{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import numpy as np\n", "import numpy.linalg as la\n", "\n", "import scipy.optimize as sopt\n", "\n", "import matplotlib.pyplot as pt\n", "from mpl_toolkits.mplot3d import axes3d" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 55 }, { "cell_type": "code", "collapsed": false, "input": [ "# Oblong bowl\n", "\n", "def f(x):\n", " return 0.5*x[0]**2 + 2.5*x[1]**2\n", "\n", "def df(x):\n", " return np.array([x[0], 5*x[1]])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 99 }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot the function in 3D\n", "\n", "fig = pt.figure()\n", "ax = fig.gca(projection=\"3d\")\n", "\n", "xmesh, ymesh = np.mgrid[-2:2:50j,-2:2:50j]\n", "fmesh = f(np.array([xmesh, ymesh]))\n", "ax.plot_surface(xmesh, ymesh, fmesh)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 100, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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aQT9fPq8lHb3BQk9rVFZWJtuaS5m++OKLL7Db9wX2FOOQX9G0biavQb+tNlPw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\n6HQ6PvroI5YtW8Yrr7wiZ7fnz5/n9OnTJCQkqPq5OTk5TJw4EavVyt/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"text": [ "" ] } ], "prompt_number": 100 }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot as a contour plot\n", "\n", "pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 101, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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tX8F720XmnhIvOt7iayE9UZZjJMNHTT1s+kIkFnsOiWTilnmw+DpxP0ByeZFC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\nB2BKjarbkcCK1cg7V5d1ycx2YZkIevEaQikFc44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"text": [ "" ] } ], "prompt_number": 101 }, { "cell_type": "code", "collapsed": false, "input": [ "# Initialize the method\n", "\n", "iterates = [np.array([2, 2./5])]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 130 }, { "cell_type": "code", "collapsed": false, "input": [ "x = iterates[-1]\n", "s = -df(x)\n", "\n", "def f1d(alpha):\n", " return f(x + alpha*s)\n", "\n", "alpha_opt = sopt.golden(f1d)\n", "next_iterate = x + alpha_opt * s\n", "iterates.append(next_iterate)\n", "\n", "# plot function and iterates\n", "pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh)\n", "it_array = np.array(iterates)\n", "pt.plot(it_array.T[0], it_array.T[1], \"x-\")" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 129, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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9XHHDDgvaBsDGVp29kwQsEa8ZNWrG/x20fwBNj4GtOzjcIPqH4xSwT7GehXTXyKCnETY2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\nXOc6w1xDINiDK2RZCTS8GSmU0CcQXrwMc40RrnO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