8sKmJrxER9BK5YrznCzU1wLBhXbexsxys6dMprPzY96otqsTlqmCnCjYK3lFh7MRG\n81DBThVsFDxRZdxUsFNsNA9V7PQVEVj+orravcBFYyMFTGgoUFbmvm9HYQahoe2/V1AAjB3LRsU9\n8ToFBQFnzwILF4r3ShAEQRAEQRB8QHKw/MX+/RRAK1ZwvbAQeOklii5NAy5edO47dSr3N4iJYUEM\ngKGANTX8OyrKWS0wLIwFKcxg3jzgzBngvvtEYAl+Q3ImBEEwC5lPBEEwC8nBCmSam535VwA9WMHB\nLNNeV+e+b9scLNeqgq7vjR/vfv6oqJ5X+xs6FPjqK2DRIhFXgiAIgiAIguAjIrB6Aa/xpG0FVlMT\nxVVICNDQ4L6v636Ae08rqxUYPJh/79lDIeS6XxdLvLebgzViBJCQAAwf3qXz9CaqxOWqYKcKNgre\nUWHsxEbzUMFOFWwUPFFl3FSwU2w0D1Xs9BURWP7CanXPn2psdAqstmEFUVHtnycoiCGDBqdOscy7\nGcyZA+zbByxebM75BEEQBEEQBOEyQ3Kw/MWHHzLfas4cru/cSQ9UQgKQl+e+79KlwEcftX+uxERW\nJDx9muuxsexVVV/PioQHDzLMz1euvprH33qr78cKQg+RnAlBEMxC5hNBEMyiO/NJSG8ZI7TBavUM\nETRysNrizYM1YQJw+DD/Dg0Fhgxh9cHqaha9+NWvembf8uXAxx8D99/fs/MIgiAIgiAIwmWMhAj2\nAu3mYLmGCGoaRVdIiKeg8iawXHOiYmPp/br+eiA5GYiO9ty/o3LuaJODFR3NKobjx9M7FiCoEper\ngp0q2Ch4R4WxExvNQwU7VbBR8ESVcVPBTrHRPFSx01fEg+Uv2ha5CAlxerHi4twLWURGeh7/+efO\nv/PygJwc4P33gWXLuK2sjOeorgbOn+drV1m5EnjnHeCRR3y6JEEQBEEQBEEQ3JEcLH/x178Cc+cC\nI0dyffduwGIBMjNZ5OLoUee+3/428Nvfep7jgQeAP/3Jub5mDfDJJ0B5Ob1eRiENX8TVrFnssZWS\nwhwsQegjJGdCEASzkPlEEASzkD5YgYw3D1ZoKEu0p6W572uztX8OV/72N4b3XXUVvWANDb6JKwAY\nOxY4dw648krfjhMEQRAEQRAEwQMRWL1Al/pgGQKrsREYNMh93+pqFrVoy8svAz/+sfu2M2foCTt3\nzjcb8/OdHrBFizrN2eoLVInLVcFOFWwUvKPC2ImN5qGCnSrYKHiiyripYKfYaB6q2OkrIrD8Rds+\nWK5NhgcMcN+3qgrIyPB+nr17gf/6r/Y/Jyena/YkJ1P06TowaVLXjhEEQRAEQRAEoUMkB8tf/O53\nwNe+xv5VAHDiBPDFF0BpKfAf/wH8z/84950+HZgyBfjzn72fa+FCYP58iqOGBnrGrFZ+RtswwvZ4\n7DHmhd18MzBsWM+uTRBMQHImBEEwC5lPBEEwC+mDFciEhbmLn5AQVhA0SrW7sncvcN11nscYfPop\nl9RUlnsvLvbNl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# extract the components of the solution trajectory\n", "t = solution[:, 0]\n", "x_vals = interp_solution[:, 1]\n", "y_vals = interp_solution[:, 2]\n", "z_vals = interp_solution[:, 3]\n", "\n", "# xy phase space projection\n", "fig, axes = plt.subplots(1, 3, figsize=(12, 6), sharex=True, sharey=True, squeeze=False)\n", "axes[0,0].plot(x_vals, y_vals, 'r', alpha=0.5)\n", "axes[0,0].set_xlabel('$x$', fontsize=20, rotation='horizontal')\n", "axes[0,0].set_ylabel('$y$', fontsize=20, rotation='horizontal')\n", "axes[0,0].set_title('$x,y$-plane', fontsize=20)\n", "axes[0,0].grid()\n", "\n", "# xz phase space projection\n", "axes[0,1].plot(x_vals, z_vals , 'b', alpha=0.5)\n", "axes[0,1].set_xlabel('$x$', fontsize=20, rotation='horizontal')\n", "axes[0,1].set_ylabel('$z$', fontsize=20, rotation='horizontal')\n", "axes[0,1].set_title('$x,z$-plane', fontsize=20)\n", "axes[0,1].grid()\n", "\n", "# yz phase space projection\n", "axes[0,2].plot(y_vals, z_vals , 'g', alpha=0.5)\n", "axes[0,2].set_xlabel('$y$', fontsize=20, rotation='horizontal')\n", "axes[0,2].set_ylabel('$z$', fontsize=20, rotation='horizontal')\n", "axes[0,2].set_title('$y,z$-plane', fontsize=20)\n", "axes[0,2].grid()\n", "\n", "plt.suptitle('Phase space projections', x=0.5, y=1.05, fontsize=25)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Step 3: Compute the residuals to assese the accuracy of our solution\n", "\n", "Finally, to assess the accuracy of our solution we need to compute and plot the solution residuals at 10000 evenly spaced points using a 5th order B-spline interpolation." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# compute the residual\n", "ti = np.linspace(0, solution[-1,0], 10000)\n", "residual = lorenz_ivp.compute_residual(solution, ti, k=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we want to confirm that the residuals are \"small\" everywhere. Patterns, if they exists, are not cause for concern." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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w3HPq7zg+COGZfNxyClHoXtxzpQihpbZBOUilktUpSFg8AsJCZC5mk+FOIO4g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\nK82sVpW4+xmEZ+6RikMivDr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QOdYZ0CAowjZ5HcIxPI+TeNGPRZBNY2+dmrkuqctFXBfK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\nQ4V9Jk6cyJw5cyo9tq6DWqNxs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# extract the raw residuals\n", "x_residuals = residual[:, 1]\n", "y_residuals = residual[:, 2]\n", "z_residuals = residual[:, 3]\n", "\n", "# typically, normalize residual by the level of the variable\n", "norm_x_residuals = np.abs(x_residuals) / x_vals\n", "norm_y_residuals = np.abs(y_residuals) / y_vals\n", "norm_z_residuals = np.abs(z_residuals) / z_vals\n", "\n", "# create the plot\n", "fig = plt.figure(figsize=(8, 6))\n", "plt.plot(ti, norm_x_residuals, 'r-', label='$x(t)$', alpha=0.5)\n", "plt.plot(ti, norm_y_residuals, 'b-', label='$y(t)$', alpha=0.5)\n", "plt.plot(ti, norm_z_residuals, 'g-', label='$z(t)$', alpha=0.5)\n", "plt.axhline(np.finfo('float').eps, linestyle='dashed', color='k', label='Machine eps')\n", "plt.xlabel('Time', fontsize=15)\n", "plt.ylim(1e-16, 1)\n", "plt.ylabel('Residuals', fontsize=15)\n", "plt.yscale('log')\n", "plt.title('Lorenz equations residuals', fontsize=20)\n", "plt.grid()\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()" ] }, { "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": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }