Gibbs_Sampling_Jupiter_grayvalue.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import all nessesary libarys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "#import cupy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.special\n",
    "from scipy import stats\n",
    "%matplotlib inline\n",
    "from ipywidgets import IntProgress\n",
    "from IPython.display import display\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definitions of all interchangeable variables of the script"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# Definitions\n",
    "\n",
    "# Matrix size\n",
    "\n",
    "matrix_width = 50\n",
    "matrix_height = 50\n",
    "\n",
    "# Grayscale value range\n",
    "\n",
    "gray_value_min = 0\n",
    "gray_value_max = 32\n",
    "\n",
    "\n",
    "# dampening factor\n",
    "\n",
    "beta = 1\n",
    "\n",
    "#itterations\n",
    "\n",
    "itteration = 10\n",
    "\n",
    "# definition Mask\n",
    "\n",
    "mask = np.array([\n",
    "        [-0.81,0,0,0,-0.81],\n",
    "        [0,0.91,0.4,0.91,0],\n",
    "        [0,0.4,0,0.4,0],\n",
    "        [0,0.91,0.4,0.91,0],\n",
    "        [-0.81,0,0,0,-0.81]\n",
    "       ])\n",
    "\n",
    "# definition Energyfunction\n",
    "\n",
    "def energy(func, vst, xs, xt):\n",
    "    #switch (func):\n",
    "        #case orgf:\n",
    "            #return np.sum(vst * (xs - xt))\n",
    "        #case l1:\n",
    "            return np.sum(vst * np.absolute(xs - xt))\n",
    "            #check formula in the book  \n",
    "        #case l2:\n",
    "            #return np.sum(vst * (xs - xt)**2 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "applys the mask to the selected data point of the matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def apply_mask(height,width, matrix, mask):\n",
    "    # create a copy of the matrix in the area of the mask\n",
    "    matrix_slice = matrix.take(range((height - (mask.shape[0]-1)//2),(height + (mask.shape[0]+1)//2)),mode='wrap', axis=0).take(range((width - (mask.shape[1]-1)//2),(width + (mask.shape[1]+1)//2)),mode='wrap',axis=1)\n",
    "    # calculate the probability of a data point to flip\n",
    "    \n",
    "    xk = np.arange(gray_value_max)\n",
    "    pk = []\n",
    "    denominator = 1\n",
    "    for i in xk :\n",
    "        pk.append((scipy.special.binom(gray_value_max, i)* np.exp(-beta*energy('l1', mask, matrix[height][width], matrix_slice))) / denominator )\n",
    "    # würfeln welchen wert der datenpunkt hat (?good englisch expression?)\n",
    "    matrix[height][width] = np.random.choice(a= xk, p= pk/np.sum(pk))\n",
    "    \n",
    "    return matrix\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "generate Matrix of white noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 20 ms, sys: 123 µs, total: 20.2 ms\n",
      "Wall time: 19.4 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[11, 24,  0, ...,  9,  3,  5],\n",
       "       [ 5, 26, 16, ...,  3, 17, 19],\n",
       "       [14, 19, 31, ..., 15, 11,  4],\n",
       "       ...,\n",
       "       [ 7,  1,  9, ...,  5,  9, 20],\n",
       "       [12, 31, 19, ..., 15, 22, 21],\n",
       "       [21, 31, 27, ..., 26,  5, 11]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "# generate Matrix of white noise\n",
    "matrix = np.random.randint(gray_value_min,gray_value_max,size=(matrix_height,matrix_width))\n",
    "# replaces 0 in the matrix with -1s (nessesary for a few masks)\n",
    "# matrix = np.where(matrix == 0, -1, matrix)\n",
    "# Print matrix as Image\n",
    "plt.imshow(matrix,cmap='gray',vmin=gray_value_min, vmax=gray_value_max-1)\n",
    "# Return (and print) matrix\n",
    "matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "apply mask to whole matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "10af404de96c46a19150dd6ccdaf59a8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "IntProgress(value=0, max=10)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 9.62 s, sys: 22.1 ms, total: 9.64 s\n",
      "Wall time: 9.64 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# itterate thrue the whole matrix and appy mask\n",
    "\n",
    "f = IntProgress(min=0, max=itteration) # instantiate the bar\n",
    "display(f) # display the bar\n",
    "counter = 0\n",
    "while counter < itteration:\n",
    "    f.value += 1 # signal to increment the progress bar\n",
    "    counter += 1\n",
    "    for h in range(0, matrix.shape[0]):\n",
    "        for w in range(0, matrix.shape[1]):\n",
    "            matrix = apply_mask(h,w,matrix,mask) #faster with inplace ?\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "plot new matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "is_executing": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7efbf516e320>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(matrix,cmap='gray',vmin=gray_value_min, vmax=gray_value_max-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "safe new matrix to file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "is_executing": true
    }
   },
   "outputs": [],
   "source": [
    "np.save(\"matrix\", matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fragen für Mittwoch:\n",
    "Formel (was liegt mit in der summe? O.o)\n",
    "        e^-2 abhängigkeit zu anz graustufen\n",
    "        mehrere pixel zeitgleich angucken (maske gerade anzahl (8x8 oder so mit 4 mittleren pixeln)\n",
    "        exponenten ersetzen.. wie genau soll ich das umsetzen? O.o\n",
    "        und wo genau brauch ich fakultäten"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}