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 "cells": [
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-27T02:43:08.537640Z",
     "start_time": "2019-12-27T02:43:08.533650Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy import *\n",
    "from pylab import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-27T02:43:09.656647Z",
     "start_time": "2019-12-27T02:43:09.640690Z"
    }
   },
   "outputs": [],
   "source": [
    "img = imread(\"images/initial.png\")[:,:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-27T02:43:10.377720Z",
     "start_time": "2019-12-27T02:43:10.337827Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x24a888d7438>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gray()\n",
    "figure(1) # prepare the canvas for figure 1.\n",
    "imshow(img)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-27T02:43:14.446841Z",
     "start_time": "2019-12-27T02:43:14.309209Z"
    }
   },
   "outputs": [],
   "source": [
    "m, n = img.shape\n",
    "U, S, Vt = svd(img)\n",
    "S = resize(S, [m,1]) * eye(m,n) # see below for a demo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-27T02:43:15.148964Z",
     "start_time": "2019-12-27T02:43:15.105081Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x24a865ca898>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = 20\n",
    "figure(2)\n",
    "imshow(dot(U[:,1:k], dot(S[1:k,1:k], Vt[1:k,:])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Demo for multiplying array with \"\\*\" operation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-27T02:42:42.627910Z",
     "start_time": "2019-12-27T02:42:42.623921Z"
    }
   },
   "outputs": [],
   "source": [
    "col_v = resize(asarray([1,2]), [2,1])\n",
    "eye_mat = eye(2,3)\n",
    "result = col_v * eye_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-27T02:42:49.248210Z",
     "start_time": "2019-12-27T02:42:49.244221Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col_v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-27T02:42:52.084627Z",
     "start_time": "2019-12-27T02:42:52.080638Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eye_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-27T02:42:55.141454Z",
     "start_time": "2019-12-27T02:42:55.137465Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 2., 0.]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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