{ "metadata": { "name": "kernel" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": true, "input": [ "import numpy as np\n", "import scipy.special as ss\n", "import matplotlib.pyplot as plt" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": true, "input": [ "def kernel(x, N=5, spectrum=None):\n", " \"\"\"\n", " Evaluate the reproducing kernel.\n", "\n", " Parameters\n", " ----------\n", " x : array_like\n", " Points at which to evaluate the kernel.\n", " N : int, optional\n", " Kernel order. Defaults to 5. If the spectrum\n", " is specified, the kernel order is not used.\n", " spectrum : array_like, optional\n", " Weights for each polynomial component of the kernel.\n", " Ones by default.\n", "\n", " \"\"\"\n", " out = np.zeros_like(x)\n", " \n", " if spectrum is None:\n", " spectrum = np.ones(N + 1)\n", " \n", " N = len(spectrum)\n", " \n", " for l in range(N):\n", " Pl = ss.legendre(l)\n", " out += spectrum[l] * (2 * l + 1) / (4 * np.pi) * Pl(x)\n", " return out" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "u = np.linspace(-1, 1, 1000)\n", "spectrum = np.ones(5)\n", "k = kernel(u, spectrum=spectrum)\n", "\n", "f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10,4))\n", "\n", "ax1.plot(u, k)\n", "ax1.set_title('Kernel value over the interval [-1, 1]')\n", "\n", "ax2.plot(spectrum, 'o-')\n", "ax2.set_title('Extended kernel spectrum')\n", "ax2.set_ylim(-0.1, 1.1);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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iIsOYeBGRxbHFi4jIMCZeRGRxbPEiIjKMTzUSkUUVFQGensCtW0Dt2pWXU9Ix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\nAmq1dGuvVy+5ozLM1VVq9Ro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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "sqrt(2)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 12, "text": [ "1.4142135623730951" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "theta = np.linspace(0, 2 * np.pi, 1000)\n", "ang = np.cos(theta)\n", "n1, n2 = 2, 3\n", "k1 = kernel(ang, n1)\n", "k2 = kernel(ang, n2)\n", "f, ax = subplots(subplot_kw=dict(polar=True))\n", "ax.plot(theta, abs(k1), color='red',label=str(n1))\n", "ax.plot(theta, abs(k2), label=str(n2))\n", "ax.legend()\n", "ax.set_title('Kernel magnitude with varying angle');" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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v4a0zJqWlpXB3d8fo0aOxbNkyodVRm+LiYhQWFrK/wlpq5urVq2jevDneeecd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\nTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "spectrum = np.zeros(10)\n", "spectrum[:5] = 1\n", "spectrum[5:] = np.linspace(1, 0, 5)\n", "k = kernel(u, spectrum=spectrum)\n", "\n", "f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10,4))\n", "\n", "ax1.plot(u, k)\n", "ax1.set_title('Linearly extended kernel')\n", "\n", "ax2.plot(spectrum, 'o-')\n", "ax2.set_title('Extended kernel spectrum')\n", "ax2.set_ylim(-0.1, 1.1);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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EhobCy8sLPXv2RFBQkCXiIiIHwTmeiOzHvHnAqVPA3r1yR6JsZp9t5+TkhDNn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\nAwd21ydLjx8DgYHAsWNAly4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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "import scipy.optimize as opt\n", "\n", "u0 = 0.8\n", "u = np.linspace(-1 + 1e-10, u0, 200)\n", "\n", "def full_spectrum(partial_spectrum):\n", " return np.hstack((np.ones(5), partial_spectrum))\n", "\n", "def cost(spectrum):\n", " return np.sum(np.abs(kernel(u, spectrum=full_spectrum(spectrum))))\n", "\n", "opt_spectrum = full_spectrum(opt.fmin(cost, np.ones(5)))\n", "print opt_spectrum\n", "\n", "f, (ax1, ax2) = plt.subplots(1, 2)\n", "\n", "u = np.linspace(-1, 1, 1000)\n", "ax1.plot(u, kernel(u, spectrum=opt_spectrum))\n", "ax1.set_title('Optimally extended kernel')\n", "\n", "ax2.plot(opt_spectrum, 'o-')\n", "ax2.set_title('Kernel spectrum')\n", "ax2.set_ylim(-0.1, 1.1);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Optimization terminated successfully.\n", " Current function value: 6.628413\n", " Iterations: 204\n", " Function evaluations: 327\n", "[ 1. 1. 1. 1. 1. 0.81402883\n", " 0.63712395 0.43044675 0.24297284 0.11031011]\n" ] }, { "output_type": "display_data", "png": 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19XHkyBFcu3YNLVq0gLW1NSZPniz9Etama5Nrg4ODA/7880/897//xcKFC5U6Vqra12Zm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\nuUde3tukLZEAVlbcw9oaaNy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