ex03.ipynb

{
 "metadata": {
  "name": ""
 },
 "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": [
      "import numpy as np\n",
      "%pylab inline\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": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "<matplotlib.text.Text at 0x3e85e90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NKvKLv3fvXhw/fhwPHjzAmTNn8H//93/o378/7OzsyrStVasWunfvjjlz5uDPP//Ehg0b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\nGnvsAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3312210>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "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": 2
    },
    {
     "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": 3
    },
    {
     "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                    [-1.83949659 -0.981338   -1.1781284  -0.52346779 -0.046267\n",
        "\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "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": [
        "(<diffpy.srfit.fitbase.parameter.Parameter object at 0x423ee10>, 3)\n",
        "(<diffpy.srfit.fitbase.parameter.Parameter object at 0x423ee90>, 5)\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "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() =', array([-25., -22., -19., -16., -13., -10.,  -7.,  -4.,  -1.,   2.,   5.,\n",
        "         8.,  11.,  14.,  17.,  20.,  23.,  26.,  29.,  32.,  35.]))\n",
        "('linefit.residual() =', array([-77.20167802, -70.06220667, -59.40623866, -51.58844071,\n",
        "       -43.17910823, -34.33121624, -25.77233125, -19.33739525,\n",
        "       -10.88984432,  -1.11893636,   5.75944657,  15.38156254,\n",
        "        24.26448016,  32.10291635,  40.61868301,  48.35937379,\n",
        "        56.38581393,  64.77457345,  73.39967781,  81.91100141,  88.04725337]))\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<matplotlib.text.Text at 0x425e950>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xdycic2OaWAB7dyLqKgz5LsbenYi6EkO+i7B3JyJLYCdvZuzdiciSmDRmIoRA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\nyI4x5ImI7BhDnojIjv0fxvLOQKwBKOAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x42463d0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " We want to find 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": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "clearFitHooks suppresses printout of iteration number"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rec.clearFitHooks()\n",
      "\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                    [-1.83949659 -0.981338   -1.1781284  -0.52346779 -0.0462\n",
        "\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " FitContributions may have many parameters.  We need to tell the recipe\n",
      " which of them should be tuned by the 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": 9,
       "text": [
        "<diffpy.srfit.fitbase.parameter.ParameterProxy at 0x445d7d0>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " The addVar function created two attributes A, B for the rec object\n",
      " which link ot 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 =', <diffpy.srfit.fitbase.parameter.ParameterProxy object at 0x445d6d0>)\n",
        "('rec.A.value =', 3)\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " The names of the declared variables are stored in a rec.names\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 =', array([3, 5]))\n",
        "('rec.names =', ['A', 'B'])\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "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() =', array([-77.20167802, -70.06220667, -59.40623866, -51.58844071,\n",
        "       -43.17910823, -34.33121624, -25.77233125, -19.33739525,\n",
        "       -10.88984432,  -1.11893636,   5.75944657,  15.38156254,\n",
        "        24.26448016,  32.10291635,  40.61868301,  48.35937379,\n",
        "        56.38581393,  64.77457345,  73.39967781,  81.91100141,  88.04725337]))\n",
        "('rec.residual([2, 4]) =', array([-47.20167802, -43.39554   , -36.07290533, -31.58844071,\n",
        "       -26.51244157, -20.99788291, -15.77233125, -12.67072859,\n",
        "        -7.55651099,  -1.11893636,   2.42611324,   8.71489588,\n",
        "        14.26448016,  18.76958302,  23.95201635,  28.35937379,\n",
        "        33.05248059,  38.10790678,  43.39967781,  48.57766807,  51.3805867 ]))\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "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": 13,
       "text": [
        "(array([ 0.5007377 ,  3.02689448]), 2)"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "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'], '-->', array([ 0.5007377 ,  3.02689448]))\n",
        "linefit\n",
        "-------------------------------------------------------------------------------\n",
        "A                    0.500737698564\n",
        "B                    3.02689447576\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                    [-1.83949659 -0.981338   -1.1781284  -0.52346779 -0.046267\n",
        "\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "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": 15,
       "text": [
        "<matplotlib.text.Text at 0x4795810>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NOpe6Di+SVbuxZk5Ux5x/eB7OZ5whJyuHDQM2wErdStwhURUob+7kCFAiCeTj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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x477f250>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The FitRecipe.scalarResidual function returns the sum of squares and can\n",
      "be used with a minimizer that expects 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: 13.247799\n",
        "         Iterations: 47\n",
        "         Function evaluations: 88\n",
        "(['A', 'B'], '-->', array([ 0.5007246 ,  3.02693361]))\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "<matplotlib.text.Text at 0x48aa550>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HmV/spcL1N0naWGYhKgFBELDz5k74HfGDmZYZlrothZmWWZH359wq9CWsmROV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\nA0zmRERy4P8AbhYMYotgYRkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4793590>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "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       13.24779867 \n",
        "Contributions  13.24779867 \n",
        "Restraints     0.00000000  \n",
        "Chi2           13.24779867 \n",
        "Reduced Chi2   0.69725256  \n",
        "Rw             0.05552977  \n",
        "\n",
        "Variables\n",
        "-------------------------------------------------------------------------------\n",
        "A  5.00724599e-01 +/- 1.08112497e-02\n",
        "B  3.02693361e+00 +/- 6.54653675e-02\n",
        "\n",
        "Variable Correlations greater than 25%\n",
        "-------------------------------------------------------------------------------\n",
        "No correlations greater than 25%\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "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": 18
    },
    {
     "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'], '-->', array([0]))\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "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       2151.06883653\n",
        "Contributions  2151.06883653\n",
        "Restraints     0.00000000  \n",
        "Chi2           2151.06883653\n",
        "Reduced Chi2   107.55344183\n",
        "Rw             0.70758917  \n",
        "\n",
        "Variables\n",
        "-------------------------------------------------------------------------------\n",
        "A  5.00737699e-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": 20,
       "text": [
        "<matplotlib.text.Text at 0x4b4ad50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3jm5ih0YmhsncBLFWLb6CpwXYlLIJSrUST8ueQi6RI8A9ABYtLMQOjUwUk7mJ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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x330c550>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Fixed variables may be released with the \"free\" function.\n",
      " free(\"all\") releases all fixed variables."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rec.free('all')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "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": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Perform linear fit where slope is twice 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       1799.85511327\n",
        "Contributions  1799.85511327\n",
        "Restraints     0.00000000  \n",
        "Chi2           1799.85511327\n",
        "Reduced Chi2   89.99275566 \n",
        "Rw             0.64725110  \n",
        "\n",
        "Variables\n",
        "-------------------------------------------------------------------------------\n",
        "B  2.69171507e-01 +/- 5.38729020e-03\n",
        "\n",
        "Variable Correlations greater than 25%\n",
        "-------------------------------------------------------------------------------\n",
        "No correlations greater than 25%\n",
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "<matplotlib.text.Text at 0x4e04790>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WrWBtbf3GYwPAmDFjEBgYiKlTp2LKlCkICAjAJ598UmD9N+nUqRPMzMxw+/Zt9O/fX7Pc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\niMgA/H8BrueGNAZRQwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4b682d0>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "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": 24
    },
    {
     "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": 25
    },
    {
     "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       780.47524838\n",
        "Contributions  773.96687418\n",
        "Restraints     6.50837420  \n",
        "Chi2           773.96687418\n",
        "Reduced Chi2   38.69834371 \n",
        "Rw             0.42443893  \n",
        "\n",
        "Variables\n",
        "-------------------------------------------------------------------------------\n",
        "A  2.02551152e-01 +/- 9.95749480e-04\n",
        "B  3.02689447e+00 +/- 6.54653672e-02\n",
        "\n",
        "Variable Correlations greater than 25%\n",
        "-------------------------------------------------------------------------------\n",
        "No correlations greater than 25%\n",
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "<matplotlib.text.Text at 0x4e34f90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x4895210>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}