{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# *Numeric Methods for Economists:* Introduction to Dynamic Programming\n", "\n", "Dynamic programming is a fundamental tool of economic analysis. The objective of this lab is to show you how to solve, via numerical dynamic programming, a textbook dynamic stochastic general equilibrium (DSGE) model of optimal consumption/savings. For those interested in learning more about numerical dynamic programming, I suggest starting with John Stachurski and Thomas Sargent's excellent set of [Python-based online lecture notes](http://quant-econ.net/). The lecture notes are also available as a [PDF](http://quant-econ.net/_static/pdfs/quant-econ.pdf). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# A model of optimal consumption/savings\n", "\n", "In this section I fully specify the decision problems faced by firms and households in a stochastic optimal savings with both inelastic labor supply. I begin by deriving the equilibrium conditions and the dynamic programming formulation of a model where the only choice variable for the household is consumption. \n", "\n", "## Firm behavior\n", "There are a large number of firms, each with access to an identical constant returns to scale, CES production technology.\n", "\n", "$$y_t = f(k_t, l_t, z_t) = e^{z_t}\\bigg(\\alpha k_t^{\\rho} + (1 - \\alpha)l_t^{\\rho}\\bigg)^{\\frac{1}{\\rho}} \\tag{1.1}$$\n", "\n", "where $0 < \\alpha < 1$ and $\\rho = \\frac{\\sigma - 1}{\\sigma}$. Recall that $f_k > 0$, $f_{kk} < 0$, and that $f$ satisfies the usual Inada conditions. Total factor productivity shocks, $z_t$, follow a standard AR(1) process.\n", "\n", "$$z_t = \\rho z_{t-1} + \\epsilon_t,\\ \\epsilon \\sim N(0, \\sigma) \\tag{1.2}$$\n", "\n", "All markets (i.e., for both factors of production and the final output good) are competitive and therefore capital and labor earn their respective marginal products, and firms earn zero profits. \n", "\\begin{align}\n", "r_t =& \\alpha e^{z_t} k_t^{\\rho - 1}\\bigg(\\alpha k_t^{\\rho} + (1 - \\alpha)l_t^{\\rho}\\bigg)^{\\frac{1}{\\rho}-1} = \\left(\\frac{\\alpha k_t^{\\rho-1}}{\\alpha k_t^{\\rho} + (1 - \\alpha)l_t^{\\rho}}\\right)f(k_t,l_t,z_t) \\tag{1.3}\\\\\n", "w_t =& (1 - \\alpha) e^{z_t} l_t^{\\rho-1}\\bigg(\\alpha k_t^{\\rho} + (1 - \\alpha)l_t^{\\rho}\\bigg)^{\\frac{1}{\\rho}-1} = \\left(\\frac{(1-\\alpha) l_t^{\\rho-1}}{\\alpha k_t^{\\rho} + (1 - \\alpha)l_t^{\\rho}}\\right)f(k_t,l_t,z_t) \\tag{1.4}\\\\\n", "y_t =& r_tk_t + w_tl_t \\tag{1.5}\n", "\\end{align} \n", "\n", "## Household behavior\n", "There are a large number of identical households with constant relative risk aversion (CRRA) preferences: \n", "\n", "$$u(c_t) = \\frac{c_t^{1-\\theta} - 1}{1 - \\theta} \\tag{1.6}$$\n", "\n", "where the parameter $0<\\theta$ is the coefficient of relative risk aversion. The representative household's objective is to choose an infinite consumption sequence, $\\{c_t\\}_{t=0}^{\\infty}$, in order to \n", "\n", "$$\\max \\ E\\left\\{\\sum_{t=0}^{\\infty} \\beta^t u(c_t)\\right\\} \\tag{1.7}$$\n", "\n", "subject to the following constraints:\n", "\n", "\\begin{align}\n", "c_t + i_t =& w_tl_t + r_t k_t \\tag{1.8}\\\\\n", "k_{t+1} =& (1-\\delta)k_t + i_t \\tag{1.9} \n", "\\end{align}\n", "\n", "where $0 < \\beta < 1$ is the discount factor.\n", "\n", "The representative household is endowed with a single unit of labor which we assume it supplies inelastically to firms (i.e., we assume that household chooses $l_t=1$ regardless of the real wage). The first order necessary condition for the household's decision problem is the consumption Euler equation\n", "\n", "$$c_t^{-\\theta} = \\beta E\\left\\{(1 + r_{t+1} - \\delta)c_{t+1}^{-\\theta} | z_t\\right\\} \\tag{1.8}$$\n", "\n", "which, together with the budget constraint\n", "\n", "$$c_t + k_{t+1} = w_t + (1 + r_t - \\delta)k_t \\tag{1.9}$$\n", "\n", "completely specifies the the behavior of the representative household.\n", "\n", "## General Equilibrium\n", "Equations 1.3, 1.4, 1.5, 1.8, and 1.9 reduce to a system of two non-linear equations in two unknowns, $k$ and $c$ that describe the equilibrium of the model.\n", "\n", "\\begin{align}\n", "c_t^{-\\theta} =& \\beta E\\left\\{\\left(1 + \\alpha e^{z_{t+1}}k_{t+1}^{\\rho-1}\\bigg(\\alpha k_{t+1}^{\\rho} + (1 - \\alpha)\\bigg)^{\\frac{1}{\\rho}-1} - \\delta\\right)c_{t+1}^{-\\theta} \\bigg| z_t\\right\\} \\tag{1.10}\\\\\n", "k_{t+1} =& (1 - \\delta)k_t + e^{z_{t+1}}\\bigg(\\alpha k_{t+1}^{\\rho} + (1 - \\alpha)\\bigg)^{\\frac{1}{\\rho}} - c_t \\tag{1.11}\n", "\\end{align} \n", " \n", "\n", "## Dynamic programming specification\n", "The stochastic optimal savings model with inelastic labor supply can be formulated as a simple dynamic programming problem with capital, $k$, and productivity $z$ as the only state variables. The most natural control variable is, perhaps, $c$. \n", "\n", "\\begin{align} \n", "V(k, z) =& \\max_{c\\in \\Gamma(k, z)}\\ \\frac{c^{1-\\theta}-1}{1-\\theta} + \\beta E\\bigg\\{V(k', z') \\bigg| z\\bigg\\} \\tag{1.13}\\\\\n", "\\Gamma(k, z) =& (1 - \\delta)k + f(k, z) \\tag{1.14} \\\\\n", "k' =& (1 - \\delta)k + f(k, z) - c \\tag{1.15}\\\\\n", "z' =& \\rho_z z + \\epsilon',\\ \\epsilon \\sim N(0, \\sigma_z) \\tag{1.16}\\\\\n", "\\end{align}\n", "\n", "Equation 1.13 is the familiar Bellman equation. Equation 1.14 defines the set of feasible values of the control (in this case consumption) as a function of the current states. **Note that this definition of $\\Gamma(k,z)$ assumes that capital can be \"eaten\".** Equations 1.15 and 1.16 are the equations of motion for capital and the productivity shock, respectively.\n", "\n", "We are going to replace 1.13 with \n", "\n", "$$W(k, z) = \\max_{c \\in \\Gamma(k, z)}\\ (1-\\beta)\\frac{c^{1-\\theta}-1}{1-\\theta} + \\beta E\\bigg\\{W(k', z') \\bigg| z\\bigg\\}. \\tag{1.13b}$$\n", "\n", "Why? Note that the current value, $W(k,z)$, is now a convex combination of the flow payoff, $u(c)$, and the expected future value (conditional on the current productivity shock!), $E\\bigg\\{W(k', z') \\bigg| z\\bigg\\}$. Transforming the value function in this manner makes the computation of the value function more numerically stable and efficient. **This transformation, which is really just a rescaling of utility by a positive constant, will not impact the optimal policy function in any way**.\n", "\n", "The optimal policy function $c(k, z)$ obeys the following first order necessary condition for optimality. \n", "\n", "$$0 = (1 - \\beta)c(k, z)^{-\\theta} - \\beta E\\left\\{W'(k', z') \\bigg| z\\right\\} \\tag{1.17}$$\n", "\n", "The envelope theorem applied to equation 1.14b yields \n", "\n", "$$W'(k, z) = \\beta\\left(1 + \\alpha e^{z}k^{\\rho-1}\\bigg(\\alpha k^{\\rho} + (1 - \\alpha)\\bigg)^{\\frac{1}{\\rho}-1} - \\delta\\right)E\\left\\{W'(k', z') \\bigg| z\\right\\} \\tag{1.18}$$\n", "\n", "which together with equation 1.17 implies that\n", "\n", "$$(1-\\beta)c(k, z)^{-\\theta}\\left(1 + \\alpha e^{z}k^{\\rho-1}\\bigg(\\alpha k^{\\rho} + (1 - \\alpha)\\bigg)^{\\frac{1}{\\rho}-1} - \\delta\\right) = W'(k, z). \\tag{1.19}$$\n", "\n", "Thus the solution to the dynamic programming problem specified in equations 1.13b through 1.16 is a policy function, $c(k, z)$, and a value function, $W(k, z)$, that jointly satisfy equations 1.19 and \n", "\n", "$$W(k, z) = (1-\\beta)\\frac{c(k, z)^{1-\\theta}-1}{1-\\theta} + \\beta E\\left\\{W\\bigg((1-\\delta)k + e^{z}\\bigg(\\alpha k^{\\rho} + (1 - \\alpha)\\bigg)^{\\frac{1}{\\rho}} - c(k, z), \\rho_z z + \\epsilon')\\right\\}. \\tag{1.20}$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from scipy import interpolate, optimize, stats" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise:\n", "\n", "Using alpha, sigma, delta, theta, and rho_z as parameters, fill in the blanks in the code below in order to define Python functions for equations 1.1, 1.2, 1.3, 1.6, 1.11, and 1.14. Confirm that your functions are correct before moving forward!" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# equation 1.1\n", "def ces_output(k, z=0.0):\n", " \"\"\"\n", " Output is generated by a CES production function. Note that output is a \n", " function of state variables (i.e., capital and possibly a productivity shock).\n", " \n", " Arguments:\n", " \n", " k: (array) Current value of capital. Inherited from previous period!\n", " z: (array) Current value of the productivity shock.\n", " \n", " Returns:\n", " \n", " y: (array) Output produced from k and z\n", " \n", " \"\"\"\n", " rho = (sigma - 1) / sigma\n", " \n", " # nest Cobb-Douglas output as special case\n", " if rho == 0:\n", " y = np.exp(z) * k**alpha\n", " else:\n", " y = np.exp(z) * (alpha * k**rho + (1 - alpha))**(1 / rho)\n", " \n", " return y\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "2.4999995181380563" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# confirm that ces_output is functioning correctly...\n", "alpha = 0.5\n", "sigma = 1e6\n", "ces_output(4, 0)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# equation 1.2\n", "def productivity_motion(z, eps):\n", " \"\"\"\n", " Equation of motion for total factor productivity.\n", " \n", " Arguments:\n", " \n", " z: (array) Current value of the total factor productivity.\n", " eps: (array) Productivity shock.\n", " \n", " Returns:\n", " \n", " zplus: (array) Next period's value of capital.\n", " \n", " \"\"\"\n", " zplus = rho_z * z + eps\n", " return zplus" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.95" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# confirm that productivity_motion is functioning correctly...\n", "rho_z = 0.95\n", "productivity_motion(1, 0)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# equation 1.3\n", "def ces_mpk(k, z=0.0):\n", " \"\"\"\n", " Marginal product of capital for the CES production function.\n", " \n", " Arguments:\n", " \n", " k: (array) Current value of capital. Inherited from previous period!\n", " z: (array) Current value of the productivity shock.\n", " \n", " Returns:\n", " \n", " mpk: (array) Output produced from k.\n", " \n", " \"\"\"\n", " rho = (sigma - 1) / sigma\n", " \n", " # nest Cobb-Douglas output as special case\n", " if rho == 0:\n", " mpk = alpha * (ces_output(k, z) / k)\n", " else:\n", " mpk = (alpha * k**(rho - 1) / (alpha * k**rho + (1 - alpha))) * ces_output(k, z)\n", " \n", " return mpk" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.49999976499814425" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# confirm that ces_mpk is functioning correctly...\n", "alpha = 0.5\n", "sigma = 1e6\n", "ces_mpk(4, 0)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# equation 1.6\n", "def crra_utility(c):\n", " \"\"\"\n", " Agent has CRRA preferences over consumption. Function makes use of np.log \n", " and np.exp functions which are optimized for array arguments.\n", "\n", " Arguments:\n", " \n", " c: (array) Current value of consumption.\n", " \n", " Returns: (array-like) \n", " \n", " utility: (array) Utility from consumption.\n", " \n", " \"\"\"\n", " # nest log utility as a special case\n", " if theta == 1:\n", " utility = np.log(c) \n", " else:\n", " utility = (c**(1 - theta) - 1) / (1 - theta)\n", " \n", " return utility" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "2.9999974548238537" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# confirm that crra_utility is working!\n", "theta = 1e-6\n", "crra_utility(4.0)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# equation 1.11\n", "def capital_motion(k, z, c):\n", " \"\"\"\n", " Equation of motion for capital.\n", " \n", " Arguments:\n", " \n", " k: (array) Current value of capital. Inherited from previous period!\n", " z: (array) Current value of the productivity shock.\n", " c: (array) Current value of consumption.\n", " \n", " Returns:\n", " \n", " kplus: (array) Next period's value of capital.\n", " \n", " \"\"\"\n", " kplus = ces_output(k, z) + (1 - delta) * k - c\n", " return kplus" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# confirm that capital_motion is functioning correctly...\n", "alpha = 0.5\n", "sigma = 1e0\n", "delta = 1.0\n", "capital_motion(4, 0, 1)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# equation 1.14\n", "def Gamma(k, z=0.0):\n", " \"\"\"\n", " The correspondence of feasible controls given current state.\n", "\n", " Arguments:\n", " \n", " k: (array) Current value of capital. Inherited from previous period!\n", " z: (array) Current value of the productivity shock.\n", " \n", " Returns: \n", " \n", " c_upper: (scalar) The upper bound on the correspondence of feasible \n", " controls given current state.\n", " \n", " \"\"\"\n", " # note that we are allowing capital to be eaten!\n", " c_upper = ces_output(k, z) + (1 - delta) * k\n", " return c_upper" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "2.4999995181380563" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# confirm that Gamma is working\n", "alpha = 0.5\n", "sigma = 1e6\n", "delta = 1.0\n", "Gamma(4, 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Solving the model:\n", "\n", "From above, our objective is to find functions $c(k,z)$ and $W(k, z)$ that jointly solve the following system of functional equations.\n", "\n", "\\begin{align}\n", "W'(k, z) =& (1-\\beta)c(k, z)^{-\\theta}\\left(1 + \\alpha e^{z}k^{\\rho-1}\\bigg(\\alpha k^{\\rho} + (1 - \\alpha)\\bigg)^{\\frac{1}{\\rho}-1} - \\delta\\right) \\\\\n", "W(k, z) =& (1-\\beta)\\frac{c(k, z)^{1-\\theta}-1}{1-\\theta} + \\beta E\\left\\{W\\bigg((1-\\delta)k + e^{z}\\bigg(\\alpha k^{\\rho} + (1 - \\alpha)\\bigg)^{\\frac{1}{\\rho}} - c(k, z), \\rho_z z + \\epsilon')\\right\\}\n", "\\end{align}\n", "\n", "The *key* theorem in infinite horizon dynamic programming is the contraction mapping theorem applied to the Bellman equation. First, a couple of definitions:\n", "\n", "* A **map** $T:Y \\rightarrow Z\\$ on ordered spaces $Y$ and $Z$ is **monotone** if and only if $y_1 \\ge y_2 \\implies Ty_1 \\ge Ty_2$.\n", "* A **map** $T:Y \\rightarrow Y\\$ on a metric space $Y$ is a **contraction mapping** with modulus $\\beta \\lt 1$ if and only if $||Ty_1 - Ty_2|| \\le \\beta||y_1 - y_2||.$\n", "\n", "**Theorem:** If $X$ is compact (i.e., closed and bounded), $\\beta \\lt 1$, and $u$ is bounded, then the map\n", "\n", "$$TW = \\max_{c \\in \\Gamma(k, z)} (1-\\beta)u(c) + \\beta E\\left\\{W(k', z')| z\\right\\}$$\n", "\n", "is monotone in $W$, and is a contraction mapping with modulus $\\beta$ in the space of bounded functions, and has a *unique* fixed point.\n", "\n", "Although the assumption of boundedness and compactness of the state space required for the theorem to hold seem restrictive, they are not! We care only about **numerically feasible** dynamic programming problems which in general can examine only compact state spaces. The contraction mapping theorem tells us how to constuct an operator, $T$, that transforms a value function into another value function and that repeated application of this operator generates a sequence of functions that eventually converges to a unique fixed point (i.e., the \"optimal\" value function)!\n", "\n", "Before I explain the basic algorithm that we will use to solve for the value function and its implied optimal policy, we need to define a couple of maps. The map $T$, which is called the Bellman operator, takes next period's value function, $V^+$, and maps it into the current value function, $W$ and is defined by\n", "\n", "$$W = \\max_{c\\in\\Gamma(k, z)} (1-\\beta)u(c) + \\beta E\\left\\{W^+(k', z')| z\\right\\} \\equiv TW^+.$$ \n", "\n", "We also need to define the map $\\mathcal{U}$, called the \"greedy\" operator, which maps next period's value function into the current policy function, $U$:\n", "\n", "$$U = \\arg \\max_{c\\in\\Gamma(k, z)} (1-\\beta)u(c) + \\beta E\\left\\{W^+(k', z')| z\\right\\} \\equiv \\mathcal{U}W^+.$$ \n", "\n", "## Value function iteration\n", "\n", "The most basic numerical procedure for computing $W^*$ is called *value function iteration* is directly motivated by the contraction mapping properties of the Bellman equation. Specifically, value function iteration computes a sequence of functions\n", "\n", "$$W^{l+1} = TW^l,\\ l=0, 1, 2, \\dots .$$\n", "\n", "The contraction mapping theorem tells us that the sequence $W^l$ will converge to the infinite-horizon value function for *any* initial guess $W^0$. Additionally, the contraction mapping theorem implies that the sequence of policy functions, $U^l$, as defined by \n", "\n", "$$U^{l+1} = \\mathcal{U}U^l\\ l=0, 1, 2, \\dots$$ \n", "\n", "will also converge to the optimal policy function. In theory, convergence is achieved only asymptotically. In practice, we will just iterate the operator $T$ until successive value functions change very little (and/or successive policy functions do not change). Below is some pseudo-code for computing the function, $W$, using value function iteration.\n", "\n", " while True:\n", " # apply the Bellman operator, T\n", " next_w = T(current_w, **kwargs)\n", " \n", " # compare successive iterates using some distance metric\n", " change = np.max(np.abs(next_w(pts) - current_w(pts)))\n", " n_iter += 1\n", " \n", " # check for convergence\n", " if change < tol:\n", " if mesg == True:\n", " print \"After\", n_iter, \"iterations, the final change is\", change\n", " final_w = next_w\n", " break\n", " \n", " current_w = next_w\n", " \n", "Once the code above terminates, we can compute the optimal policy by applying the map $\\mathcal{U}$ to final_w. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Approximation of value and policy functions\n", "\n", "In order to implement value function iteration, we need to first choose a method for representing the functions used to approximate successive value and policy function iterates on the computer. Two widely used function approximation schemes are linear interpolation and cubic spline interpolation. " ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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p0yb+/vtv5syZw6BBg/LtswuRr+Li4MwZ9MFBRB47SGLgP9ievYhNeDRXPawI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\n6+IuOtfpnOWlEREQEAD16jkwn4iIiJ0KTid87BgkJxP1+Bk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# grid of values to use as interpolation nodes\n", "xgrid = np.linspace(0, 5, 5)\n", "\n", "# values of the function we wish to approximate at the interpolation nodes\n", "vals = 1 - np.exp(-xgrid)\n", "\n", "# both spline interpolation nests linear interpolation as a special case\n", "linear_interp = interpolate.UnivariateSpline(xgrid, vals, k=1, s=0)\n", "cubic_interp = interpolate.UnivariateSpline(xgrid, vals, k=3, s=0)\n", "\n", "# plot the approximating functions as well as the true function\n", "plt.figure(figsize=(8,6))\n", "plot_grid = np.linspace(0, 5, 1000)\n", "plt.plot(plot_grid, linear_interp(plot_grid), 'b', label='Linear')\n", "plt.plot(plot_grid, cubic_interp(plot_grid), 'g', label='Cubic')\n", "plt.plot(plot_grid, 1 - np.exp(-plot_grid), 'r', label='Analytic')\n", "\n", "# axes, labels, title, etc\n", "plt.xlabel('$x$', fontsize=20)\n", "plt.title('Linear vs Cubic spline interpolation', fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False, prop={'family':'serif'})\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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TeHh4OLp166aQlAcPHowjR44o7GdpaQkrKytIpdJSZxK0sbHB0KFDkZaWppAYAV4LUNwX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\nIesa+dy51nKp3bubTgkACEYspRoE3G5rudWTJ6XrrrPKvFM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# compute the residuals\n", "linear_resid = linear_interp(plot_grid) - (1 - np.exp(-plot_grid))\n", "cubic_resid = cubic_interp(plot_grid) - (1 - np.exp(-plot_grid))\n", "\n", "# plot the residuals\n", "plt.figure(figsize=(8,6))\n", "plt.plot(plot_grid, linear_resid, 'b', label='Linear')\n", "plt.plot(plot_grid, cubic_resid, 'g', label='Cubic')\n", "plt.axhline(0, ls='dashed', color='k')\n", "\n", "# axes, labels, title, etc\n", "plt.xlabel('$x$', fontsize=20)\n", "plt.title('Approximation residuals', fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False, prop={'family':'serif'})\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Ybt3Q0FDcv39fmNL0c4yNjXH58uXaEr3SsBE2g8FgMOo1fD4fM2fOxLfffosO\nHToAAJo0aQI/Pz+4uLhIJNW1urp6jduoKUxhMxgMBqNek5iYiDt37qBfv35ljp04cQJnz56Fnp4e\nFi5cCABYsGCBWBP4ixcv0LdvX9jZ2WHDhg1CU3rv3r3B4/Hw7NkzAPQDYc+ePejbty9sbW3h6+uL\npKSkWr5KZhJnMBgMRj3n8ePHAIBWrVqVOaaoqIjZs2cjPj5eaPJeuHAhoqOjRUzghBAcOnQIJ0+e\nBI/HQ79+/cDj8TBt2jScPXsWPN7H8e2uXbsQEhKCY8eOQVNTE2PGjEF0dDRMTExq9TrZCJvBYDAY\njYKKTOMcx6F3797Q0tKChoYGfHx88N9//4ktu3//fvTv3x9aWlrgOA7Lly+Hi4tLbYktpM5H2IcP\nH8bx48dRUlKCqVOnwtHRsa5FYDAYDEYtwC0U77RVVciCqs05t2vXDgCQlpaGNm3aVPu87du3F/n/\nypUrxZa7cOECxo0bJ/y7devW1T5nVahzhT1w4EAMHDgQr169woIFC5jCZjAYjAZCVRWtpGjXrh06\ndeqEo0ePYtasWcL9fD4fo0ePxuLFi6GmpoacnBzhMYEZ/VMePHgg8v+uXbuKPV/Pnj2RkJCAgQMH\nAgAyMzPx/v17GBgYSOqSxFJtk/j48eOhq6sLa2trkf3R0dGwsLBA27ZtsX79+nLrBwcHY8qUKdU9\nPYPBYDAYAKg5OzQ0FOvWrcPdu3cBAB8+fMDy5cuhrKwMMzMzdO3aFbdu3QKfz8fVq1eRlZUlYiIn\nhODUqVPIzs5GTk4Ojh8/Dm9vb5HzCMoPHToUx44dQ3Z2NgghmD59OrKysmr/Okk1/d0vXLgAVVVV\njBs3DvHx8cL9dnZ2WLt2LYyMjNCnTx9cvHgRJ06cwI0bNzBnzhzo6elh7ty56NOnD3r37i1eKI6T\niBt+XUAIUFgI5ObSrbAQKC39uHEcoKxMNxUVuqmr0/0MBoPBkBx37tzB3LlzUVBQAEVFRfTs2RPT\np0+HhoYGsrOzMXPmTCQkJMDT0xOXL1/Gy5cvsXLlShw7dgy7du3C9OnTcenSJWRlZWHixImYOnUq\nmjRpgt69eyMyMhJdunTBvn370LJlS+zbtw9//fUXSktL0b9/fwQGBtZI9srovWorbIBmf+nfv79Q\nYefl5cHV1RU3b94EAAQGBqJPnz7w8fER1lm3bh22b98OBwcH2Nraih1ly5rCfvMGuHsXiI8Hnj4F\nUlKAZ88nekJYAAAgAElEQVTo9vo1LaOlBWhqAoqKgJzcx40QoKAAePeO/vv2LVBUBOjqAi1b0q11\na6BtW7q1aweYmgLy8tK9ZgaDwWDUHZXRexKdw46Li4O5ubnwb0tLS8TGxooo7MDAwBp/idQmfD5V\nzhcu0O3KFeDVK8DSErC2pkq1Y0fAyAgwMKCKV1GxaucoLARevqRbRgaQmgo8egScOwc8fEj/btMG\n6NSJbp07038VFGrnmhkMBoMh+8hsHLarqyuMjY1hbGwMV1dXuLq61tq53r0DTp8GDh8Gjh0DmjUD\nnJ2Bvn2BRYsAMzM6WpYUiopU4RsZiT9eXAzcuwdcvw5cuwZs3w4kJgKOjoCbG926dAGayOzdYzAY\nDEZFREZGIjIyEsnJyUhOTq5UnVo1ic+YMQNeXl4iI+xKCVUHJnFCgOhoYOtWqqgdHIBBg4ABAwBD\nw1o9dbV484aO+M+do1tqKtCvH5XZ05POkTMYDAajflIZvSfRxCkaGhoAqKd4cnIyzpw5gy5dukjy\nFDWmsBDYuBFo3x6YNg2wtQUePwYiIoDp02VTWQPUUc3HB1i1Crh5E7hxg5rKN2wAWrUC/P2BqChq\n0mcwGAxGw6PaI+yRI0ciKioKWVlZ0NHRwaJFixAQEICoqChMnToVHz58qPZ8dW2MsIuKgJAQYOVK\nwN4emDsX6NGjYXhrv3wJ7NwJhIVR8/6UKcDkydQRjsFgMBiyT617idcWklTYhABHjgDffQdYWACL\nFwM2NhJpWuYghM57r18PHD0KjBkDzJ4NGBtLWzIGg8FgVESjV9gZGcCkSTQUa/VqOtfbWEhLo+by\nP/8EfH2B+fMBPT1pS8VgMBgMcdT5HLYscfgwnZ+2taVzvo1JWQN0Xvv334EHDwAlJaBDB2DePBoL\nzmAwGIz6R4MbYfP5NBQrLAzYvRtwcpKwcPWU58+BH34ALl+mJnMxy8YyGAwGQ0o0OpN4YSEwdizw\n4gVw8CBNasIQJSKCesc7OAChocD/HPsZDAaDIUUalUn8/XsakwwA588zZV0e7u7ArVtUUdvaApcu\nSVsiBoPBYFSGBjHC/vCBmnibNwe2bWMZwCrLkSM0/GvePBqD3hBC3BgMBqM+0ihM4oQA48cDWVnA\ngQNMWVeVpCSa3a17dzq33bSptCViMBiMxkejMIkHB9PFOv79lynr6mBiAsTE0FSnw4bRBDMMBoPB\nkD3q9Qg7JgYYPJgmC9HXrwPBGjDFxcDo0UB+PrVUsNzkDAaDUXc06BF2bi5VMH/+yZS1JJCXp1aK\n5s2BoUOpXwCDwWAwZId6O8KeNg0oLQU2baojoRoJJSXU2755cxrLzhzRGAwGo/ZpsE5ncXHUUSoh\ngS1wURu8e0fX3B48GPjpJ2lLw2AwGA2fBqmwCQGcnYGJE+mSkoza4flzmlxl506gVy9pS8NgMBgN\nmwY5h33qFJCTQzOaMWoPfX3g77+pn8CrV9KWhsFgMBj1aoRNCNClCzBnDg1BYtQ+c+cCyck0LzuD\nwWAwaocGZxK/cIEul5mQAPDqnW2gfvL+PU1hunQpMGSItKWRDHw+8PIlNftnZ9OIg9xcIC+POt2V\nltIyfD4gJweoqHzc1NQAHR2gZUu6sfA3BoMhCRqcwh4xAujWDQgMlIJQjZiLF+ma2omJgKqqtKWp\nPG/fAnfuAPHxdEtIAFJSqKLW1KRmf21t+n9NTUBdnYa38XhUUfN4VIG/e/dxe/OGThFkZNBNQQEw\nMgLatQPatqX/tm8P2NhQBc9gMBiVoUEp7PR0wNKSmmfZClN1z6hRVBkFBUlbkvJ58wY4dw6IjqbW\nmIQE+puxtqablRXN7KavT9cIrymE0JF5Sgrw8OHHLSGBbiYmQOfO1HnPxYWen1mGGAyGOBqUwl65\nEnjwANiyRUpCNXKSk4FOnWgaWD09aUvzkVevgH376EImMTF0/XNXVxpJ4OAAKCpKR67iYuDePeDa\nNeDKFSAykn5QuLkBvXvTxWpatZKObAwGQ/ZoUAq7Sxfgt98AT08pCcVAYCBVgMuXS1eOkhIaLbB1\nKx1R9+tHk7306UPnmGWVZ8/o0q+nTwMnTlCLxaBB1IHSzEza0jEYDGnSYBR2Sgod3aWns9WkpElK\nCmBnBzx5Ip2ENYWFdPnU5ctpJraJE+ncurp63ctSUz58oKPugwephcDCguYVGDasfvkJMBgMydBg\n4rD376cjEaaspYuREdC/P/DHH3V73tJSOhViZgYcPUqV9pUrNGKgPiprgP6WPTyA0FDqBDdzJlXe\nBgbUkvH0qbQlZDAYska9UNhHjlCFzZA+M2YAmzfTkKe6IDqaWle2bQMOHwaOHQN69Kibc9cV8vI0\nDeyRI9RHQEUFcHQEvvoKuHVL2tIxGAxZQeZN4gUFNO41I6NuTIWEEOQV5eHFmxd4U/QG+cX5eFv8\nFh9KP0COJwc5Tg5NeE2gqaiJZkrNhJtCE4XaF04GIISaxVeuBNzda+88BQXAjz/SpT7/7/+oqbgx\nLUTy9i21KgQHUye6RYto2BiDwWiYVMYk3qSOZKk2ly7RxB21oaxzC3MR+zwWtzJu4VbGLdx7fQ8p\nuSkgINBX14eGggbUFNSgJq+GJrwmKCWlKOWXooRfgryiPGS/z0b2+2xkFWRBS0kLJpomMNEygYmm\nCaxaWKGjbkeYNzdHU7mGY8vnOGqK3rKl9hR2QgJN0tKpE42fbowLvKiqUjP5xInA2rVA167AmDFU\ncdfXaQAGg1EzZH6E/dNPdL5v0SLJtH3/9X3svrcbp56cwt1Xd9G5VWfYt7SHbUtbWOtaw1jTGBoK\nGuCqMJzjEz4y3mYgKScJybnJeJLzBHdf3cWdl3eQkpeC9trt4aTvhB6GPdDdoDuMNY2r1L6skZMD\nGBsDL15I/kPq6FFgwgRgxQrAz0+ybddnMjNpmthTp4DVq6m5vB7/hBgMxmc0CC/xXr1o7vC+favf\n3rvidwi/FY6wW2FIy0/DiA4j4N3WGz0Me0CxSe0G6hZ8KED8y3hcfn4Zl1Iv4eKzi+BxPLibuqNv\nm77wMPWAtrJ2rcpQG3h5AePHA8OHS67N0FDg99+pk2GXLpJrtyFx8SIweTKdlggNZUmEGIyGQr1X\n2Hw+NYc+eULDeKpKflE+Vl1ehdC4UDgbOWNqp6noZdILcjw5yQtdSQgheJLzBKefnMaJxycQlRwF\nKx0rDDYfjOFWw2GsaSw12arC5s1ARITkFgVZtQoICQHOnqUZwhjlU1AAfPcdHW3v3EnN5QwGo35T\n7xV2YiIdySUlVa0+n/ARfisc88/Nh7upO37p+Qvaasumx05RSRGiUqKwP2E/Djw4AFMtUwy3HI5R\n1qOgpyZDKcU+Iz2dptp89QpoUkNPiM2bgWXLaFyygYFExGsUHDpER9vLl7O14RmM+k69V9g7d9KX\n0t69la/7/M1z+B/yR35xPtb3XQ/H1o61J6iE+VD6AZHJkdh1dxcOPDgAV2NXTLSbCK82XlK1CpSH\ntTVVtk5O1W/jv//onHV0NPOCrg7379PY+KFD6YpqLFc5g1E/qfeJU+LjqYd4ZTmXdA6d/uwEV2NX\nXBp/qV4pawBoKtcUHmYe2DpwK57NfAaftj74Lfo3GK81xtILS5H9PlvaIorg6QmcOVP9+k+e0JHh\ngQNMWVcXCwuaRObCBWDKlLqLj2cwGHWPVBT2u3fv4ODggOPHj1dYLjGRLlVYGbbc2IJR+0dh19Bd\nmN9zPprwZD5irULUFNQw0X4iYifG4tjIY0jMSkSbdW0QeCIQT3NkIw1Wr17UjF0diovpcqnz57M5\n2JqirU3nsx8+BAICaGY4BoPR8JCKwl6+fDl8fX2/WC4xkS6Q8CVC40KxOHoxLo6/CDcTNwlIKFvY\ntLRB+KBwxH8dD+WmynDc7IhxB8dJXXE7OQFxcdVTEL/+Slf9mjFD8nI1RtTU6IIiqam0T2VvoovB\nYNSUaivs8ePHQ1dXF9bW1iL7o6OjYWFhgbZt22L9+vVl6p05cwaWlpZo0aJFhe2XlNB8yl8ylYbd\nDEPwpWCc9zuPNs3aVPk66hOt1VtjmfsyPP32Kcy0zOC42RFTjk5Bal6qVOTR1qZKNyGhavXi44G/\n/qLz3yyWWHIoK1Ofj5gY6sTHYDAaFtVW2AEBATh58mSZ/d9++y02bdqEiIgIhISEIDMzEzt27MCs\nWbOQlpaGqKgoxMbG4p9//sHmzZvLnWRPTgZatgSUlMqX4dKzS5gbMRenx5yGiVbjiQVSV1DHAtcF\nSJyeiGZKzWC3yQ5BkUEo+FBQ57I4OQGxsZUvTwjw9dd0qVRd3dqTq7Girk4d+UJDad51BoPRgCA1\nICkpiXTo0EH4d25uLrG1tRX+PWPGDHLs2DGxdcPDw8nx48fFHgNAjh8nxNOz/HO/ePOCtFrVihx/\nKL6NxkRKbgrx3etLDFcbkr339hI+n19n516/npDJkytf/tAhQjp2JKS0tPZkYhBy6RIhOjqEPH0q\nbUkYDEZlqIw6lugcdlxcHMzNzYV/W1paIrac4Zefnx+8vb3LbSslhaa/FAchBJOOTsJEu4nwblt+\nG40FQw1D7PpqF7YP2o7fon9D35198SzvWZ2cu0MH4N69ypXl84FffgEWL2bhR7VNt2508ZQRI+j0\nEoPBqP/I7Gtz2TJXXLnij6CgIER+5oq8484OvHjzAvN7zpeOcDKKi7ELrk26BmdDZ3T6sxM2Xdv0\nxbi+mmJlRRV2ZU5z6BCd4ujXr1ZFYvyPmTPpUp1r10pbEgaD8TmRkZEICgqCv78/XF1dK1WnRolT\nkpOT0b9/f8THxwMA8vLy4Orqips3bwIAZsyYAS8vL/j4+FSpXY7jMHEiQefONLb0U/KL8tF+Q3sc\nGXkEnVt1rq7oDZ57r+4h4HAAmik1w/bB26GjolNr59LRoes2t2pVcTkXF+CbbySbf5xRMY8fUz+D\nK1cAMzNpS1N9CAGysoBnz6gn/LNnNNtebi7d8vLokqR8Po1a4PPppqhIP1pUVOhCNRoa1DdGT+/j\nZmpaN0v3MhgVUefLa2r8byWC6OhoGBoa4syZM1iwYEG12kpPpw/T56yMWYnepr2Zsv4CVjpWiJkQ\ng1/P/wr7Tfb4e8jfcDV2rZ1z/W+UXZHCvn2bJkoZPLhWRGCUQ5s2dJWvwEDgC2kPZAY+n2Zwu3QJ\nuHOHRhXcvUv3Gxp+3Fq1Alq3BjQ1qSJWVQXk5Oh0i5wcjUAoLATevaPK/N07utJcRgZtPz0dSEuj\nqY+1tGgIabt2gKUl0LkzTdqkoiLt3mAwPlLtEfbIkSMRFRWFrKws6OjoYNGiRQgICEBUVBSmTp2K\nDx8+IDAwEIGBgVUXiuNgb0+waRN9cARkFWSh7fq2uDnlJow0jaojdqPk1ONT8D/sj28cvsE853kS\nX9pz+nQafvftt+WXmTqVvlx/+UWip2ZUguJimhFtyxbATUbTFCQl0aVVIyKootbUBHr0oKuSdehA\nN13d2gkD5POB589p4pnERPqBcP06/Qg1M6Mrx/XqRftO3CCCwZAE9TqXeMuWBNeu0Ze8gN8v/I5H\n2Y8QNjBMesLVU9Ly0zBk9xCYaJngrwF/QalpBfFyVWTVKro29v/9n/jjHz7QF93164AR+86SCrt3\nAytXAlevyk7se0oKsG0bsG8fHfX260cX++nR48vTK3VBcTEd2V+6BJw/T7P6tWwJeHgAgwYBzs41\nX/iGwRBQr3OJZ2aKxukWlxYjJC4Es5xmSU+oekwrtVY473ceHDi4hLsg422GxNo2MKBziuVx7hw1\nzTJlLT2GD6fm4ZrkfpcEpaV0MR8PD8Denq729scf1Dz9119UTllQ1gAgL09lnDGD5rt//Rr4+2/q\nszFnDlXeAQHUKsByuDPqAplV2M2aiX69Hrh/AObNzdFRt6P0hKrnKDVVws4hO+HT1gfOYc5IyU2R\nSLuGhhUr7N27gUpkomXUIhxHlUxwsHTOX1QEbNpE1wZYs4au0PbiBbBhA9C9O51zlnXk5KgCnzcP\nuHaNWow6dqT9amoKLFhAEz4xGLWFzCrsz+eK/on/B342ftIRpgHBcRwWuC7ADMcZcA5zRmJmYo3b\nNDSknrviKCkBDh8Gvvqqxqdh1JCRI4FHj4AbN+runITQEbWFBf0dhIdTE/OIEdSDuz5jZATMmgXc\nvAkcPEgd2jp3pr/1qmT/YzAqi8zOYbu7E6H5Lud9DozXGiN1VirUFdSlK1wDIuxmGOadm4ez487C\nooVFtdvh82l89Zs3gIKC6LHYWGDyZOrtW9cQQpCWn4Y7L+/gQeYDpL5JReqbVDx/8xzZ77ORX5SP\nN0VvUPChABzHgcfxwON4aMprCk1FTWgpaUFLUQstVFrASMMIxprGMNY0hqmWKdprt0dTuaZ1f1E1\n5LffqPk5NLT2z/XgAb33b95Q/4ZevWr/nNLm7VsgLAxYvZqa9hcvBioZYsto5NR5WJck0dT8+P8D\n9w/Aw9SDKWsJE2AXAB7Hg+ffnrgQcAHGmsbVaofHo86Bz5+XjfWNiADc3Wsua2UoLCnEledXEJkc\niQvPLuBWxi3wOB5sWtrAXNschhqGcGztCH11fWgraUNdQR3qCupQbqoMAgJCCPiEj+LSYuQW5iL7\nfTZyCnPw+t1rpOSl4GHWQ5x6cgqPsx/jWd4zWDS3gE1LG9i3tIezkTM66nYEj5NZoxUAuv64rS11\nFKwoT39N4PNpspbffwcWLqS5FOqDyVsSqKrSOe9p0+hU0IQJNILi99+pOZ3BqAn1QmHvv78f/rb+\nUpOlIeNn64f84ny4b3fHpfGXoKtavRU5BI5n4hT23LkSELQc8grzcOzhMey7vw8RTyNg2cISrkau\nmOU0C51bda7W9Sg0UYCaghoMNAzKLfOu+B3uvrqL2y9v41raNYTEheDVu1foYdgDbsZu6NeuH9pq\nf2GpOSlgYAA4OFAT7qhRkm8/Lw8YPZqah2Nj63eylpogJ0f796uvgK1bqQd8//7A0qXUP4fBqA4y\naxL//nuCFSuAopIitFjRAikzU6ClpCVt0RosC84vwOmnp3He7zwUm1R9cnH0aKBvX2DMmI/7Pnyg\nH17p6XQVKUlBCMGFZxew8dpGHH90HD2NeuIri68woP0Aqf5G0vPTEZ0SjYinETj26Bi0FLUwsP1A\nDLMaBruWdhKPf68u//wD7Nwp+UQqDx8CAwZQi8rq1UDT+jdjUGvk5VFntf376fTAyJHSlogha9Tr\nOOzffiOYPx84n3QeP579EVcmXpG2WA0aQghG7B8BeTl5bB+0vcrKZebMj044Am7cAMaOrfziIF+i\nlF+KfQn7sOTCEpTwSzC181SM7ThWJj/k+ISPuBdxOPTgEHbd2wVVeVX42fhhtPVo6KlJN/vGmzeA\nvj6dwpDUh9Tt2zSGetEiYNIkybTZELl6lU5L2NtTPwJJfsgy6jf1Og5bYBKPeBoBD1MP6QrTCOA4\nDmEDw/Ag8wFWXV5V5frNm9PY+U+5epVmiaophBAcvH8QHTd2xOrY1VjusRz3pt1DYJdAmVTWAMDj\neOii3wVL3ZfiSeATbOi7AQmvE2AZagnffb6IfS49N2J1dZqc5MQJybR34wbg6QmsX8+U9ZdwdKQh\nYSoqNIvb9evSlohRn5B5hR37IhY9DHtIV5hGgnJTZewfvh8rYlYg7kVcleq2aEETS3zKlSv0BVUT\nHmY9hNdOL8w/Px+rPFfh8oTL8GrjJTPm5crA43hwMXbBXwP/QsrMFHTV74pR+0eh69au2J+wH3xS\n91k3+veXjMJ++pTOz/7xBwvdqyzKyjQmfdkyapXYv1/aEjHqCzKrsNXUqFnxWto1ttBHHWKoYYgQ\n7xCM3D8S+UX5la4nboR961b1PWMJIdhwdQO6/9Udfcz64NaUW/VOUYtDXUEdM51m4tGMR5jTbQ6W\nXlwK+032OJp4tNaXQv0Ud3fqEFiTU+bkUL+FefOAIUMkJ1tjYdgw4PRpOo20fLm0pWHUB2R2Dvv0\naQJ92/vo928/PAl8Im2RGh2Tj05GcWkxwgeFV6p8dDR9cV+4QP/m8+lHV3UcznLe52D0gdHILMjE\nziE7ZdLbWlIQQnA48TB+Pf8rVORVsM5rHRxaO9TBeanPwZkzNPtYdeoPHUrD+davl7x8jYm0NPoB\n5esL/Pqr7OR6Z9Qt9XoOW0kJuPriKhxb19CmyqgWq/usRmRyJCKeRlSqvJYWXZdYQGoq3VdVZf0o\n6xGctjqhvXZ7XBp/qUEra4A+pIPMB+HW1FuYbD8ZA3YNwMQjE/H63esvV67ReWkik/Pnq1c/JIQu\n3rFypWTlaoy0akXvw759bDU7RsXItMKOfxUPG10baYvSKFGRV0GIdwimHpuK9x/ef7G8ujr1PhZw\n/z5gbl61c8Y+j0WPsB74rut3WO21ul5mEqsuPI6HALsAPPjmAdTk1WAVaoV/4v+pVTN5167Uz6Cq\nPH4MBAXRxCCfZ7ZjVA9dXbpIzoEDNOkMgyEOmVXYysrAg8wHMG9exbc+Q2L4tPOBvZ49ll1c9sWy\nnyvsBw+qprBjn8diwL8DEDYwDJM7Ta6GtA0DDUUNrPZajf9G/4clF5Zg2N5htTbadnSsusImBPj6\na+Cnn+gKbAzJ0aIFdQRcsYI5ojHEI7MKW0kJSMxKZApbyqzwWIENcRuQnp9eYTk1NSA//6MTU1UU\n9p2XdzDg3wHYNmgbvNt611DihkHnVp1xffJ1mGiawGajDc4lnZP4OTp0oNnp8vIqX+fAAbok5rff\nSlwcBqhfwZEjwNSp1ErFYHyKzCpsnnwRUvNSYaplKm1RGjVGmkYIsA3AoqhFFZZr0oSaRwsK6N8p\nKYCx8ZfbT89PR/9/+2Nd33Xo27ZvzQVuQCg2UcQKzxXYMXgHRh8YjeWXlkvURN60Kc0rXtlY4JIS\n6li4fLno0rcMyWJvT1OYDhsGvHsnbWkYsoTMKuyMoicw0jSCvJy8tEVp9Pzs/DP23d+Hh1kPKyz3\nqVn8xQvqQVwRH0o/YPDuwZhoNxEjOoyQkLQNj96mvXF14lXsv78fw/cNr5RPQWXp0AFISKhc2R07\ngJYtaZIURu0yYQJNrPL999KWhCFLyKzCTnmXiPba1Yg3YUicZkrNEOgYiOCLwRWWq6rCXhC5ANrK\n2pjfc76EJG24GGgYINo/Gk15TeH5tyey32dLpF0Li8qZXgmhc6ss7Khu4DgaLnfkyMdQyYZMSQnw\n/j1dnjQvD8jOpv+WlEhbMtlCZg1b6e9SYahhKG0xGP/jG8dv0GZdGyxyW4TW6uI1sUBhCx685s3L\nby8qOQrht8Jxa+qtep8Mpa5QaKKAv4f8jbln5qLHXz1wcszJGj8jlpbAoUNfLnfmDDWhu7nV6HSM\nKqCpSZX25MnAzZuAYtXX5JE6hNA483v3gKQk6jORkkLDPrOzafKdnBygsJD+vuTkPm6lpXRKQE6O\nOiGrqgI6OtTKI9gMDenypW3b0vz4PJkdgkoG2VXY+elopdZK2mIw/kczpWbws/HDmtg1WOG5QmwZ\nZWWqqNPSAD298h+eopIiTDw6EZv6bYKOik4tSt3w4HE8rPBcAT01PbiGuyLSP7JGSruyI+y1a4HA\nQDa6rmuGDAG2baP9X5vL1EqKrCzg4kWaSOnGDeDOHapwra0BExPqVOfpSZd51damuRq0tGhudXG/\nLUKA4mLqG5OfTx0eMzKAly9pUqbr14Fdu4BHj6jib9OGTiXY2wOdOlEfDVXVuu+H2kJmFXba2zS4\nartKWwzGJ8zoMgNdtnTBb71+E7sEp6IiUFT0ZXP4ypiVsGphhf7t+9eitA2b2V1ngwOHXtt6IdI/\nEvrq+tVqp3Vr+jLMyaEvTnGkpwMxMTSxB6PuWb6cLtYyaZLsraXN59NFfg4dAv77D0hOpvH9PXvS\n0D8bGxpjXl04jjqzKijQ36dhBd+mb98CiYn0Q+HGDbqEbEICYGVFLUNubrQfVVSqL4+0kV2FnZ/G\nRtgyhqmWKexa2uHA/QMYZT2qzHEFBaqwc3LKV9gv377E/8X+H65NulbL0jZ8ZnWdhRJ+CTx2eCBm\nfEy1Vi7jOKBdOzpCKW+hlj176DrXSko1FJhRLdq3p2lgly2TnZzj9+4BW7cC//5LR8qDBgGbN9NR\nrbQiCFRV6fk7dfq4r7AQiI2lmeSWLKFTC927U3kHDKBZ5uoTMmvxT89Pl/q6wYyyTO40GZuubxJ7\nTFGRPiAVjbCDLwVjtPVomGiZ1KKUjYc53eegb5u+GLx7MIpKiqrVhrExnVcsj127gBHMiV+q/Pwz\nsGWLaPrfuqakhCrobt0ADw/6vEdGAnfvAosX06V0ZS3cT1ERcHUFFi6kZvq0NOqBf+ECjZDo0YP2\n66dJn2QZmVXYbIQtmwxoPwD3Xt1DSm7ZN7xghJ2RQeewPyc9Px3ht8LxY48f60DSxsNKz5Vortwc\nE45MqFactrExNWWKIzmZpiJ1d6+JhIyaYmgI+PjQZTnrmpISqtTMzWkO+blzqfPY779Xb+EYaaKm\nRuPbd+6k76kffqCmfENDYMwYOhqXZWRWYb/78A7aStrSFoPxGfJy8hhkPgj7EspOaArmsHNyxM+1\nhcaFYmSHkexDTMLwOB52DN6BhNcJCIkLqXJ9I6PyFfbx41RRNG08ad1llu+/p85nHz7U3TkjIug8\n9D//AH/9RR3KBg6UvZF0dZCXp2bxAwfolFCnTsDIkdSCsG8f9VKXNWRWYbdUbcnCfWSU4VbDsTdh\nb5n9CgrUJJ6dXVZhF5cWY8vNLfjG8Zs6krJxodRUCXuH7cWiqEWIexFXpbqtW9NpDHGcPg306SMB\nARk1xsaGWkNOnqz9c716BXz1FQ0pW7IEOHuWOpI1VFq0oOuSP34MfPcdsGoV0LEjVeaytAC1zCps\nPVU2fy2ruBm74XH2YzzLeyay/1Ons889jvcn7IdFcwtYtrCsQ0kbF2bNzLCx30YM3zccuYWVn+xs\n1UivZh4AACAASURBVIp6gn/Ohw90jpKZw2WHgAAgPLx2z3HsGP04MDOjXtaDBjWecD45OergFxND\nEwX99hvg4ABERUlbMorMKmxtZWYOl1WayjVF//b9cSTxiMh+gdOZOJN42K0wTOk0pQ6lbJwMsRgC\nLzMvfH+68jkt9fTEK+wbN2jsbIsWEhSQUSOGD6dm6sxMybfN59P1uL/5hkYGBAfXz2QtkoDjAG9v\nGuc9Zw6d3x43jsZ/SxOZVdiaiprSFoFRAX3M+uD0k9Mi+wQj7Oxs0RF2ZkEmrry4wuKu64jlHssR\n8TQCpx6fqlT5li2pAw6fL7o/NpbG1DJkBw0NoG9fyS+/+e4dNYGfPw/ExQHOzpJtv77C4wG+vjS5\nUMuWNAHMrl3Sk0dmXQc0FDSkLQKjAjxMPTDl2BQUlxYLF2hRVKTJCz43iR96cAieZp5QbqosJWkb\nF2oKatgyYAsmHJmA+9/c/2K/KyjQGNacHBpTKyA2FvDyqj05+YSP1LxUPMx6iMSsRCTnJiOzIBOv\nC14jtzAXJfwSlPJLUcIvgUITBajKq0JVXhXqCurQU9WDvro+Wqu1hoGGAdprt4eGYuN4ZwweTLOf\nTZGQwertW6BfP5ra8+xZ+ntgiKKqSmPgfX2BUaOoZ/mGDTQdc10iFYW9YcMGPH36FLa2thg3bpzY\nMmyELdtoK2ujnXY7XHl+Bc5G9HNcsLxmQYFoOsC9CXsxwW6ClCRtnLibuqOrflesuLQCC1wXfLG8\ntjZNK/m5wl64UHIyEUJw++Vt/PfoP1xKvYTLqZeh1FQJ7bXbo712e5homcCqhRWaKzeHlpIWmvCa\noAmvCeQ4ORSXFuNt8Vu8LX6L3MJcpL9Nx8OshziffB7P8p4hMTMRmoqasGxhCasWVnBo7QAnfSeY\naJo0OOfVvn1p1rP8fBqmVBMKCmh77dsDf/7Z8HNx15ROnehU0ezZ9P9HjtD0vnVFnSvsmzdv4tSp\nUzA3N4dFBVfKFLbs08OgBy4+uyhU2IqKdJSmpPTRSSW/KB+Xnl3C/uEStuExvshyj+Ww22SHALuA\nL+YbFyhsAVlZ9F62bVtzOR5mPcTm65ux7/4+cOAwoP0ATLCbgC39t0gsOZJgtJ7wOgHxr+Jx4P4B\n/HDmBxSXFqOrQVf0Mu4FDzMPWDS3qPcKXF2dJik5f56GJVWX0lI6N2tszJR1VVBRofHw4eGAiwv9\n19u7bs5d7Vs0fvx46OrqwtraWmR/dHQ0LCws0LZtW6xfv75MvYsXL8LNzQ3Lly9HaGhoue0zhS37\ndDfsjkupl4R/KyjQ+etPc/VGp0TDobUDVOUbUAb+eoKhhiGmO0zHz2d//mLZZs1EFXZCAl3Jqya6\nLSo5Ch47POAc5gw5nhwOjziMJ4FPsMZrDYZYDJFoJkMex4ORphH6tu2LH7r/gH3D9+H57Oe4MeUG\nRluPxr3X9+C90xsGqw0QcDgAhx8clui64nVN797AuXM1a+PHH+nzumULU9bVwd+f5lCfMAHYvr1u\nzlnt2xQQEICTYgICv/32W2zatAkREREICQlBZmYmduzYgVmzZiEtLQ0dO3ZEs2bNwHEcSiuITGdz\n2LJPd4PuiEmNAZ9QbyUFBfrS/1Rhn006C3cTFhckLb7v9j1OPzmNxMzECstpa9OXt4B796jCrg53\nXt6Bxw4PjD8yHmOsx+DZzGdY5r4MHXU71vnoVl9dH8OthuPP/n8i6dsknPc7D7uWdlhzZQ1armqJ\n4XuHY8+9PfVOeffqVTOFfewYsHcvjTNmc9bVp1s3eh9+/rlustBVW2E7OztD67Ng27y8PABAz549\nYWRkBE9PT1y5cgVjx47F6tWr0apVK3Tt2hWPHz/G7Nmz4ePjU277bEQm++ip6UFDUQOPsx8DoA9+\nTo6owj6XdA69TXtLSUKGmoIaArsEYsmFJRWW+9wkLhhhV4WikiL8cu4X9N7eG4PNB+PBNw/gZ+sH\nhSayoRE4jkNb7bYI7BKI837n8WjGI3iYemDzjc3QX62Pqcem4srzK9VK71rX2NvT9KCvX1e9bno6\nMHEi8Pffsrf6V33EwoLGaS9dSq0VtYlE57Dj4uJgbm4u/NvS0hKxsbEiilleXh6LFy/+YlvMo7h+\nYNvSFrczbqOddjs0aUKT6Bsb02Nvi9/iUfYj2OvZS1XGxs4MxxkwW2eGx9mP0aZZG7FlmjWjH1sC\nEhKqNi+XkpuCIXuGQF9dH7en3q4X6Wd1VHQwqdMkTOo0Cal5qdh+ezvGHBwDeTl5fOPwDcbZjJPZ\ngUOTJtTp6do16jRWFaZOpU5rPXrUjmyNETMzmhXQxQXQ0amZb0FFyOzMxXejvoO/vz+CgoIQGRkp\nbXEY5WCja4PbL28DoFmC3rwBlP/3rXUj/QasdayFYV8M6aChqIFpDtOwKmZVuWXU1KjXsYD79yvv\n/RqTGgOnrU4YbT0ah3wP1Qtl/TkGGgaY13MeHk5/iFDvUJxNOgvjNcb44cwPYhe6kQUcHGjMdFU4\nehR48ACYP792ZGrMtGtHvcYnTABu3/5y+cjISAQFBcHf3x+urq6VOodER9gODg6YM2eO8O979+7B\nq5qBnGEHw2DT0kZSojFqCRtdG2y9uRUAVdiFhR9N4ldfXIVj63IWWWbUKVM7T4VVqBWWuS8TG6+s\nqkrjcQGa/Ob1axqX+yXOJ53H8H3DsX3QdvRtW8WhngzCcRxcjF3gYuyCpJwkbLi6AfZ/2qN/u/6Y\n33N+uRYKaeDgULU0pcXFwMyZwB9/sHnr2sLBAVi3jqY3jYsrm6L5U1xdXUUUdWX8OyQ6wtbQoC+C\n6OhoJCcn48yZM+jSpUu12lJqqiRJ0Ri1REfdjiIjbIApbFmklVoreJp5Yvtt8e6sqqofR9hpaTRd\nqeB+lkfs81gM3zcce77a0yCU9eeYaJlgVZ9VeBL4BCaaJnDa4oSAwwFCnw1pU9URdlgY0KYN4OlZ\nezIx6Ipf3t4077uk3SGqrbBHjhyJbt264eHDhzAwMEBY2P+3d+dxUdV7H8A/szAzDJuDgyiKDK6A\ne0QgTyAaWWlPeW3xUmFBPlJaGXa791ZP92Z6S+u+1PuopV3L7jWvbZZZmnuISyq5pSiuoCyCIvu+\nzfPHiVEEZRhm5swZPu/Xq9erOZzlK7z0w/d3fud3VgEAFi9ejKSkJMTGxmLGjBnQ6/UWnd9VycCW\ngkBdIIqqi1BWW2Z65V5zYJ+4cgLDfYeLVxy1MOPOGVh+aHmbk6o8PK532NnZgL//7c91seQiJn8x\nGaseXoWxgWNtUK3j6Kbphr/G/BXnXjoHg5cBESsjMHPjTBRW2WBB7w7w9xdGtMxZV7y2VnjrljUX\nwqFb+/vfgQsXhNeSWpPFgb127Vrk5eWhtrYW2dnZSEhIAACMGTMGp06dwrlz5/DSSy9ZXBgnnUmD\nXCZHP10/XCi+YOrIXF2B+sZ6XCi+gEHdB4lbIJlEB0Sjqr4KR/OPtvrajR12Ts7th8NrGmrw8OcP\n49XIV/HgoAdtVK3jaQ7u0y+chkKuQPCyYCz8eSHqGutEqUcmA4KCgNO3f2IPgBAcwcFARITt6yLh\nXdurVgkrouXnW++8DjvpjEPi0tFf1x/ni86bAlulAjJLMtHbszc0yi76uh8HJJPJ8MTQJ7Dm+JpW\nX7vxHnZ7HfabO99Ef+/+eDniZRtV6ti6a7vj/x74P+xO2I2dmTsx7MNh2JUlzvsXBw8WJpG154MP\ngFmzbF8PXRcaKkxAmz3beud02MDmP/TS0V/XH+eLz5uGxBUKIKMwA0H6oNsfSHb35PAnsfbEWjQ2\ntVy06MYh8ZycWwf2z9k/Y83xNVjx4ArJL/HZWUH6IPzwxA9YELsAT37zJJK+T+rQe8itUkNQ+4H9\nyy/CsPl999mnJrrujTeA1FRhXX5rcNjAlssctjS6SX9v4Rnf5g5bqfwtsLszsB1NiE8I9Fo9fs75\nucX2G4fEb9VhNxmbMGvzLCyIXQC91rK5Kc5oUtAkpM9Ih1wmx9APhmLT2U12u7Y5Q+IffSS82au9\nSYRkfW5uwLx5wCuvWGcCGlOROm2A9wCcLz7fIrBPF57GYP1gcQujNj048EFsPLOxxbYbh8RzcoDe\nvVsft+bXNZDJZHhy+JN2qFJavDRe+PDBD7Fm8ho8v/F5vLz5ZdQ01Nj8uu0NiTc0AN9+K7wSksQR\nHy+sItjZtd8BBjZZwc33sJVK4FLZpXbfEEXimDhoIjaebRnYarUwkxgQnsHu0aPlMY1NjZibOhcL\nYhdw9Os2xhjG4GjSUeSW5yJ8ZTgyCs24wdwJBoOwRGlTU9tf37VL2Kcv/yqKRqEAXntNmKXfWfyb\nR53Wx7MPLldchlwh/KuhVAJ55Xno7dFGm0aiC+8djrzyPFwqvWTaplIJC2sYja3fiw0A6zPWw9vV\nG2MCxti5WunRuerw5aNf4sW7XkT0qmh8f/p7m11LqxXmH9xqTfF164RFPEhcTzwhPObV0ZXpbsbA\npk5TK9XwUHmgvEF4e4RSCeSW5aK3JwPbESnkCtw34D78ePZH0za5XPi5VVQIwe1+0xLa7+97H3/6\nrz91+Ylm5pLJZJh2xzR8H/c9ZmyagXmp80xvtbO2vn2FLvtmTU3C6x8nT7bJZakDXFyENdw7+0Yv\nBjZZhZ+HHwrr8gAATYpK1DbWQqe5zbp8JKrYwFikXExpsU2tFlY50+tbvgf7xJUTyCnLwUODbfRG\nAycW3iccB6cdxKazm/DkN0+itqHW6tfo21eYKHiz9HShAx/EpRAcwjPPAF9/LbxvwVIMbLIKPw8/\nXK3JBQBUyHPh5+HHbsyBRQVEIfViaotVz1QqIbBvHg5ffWw1nhz2JBRyTjO2RC+PXtj59E7UNdbh\nwbUPory2vP2DOqBnz7YX5/jpJ8DMd0qQHfTsCdxzT+dWP2Ngk1X0dO+JojrhX40KeS7vXzu4/rr+\nMBqNyCzJNG1Tq4V3Jd/4juTGpkasOb4G8SPiRajSeWiUGnz56Jfor+uPsf8aa9VlTW8X2GOde9VY\nyXnmGQY2OQC9Vo/SOuEedgXyeP/awclkMkQFRGHPpT2mbSqVsMCG1w0v89pzaQ983HwwtMdQEap0\nLgq5Ah9O/BDj+49H7L9jUVRdZJXzthXYRiOwZ4/wfmZyHOPHA8ePC78YW4KBTVah1+pRXCd0DWVg\nhy0FYX5hOHz5sOmzWi3MEL9xwtnGsxvx0CDeu7YWmUyGv437G8b3H497V9+L4uriTp/T1xcoKGi5\nLTtbeJyorefpSTxqNfDgg8Kz8ZZgYJNV6LV6lNQKgV1uLEBP954iV0TtuaPXHS0CW6USAtvD4/o+\nm85uwoSBE0SoznnJZDIsiF2A6L7RuH/N/aisq+zU+doK7EOHhLWsOY3E8UycCPz4Y/v7tYWBTVah\n1+pR9FtgVxuL4O3q3c4RJLZRPUfhaP5R0+NGN3fYOWU5yK/Ix51+d4pYpXOSyWRYeN9CBOuD8cQ3\nT7Ra270jdDqg+KZGvTmwyfHce6+woE2dBS95Y2CTVei1ehTVCIFdZSzmI10SoHPVQa/V41zROQCt\nO+y9l/YiKiCKs8NtRCaT4aP//ggVdRVI3pLc5nvKzaHTAUU33Q4/fBi44w4rFElW1727sAb83r0d\nP5aBTVbRTdMNZXWlAH4LbFcGthQM9x2OXwt+BdC6w96XvQ+RfSJFrM75qRQqfPP4N9iRuQMfH/nY\nonPodEBJScuXS5w6BQwZYqUiyerGjQN27+74cQxssgpPtScq6oQVASqbOCQuFYO7D8aZa2cAXO+w\nTYGdsw+R/gxsW/PSeGHd4+vw2o7XcOTykQ4fr1IJv2w1v7yltlZ4nt5gsG6dZD2jRwP79nX8OKX1\nS6GuyEPlgbLa3wK7kUPiUjGo+yCkXkoFcL3D9vAAahpqkH4lHaF+vBFqD0H6ICx9YCke/epRHJp+\nCN003Tp0fPN9bA8PYc3qvn2F5TBt7WLJRRy6fAgnr57EqcJTyC3LxZXKK7hSeQVV9VVoNDaiydgE\nF7kLvDRe8FJ7wcfNB4ZuBgR2C8RA74EY1WsUgvRBUMq7ThyNHg08/bSwfKy8A21z1/kOkU15qD1Q\nUVcBwIiKRg6JS8Vg/WCsPLISgNCpVVQIHXZGYQb66fpBo9SIXGHXMWXoFOy+tBsvbHoBn03+rEPH\nNt/H7tsXOHsWGDjQNjVW1Vdh09lN2HB6A3Zd3IXq+mqE9wlHiD4E9/a7F329+qKHWw/0cOsBd5U7\n5DI5FDIF6hrrUFpbipKaElypvILM4kxklmRi49mNmJs6F3nleRjRcwTGGcYhtl8sRvuPhkqhss0f\nwgH06AH4+AAnTwJDO7DEAQObrEIpV0KtVKNKXY66pmq4ubiJXRKZYVD3QThdeBpGoxFqtfAMkKur\nsH74kB68CWpv7937HkYuH4l1J9fhkRDzX7Pl6QmU/7bi6Zkz1g1so9GIvdl7sSxtGTad3YS7et+F\nyUGT8UbUGxjUfZBZSxC7KFzgpnKDn4cfQnxCEGOIafH1stoypOWmYUfmDry67VWcvnYaDwx4AFOG\nTMH9A+6Hq4ur9f5ADiI0FDh6lIFNIvFUe6LKrQBquZbriEuEj9YHRhhxrfoaVCo9AKHTTr+SjiE+\nDGx707po8emkTzH5i8mIDoiGj5uPWce5uQGVvz3OffYsMGxY52sxGo3YcHoD5uyag8r6SswMm4kl\nDyyBXqvv/Mlv4qn2xD397sE9/e7BO/e8g6uVV/FtxrdYmrYUiRsSMWXIFMwIm4HhvsOtfm2xDB0K\nnDjRsWM46YysxkPlAXhchkbO7loqZDIZ+un6IbM4E2q1sM3FBUi/ms7lSEUS6R+J3w/9PV7f8brZ\nx2i11wM7OxsICOhcDWm5aRj98Wj8JeUveCvmLZyaeQovhb9kk7Bui4+bD6aHTseOqTtwcsZJ9Pbo\njQlrJuDuT+7GdxnfWfwInCMZNkxYprQjGNhkNZ5qT8D9MjQKBraU9PbojdzyXKh+u2WoUgmBzQ5b\nPHNi5mDj2Y04mHvQrP3d3ICqKuH/CwqE9cUtUVVfhT9s/QP+e+1/4/k7n8eRpCN4aPBDkMvEi4pe\nHr3w5pg3kfVyFl6OeBlzds3BHR/dgfUZ6yUd3EOHMrBJRG4qN8DtCtRyrdilUAf09uiN3LJcU4et\ncGlEdmk2AnWB4hbWhXlpvDA/dj5mbpppWonudm4cEs/Ptyywz1w7g/CV4cgpy8Hx54/j6ZFPixrU\nN1PKlXg0RJhFPydmDuamzkXExxE4kHNA7NIsEhgoTBQsKTH/GMf5aZDkaZQawLWIQ+IS09uzZYdd\n2ngZeq3eqWfpSkH88HgYjUZ8e6r9N0U0D4k3NQFXrwqzkDti2/ltuPuTu/FC2AtY+8has++di0Em\nk+GhwQ8h7X/SMDNsJn73xe/wzPpnrPrKUnuQy4XJgefPd+AY25VDXY1aoRYCm0PikuLn4Yfc8usd\ndmFdNvy9/MUtiiCTyTB37Fz8JeUv7a413jwkXlQkPJbX/LM0x9cnv8ZT3z6FdY+vQ9KdSZKZMCqX\nyTF1xFScfuE0vF29MfzD4VifsV7ssjrEYACysszfn4FNVqNWMrClqHlIvLnDvlqXDX9PBrYjuH/A\n/eim6YbPT3x+2/2ah8QLCoS3d5lrfcZ6vPjji9jy1BZEBUR1slpxeKg9sPC+hfjysS/x6rZXMfXb\nqb+tCeH4AgIY2CSS60PivIctJc1D4s1d2ZUaBrajkMlkeDvmbczbPe+297KbA7sj96/3XNqD6d9P\nxw9xP2Bkz5FWqlg8d/e9G0eTjkIhVyB8ZTgyCjPELqldBgNw8aL5+zOwyWqah8R17uywpeTmDju/\nmkPijmRc4DholBpsObfllvtotcKQeH6+eR12TlkOHv3yUXw2+TOnWn7WTeWGTx76BMkRyYhaFYXv\nMr4Tu6TbYodNolEr1Bg0ogh+Ps63KpEz66bphoamBhhdhGHEvMpL6OvVV+SqqJlMJkNyRDIW7l94\ny31uHBJvr8NuaGpA3Lo4zAqfhfH9x1u5WvHJZDJMu2MaNj2xCTM2zcCHaR+KXdItBQSwwyaRaJQa\nVNRXcHaxxMhkMui1etQrrwEALlfmoI9nH5Grohv9fujvceLKiVsO87q4AA0N5t3Dnpc6D65KV/zp\n7j/ZoFLHEdY7DLsTdmPR/kV4Y8cbDvnMtsNPOistLUVCQgKSk5Pxz3/+096XJxtSK9WorKvsUm/d\ncRbert6oVRQBAK5WXYGvWwdmLpHNqRQqPDXsKXx69NM2v65UCoFdUiK8CORWMgozsPTgUqx6eJVD\nPWNtK/10/bA3cS+2XtiK2VtmO1xo63TCz62szLz97f4TO3DgAEaPHo1FixZh+/bt9r482ZBaoUZl\nfSUUcoXYpVAHebt6o8ooBPa16mvoru0uckV0s4RRCVj962o0NDW0+lpzYJeVCS8CaYvRaMTMTTPx\nZvSb6O3Z28bVOg4fNx9sfWorUi+l4s/b/+xQoS2TCSMiV6+at7/FgZ2YmAhfX18Mu2mV+dTUVAQH\nB2PgwIFYsmRJq+MiIiKwZs0a3HPPPXjggQcsvTw5II1Sg4amBnbYEtRd2x2VTUWAoha1DbXCuvDk\nUEJ8QuDv6Y+t57e2+po5gb3l/Bbkledh5l0zbVyp49G56rD1qa3YfH4z3tn9jtjltNCjB3Dlinn7\nWhzYCQkJ2Lx5c6vts2bNwooVK7B9+3YsW7YMhYWFWL16NZKTk5GXl4cvvvgCf/7zn7Fjxw788MMP\nll6eHJBaKTwXxMCWHm+NNyobiwCt0F1LZfGMruaJYU/gq5Nftdp+Y2B7ebU+zmg04s2f3sScmDld\n9u9nd213/Pjkj/jo8EdYe3yt2OWYdCSwLf7JRUVFIeumu+WlpaUAgOjoaADA+PHjceDAAcTHxyM+\nPt60bc6cOdi5cyfuuusuSy9PDkij1ABgYEuRt6s3LjZeA1yvobsrh8Md1cODH8bc1LmtRrLa67A3\nn9uM2oZaPBryqB2rdTx+Hn74Pu57xP47FgHdAhDpHyl2SfYJ7LakpaUhKCjI9DkkJAT79+/HxIkT\nTdsCAgLwySeftHuumJgYGAwGGAwGxMTEICYmxpqlkg2oFeywpcpL44XqphJTh02OKaBbAPp69cWe\nS3sQY4gxbW8vsJccXILkiOQuMdGsPcN9h+PTSZ/i8a8ex+Gkw+jh1sGF160kJSUFKSkpOHAgCzt2\nZJl1jMP+y5qSkiJ2CdRBHBKXLneVO2qacgB1GbzUbYypksOYNHgS1mesNzuwzxedR1peGtY9vs6+\nhTqwCQMnYOqIqYj/Nh4/PvmjKL/INDeiWi1QWAi8/377t6GsWmVYWBgyMq4/J5ieno6IiAhrXoIc\nGIfEpctd5Y4mZQWgKoe7yl3scug2Hhr8EDad3dRim1IJ1NcLge1x03zBjw59hGdGPANXFy5odKO3\nx76NqvoqzN8zX9Q6vLzMf8WmVQPb67fZDqmpqcjKysK2bdsQHh5uzUuQA2teMIWBLT3uKnd4dK/A\n/IUVnCHu4Ib5DkNxTTGyS7NN2xQKoKZG+H/VDesWGY1GfJ7+OZ4e+bSdq3R8SrkSax9Zi8X7F+NY\n/jHR6ujWzQ6BHRcXh8jISJw5cwb+/v5YtWoVAGDx4sVISkpCbGwsZsyYAb1eb+klSGJc5C4AGNhS\n5K5yR0VdBRRadtiOTi6TY6xhLHZm7jRtUyqFpUk1mpb7/pL3CzRKDYb4DLFzldLQx7MP5sfOR+KG\nxDafb7eHbt2A3+Zrt8vif1nXrm17WvyYMWNw6tQpS09LEsYOW7qaA7u8thweanbYjm5c4DjszNpp\n6pyVSqCiovV7sNedWodHgx/lY3q3kTAyAWtPrMXCnxfij//1R7tfX7QhceraGNjS5a5yR3ldOSrq\nKthhS0CkfyT25+w3fW7usG8MbKPRiHWn1uGRkEdEqFA6ZDIZlk9cjvf2vofL5Zftfn27DIkT3aw5\nsBUyLk0qNaYOu66c97AlYIjPEFwuv4zi6mIAQmDX1LQcEr9QfAGVdZUY1XOUSFVKR3/v/kgclYj/\n3fm/dr82O2wShYuC97Clqjmw2WFLg0KuQKhfKA7mHgQgBDbQssP+KesnjA0cy+FwM70R9QY2nt2I\nw5cP2/W6za9GNQcDm6yGQ+LS5ebihsq6SpTXcdKZVIT3DseB3AMArgf2jR32T1k/YaxhrAiVSZOX\nxgtvRr+Jv6b81a7XdXUFqqvN25eBTVbDwJYulUKF+qZ61DTU8HldiRjZcyR+LfgVQNsd9q6sXS0W\nV6H2PXvHszh8+TCOXD5it2u6uAByM5OYgU1Ww8CWLheFC+oa61DXWGf6OZJjG9pjKNKvpgNo3WHn\nV+Sjqr4K/XX9RapOmjRKDV6NfBXzds+z63VdzfwdmYFNVsPnsKVLLpNDIVOgqr6KgS0Rg7oPQlZJ\nFmoaalp12IcvH8Ydve7g/WsLTA+djn3Z+3Dy6km7XZOBTXbHDlvaVAoVKusqTb94kWNTKVTop+uH\n04WnW3XYh/IOIbRXqHjFSZjWRYvnQp/D0oNL7XZNBjbZHQNb2lQKFSrqKthhS8jQHkNx4sqJVh32\nocuHEOrHwLbU9NDp+PzE5yitMXMJsk5iYJPdMbClzUXhgsr6Sga2hAzyHoRzReeg+G3pg+bAPnn1\nJIb2GCpeYRLXy6MXxvcfj38d+5ddrsfAJrtrfg5bIefCKVLUPCTOwJYOQzcDskqzTLOMXVyA+sZ6\nXCy9yAlnnTQ9dDpWHV1ll2sxsMnumt8pKwMnukiRSqFCbWOt6RcvcnwB3QJwseSi6bNCAWSVZMHP\nw8/0fnqyTIwhBoVVhThx5YTNr8XAJtE0GhvFLoEs0DzZjB22dBi6GZBVkmX67OoKnC06i4HeA8Ur\nyknIZXI8OexJrD622ubX0mrN24+BTVbXZGwSuwSyQHNQM7Clw9/TH7nluWhsEn5J9vEBzl5j7LDY\nJwAAFlZJREFUYFvLU8Ofwn9O/AdGo9Gm12GHTaJhYEsTA1t61Eo19Fo98srzAPwW2EVnMbA7A9sa\nhvYYClelK47k23bls8BA8/ZjYJPV2fq3UbKN5nvXDGxpuXFY3McHuFh6EYZuBlFrciYPDX4IG05v\nsOk15s83bz8GNlmdj5uP2CWQBZrvYXPhFGnx9/RHdlm28P/+wrKkvdx7iVyV87BHYJuLD8ySVdW/\nWc/nsCXKNMufy1lKiq+bLwoqCnD2LDBgAFCwpwC+7r5il+U0Iv0jcan0ErJLs+Hv5S9qLeywyaoY\n1tJlBG9lSJGvuy8KKgswYIBwO6qgsgC+bgxsa1HKlYjtF4sdmTvELoWBTUQkZb5uQmADQElNCTRK\nDV+RamXRAdFIvZgqdhkMbCIiKfN1F4bEAeH+dU/3niJX5HzGBIzBrou7xC6DgU1EJGU+Wh9crboK\nABwOt5Fgn2CU1pQipyxH1DoY2EREEqZz1aGkpgQAO2xbkcvkFg2L55Xn4bXtr2HS55MwJ2WO6edk\ncR2dOpqInMawHsPELoEsoNPoUFxdDAAoqGCHbStRfaOw++Jus/dPy01D6EehqGmowVPDn0JWaRZC\nPwpFdmm2xTUwsIkIALBswjJUvFYhdhnUQd003VBSUwKj0Yj8inw+0mUjYb3DcDj/sFn75pXnYdIX\nk/DhxA+x6P5FeDTkUax6eBX+547/wSNfPoKGpgaLamBgExEA4flrN5Wb2GVQB7koXKBRalBeV46S\nmhJ4u3qLXZJTGuE7AieunDArbJO3JOOZEc9gUtCkFtv/9F9/grvKHR8f/tiiGhjYREQSp3MVhsXL\n6srgpfYSuxyn5KH2gL+nPzIKM26738Hcg/g5+2e8Ef1Gq6/JZDK8f+/7mLNrDuob6ztcAwObiEji\ndBodimuKUVpTCk+1p9jlOK07et2Bw5dvPyy+8OeFmD16NrQubb8zM9QvFP10/bDp7KYOX5+BTUQk\ncZ5qT5TXlqOstoyBbUPDfYfj14Jfb/n1gooCbDm/BYmjEm97nmdHPYtPjn7S4eszsImIJE7rokVV\nfRUD28YGdx+M09dO3/Lr606tw4SBE9r9GUwKmoSdmTtR01DToeszsImIJM5N5YbK+koGto0N1g/G\n6cJbB/ZXJ7/CYyGPtXsenasOQ3yGYF/2vg5d36aBnZmZiWnTpuGxx4Q/QE1NDWbPno3nn38emzdv\ntuWliYi6DDcXN1TWCYHtpeGkM1vpr+uPS6WXUNdY1+pr5bXlSMtNw3397zPrXPf2uxfbzm/r0PVt\nGtiBgYFYuXKl6fO+ffsQFhaGDz/8EN98840tL01E1GXcOCTuofIQuxynpVaq4e/lj/NF51t9bV/2\nPoT6hZr94pUYQwz2ZO/p0PXNCuzExET4+vpi2LCWKyGlpqYiODgYAwcOxJIlS9o9z/Hjx9G/f38A\nQHV1dYcKJSKitrm5uKGstgxNxiaolWqxy3Fqt7qPveviLowJGGP2eYb7DsfxguMwGs1/ra1ZgZ2Q\nkNDmEPasWbOwYsUKbN++HcuWLUNhYSFWr16N5ORk5OXltS5w+HBcuHABAKDVtj3lnYiIOkbrokVx\nTTFUCpXYpTi9frp+yCrJarV996XdiA6INvs8Pm4+0Lpocan0ktnHmBXYUVFR0Ol0LbaVlpYCAKKj\noxEQEIDx48fjwIEDiI+Px6JFi+Dn54eioiI899xzOHLkCBYsWIDIyEj88ssvePHFFzF58mSziyQi\noltzU7mhuLqY3bUd9PHs0+qtXU3GJhzLP4bQXqEdOteIniNwrOCY2fsrO3T2G6SlpSEoKMj0OSQk\nBPv378fEiRNN27y9vbF8+fIWx/3973836/wxMTEwGAwwGAyIiYlBTEyMpaUSETk1dtj208ezT6vF\nUy6VXoKn2hM6V90tjmotJSUFZZvL8NfVf8XCmoVmHWNxYNtaSkqK2CUQEUmCm4sbimuKoVaww7Y1\nf09/ZJe1fOPWiSsnMLTH0A6dJyYmBtO7Tce2C9vw2eTPIJPJ2j3G4lniYWFhyMi4vqZqeno6IiIi\nLD0dERFZyE3lhqLqInbYdtDWkLglgQ0AgbpAZJZkmr2/xYHt5SU865eamoqsrCxs27YN4eHhlp6O\niIgs5CJ3QUVdBe9h24Gfhx8ul19GY1OjaZvFgd0tEJnFVg7suLg4REZG4syZM/D398eqVasAAIsX\nL0ZSUhJiY2MxY8YM6PX6DhdMRESdo5QrUVVfxQ7bDtRKNXSuOlypvGLadr74PAZ4D+jwufw8/HCt\n+prZS5SadQ977dq1bW4fM2YMTp06ZX51RERkdUq5EpV1lejl3kvsUrqE5vvYvTyE73duWS76ePbp\n8HkUcgV83XxRUFFg1v5cS5yISOLYYdtXT/eeppBtbGpEfkU+/Dz8LD7X5YrLZu3LwCYikjilXInq\nhmrew7YTvVaPq1VXAQBXKq9A56qz+JelXh69kF+Rb9a+DGwiIolTyoW7m+yw7UOv1aOwqhAAkFOW\nY9FweLOebj1xuZwdNhFRl9Ac2HwO2z58tD5WC2xfd98WE9huh4FNRCRx7LDt68YOO7c8F709elt8\nLp1Gh+KaYrP2ZWATEUmcqcPmPWy76K7tbrUOW+fKwCYi6jJMHbacHbY9dNN0Q2mt8AKs/Ip89HTv\n2alzFVczsImIugR22PblpfZCaY0Q2EXVRfB29bb4XBwSJyLqQngP27481Z4oqy0DABTXFEOnMf8t\nXTfTuepQUlNi1r4MbCIiiVPIFQA4S9xeWgR2dXGHXqt5M51GxyFxIqKugh22fTUHttFo7HSH7aH2\nMIV/exjYREQSx3vY9qVWqiGXyVHbWIvi6uJO3cPWumhR3VBt1r4MbCIiiWOHbX+eak9crbyKhqYG\naF20Fp/HRe6CJmOTWfsysImIJI4rndmfl8YLOWU58FR7QiaTWXwemUxmduAzsImIJI4dtv1pXbS4\nVn2tU911M1elq1n7MbCJiCSOgW1/GqUGRdVFVglsdthERF0EJ53ZnzUD29WFHTYRUZfADtv+NEoN\nrlVZZ0icHTYRURfBSWf2p1FqeA+biIg6Ri6TQwYZO2w74j1sIiKyiFKu5D1sO+I9bCIisohCrmCH\nbUcaBTtsIiKygFKu5D1sO3J1cbXaPezx/cabtR8Dm4jICSjlSnbYdmTNIfGEUQlm7cfAJiJyAryH\nbV8apQZltWXQKDV2uyYDm4jICbDDtq/moFbIFHa7JgObiMgJzImZAz8PP7HL6DJMgS23X2Ar7XYl\nIiKymemh08UuoUthh01ERCQBzavL2bPDZmATERF1UHNnzQ6biIjIgTV31nKZ/WLU5lfKzMzEtGnT\n8NhjjwEAvvvuO0yfPh2JiYk4ePCgrS9PRERkdaYO25mGxAMDA7Fy5UrT54cffhgfffQR5s+fj1Wr\nVtn68kRERFbXHNQOOSSemJgIX19fDBs2rMX21NRUBAcHY+DAgViyZInZF16wYAGSkpLMr5SIiMhB\nOHSHnZCQgM2bN7faPmvWLKxYsQLbt2/HsmXLUFhYiNWrVyM5ORl5eXmt9jcajfjjH/+ICRMmYOTI\nkZ2rnoiISARidNhmP4cdFRWFrKysFttKS0sBANHR0QCA8ePH48CBA4iPj0d8fDwAoKioCK+//jqO\nHj2K+fPnw83NDTt37kR5eTnOnTvHLpuIiCSnOajtOemsUwunpKWlISgoyPQ5JCQE+/fvx8SJE03b\nvL29sXz58hbHvfjii+2eOyYmBgaDAQaDATExMYiJielMqURERFZj6rAtHBJPSUlBSkoKsrKyWjXD\nt+KwK52lpKSIXQIREVGbOvsc9s2NqEwma/eYTvXyYWFhyMjIMH1OT09HREREZ05JRETk8DrbYVui\nU4Ht5eUFQJgpnpWVhW3btiE8PNwqhRERETkqMe5hm32luLg4REZG4syZM/D39zc9Q7148WIkJSUh\nNjYWM2bMgF6vt1mxREREjsChZ4mvXbu2ze1jxozBqVOnrFYQERGRo3Po57CJiIhI4NArnREREZGA\nHTYREZEEOOXbuoiIiJwN34dNREQkAUq5MGebQ+JEREQOjJPOiIiIJICTzoiIiCSAk86IiIgkgJPO\niIiIJEByL/8gIiLqithhExERSQDvYRMREUkAZ4kTERFJAJ/DJiIikgB22ERERBLADpuIiEgCmoOa\nk86IiIgcGJ/DJiIikgA+h01ERCQBzUPhHBInIiJyYDKZzO7XZGATERFJAAObiIhIAhjYREREFtK6\naO12LZnRaDTa7WpmkslkcMCyiIiIbMKc3GOHTUREJAEMbCIiIglgYBMREUkAA5uIiEgCGNhEREQS\nwMAmIiKSAJsGdmZmJqZNm4bHHnvMtK2yshJhYWHYuHGjLS9NRETkVGwa2IGBgVi5cmWLbe+99x6m\nTJliy8sSERE5HbMCOzExEb6+vhg2bFiL7ampqQgODsbAgQOxZMmSds+zbds2hISEwMfHx7JqiYiI\nuiizAjshIQGbN29utX3WrFlYsWIFtm/fjmXLlqGwsBCrV69GcnIy8vLyWu2/a9cu7N+/H//5z3/w\nz3/+k6uZERERmUlpzk5RUVHIyspqsa20tBQAEB0dDQAYP348Dhw4gPj4eMTHxwMAioqK8Prrr+Po\n0aNYsGAB5s2bBwD417/+BR8fH1FeT0ZERCRFZgV2W9LS0hAUFGT6HBISgv3792PixImmbd7e3li+\nfHmrY59++ul2zx8TEwODwQCDwYCYmBjExMRYWioREZFDSUlJQUpKCrKyslo1xLdicWDbWkpKitgl\nEBER2cTNjag5I84WzxIPCwtDRkaG6XN6ejoiIiIsPR0RERHdhsWB7eXlBUCYKZ6VlYVt27YhPDzc\naoURERHRdWYFdlxcHCIjI3HmzBn4+/tj1apVAIDFixcjKSkJsbGxmDFjBvR6vU2LJSIi6qpkRgd8\ntsqcF3kTERE5C3Nyj2uJExERSQADm4iISAIY2ERERBLAwCYiIpIABjYREZEEMLCJiIgkgIFNREQk\nAQxsIiIiCWBgExERSQADm4iISAIY2ERERBLAwCYiIpIABjYREZEEMLCJiIgkgIFNREQkAQxsIiIi\nCWBgExERSQADm4iISAIY2ERERBLAwCYiIpIABjYREZEEMLCJiIgkgIFNREQkAQxsIiIiCWBgExER\nSQADm4iISAIY2ERERBLAwCYiIpIABjYREZEEOGxgy2SyVv+99dZbbe771ltvcX/uz/25P/fn/pLd\n3xwyo9FoNGtPC2RmZuJvf/sbSktL8dVXXwEAli5digsXLmDkyJGYOnVq20XJZLBhWURERA7FnNyz\naYcdGBiIlStXmj4fOXIEW7ZsgUKhQHBwsC0vTURE5FTMCuzExET4+vpi2LBhLbanpqYiODgYAwcO\nxJIlS9o9z+7duzF27Fi89957+OCDDyyrmKwiJSVF7BKcHr/H9sHvs+3xe+wYzArshIQEbN68udX2\nWbNmYcWKFdi+fTuWLVuGwsJCrF69GsnJycjLy2u1/4gRI+Dt7Q2ZTIbGxsbOV08W419A2+P32D74\nfbY9fo8dg1mBHRUVBZ1O12JbaWkpACA6OhoBAQEYP348Dhw4gPj4eCxatAh+fn4oKirCc889hyNH\njmDBggUYPXo0zp07h9mzZ2PixInW/9MQERE5KaWlB6alpSEoKMj0OSQkBPv3728RxN7e3li+fHmL\n4+bNm2fpJYmIiLosiwPblvz8/Mye5k6WmzNnjtglOD1+j+2D32fb4/fYtvz8/Nrdx+LADgsLw6uv\nvmr6nJ6ejvvvv9/S07WQm5trlfMQERE5C4sf6/Ly8gIgzBTPysrCtm3bEB4ebrXCiIiI6DqzAjsu\nLg6RkZE4c+YM/P39sWrVKgDA4sWLkZSUhNjYWMyYMQN6vd6mxRIREXVVNl3prKNSU1ORlJSEhoYG\nvPTSS3jxxRfFLsnpJCYmYuPGjejRoweOHz8udjlOKTs7G1OnTsWVK1fg4+OD6dOn44knnhC7LKdS\nU1ODMWPGoLa2FhqNBlOmTEFycrLYZTmlxsZG3HnnnejTpw++//57sctxSgaDAZ6enlAoFHBxccHB\ngwfb3M+hAnvUqFH4xz/+gYCAANx3333Ys2cPu3Yr2717N9zd3TF16lQGto3k5+cjPz8fI0eORGFh\nIe666y4cO3YMHh4eYpfmVKqqqqDValFbW4vQ0FCsX78eAwYMELssp7Nw4UIcOnQI5eXl2LBhg9jl\nOKXAwEAcOnQI3t7et93PYV7+cavnusm62nqmnqyrZ8+eGDlyJABAr9djyJAh+OWXX0SuyvlotVoA\nQEVFBRoaGqBWq0WuyPnk5ORg06ZNmDZtGt/vYGPmfH8dJrBv9Vw3kZSdO3cO6enpuOuuu8Quxek0\nNTVhxIgR8PX1xQsvvAB/f3+xS3I6ycnJeP/99yGXO0xUOCWZTIZx48Zh0qRJtx3F4E+ByEbKy8sx\nZcoULFq0CG5ubmKX43TkcjmOHTuGc+fO4YMPPsCRI0fELsmp/PDDD+jRowdGjRrF7trG9u7di2PH\njuHdd9/F7NmzkZ+f3+Z+DhPYYWFhyMjIMH1OT09HRESEiBURWa6+vh6PPPII4uPj8fDDD4tdjlMz\nGAyYMGECb6FZ2b59+7BhwwYEBgYiLi4OO3fuvOUrkalzevXqBQAIDg7GQw89dMvJfQ4T2Hyum5yF\n0WjEs88+i6FDh+Lll18WuxynVFhYiJKSEgDAtWvXsHXrVv5iZGXvvPMOsrOzkZmZic8//xzjxo3D\nv//9b7HLcjpVVVUoLy8HAFy9ehVbtmy55SJkDrU0afNz3fX19XjppZc4Q9wG4uLisGvXLly7dg3+\n/v54++23kZCQIHZZTmXv3r347LPPMHz4cIwaNQoA8O6771ptJUACLl++jKeffhqNjY3o2bMn/vCH\nP5i6FLINLhdtGwUFBfjd734HAOjevTteeeWVW87HcKjHuoiIiKhtDjMkTkRERLfGwCYiIpIABjYR\nEZEEMLCJiIgkgIFNREQkAQxsIiIiCWBgExERSQADm4iISAIY2ERERBLAwCYiIpIABjYREZEEMLCJ\niIgkwKHe1kVE9nfy5El8+umnqK2tRWlpKVasWIH3338f165dQ0FBAebPn4++ffuKXSZRl8cOm6gL\nu3jxIj7++GO89957+Mc//oGqqiqEhoZi9OjReOqpp/D1119j69atYpdJRGBgE3VpS5cuxdtvv236\nXFdXB61Wi3vuuQe+vr54/fXX8fjjj4tYIRE14/uwibqwrKwsGAwG0+c+ffogISEBc+fOFa8oImoT\nO2yiLuzGsD59+jTy8vIwduxY8QoioltiYBMRAGDnzp1QqVSIjIw0bbtw4YKIFRHRjRjYRF1UbW0t\n3n77bZw4cQIAsHnzZgQHB0Oj0QAAKioqsHTpUjFLJKIb8LEuoi4qJSUFb731FkaMGIH6+npcvHgR\nLi4uAITJZ3PnzkVycrLIVRJRM046I+qiSktLMXPmTHh7e0OtVuPdd9/FK6+8gpqaGuh0OsTFxWHE\niBFil0lEv2FgExERSQDvYRMREUkAA5uIiEgCGNhEREQSwMAmIiKSAAY2ERGRBDCwiYiIJICBTURE\nJAEMbCIiIglgYBMREUkAA5uIiEgC/h+KJZ+AdiNXTQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# compute the squared residuals\n", "linear_resid = linear_interp(plot_grid) - (1 - np.exp(-plot_grid))\n", "cubic_resid = cubic_interp(plot_grid) - (1 - np.exp(-plot_grid))\n", "\n", "# plot the residuals\n", "plt.figure(figsize=(8,6))\n", "plt.plot(plot_grid, linear_resid**2, 'b', label='Linear')\n", "plt.plot(plot_grid, cubic_resid**2, 'g', label='Cubic')\n", "\n", "# demarcate machine epsilon\n", "plt.axhline(np.finfo('float').eps, ls='dashed', color='k')\n", "\n", "# axes, labels, title, etc\n", "plt.xlabel('$x$', fontsize=20)\n", "plt.yscale('log')\n", "plt.ylim(1e-16, 1e0)\n", "plt.title('Squared approximation residuals', fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False, prop={'family':'serif'})\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although cubic spline interpolation strictly dominates linear interpolation in this example, linear interpolation is generally more robust (and has the added benefit that it will preserve many important properties, such as monotonicity, of the function being approximated)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Coding the maps $T$ and $\\mathcal{U}$:\n", "\n", "Now that we have decided on a method for approximating the value and policy functions, we are ready to discuss constructing the Bellman and greedy operators." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def maximize(w, lower, upper):\n", " \"\"\"\n", " Wraps fminbound to find the value the minimizes -v on the closed interval\n", " [lower, upper] using Brent's method.\n", "\n", " Arguments:\n", "\n", " w: (callable) A function representing the current value function \n", " iterate.\n", " lower: (scalar) Lower bound on the correspondence of feasible controls.\n", " upper: (scalar) Upper bound on the correspondence of feasbile controls.\n", "\n", " Returns: \n", "\n", " pol: Value of the control that maximizes the function w.\n", " \n", " \"\"\" \n", " pol = optimize.fminbound(lambda x: -w(x), lower, upper)\n", " return pol\n", "\n", "def deterministic_bellman_operator(w):\n", " \"\"\"\n", " Naive Bellman operator for the optimal savings model with inelastic \n", " labor supply. Approximation of the value function is done using \n", " linear interpolation.\n", "\n", " Arguments:\n", "\n", " w: (object) An instance of the Univariatespline class.\n", "\n", " Returns: \n", "\n", " Tw: (object) A callable UnivariateSpline object.\n", "\n", " \"\"\"\n", " vals = np.empty(Nk)\n", " \n", " # loop over each state and...\n", " for i, k in enumerate(Gk):\n", " \n", " def obj(c):\n", " \"\"\"Current value function.\"\"\"\n", " # next period's value of capital (don't forget to set z=0)\n", " kplus = capital_motion(k, 0, c)\n", " \n", " # compute the value function\n", " tmp_w = (1 - beta) * crra_utility(c) + beta * w(kplus)\n", " \n", " return tmp_w\n", " \n", " # compute the maximizer\n", " pol = maximize(obj, 0, Gamma(k))\n", " # store the new value and policy\n", " vals[i] = obj(pol)\n", " \n", " # interpolate!\n", " Tw = interpolate.UnivariateSpline(Gk, vals, k=1, s=0)\n", " \n", " return Tw\n", "\n", "def deterministic_greedy_operator(w):\n", " \"\"\"\n", " Naive Greedy operator for the optimal savings model with inelastic \n", " labor supply. Approximation of the policy function is done using \n", " linear interpolation.\n", "\n", " Arguments:\n", "\n", " w: (object) An instance of the UnivariateSpline class.\n", "\n", " Returns: \n", "\n", " greedy_policy: (object) A callable UnivariateSpline object.\n", "\n", " \"\"\"\n", " pols = np.empty(Nk)\n", " \n", " # loop over each state and...\n", " for i, k in enumerate(Gk):\n", " \n", " def obj(c):\n", " \"\"\"Current value function.\"\"\"\n", " # next period's value of capital (don't forget to set z=0)\n", " kplus = capital_motion(k, 0, c)\n", " \n", " # compute the value function\n", " tmp_w = (1 - beta) * crra_utility(c) + beta * w(kplus)\n", " \n", " return tmp_w\n", " \n", " # compute the maximizer\n", " pol = maximize(obj, 0, Gamma(k))\n", " # store the new value and policy\n", " pols[i] = pol\n", " \n", " # interpolate!\n", " greedy_policy = interpolate.UnivariateSpline(Gk, pols, k=1, s=0)\n", " \n", " return greedy_policy\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def solve_VFI(init_v, T, tol, pts, mesg=False, **kwargs):\n", " \"\"\"\n", " Basic implementation of Value Iteration Algorithm.\n", "\n", " Arguments:\n", "\n", " init_v: Initial guess of the true value function. A good initial\n", " guess can save a substantial amount of computational time.\n", " \n", " T: A pre-defined Bellman operator.\n", " \n", " tol: Convergence criterion. Algorithm will terminate when \n", " the supremum norm distance between successive value \n", " function iterates is less than tol.\n", " \n", " pts: Grid of points over which to compare value function iterates.\n", " \n", " mesg: Should messages be printed detailing convergence progress?\n", " Default is False.\n", "\n", " Returns: \n", "\n", " final_v: (object) Callable object representing the value function.\n", " \n", " \"\"\"\n", "\n", " # keep track of number of iterations\n", " n_iter = 0\n", "\n", " ##### Value iteration algorithm #####\n", " current_v = init_v\n", "\n", " while True:\n", " next_v = T(current_v, **kwargs)\n", " # supremum norm convergence criterion\n", " change = np.max(np.abs(next_v(pts) - current_v(pts)))\n", " n_iter += 1\n", " \n", " # check for convergence\n", " if change < tol:\n", " if mesg == True:\n", " print \"After\", n_iter, \"iterations, the final change is\", change\n", " final_v = next_v\n", " break\n", " \n", " # print progress every 10 iterations\n", " if n_iter % 10 == 0 and mesg == True:\n", " print \"After\", n_iter, \"iterations, the change is\", change\n", " \n", " current_v = next_v\n", " \n", " return final_v" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will construct a grid around the steady state value of capital... " ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def k_star():\n", " \"\"\"Deterministic steady state value of capital.\"\"\"\n", " rho = (sigma - 1) / sigma\n", " \n", " # nest Cobb-Douglas as special case\n", " if rho == 0:\n", " kss = ((alpha * beta) / (1 - beta * (1 - delta)))**(1 / (1 - alpha))\n", " else:\n", " kss = ((1 / (1 - alpha)) * (((alpha * beta) / (1 - beta * (1 - delta)))**(rho / (rho - 1)) - alpha))**(-1 / rho)\n", " \n", " return kss\n", "\n", "def c_star():\n", " \"\"\"Deterministic steady state value of consumption.\"\"\"\n", " css = ces_output(k_star()) - delta * k_star()\n", " return css" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Important to make sure that $k^* < \\infty$. For $\\sigma=1.0$ this is always satisfied. For $\\sigma \\neq 1$, we need to be more careful. " ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def k_star_isfinite():\n", " \"\"\"Returns true if steady state capital is finite.\"\"\"\n", " # compute rho\n", " rho = (sigma - 1) / sigma\n", " \n", " if rho == 0:\n", " finite = True\n", " elif rho > 0:\n", " finite = beta < (1 / (alpha**(sigma / (sigma - 1)) + (1 - delta)))\n", " else:\n", " finite = beta > (1 / (alpha**(sigma / (sigma - 1)) + (1 - delta)))\n", " \n", " return finite" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# specify some \"sensible\" values for the parameters\n", "alpha = 0.75\n", "sigma = 0.25\n", "delta = 0.05\n", "beta = 0.96\n", "theta = 2.5\n", "\n", "# confirm that k_star is finite!\n", "k_star_isfinite()" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# construct a grid of values for capital\n", "Nk = 100\n", "kmin = 0.5 * k_star()\n", "kmax = 2.0 * k_star()\n", "Gk = np.linspace(kmin, kmax, Nk)\n", "\n", "# specify an initial guess for the consumption policy function\n", "s = 1 - (c_star() / ces_output(k_star()))\n", "solow_consumption = (1 - s) * ces_output(Gk)\n", "w0 = interpolate.UnivariateSpline(Gk, crra_utility(solow_consumption), k=1, s=0) " ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "After 10 iterations, the final change is 0.000304029158548\n" ] } ], "source": [ "# compute the value function using VFI\n", "final_w = solve_VFI(init_v=w0, \n", " T=deterministic_bellman_operator,\n", " tol=0.01 * (1 - beta),\n", " pts=Gk,\n", " mesg=True)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# compute the optimal, greedy policy\n", "consumption_policy = deterministic_greedy_operator(final_w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the results..." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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cGIfDweDBg3E6nfEu+yAiIqlfp06diI6OJk+ePDz++ONxsxVL8lDOlOQWGBiI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\ng8xwQnm99/3331dBQYG++OILvfHGG3r22Wcdz7hunfTzz1L37tX3Pf3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(16, 6))\n", "\n", "##### value function #####\n", "\n", "# plot the value function\n", "axes[0].plot(Gk, final_w(Gk), 'r')\n", "\n", "# labels, title, legend, etc\n", "axes[0].set_xlabel('$k$', fontsize=15)\n", "axes[0].set_ylabel(\"$W(k)$\", rotation='horizontal', fontsize=15)\n", "axes[0].set_title('Optimal value function', fontsize=20, family='serif')\n", "\n", "##### consumption policy function #####\n", "\n", "# plot the consumption policy function\n", "axes[1].plot(Gk, consumption_policy(Gk), 'b')\n", "\n", "# labels, title, legend, etc\n", "axes[1].set_xlabel('$k$', fontsize=15)\n", "axes[1].set_ylabel('$c(k)$', rotation='horizontal', fontsize=15)\n", "axes[1].set_title('Optimal consumption policy', fontsize=20, family='serif')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although the results above look sensible, it would be nice if we had an analytic result against which we could compare our numerical approximation. Turns out that the optimal savings mode with Cobb-Douglas production (i.e., $\\sigma=1.0$), logarithmic preferences (i.e., $\\theta=1.0$), and full depreciation (i.e., $\\delta=1.0$) is known to have a closed form solution.\n", "\n", "To derive the solution we use the \"guess-and-verify\" method. With these parameter restrictions, equation 1.19 implies that \n", "\n", "$$(1-\\beta)\\frac{1}{c(k, z)}\\alpha e^{z}k^{\\alpha-1} = W'(k, z). \\tag{2.1}$$\n", "\n", "Guess that value function is log-linear: \n", "\n", "$$W(k, z) = A + B\\ln\\ k + C\\ln e^z = A + B\\ln\\ k + C z \\implies W'(k,z) = \\frac{B}{k}.$$\n", "\n", "Substitute this result into equation 2.1 and solve for the implied policy function $c(k, z)$:\n", "\n", "$$\\frac{B}{k} = (1-\\beta)\\frac{1}{c(k, z)}\\alpha e^{z}k^{\\alpha-1} \\implies c(k, z) = \\frac{\\alpha(1-\\beta)}{B} e^{z}k^{\\alpha}$$\n", "\n", "Now plug value function guess and its implied policy function into equation 1.20.\n", "\n", "\\begin{align}\n", "A + B\\ln k + Cz =& (1 - \\beta) \\ln\\bigg(c(k, z)\\bigg) + \\beta E\\left\\{A + B\\ln\\bigg(e^{z}k^{\\alpha} - c(k, z)\\bigg) + C \\bigg(\\rho_z z + \\epsilon'\\bigg)\\right\\} \\\\\n", "=& (1 - \\beta) \\ln\\bigg(\\frac{\\alpha(1-\\beta)}{B} e^{z}k^{\\alpha}\\bigg) + \\beta E\\left\\{A + B\\ln\\bigg(e^{z}k^{\\alpha} - \\frac{\\alpha(1-\\beta)}{B} e^{z}k^{\\alpha}\\bigg) + C \\bigg(\\rho_z z + \\epsilon'\\bigg)\\right\\}\\\\\n", "=& (1 - \\beta) \\ln\\bigg(\\frac{\\alpha(1-\\beta)}{B} e^{z}k^{\\alpha}\\bigg) + \\beta E\\left\\{A + B\\ln\\bigg(\\frac{B - \\alpha(1-\\beta)}{B} e^{z}k^{\\alpha}\\bigg) + C \\bigg(\\rho_z z + \\epsilon'\\bigg)\\right\\}\\\\\n", "=& (1 - \\beta) \\ln\\bigg(\\frac{\\alpha(1-\\beta)}{B}\\bigg) + (1 - \\beta)z + \\alpha(1-\\beta)\\ln k + \\beta A + \\beta B\\ln\\bigg(\\frac{B - \\alpha(1-\\beta)}{B}\\bigg) + \\beta B z + \\alpha\\beta B \\ln k + \\beta\\rho_z C z\\\\\n", "=& \\Bigg[\\beta A + \\beta B\\ln\\bigg(\\frac{B - \\alpha(1-\\beta)}{B}\\bigg) + (1 - \\beta) \\ln\\bigg(\\frac{\\alpha(1-\\beta)}{B}\\bigg)\\Bigg] + \\Bigg[\\alpha(1-\\beta) + \\alpha\\beta B\\Bigg] \\ln k + \\Bigg[(1 - \\beta) + \\beta B + \\beta\\rho_z C\\Bigg] z\\\\\n", "\\end{align}\n", "\n", "Applying the method of undetermined coefficients implies that...\n", "\n", "\\begin{align}\n", "A =& \\beta A + \\beta B\\ln\\bigg(\\frac{B - \\alpha(1-\\beta)}{B}\\bigg) + (1 - \\beta) \\ln\\bigg(\\frac{\\alpha(1-\\beta)}{B}\\bigg) \\\\\n", "B =& \\alpha(1-\\beta) + \\alpha\\beta B \\\\\n", "C =& (1 - \\beta) + \\beta B + \\beta\\rho_z C\n", "\\end{align}\n", "\n", "Solving this system of non-linear equations for the unknown coefficients $A$, $B$, and $C$ yields...\n", "\n", "\\begin{align}\n", "A = & \\frac{\\alpha\\beta}{1 - \\alpha\\beta}\\ln(\\alpha\\beta) + \\ln(1 - \\alpha\\beta) \\\\\n", "B = & \\frac{\\alpha(1-\\beta)}{1 - \\alpha\\beta} \\\\\n", "C = & \\frac{1 - \\beta}{1 - \\beta\\rho_z} + \\frac{\\alpha\\beta(1-\\beta)}{1 - \\alpha\\beta}\n", "\\end{align}\n", "\n", "In order to confirm that our guess of the value function was correct, we can substitute its implied policy function\n", "\n", "$$c(k, z) = (1 - \\alpha\\beta)e^{z}k^{\\alpha} \\tag{2.2}$$\n", "\n", "into equation 1.10 (i.e., the consumption Euler equation) and check whether or not we recover the correct equation of motion for capital." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# anaytic values for the parameters\n", "alpha = 0.33\n", "sigma = 1.0\n", "delta = 1.0\n", "beta = 0.96\n", "theta = 1.0\n", "\n", "# confirm that k_star is finite!\n", "k_star_isfinite()" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# coefficients used to define the analytic value and policy functions\n", "A = ((alpha * beta) / (1 - alpha * beta)) * np.log(alpha * beta) + np.log(1 - alpha * beta)\n", "B = (alpha * (1 - beta)) / (1 - alpha * beta)\n", "C = ((1 - beta) / (1 - beta * rho_z)) + ((alpha * beta * (1 - beta)) / (1 - alpha * beta))" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def analytic_w(k, z=0.0):\n", " \"\"\"\n", " Analytic solution for the value function with Cobb-Douglas production,\n", " logarithmic preferences and full deprectiation.\n", "\n", " \"\"\"\n", " return A + B * np.log(k) + C * z\n", "\n", "def analytic_c(k, z=0.0):\n", " \"\"\"\n", " Analytic solution for the optimal consumption policy function\n", " with Cobb-Douglas production, logarithmic preferences and full depreciation.\n", " \n", " \"\"\"\n", " return (1 - alpha * beta) * np.exp(z) * k**alpha" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# construct a grid of values for capital\n", "Nk = 100\n", "kmin = 0.5 * k_star()\n", "kmax = 2.0 * k_star()\n", "Gk = np.linspace(kmin, kmax, Nk)\n", "\n", "# define a convergence tolerance\n", "tol = 0.01 * (1 - beta)\n", "\n", "# specify an initial guess of zero net investment\n", "init_vals = crra_utility(ces_output(Gk) - delta * Gk)\n", "w0 = interpolate.UnivariateSpline(Gk, init_vals, k=1, s=0) " ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "After 3 iterations, the final change is 6.26972116304e-05\n" ] } ], "source": [ "# compute the value function using VFI\n", "final_w = solve_VFI(init_v=w0, \n", " T=deterministic_bellman_operator,\n", " tol=tol,\n", " pts=Gk,\n", " mesg=True)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# compute the optimal consumption policy\n", "consumption_policy = deterministic_greedy_operator(final_w)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CS0tLuLm5QQhRpEPVUNETvLeTiEjr5Aey5Q+v6dSpk9rcre47u6DzUuExZ5Km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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(16, 6))\n", "\n", "##### value function #####\n", "\n", "# plot the value function\n", "axes[0].plot(Gk, final_w(Gk), 'b', label='numeric')\n", "\n", "# plot the analytic value function\n", "axes[0].plot(Gk, analytic_w(Gk), 'r', label='analytic')\n", " \n", "# labels, title, legend, etc\n", "axes[0].set_xlabel('$k$', fontsize=15)\n", "axes[0].set_ylabel(\"$W(k)$\", rotation='horizontal', fontsize=15)\n", "axes[0].set_title('Optimal value function', fontsize=20, family='serif')\n", "axes[0].legend(loc='best', frameon=False, prop={'family':'serif'})\n", "\n", "##### consumption policy function #####\n", "\n", "# plot the consumption policy function\n", "axes[1].plot(Gk, consumption_policy(Gk), 'b', label='numeric')\n", "\n", "# plot the analytic consumption policy function\n", "axes[1].plot(Gk, analytic_c(Gk), 'r', label='analytic')\n", "\n", "# labels, title, legend, etc\n", "axes[1].set_xlabel('$k$', fontsize=15)\n", "axes[1].set_ylabel('$c(k)$', rotation='horizontal', fontsize=15)\n", "axes[1].set_title('Optimal consumption policy', fontsize=20, family='serif')\n", "axes[1].legend(loc='best', frameon=False, prop={'family':'serif'})\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Assessing approximation error\n", "\n", "Assessing numerical approximation error is an important part of any computational analysis. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Graphical measure of approximation error\n", "\n", "Always plot your residuals!" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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xSp7P9evXxfjx40VgYKBwdXUVYWFhYt68eQbzAqv9zvbt26ed01Wj0WjXlTVH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\npW21vLeJicbuU6CUlMibzhUVASNH6jsuJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(16, 6))\n", "\n", "##### value function residual #####\n", "\n", "# plot the value function residual\n", "residual = final_w(Gk) - analytic_w(Gk)\n", "axes[0].plot(Gk, residual, 'r')\n", "\n", "# labels, title, legend, etc\n", "axes[0].set_xlabel('$k$', fontsize=15)\n", "axes[0].set_ylabel(\"$\\hat{W}(k) - W(k)$\", fontsize=15)\n", "axes[0].set_title('Value function residual', fontsize=20, family='serif')\n", "\n", "##### consumption policy residual #####\n", "\n", "## plot the consumption policy residual\n", "residual = consumption_policy(Gk) - analytic_c(Gk)\n", "axes[1].plot(Gk, residual, 'b')\n", "\n", "# labels, title, legend, etc\n", "axes[1].set_xlabel('$k$', fontsize=15)\n", "axes[1].set_ylabel(\"$\\hat{c}(k) - c(k)$\", fontsize=15)\n", "axes[1].set_title('Consumption policy residual', fontsize=20, family='serif')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mathematical measures of approximation error\n", "We can compare our numerical approximations of the closed-form policy functions using the $L^2$ and $L^{\\infty}$ norms. Recall that the $L^2$ norm, which is defined as\n", "\n", "$$L^2 errors = \\left[\\sum_{k\\in G_k} \\bigg(\\hat{k}'(k) - k'(k)\\bigg)^2\\right]^{\\frac{1}{2}}$$\n", "\n", "is a measure of the *total* approximation error. Meanwhile, the $L^{\\infty}$ norm, which is defined as\n", "\n", "$$L^{\\infty} errors = \\max_{k\\in G_k} \\bigg|\\hat{k}'(k) - k'(k)\\bigg|$$\n", "\n", "is a measure of the point-wise approximation error." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def get_L2_errors(pol1, pol2):\n", " \"\"\"\n", " Computes a measure of total difference between policy functions \n", " using the L2 norm. Function requires that both pol1 and pol2 have \n", " the same shape.\n", " \n", " Arguments:\n", " \n", " pol1: (array) Array of values representing a policy function.\n", " pol2: (array) Array of values representing a policy function.\n", " \n", " Returns:\n", " \n", " error: (float) L2 error.\n", " \n", " \"\"\"\n", " error = np.sum((pol1 - pol2)**2)**0.5\n", " return error\n", "\n", "def get_maximal_errors(pol1, pol2):\n", " \"\"\"\n", " Computes a measure of point-wise difference between policy functions \n", " using the L_infty norm. Function requires that both pol1 and pol2 \n", " have the same shape.\n", " \n", " Arguments:\n", " \n", " pol1: (array) Array of values representing a policy function.\n", " pol2: (array) Array of values representing a policy function.\n", " \n", " Returns:\n", " \n", " error: (float) L_infty error.\n", " \n", " \"\"\"\n", " error = np.max(np.abs(pol1 - pol2))\n", " return error" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.0053022270615602869" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# L2 errors for the consumption_policy policy function\n", "get_L2_errors(pol1=consumption_policy(Gk), pol2=analytic_c(Gk))" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.0011624262883965231" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# maximal error for the consumption policy function\n", "get_maximal_errors(pol1=consumption_policy(Gk), pol2=analytic_c(Gk))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Economic measures of approximation error\n", "In cases for which no analytic solution exists we can still find an economic measure of approximation error. We know that the following Euler equation must hold\n", "\n", "$$c(k, k'(k))^{-\\theta} = \\beta c(k'(k), k''(k'))^{-\\theta}(1 + r(k'(k))$$\n", "\n", "Define the Euler residual " ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def get_euler_residual(cpol, k, z=None, T=100, normed=True):\n", " \"\"\"\n", " Residual of the consumption Euler equation.\n", " \n", " Arguments:\n", " \n", " cpol: (callable) Callable consumption policy function.\n", " k: (array) Values of capital at which to compute the \n", " Euler residual.\n", " z: (array) Values of total factor productivity at which \n", " to compute the Euler residual. Default is None.\n", " T: (int) Number of draws to use when computing \n", " normed: (boolean) Whether or not you wish to normalize the\n", " Euler residuals by the level of consumption.\n", " \n", " Returns:\n", " \n", " resid: (array) Array of values containing the Euler residuals.\n", " \n", " \"\"\"\n", " # deterministic case\n", " if z == None:\n", " # compute next period's capital stock and mpk\n", " kplus = capital_motion(k, 0, cpol(k))\n", " rplus = ces_mpk(kplus)\n", " \n", " # compute the Euler residual\n", " resid = cpol(k)**-theta - beta * cpol(kplus)**-theta * (1 + rplus - delta)\n", " \n", " if normed == True:\n", " resid = resid / cpol(k)\n", " \n", " # stochastic case\n", " else:\n", " # storage container for residual\n", " resid = np.empty((Nk, Nz))\n", " \n", " # to compute next period's mpk need to simulate some shocks\n", " eps = stats.norm(0, sigma_z)\n", " \n", " # compute the Euler residual (should be more efficient way to do this using broadcasting)\n", " for j, zval in enumerate(z):\n", " zplus = productivity_motion(zval, eps.rvs(T))\n", " for i, kval in enumerate(k):\n", " \n", " # compute next period's capital stock \n", " kplus = np.repeat(capital_motion(kval, zval, cpol(kval, zval)), zplus.size)\n", " rplus = ces_mpk(kplus, zplus)\n", " \n", " # compute the residual using Monte Carlo integration\n", " resid[i,j] = (cpol.ev(kval, zval)**-theta - \n", " beta * np.mean(cpol.ev(kplus, zplus)**-theta * (1 + rplus - delta)))\n", " \n", " if normed == True:\n", " resid = resid / cpol(k[:,np.newaxis], z)\n", " \n", " return resid" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the Euler residuals is a good way to understand which portions of the state space you are relatively approximating well." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0KPuMJ05U30ZaGvscpLM3pFRXs/1FWiaQlggA39RCNTHDT9hGr8D5PqHkDDQ0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\nBx8gJycHycnJAICKigpbBmMHlBkgggZyBtyBygREhOBKZiA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "\n", "# compute Euler residuals\n", "euler_residuals = get_euler_residual(cpol=consumption_policy, k=Gk, normed=True)\n", "\n", "# standard is to plot squared Euler residuals\n", "plt.plot(Gk, euler_residuals**2, 'r')\n", "plt.yscale('log')\n", "\n", "plt.xlabel('$k$', fontsize=15)\n", "plt.ylabel('Euler residuals (normalized)', fontsize=15, family='serif')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.00059534797351319679" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# for a point estimate of approximation error use the average Euler residual\n", "np.mean(euler_residuals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise\n", "\n", "Now that we have confirmed that the code is working, and discussed how to use it, I want you to play around with solving for the optimal value and policy functions. Some things to think about...\n", "\n", "* Change parameters. For which values of the parameters is the consumption policy function \"roughly\" linear? For which values of the parameters is the consumption policy function highly non-linear?\n", "* Increase the number of grid points, Nk. What is the relationship between the number of grid points and the time it takes to compute the solution? What is the relationship between the number of grid points and the accuracy of the computed solution?\n", "* Change kmin and/or kmax. What is the relationship between the size of the grid and the time it takes to compute the solution? What is the relationship between the size of the grid and the accuracy of the computed solution?\n", "* Change the convergence tolerance. What is the relationship between the convergence tolerance and the he time it takes to compute the solution?" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# define model parameters\n", "alpha = 0.45\n", "beta = 0.96\n", "delta = 0.05\n", "sigma = 0.85\n", "theta = 2.5\n", "\n", "# confirm that k_star is finite!\n", "k_star_isfinite()" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# construct a grid of values for capital\n", "Nk = 1000\n", "kmin = 0.5 * k_star()\n", "kmax = 2.5 * k_star()\n", "Gk = np.linspace(kmin, kmax, Nk)\n", "\n", "# define a convergence tolerance\n", "tol = 0.01 * (1 - beta)\n", "\n", "# specify an initial guess of zero net investment\n", "init_vals = crra_utility(ces_output(Gk) - delta * Gk)\n", "w0 = interpolate.UnivariateSpline(Gk, init_vals, k=1, s=0) " ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "After 10 iterations, the change is 0.000839931121629\n", "After 15 iterations, the final change is 0.000395013439509\n" ] } ], "source": [ "# compute the value function using VFI\n", "final_w = solve_VFI(init_v=w0, \n", " T=deterministic_bellman_operator,\n", " tol=tol,\n", " pts=Gk,\n", " mesg=True)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 loops, best of 1: 43 s per loop\n" ] } ], "source": [ "# how long does it take to compute the solution?\n", "%timeit -n 1 -r 1 solve_VFI(init_v=w0, T=deterministic_bellman_operator, tol=tol, pts=Gk)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# compute the optimal consumption policy\n", "consumption_policy = deterministic_greedy_operator(final_w)" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 loops, best of 1: 2.77 s per loop\n" ] } ], "source": [ "# how long does it take to compute the policy function\n", "%timeit -n 1 -r 1 deterministic_greedy_operator(final_w)" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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gTJ8+HQ8ePMAHH3yAIUOGaDsppZxRpPiNiopC/fr1tc8bNmyI48eP6ywjSRKO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\nSDCdBgCK+XNdsSxLI0aMUFBQkGbNmlXmNRc3vEpNTdX69eu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(16, 6))\n", "\n", "##### value function #####\n", "\n", "# plot the value function\n", "axes[0].plot(Gk, final_w(Gk), 'r')\n", "\n", "# labels, title, legend, etc\n", "axes[0].set_xlabel('$k$', fontsize=15)\n", "axes[0].set_ylabel(\"$W(k)$\", rotation='horizontal', fontsize=15)\n", "axes[0].set_title('Optimal value function', fontsize=20, family='serif')\n", "\n", "##### consumption policy function #####\n", "\n", "# plot the consumption policy function\n", "axes[1].plot(Gk, consumption_policy(Gk), 'b')\n", "\n", "# labels, title, legend, etc\n", "axes[1].set_xlabel('$k$', fontsize=15)\n", "axes[1].set_ylabel('$c(k)$', rotation='horizontal', fontsize=15)\n", "axes[1].set_title('Optimal consumption policy', fontsize=20, family='serif')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0hRfkf62oSCZjQKxtq1YBWVkiZu6/X6wV8+cDf/2rfObBB2XCLS2Vlf7atRLM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\nX6hr1641fJ+rfaEA6wxEKEaTfahYBtzRqpVx3IA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "\n", "# compute Euler residuals\n", "euler_residuals = get_euler_residual(cpol=consumption_policy, k=Gk, normed=True)\n", "plt.plot(Gk, euler_residuals**2, 'r')\n", "plt.yscale('log')\n", "\n", "plt.xlabel('$k$', fontsize=15)\n", "plt.ylabel('Euler residual (normalized)', fontsize=15, family='serif')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-5.6875794302890246e-05" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# average Euler residual\n", "np.mean(euler_residuals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Stochastic dynamic programming\n", "\n", "Now we extend the model by incorporating an AR(1) process driving total factor productivity. Incorporating a correlated productivity shock requires us to keep track of a second state variable (i.e., the current value of total factor productivity!). " ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def randomized_bellman_operator(w):\n", " \"\"\"\n", " The randomized Bellman operator, R, from Stachurski and Pal (2012). \n", " Approximation of the value surface is done using bi-linear interpolation.\n", "\n", " Arguments:\n", "\n", " w: (object) An instance of the RectBivariateSpline class.\n", "\n", " Returns: \n", "\n", " Tw: (object) A callable RectBivariateSpline object.\n", "\n", " \"\"\"\n", " new_vals = np.zeros((Nk, Nz))\n", " \n", " for j, z in enumerate(Gz):\n", " \n", " # make next period's shock conditional on current z\n", " zplus = rho_z * z + epsilon_z\n", " \n", " for i, k in enumerate(Gk):\n", " \n", " def obj(c):\n", " \"\"\"Current value function.\"\"\"\n", " # for some reason, v.ev doesn't broadcast!\n", " kplus = np.repeat(capital_motion(k, z, c), zplus.size)\n", " \n", " # note use of convex combination of u and E[v]!\n", " tmp_v = (1 - beta) * crra_utility(c) + beta * np.mean(w.ev(kplus, zplus))\n", " \n", " return tmp_v\n", " \n", " # find the value of the control that maximizes the current value function \n", " pol = maximize(obj, 0, Gamma(k, z))\n", " # update the value function with maximum value of obj\n", " new_vals[i, j] = obj(pol)\n", " \n", " # interpolate\n", " \n", " Tv = interpolate.RectBivariateSpline(Gk, Gz, new_vals, kx=1, ky=1)\n", " \n", " return Tv\n", "\n", "def randomized_greedy_operator(w):\n", " \"\"\"\n", " The randomized Greedy operator, R, from Stachurski and Pal (2012). \n", " Approximation of the policy surface is done using bi-linear interpolation.\n", "\n", " Arguments:\n", "\n", " w: (object) An instance of the RectBivariateSpline class.\n", "\n", " Returns: \n", "\n", " Tw: (object) A callable RectBivariateSpline object.\n", "\n", " \"\"\"\n", " new_pols = np.zeros((Nk, Nz))\n", " \n", " for j, z in enumerate(Gz):\n", " \n", " # make next period's shock conditional on current z\n", " zplus = rho_z * z + epsilon_z\n", " \n", " for i, k in enumerate(Gk):\n", " \n", " def obj(c):\n", " \"\"\"Current value function.\"\"\"\n", " # for some reason, v.ev doesn't broadcast!\n", " kplus = np.repeat(capital_motion(k, z, c), zplus.size)\n", " \n", " # note use of convex combination of u and E[w]!\n", " tmp_v = (1 - beta) * crra_utility(c) + beta * np.mean(w.ev(kplus, zplus))\n", " \n", " return tmp_v\n", " \n", " # find the value of the control that maximizes the current value function \n", " pol = maximize(obj, 0, Gamma(k, z))\n", " # update the policy function with maximizer of obj\n", " new_pols[i, j] = pol\n", " \n", " # interpolate\n", " Tv = interpolate.RectBivariateSpline(Gk, Gz, new_pols, kx=1, ky=1)\n", " \n", " return Tv" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def solve_VFI_2D(init_v, T, tol, kpts, zpts, mesg=False, **kwargs):\n", " \"\"\"\n", " Basic implementation of Value Iteration Algorithm.\n", "\n", " Arguments:\n", "\n", " init_v: Initial guess of the true value function. A good initial\n", " guess can save a substantial amount of computational time.\n", " \n", " T: A pre-defined Bellman operator.\n", " \n", " tol: Convergence criterion. Algorithm will terminate when \n", " the supremum norm distance between successive value \n", " function iterates is less than tol.\n", " \n", " kpts: Grid of value for capital over which to compare value \n", " function iterates.\n", " \n", " zpts: Grid of value for total factor productivity over which to \n", " compare value function iterates.\n", " \n", " mesg: Should messages be printed detailing convergence progress?\n", " Default is False.\n", "\n", " Returns: \n", "\n", " final_v: (object) Callable object representing the value function.\n", " \n", " \"\"\"\n", "\n", " # keep track of number of iterations\n", " n_iter = 0\n", "\n", " ##### Value iteration algorithm #####\n", " current_v = init_v\n", "\n", " while True:\n", " next_v = T(current_v, **kwargs)\n", " # supremum norm convergence criterion\n", " change = np.max(np.abs(next_v(kpts, zpts) - current_v(kpts, zpts)))\n", " n_iter += 1\n", " \n", " # check for convergence\n", " if change < tol:\n", " if mesg == True:\n", " print \"After\", n_iter, \"iterations, the final change is\", change\n", " final_v = next_v\n", " break\n", " \n", " # print progress every 5 iterations\n", " if n_iter % 5 == 0 and mesg == True:\n", " print \"After\", n_iter, \"iterations, the change is\", change\n", " \n", " current_v = next_v\n", " \n", " return final_v" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# define model parameters\n", "alpha = 0.33\n", "beta = 0.96\n", "delta = 1.0\n", "sigma = 1.0\n", "theta = 1.0\n", "sigma_z = 0.01\n", "rho_z = 0.95\n", "\n", "# confirm that k_star is finite!\n", "k_star_isfinite()" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# grid of values for k\n", "Nk = 100\n", "kmax = 1.5 * k_star()\n", "kmin = 0.5 * k_star()\n", "Gk = np.linspace(kmin, kmax, Nk)\n", "\n", "# grid of values for z (always make Nz odd!)\n", "Nz = 11\n", "zmin = -3 * sigma_z\n", "zmax = 3 * sigma_z\n", "Gz = np.linspace(zmin, zmax, Nz)\n", "\n", "# specify a convergence criterion\n", "tol = 0.01 * (1 - beta)\n", "\n", "# number of random draws for TFP shock (only need to do this once!)\n", "np.random.seed(42)\n", "T = 100\n", "epsilon_z = np.random.normal(0, sigma_z, T)\n", "\n", "# initialize value function using consumption policy that leads to zero net investment\n", "zero_net_policy = ces_output(Gk[:,np.newaxis], Gz) - delta * Gk[:,np.newaxis]\n", "init_vals = crra_utility(zero_net_policy)\n", "w0 = interpolate.RectBivariateSpline(Gk, Gz, init_vals, kx=1, ky=1, s=0)" ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "After 5 iterations, the change is 0.00298711235442\n", "After 10 iterations, the change is 0.00138105436677\n", "After 15 iterations, the change is 0.000623535406505\n", "After 18 iterations, the final change is 0.00038461043733\n" ] } ], "source": [ "# compute the value function using VFI\n", "final_w = solve_VFI_2D(init_v=w0, \n", " T=randomized_bellman_operator,\n", " tol=tol,\n", " kpts=Gk,\n", " zpts=Gz,\n", " mesg=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the value surface in 3D..." ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Izc3F9u3b8cgjj7iuxW0QGRkJsVhs85pKpYJYLLa5j7A3BAIBVq5cid9++w1P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S5saQzX0F9/LopJ+7ipH1O5QcjvRMULkMok1g3/AklvRpdn8Q0HP04Lqouy7MIUbuMIZvkycdPh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AzL8pbiTEuSpYCkOAR5uZah64q8HEN1leb2jJeGak0UweqWw/a9cUcSSwgGOp3ZaG625VCN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\nOVy5ckXaK/Lw8MBsNlNWViZV8dkjY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,6))\n", "ax = fig.add_subplot(111, projection='3d', azim=-125)\n", "\n", "# generate the coordinates for plotting\n", "k_coords, z_coords = np.meshgrid(Gk, Gz, indexing='ij')\n", "\n", "# generate a surface plot\n", "ax.plot_surface(k_coords, z_coords, final_w(Gk, Gz), rstride=1, cstride=1, cmap=mpl.cm.jet,\n", " linewidth=0.0)\n", "\n", "# axes, labels, title, etc\n", "ax.set_ylabel('$z$', fontsize=20)\n", "ax.set_xlabel('$k$', fontsize=20)\n", "ax.set_title('$W(k, z)$ for stochastic optimal savings model\\n' + \\\n", " r'$\\alpha=%g, \\beta=%g, \\delta=%g, \\sigma=%g, \\theta=%g, \\rho_z=%g, \\sigma_z=%g$' \\\n", " %(alpha, beta, delta, sigma, theta, rho_z, sigma_z), fontsize=20, family='serif')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "...and, because we derived an analytic result for these parameters, we can compute $L^2$ and $L^{\\infty}$ errors." ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.25554003851924406" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# compute the L2 errors\n", "get_L2_errors(final_w(Gk, Gz), analytic_w(Gk[:,np.newaxis], Gz))" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.0085297373147352751" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# compute the maximal errors\n", "get_maximal_errors(final_w(Gk, Gz), analytic_w(Gk[:,np.newaxis], Gz))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we compute the optimal consumption policy" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# compute the optimal consumption policy\n", "consumption_policy = randomized_greedy_operator(final_w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another way of plotting functions of two variables is to make use of contour plots." ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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uxIkTqFKlivQ5bR38fj/Gjh2L77//Hg8++GDUchZ+/PFH5QgmLS0NhYWFoOXw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HzaebAR6+TBFAX29PRzcHeQz1dMzzP3JFhwwCWXd3DLTb4aRuT0RkOKtllFA0orCCiRy3VoAFdq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jwlOXJQhuXyKlMgRM66g9SUYjJYoUkgdwzqnA85uA/f2RmGPEmCKb0g8ppEz9c4TPxUVRxodW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\nKK7/YnY0XQUdSPAxYtWYhtONsYrGlpK/DGc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,6))\n", "ax = fig.add_subplot(111)\n", "\n", "# one way of generating a contour plot using Matplotlib\n", "ax.imshow(consumption_policy(Gk, Gz).T, cmap=mpl.cm.jet, origin='lower', interpolation='gaussian', \n", " aspect='auto', extent=[kmin, kmax, zmin, zmax])\n", "\n", "# add contour lines\n", "CS = ax.contour(k_coords, z_coords, consumption_policy(Gk, Gz), 10, colors='k')\n", "CS.clabel(colors='k')\n", "\n", "# axes, labels, title, etc\n", "ax.set_ylabel('$z$', fontsize=20, rotation='horizontal')\n", "ax.set_xlabel('$k$', fontsize=20)\n", "ax.set_title('$c(k, z)$ for stochastic optimal savings model\\n' + \\\n", " r'$\\alpha=%g, \\beta=%g, \\delta=%g, \\sigma=%g, \\theta=%g, \\rho_z=%g, \\sigma_z=%g$' \\\n", " %(alpha, beta, delta, sigma, theta, rho_z, sigma_z), fontsize=20, family='serif')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can even use contour plots to look for patterns in the Euler residuals!" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ChQpUoUIF6tq1q+WdKTxeffVVM261bNmSpk2bZo5J4x///hEiorfffpvatm1L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4PGtOSHXS+KNiByhWg411QkMPTwZ6xDUKgHLprohvhT8D6Si86rASVCBWAdNrA67MihlNsdORhh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\nun7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,6))\n", "ax = fig.add_subplot(111)\n", "\n", "# compute and store normalized Euler residuals for all points in the state space\n", "euler_residuals = get_euler_residual(cpol=consumption_policy, k=Gk, z=Gz, T=1000)\n", "log_square_euler_resids = np.log10(euler_residuals**2)\n", "\n", "# plot the Euler residuals\n", "resid_plot = ax.imshow(log_square_euler_resids.T, cmap=mpl.cm.cool, origin='lower', \n", " interpolation='gaussian', aspect='auto', extent=[kmin, kmax, zmin, zmax])\n", "\n", "# add a colorbar to the plot\n", "fig.colorbar(resid_plot)\n", "\n", "# axes, labels, title, etc\n", "ax.set_ylabel('$z$', fontsize=20, rotation='horizontal')\n", "ax.set_xlabel('$k$', fontsize=20)\n", "ax.set_title('Euler residuals for stochastic optimal savings model\\n' + \\\n", " r'$\\alpha=%g, \\beta=%g, \\delta=%g, \\sigma=%g, \\theta=%g, \\rho_z=%g, \\sigma_z=%g$' \\\n", " %(alpha, beta, delta, sigma, theta, rho_z, sigma_z), fontsize=20, family='serif')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-3.6893922788297808" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# point estimate for the Euler residual is just the global average\n", "np.mean(log_square_euler_resids)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can plot the Euler residual for a particular value of either capital or TFP. Here is an example plot of the Euler residual for different values of capital assuming that the productivity shock is $z=0$." ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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vtj0XUPLGT6NGqbv8z54FatUq+js8XN0j8PnnIixVHC5eFEmRap4YAOjevXgi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\n0KVLF9XXR44ciYSEBA9bRQghhJRuArxtgEKjRo3svrZ06VL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "\n", "# plot the squared Euler residual for z=0\n", "plt.plot(Gk, log_square_euler_resids[:, 5])\n", "plt.axhline(np.log10(np.finfo('float').eps), ls='dashed', color='k')\n", "\n", "# axes, labels, title, etc\n", "plt.xlabel('Capital, $k$', fontsize=15, family='serif')\n", "plt.ylabel('Residuals (log-scale)', fontsize=15, family='serif')\n", "plt.title('Normalized Euler residuals', fontsize=20, family='serif')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise\n", "\n", "Now that we have confirmed that the code is working, and discussed how to use it, I want you to play around with solving for the optimal value and policy functions. Some things to think about...\n", "\n", "* Change parameters. For which values of the parameters is the consumption policy function \"roughly\" linear? For which values of the parameters is the consumption policy function highly non-linear?\n", "* Increase the number of grid points, Nk. What is the relationship between the number of grid points and the time it takes to compute the solution? What is the relationship between the number of grid points and the accuracy of the computed solution?\n", "* Change kmin and/or kmax. What is the relationship between the size of the grid and the time it takes to compute the solution? What is the relationship between the size of the grid and the accuracy of the computed solution?\n", "* Change the convergence tolerance. What is the relationship between the convergence tolerance and the he time it takes to compute the solution?" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# define model parameters\n", "alpha = 0.45\n", "beta = 0.96\n", "delta = 0.05\n", "sigma = 0.85\n", "theta = 2.5\n", "sigma_z = 0.01\n", "rho_z = 0.95\n", "\n", "# confirm that k_star is finite!\n", "k_star_isfinite()" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# grid of values for k\n", "Nk = 100\n", "kmax = 1.25 * k_star()\n", "kmin = 0.75 * k_star()\n", "Gk = np.linspace(kmin, kmax, Nk)\n", "\n", "# grid of values for z (always make Nz odd!)\n", "Nz = 11\n", "zmin = -5 * sigma_z\n", "zmax = 5 * sigma_z\n", "Gz = np.linspace(zmin, zmax, Nz)\n", "\n", "# specify a convergence criterion\n", "tol = 0.01 * (1 - beta)\n", "\n", "# number of random draws for TFP shock (only need to do this once!)\n", "np.random.seed(42)\n", "T = 1000\n", "epsilon_z = np.random.normal(0, sigma_z, T)\n", "\n", "# initialize value function using consumption policy that results in zero net investment \n", "zero_net_policy = ces_output(Gk[:,np.newaxis], Gz) - delta * Gk[:,np.newaxis]\n", "init_vals = crra_utility(zero_net_policy)\n", "\n", "w0 = interpolate.RectBivariateSpline(Gk, Gz, init_vals, kx=1, ky=1)" ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "After 5 iterations, the change is 0.00963138020099\n", "After 10 iterations, the change is 0.00737228007105\n", "After 15 iterations, the change is 0.00578128452752\n", "After 20 iterations, the change is 0.00458935005222\n", "After 25 iterations, the change is 0.0036728257006\n", "After 30 iterations, the change is 0.00295604030646\n", "After 35 iterations, the change is 0.00238861387372\n", "After 40 iterations, the change is 0.00193547209708\n", "After 45 iterations, the change is 0.00157132652455\n", "After 50 iterations, the change is 0.0012774015982\n", "After 55 iterations, the change is 0.0010394191588\n", "After 60 iterations, the change is 0.000846314447741\n", "After 65 iterations, the change is 0.000689389039021\n", "After 70 iterations, the change is 0.000561731802724\n", "After 75 iterations, the change is 0.000457809257089\n", "After 79 iterations, the final change is 0.000388736319336\n" ] } ], "source": [ "# compute the value function using VFI\n", "final_w = solve_VFI_2D(init_v=w0, \n", " T=randomized_bellman_operator,\n", " tol=tol,\n", " kpts=Gk,\n", " zpts=Gz,\n", " mesg=True)" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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1rjN2+vHHHyGVSrF06VJTml6vx4kTJ3DbbbdZne+sbQBAIBBYfaA//fRTsCyL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G51TmZpiKjruHNKpVdc86X0akRURlYuE+z4ErL1PsnaD4haD7mxztVXXfOoRBsynEHqWXRuK8KG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\nvFcCJD7KwqiUolgsUiwW01RLz/M+1jkbf5vO8Xe1lgDEG1Qvmsj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