MCMC.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAB2CAYAAADGFVhfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\njH2OmOhjxIgRY5/j/wOVfMJkvJBYpwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20faee7b860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---4 neighbours ---\n",
      "1 iteration:\n",
      "1. done, 2. done, 3. done\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAB2CAYAAADGFVhfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nyz3f3AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20faf3c8048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 iteration:\n",
      "1. done, 2. done, 3. done\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAB2CAYAAADGFVhfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nbx0yAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20faf7fb6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 iteration:\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-2-273b615c3817>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m    179\u001b[0m \u001b[0mdo_plot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mim3\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mprop\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0.1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msize\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m4\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0miterations\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    180\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"10 iteration:\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 181\u001b[1;33m \u001b[0mdo_plot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mim3\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mprop\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0.1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msize\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m4\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0miterations\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    182\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"15 iteration:\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    183\u001b[0m \u001b[0mdo_plot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mim3\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mprop\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0.1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msize\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m4\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0miterations\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m15\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-2-273b615c3817>\u001b[0m in \u001b[0;36mdo_plot\u001b[1;34m(image, prop, size, iterations)\u001b[0m\n\u001b[0;32m    138\u001b[0m     \u001b[0mfig\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    139\u001b[0m     \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mchoice\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mimage\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 140\u001b[1;33m     \u001b[0mmcmc_image\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mMCMC_Gibbs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mimage\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0miteration\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0miterations\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    141\u001b[0m     \u001b[0max1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfig\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0madd_subplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m131\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    142\u001b[0m     \u001b[0max1\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mimshow\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmcmc_image\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcmap\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;34m'gray'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-2-273b615c3817>\u001b[0m in \u001b[0;36mMCMC_Gibbs\u001b[1;34m(y, x, w, iteration, size)\u001b[0m\n\u001b[0;32m     78\u001b[0m                 \u001b[0mdenominator\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdenom_left\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mdenom_right\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     79\u001b[0m                 \u001b[0mp_i\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnominator\u001b[0m \u001b[1;33m/\u001b[0m \u001b[0mdenominator\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 80\u001b[1;33m                 \u001b[0mt\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0muniform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     81\u001b[0m                 \u001b[1;32mif\u001b[0m \u001b[0mp_i\u001b[0m \u001b[1;33m>\u001b[0m \u001b[0mt\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     82\u001b[0m                     \u001b[0mxt\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.misc import imread\n",
    "\n",
    "def add_gaussian_noise(im,prop,varSigma):\n",
    "    N = int(np.round(np.prod(im.shape)*prop))\n",
    "    index = np.unravel_index(np.random.permutation(np.prod(im.shape))[1:N],im.shape)\n",
    "    e = varSigma*np.random.randn(np.prod(im.shape)).reshape(im.shape)\n",
    "    im2 = np.copy(im).astype('float')\n",
    "    im2[index] += e[index]\n",
    "    return im2\n",
    "\n",
    "def add_saltnpeppar_noise(im,prop):\n",
    "    N = int(np.round(np.prod(im.shape)*prop))\n",
    "    index = np.unravel_index(np.random.permutation(np.prod(im.shape))[1:N],im.shape)\n",
    "    im2 = np.copy(im).astype('float')\n",
    "    im2[index] = 1-im2[index]\n",
    "    return im2\n",
    "\n",
    "def neighbours(i,j,M,N,size=4):\n",
    "    if size==4:\n",
    "        if (i==0 and j==0):\n",
    "            n=[(0,1), (1,0)]\n",
    "        elif i==0 and j==N-1:\n",
    "            n=[(0,N-2), (1,N-1)]\n",
    "        elif i==M-1 and j==0:\n",
    "            n=[(M-1,1), (M-2,0)]\n",
    "        elif i==M-1 and j==N-1:\n",
    "            n=[(M-1,N-2), (M-2,N-1)]\n",
    "        elif i==0:\n",
    "            n=[(0,j-1), (0,j+1), (1,j)]\n",
    "        elif i==M-1:\n",
    "            n=[(M-1,j-1), (M-1,j+1), (M-2,j)]\n",
    "        elif j==0:\n",
    "            n=[(i-1,0), (i+1,0), (i,1)]\n",
    "        elif j==N-1:\n",
    "            n=[(i-1,N-1), (i+1,N-1), (i,N-2)]\n",
    "        else:\n",
    "            n=[(i-1,j), (i+1,j), (i,j-1), (i,j+1)]\n",
    "\n",
    "        return n\n",
    "\n",
    "    if(size == 8):\n",
    "        n = []\n",
    "        for x in range (i-1, i+1+1):\n",
    "            for y in range(j-1, j+1+1):\n",
    "                if (x >= 0 and x < M):\n",
    "                    if (y >= 0 and y < N):\n",
    "                        if (y != j or x != i):\n",
    "                            n.append((x,y))\n",
    "        return n\n",
    "\n",
    "def L(x, y):\n",
    "    if y == 0:\n",
    "        y = -1\n",
    "    return x * y\n",
    "\n",
    "def E(w, x, i, j, size = 4):\n",
    "    sum = 0\n",
    "    for neighbour in neighbours(i, j, x.shape[0], x.shape[1], size = size):\n",
    "        sum += w[i][j] * x[i][j] * x[neighbour[0]][neighbour[1]]\n",
    "    return sum\n",
    "\n",
    "def MCMC_Gibbs(y, x, w = np.ones(1), iteration = 1, size = 4):\n",
    "    xt = np.copy(x)\n",
    "    if(w == np.ones(1)):\n",
    "        w = np.ones(x.shape)\n",
    "        \n",
    "    for T in range (0, iteration):\n",
    "        for i in range (xt.shape[0]):\n",
    "            for j in range (xt.shape[1]):\n",
    "                xt[i][j] = 1\n",
    "                nominator = np.exp(L(xt[i][j], y[i][j])) * np.exp(E(w, xt, i, j, size = size))\n",
    "\n",
    "                denom_left = np.exp(L(xt[i][j], y[i][j])) * np.exp(E(w, xt, i, j, size = size))\n",
    "                xt[i][j] = -1\n",
    "                denom_right = np.exp(L(xt[i][j], y[i][j])) * np.exp(E(w, xt, i, j, size = size))\n",
    "                denominator = denom_left + denom_right\n",
    "                p_i = nominator / denominator\n",
    "                t = np.random.uniform(0,1)\n",
    "                if p_i > t:\n",
    "                    xt[i][j] = 1\n",
    "                else:\n",
    "                    xt[i][j] = -1\n",
    "    return(xt)\n",
    "\n",
    "def MCMC_Gibbs_randOrd(y, x, w = np.ones(1), iteration = 1, size = 4):\n",
    "    xt = np.copy(x)\n",
    "    if(w == np.ones(1)):\n",
    "        w = np.ones(x.shape)\n",
    "        \n",
    "    for T in range (0, iteration):\n",
    "        N = int(np.round(np.prod(x.shape)))\n",
    "        index = np.unravel_index(np.random.permutation(np.prod(x.shape))[1:N],x.shape)    \n",
    "        zipindex = list(zip(index[0],index[1]))\n",
    "        for i in range (0, len(zipindex)):\n",
    "            xt[zipindex[i]] = 1\n",
    "            nominator = np.exp(L(xt[zipindex[i]], y[zipindex[i]])) * np.exp(E(w, xt, zipindex[i][0], zipindex[i][1], size = size))\n",
    "\n",
    "            denom_left = np.exp(L(xt[zipindex[i]], y[zipindex[i]])) * np.exp(E(w, xt, zipindex[i][0], zipindex[i][1], size = size))\n",
    "            xt[zipindex[i]] = -1\n",
    "            denom_right = np.exp(L(xt[zipindex[i]], y[zipindex[i]])) * np.exp(E(w, xt, zipindex[i][0], zipindex[i][1], size = size))\n",
    "            denominator = denom_left + denom_right\n",
    "            p_i = nominator / denominator\n",
    "            t = np.random.uniform(0,1)\n",
    "            if p_i > t:\n",
    "                xt[zipindex[i]] = 1\n",
    "            else:\n",
    "                xt[zipindex[i]] = -1\n",
    "    return(xt)\n",
    "\n",
    "def MCMC_Gibbs_randOrdNum(y, x, w = np.ones(1), iteration = 1, size = 4):\n",
    "    xt = np.copy(x)\n",
    "    if(w == np.ones(1)):\n",
    "        w = np.ones(x.shape)\n",
    "        \n",
    "    for T in range (0, iteration):\n",
    "        i = np.random.randint(0, x.shape[0]-1)\n",
    "        j = np.random.randint(0, x.shape[1]-1)\n",
    "        \n",
    "        xt[i][j] = 1\n",
    "        nominator = np.exp(L(xt[i][j], y[i][j])) * np.exp(E(w, xt, i, j, size = size))\n",
    "\n",
    "        denom_left = np.exp(L(xt[i][j], y[i][j])) * np.exp(E(w, xt, i, j, size = size))\n",
    "        xt[i][j] = -1\n",
    "        denom_right = np.exp(L(xt[i][j], y[i][j])) * np.exp(E(w, xt, i, j, size = size))\n",
    "        denominator = denom_left + denom_right\n",
    "        p_i = nominator / denominator\n",
    "        t = np.random.uniform(0,1)\n",
    "        if p_i > t:\n",
    "            xt[i][j] = 1\n",
    "        else:\n",
    "            xt[i][j] = -1\n",
    "    return(xt)\n",
    "\n",
    "\n",
    "def do_plot(image, prop = 0.1, size = 4, iterations = 10):\n",
    "    fig = plt.figure()\n",
    "    x = np.random.choice((-1, 1), image.shape)\n",
    "    mcmc_image = MCMC_Gibbs(image, x, iteration = iterations)\n",
    "    ax1 = fig.add_subplot(131)\n",
    "    ax1.imshow(mcmc_image, cmap = 'gray')\n",
    "    print(\"1. done,\", end=' ')\n",
    "    x = np.random.choice((-1, 1), im2.shape)\n",
    "    mcmc_image_randOrd = MCMC_Gibbs_randOrd(image, x, iteration = iterations)\n",
    "    ax2 = fig.add_subplot(132)\n",
    "    ax2.imshow(mcmc_image_randOrd, cmap = 'gray')\n",
    "    print(\"2. done,\", end =' ')\n",
    "    x = np.random.choice((-1, 1), im2.shape)\n",
    "    mcmc_image_randOrd = MCMC_Gibbs_randOrdNum(image, x, iteration = x.shape[0] * x.shape[1] * iterations)\n",
    "    ax3 = fig.add_subplot(133)\n",
    "    ax3.imshow(mcmc_image_randOrd, cmap = 'gray')\n",
    "    print(\"3. done\")\n",
    "    plt.show()\n",
    "    \n",
    "np.random.seed(42)\n",
    "\n",
    "# proportion of pixels to alter\n",
    "prop = 0.2\n",
    "varSigma = 0.1\n",
    "im = imread('resized_gray_pug.png')\n",
    "im = im/255\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(131)\n",
    "ax.imshow(im,cmap='gray')\n",
    "im2 = add_gaussian_noise(im,prop,varSigma)\n",
    "ax2 = fig.add_subplot(132)\n",
    "ax2.imshow(im2,cmap='gray')\n",
    "im3 = add_saltnpeppar_noise(im,prop)\n",
    "ax3 = fig.add_subplot(133)\n",
    "ax3.imshow(im3,cmap='gray')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "print(\"---4 neighbours ---\")\n",
    "print(\"1 iteration:\")\n",
    "do_plot(im3, prop = 0.1, size = 4, iterations = 1)\n",
    "print(\"2 iteration:\")\n",
    "do_plot(im3, prop = 0.1, size = 4, iterations = 2)\n",
    "print(\"10 iteration:\")\n",
    "do_plot(im3, prop = 0.1, size = 4, iterations = 10)\n",
    "print(\"15 iteration:\")\n",
    "do_plot(im3, prop = 0.1, size = 4, iterations = 15)\n",
    "print(\"20 iteration:\")\n",
    "do_plot(im3, prop = 0.1, size = 4, iterations = 20)\n",
    "print(\"100 iteration:\")\n",
    "do_plot(im3, prop = 0.1, size = 4, iterations = 100)\n"
   ]
  },
  {
   "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}