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 },
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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Fisher Score Mixin Example"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This notebook demonstrates how to use the ``qinfer.ScoreMixin`` class to develop models that use numerical differentiation to calculate the Fisher information. We test the mixin class with two examples where the Fisher information is known analytically."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Preamble"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qinfer import ScoreMixin, SimplePrecessionModel, RandomizedBenchmarkingModel\n",
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "try:\n",
      "    from mpltools import style\n",
      "    style.use('ggplot')\n",
      "except:\n",
      "    pass"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Simple Precession Model Test"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Create two models, one that uses ScoreMixin's numerical ``score`` method, and one that uses ``SimplePrecessionModel``'s analytic ``score`` method. To make the first model, we declare a class that does nothing but inherits from both the ``ScoreMixin`` class and ``SimplePrecessionModel``; note that ``ScoreMixin`` is first, such that its implementation of ``Model.score()`` overrides that of ``SimplePrecessionModel``."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class NumericalSimplePrecessionModel(ScoreMixin, SimplePrecessionModel):\n",
      "    pass\n",
      "\n",
      "analytic_model = SimplePrecessionModel()\n",
      "numerical_model = NumericalSimplePrecessionModel()\n",
      "\n",
      "expparams = np.linspace(1, 10, 50)\n",
      "modelparams = np.linspace(.1,1,50)[:, np.newaxis]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We verify that both models compute the same score by plotting the score for a range of experiment and model parameters. Since this is a single-parameter model, the score is a scalar."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "analytic_score = analytic_model.score(np.array([0],dtype=int),modelparams, expparams)[0,0,...]\n",
      "print analytic_score.shape\n",
      "numerical_score = numerical_model.score(np.array([0],dtype=int),modelparams, expparams)[0,0,...]\n",
      "print numerical_score.shape\n",
      "\n",
      "plt.subplot(1,2,1)\n",
      "plt.imshow(analytic_score)\n",
      "plt.subplot(1,2,2)\n",
      "plt.imshow(numerical_score)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(50, 50)\n",
        "(50, 50)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<matplotlib.image.AxesImage at 0x451f8d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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PuO+++5oytnOOEydOcPnyZb785S+zZ8+epp3zj3/8Y775zW8yOzub\n/a7Z17tVtFrbrbjO3aLtPOi6Kxcxldrcxj5zc3OcOnWKb33rW/T0NHaC26yxtdZ8//vf58UXX+Tt\nt9/mrbfeasq4r732GqVSiX379uFvkpG62ddbSGnGde4WbedF103xwAcHBxkbG8seX716lcHBwWYM\nnVEqlZiYmGBgYIDx8XFKpdKmjJMkCadOneKRRx7hi1/8YlPHBujt7eXgwYO8//77TRn33XffZWRk\nhNdff504jpmdneWHP/xhU8+5lbRa2828zt2k7bzouike+L333ssnn3zClStXSJKEn/3sZxw6dKgZ\nQ2ccOnSI8+fPA/DKK68wPDy84WN473nxxRfZvXs3X/3qV5s29tTUFDdu3ADSVfs333yTffv2NeWc\nH3/8cV544QWef/55/vzP/5wHH3yQb3/7200Zux1otbabdZ27Tdt50XXTKjHfeOONhlSrP/zDP9y0\nsc6cOcPo6ChTU1MMDAzw9a9/neHh4U1P/3nnnXf47ne/y969e7Pp1RNPPMGnP/3pTR3717/+Nc8/\n/zzOObz3PPLII/zBH/xB01OeRkdHeemll9oz3WoTaZa2W6Vr6G5tt7OupZReEAQhp3TlIqYgCEIn\nIAZcEAQhp4gBFwRByCliwAVBEHKKGHBBEIScIgZcEAQhp4gBFwRByCn/H4wEDErAYlcxAAAAAElF\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4532d90>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we verify that both models give the same Fisher information."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "analytic_fisher_info = analytic_model.fisher_information(modelparams, expparams)[0,0,...]\n",
      "numerical_fisher_info = numerical_model.fisher_information(modelparams, expparams)[0,0,...]\n",
      "\n",
      "plt.subplot(1,2,1)\n",
      "plt.imshow(analytic_fisher_info)\n",
      "plt.subplot(1,2,2)\n",
      "plt.imshow(numerical_fisher_info)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.image.AxesImage at 0x4791d10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x476ccd0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Randomized Benchmarking Model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To test that we get multiparameter Fisher information calculations correct as well, we compare to the zeroth-order non-interlaced randomized benchmarking model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class NumericalRandomizedBenchmarkingModel(ScoreMixin, RandomizedBenchmarkingModel):\n",
      "    pass\n",
      "\n",
      "analytic_model = RandomizedBenchmarkingModel()\n",
      "numerical_model = NumericalRandomizedBenchmarkingModel()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We now make experiment and parameters to test with."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expparams = np.empty((150,), dtype=analytic_model.expparams_dtype)\n",
      "expparams['m'] = np.arange(1, 151)\n",
      "\n",
      "modelparams = np.empty((500, 3))\n",
      "modelparams[:, 0] = np.linspace(0.1, 0.999, 500)\n",
      "modelparams[:, 1] = 0.5\n",
      "modelparams[:, 2] = 0.5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 99
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's make sure that the returned Fisher information has the right shape. Note that the Fisher information is a four-index tensor here, with the two indices for the information matrix itself, plus two indices that vary over the input model parameters and experiment parameters."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "afi = analytic_model.fisher_information(modelparams, expparams)\n",
      "assert afi.shape == (3, 3, modelparams.shape[0], expparams.shape[0])\n",
      "nfi = numerical_model.fisher_information(modelparams, expparams)\n",
      "assert nfi.shape == (3, 3, modelparams.shape[0], expparams.shape[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 100
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We check that each Fisher information matrix has errors that are small compared to the analytic FI alone."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "norm(afi - nfi) / norm(afi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 101,
       "text": [
        "1.662610344524985e-07"
       ]
      }
     ],
     "prompt_number": 101
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we plot the trace-inverse of each to check that we get the same Cramer-Rao bounds."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def tr_inv(arr):\n",
      "    try:\n",
      "        return trace(inv(arr.reshape(3, 3)))\n",
      "    except LinAlgError:\n",
      "        return float('inf')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 102
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def crb(fi):\n",
      "    return apply_along_axis(tr_inv, 0, np.sum(fi.reshape((9, modelparams.shape[0], expparams.shape[0])), axis=-1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 104
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(15, 6))\n",
      "for idx, fi in enumerate([afi, nfi]):\n",
      "    subplot(1,2, 1 + idx)\n",
      "    semilogy(modelparams[:, 0], crb(fi))\n",
      "    ylabel(r'$\\operatorname{Tr}\\left(\\left(\\sum_m F(p, m)\\right)^{-1}\\right)$')\n",
      "    xlabel('$p$')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nn3PjjTfyxhtv/O45XyLxZprsiXflJEzPfvj33IT/5HTs+nVhZ4lI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\nfwgTAdEiF122AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x733fb90>"
       ]
      }
     ],
     "prompt_number": 105
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, we note that the numerical FI calculations are not much slower than the analytic calculations."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit analytic_model.fisher_information(modelparams, expparams)\n",
      "%timeit numerical_model.fisher_information(modelparams, expparams)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10 loops, best of 3: 29.7 ms per loop\n",
        "10 loops, best of 3: 60.9 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 106
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}