{"nbformat_minor": 0, "metadata": {"signature": "sha256:18f877e1f5fc11192498f6ad1e1684f1ee948a2ea85d54ff445f87dfe57c0bd7", "name": ""}, "nbformat": 3, "worksheets": [{"metadata": {}, "cells": [{"cell_type": "markdown", "metadata": {}, "source": ["# Steepest Descent"]}, {"collapsed": false, "input": ["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", "outputs": [], "cell_type": "code", "metadata": {}, "prompt_number": 1}, {"cell_type": "markdown", "metadata": {}, "source": ["Here's a function. It's an oblong bowl made of two quadratic functions.\n", "\n", "This is pretty much the easiest 2D optimization job out there."]}, {"collapsed": false, "input": ["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", "outputs": [], "cell_type": "code", "metadata": {}, "prompt_number": 2}, {"cell_type": "markdown", "metadata": {}, "source": ["Let's take a look at the function. First in 3D:"]}, {"collapsed": false, "input": ["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", "outputs": [{"metadata": {}, "output_type": "pyout", "prompt_number": 3, "text": [""]}, {"stream": "stderr", "output_type": "stream", "text": ["/usr/lib/python3/dist-packages/matplotlib/backends/backend_agg.py:517: DeprecationWarning: npy_PyFile_Dup is deprecated, use npy_PyFile_Dup2\n", " filename_or_obj, self.figure.dpi)\n"]}, {"metadata": {}, "output_type": "display_data", "png": 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kIX/96xp69jyE559/PjVbzia2xsy22GwE43jFvJdMjAKLurq6lNgaZc2VDF+8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\nLCpKHjy6evVqbrvtNi8cXctBm5GMNTeMRiO//PKLQkscPXqUsLAwYmN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"text": [""]}], "cell_type": "code", "metadata": {}, "prompt_number": 3}, {"cell_type": "markdown", "metadata": {}, "source": ["And then as a \"contour plot\":"]}, {"collapsed": false, "input": ["pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh)"], "language": "python", "outputs": [{"metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [""]}, {"metadata": {}, "output_type": "display_data", "png": 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7u4Xubis6XTBxcaHExYURHR1CZKRxUJjDww2EhuoHRdto1KHTnbhylqIouN3K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\nVwAAAABJRU5ErkJggg==\n", "text": [""]}], "cell_type": "code", "metadata": {}, "prompt_number": 4}, {"cell_type": "markdown", "metadata": {}, "source": ["Next, initialize steepest descent with a starting guess:"]}, {"collapsed": false, "input": ["guesses = [np.array([2, 2./5])]"], "language": "python", "outputs": [], "cell_type": "code", "metadata": {}, "prompt_number": 15}, {"cell_type": "markdown", "metadata": {}, "source": ["Next, run Steepest Descent:"]}, {"collapsed": false, "input": ["x = guesses[-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_guess = x + alpha_opt * s\n", "guesses.append(next_guess)\n", "\n", "print(next_guess)"], "language": "python", "outputs": [{"stream": "stdout", "output_type": "stream", "text": ["[ 0.17558299 0.0351166 ]\n"]}], "cell_type": "code", "metadata": {}, "prompt_number": 27}, {"cell_type": "markdown", "metadata": {}, "source": ["Here's some plotting code to illustrate what just happened:"]}, {"collapsed": false, "input": ["pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh, 50)\n", "it_array = np.array(guesses)\n", "pt.plot(it_array.T[0], it_array.T[1], \"x-\")"], "language": "python", "outputs": [{"metadata": {}, "output_type": "pyout", "prompt_number": 28, "text": ["[]"]}, {"metadata": {}, "output_type": "display_data", "png": 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6IEX19HVB/Bz4NlTbCct9If/MRei7DfmbUlSuV+DgAex+KXWknlkYfgf6bsp5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\nHy/g4wgeygrOqzKvWSV+ZpWooHjRdPGi6eIZw0nQMNmqKV4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WHBKS+SKwdc/vPrDKvT5K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\nB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7162Tf5/CuByaSRlFRIZGQukZE5JCUVkpZWQnp6MWlpxWRklFBa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\nCwsy+JaWKC8tyWBcWcFqa8MeHaXz+oKkjq2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