Logarithmic fit.ipynb

Fit_Exponential.ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Fit to a curve in a logarithmic plane"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import pandas as pd"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Consider the following set of points:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x=pd.read_csv('xenon.csv')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x.columns"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "Index([u'M', u'sigma'], dtype=object)"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.loglog(x['M'],x['sigma'],'ro')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "[<matplotlib.lines.Line2D at 0x3e0ae10>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wCUD75MlYaTTiWwYDkJio6XJMOTHnTxSAsUpBORYwNmHs5P+cP4/Uf/wD5S6X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\nMgnhJhFMiAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3d71c10>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exponential fit"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The curve can be decomposed in approximately straight lines. In the $(\\log x,\\log y)$-plan one straight line is described by $y = Ae^{Bx}$ for some $A$ and $B$.\n",
      "\n",
      "\n",
      "For fitting $y = Ae^{Bx}$, take the logarithm of both side gives $\\log y = \\log A + Bx$. So just fit $\\log y$ against $x$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Initialization of the set of constants: `100` is by far enough"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m=np.zeros(100)\n",
      "A=np.zeros(100)\n",
      "B=np.zeros(100)\n",
      "m[0]=x['M'].values[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Straight segments"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Obtained by trial and error. At the end with 9 was enough"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First a general definition"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def straight_segment(i,m,ShowPlot=True):\n",
      "    d=x[np.logical_and(x['M']>m[i-1],x['M']<m[i])]\n",
      "    z = np.polyfit(d['M'], np.log(d['sigma']), 1)\n",
      "    p = np.poly1d(z)\n",
      "    print 'logy=',p\n",
      "    A=exp(p[0])\n",
      "    B=p[1]\n",
      "    if ShowPlot:\n",
      "        xlin=np.linspace(d['M'].values[0],d['M'].values[-1])\n",
      "        plt.semilogy(d['M'],d['sigma'],'ro')\n",
      "        plt.semilogy(xlin,A*np.exp(B*xlin))\n",
      "    return A,B"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Specific straight segments in `semilogy`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i=1\n",
      "m[i]=7\n",
      "A[i],B[i]=straight_segment(i,m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "logy=  \n",
        "-4.183 x + 17.56\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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tWpa1iYhIGbMp9Hv16kXr1q05dOgQ/v7+vPXWW3h7ezNr1iwiIiJo3LgxPXv2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\nldsy8RWfswAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x410d8d0>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i=2\n",
      "m[i]=10\n",
      "A[i],B[i]=straight_segment(i,m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "logy=  \n",
        "-1.321 x - 2.5\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zC+Vz8xa3EsDQoUPJzMws8VphYSEjRowgMzOT7Oxsli1bxp49exgyZAizZ8+m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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x454a4d0>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i=3\n",
      "m[i]=15\n",
      "A[i],B[i]=straight_segment(i,m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "logy=  \n",
        "-0.489 x - 10.6\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x4733150>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i=4\n",
      "m[i]=25\n",
      "A[i],B[i]=straight_segment(i,m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "logy=  \n",
        "-0.164 x - 15.41\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x3dbea50>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i=5\n",
      "m[i]=35\n",
      "A[i],B[i]=straight_segment(i,m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "logy=  \n",
        "-0.05048 x - 18.15\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WLpfLa39paanS09OVmpqqtWvXSpK2bNmip59+WqdPn1ZMTIw2btyo1atXa/z48cGvfhAI\n9390jG9wC+fxhfPYAtWjwH/sscdUWlrqta+1tVVPPvmkSktLdfToUW3btk3Hjh3TkiVL9POf/1yT\nJk3Sxx9/rG9961taunSpnnnmmZAMAADQM5E9+aI5c+aopqbGa195eblSUlKUmJgoSVq0aJF27Nih\njIyM9q+588479fzzzwetWABAH5geqq6uNllZWe2fv/rqq+ab3/xm++dbtmwxTz75ZE+/Xbvk5GQj\niY2NjY2tF1tycnKv87ZHZ/j+REREBPpSLydOnAjK9wEA3FzAq3Ti4uJUW1vb/nltba3i4+ODUhQA\nIPgCDvx7771Xx48fV01NjZqbm7V9+3YVFBQEszYAQBD1KPAXL16s2bNnq7KyUgkJCdq0aZMiIyO1\nceNG5efnKzMzU4WFhV5v2PpTW1ur+++/X1OnTlVWVpbWr1/v9ffPPfechgwZoosXLwY+IgfdbHwb\nNmxQRkaGsrKyVFxc7GCVgelubOXl5Zo5c6amTZumGTNm6ODBgw5XGphr164pNzdXOTk5yszM1PLl\nyyVJFy9e1Lx585SWlqb58+eroaHB4UoD0934ioqKlJGRoezsbC1YsECNjY0OVxqY7sbnMdiz5Wbj\n61W29HrWvw/OnDljDh8+bIwx5vLlyyYtLc0cPXrUGGPMyZMnTX5+vklMTDT19fX9WVbQdDe+vXv3\nmgceeMA0NzcbY4w5f/68k2UGpLuxfelLXzKlpaXGGGN27txp8vLynCyzT65cuWKMMaalpcXk5uaa\n/fv3m6KiIrN27VpjjDFr1qwxxcXFTpbYJ/7Gt2vXLtPa2mqMMaa4uDjsxmdMeGSLMf7H19ts6deb\np02YMEE5OTmSpJEjRyojI0OnT5+WJH3ve9/TunXr+rOcoPM3vlOnTuk3v/mNli9frmHDhkmSYmJi\nnCwzIN2NbeLEie1nhQ0NDYqLi3OyzD4ZMWKEJKm5uVmtra2Kjo7Wm2++qaVLl0qSli5dqj/+8Y9O\nltgnXcf3+c9/XvPmzdOQIe4YyM3NVV1dnZMl9om/8UnhkS2S/3+fvc0Wx+6WWVNTo8OHDys3N1c7\nduxQfHy87r77bqfKCbrO46usrNS+ffs0a9Ys5eXl6b333nO6vD7xjG3WrFlas2aNvv/972vy5Mkq\nKirS6tWrnS4vYG1tbcrJyVFsbGz79NW5c+cUGxsrSYqNjdW5c+ccrjJwXceXmZnp9fcvvviiHnzw\nQYeq6zt/4wunbPH377PX2RLy6xA/Ll++bKZPn27+8Ic/mCtXrpiZM2eaxsZGY4wxiYmJ5sKFC06U\nFTSdx2eMMVlZWWbZsmXGGGPKy8tNUlKSk+X1SdexzZ0717zxxhvGGGN+//vfmwceeMDJ8oKioaHB\n5Obmmr1795qxY8d6/V10dLRDVQWPZ3xvv/12+75Vq1aZBQsWOFdUEHnGV1JSYnJzc8MqW4zx/v31\nNlv6/Qy/paVFCxcu1COPPKKHH35YVVVVqqmpUXZ2tpKSklRXV6fp06fr/Pnz/V1aUHQdnyTFx8dr\nwYIFkqQZM2ZoyJAhg/Jmcv7GVl5erq985SuSpK9+9asqLy93ssSgGDNmjB566CG9//77io2N1dmz\nZyVJZ86c0R133OFwdX3nGZ/nbPCll17Szp07tXXrVocrCw7P+A4dOqTq6uqwyRaPzr+/3mZLvwa+\nMUbf+MY3lJmZqe9+97uSJJfLpXPnzqm6ulrV1dWKj4/XoUOHBuV/LH/jk6SHH35Ye/fulSRVVlaq\nublZ48aNc6rMgHQ3tpSUFL3zzjuSpL179yotLc2pEvvkwoUL7Stwrl69qt27d2vatGkqKCjQ5s2b\nJUmbN29uP9ANNt2Nr7S0VD/72c+0Y8cORUVFOVxl4PyN77777gubbOnu99frbAn59Ucn+/fvNxER\nESY7O9vk5OSYnJwcs3PnTq+vSUpKGrTvpPsb31tvvWWam5vNI488YrKyssw999zjdSk9WHT3uzt4\n8KCZOXOmyc7ONrNmzTKHDh1yutSAfPjhh2batGkmOzvbuFwus27dOmOMMfX19Wbu3LkmNTXVzJs3\nz1y6dMnhSgPT3fhSUlLM5MmT23+nTzzxhMOVBqa78XU2mLOlu/H1NlsijDGmP45QAABn8UxbALAE\ngQ8AliDwAcASBD4AWILABwBLEPgAYAkCHwAsQeADgCX+HyIB3d1JM89mAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x470ded0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i=6\n",
      "m[i]=70\n",
      "A[i],B[i]=straight_segment(i,m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "logy=  \n",
        "-0.002356 x - 19.86\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x4378610>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i=7\n",
      "m[i]=200\n",
      "A[i],B[i]=straight_segment(i,m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "logy=  \n",
        "0.006007 x - 20.34\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEDCAYAAADdpATdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nNkGkBij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,
       "text": [
        "<matplotlib.figure.Figure at 0x427c910>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i=8\n",
      "m[i]=500\n",
      "A[i],B[i]=straight_segment(i,m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "logy=  \n",
        "0.002774 x - 19.7\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x455e290>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i=9\n",
      "m[i]=x['M'].values[-1]\n",
      "A[i],B[i]=straight_segment(i,m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "logy=  \n",
        "0.001402 x - 19.03\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x4737b10>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Define step function"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The function takes a float as argument and internally the proper range is selected\n",
      "\n",
      "From the previous output, the same function could be defined manually"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fitexp(x,m,A,B):\n",
      "    imax=9\n",
      "    for i in range(1,imax+1):\n",
      "        if x>=m[i-1] and x<=m[i]:\n",
      "            return A[i]*np.exp(B[i]*x)\n",
      "        if x<m[0] or x>m[imax]:\n",
      "            return 'ERROR: Out or range'\n",
      "        "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The python list comprehension: `ylin` below, can be used to map a list to a function with arguments: http://stackoverflow.com/a/10212468/2268280"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xlin=np.logspace(np.log10(m[0]),np.log10(m[9]),100)\n",
      "ylin=[fitexp(xx,m,A,B) for xx in xlin]\n",
      "plt.loglog(x['M'],x['sigma'],'ro')\n",
      "plt.loglog(xlin,ylin,'b-',lw=3)\n",
      "plt.xlim(3,m[9])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "(3, 990.54922145)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FVYWFBBq9uZ5E1nAH75FECa1rPD6EQuJYgYHljGE764H5gBcosAs8fvNgVn3y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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x435b3d0>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Evaluation of the final function in some specific points"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fitexp(2,m,A,B)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "'ERROR: Out or range'"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fitexp(8,m,A,B)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "2.1178476384931308e-06"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fitexp(2000,m,A,B)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "'ERROR: Out or range'"
       ]
      }
     ],
     "prompt_number": 24
    }
   ],
   "metadata": {}
  }
 ]
}

xenon.csv