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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##EE16A: Homework 3\n",
      "This notebook contains the code for Homework problem 3.1 and 3.4"
     ]
    },
    {
     "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": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from scipy import ndimage as nd\n",
      "from scipy import misc\n",
      "from scipy import io"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Problem 3.1 (b)\n",
      "Download the campanile image. Again, make sure to check the dimensions of the image using the shape command"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "campanile = np.load('campanile.npy')\n",
      "plt.imshow(campanile, cmap='gray', interpolation='nearest')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Design the distortion matrix and plot the resultant image."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#D = \n",
      "\n",
      "#blurred_image = \n",
      "\n",
      "\n",
      "figure(figsize=(15,10))\n",
      "subplot(1,2,1)\n",
      "plt.imshow(campanile, cmap='gray', interpolation='nearest')\n",
      "title('Original Image')\n",
      "subplot(1,2,2)\n",
      "plt.imshow(blurred_image, cmap='gray', interpolation='nearest')\n",
      "title('Blurred Image')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Problem 3.1 (d)\n",
      "Download the distortion matrix and blurred image"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "blur_rand = np.load('distortion.npy') #this is the new distortion matrix!\n",
      "blurred = np.load('blurred.npy') #this is the blurred image\n",
      "plt.imshow(blurred, cmap='gray', interpolation='nearest')\n",
      "title('Blurred Image')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Recover the original image"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#original = \n",
      "plt.imshow(original, cmap='gray', interpolation='nearest')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Problem 3.4 (b)\n",
      "Load Pattern Image. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pattern = np.load('pattern.npy')\n",
      "plt.imshow(pattern, cmap='gray', interpolation='nearest')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "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] "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Problem 3.4 (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 might find the command [np.diag](http://docs.scipy.org/doc/numpy/reference/generated/numpy.diag.html) useful\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#pattern_approx_100 = \n",
      "plt.imshow(pattern_approx_100, cmap='gray', vmin=0, vmax=255)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Problem 3.4 (d)\n",
      "Find the pattern approximation using 50 largest eigenvalues/eigenvectors"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#pattern_approx_50 = \n",
      "\n",
      "plt.imshow(pattern_approx_50, cmap='gray', vmin=0, vmax=255)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}