{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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sfXpb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\nphy+Op7fwL/jxx5Kfzf+uLH2p/xfT/HH/9k=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image \n",
    "Image('../../../python_for_probability_statistics_and_machine_learning.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Python for Probability, Statistics, and Machine Learning](https://www.springer.com/fr/book/9783319307152)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section, we  consider the famous Gauss-Markov problem which will give\n",
    "us an opportunity to use all the material we have so far developed. The\n",
    "Gauss-Markov model is the fundamental model for noisy parameter estimation because it\n",
    "estimates unobservable parameters given a noisy indirect measurement.\n",
    "Incarnations of the same model appear in all studies of Gaussian models. This\n",
    "case is an excellent opportunity to use everything we have so far learned about\n",
    "projection and conditional expectation.\n",
    "\n",
    "Following Luenberger [[luenberger1968optimization]](#luenberger1968optimization) let's  consider the\n",
    "following problem:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbf{y} = \\mathbf{W} \\boldsymbol{\\beta} + \\boldsymbol{\\epsilon}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " where $\\mathbf{W}$ is a $ n \\times m $ matrix, and $\\mathbf{y}$ is a\n",
    "$n \\times 1$ vector. Also, $\\boldsymbol{\\epsilon}$ is a $n$-dimensional normally\n",
    "distributed random vector with zero-mean and covariance,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbb{E}( \\boldsymbol{\\epsilon} \\boldsymbol{\\epsilon}^T) = \\mathbf{Q}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Note that engineering systems usually provide a *calibration mode*\n",
    "where you can estimate $\\mathbf{Q}$ so it's not fantastical to assume you have\n",
    "some knowledge of the noise statistics. The problem is to find a matrix\n",
    "$\\mathbf{K}$ so that $ \\boldsymbol{\\hat{\\beta}}=\\mathbf{K} \\mathbf{y}$\n",
    "approximates $ \\boldsymbol{\\beta}$.  Note that we only have knowledge of\n",
    "$\\boldsymbol{\\beta}$ via $ \\mathbf{y}$ so we can't measure it directly.\n",
    "Further, note that $\\mathbf{K} $ is a matrix, not a vector, so there are $m\n",
    "\\times n$ entries to compute. \n",
    "\n",
    "We can approach this problem the usual way by trying to solve the MMSE\n",
    "problem:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\min_K\\mathbb{E}(\\Vert\\boldsymbol{\\hat{\\beta}}-\\boldsymbol{\\beta} \\Vert^2)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " which we can write out as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\min_K \\mathbb{E}(\\Vert \\boldsymbol{\\hat{\\beta}}-\\boldsymbol{\\beta} \\Vert^2) =  \\min_K\\mathbb{E}(\\Vert \\mathbf{K}\\mathbf{y}- \\boldsymbol{\\beta} \\Vert^2) =  \\min_K\\mathbb{E}(\\Vert \\mathbf{K}\\mathbf{W}\\mathbf{\\boldsymbol{\\beta}}+\\mathbf{K}\\boldsymbol{\\epsilon}- \\boldsymbol{\\beta} \\Vert^2)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " and since $\\boldsymbol{\\epsilon}$ is the only random variable here,\n",
    "this simplifies to"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\min_K \\Vert \\mathbf{K}\\mathbf{W}\\mathbf{\\boldsymbol{\\beta}}-\\boldsymbol{\\beta} \\Vert^2 + \\mathbb{E}(\\Vert\\mathbf{K}\\boldsymbol{\\epsilon} \\Vert^2)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The next step is to compute"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbb{E}(\\Vert\\mathbf{K}\\boldsymbol{\\epsilon} \\Vert^2) = \\mathbb{E}(\\boldsymbol{\\epsilon}^T \\mathbf{K}^T \\mathbf{K}^T \\boldsymbol{\\epsilon})=\\Tr(\\mathbf{K \\mathbb{E}(\\boldsymbol{\\epsilon}\\boldsymbol{\\epsilon}^T) K}^T)=\\Tr(\\mathbf{K Q K}^T)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " using the properties of the trace of  a matrix. We can assemble\n",
    "everything as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\min_K \\Vert \\mathbf{K W} \\boldsymbol{\\beta} -  \\boldsymbol{\\beta}\\Vert^2 + \\Tr(\\mathbf{K Q K}^T)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Now, if we were to solve this for $\\mathbf{K}$, it would be a\n",
    "function of $ \\boldsymbol{\\beta}$, which is the same thing as saying that the\n",
    "estimator, $ \\boldsymbol{\\hat{\\beta}}$, is a function of what we are trying to\n",
    "estimate, $\\boldsymbol{\\beta}$, which makes no sense. However, writing this out\n",
    "tells us that if we had $\\mathbf{K W}= \\mathbf{I}$, then the first term\n",
    "vanishes and the problem simplifies to"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\min_K \\Tr(\\mathbf{K Q K}^T)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " with the contraint,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbf{KW} = \\mathbf{I}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " This requirement is the same as asserting that the estimator is unbiased,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbb{E}(\\boldsymbol{\\hat{\\beta}})=\\mathbf{KW}  \\boldsymbol{\\beta} =  \\boldsymbol{\\beta}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " To line this problem up with our earlier work, let's consider  the\n",
    "$i^{th}$ column of $\\mathbf{K}$, $\\mathbf{k}_i$. Now, we can re-write the\n",
    "problem as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\min_k (\\mathbf{k}_i^T \\mathbf{Q} \\mathbf{k}_i)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " with"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbf{k}_i^T \\mathbf{W} = \\mathbf{e}_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " and from our previous work on contrained optimization, we know the\n",
    "solution to this:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbf{k}_i  = \\mathbf{Q}^{-1} \\mathbf{W}(\\mathbf{W}^T \\mathbf{Q^{-1} W})^{-1}\\mathbf{e}_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Now all we have to do is stack these together for the general solution:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbf{K}  = (\\mathbf{W}^T \\mathbf{Q^{-1} W})^{-1} \\mathbf{W}^T\\mathbf{Q}^{-1}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " It's easy when you have all of the concepts lined up! For completeness, the\n",
    "covariance of the error is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbb{E}(\\hat{\\boldsymbol{\\beta}}-\\boldsymbol{\\beta}) (\\hat{\\boldsymbol{\\beta}}-\\boldsymbol{\\beta})^T = \\mathbb{E}(\\mathbf{K} \\boldsymbol{\\epsilon} \\boldsymbol{\\epsilon}^T \\mathbf{K}^T)=\\mathbf{K}\\mathbf{Q}\\mathbf{K}^T =(\\mathbf{W}^T \\mathbf{Q}^{-1} \\mathbf{W})^{-1}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- # !bc pycod -->\n",
    "<!-- # from mpl_toolkits.mplot3d import proj3d -->\n",
    "<!-- # from numpy.linalg import inv -->\n",
    "<!-- # import matplotlib.pyplot as plt -->\n",
    "<!-- # import numpy as np -->\n",
    "<!-- # from numpy import matrix, linalg, ones, array -->\n",
    "<!-- # Q = np.eye(3)*.1 # error covariance matrix -->\n",
    "<!-- # beta = matrix(ones((2,1))) # this is what we are trying estimate -->\n",
    "<!-- # W = matrix([[1,2], -->\n",
    "<!-- #             [2,3], -->\n",
    "<!-- #             [1,1]]) -->\n",
    "<!-- # ntrials = 50 -->\n",
    "<!-- # epsilon = np.random.multivariate_normal((0,0,0),Q,ntrials).T -->\n",
    "<!-- # y=W*beta+epsilon -->\n",
    "<!-- # -->\n",
    "<!-- # K=inv(W.T*inv(Q)*W)*matrix(W.T)*inv(Q) -->\n",
    "<!-- # b=K*y #estimated beta from data -->\n",
    "<!-- # -->\n",
    "<!-- # fig = plt.figure() -->\n",
    "<!-- # fig.set_size_inches([6,6]) -->\n",
    "<!-- # -->\n",
    "<!-- # # some convenience definitions for plotting -->\n",
    "<!-- # bb = array(b) -->\n",
    "<!-- # bm = bb.mean(1) -->\n",
    "<!-- # yy = array(y) -->\n",
    "<!-- # ax = fig.add_subplot(111, projection='3d') -->\n",
    "<!-- # -->\n",
    "<!-- # ax.plot3D(yy[0,:],yy[1,:],yy[2,:],'mo',label='y',alpha=0.3) -->\n",
    "<!-- # ax.plot3D([beta[0,0],0],[beta[1,0],0],[0,0],'r-',label=r'$\\beta$') -->\n",
    "<!-- # ax.plot3D([bm[0],0],[bm[1],0],[0,0],'g-',lw=1,label=r'$\\widehat{\\beta}_m$') -->\n",
    "<!-- # ax.plot3D(bb[0,:],bb[1,:],0*bb[1,:],'.g',alpha=0.5,lw=3,label=r'$\\hat{\\beta}$') -->\n",
    "<!-- # ax.legend(loc=0,fontsize=18) -->\n",
    "<!-- # plt.show() -->\n",
    "<!-- # !ec -->\n",
    "\n",
    "<!-- dom:FIGURE: [fig-statistics/Gauss_Markov_001.png, width=500 frac=0.85] The red circles show the points to be estimated in the *xy*-plane by the black points. <div id=\"fig:Gauss_Markov_001\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:Gauss_Markov_001\"></div>\n",
    "\n",
    "<p>The red circles show the points to be estimated in the <em>xy</em>-plane by the black points.</p>\n",
    "<img src=\"fig-statistics/Gauss_Markov_001.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "[Figure](#fig:Gauss_Markov_001) shows the simulated $\\mathbf{y}$ data as red\n",
    "circles. The black dots show the corresponding estimates,\n",
    "$\\boldsymbol{\\hat{\\beta}}$ for each sample. The black lines show the true value\n",
    "of $\\boldsymbol{\\beta}$ versus the average of the estimated\n",
    "$\\boldsymbol{\\beta}$-values, $\\widehat{\\boldsymbol{\\beta}_m}$. The matrix\n",
    "$\\mathbf{K}$ maps the red circles in the corresponding dots. Note there are\n",
    "many possible ways to map the red circles to the plane, but the $\\mathbf{K}$ is\n",
    "the one that minimizes the MSE for $\\boldsymbol{\\beta}$. \n",
    "\n",
    "**Programming Tip.**\n",
    "\n",
    "Although the full source code is available in the corresponding\n",
    "IPython Notebook, the following snippets provide a quick walkthrough. \n",
    "To simulate the target data, we define the relevant \n",
    "matrices below,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Q = np.eye(3)*0.1 # error covariance matrix\n",
    "# this is what we are trying estimate\n",
    "beta = matrix(ones((2,1))) \n",
    "W = matrix([[1,2],\n",
    "            [2,3],\n",
    "            [1,1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "  Then, we generate the noise terms and create\n",
    "the simulated data, $y$,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ntrials = 50 \n",
    "epsilon = np.random.multivariate_normal((0,0,0),Q,ntrials).T \n",
    "y=W*beta+epsilon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-statistics/Gauss_Markov_002.png, width=500 frac=0.85] Focusing on the *xy*-plane in [Figure](#fig:Gauss_Markov_001), the dashed line shows the true value for $\\boldsymbol{\\beta}$ versus the mean of the estimated values $\\widehat{\\boldsymbol{\\beta}}_m$. <div id=\"fig:Gauss_Markov_002\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:Gauss_Markov_002\"></div>\n",
    "\n",
    "<p>Focusing on the <em>xy</em>-plane in [Figure](#fig:Gauss_Markov_001), the dashed line shows the true value for $\\boldsymbol{\\beta}$ versus the mean of the estimated values $\\widehat{\\boldsymbol{\\beta}}_m$.</p>\n",
    "<img src=\"fig-statistics/Gauss_Markov_002.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "[Figure](#fig:Gauss_Markov_002) shows more detail in the horizontal *xy*-plane\n",
    "of [Figure](#fig:Gauss_Markov_001).  [Figure](#fig:Gauss_Markov_002) shows\n",
    "the dots, which are individual estimates of $\\boldsymbol{\\hat{\\beta}}$ from the\n",
    "corresponding simulated $\\mathbf{y}$ data. The dashed line is the true value\n",
    "for $\\boldsymbol{\\beta}$ and the filled line ($\\widehat{\\boldsymbol{\\beta}}_m$)\n",
    "is the average of all the dots.  The gray ellipse provides an error ellipse\n",
    "for the covariance of the estimated $\\boldsymbol{\\beta}$ values.  \n",
    "\n",
    "**Programming Tip.**\n",
    "\n",
    "Although the full source code is available in the corresponding\n",
    "IPython Notebook, the following snippets provide a quick walkthrough of\n",
    "the construction of [Figure](#fig:Gauss_Markov_002). To draw\n",
    "the ellipse, we need to import the patch primitive,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# %matplotlib inline\n",
    "\n",
    "# from  matplotlib.patches import Ellipse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " To compute the parameters of the error ellipse based on the\n",
    "covariance matrix of the individual estimates of $\\boldsymbol{\\beta}$\n",
    "in the `bm_cov` variable below,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# U,S,V = linalg.svd(bm_cov) \n",
    "# err = np.sqrt((matrix(bm))*(bm_cov)*(matrix(bm).T))\n",
    "# theta = np.arccos(U[0,1])/np.pi*180"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Then, we draw the add the scaled ellipse\n",
    "in the following,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# ax.add_patch(Ellipse(bm,err*2/np.sqrt(S[0]),\n",
    "#                      err*2/np.sqrt(S[1]),\n",
    "#                      angle=theta,color='gray'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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icSzgeQxu2+boc+r04YfuM8dxiEajiMVimmuwVCohl8tpHoVyuWz7vbAsvi5H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\ntRL/D1bHg/Z/iVzWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb4cc470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UOgokPJPJhNfrxWq1BhOex+PB7/fT1NQkral+SEtLw+fzUV5eTlVVFTNnzmTQ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb5fb780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from mpl_toolkits.mplot3d import proj3d\n",
    "from numpy.linalg import inv\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from numpy import matrix, linalg, ones, array\n",
    "\n",
    "Q = np.eye(3)*.1 # error covariance matrix\n",
    "\n",
    "beta = matrix(ones((2,1))) # this is what we are trying estimate\n",
    "W = matrix([[1,2],\n",
    "            [2,3],\n",
    "            [1,1]])\n",
    "\n",
    "ntrials = 50 \n",
    "epsilon = np.random.multivariate_normal((0,0,0),Q,ntrials).T \n",
    "y=W*beta+epsilon\n",
    "\n",
    "K=inv(W.T*inv(Q)*W)*matrix(W.T)*inv(Q) \n",
    "b=K*y #estimated beta from data\n",
    "\n",
    "fig = plt.figure()\n",
    "fig.set_size_inches([6,6])\n",
    "\n",
    "# some convenience definitions for plotting\n",
    "bb = array(b)\n",
    "bm = bb.mean(1)\n",
    "yy = array(y)\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "ax.plot3D(yy[0,:],yy[1,:],yy[2,:],'ro',label='y',alpha=0.3)\n",
    "ax.plot3D([beta[0,0],0],[beta[1,0],0],[0,0],'k--',label=r'$\\beta$')\n",
    "ax.plot3D([bm[0],0],[bm[1],0],[0,0],'k-',lw=1,label=r'$\\widehat{\\beta}_m$')\n",
    "ax.plot3D(bb[0,:],bb[1,:],0*bb[1,:],'.k',alpha=0.5,lw=3,label=r'$\\widehat{\\beta}$')\n",
    "ax.legend(loc=0,fontsize=18)\n",
    "ax.set_xlabel('$x_1$',fontsize=20)\n",
    "ax.set_ylabel('$x_2$',fontsize=20)\n",
    "ax.set_zlabel('$x_3$',fontsize=20)\n",
    "fig.tight_layout()\n",
    "\n",
    "from  matplotlib.patches import Ellipse\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "fig.set_size_inches((6,6))\n",
    "ax.set_aspect(1)\n",
    "ax.plot(bb[0,:],bb[1,:],'ko',alpha=.3)\n",
    "ax.plot([beta[0,0],0],[beta[1,0],0],'k--',label=r'$\\beta$',lw=3)\n",
    "ax.plot([bm[0],0],[bm[1],0],'k-',lw=3,label=r'$\\widehat{\\beta}_m$')\n",
    "ax.legend(loc=0,fontsize=18)\n",
    "\n",
    "bm_cov = inv(W.T*Q*W)\n",
    "U,S,V = linalg.svd(bm_cov) \n",
    "\n",
    "err = np.sqrt((matrix(bm))*(bm_cov)*(matrix(bm).T))\n",
    "theta = np.arccos(U[0,1])/np.pi*180\n",
    "\n",
    "ax.add_patch(Ellipse(bm,err*2/np.sqrt(S[0]),err*2/np.sqrt(S[1])\n",
    "                       ,angle=theta,color='gray',alpha=0.5))\n",
    "\n",
    "ax.set_xlabel('$x_1$',fontsize=20)\n",
    "ax.set_ylabel('$x_2$',fontsize=20)\n",
    "fig.tight_layout()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- References -->\n",
    "<!-- --------------- -->\n",
    "<!--  -->\n",
    "<!-- * Luenberger, David G. *Optimization by vector space methods*. Wiley-Interscience, 1997. -->"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
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