lidavidm/EigenvaluePlot.ipynb

## EigenvaluePlot.ipynb
{
 "metadata": {
  "name": "EigenvaluePlot"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%pylab inline --no-import-all\nimport matplotlib\nimport matplotlib.pyplot as plt\nfrom pylab import *\nimport pickle",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "Populating the interactive namespace from numpy and matplotlib\n"
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "eigenvalues = pickle.load(open('eigenvals.pickle', 'rb'))",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "eigenvalues[1][1].as_real_imag()\nis_complex = lambda x: x.as_real_imag()[1] > 1e-20\nfiltered_eigenvalues = [(row[0], max(filter(is_complex, row[1:]), key=lambda x:x.as_real_imag()[0]).as_real_imag()[0]) for row in eigenvalues[4:]]\na15s = [row[0] for row in filtered_eigenvalues]\nlambdas = [row[1] for row in filtered_eigenvalues]",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figure()\nplot(a15s, lambdas)\nxlim(0, 2)\nylim(-0.5, 0.1)\naxvline(0.5707, color='black')\naxhline(color='black')\nshow()",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": "<matplotlib.figure.Figure at 0x7f3fe4075210>"
      }
     ],
     "prompt_number": 91
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figure()\nplot(a15s, lambdas)\naxvline(0.5707, color='black')\naxhline(color='black')\nshow()",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": "<matplotlib.figure.Figure at 0x7f3fcb00f790>"
      }
     ],
     "prompt_number": 70
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import scipy.integrate\nscipy.integrate.simps(lambdas[:51], a15s[:51])",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 48,
       "text": "-0.0365763523726227"
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "a15s[50]",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 94,
       "text": "0.570751"
      }
     ],
     "prompt_number": 94
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "a15s[139]",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 95,
       "text": "1.45449"
      }
     ],
     "prompt_number": 95
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "upper = 140\nscipy.integrate.simps(lambdas[51:upper], a15s[51:upper])",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 88,
       "text": "0.00997222710664623"
      }
     ],
     "prompt_number": 88
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "a15s[140]",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 87,
       "text": "1.46442"
      }
     ],
     "prompt_number": 87
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import numpy",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 69
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "fitted = numpy.polyfit(a15s, lambdas, 20)\np = numpy.poly1d(fitted)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "/usr/lib/python3.3/site-packages/numpy/lib/polynomial.py:587: RankWarning: Polyfit may be poorly conditioned\n  warnings.warn(msg, RankWarning)\n"
      }
     ],
     "prompt_number": 83
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figure()\nplot(a15s, p(a15s))\naxvline(0.5707, color='black')\naxhline(color='black')\nshow()",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ECRPQ1NSES5cu4fDhwwPpv2bNGly4cAFNTU2YNWsWNmzYEJ4tIiKiwIkgzZ8/\nXzgcDiGEEG1tbWL+/Pm3rfOb3/xGvPnmmx7PX7hwQSxcuNBrnXnz5gkAXLhw4cIlgGXevHkB9elB\n3w+0uLgY1dXV2LhxI6qrq1FSUuJR5uuvv0ZUVBRiY2PR2dmJhoYGvP766wAAh8OBWbNmAQD27duH\nzMxMr+s5d+5csE0kIiI/BX2jOrfbjaeeegoXL15EcnIy3n33XcTGxqKtrQ2rV69GXV0djh8/jmee\neQZ9fX3o6+vDqlWr8PLLLwMAnn76aTQ1NUFRFNx3333YsWPHwDkIIiIaWXf8XUuJiCjy7ugZyPX1\n9UhLS0Nqaiq2bNky2s3RtOTkZGRlZSEnJwcPPPDAaDdHc5577jmoqjpkONOfiZfknbf3kxNRg2O3\n25GXl4cFCxZg4cKFeOuttwAE/vm8Y8Ogt7cXa9euRX19PU6dOoU9e/bg9OnTo90szVIUBVarFTab\nDY2NjaPdHM159tlnPTonfyZeknfe3k9ORA1OdHQ0KisrcfLkSRw7dgxVVVU4ffp0wJ/POzYMGhsb\nkZKSguTkZERHR6O0tBT79+8f7WZpGkcEg7dkyZIhEyYB/ydekidv7yfAz2gwEhISkJ2dDQCIiYlB\neno6WltbA/583rFh0NraiqSkpIHHOp0Ora2to9gibVMUBY888ggWLVqEnTt3jnZzxgR/J16S/zgR\nNTQtLS2w2WzIzc0N+PN5x4bBcJPYKDhHjx6FzWbDe++9h6qqKnz88cej3aQxxdfES/IPJ6KGpqOj\nA0888QS2bt2K6dOnD3nNn8/nHRsGiYmJsNvtA4/tdjt0Ot0otkjb+ud0zJw5EytWrOB5gzBQVRVO\npxOAnDcTHx8/yi3Stvj4+IFO6/nnn+dnNADd3d144oknsGrVqoE5X4F+Pu/YMFi0aBHOnj2LlpYW\ndHV1Ye/evSguLh7tZmnS9evXcfXqVQDAtWvX8MEHHww7yY/81z/xEsCwEy/Jfw6HY+BnXxNRaSgh\nBMrKypCRkYF169YNPB/w5zOg+coj7MCBA0Kv14t58+aJ3/72t6PdHM368ssvhcFgEAaDQSxYsIDv\nZRBKS0vFrFmzRHR0tNDpdOLtt98WV65cEfn5+SI1NVWYTCbxzTffjHYzNeOH7+euXbvEqlWrRGZm\npsjKyhI//elPhdPpHO1masLHH38sFEURBoNBZGdni+zsbPHee+8F/PnkpDMiIrpzh4mIiGjkMAyI\niIhhQES/chPgAAAAH0lEQVREDAMiIgLDgIiIwDAgIiIwDIiICAwDIiIC8P+B2Bkrh7UbuAAAAABJ\nRU5ErkJggg==\n",
       "text": "<matplotlib.figure.Figure at 0x7f3fcafe5b10>"
      }
     ],
     "prompt_number": 84
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}