cmi_scripts/linearfit/LinearFit.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:5e1cef948da600609ea3822f5bab32323b5345f9b357bd8e4b93024ab92ec88d"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "SrFit example for a simple linear fit to a noisy data."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Simulate linear data with some random Gaussian noise and plot the generated \"observed\" data (xobs, yobs)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "from __future__ import print_function\n",
      "import numpy as np\n",
      "xobs = np.arange(-10, 10.1)\n",
      "dyobs = 0.3 * np.ones_like(xobs)\n",
      "yobs = 0.5 * xobs + 3 + dyobs * np.random.randn(xobs.size)\n",
      "plot(xobs, yobs, 'x')\n",
      "title('y = 0.5*x + 3 generated with a normal noise at sigma=0.3')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Using matplotlib backend: module://IPython.kernel.zmq.pylab.backend_inline\n",
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "<matplotlib.text.Text at 0x348f9d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sgycikij2wRMRkVYMeCIiiWLA1wLGuIKUV6ESWR4GfC3QubP6aJXS0SydO9ds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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3417650>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We are going to define a line fitting regression using SrFit.\n",
      "At first we create a SrFit Profile object that holds the observed data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from diffpy.srfit.fitbase import Profile\n",
      "linedata = Profile()\n",
      "linedata.setObservedProfile(xobs, yobs, dyobs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The second step is to create a FitContribution object, which associates observed profile with a mathematical model for the dependent variable."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from diffpy.srfit.fitbase import FitContribution\n",
      "linefit = FitContribution('linefit')\n",
      "linefit.setProfile(linedata)\n",
      "linefit.setEquation(\"A * x + B\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " SrFit objects can be examined by calling their **show()** function.  SrFit\n",
      " parses the model equation and finds two parameters A, B at independent\n",
      " variable x.  The values of parameters A, B are at this stage undefined.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "linefit.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "linefit\n",
        "-------------------------------------------------------------------------------\n",
        "A                    None\n",
        "B                    None\n",
        "dy                   [ 0.3  0.3  0.3  0.3  0.3  0.3  0.3  0.3  0.3  0.3  0.3  0\n",
        "x                    [-10.  -9.  -8.  -7.  -6.  -5.  -4.  -3.  -2.  -1.   0.   \n",
        "y                    [-1.82250666 -1.6817787  -1.37786885  0.28259586 -0.423625\n",
        "\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can set A and B to some specific values and calculate model\n",
      "observations.  The x and y attributes of the FitContribution are \n",
      "the observed values, which may be re-sampled or truncated to a shorter \n",
      "fitting range."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "linefit.A\n",
      "linefit.A = 3\n",
      "linefit.B = 5\n",
      "print(linefit.A, linefit.A.value)\n",
      "print(linefit.B, linefit.B.value)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Parameter(A) 3\n",
        "Parameter(B) 5\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "`linefit.evaluate()` returns the modeled values and `linefit.residual()`,\n",
      "the difference between observed and modeled data scaled by estimated\n",
      "standard deviations."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(\"linefit.evaluate() =\", linefit.evaluate())\n",
      "print(\"linefit.residual() =\", linefit.residual())\n",
      "plot(xobs, yobs, 'x', linedata.x, linefit.evaluate(), '-')\n",
      "title('Line simulated at A=3, B=5')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "linefit.evaluate() = [-25. -22. -19. -16. -13. -10.  -7.  -4.  -1.   2.   5.   8.  11.  14.  17.\n",
        "  20.  23.  26.  29.  32.  35.]\n",
        "linefit.residual() = [-77.25831114 -67.72740435 -58.74043717 -54.27531953 -41.92124932\n",
        " -35.13272106 -27.13771558 -17.19014009  -9.0058639   -2.20367056\n",
        "   7.48349382  15.42490371  24.0876991   31.96096047  38.44689144\n",
        "  47.56940293  55.64124334  65.7878908   73.60530021  82.03035839\n",
        "  88.75175173]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "<matplotlib.text.Text at 0x3a340d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+jYSJCejj2MfawyKiDmBsdkpy2md4wODgYMTFxaGsrAyXLl2Cg4MD+3iJsHcn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\nEFX9n7QAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3a18d50>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " We want to find the optimum model parameters that fit the simulated curve\n",
      " to the observations.  This is done by associating FitContribution with\n",
      " a FitRecipe object.  FitRecipe can manage multiple fit contributions and\n",
      " optimize all models to fit their respective profiles."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from diffpy.srfit.fitbase import FitRecipe\n",
      "rec = FitRecipe()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The `clearFitHooks()` function suppresses printout of iteration numbers.  The `addContribution()` function includes the specified FitContribution in the FitRecipe, which acts as a top-level manager of all associated fits. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rec.clearFitHooks()\n",
      "rec.addContribution(linefit)\n",
      "rec.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "fit\n",
        "\n",
        "  linefit\n",
        "  -----------------------------------------------------------------------------\n",
        "  A                    3\n",
        "  B                    5\n",
        "  dy                   [ 0.3  0.3  0.3  0.3  0.3  0.3  0.3  0.3  0.3  0.3  0.3 \n",
        "  x                    [-10.  -9.  -8.  -7.  -6.  -5.  -4.  -3.  -2.  -1.   0. \n",
        "  y                    [-1.82250666 -1.6817787  -1.37786885  0.28259586 -0.4236\n",
        "\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " FitContributions may have many parameters.  We need to tell the recipe\n",
      " which of them should be controlled and potentially optimized in a fit."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rec.addVar(rec.linefit.A)\n",
      "rec.addVar(rec.linefit.B)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<diffpy.srfit.fitbase.parameter.ParameterProxy at 0x3b18e10>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " The call of the addVar function also created two attributes A and B for the rec object,\n",
      " which link to the A and B parameters of the linefit contribution.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(\"rec.A =\", rec.A)\n",
      "print(\"rec.A.value =\", rec.A.value)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "rec.A = ParameterProxy(A)\n",
        "rec.A.value = 3\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " The names of the declared variables are stored in the `rec.names` attribute\n",
      " and the corresponding values in `rec.values`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(\"rec.values =\", rec.values)\n",
      "print(\"rec.names =\", rec.names)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "rec.values = [3 5]\n",
        "rec.names = ['A', 'B']\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " Finally the recipe objects provides a residual() function to calculate\n",
      " the difference between the observed and simulated values.  The residual\n",
      " function can accept a list of new variable values in the same order as\n",
      " rec.names."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(\"rec.residual() =\", rec.residual())\n",
      "print(\"rec.residual([2, 4]) =\", rec.residual([2, 4]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "rec.residual() = [-77.25831114 -67.72740435 -58.74043717 -54.27531953 -41.92124932\n",
        " -35.13272106 -27.13771558 -17.19014009  -9.0058639   -2.20367056\n",
        "   7.48349382  15.42490371  24.0876991   31.96096047  38.44689144\n",
        "  47.56940293  55.64124334  65.7878908   73.60530021  82.03035839\n",
        "  88.75175173]\n",
        "rec.residual([2, 4]) = [-47.25831114 -41.06073768 -35.40710383 -34.27531953 -25.25458265\n",
        " -21.79938773 -17.13771558 -10.52347342  -5.67253057  -2.20367056\n",
        "   4.15016049   8.75823704  14.0876991   18.62762714  21.78022477\n",
        "  27.56940293  32.30791     39.12122414  43.60530021  48.69702506\n",
        "  52.08508507]\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The FitRecipe.residual function can be directly used with the scipy\n",
      "leastsq function for minimizing a sum of squares."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.optimize import leastsq\n",
      "leastsq(rec.residual, rec.values)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "(array([ 0.50664083,  2.99718481]), 3)"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " Recipe variables and the linked line-function parameters are set to the\n",
      " new optimized values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(rec.names, \"-->\", rec.values)\n",
      "linefit.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "['A', 'B'] --> [ 0.50664083  2.99718481]\n",
        "linefit\n",
        "-------------------------------------------------------------------------------\n",
        "A                    0.506640829571\n",
        "B                    2.99718481036\n",
        "dy                   [ 0.3  0.3  0.3  0.3  0.3  0.3  0.3  0.3  0.3  0.3  0.3  0\n",
        "x                    [-10.  -9.  -8.  -7.  -6.  -5.  -4.  -3.  -2.  -1.   0.   \n",
        "y                    [-1.82250666 -1.6817787  -1.37786885  0.28259586 -0.423625\n",
        "\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " The calculated function is available in the `ycalc` attribute of the profile.\n",
      " It can be also accessed from the `linefit` contribution attribute of the\n",
      " recipe as `rec.linefit.profile.ycalc`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(linedata.x, linedata.y, 'x', linedata.x, linedata.ycalc, '-')\n",
      "title('Line fit using the leastsq least-squares optimizer')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "<matplotlib.text.Text at 0x40578d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YJ8DRQUdFibzghSW+XMuTqh+JJPPs7GxYWFhgwIABktgcUbX3NPUpZp2bBZMt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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3e0a210>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The `FitRecipe.scalarResidual()` function returns the sum of squares and can\n",
      "be used with a minimizer that requires a scalar function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.optimize import fmin\n",
      "fmin(rec.scalarResidual, [1, 1])\n",
      "print(rec.names, \"-->\", rec.values)\n",
      "plot(linedata.x, linedata.y, 'x', linedata.x, linedata.ycalc, '-')\n",
      "title('Line fit using the fmin scalar optimizer')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 21.482450\n",
        "         Iterations: 49\n",
        "         Function evaluations: 93\n",
        "['A', 'B'] --> [ 0.50664359  2.99724135]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "<matplotlib.text.Text at 0x414fb10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AtafX4B/hj6PxRzHZcTKmOU9D3Zp1Ja9zJgpVBF4AJSqji48vwi/cD5EPIjGz\n3UxMcpyEOjXqfLQdZ6JQRWAyJyqliMQI+IX7ITY5FnM6zME4h3GoqVFT0WGRiuMKUKISEAQBJ++d\nhG+YLxJfJmK+63zsH7ofNarVUHRoRGXCZE4qRRAEHLp1CL7hvkh/m46Frgsx3G44qqnxrUBVG3+D\nSSXk5uViT9we+IX7ISNdhEWdveHhMFBSwZBj3lTVcWoiKbXs3Gz8ful32AbZYum5pfDv4o+L42IQ\ntWkwMtL/TeReXvkXNYmqKl4ApSqlpDNJ3uS8kVQwbKzbGN4dvdHZvLOkguH7BM5a4lRZcTYLKbVP\nzfHOfJeZX8Hw7M9obdgaXm5e6NCog9S2WEucKjPWZiGlpqv77x16EhL+TeQizZfwD/eHxQoLRD6I\nxMHhBxH6VWiRiZwrOEnZsGdOVdL7XvXFuFTse7wcwdHB6GXVCwtcF8Cmnk2x+3IFJ1UFHGYhpZeW\nBsz8PgkanX7B5tj1GNZyML7vPA+W+pYl2p8rOKkq4DALKbXYxES4LZ6C/cY20Kz1FtHfXEatU2tR\nV61kiRzIT9gf9sB1dZnIqWpjz5yqhNvPbmNJxBLsit0Pz9bjsMB9JhrUbgCAvWpSThxmIaUSmxwL\n/wh/nLh7AlMcp2Cq81Toa+krOiyicsdkTkrhwqML8Av3w7mH5zCr/SxMbDsR2jW0FR0WUYWp8DHz\nBw8eoHPnzrC1tYW7uzu2bdsma5OkwsLvh6PnHz0xaOcgdG3cFXen38Vcl7lM5ESfIHPPPCkpCUlJ\nSWjdujVSU1Ph5OSEy5cvQ1s7/83Hnjl9iiAIOH73OPzC/fAo/RHmu87HqFajUF29uqJDI1KYCi+B\na2hoCENDQwCAgYEBbG1tER0djc6dO8vaNCm5PCEPB28ehF+4HzKzM7HQdSGGthjKCoZEZSDXd018\nfDyuXbsGJycneTZLSiY3Lxe7ru+Cf7g/NNQ14OXmhQHWA6Am4kxZorKSWzLPyMjA0KFDsXTpUtSq\nVavQaz4+PpK/u7u7w93dXV6HpSokOzcbf1z5A0sil8CgpgECugWgZ5OekuJXRKpMLBZDLBaXeX+5\nzGbJzs5Gnz590Lt3b8yYMaPwAThmrvLe5LzBxpiNCIgMgFVdK3i5eaGTWScmcaJiVPjUREEQ8PXX\nX8PAwAC//vqrzAGR8nj17hXWRK/Br+d+hYORA9zVvODZw5nL6IlKoMKnJkZGRuKPP/7AqVOnYG9v\nD3t7exykp0TGAAAPS0lEQVQ5ckTWZqkKS3uTBr8wP1iusETU4yj89dVfODD8ADx7OMPL698Khbwp\nBJH8cNEQyU1qViqWnVuG1dGr0adpHyxwXQBrA+tC2/CmEEQlwxWgVOEeZzzGL3//go2XNmKI7RDM\nc5mHxnqNi9yeN4Ug+jRWTaQKk5CWgEmhk9AiqAXyhDzETozF6s9XF5vIeVMIovLBZE6lduvZLYwJ\nGQOHtQ7Q1dTFjSk3sLTnUhjXMS52v4I3gTA3//eOQUzoRLLjMAuV2JXkK/AP98epe6cw1WkqpjhN\ngZ6WXon3500hiEqOY+Ykd1GPouAX7oeoR1H4rv13mNB2AmpXr63osIiUWoXXZiHlFXY/DL5hvriR\negPzXOZhxxc7oKWhpeiwiEgKjpmriNDQj8em09Lyny9IEAQciT8Ct41uGHtgLIa1GIb4afEwT5mM\nt5lan9yfiBSDyVxFuLig2AU7eUIe9sXtg+M6R8w+NhuT2k5C3OQ4eNp7orp69U/uT0SKxTFzFSJt\nwU7tOjnYeW0n/MP9oVlNE94dvdGvWT+pFQy54Ieo4vACKBXr/YKdm/HvEP5yCxZHLIaRthG83bzR\n3bL7J4tfccEPUcXgBVAqUloasDjwNXz+Wg+H33+CY2NrbOi/AR3NOpZ4/4ILftgzJ6o8OGauIh48\nzUBvv0CEmFvgn5fHsf+r3WgefQwtdUqeyLngh6jy4jCLknvx+gVWRq3ELxEr0dWiK3y6LETLBi0B\nlG7BDhf8EFUsjpkTAOBp5lMsPbsUa/9Zi37N+mG+y3w0M2im6LCIqIQ4Zq7iHqU/QuDfgdh8eTOG\ntRiGi99ehLmuuaLDIqJyxjHzKqAkC37uvriL8QfHwy7YDuoidVyddBVBfYKYyIlUBJN5FVDcgp24\nlDiM2jcKjuscUa9WPdycchO/9PgFDbUbKjZoIqpQHDOvIj5csDNsxiWsvOQPcYIY052nY7LTZOhq\ncp4gkbLgBVAllpAANHY7hy4+fohLu4jv2n+H8W3Hs4IhkRJiMldCgiDg0FUxJu3wQ57ebTRJmo8/\n54+BoYGmokMjonLC28bJUUkrDZYXQRDw1+2/0G6dK0buHI/5vUfg3szbCPGeiP8u0uSCHSKSYM+8\nGAVXPerqfvy4vLyvYOgX7ofsvGz0qu2FeX2+RF199UKxccEOkfLiMIucVWSlwJy8HPx59U/4R/ij\npkZNeLt5o2+zvlIrGBKRcqvwZB4WFobx48cjJycH06ZNw9SpU2UKqDIq70qBb3PeYvPlzVgSuQTG\n2sbw7uiNzyw++2QFQyJSXhU+Zj59+nSsWbMGJ06cwKpVq5Camiprk5XKh5UC5TlOnZWdhRXnV6DJ\nyibYHbcbG/tvRNiYsBKVoiUiKkimZP7y5UsAQMeOHWFmZobu3bvj/PnzcgmsMiivSoEZbzMQEBEA\ni+UWOHXvFPYO2YujHkdLXIqWiOhDMiXzCxcuwNraWvLYxsYG586dkzmoyiIysvAYua5u/uPIyLK1\n9/z1c/iIfWCxwgKXki/h+Mjj2D9sPxyNHeUXNBGppAoptOXj4yP5u7u7O9zd3SvisDKTNlNEV7f0\nM0iSXyVj6bmlWPfPOvRv1h+RnpFoWrepfIIkIqUgFoshFovLvL9MF0BfvnwJd3d3xMTEAACmTp2K\nnj17ok+BbKcMF0DL6mH6QwRGBmLLlS0Y3mI45rrMhZmumaLDIqIqoEIvgOro6ADIn9GSkJCA48eP\nw9nZWZYmlcKd53fw7cFv0TK4JTTUNXBt0jWs6rOKiZyIyo3MwyzLli3D+PHjkZ2djWnTpsHAwEAe\ncVVJ11OuY3HEYhy+fRgT207Eram3YFBTdc8HEVUcLhqSg5gnMfAL90N4Ynh+BUPHydDRzP/Wwtut\nEVFZsDZLBTr74Cz6bOuDz7d/DpdGLrg77S4Wui2UJHKg+FrkRETywp55KQmCgNMJp+Eb5ot7afcw\nz2UeRrceDc1qRVcwrMiSAESkHFibpZy8r2DoG+6LF69fYIHrAnxl9xU01DVKtH95lwQgIuXCGzrL\nWZ6Qh71xe+EX7oc8IQ9ebl74ovkXUFdT//TO/+/DkgDsmRORvLFnXoScvBxsj90O/wh/6NTQgZeb\nFz5v+nmpa6YoqowuEVVtHGaR0duct/j98u8IiAyAqY4pvN280aVxlzIXvuJsFiIqCybzMsrKzsK6\ni+sQ+HcgWjZoCS83L7iYcsoJESkGx8xLKf1tOoIuBGHZuWVwMXVByLAQODR0UHRYRESlorLJ/FnW\nM6w4vwJB0UHoYdkDJ0edhG19W0WHRURUJiqXzJNeJeHXs79ifcx6DLQeiLNjz6KJfhNFh0VEJBOV\nSeaJLxMRGBmIrbFbMcJuBGLGx8BUx1TRYRERyYXSJ/P45/FYErEE+27sw1j7sbg++ToMaxsqOiwi\nIrlS2mR+7ek1+Ef449idY5jUdhJuTbmFujXrKjosIqJyoXRTEy8+vgi/cD/8/eBvzGg3A5McJ6FO\njToVdnwiInlQ2aqJEYkR6LW1F/rv6I9OZp1wd/pd2L2cj7zXhRN5Wlr+Qh4iImVSpZO5IAg4cfcE\n3De5Y9S+URhoPRB3pt3B9HbTUVOjJsvPEpHKqJLDLIIg4NCtQ/AN90X623QsdF2I4XbDUU3t40sA\nLD9LRFWRUi/nz83Lxe7ru+Ef4Q81kRq83LwwqPkgqImK/4LB8rNEVNUo5XL+7NxsbIvdBv8If+hr\n6cO/iz96W/UuUfErlp8lIlVQaXvmoaGAg/Mb7E/YhIDIADTWbYwZbbyhdr8zPv+8ZBUMWX6WiKoq\npZjNkvkuE5e1lqLJCkvsvXYQWwdtxd7+p3B0dRe4upa8FG1kZOHEraub/zgyspwCJyJSkApL5iWZ\nEvjyzUv4h/vDYoUF/kmNxF8eh2AVFYqGuR3K1KPu0+fj7XV1WUeciJRPhYyZFxzekCY1KxXLzy1H\ncHQweln1wumvT8Omng0AwHTOvxcvOTRCRCSdTD3zOXPmoHnz5mjTpg1mzJiB169fS92uqF71k4wn\nmH1sNpqubIrkzGSc/+Y8tgzcIknkH168fD9fnIiICpMpmXfv3h3Xrl1DdHQ0MjMzsW3bNqnbzZlT\nOJHfT7uPyaGTYRtki+zcbFyZeAVr+66Fpb6lZJuCvXlz8/w/Cy4AIiKif8mUzD/77DOoqalBTU0N\nPXr0wJkzZ6Ru975XfevZLXiGeKLN2jbQrqGNuMlxWN5rOUzqmHy0Dy9eEhGVnNymJvbo0QPffPMN\nvvzyy8IHEIkQcfsKRq/3xwu9E5jqNAVTnadCX0tfHoclIlJKcl809NlnnyEpKemj5/39/dG3b18A\nwI8//ghtbe2PEvl7PSa1R1vD9mid8A06OXViIici+oBYLIZYLC7z/jL3zDdt2oR169bh5MmT0NTU\n/PgAIhGy3mVBS0NLlsMQEamUCl3Of+TIEQQGBiIsLExqIn+PiZyIqHzJ1DO3srLCu3fvoK+fP2zS\nvn17BAUFFT5ABd+cgohIGSh11UQiIlWhFLVZiIiodJjMiYiUAJM5EZESYDInIlICTOZEREqAyZyI\nSAkwmRMRKQEmcyIiJcBkTkSkBJjMiYiUAJM5EZESYDInIlICTOZEREqAyZyISAkwmRMRKQEmcyIi\nJcBkTkSkBJjMiYiUAJM5EZESYDInIlICTOZEREqAyZyISAnInMx/+eUXqKmp4fnz5/KIh4iIykCm\nZP7gwQMcP34cZmZm8oqHPkEsFis6BKXC8yk/PJeKJVMynzVrFn766Sd5xUIlwDeMfPF8yg/PpWKV\nOZmHhITAxMQELVu2lGc8RERUBtWKe/Gzzz5DUlLSR8/7+flh8eLFOHbsmOQ5QRDkHx0REZWISChD\nFr569Sq6du2KmjVrAgAePnwIY2NjREVFoX79+oW2bdKkCe7cuSOfaImIVISlpSXi4+NLvH2ZkvmH\nGjdujIsXL0JfX1/WpoiIqAzkMs9cJBLJoxkiIiojufTMiYhIscptBeiuXbtga2sLdXV1/PPPP4Ve\nW7FiBaysrGBjY4OIiIjyCkFp+fj4wMTEBPb29rC3t8eRI0cUHVKVExYWhubNm8PKygorV65UdDhV\nnrm5OVq2bAl7e3s4OTkpOpwqx9PTEw0aNICdnZ3kuYyMDPTv3x+mpqYYMGAAXr16VWwb5ZbM7ezs\nsG/fPnTs2LHQ80+fPkVQUBBOnjyJ4OBgTJs2rbxCUFoikQizZs1CTEwMYmJi0LNnT0WHVOVMnz4d\na9aswYkTJ7Bq1SqkpqYqOqQqTSQSQSwWIyYmBlFRUYoOp8oZM2bMR52y4OBgmJqa4vbt2zAxMcHq\n1auLbaPckrm1tTWaNm360fPnz59Hz549YWpqik6dOkEQBGRkZJRXGEqLo2Nl9/LlSwBAx44dYWZm\nhu7du+P8+fMKjqrq4+9k2bm5uUFPT6/Qc1FRURg7dixq1KgBT0/PT/6OVnihraioKDRv3lzyuFmz\nZvwkL4OVK1eiXbt2CAgI4IdhKV24cAHW1taSxzY2Njh37pwCI6r6RCIRunTpggEDBuDAgQOKDkcp\nFPw9tba2/mSeLHbR0KcUtajI398fffv2lbqPtE9vzob5WHELtiZOnIj//Oc/SE9Px5w5c7BmzRrM\nnj1bAVES5YuMjISRkRHi4uLQt29fODk5wdDQUNFhVWml/aYjUzI/fvx4qfdxdnbGiRMnJI9v3LgB\nR0dHWcJQSiU5tzo6Opg8eTImTZrEZF4Kjo6OmDNnjuTxtWvXeN1BRkZGRgCA5s2bo1+/fjh48CDG\njRun4KiqNkdHR8TFxcHe3h5xcXGfzJMVMsxS8BPGyckJR48eRWJiIsRiMdTU1KCtrV0RYSiNJ0+e\nAABycnKwbds29O7dW8ERVS06OjoA8me0JCQk4Pjx43B2dlZwVFVXVlaWZKgvJSUFR48e5YejHDg7\nO2PDhg14/fo1NmzYgHbt2hW/g1BO9u7dK5iYmAiamppCgwYNhJ49e0peW7ZsmWBpaSk0b95cCAsL\nK68QlNbIkSMFOzs7wcHBQZg5c6bw7NkzRYdU5YjFYsHa2lqwtLQUli9fruhwqrS7d+8KrVq1Elq1\naiV06dJFWL9+vaJDqnKGDRsmGBkZCdWrVxdMTEyEDRs2COnp6UK/fv2ERo0aCf379xcyMjKKbYOL\nhoiIlABvG0dEpASYzImIlACTORGREmAyJyJSAkzmRERKgMmciEgJMJkTESkBJnMiIiXwf031D+OW\n3GvbAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4078f90>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For a converged fit recipe, the details of the fit can be extracted\n",
      " with the FitResults class."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from diffpy.srfit.fitbase import FitResults\n",
      "res = FitResults(rec)\n",
      "print(res)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overall\n",
        "-------------------------------------------------------------------------------\n",
        "Residual       21.48244998 \n",
        "Contributions  21.48244998 \n",
        "Restraints     0.00000000  \n",
        "Chi2           21.48244998 \n",
        "Reduced Chi2   1.13065526  \n",
        "Rw             0.07057009  \n",
        "\n",
        "Variables\n",
        "-------------------------------------------------------------------------------\n",
        "A  5.06643592e-01 +/- 1.08112495e-02\n",
        "B  2.99724135e+00 +/- 6.54653673e-02\n",
        "\n",
        "Variable Correlations greater than 25%\n",
        "-------------------------------------------------------------------------------\n",
        "No correlations greater than 25%\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Variables defined in the recipe can be fixed to a constant value."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rec.fix(B=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The fixed variables can be checked using the \"fixednames\" and\n",
      " \"fixedvalues\" attributes of a recipe."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(\"free:\", rec.names, \"-->\", rec.names)\n",
      "print(\"fixed:\", rec.fixednames, \"-->\", rec.fixedvalues)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "free: ['A'] --> ['A']\n",
        "fixed: ['B'] --> [0]\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The fit can be rerun with a constant variable B."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "leastsq(rec.residual, rec.values)\n",
      "print(FitResults(rec))\n",
      "plot(linedata.x, linedata.y, 'x', linedata.x, linedata.ycalc, '-')\n",
      "title('Line fit for variable B fixed to B=0')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overall\n",
        "-------------------------------------------------------------------------------\n",
        "Residual       2117.54303318\n",
        "Contributions  2117.54303318\n",
        "Restraints     0.00000000  \n",
        "Chi2           2117.54303318\n",
        "Reduced Chi2   105.87715166\n",
        "Rw             0.70063998  \n",
        "\n",
        "Variables\n",
        "-------------------------------------------------------------------------------\n",
        "A  5.06640829e-01 +/- 1.08112496e-02\n",
        "\n",
        "Fixed Variables\n",
        "-------------------------------------------------------------------------------\n",
        "B  0.00000000e+00\n",
        "\n",
        "Variable Correlations greater than 25%\n",
        "-------------------------------------------------------------------------------\n",
        "No correlations greater than 25%\n",
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "<matplotlib.text.Text at 0x3eb0a10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xYgR8fX2xdOlSbZsjImrWCgqATz5Rfz+tkvnDhw+xevVqHD9+HEqlEleuXMHRo0e1aZKI\nqNmqGmL54AP197XW5sBt27aFIAh49OgRAODJkyewt7fXpkkiomYrNbUykdvZqb+vVj3ztm3bYv36\n9XB1dYWjoyNGjhwJsVisTZNERM3WlCmaJXJAy2R+//59RERE4NKlS7h+/Tp++uknJCYmatMkERFp\nQKthFoVCAX9/f/Tt2xcAMHPmTCQnJ2PKlCk1touJiVF9LZFIIJFItDksEZHFkcvlkMvlGu+v1dTE\nwsJCDB06FAqFAu3bt8fMmTOxZMkSjBs37o8DcGoiEZHa1M2dWvXMO3bsiL/97W+YNm0anjx5gsDA\nQLz44ovaNElERBrgoiEiIhOkbu7kvVmIiCwAkzkRkQ7Ud8fDgoLK1w2ByZyISAdq3/GwajXnyJGG\nOT7HzImIdKQqga9YUXl/FU1XcwLq504mcyIiHaq84yFw7Rrg6qp5O7wASkRkJFV3PLx2rfJfTasG\naYLJnIhIB6rf8dDVtfJfTasGaYLDLEREOpCYWHmxs/oYeUFB5Z0Qa93hpEk4Zk5EpAFdJ2Ntccyc\niEgDxp5aqC32zImI/keXUwu1xWEWIiIt6GpqobY4zEJEpCFjTi3UFpM5ERGMP7VQWxxmISKC+c9m\nYTInIjJBHDMnIrNi7FvHWgomcyIyKl3M7+YvBCZzIjIyO7s/LjZev/7HRUh15neb+4IfXdB6zLy4\nuBiRkZH46aefYG1tjc2bN8Pf3/+PA3DMnIiaQNv53aa04EcXDD5mvnLlSjg7OyMjIwMZGRnw9PTU\ntkkiamZ0Mb/bzq4ykffuXfmvOSdyTWidzJOSkvDee++hTZs2sLa2hq2trS7iIqJmQlfzu815wY8u\naJXMb9++jZKSEkRERGDYsGFYs2YNSkpKdBUbETUDqak1h0SqxtBTU5vehrkv+NEFrcbMs7Oz0a9f\nP+zfvx/jx4/HokWLMH78eISGhv5xACsrrFy5UvVcIpFAIpFoFTQRUXWmtuBHE3K5HHK5XPV81apV\nhl005OnpiczMTADAkSNHsG3bNuzevfuPA/ACKJHFsoQkaqoMfgHU3d0dp0+fRkVFBRITEzF+/Hht\nmyQiM8EpgaZD6575lStXEBoaipKSEowfPx6rVq1C+/bt/zgAe+ZEFs3SpgSaCt6bhYgMzlTuAW5J\neG8WImoyXSyDb+5TAk0FkzlRM6btmDenBJoODrMQNXPajHlzNov+cMyciNTGMW/TwzFzIlILx7wt\nA5M5UTPGMW/LwWEWomaMY96mi2PmRERmrqyiDK1atuKYORGROfqt+Df8I/kfcP3cVe19mcyJiIxI\nEAScvn0ac7+di/6y/rhRcAOJr6tfvJTDLERERlBSVoL/XPgPZEoZHj59iEi/SMz3mY9ObTsB4Jg5\nEZFJu1FwA/Fn4rEpfRN8e/hCKpIisG8gWrZoWWM7dXOnta4DJSKimgRBwA/Xf8A6xTok30hG6OBQ\npIalwr2zu86OwZ45EZGeFP1ehO0Z2yFTyNDCqgWixdGYPXg2OrzQ4bn7cpiFiMjIfsn7BbHKWOzI\n2IGxvcdCKpZijMsYWFlZNbkNLucnaiZ0cfta0p3yinIc+OUAJm6fiICtAejYuiPOLT6HPbP2QOIq\nUSuRa4I9cyIzVX0pvp1d3edkGA+ePMCm9E2IU8bBsYMjpGIpZnrNRGvr1lq1y2EWomaEJduM5+zd\ns5ApZPj28rcI7h+MKFEURD1FOmufyZyomeHtaw3nWfkz7Lm0B7HKWNx6dAuRokgs8FmAru276vxY\nRpmaWF5eDj8/Pzg5OeHgwYO6aJKImqD27WvZM9ePO0V3sOHMBmw8uxFeXb3wzvB3MLX/VFi3MJ3Z\n3Tq5APrFF1/Ay8tL7wP8RPQH3r5WvwRBwMkbJ/HKnlcwMG4g8p7k4UToCZwIPYFpntNMKpEDOkjm\nt2/fxuHDhxEeHs7hFCIDSk2t2RO3s6t8nppq3LjMXfGzYiSkJWDIhiEIPxiOUb1G4dqSa4idEguv\nrl7GDq9BWv9qWbZsGT755BMUFhbqIh4iaqL67jduZ8f7kGvq6sOriFPG4ctzX2Kk80isnbAW4/qM\nQwsr85jBrVUyP3ToEBwcHODj4wO5XN7gdjExMaqvJRIJJBKJNoclMnssCmEaKoQKHM0+CplSBkWO\nAmFDwqBcqERv+94Gj0UulzeaR59Hq9ks7733HrZv3w5ra2uUlJSgsLAQ06dPx7Zt2/44AGezENXB\nOeLGVVBSgC3pWxB3Jg42L9ggWhyNVwe+irat2ho7NBWjTU388ccfsXbt2jqzWZjMierHOeKGd/7e\necQqY/Gfi//B5L6TES2Ohr+Tv0lO3jDqXRNN8YQQmSo7u8pEXjVHnIlcP0rLS7H/l/2QKWTIepiF\nRb6LcCnyErrbdDd2aDrFRUNERsKeuX7de3wPCWcTEH8mHn3s+0AqlmKaxzS0atnK2KE1CVeAEpkB\njpnrhyAIOJ1zGjKFDIlZiZjpNRNRoih4O3obOzS1MZkT6ZkuZqJwNotuVZVgW6dYh/ySfESJojB/\nyHzYt7U3dmgaYzIn0jP2qk1H9RJsfj38ECWKwmT3yWYzN7wxTOZEBsDxbuMRBAHfX/seMqUMyTeS\n8Yb3G4jwi9BpCTZTwGROZCC8W6FhFf1ehG3ntkGmlMG6hTWkImmTS7CZIxZ0JjIA3q3QcC7nXUas\nIhY7z+/EuD7jED8lHgEuAZwKXQt75kRq4pi5/pVXlCMxKxEyhQwZ9zKwcOhCLPJbBKeOTsYOzWA4\nzEKkZ5yJoj/6KsFmjpjMicjs6LsEmznimDkRmYWqEmwyhQy3C28jwi8CV6RX9FKCrTlgz5yaHQ6T\nGFdOYQ42pG1AwtkEDOg6AFKxFC/1e8nkKvcYm7q50/xn1lOzkphYtyxaQUHl6001cmTN8mpVFzBH\njtRdnFRTVQm2WV/PwsD1A/HgyQOcCD2BpNAkhHiEMJHrAHvmZFZ0NZOEi34Mo/hZMXad3wWZUoaS\nshJIRVKEeofCto2tsUMzebwAShZPV4mYi370p3YJNqlIalYl2EwBL4CSxdPFfcC56Ef3TKkEW3PE\nnjmZHW175lz0o1sFJQXY+vNWxCpj0eGFDogWR+O1ga+ZVAk2c8RhFrJoukjEnM2iG7VLsEWJojCi\n1wgus9cRJnOyaEzExlVfCbaFQxdaXAk2U8BkTkQ6Z+4l2MyRweeZ37p1Cy+++CIGDBgAiUSCXbt2\nadskEZkAQRBw6vYpzNk7Bx6xHrj56CYSX09E8vxkzBowi4ncxGjdM8/NzUVubi6GDBmCvLw8iMVi\nnDt3DjY2NpUHYM+cyKyUlJXg3xf+DZlCZjEl2MyRwacmOjo6wtHREQDQpUsXDBgwAGfOnMGLL76o\nbdNEZEC1S7D9/cW/I7BvIOeGmwmdzjPPzs7GxYsXIRaLddksEelJfSXYUsNSLa4EW3Ogs2ReVFSE\nV155BZ999hnat29f472YmBjV1xKJBBKJRFeHJSIN1C7BFiWKwvZp2y22BJs5kMvlkMvlGu+vk9ks\npaWlmDJlCoKCgrB06dKaB+CYOf0PpxUaX+0SbFKRlCXYTJTBZ7MIgoAFCxZg4MCBdRI5UXW8W6Fx\nlFeUY//l/ZiwfQIkWyWwa2OHjIgMfD3za4xxHcNEbiG07pmnpKQgICAAgwcPVv1QfPjhhwgMDKw8\nAHvmVA3vVmg41UuwdbfpDqlIihleM5plCTZzxEVDZPJ4t0L9ql2CTSqWwq+Hn7HDIjXxrolk0ni3\nQv2oXYItUhTJEmzNDHvmZDC8W6Hu5RTmYGPaRmw8u5El2CwMh1nIZHE2i24IgoCUmylYp1iH478e\nx+sDX0eUOApeXb2MHRrpEJM5kYViCbbmhQWdqV7aFkLWRSFl0szVh1ex/OhyuHzugkNZh7B2wlpk\nRmUielg0EzmpMJk3E9rO8eYcccOqECpwJOsIpuyaAv9N/rBuYQ3lQiX2v7ofE9wm8H4pVAeHWZoR\nXZVb4xxx/SkoKcCW9C2IOxMHmxdsEC2OxqsDX2UJtmaIY+bUKG3neHOOuH6cv3ceMoUMX136CkHu\nQZCKpPB38ufqzGaMY+bUoNpzvGuPget7f6qptLwUey7tgWSrBIE7A+HU0QmZUZnY+aedGN5rOBM5\nqYU982ZC2znenCOuO7VLsEWJovAnzz+xcg/VwGEWqpe2c7w5R1w7giDgdM5pyBQyJGYlYqbXTESJ\nouDt6G3s0MhEMZkTmZCnpU/xn4v/YQk2UhuTOZEJuFFwA+vPrMfm9M3w6+EHqVjKEmykFl4AtUBc\nsGMeBEFA0q9JCPl3CIZuHIpn5c+QGpaKw7MPI8g9iImc9Io9czPAi4+mrfD3Qmw7tw2xylhYt7BG\ntDgaswfNRvsX2j9/Z6IGcJjFQnHBjulhCTbSJyZzHTK1GRxcsGN85RXlOHTlEGRKGc7fO4/woeFY\n7LcYTh2djB0aWRiOmeuQKd2PhAt2jCvvSR7WpKyB27/c8FHqR5jnPQ83lt7AP8b+g4mcTAJ75s9h\nCsMbHDM3nrN3z2KdYh32Xd6HEI8QRImiWIKNDMLgwyzJyclYtGgRysrK8NZbbyE6OlqrgEyRsYc3\nTG24x9JVL8GWU5SDCL8IhA8NR5d2XYwdGjUjBk/mPj4++OKLL+Di4oJJkyYhJSUFXbr88UNv7snc\nFHrmZBg5hTnYkLYBCWcTWIKNjM6gY+aPHj0CAAQEBMDFxQUTJ07E6dOntWnSpFQfznB1rfy3+hg6\nmT9BEHDyxknM+noWBq0fhIdPH+JE6AkkhSYhxCOEiZzMhlbJXKlUwsPDQ/Xcy8sLp06d0jooU5Ga\nWrMnbmdX+Tw11bhxkfaKnxUjIS0BQzYMwcKDCxHgEoDrS69DFiRjLU0ySwbpdsTExKi+lkgkkEgk\nhjis1uobj7az4zi1Obv68CrilHH48tyXGNFrBNZOWIvxfcZzbjgZnVwuh1wu13h/rcbMHz16BIlE\ngvT0dABAdHQ0AgMDMaVatjP3MXMyfxVCBY5mH4VMKYMiR4GwIWGIEEXA1c7V2KERNUjd3KlVz9zW\ntrKYbHJyMpydnXH8+HGsXLlSmyaJdKaqBFusMhYdW3dEtDgae2buYQk2skhaD7N8/vnnWLRoEUpL\nS/HWW2/VmMlCnFZoDBn3MhCriFWVYNs+bTtLsJHF46IhPeOCH8MoLS/Fvsv7IFPKkP0wG4t9F2Oh\n70I4dnA0dmhEGuG9WUwQ56rrT+7jXCSkJWBD2gb0se8DqViKaR7TWIKNzB6TuYky9ipSS8ISbNQc\nGPQCKDVN7ZtksWeumdol2CL9IrFu8jqWYCMCe+Z6xzFz7bEEGzVHHGYxMZzNohlBEHDi2gnIFDKc\nvHkSb3i/gQi/CLh3djd2aEQGwWROZo0l2IgqccyczNLlvMuQKWTYdX4XxvUZh/gp8SzBRqQGJnMy\nmtol2BYOXYiMiAxW7iHSAJM5GVzekzxsOrsJ68+sR3eb7pCKpJjhNQOtrVsbOzQis8VkTgaTdicN\nMqUM+y7vQ3D/YOyZtYcl2Ih0hMmc9OpZ+TN8ffFryJQy3Cm6g0i/SGRFZ7EEG5GOWfRsFk4LNJ6q\nEmwb0zZioMNARIuj8VK/l9CyRUtjh0ZkFgxaNs7UjRxZs8xb1YKdkSONG5elEgQByTeSa5Rg++GN\nH5AUmoRgj2AmciI9suieOcCbXBlC8bNi7Dy/EzKFDM/Kn0EqliLUOxQdW3c0dmhEZouLhurBm1zp\nR/bDbFUJttHOoyEVSzGu9zjODSfSAQ6z1FL7JldVQy6kmQqhAkeyjmDKrikYsWkEXmj5AtLeTMO+\nV/exliaREZlsz1wXFy95kyvdyX+aj60/b0WsMha2bWwRLY7GKwNeYQk2Ij2xmGEWXSRizmbRXvUS\nbFPcp0AqlmJYz2HsgRPpmckmc02SKC9eGkd9Jdje9H0T3Tp0M3ZoRM2GQZP5ihUrcOjQIbRt2xYB\nAQH48MMP0bZtzT+7rayskJ8vaDy8wYuXhlO9BJtbJzdIRVKEeISwBBuRERj0AujEiRNx8eJFnDlz\nBsXFxdi1a1e922mayHnxUv8EQcCp26cwZ+8ceMZ64nbhbRyefRg/zvsRMwfMZCInMhM6G2bZs2cP\nDhw4gG0MFybPAAAJjUlEQVTbttU8gJUVrl0T1O5V8+KlftUuwRYlisL8IfNZgo3IRBhtzHzSpEkI\nDw/HzJkz6wQUGSmonYR58VI/WIKNyDzovDjFhAkTkJubW+f11atXY+rUqQCAv//977CxsamTyKvY\n2MRgwgRg3DggMFACiUTy3MDqS9h2dkzkmqivBFtqWCpLsBGZELlcDrlcrvH+WvfMt27dioSEBJw4\ncQJt2rSpewAtZrOQdliCjch8GXSY5bvvvsPy5cuRnJyMzp076yQg0l7tEmxSkZQl2IjMjEGTubu7\nO549e4ZOnToBAIYPH464uDitAiLN1FeCbZHfIpZgIzJTJrtoiPSjqgRb3Jk49LDpwRJsRBZC5xdA\nyTRVL8EW4hGCb2Z9wxJsRM0Yk7kZYQk2ImoIh1nMwO3C29hwZgMSziawBBtRM8FhFgshCAJO3jwJ\nmUKGpF+TMHvQbPzwxg/w7Opp7NCIyASxZ25iqpdgK60ohVQkxVzvuSzBRtTMcDaLmWIJNiKqjsMs\nZqRCqMDR7KOQKWVQ5igR5hOGtDfT4GrnauzQiMjMsGduBCzBRkTPw565Catdgm3Hn3awBBsR6QST\nuZ7VV4LtctRllmAjIp1iMteT2iXYosXRCO4fzMo9RKQXTOY6JAgCTuechkwhQ2JWImZ5zcLh2Ycx\nuNtgY4dGRBaOF0B1oHoJtoKSAkSJojBvyDyWYCMijXGeuQFVL8Em6imCVCTFpL6TWIKNiLTG2Sx6\nVl8Jtv8u+C/6dupr7NCIqBljz7yJqpdga9WiFaRiKUuwEZHesGeuY5fzLiNWEYud53difJ/x2PDS\nBox2Hs254URkUpjM61G7BNubvm8iIyKDJdiIyGRpncw//fRTrFixAnl5eapaoOaqdgm2aHE0pntO\nZwk2IjJ5WiXzW7du4fjx43BxcdFVPEbBEmxEZO60SuZvv/02Pv74YwQHB+sqHoP5vex37Lm0hyXY\niMgiaJzM9+/fDycnJwwebF6rG6uXYBvUbRD+MvIvLMFGRGav0WQ+YcIE5Obm1nn9gw8+wIcffohj\nx46pXjPl6YeCICD5RjJkShlO/HqCJdiIyOI0msyPHz9e7+sXLlzAtWvX4O3tDQC4ffs2fH19oVAo\n4ODgUGf7mJgY1dcSiQQSiUTziNVQ/KwYOzJ2QKaUoayiDFKRFJte3sQSbERkcuRyOeRyucb762TR\nUO/evZGWllbvbBZjLBrKfpiNWEUstmVsw2jn0YgSRWF8n/GcG05EZsMoi4ZMIUlWCBX4Lvs7yBQy\nKO8oscBnAUuwEVGzYfbL+fOf5mPLz1sQp4xjCTYishjNZjk/S7AREf3BrJJ59RJsVx9exWI/lmAj\nIgLMJJlXL8HWt1NflmAjIqrFZJN59RJsh7MOY9aAWTgy+wgGdRtk7NCIiEyOyV0AZQk2IiIzLht3\nveA64s/EswQbERHMbDZL9RJsKTdTWIKNiEhDRumZ1y7BFi2OxuuDXmcJNiKi/zHpnnnm/UzEKmOx\n6/wuTHCbwBJsREQ6YpBkvu/yPsgUMlz47QLe9H0T5yPOo2fHnoY4NBFRs2CQYZbh/284pGIpS7AR\nETWR2c5mISKiP6ibOznvj4jIAjCZExFZACZzIiILwGRORGQBmMyJiCwAkzkRkQVgMicisgBaJfMt\nW7bA09MTAwYMwJ///GddxURERGrSOJlfuHABGzduxIEDB3Dx4kW88847uoyLGiCXy40dgkXh+dQd\nnkvj0jiZHzlyBAsWLIC7uzsAoGvXrjoLihrG/zC6xfOpOzyXxqVxMj927BguXLgAPz8/hIeH49Kl\nS7qMi4iI1NDoXRMnTJiA3NzcOq9/8MEHKCkpwcOHD3Hy5EkkJSVBKpXi+++/11ugRETUCEFD77zz\njnDo0CHV8+7duwtPnz6ts52bm5sAgA8++OCDDzUebm5uauVkje9nPnz4cBw5cgRBQUFQKBRwc3ND\nmzZt6myXnZ2t6SGIiKiJNE7mwcHBOHbsGLy8vODh4YF//vOfuoyLiIjUoPf7mRMRkf7pbQXo119/\njQEDBqBly5Y4e/Zsjff+9a9/wd3dHV5eXkhJSdFXCBYrJiYGTk5O8PHxgY+PD7777jtjh2R2kpOT\n4enpCXd3d6xbt87Y4Zg9V1dXDB48GD4+PhCLxcYOx+yEhYWhW7duGDRokOq1oqIiBAcHw9nZGSEh\nIXj8+HGjbegtmQ8aNAjffvstAgICarz+22+/IS4uDidOnMD69evx1ltv6SsEi2VlZYW3334b6enp\nSE9PR2BgoLFDMjtLlizBhg0bkJSUhNjYWOTl5Rk7JLNmZWUFuVyO9PR0KBQKY4djdubPn1+nU7Z+\n/Xo4OzsjKysLTk5OiI+Pb7QNvSVzDw8P9OvXr87rp0+fRmBgIJydnTFmzBgIgoCioiJ9hWGxODqm\nuUePHgEAAgIC4OLigokTJ+L06dNGjsr88WdSc6NHj4a9vX2N1xQKBRYsWIDWrVsjLCzsuT+jBr/R\nlkKhgKenp+p5//79+ZtcA+vWrYO/vz/WrFnDX4ZqUiqV8PDwUD338vLCqVOnjBiR+bOyssLYsWMR\nEhKCAwcOGDsci1D959TDw+O5eVLj2SxAw4uKVq9ejalTp9a7T32/va2srLQJwyI1tmArIiIC77//\nPgoLC7FixQps2LCB98Yho0pNTUX37t2RmZmJqVOnQiwWw9HR0dhhmTV1/9LRKpkfP35c7X2GDRuG\npKQk1fPLly9DJBJpE4ZFasq5tbW1RVRUFCIjI5nM1SASibBixQrV84sXL/K6g5a6d+8OAPD09MTL\nL7+MgwcPYuHChUaOyryJRCJkZmbCx8cHmZmZz82TBhlmqf4bRiwW4+jRo7h58ybkcjlatGgBGxsb\nQ4RhMe7evQsAKCsrw65duxAUFGTkiMyLra0tgMoZLdevX8fx48cxbNgwI0dlvp48eaIa6rt//z6O\nHj3KX446MGzYMGzevBlPnz7F5s2b4e/v3/gOmi7nf569e/cKTk5OQps2bYRu3boJgYGBqvc+//xz\nwc3NTfD09BSSk5P1FYLFmjt3rjBo0CDB19dXWLZsmfDgwQNjh2R25HK54OHhIbi5uQlffPGFscMx\na7/++qvg7e0teHt7C2PHjhU2bdpk7JDMzquvvip0795deOGFFwQnJydh8+bNQmFhofDyyy8LvXr1\nEoKDg4WioqJG2+CiISIiC8CycUREFoDJnIjIAjCZExFZACZzIiILwGRORGQBmMyJiCwAkzkRkQVg\nMicisgD/H9puIL/YOJ46AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3489fd0>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Fixed variables may be released with the `free()` function.\n",
      " Calling it as `free(\"all\")` releases all fixed variables."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rec.free('all')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Variables may be constrained to a result of an expression."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rec.constrain(rec.A, \"2 * B\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Perform linear fit where the slope value must be two times the offset."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "leastsq(rec.residual, rec.values)\n",
      "print(FitResults(rec))\n",
      "plot(linedata.x, linedata.y, 'x', linedata.x, linedata.ycalc, '-')\n",
      "title('Line fit for variable A constrained to A = 2*B')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overall\n",
        "-------------------------------------------------------------------------------\n",
        "Residual       1766.30403027\n",
        "Contributions  1766.30403027\n",
        "Restraints     0.00000000  \n",
        "Chi2           1766.30403027\n",
        "Reduced Chi2   88.31520151 \n",
        "Rw             0.63989914  \n",
        "\n",
        "Variables\n",
        "-------------------------------------------------------------------------------\n",
        "B  2.71901889e-01 +/- 5.38729019e-03\n",
        "\n",
        "Variable Correlations greater than 25%\n",
        "-------------------------------------------------------------------------------\n",
        "No correlations greater than 25%\n",
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "<matplotlib.text.Text at 0x3ee44d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LLKRV1HH1JUezFHX98XWExoZi4+mNGNJ+CALcA9DNvJvUYdV4HJpIOo2JWH0S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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3b101d0>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Constraint expressions can be removed by calling the unconstrain function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rec.unconstrain(rec.A)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " Variables may be restrained to a specific range.  Here \"ub\" is the upper\n",
      " boundary and \"sig\" acts as a standard deviation for ((x - ub)/sig)**2\n",
      " penalty function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "arst = rec.restrain(rec.A, ub=0.2, sig=0.001)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Perform fit with the line slope restrained to a maximum value of 0.2:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "leastsq(rec.residual, rec.values)\n",
      "print(FitResults(rec))\n",
      "plot(linedata.x, linedata.y, 'x', linedata.x, linedata.ycalc, '-')\n",
      "title('Line fit with A restrained to an upper bound of 0.2')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overall\n",
        "-------------------------------------------------------------------------------\n",
        "Residual       819.12507052\n",
        "Contributions  812.35868498\n",
        "Restraints     6.76638555  \n",
        "Chi2           812.35868498\n",
        "Reduced Chi2   40.61793425 \n",
        "Rw             0.43396301  \n",
        "\n",
        "Variables\n",
        "-------------------------------------------------------------------------------\n",
        "A  2.02601228e-01 +/- 9.95749478e-04\n",
        "B  2.99718481e+00 +/- 6.54653670e-02\n",
        "\n",
        "Variable Correlations greater than 25%\n",
        "-------------------------------------------------------------------------------\n",
        "No correlations greater than 25%\n",
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<matplotlib.text.Text at 0x3e98c50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x407a0d0>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    }
   ],
   "metadata": {}
  }
 ]
}