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": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "eigenvalues = pickle.load(open('eigenvals.pickle', 'rb'))",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "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": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "This is a closeup of the plot."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figure()\nplot(a15s, lambdas)\nxlim(0, 2)\nxlabel(\"Parameter\u2014delta_p = a15\")\nylim(-0.5, 0.1)\nylabel(\"Re(lambda)\")\naxvline(0.5707, color='black')\naxhline(color='black')\nshow()",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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P4OBgBAUFwcvLCzNnzsTWrVtbtLn+wMK4uDhUV1ebPUbEnVmzLgHw4EsrjR8/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\nrkJggg==\n",
       "text": "<matplotlib.figure.Figure at 0x7f4e6313ca50>"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "This is the full plot."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figure()\nplot(a15s, lambdas)\nxlabel(\"Parameter\u2014delta_p = a15\")\nylabel(\"Re(lambda)\")\naxvline(0.5707, color='black')\naxhline(color='black')\nshow()",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2mDVrlvD29haurq7C19dXfPrpp+L69esiPj5eDBo0SOj1enHjxg21y+ww7v0+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\niGRhYBARkSwMDCIikoWBQUREsvw/5CIOJFp7Y0wAAAAASUVORK5CYII=\n",
       "text": "<matplotlib.figure.Figure at 0x7f4e6391a0d0>"
      }
     ],
     "prompt_number": 6
    },
    {
     "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/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\nRU5ErkJggg==\n",
       "text": "<matplotlib.figure.Figure at 0x7f3fcafe5b10>"
      }
     ],
     "prompt_number": 84
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}