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   "source": [
    "## EE16A: Homework 4\n",
    "This notebook contains the code for Homework 4 problem 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import ndimage as nd\n",
    "from scipy import misc\n",
    "from scipy import io"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 4 (b)\n",
    "Load Pattern Image. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pattern = np.load('pattern.npy')\n",
    "plt.imshow(pattern, cmap='gray', interpolation='nearest')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the command [shape](http://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.shape.html) to find the dimensions of the image. How many eigenvalues do you expect? \n",
    "\n",
    "Run the code below to find the eigenvector and eigenvalues of ``pattern`` and sort them in descending order (first eigenvalue/vector corresponds to the largest eigenvalue)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "eig_vals, eig_vectors = np.linalg.eig(pattern)\n",
    "idx = (eig_vals.argsort())\n",
    "idx = idx[::-1]\n",
    "eig_vals = eig_vals[idx]\n",
    "eig_vectors = eig_vectors[:,idx] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 4 (c)\n",
    "Find the pattern approximation using 100 largest eigenvalues/eigenvectors.\n",
    "\n",
    "* Index into above variables to choose the first 100 eigenvalues and eigenvectors.\n",
    "* You can use the command [np.outer](http://docs.scipy.org/doc/numpy/reference/generated/numpy.outer.html) to find the outer product of two vectors\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rank = 100\n",
    "S = np.zeros(pattern.shape)\n",
    "for i in range(rank):\n",
    "    vec_i = eig_vectors[:,i]  # i-th largest eigenvector\n",
    "    val_i = eig_vals[i]       # i-th largest eigenvalue\n",
    "    S += # Your Code Here\n",
    "    \n",
    "plt.imshow(S, cmap='gray', vmin=0, vmax=255)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 4 (d)\n",
    "Find the pattern approximation using 50 largest eigenvalues/eigenvectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rank = 50\n",
    "S = np.zeros(pattern.shape)\n",
    "for i in range(rank):\n",
    "    vec_i = eig_vectors[:,i]  # i-th largest eigenvector\n",
    "    val_i = eig_vals[i]       # i-th largest eigenvalue\n",
    "    S += # Your Code Here\n",
    "    \n",
    "plt.imshow(S, cmap='gray', vmin=0, vmax=255)"
   ]
  }
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