Get R from T using fsolve

GetRfromT.ipynb

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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.optimize import fsolve\n",
      "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": [
      "def GetR(T0,RGuess):\n",
      "\tz = lambda x: (-13.6166758013299+10.2356001221111*(np.log(x))-3.19829122516485*(np.log(x))**2+0.531184784158533*(np.log(x))**3-0.0494265659369382*(np.log(x))**4+0.00244176088050218*(np.log(x))**5-4.99016352109802E-05*(np.log(x))**6)**(-1)\n",
      "\treturn fsolve(lambda x: z(x)-float(T0), float(RGuess)) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"%.8f\"%  GetR(100.,1350.)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1369.72380764\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "z = lambda x: (-13.6166758013299+10.2356001221111*(np.log(x))-3.19829122516485*(np.log(x))**2+0.531184784158533*(np.log(x))**3-0.0494265659369382*(np.log(x))**4+0.00244176088050218*(np.log(x))**5-4.99016352109802E-05*(np.log(x))**6)**(-1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"%.8f\"% z(1369.72380764)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100.00000000\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.arange(745, 10000, 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(x,z(x))\n",
      "T0 = 100. \n",
      "R =GetR(T0,1350.)\n",
      "plt.plot(R,T0,marker='o', )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7f5b3a29c310>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f5b3a29c2d0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}