{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## A First Scientific Python Program\n", "\n", "#### John Stachurski\n", "#### Prepared for the HCMC Workshop, Nov 2016" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's import some scientific libraries" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next instruction tells Jupyter to show plots inside the browser" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now here's our code. It plots the time series\n", "\n", "$$ X_{t+1} = \\alpha X_t + W_{t+1} $$\n", "\n", "where \n", "\n", "* $\\{W_t\\}$ is standard normal,\n", "* $X_0 = 0$\n", "\n", "and $\\alpha$ takes three different values" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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3KlV2maU9XicPcGr+qewx7Zne1sPjdPLTJfIdPR1093eTFuvXQbSigr7yBd7Y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\nvf1Glqef5bHuI0cCi3xGhvz+cFsS8YPt5FpyKUkpIT6zmr/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hJlRenses2oICeHX4PI44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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alphas = [0.0, 0.8, 0.98]\n", "ts_length = 200\n", "\n", "fig, ax = plt.subplots()\n", "\n", "for α in alphas: \n", " X = np.zeros(ts_length) # Allocate an array of zeros\n", "\n", " for t in range(ts_length - 1):\n", " X[t+1] = α * X[t] + np.random.randn()\n", " \n", " ax.plot(X, label=r'$\\alpha = {}$'.format(α))\n", " \n", "ax.legend(loc='lower left', frameon=False, ncol=3)\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### Exercise 1\n", "\n", "Generate a single time series following an AR(1) process as above when $\\alpha = 0.99$. However, let's now add reflecting barriers at $-2$ and $2$. Thus, \n", "\n", "$$ y_{t+1} = \\alpha X_t + W_{t+1} $$\n", "\n", "and \n", "\n", "$$ X_{t+1} = \n", "\\begin{cases}\n", " -2 & \\text{ if } y_{t+1} < -2 \\\\\n", " 2 & \\text{ if } y_{t+1} > 2 \\\\\n", " y_{t+1} & \\text{ otherwise}\n", " \\end{cases}\n", "$$\n", "\n", "Plot the time series." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n" ] } ], "source": [ "for i in range(40):\n", " print(\"solution below!\")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ckfz9n/8EurqAr3/d3f5cfz2wdi39/PWvA9/9bvK+Dz4A3n0X+M533D0Hw1jhj38E/vEP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\nwGEBwjAMwzBM4LAAYRiGYRgmcFiAMAzDMAwTOCxAGIZhGIYJHBYgDMM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "α = 0.99\n", "X = np.zeros(ts_length)\n", "\n", "for t in range(ts_length-1):\n", " y = α * X[t] + np.random.randn()\n", " if y > 2:\n", " X[t+1] = 2\n", " elif y < -2:\n", " X[t+1] = -2\n", " else:\n", " X[t+1] = y\n", " \n", "fig, ax = plt.subplots(figsize=(9, 6))\n", "ax.set_ylim(-3, 3)\n", "ax.plot(X, label=\"AR1 with reflecting barriers\")\n", "ax.legend(frameon=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Assuming that the spectral radius of the $n \\times n$ matrix $\\Pi$ is strictly less\n", "than one, the equation\n", "\n", "$$ x = \\Pi x + b $$\n", "\n", "has a unique $n \\times 1$ solution vector $x$ for each choice of the vector $b$. The\n", "solution satisfies\n", "\n", "$$\n", " x^* = (I - \\Pi)^{-1} b = \\sum_{t=0}^\\infty \\Pi^t b\n", "$$\n", "\n", "where $I$ is the identity matrix. Try computing this solution both ways, for the matrix\n", "\n", "$$\n", "\\Pi = \n", "\\begin{pmatrix}\n", " 0.4 & 0.2 \\\\\n", " 0.6 & 0.2\n", "\\end{pmatrix}\n", "$$\n", "\n", "and vector $b = \\begin{pmatrix} 1 \\\\ 1 \\end{pmatrix}$. In the second case you will have\n", "to truncate the infinite sum at some reasonable level." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n", "solution below!\n" ] } ], "source": [ "for i in range(40):\n", " print(\"solution below!\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First let's solve it by matrix inversion." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 2.77777778]\n", " [ 3.33333333]]\n" ] } ], "source": [ "from numpy.linalg import solve\n", "\n", "Π = np.array([[0.4, 0.2],\n", " [0.6, 0.2]])\n", "b = np.ones(2).reshape(2, 1)\n", "\n", "x_star = solve(np.eye(2) - Π, b)\n", "print(x_star)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's try using the sum and see if we get the same answer:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 2.77777778]\n", " [ 3.33333333]]\n" ] } ], "source": [ "E = np.eye(2)\n", "x_star = np.zeros((2, 1))\n", "for i in range(100):\n", " x_star += E @ b\n", " E = E @ Π\n", "print(x_star)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 1 }