{ "metadata": { "name": "", "signature": "sha256:0df27369ed05813959062266d1cf6e519632b3b618059690f148c751ae400bc0" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "a = 0.\n", "b = 1." ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "N = 30\n", "\n", "plt.hold(True)\n", "\n", "while (N<31):\n", " A = np.zeros([N,N])\n", " eigval = np.zeros([N])\n", " eigvec = np.zeros([N,N])\n", "\n", " h = (b-a)/(N-1)\n", " #print h\n", "\n", " for i in range(len(A)):\n", " for j in range(len(A[0])):\n", " # loading A\n", " if i==j:\n", " A[i][j] = 2\n", " if abs(i-j) == 1:\n", " A[i][j] = -1\n", "\n", " #print a+i*h, b\n", " #print A, '\\n', B, '\\n'\n", "\n", " #print np.linalg.eig(A)\n", " (eigval, eigvec) = np.linalg.eig(A)\n", " #print B\n", "\n", " #print eigval\n", "\n", " idx = eigval.argsort()\n", " eigval = eigval[idx]\n", " eigvec = eigvec[:,idx]\n", "\n", " #print eigval\n", "\n", " #or np.linalg.inv(A)\n", " #print X, '\\n', U\n", "\n", " plt.plot(np.linspace(0,1,N), np.abs(eigvec[0]/h**(1./2)), label=0)\n", " plt.plot(np.linspace(0,1,N), np.abs(eigvec[1]/h**(1./2)), label=1)\n", " plt.plot(np.linspace(0,1,N), np.abs(eigvec[2]/h**(1./2)), label=2)\n", " plt.plot(np.linspace(0,1,N), np.abs(eigvec[3]/h**(1./2)), label=3)\n", " plt.legend(loc='upper right')\n", " N = 2*N" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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7bSA1FfjjD7ZgulBbi1KtFktHzMeWzC24UnnFbnOJ9PODr5sbztfWmj9ApQIS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\n9ZVcN/I6S+/ftg127hQRnH2ZawcMoNLv54zFdcyGizu4U9wbG8NGwXq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