{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Speeding up OMP\n",
    "\n",
    "This example generates a sparse signal and tries to recover it using the orthogonal matching pursuit algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: Much of the following is copied from last weeks solution notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# imports\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy import misc\n",
    "from IPython import display\n",
    "from simulator import *\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x109064940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the setting\n",
    "\n",
    "# file name for the sparse image\n",
    "fname = 'pika.png'\n",
    "# number of measurements to be taken from the sparse image\n",
    "numMeasurements = 9000\n",
    "# the sparsity of the image\n",
    "sparsity = 800\n",
    "\n",
    "# read the image in black and white\n",
    "I = misc.imread(fname, flatten=1)\n",
    "# normalize the image to be between 0 and 1\n",
    "I = I/np.max(I)\n",
    "\n",
    "# shape of the image\n",
    "imageShape = I.shape\n",
    "# number of pixels in the image\n",
    "numPixels = I.size\n",
    "\n",
    "plt.title('input image')\n",
    "plt.imshow(I, cmap=plt.cm.gray, interpolation='nearest');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# generate your image masks and the underlying measurement matrix\n",
    "Mask, A = randMasks(numMeasurements,numPixels)\n",
    "# vectorize your image\n",
    "full_signal = I.reshape((numPixels,1))\n",
    "# get the measurements\n",
    "measurements = np.dot(Mask,full_signal)\n",
    "# remove the mean from your measurements\n",
    "measurements = measurements - np.mean(measurements)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wdQbffFNrMbsO8k7zObz5+uv43Qk326w2NpOUDTc0H9ejcVGUuRLb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\nAioDQgghAP4/qM1w7p4K4asAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106887978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# measurements\n",
    "plt.title('measurements')\n",
    "plt.plot(measurements)\n",
    "plt.xlabel('measurement index')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# WRITE A FUNCTION THAT RETURNS a MATRIX U WHOSE COLUMNS FORM\n",
    "# AN ORTHONORMAL BASIS FOR THE COLUMNS OF THE MATRIX A\n",
    "def gramschmidt(A):\n",
    "    ### ADD YOU WORK HERE\n",
    "    return U\n",
    "\n",
    "\n",
    "### ANOTHER -- BETTER -- OPTION IS TO WRITE A FUNCTION THAT TAKES IN a MATRIX U0\n",
    "## WITH ORTHONORMAL COLUMNS AND A SINGLE NEW VECTOR v AND ADDS ANOTHER \n",
    "## ORTHONORMAL COLUMN TO U0 CREATING A NEW MATRIX U WHOSE COLUMNS ARE OTHORNORMAL\n",
    "## AND SPAN THE COLUMN SPACE OF [U0,v]\n",
    "## NOTE: USING THIS FUNCTION WILL MAKE YOUR CODE FASTER\n",
    "\n",
    "def gramschmidt_addone(U0,v):\n",
    "    ## ADD YOUR WORK HERE\n",
    "    return U\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# THERE ARE MISSING LINES THAT YOU NEED TO FILL\n",
    "def OMP(imDims, sparsity, measurements, A):\n",
    "    r = measurements.copy()\n",
    "    indices = []\n",
    "    \n",
    "    # threshold to check error. if error is below this value stop\n",
    "    THRESHOLD = 0.1\n",
    "    \n",
    "    # for iterating to recover all signal\n",
    "    i = 0\n",
    "    \n",
    "    ######################################\n",
    "    ### THIS LINE INITIALIZES THE MATRIX U\n",
    "    U = np.zeros([np.size(A,0),0])\n",
    "    ########################################\n",
    "    \n",
    "    while i < sparsity and np.linalg.norm(r) > THRESHOLD: \n",
    "        # calculate the correlations\n",
    "        print('%d - '%i,end=\"\",flush=True)\n",
    "        corrs = A.T.dot(r)\n",
    "\n",
    "        # Choose highest-correlated pixel location and add to collection\n",
    "        # COMPLETE THE LINE BELOW\n",
    "        best_index = np.argmax(np.abs(corrs))\n",
    "        \n",
    "        ###########################\n",
    "        ### MODIFY THIS SECTION ###\n",
    "        ## TO USE GRAM-SCHMIDT  ###\n",
    "        ###########################\n",
    "                \n",
    "        indices.append(best_index)\n",
    "        \n",
    "        # Build the matrix made up of selected indices so far\n",
    "        Atrunc = A[:,indices]\n",
    "        \n",
    "        #############################\n",
    "        ## COMPLETE ONE OF THESE LINES\n",
    "        U = gramschmidt(Atrunc)\n",
    "        ### OR\n",
    "        v = A[:,best_index]\n",
    "        U = gramschmidt_addone(U,v)\n",
    "        ##########################\n",
    "        \n",
    "        # Find orthogonal projection of measurements to subspace\n",
    "        # spanned by recovered codewords\n",
    "        b = measurements\n",
    "        \n",
    "        ###################################\n",
    "        ## REWRITE THESE LINES USING GRAMSCHMIDT TO SPEED UP LEAST SQUARES\n",
    "        #xhat = np.linalg.lstsq(Atrunc, b)[0]  \n",
    "        xhat = np.linalg.inv(np.dot(Atrunc.T,Atrunc)).dot(Atrunc.T).dot(b)\n",
    "        r = b - Atrunc.dot(xhat)\n",
    "        ####################################\n",
    "        \n",
    "        # Find component orthogonal to subspace to use for next measurement\n",
    "        ## CHANGE THIS LINE        \n",
    "\n",
    "        \n",
    "        ###########################\n",
    "        ### ------------------- ###\n",
    "        ###########################\n",
    "        \n",
    "        \n",
    "        # this is for viewing the recovery process\n",
    "        if i%100 == 0 or i == sparsity-1 or np.linalg.norm(r) <= THRESHOLD:\n",
    "            \n",
    "            # RECOVERING xhat for plotting\n",
    "            xhat = np.dot(np.linalg.inv(np.dot(Atrunc.T,Atrunc)),np.dot(Atrunc.T,b-r))\n",
    "            \n",
    "            recovered_signal = np.zeros(numPixels)\n",
    "            for j, x in zip(indices, xhat):\n",
    "                recovered_signal[j] = x\n",
    "            Ihat = recovered_signal.reshape(imDims)\n",
    "            plt.title('estimated image')\n",
    "            plt.imshow(Ihat, cmap=plt.cm.gray, interpolation='nearest') \n",
    "            display.clear_output(wait=True)\n",
    "            display.display(plt.gcf())\n",
    "        \n",
    "        i = i + 1\n",
    "        \n",
    "    display.clear_output(wait=True)\n",
    "\n",
    "    # fill in the recovered signal\n",
    "    recovered_signal = np.zeros(numPixels)\n",
    "    for i, x in zip(indices, xhat):\n",
    "        recovered_signal[i] = x\n",
    "    \n",
    "    return recovered_signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+7WtfAxo5/Tvf+U4A7rvvvvo5qdvsqaeearpOakeARikgDcYp59rQ/LDLlFtXH4xRHlhU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\n0Jtl5v8BkjPI4SUxokkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1091f25f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rec = OMP(imageShape,sparsity,measurements,A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  },
  "name": "_merged"
 },
 "nbformat": 4,
 "nbformat_minor": 0
}