Deterministic stability.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hopfield model project\n",
    "Artificial Neural Networks (ANN) are computational techniques that aim to realize a very simplified model of the human brain. In this way, ANN try to learn tasks mimicking the behavior of brain. The brain is composed of a large set of elements, specialized cells called neurons. In analogy with the human brain, ANN are computational methods that use a large set of elementary computational: the neurons. Each single neuron is a very simple entity but the power of the brain is given by the fact that neurons are numerous and strongly interconnected between them. The human brain is one of the most computationally efficient device that is why in the late years a lot of effort has been done in order to develop an artificial version of it, as a matter of fact companies like Telsa motors are developing self driving cars which are based on ANN to implement the behavior of the human brain in computer systems. \n",
    "\n",
    "The easiest way to represent a neuron is either (on or off) or spin up/down in physics) with the synapsys either eccitative or inibitive. We can easily map the neural network into a spin system by mapping neurons in spins $\\{s_i\\}_{i=1,\\cdots,N}$ and synapsys into the magnetic coupling $J_{ij}$.\n",
    "By a specific representation of these coupling costant we can define the Hopfield model.\n",
    "\n",
    "## The Hopfield Model\n",
    "The Hopfield model is a fully connected neural network able to recall stored memories starting from a noisy or distorted input. The Hopfield network consists of N neurons connected through symmetric bidirectional links.The neuron interactions are encoded in the connection matrix, a N × N real symmetric matrix without self-interaction terms whose $J_{ij}$ entries define the weight of the connection between neuron i and j. \n",
    "\n",
    "The model respect the following mapping:\n",
    "\n",
    "$$\n",
    "n = \\{0,1\\} \\longrightarrow s = \\{-1,1\\}      \\mbox {     where n  is the binary operator and s the spin}\n",
    "$$\n",
    "                                   \n",
    "\n",
    "The correct transformation of this mapping is:\n",
    "$$\n",
    "\\begin{equation}\n",
    "s = f(n) = \\frac{2n-1}{2}\n",
    "\\end{equation}\n",
    "$$\n",
    "We define the synapses as:\n",
    "$$\n",
    "J_{ij}=\\begin{cases}\n",
    "+1 & \\mbox{ excitatory synapses} \\\\\n",
    "-1 & \\mbox{ inhibitory synapses}\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "A neuron is activated if it receives a sufficient number of active impulsive, and we can compute these impulses as follows:\n",
    "$$\n",
    "\\begin{equation}\n",
    "h_i(t) = \\sum^N_{j=1,j\\neq i} J_{ij}(s_j(t)+1)\n",
    "\\label{eq:h} \n",
    "\\end{equation}\n",
    "$$\n",
    "It is important to notice that $j\\neq i$ since the neuron DOES NOT interacts with itself.\n",
    "To decide if these impulses are sufficient to activate the neuron we apply a non-linear function to the impulses:\n",
    "$$\n",
    "\\begin{equation}\n",
    "s_i(t+1)=sign{\\left(h_i(t)-\\theta_i\\right)}\n",
    "\\end{equation}\n",
    "$$\n",
    "where $\\theta_i$ is the threshold. We choose this threshold in a way that is useful for the calculations:\n",
    "$$\n",
    "\\theta_i = \\sum^N_{j=1,j\\neq i} J_{ij}.\n",
    "$$\n",
    "By applying this threshold we obtain in Equation $\\eqref{eq:upd}$ $\\textbf{update rule}$ that we will use below in the code:\n",
    "$$\n",
    "\\begin{equation}\n",
    "s_i(t+1)=sign{\\left(\\sum^N_{j=1,j\\neq i} J_{ij}s_j(t)\\right)}\n",
    "\\label{eq:upd}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "The $\\textbf{Hopfield model}$ that we will use in the following consists in a specific choice of the synapses (ferromagnetic couplings):\n",
    "$$\n",
    "\\\n",
    "\\begin{equation}\n",
    "\\begin{cases}\n",
    "J_{ii}=0 & \\mbox{ known as Hebb rule} \\\\\n",
    "J_{ij}=\\frac{1}{N}\\sum_{\\mu=1}^{p} \\xi^\\mu_i\\xi^\\mu_j\n",
    "\\end{cases}\n",
    "\\label{eq:hop}\n",
    "\\end{equation}\n",
    "$$\n",
    "where the $\\vec{\\xi^\\mu}$ are $p<<N$ excitatory pattern with $\\xi^\\mu_i=\\{+1,-1\\}$.\n",
    "This choice encode these patterns in the couplings and gives to the system some interesting properties:\n",
    "- if the system start from a configuration equal to a pattern $\\vec{\\xi^\\mu}$ and apply the update rule of Eq $\\eqref{eq:upd}$ it stays in that pattern $\\forall t$.\n",
    "- by solving the system from a statistical mechanics point of view turns out that the system has many minima and this minima are all and only the patterns.\n",
    "\n",
    "The actual resolution of this system is quite long and it is not the aim of this work, but it is instructive to see the proof of the stability of the patterns.\n",
    "$$\n",
    "s(1)=sign{\\left(\\sum^N_{j=1} J_{ij}s_j(0)\\right)}\\overset{s_j(0)=\\xi^\\mu_j}{=}\n",
    "sign{\\left(\\sum^N_{j=1} \\frac{1}{N}\\sum^p_{\\nu=1}\\xi_i^\\nu\\xi_j^\\nu\\xi_j^\\mu\\right)} \n",
    "\\\\=sign{\\left(\\sum^N_{\\nu=1}\\xi_i^\\nu\\frac{1}{N}\\sum^p_{j=1}\\xi_j^\\nu\\xi_j^\\mu \\right)} \n",
    "=sign{\\left(\\sum^N_{\\nu=1}\\xi_i^\\nu(\\delta_{\\mu\\nu}+O(N^{-\\frac{1}{2}}) \\right)}\n",
    "\\simeq sign\\left(\\xi^\\mu_i \\right)=\\xi^\\mu_i\n",
    "$$\n",
    "And so the property enuciated before holds.\n",
    "\n",
    "From now on we will talk about spins and not neurons anymore.\n",
    "\n",
    "This model take into account fully connected system, where each spin is connected to all the others. But what happen if we consider an interaction lenght $R$? It is an interesting question to look at how the results vary with this assumption.\n",
    "\n",
    "It is also really interesting to notice that this type of system does not need training, and so it can be reallly interesting if the results are good."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy as scp\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters\n",
    "L = 10   # Lenght of the edge of the image (change to 11?)\n",
    "N = L**2 # Number of spins \n",
    "p = 10   # Number of patterns\n",
    "MF = 0   # Use or not the Mean Field strategy: if MF=1 uses MF, if MF = 0 only spins at\n",
    "         # a distance R interacts\n",
    "R = 3    # The 3-nearest neighbor interacts\n",
    "np.random.seed(1234) # Seed to make the random process reproducible"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x224295e3940>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPUAAAD4CAYAAAA0L6C7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAAKQElEQVR4nO3dz4vkd53H8edrZww6cUXBuTgTNhHEHwhL7EaiAZHEBXcN5rKHCAp6mcuqURTJ7t8gogcRhqgXgzmMOYgs6sJ62cuQmklAJ60Sopu0idh7WBUvY/DtoVscZ7qnvl1d33z7+57nAwLTNTWVNzX1nM+3vt9vfStVhaQ+/m7qASStl1FLzRi11IxRS80YtdTMyTEeNMktv0t9Y2Nj6hEO5dKlS1OPMLmx/s7Gem6rKvvdnjEOaRk1zO1QYbLv6+OWMtbf2VjP7UFRu/ktNWPUUjNGLTVj1FIzRi01Y9RSM4OiTvLBJD9L8mySR8YeStLqlh6nTnIC+DnwT8A28CTwkap65iZ/Zl4HaUfgcer5uZWOU78beLaqnquqq8DjwIPrHE7S+gyJ+gzwwjU/b+/d9jeSnEuySLJY13CSDm/Iud/7LfE3bKdU1XngPLj5LU1pyEq9Ddxxzc9ngRfHGUfSUQ2J+kngLUnuSnIb8BDw3XHHkrSqpZvfVfVykk8CPwBOAN+oqiujTyZpJX70ciQe0pqfW+mQlqQZMWqpGaOWmjFqqRmjlpoZ5WqiGxsbLBbzOVt0jL2T7k3eNbejAB24UkvNGLXUjFFLzRi11IxRS80YtdSMUUvNGLXUjFFLzRi11IxRS80YtdSMUUvNGLXUjFFLzRi11IxRS80YtdSMUUvNGLXUjFFLzYxyNdGxjPidRGt/TK8mumtOz0OXK5+6UkvNGLXUjFFLzRi11IxRS80YtdSMUUvNLI06yR1JfpRkK8mVJA+/EoNJWs2Qk09eBj5XVZeT/D1wKcl/VdUzI88maQVLV+qqeqmqLu/9+vfAFnBm7MEkreZQ76mT3AncDVzc5/fOJVkkWezs7KxnOkmHNjjqJK8FvgN8pqp+d/3vV9X5qtqsqs3Tp0+vc0ZJhzAo6iSvYjfox6rqiXFHknQUQ/Z+B/g6sFVVXxp/JElHMWSlvhf4GHBfkqf3/vuXkeeStKKlh7Sq6n+A+XwoVrrFeUaZ1IxRS80YtdSMUUvNZKSL7o1yBbcuF4a7lczpwoNzU1X7Prmu1FIzRi01Y9RSM0YtNWPUUjNGLTVj1FIzRi01Y9RSM0YtNWPUUjNGLTVj1FIzRi01Y9RSM0YtNWPUUjNGLTVj1FIzRi01Y9RSM0u/duc4GevKlCNdUXXtj6m/mtOVZV/p14IrtdSMUUvNGLXUjFFLzRi11IxRS80YtdTM4KiTnEjyVJLvjTmQpKM5zEr9MLA11iCS1mNQ1EnOAh8CHh13HElHNXSl/jLwBeBPB90hybkkiySLtUwmaSVLo07yAPCbqrp0s/tV1fmq2qyqzbVNJ+nQhqzU9wIfTvJL4HHgviTfGnUqSSvLYT7tkuT9wOer6oEl95vPR2jwU1pz5Ke0oKr2fWCPU0vNHGqlHvygrtSu1CNzpXallm4ZRi01Y9RSM0YtNWPUUjOzuproWHs8x9g7Oae9s2Maa8+vRxcO5kotNWPUUjNGLTVj1FIzRi01Y9RSM0YtNWPUUjNGLTVj1FIzRi01Y9RSM0YtNWPUUjNGLTVj1FIzRi01Y9RSM0YtNWPUUjNGLTUzytVENzY2WCzm893zXvlz1O97GuVx53QF2Ff6yqeu1FIzRi01Y9RSM0YtNWPUUjNGLTVj1FIzg6JO8vokF5L8NMlWkveMPZik1Qw9+eQrwPer6l+T3AacGnEmSUewNOokrwPeB3wcoKquAlfHHUvSqoZsfr8Z2AG+meSpJI8muf36OyU5l2SRZLGzs7P2QSUNMyTqk8C7gK9V1d3AH4BHrr9TVZ2vqs2q2jx9+vSax5Q01JCot4Htqrq49/MFdiOXdAwtjbqqfg28kOStezfdDzwz6lSSVjZ07/engMf29nw/B3xivJEkHcWgqKvqaWBz5FkkrYFnlEnNGLXUjFFLzRi11IxRS81kjCsoJhnlsoxdrvZ4FHO78umcrlI6p9cBQFXtO7ArtdSMUUvNGLXUjFFLzRi11IxRS80YtdSMUUvNGLXUjFFLzRi11IxRS80YtdSMUUvNGLXUjFFLzRi11IxRS80YtdSMUUvNDP0urWNhbheGG4PPwS6fh4O5UkvNGLXUjFFLzRi11IxRS80YtdSMUUvNDIo6yWeTXEnykyTfTvLqsQeTtJqlUSc5A3wa2KyqdwIngIfGHkzSaoZufp8EXpPkJHAKeHG8kSQdxdKoq+pXwBeB54GXgN9W1Q+vv1+Sc0kWSRbrH1PSUEM2v98APAjcBbwJuD3JR6+/X1Wdr6rNqtpc/5iShhqy+f0B4BdVtVNVfwSeAN477liSVjUk6ueBe5Kcyu5HY+4HtsYdS9KqhrynvghcAC4DP977M+dHnkvSilJV63/QZP0PKulvVNW+Hyr3jDKpGaOWmjFqqRmjlpoxaqmZUa4murGxwWKx/rNFx7qC5EhHANb+mHM0xnM7ljm9vjY3Dz5x05VaasaopWaMWmrGqKVmjFpqxqilZoxaasaopWaMWmrGqKVmjFpqxqilZoxaasaopWaMWmrGqKVmjFpqxqilZoxaasaopWaMWmpmrO/S2gH+d8Bd3wj839oHGM+c5p3TrDCveY/DrP9QVaf3+41Roh4qyWJOX1I/p3nnNCvMa97jPqub31IzRi01M3XUc/vy+jnNO6dZYV7zHutZJ31PLWn9pl6pJa2ZUUvNTBZ1kg8m+VmSZ5M8MtUcyyS5I8mPkmwluZLk4alnGiLJiSRPJfne1LPcTJLXJ7mQ5Kd7z/F7pp7pZpJ8du918JMk307y6qlnut4kUSc5AXwV+GfgHcBHkrxjilkGeBn4XFW9HbgH+LdjPOu1Hga2ph5igK8A36+qtwH/yDGeOckZ4NPAZlW9EzgBPDTtVDeaaqV+N/BsVT1XVVeBx4EHJ5rlpqrqpaq6vPfr37P7ojsz7VQ3l+Qs8CHg0alnuZkkrwPeB3wdoKquVtX/TzvVUieB1yQ5CZwCXpx4nhtMFfUZ4IVrft7mmIcCkORO4G7g4rSTLPVl4AvAn6YeZIk3AzvAN/feKjya5PaphzpIVf0K+CLwPPAS8Nuq+uG0U91oqqizz23H+thaktcC3wE+U1W/m3qegyR5APhNVV2aepYBTgLvAr5WVXcDfwCO8/6VN7C7RXkX8Cbg9iQfnXaqG00V9TZwxzU/n+UYbsb8RZJXsRv0Y1X1xNTzLHEv8OEkv2T3bc19Sb417UgH2ga2q+ovWz4X2I38uPoA8Iuq2qmqPwJPAO+deKYbTBX1k8BbktyV5DZ2dzZ8d6JZbipJ2H3Pt1VVX5p6nmWq6t+r6mxV3cnu8/rfVXXsVhOAqvo18EKSt+7ddD/wzIQjLfM8cE+SU3uvi/s5hjv2Tk7xP62ql5N8EvgBu3sQv1FVV6aYZYB7gY8BP07y9N5t/1FV/znhTJ18Cnhs7x/354BPTDzPgarqYpILwGV2j4o8xTE8ZdTTRKVmPKNMasaopWaMWmrGqKVmjFpqxqilZoxaaubPzqB4tvcxqCMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Patterns\n",
    "def random_patterns(N,p):\n",
    "    xi = np.random.randint(0,2,N*p).reshape(p,N) # Each line is a pattern\n",
    "    xi[xi==0]=-1\n",
    "    return xi\n",
    "\n",
    "xi = random_patterns(N,p)\n",
    "idx = np.random.randint(0,p)\n",
    "plt.imshow(xi[idx].reshape(L,L),cmap='Greys') # This is an example of pattern \n",
    "# -1 = white, +1 = black"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Coupling constant\n",
    "# Row i is the connections of the i-th neuron with the others.\n",
    "# Note that the Hopfield model requires Jii=0\n",
    "# Note that J is a symmetrical matrix (J=J.T)\n",
    "def MF_coupling(xi,N):\n",
    "    J = 1/N * np.array( [ (xi[:,i]*xi[:,j]).sum() for i in range(N) for j in range(N) ] )\n",
    "    J = J.reshape(N,N)        \n",
    "    for i in range(len(J)):\n",
    "        J[i,i] = 0\n",
    "    return J\n",
    "def R_coupling(xi,N,R):\n",
    "    J = MF_coupling(xi,N)\n",
    "    for i in range( J.shape[0] ):\n",
    "        J_temp = J[i].reshape(L,L)\n",
    "        for j in range(L):\n",
    "            y = (i%L -j)**2 # Look at indexes should be ok -1\n",
    "            for k in range(L):\n",
    "                if np.sqrt( (i//L - k)**2 + y ) > R: J_temp[j,k] = 0\n",
    "        J[i] = J_temp.reshape(1,N)\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "if MF: J = MF_coupling(xi,N)\n",
    "else: J = R_coupling(xi,N,R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Update rule\n",
    "# def update(sys):\n",
    "#     N = len(sys)\n",
    "#     for i in range(N):\n",
    "#         temp = 0\n",
    "#         for j in range(N): #Maybe it is possible to set the cycle on J[i][j]!=0 only\n",
    "#             temp +=  J[i][j]*sys[j] \n",
    "#         if temp == 0: temp = 2*np.random.randint(0,2)-1\n",
    "#         sys[i] = np.sign(temp)\n",
    "#     return np.sign(sys)\n",
    "\n",
    "def update(sys1):\n",
    "    sys = deepcopy(sys1)\n",
    "    N = len(sys)\n",
    "    temp = np.zeros(N) \n",
    "    for i in range(N):\n",
    "        for j in range(N): #Maybe it is possible to set the cycle on J[i][j]!=0 only\n",
    "            temp[i] +=  J[i][j]*sys[j]\n",
    "        if temp[i] == 0: temp[i] = 2*np.random.randint(0,2)-1\n",
    "    sys = np.sign(temp)\n",
    "    return np.sign(sys)\n",
    "\n",
    "def deterministic_hopfield(sys, t):\n",
    "    for i in range(t):\n",
    "        sys = update(sys)\n",
    "    return sys\n",
    "\n",
    "def error_im(xi_idx, sys):\n",
    "    wrong_pixels = (np.abs( sys-xi_idx )/2).sum()\n",
    "    return wrong_pixels/len(sys)\n",
    "\n",
    "def assign_pattern(xi,sys):\n",
    "    errors = [ error_im(i,sys) for i in xi ]\n",
    "    correct = np.argmin(errors)\n",
    "    return correct\n",
    "\n",
    "def total_error(xi,t):\n",
    "    errors = []\n",
    "    prediction = []\n",
    "    for mu in range(len(xi)):\n",
    "        sys = deterministic_hopfield(xi[mu],t)\n",
    "        errors.append( error_im(xi[mu],sys) )\n",
    "        if assign_pattern(xi,sys)==mu:\n",
    "            prediction.append( 1 )\n",
    "        else: prediction.append( 0 )\n",
    "    errors = (np.array(errors)).mean()\n",
    "    prediction = np.array(prediction).sum()/len(xi)\n",
    "    return errors, prediction\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.160000\n",
      "The algorithm recognised the pattern 2 and the correct pattern is 2\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# actual algorithm\n",
    "from copy import deepcopy\n",
    "idx = np.random.randint(0,p)\n",
    "sys = deepcopy(xi[idx])\n",
    "\n",
    "sys = deterministic_hopfield(sys,100)\n",
    "wrong_pixels = error_im(xi[idx],sys)\n",
    "assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "fig, ax = plt.subplots(1,2, figsize = (10,6))\n",
    "ax[0].set_title('Pattern')\n",
    "ax[0].imshow(xi[idx].reshape(L,L), cmap='Greys')\n",
    "ax[1].set_title('Finishing configuration')\n",
    "ax[1].imshow(sys.reshape(L,L), cmap='Greys')\n",
    "print('The error of the algorithm is %f' %(wrong_pixels))\n",
    "print('The algorithm recognised the pattern %i and the correct pattern is %i' %(assigned_pattern,idx))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analisys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We now look at the scaling with regards to the parameters\n",
    "L = 16\n",
    "N = L**2\n",
    "\n",
    "P = np.arange(5,N/2,20)\n",
    "scores_16 = [[],[]]\n",
    "errors_16 = [[],[]]\n",
    "\n",
    "for MF in range(2):\n",
    "    for p in P: \n",
    "        p = int(p)\n",
    "        xi = random_patterns(N,p)\n",
    "        if MF: J = MF_coupling(xi,N)\n",
    "        else: J = R_coupling(xi,N,R)\n",
    "        err, pred = total_error(xi,30)    \n",
    "        scores_16[MF].append( pred )\n",
    "        errors_16[MF].append(err)\n",
    "       "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c38195d860>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figp, axp = plt.subplots(1,2, figsize=(14,6))\n",
    "axp[0].set_title('Dependance of the error by number of pattern p')\n",
    "axp[0].set_xlabel('Number of pattern p')\n",
    "axp[0].set_ylabel('Average error along the p patterns')\n",
    "axp[0].plot(P,errors_16[0],  '--bo', label='Error, no MF')\n",
    "axp[0].plot(P,errors_16[1], '--go', label='Error, MF')\n",
    "axp[0].legend()\n",
    "\n",
    "axp[1].set_title('Dependance of the prediction of the correct pattern by number of pattern p')\n",
    "axp[1].set_xlabel('Number of pattern p')\n",
    "axp[1].set_ylabel('Fraction of pattern correctly predicted')\n",
    "axp[1].plot(P,scores_16[0], '--bo', label='Score, no MF')\n",
    "axp[1].plot(P,scores_16[1], '--go', label='Score, MF')\n",
    "axp[1].legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dependance of error with patterns generally follows an increasing tendency at the beginning of the curve, which then flatters, reaching a plateau. The growth is particularly steep in the case of the Non Mean Field model, which reaches it maximum within the first $40$ $p$-patterns. It is instead is less pronounced for the Mean Field theory: here the highest value ($\\approx 0.25$) is reached only after about $70$ patterns. The plateau of the Non Mean Field graph is, on the contrary, very stable, showing almost no oscillation around the value of $0.15$, which is also lower.\n",
    "\n",
    "Concerning the dependence of the prediction of the correct pattern with number of patterns, it can be observed that, in case of Non Mean Field model, the score is always constant whichever the pattern, thus the independence of the error with  number of patterns and the perfect effectivness of the predictions. With the Mean Field model, however, this stability is not preserved: in fact, after passing the first few patterns, the score drops to about $70\\%$, and oscillates around that value.\n",
    "\n",
    "By observing both graphs, it can be stated that there exist an optimal value of $p$ patterns which optimize the performances of the algorithm, which in this case is around $20$ (about $8\\%$ of the system size). In order to check if this tendency is preserved with other sizes of the system, different sizes are studied.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 10\n",
    "N = L**2\n",
    "P_10 = np.arange(5,N/2,5)\n",
    "scores_10 = []\n",
    "errors_10 = []\n",
    "sigma_10 = []\n",
    "\n",
    "MF = 0\n",
    "for pi in P_10: \n",
    "    err = []\n",
    "    pred = []\n",
    "    for n in range(20):\n",
    "        p = int(pi)\n",
    "        xi = random_patterns(N,p)\n",
    "        if MF: J = MF_coupling(xi,N)\n",
    "        else: J = R_coupling(xi,N,R)\n",
    "        e, p = total_error(xi,30)    \n",
    "        err.append(e)\n",
    "        pred.append(p)\n",
    "    pred = np.array(pred)\n",
    "    err = np.array(err)\n",
    "    sigma_10.append( pred.std() )\n",
    "    scores_10.append( pred.mean() )\n",
    "    errors_10.append( err.mean() )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "figp, axp = plt.subplots(1,2, figsize=(14,6))\n",
    "axp[0].set_title('Dependance of the error by number of pattern p')\n",
    "axp[0].set_xlabel('Number of pattern p')\n",
    "axp[0].set_ylabel('Average error along the p patterns')\n",
    "axp[0].plot(P_10,errors_10,  '--co', label='Error, no MF, L =10')\n",
    "axp[0].plot(P,errors_16[0],  '--bo', label='Error, no MF, L =16')\n",
    "axp[0].legend() \n",
    "\n",
    "axp[1].set_title('Dependance of the prediction of the correct pattern by number of pattern p')\n",
    "axp[1].set_xlabel('Number of pattern p')\n",
    "axp[1].set_ylabel('Fraction of pattern correctly predicted')\n",
    "axp[1].plot(P_10,scores_10, '--co', label='Score, no MF, L =10')\n",
    "axp[1].plot(P,scores_16[0],  '--bo', label='Score, no MF, L =16')\n",
    "axp[1].legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 6\n",
    "N = L**2\n",
    "P_6 = np.arange(2,N/2,1)\n",
    "scores_6 = []\n",
    "errors_6 = []\n",
    "sigma_6 = []\n",
    "\n",
    "MF = 0\n",
    "\n",
    "for pi in P_6: \n",
    "    err = []\n",
    "    pred = []\n",
    "    for n in range(50):\n",
    "        p = int(pi)\n",
    "        xi = random_patterns(N,p)\n",
    "        if MF: J = MF_coupling(xi,N)\n",
    "        else: J = R_coupling(xi,N,R)\n",
    "        e, p = total_error(xi,30)    \n",
    "        err.append(e)\n",
    "        pred.append(p)\n",
    "    pred = np.array(pred)\n",
    "    err = np.array(err)\n",
    "    sigma_6.append( pred.std() )\n",
    "    scores_6.append( pred.mean() )\n",
    "    errors_6.append( err.mean() )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 8\n",
    "N = L**2\n",
    "P_8 = np.arange(2,N/2,2)\n",
    "scores_8 = []\n",
    "errors_8 = []\n",
    "sigma_8 = []\n",
    "\n",
    "MF = 0\n",
    "\n",
    "for pi in P_8: \n",
    "    err = []\n",
    "    pred = []\n",
    "    for n in range(40):\n",
    "        p = int(pi)\n",
    "        xi = random_patterns(N,p)\n",
    "        if MF: J = MF_coupling(xi,N)\n",
    "        else: J = R_coupling(xi,N,R)\n",
    "        e, p = total_error(xi,30)    \n",
    "        err.append(e)\n",
    "        pred.append(p)\n",
    "    pred = np.array(pred)\n",
    "    err = np.array(err)\n",
    "    sigma_8.append( pred.std() )\n",
    "    scores_8.append( pred.mean() )\n",
    "    errors_8.append( err.mean() )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x210982777b8>"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figp, axp = plt.subplots(1,2, figsize=(14,6))\n",
    "axp[0].set_title('Dependance of the error by number of pattern p')\n",
    "axp[0].set_xlabel('Number of pattern p')\n",
    "axp[0].set_ylabel('Average error along the p patterns')\n",
    "axp[0].plot(P_6,errors_6, '--co', label='Error, no MF, L = 6')\n",
    "axp[0].plot(P_8,errors_8, '--ro', label='Error, no MF, L = 8')\n",
    "axp[0].plot(P_10,errors_10, '--ko', label='Error, no MF, L = 10')\n",
    "axp[0].legend() \n",
    "\n",
    "axp[1].set_title('Dependance of the prediction of the correct pattern by number of pattern p')\n",
    "axp[1].set_xlabel('Number of pattern p')\n",
    "axp[1].set_ylabel('Fraction of pattern correctly predicted')\n",
    "axp[1].plot(P_6, scores_6, '--co', label='Score, no MF, L = 6')\n",
    "axp[1].plot(P_8, scores_8, '--ro', label='Score, no MF, L = 8')\n",
    "axp[1].plot(P_10, scores_10, '--ko', label='Score, no MF, L = 10')\n",
    "axp[1].legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comment these results\n",
    "- optimal number of patterns <20, so % of system\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# How does the time scales with the number of spins N?\n",
    "import time as time\n",
    "L = np.arange(10,28,4)\n",
    "N = L**2 \n",
    "p = 10\n",
    "times = [[],[]]\n",
    "\n",
    "for MF in range(2):\n",
    "    for n in N:\n",
    "        xi = np.random.randint(0,2,n*p).reshape(p,n)\n",
    "        xi[xi==0]=-1\n",
    "        J = 1/n * np.array( [ (xi[:,i]*xi[:,j]).sum() for i in range(n) for j in range(n) ] )\n",
    "        J = J.reshape(n,n)\n",
    "        for k in range(len(J)):\n",
    "            J[k,k] = 0\n",
    "        idx = np.random.randint(0,p)\n",
    "        start = time.time()\n",
    "        deterministic_hopfield(xi[idx],30)\n",
    "        end = time.time()\n",
    "        times[MF].append(end-start)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c38215b0f0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (8, 8))\n",
    "ax.plot(N,times[0], '--bo', label = 'Data with 10 patterns, no MF')\n",
    "ax.plot(N,times[1], '--go', label = 'Data with 10 patterns, MF')\n",
    "ax.set(xlabel = ' Number of spins N', ylabel =' Implementation time [s]', \n",
    "              title = '  Dependency of the time implementation on the size of the system')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two curves above show both an exponential growth of the implementation time as a function of the size of the system. The tendency does not change for both Mean Field and Non Mean Field models: this is consistent with the fact that the two algorithms are implemented with the same logic, just by changing the couplong rule.\n",
    "\n",
    "\n",
    "The variation of implementation time with the number of spins follows a linear form with different slopes. Implementation time increases as the number of spins increases, for N in (500, 700), the implementation time increases slowly meaning that more time is required when a number of spins are used. In general the implementation time grows exponentially with number of spins.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# How does the time scales with the number of pattern p with a fixed N?\n",
    "\n",
    "L = 16\n",
    "N = L**2 \n",
    "P = np.arange(10,N,16)\n",
    "times = [[],[]]\n",
    "\n",
    "for MF in range(2):\n",
    "    for p in P:\n",
    "        p = int(p)\n",
    "        xi = np.random.randint(0,2,N*p).reshape(p,N)\n",
    "        xi[xi==0]=-1\n",
    "        J = 1/N * np.array( [ (xi[:,i]*xi[:,j]).sum() for i in range(N) for j in range(N) ] )\n",
    "        J = J.reshape(N,N)\n",
    "        for k in range(len(J)):\n",
    "            J[k,k] = 0\n",
    "        idx = np.random.randint(0,p)\n",
    "        start = time.time()\n",
    "        deterministic_hopfield(xi[idx],30)\n",
    "        end = time.time()\n",
    "        times[MF].append(end-start)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c3821d1128>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (8, 8))\n",
    "ax.plot(P,times[0], '--bo', label = 'Data with 16x16 spins, no MF')\n",
    "ax.plot(P,times[1], '--go', label = 'Data with 16x16 spins, MF')\n",
    "ax.set(xlabel = 'Number of patterns p', ylabel =' Implementation time [s]', \n",
    "              title = ' Dependency of the time implementation on the number of patterns')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this graph the implementation time ad a function of the number of patterns is displayed. The shape of the curve does not outline any particular tendency, and oscillates randomly showing instability.\n",
    "The Mean Field model has less pronounced fluctuations with respect to the Non Mean Field one.\n",
    "\n",
    "It can be concluded that the Non Mean Field model is more stable and leads to smaller errors, but is less computationally efficient with respect to the Mean Field one, which is unstable given the considerations stated in the cells above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "MF = 0\n",
    "L = 10\n",
    "N = L**2 \n",
    "P = 10\n",
    "error_R = [[],[]]\n",
    "sigmas_R = [[],[]]\n",
    "R = np.arange(3,L)\n",
    "\n",
    "for MF in range(2):\n",
    "    for r in R: \n",
    "        supp = []\n",
    "        for n in range(50):\n",
    "            xi = random_patterns(N,P)\n",
    "            if MF: J = MF_coupling(xi,N)\n",
    "            else: J = R_coupling(xi,N,r)\n",
    "            err, pred = total_error(xi,30)    \n",
    "            supp.append(err)\n",
    "        supp = np.array(supp)\n",
    "        error_R[MF].append(supp.mean())\n",
    "        sigmas_R[MF].append(supp.std())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x21096f8a390>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (8,8))\n",
    "ax.plot(R,error_R[0], '--bo', label = 'no MF')\n",
    "ax.errorbar(R,error_R[0], yerr=sigmas_R[0], fmt='none', color='b')\n",
    "ax.plot(R,error_R[1], '--go', label = 'MF')\n",
    "ax.errorbar(R,error_R[1], yerr=sigmas_R[1], fmt='none', color='g')\n",
    "\n",
    "ax.set(xlabel = 'Number of neighbors R', ylabel =' Error ', \n",
    "              title = ' Dependency of the error on the number of neighbors')\n",
    "ax.legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distinguish criteria of similar patterns\n",
    "\n",
    "The aim of this section is to define in a more rigorous way when two patterns are considered $\\textit{similar}$ and when they are easily distinguishable by the MF and NMF models.\n",
    "\n",
    "In order to do so, we define a new error function which weights the different pixels between two patterns with respect to their distance: so we will consider bigger the error if wrong pixels are close to each other. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "L=10\n",
    "N=L**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def w_error(sys11, sys22, alpha): \n",
    "    sys1 = deepcopy(sys11)\n",
    "    sys2 = deepcopy(sys22)\n",
    "    N = sys1.shape[0]\n",
    "    L = int(np.sqrt(N))\n",
    "    sys1 = sys1.reshape(L,L)\n",
    "    sys2 = sys2.reshape(L,L)\n",
    "    wrong1 = [] #wrong black pixels in sys1\n",
    "    wrong2 = [] # in sys2\n",
    "    min_dist = [] \n",
    "    for i in range(L):\n",
    "        for j in range(L):\n",
    "            if sys1[i][j] == sys2[i][j]: continue\n",
    "            elif sys1[i][j]== 1 : # if black in sys1\n",
    "                wrong1.append( np.array([i,j]) )\n",
    "            elif sys2[i][j]== 1: # if black in sys2\n",
    "                wrong2.append( np.array([i,j]) )\n",
    "    # compute distances between wrong pixels of the two systems\n",
    "    for i in wrong1:\n",
    "        distances = []\n",
    "        for j in wrong2:\n",
    "            if np.linalg.norm(i-j) !=0 :\n",
    "                distances.append( np.linalg.norm(i-j) )\n",
    "        min_dist.append( np.array(distances).min() )\n",
    "    min_dist = np.array(min_dist)\n",
    "    err =  (1/(min_dist)**alpha).sum()\n",
    "    err = err/((N+1)//2) #normalization due to worst case scenario (a chessboard with more black cells)\n",
    "    return err\n",
    "                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot(x, y):\n",
    "    L = int(np.sqrt(x.shape[0]))\n",
    "    fig, ax = plt.subplots(1,2, figsize=(10,6))\n",
    "    ax[0].set_title('Original pattern')\n",
    "    ax[0].imshow(x.reshape(L,L),cmap='Greys')\n",
    "    ax[1].set_title('Corrupted pattern')\n",
    "    ax[1].imshow(y.reshape(L,L),cmap='Greys')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1584x720 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "# straight verical lines patterns\n",
    "\n",
    "patt = [np.zeros(N)-1 for j in range(L)]\n",
    "for i in range(L):\n",
    "    for j in range(L):\n",
    "        patt[i][i+L*j]=1\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(2, int(len(patt)/2), figsize=(22,10))\n",
    "err_patt = []\n",
    "\n",
    "for i in range(int(len(patt)/2)):\n",
    "    ax[0][i].set_title('Pattern %i' %(i+1))\n",
    "    ax[0][i].imshow(patt[i].reshape(L,L),cmap='Greys')\n",
    "    ax[1][i].set_title('Pattern %i' %(i+int(len(patt)/2)+1))\n",
    "    ax[1][i].imshow(patt[i+int(len(patt)/2)].reshape(L,L),cmap='Greys')\n",
    "plt.show()\n",
    "    \n",
    "for i in patt:    \n",
    "    err_patt.append(w_error(patt[0],i,2))\n",
    "\n",
    "figure = plt.figure(figsize=(6,4))\n",
    "plt.grid('-.', alpha=0.5)\n",
    "plt.scatter(np.arange(1, len(err_patt)+1), err_patt, marker='X', color='darkred')\n",
    "plt.title(\"Error with respect to pattern 1\")\n",
    "plt.xlabel(\"Pattern number\")\n",
    "plt.ylabel(\"Error\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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JMmA7YF27kiQ1ZC9Li2zBoK2qm4CTgRuA9cBtVXXR7HFJjk6yKsmq6enp8VcqabPYy1I/Rpk63gU4DNgbWAFsn+SI2eOq6tSqmqqqqeXLl4+/UkmbxV6W+jHK1PGzgO9V1XRV/RI4D3hq27IkNWAvSz0YJWhvAJ6SZLskAQ4C1rQtS1ID9rLUg1GO0V4KnAtcBnyju82pjeuSNGb2stSPZaMMqqoTgRMb1yKpMXtZWnx+MpQkSQ0ZtJIkNWTQSpLUkEErSVJDBq0kSQ0ZtJIkNWTQSpLUkEErSVJDBq0kSQ0ZtJIkNWTQSpLUkEErSVJDBq0kSQ0ZtJIkNWTQSpLUkEErSVJDBq0kSQ0ZtJIkNWTQSpLUkEErSVJDBq0kSQ0ZtJIkNWTQSpLUkEErSVJDBq0kSQ2lqsa/0mQauH6EobsCt4y9gPGZ9Ppg8muc9Pqgvxr3qqrlPdzvyLagXobJr3HS6wNrnM9G+7lJ0I4qyaqqmuqtgAVMen0w+TVOen2wNGqcdEvhOZz0Gie9PrDG+8qpY0mSGjJoJUlqqO+gPbXn+1/IpNcHk1/jpNcHS6PGSbcUnsNJr3HS6wNrvE96PUYrSdKWru89WkmStmi9BG2Sg5N8O8nVSd7cRw3zSbJnki8lWZPkyiTH9V3TXJJsneTyJJ/pu5a5JNk5yblJruqey/37rmm2JG/o/sbfTHJ2km37rmmpmeR+Xiq9DPbz5prkXl70oE2yNfAB4BBgX+DFSfZd7DoWcDfwxqp6LPAU4LUTWCPAccCavouYx3uBz1fVY4DHM2G1JtkdOBaYqqrHAVsDh/db1dKyBPp5qfQy2M/32aT3ch97tE8Grq6qa6vqLuAc4LAe6tioqlpfVZd1v9/O4AW1e79VbSjJHsBzgdP6rmUuSXYCngGcDlBVd1XVj/utak7LgAckWQZsB6zruZ6lZqL7eSn0MtjPYzKxvdxH0O4O3Dh0eS0T+MKfkWQlsB9wab+V3Mt7gOOBe/ouZCMeDkwDH+6mw05Lsn3fRQ2rqpuAk4EbgPXAbVV1Ub9VLTlLpp8nuJfBft4sk97LfQRt5lg2kac+J9kB+BTw+qr6Sd/1zEjyPODmqlrddy3zWAY8AfhgVe0H3AlM2vG7XRjsfe0NrAC2T3JEv1UtOUuinye1l8F+HodJ7+U+gnYtsOfQ5T2YoF38GUnux6Axz6qq8/quZ5YDgEOTXMdgqu7AJGf2W9K9rAXWVtXM3sO5DBp1kjwL+F5VTVfVL4HzgKf2XNNSM/H9POG9DPbzOEx0L/cRtF8DHpVk7yTbMDhgfX4PdWxUkjA4FrGmqt7ddz2zVdVbqmqPqlrJ4Pn7YlVNzLs3gKr6PnBjkn26RQcB3+qxpLncADwlyXbd3/wgJugEjyViovt50nsZ7OcxmeheXrbYd1hVdyd5HXAhgzPDzqiqKxe7jgUcALwM+EaSK7plb62qC3qsaSk6Bjir2wBfCxzVcz0bqKpLk5wLXMbg7NTLmcBPlZlkS6Cf7eXxmdh+nvRe9pOhJElqyE+GkiSpIYNWkqSGDFpJkhoyaCVJasiglSSpIYNWkqSGDFpJkhoyaCVJauh/AWFgrh2pWbagAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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vyTJgO2Bdu5IkNWQvS4tswaCtquuAE4BrgPXALVX15dnjkhyVZFWSVdPT0+OvVNIWsZelfowydbwLcBiwN7AC2D7JS2aPq6oTq2qqqqaWL18+/kolbRF7WerHKFPHzwCurKrpqvoVcBbw5LZlSWrAXpZ6MErQXgM8Kcl2SQIcBKxpW5akBuxlqQejHKO9ADgTuBD4TnebExvXJWnM7GWpH8tGGVRVbwPe1rgWSY3Zy9Li85OhJElqyKCVJKkhg1aSpIYMWkmSGjJoJUlqyKCVJKkhg1aSpIYMWkmSGjJoJUlqyKCVJKkhg1aSpIYMWkmSGjJoJUlqyKCVJKkhg1aSpIYMWkmSGjJoJUlqyKCVJKkhg1aSpIYMWkmSGjJoJUlqyKCVJKkhg1aSpIYMWkmSGjJoJUlqKFU1/pUm08DVIwzdFbhx7AWMz6TXB5Nf46TXB/3VuFdVLe/hfkd2D+plmPwaJ70+sMb5bLSfmwTtqJKsqqqp3gpYwKTXB5Nf46TXB0ujxkm3FJ7DSa9x0usDa9xcTh1LktSQQStJUkN9B+2JPd//Qia9Ppj8Gie9PlgaNU66pfAcTnqNk14fWONm6fUYrSRJ93R979FKknSP1kvQJjk4yfeTXJbkTX3UMJ8keyb5WpI1SS5JcmzfNc0lydZJLkry+b5rmUuSnZOcmeTS7rncv++aZkvy+u5v/N0kpyfZtu+alppJ7uel0stgP2+pSe7lRQ/aJFsDHwYOAfYFXphk38WuYwF3AsdV1aOBJwGvmcAaAY4F1vRdxDw+AHypqh4FPJYJqzXJ7sAxwFRVPQbYGji836qWliXQz0ull8F+3myT3st97NE+Ebisqq6oqjuAM4DDeqhjo6pqfVVd2P1+K4MX1O79VrWhJHsAzwZO6ruWuSTZCXgacDJAVd1RVTf3W9WclgH3S7IM2A5Y13M9S81E9/NS6GWwn8dkYnu5j6DdHbh26PJaJvCFPyPJSmA/4IJ+K7mb9wNvAO7qu5CNeCgwDXysmw47Kcn2fRc1rKquA04ArgHWA7dU1Zf7rWrJWTL9PMG9DPbzFpn0Xu4jaDPHsok89TnJDsBngddV1U/7rmdGkucAN1TV6r5rmccy4HHAR6pqP+B2YNKO3+3CYO9rb2AFsH2Sl/Rb1ZKzJPp5UnsZ7OdxmPRe7iNo1wJ7Dl3egwnaxZ+R5D4MGvO0qjqr73pmOQA4NMlVDKbqDkxyar8l3c1aYG1Vzew9nMmgUSfJM4Arq2q6qn4FnAU8ueealpqJ7+cJ72Wwn8dhonu5j6D9FvCIJHsn2YbBAeuze6hjo5KEwbGINVX13r7rma2q3lxVe1TVSgbP31eramLevQFU1fXAtUn26RYdBHyvx5Lmcg3wpCTbdX/zg5igEzyWiInu50nvZbCfx2Sie3nZYt9hVd2Z5LXAuQzODDulqi5Z7DoWcADwUuA7SS7ulr2lqs7psaal6GjgtG4DfAVwZM/1bKCqLkhyJnAhg7NTL2ICP1Vmki2BfraXx2di+3nSe9lPhpIkqSE/GUqSpIYMWkmSGjJoJUlqyKCVJKkhg1aSpIYMWkmSGjJoJUlqyKCVJKmh/wP3HK4d6WPfGAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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Bje1KktSQvSwtsUWDtqquA94KXANsAm6uqs/PHZfkuCRrk6ydmZkZf6WStou9LPVjlKnjPYGjgQOAVcAuSZ49d1xVnVxV01U1PTU1Nf5KJW0Xe1nqxyhTx48HvltVM1X1C+Bs4JFty5LUgL0s9WCUoL0GeESSnZMEOBxY37YsSQ3Yy1IPRjlGewFwFnAh8I3uNic3rkvSmNnLUj9WjjKoqk4ETmxci6TG7GVp6fnJUJIkNWTQSpLUkEErSVJDBq0kSQ0ZtJIkNWTQSpLUkEErSVJDBq0kSQ0ZtJIkNWTQSpLUkEErSVJDBq0kSQ0ZtJIkNWTQSpLUkEErSVJDBq0kSQ0ZtJIkNWTQSpLUkEErSVJDBq0kSQ0ZtJIkNWTQSpLUkEErSVJDBq0kSQ0ZtJIkNZSqGv9Kkxng6hGG7gXcMPYCxmfS64PJr3HS64P+aty/qqZ6uN+R3Yl6GSa/xkmvD6xxIVvt5yZBO6oka6tqurcCFjHp9cHk1zjp9cHyqHHSLYfncNJrnPT6wBrvKKeOJUlqyKCVJKmhvoP25J7vfzGTXh9Mfo2TXh8sjxon3XJ4Die9xkmvD6zxDun1GK0kSXd2fe/RSpJ0p9ZL0CY5Ism3klye5LV91LCQJPsm+VKS9UkuSfKKvmuaT5IVSS5K8qm+a5lPkj2SnJXksu65PLTvmuZK8qrub/zNJGck2anvmpabSe7n5dLLYD9vr0nu5SUP2iQrgPcCRwIHAc9IctBS17GIzcCrq+pBwCOAl0xgjQCvANb3XcQC3gV8tqoeCDyECas1yWrg5cB0VT0YWAEc029Vy8sy6Ofl0stgP99hk97LfezRPhy4vKqurKrbgDOBo3uoY6uqalNVXdj9fguDF9TqfqvaUpJ9gCcBp/Rdy3yS7A48FjgVoKpuq6qb+q1qXiuBuyVZCewMbOy5nuVmovt5OfQy2M9jMrG93EfQrgauHbq8gQl84c9KsgY4GLig30pu553A8cCv+i5kK+4DzAAf7KbDTkmyS99FDauq64C3AtcAm4Cbq+rz/Va17Cybfp7gXgb7ebtMei/3EbSZZ9lEnvqcZFfgE8Arq+pHfdczK8mTgeural3ftSxgJXAI8L6qOhi4FZi043d7Mtj7OgBYBeyS5Nn9VrXsLIt+ntReBvt5HCa9l/sI2g3AvkOX92GCdvFnJbkLg8Y8varO7rueOR4FHJXkKgZTdYclOa3fkm5nA7Chqmb3Hs5i0KiT5PHAd6tqpqp+AZwNPLLnmpabie/nCe9lsJ/HYaJ7uY+g/Rpw/yQHJNmRwQHrc3qoY6uShMGxiPVV9fa+65mrql5XVftU1RoGz98Xq2pi3r0BVNX3gGuTHNgtOhy4tMeS5nMN8IgkO3d/88OZoBM8lomJ7udJ72Wwn8dkont55VLfYVVtTvJS4HMMzgz7QFVdstR1LOJRwHOAbyS5uFv2+qo6t8ealqOXAad3G+ArgWN7rmcLVXVBkrOACxmcnXoRE/ipMpNsGfSzvTw+E9vPk97LfjKUJEkN+clQkiQ1ZNBKktSQQStJUkMGrSRJDRm0kiQ1ZNBKktSQQStJUkMGrSRJDf0fRt2uHYpyA4IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 4\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 4\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 5\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 5\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 6\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 6\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 7\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 7\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 8\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 8\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 9\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 9\n"
     ]
    }
   ],
   "source": [
    "# we try our algorithm to see if the patterns are distinguishable.\n",
    "\n",
    "patt = np.array(patt)\n",
    "ind = np.arange(len(patt))\n",
    "\n",
    "for idx in ind: \n",
    "    for MF in range(2):\n",
    "        if MF: J = MF_coupling(patt,N)\n",
    "        else: J = R_coupling(patt,N,R)\n",
    "\n",
    "        sys = deepcopy(patt[idx])\n",
    "\n",
    "        sys = deterministic_hopfield(sys,100)\n",
    "        wrong_pixels = error_im(patt[idx],sys)\n",
    "        assigned_pattern = assign_pattern(patt,sys)\n",
    "\n",
    "        fig, ax = plt.subplots(1,2, figsize = (8,5))\n",
    "        ax[0].set_title('Pattern')\n",
    "        ax[0].imshow(patt[idx].reshape(L,L), cmap='Greys')\n",
    "        ax[1].set_title('Finishing configuration')\n",
    "        ax[1].imshow(sys.reshape(L,L), cmap='Greys')\n",
    "        plt.show()\n",
    "        print('The error of the algorithm is %f' %(wrong_pixels))\n",
    "        print('The algorithm recognised the pattern %i and the correct pattern is %i' %(assigned_pattern,idx))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063]\n",
      " [0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063]\n",
      " [0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063]\n",
      " [0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063]\n",
      " [0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063]\n",
      " [0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063]\n",
      " [0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063]\n",
      " [0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063]\n",
      " [0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063]\n",
      " [0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063]]\n"
     ]
    }
   ],
   "source": [
    "print(J.mean(axis=0).reshape(L,L))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error between the two patterns:  1.0\n"
     ]
    }
   ],
   "source": [
    "# chessboard\n",
    "chess = [np.zeros(N)-1 for j in range(2)]\n",
    "c = np.array([np.zeros((L,L))-1 for j in range(2)])\n",
    "\n",
    "for i in range(2):\n",
    "    if i == 0:\n",
    "        c[i][::2, ::2] = 1\n",
    "        c[i][1::2, 1::2] = 1\n",
    "    else:\n",
    "        c[i][1::2, ::2] = 1\n",
    "        c[i][::2, 1::2] = 1\n",
    "    chess[i] = c[i].reshape(1,N)[0]\n",
    "\n",
    "err_chess = []   \n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(16,6))\n",
    "\n",
    "ax[0].set_title('Pattern 1')\n",
    "ax[0].imshow(chess[0].reshape(L,L),cmap='Greys')\n",
    "ax[1].set_title('Pattern 2')\n",
    "ax[1].imshow(chess[1].reshape(L,L),cmap='Greys')\n",
    "plt.show()    \n",
    "    \n",
    "for i in chess:    \n",
    "    err_chess.append(w_error(chess[0],i,2))\n",
    "\n",
    "print(\"Error between the two patterns: \", err_chess[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.000000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.000000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.000000\n",
      "The algorithm recognised the pattern 1 and the correct pattern is 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.000000\n",
      "The algorithm recognised the pattern 1 and the correct pattern is 1\n"
     ]
    }
   ],
   "source": [
    "# we try our algorithm to see if the two chessboards are distinguishable.\n",
    "\n",
    "chess = np.array(chess)\n",
    "ind = [0,1]\n",
    "\n",
    "for idx in ind: \n",
    "    for MF in range(2):\n",
    "        if MF: J = MF_coupling(chess,N)\n",
    "        else: J = R_coupling(chess,N,R)\n",
    "\n",
    "        sys = deepcopy(chess[idx])\n",
    "\n",
    "        sys = deterministic_hopfield(sys,100)\n",
    "        wrong_pixels = error_im(chess[idx],sys)\n",
    "        assigned_pattern = assign_pattern(chess,sys)\n",
    "\n",
    "        fig, ax = plt.subplots(1,2, figsize = (8,5))\n",
    "        ax[0].set_title('Pattern')\n",
    "        ax[0].imshow(chess[idx].reshape(L,L), cmap='Greys')\n",
    "        ax[1].set_title('Finishing configuration')\n",
    "        ax[1].imshow(sys.reshape(L,L), cmap='Greys')\n",
    "        plt.show()\n",
    "        print('The error of the algorithm is %f' %(wrong_pixels))\n",
    "        print('The algorithm recognised the pattern %i and the correct pattern is %i' %(assigned_pattern,idx))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002\n",
      " -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002\n",
      " -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002\n",
      " -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002\n",
      " -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002\n",
      " -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002\n",
      " -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002\n",
      " -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002\n",
      " -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002\n",
      " -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002\n",
      " -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002\n",
      " -0.0002]\n"
     ]
    }
   ],
   "source": [
    "print(J.mean(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEWCAYAAABrDZDcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAAcLklEQVR4nO3df5RddX3u8ffjhIFcQFD5cXESmSjRNnBtKGPQ2qVUwWa0ZvSaaLDcKwWNLkmhUoFAvVyaVm1ktdplU2t6oVcFDSQSM2IgsBRCQdEEiEDIjcR4ICMIMoARiTNM+Nw/zp64c3LOzDkzs+fM5Pu81jor+8d37/0538mcZ/beZ++tiMDMzNL1kmYXYGZmzeUgMDNLnIPAzCxxDgIzs8Q5CMzMEucgMDNLnIPAJgxJfy7pliHmnyapZzxrMkuBg+AAJ6kkabek53Kvf2l2XdVExLUR8Y7BcUkh6YRm1lQkSVdIumaYNiVJp49XTUNtW1J79jOZMo41nCRpvaSnJPmip4I4CNLw7og4LPdaXK1RtV/wRn/px/NDohEq8//3Jhrh/40XgOuBc8e4HMvxL0bCJJ0t6S5Jn5f0NHBFjWkvkfQpSY9IelLSVyUdka1j8K/EcyU9CnyvynY2SHpfNvzHWft3ZuOnS9qcq+fObPiObPEfZ3sxH8it76+zOh6X9BdDvL/bJX1a0l3A88CrJR0h6aps2Z9L+ntJLVn7E7Jaf5X9BXpdbl0h6XxJO7J5V+aDRdI5krZKeib7C/b43LwTJd0q6WlJT0i6TNJc4DLgA9n7+3GV+r8GvAr4dtbm4mz6PElbJD2bvcffH6IPatYt6TWSviepN5t3raQjh9j24M/k2Wzam+p47yHpPEkPAw/npn1M0sPZMsslqVr9EbEtIq4CttR6jzYGIsKvA/gFlIDTa8w7GxgA/hKYAkytMe0cYDvwauAw4Abga9k62oEAvgocCkytsp2lwBez4cuAnwLLcvP+OVfPnbnlAjghN35aVttS4CDgnZQ/4F9W4/3dDjwKnJi9l4OAbwFfzmo9BvgR8NGs/TeAv6H8B9IhwB9X1HIb8HLKH5A/AT6czXtP1j+/n23nU8D3s3mHA48Df52t83Dg1GzeFcA1jfz8gNcCvwHOyN7Pxdm2W2ssP1TdJ2TrORg4mvIH/ReG2Pbgz3pKblrN957b/q3Z9qfmpt0IHJnV9Etg7jD9cAIQzf59OlBfTS/Ar4J/wOVf5ueAZ3Ovj2TzzgYerWhfbdp3gY/nxl9HeZd9Su7D4dVD1PB24P5s+Gbgw8Dd2fgG4L/ntj1cEOyu+CB6Enhjje3eDizNjR8L9JELK+BM4LZs+KvACmBalXVF/sMK+Djw3Wz4JuDc3LyXUA6o47P131ejvitoPAj+F3B9xbZ+DpxWY/madVdp+558rVW2Pfizzvd/zfee2/7bqtSUD9nrgSXD9IODoMCXDw2l4T0RcWTu9e+5eTurtK+c9krgkdz4I5RD4Nhh1jPoB8BrJR0LzKb8gTtd0lHAHH53yKEevRExkBt/nvJeSi35uo6n/Ff049lhlWcp7x0ck82/GBDwo+zQyzlDrOsRyv0yuN5/zq3z6Ww9bcB0yntAY2Wfn0VEvJjV1TbEMlXrlnSMpJXZIbJdwDXAUQ3WM9R7r7b9Qb/IDQ/3M7SCOQis2jcxKqc9RvkXftCrKB+ieWKY9ZRnRDwP3ANcADwYEf3A94ELgZ9GxFMjqLte+bp2Ut4jOCoXii+NiBOzOn8RER+JiFcCHwX+Vft+a2l6bvhVlPtlcL0frQjbqRHx/Wzea+qorZ76oeJnkR1bn055r6CWWnV/Nlv/6yPipcBZlD/Ea227Wr1DvfehlrMJxEFg9fgG8AlJMyQdBnwGuK7iL/PhbAAWZ/9C+bBNfryaJyiflxgTEfE4cAvwj5Jemp0Ef42ktwJIWiBpWtb8GcofYHtyq7hI0sskTaccaoMnk/8NuFTSidl6jpC0IJt3I/BfJf2VpIMlHS7p1Nz7a9fQ32aq7IPrgXdJerukgyife+ijHKy11Kr7cLLDhpLagIuG2fYvgRcrpg313kdNZYcArdn4IZIOHqv1W5mDIA2D3/wYfK1pcPmrga9RPoTzM+C3lE8mN2ID5Q+eO2qMV3MF8JXssMP7G9xeLf+T8ofKQ5Q/7FcDx2Xz3gD8UNJzQDdwQUT8LLfsWsp7NpuB7wBXAUTEGmAZsDI7xPIg0JnN+zXlE7Lvpnw45GHgT7L1rcr+7ZV0b416Pwt8KuuDT0bENsp/uX8ReCpb77uzvaxaqtYN/C3wh8Cvsuk3DLPt54FPA3dl09441HsfI8dTPi80+K2h3cC2MVy/AcpOxJjZEFS+mGlmRGxvdi2NmKx12/jyHoGZWeIcBGZmifOhITOzxHmPwMwscRPyBmFDOeqoo6K9vX3Ey/f399Pa2jp2BR3g3F/1c181xv3VmNH21z333PNURBxdbd6kC4L29nY2bdo04uVLpRKjCZLUuL/q575qjPurMaPtL0mP1JrnQ0NmZolzEJiZJc5BYGaWuEKDQNJcSdskbZe0pMr8z0vanL1+kt290MzMxlFhJ4tVfurTcsr3WekBNkrqjoiHBttExCdy7f8SOLmoeszMrLoi9wjmANsjYkd2Q6yVQNcQ7c+kfJdLMzMbR0UGQRv7PpCihxoPz8iecTqDKs+7NTOzYhV5HUG1h1HXup/FQmB1ROypNlPSImARQFtbG6VSacRF9fb2jnjZFLm/6ue+aoz7qzFF9leRQdDDvk9GmsbvnoxUaSFwXq0VRcQKys+SpaOjY1RXFgO+iKVB7q/6ua8a4/5qTFH9VeShoY3AzOypVq2UP+y7KxtJeh3wMsrPtbUJYE9/P6s7O1nd2clAX9/e4T39Qz37xMwmq8L2CCJiQNJiYD3QAlwdEVskLQU2RcRgKJwJrAzfBnXCWNPVRc+G8hMkd11yCbuy4TVdXcy/6aZmlmZmBSj0XkMRsQ5YVzHt8orxK4qswUZuYPfuva8pU6c2uxwzK4ivLLb9zFu1ipaKuxy2tLYyb/XqJlVkZkVyENh+uhcs2O98wJ7+frrnz29SRWZWJAeB1TRl6tS9LzM7cE265xFY8d67di1rusoXgc9etozNfX17p5vZgcdBYPtpaW3d++2gUqnkbwqZHeB8aMjMLHEOAjOzxDkIzMwS5yAwM0ucg8DMLHEOAjOzxDkIzMwS5yAwM0ucg8DMLHEOAjOzxDkIzMwS5yAwM0ucg8DMLHEOAjOzxBUaBJLmStomabukJTXavF/SQ5K2SPp6kfWYmdn+CnsegaQWYDlwBtADbJTUHREP5drMBC4F3hwRz0g6pqh6zMysuiL3COYA2yNiR0T0AyuBroo2HwGWR8QzABHxZIH1mJlZFUU+oawN2Jkb7wFOrWjzWgBJdwEtwBURcXPliiQtAhYBtLW1USqVRlxUb2/viJdNkfurfu6rxri/GlNkfxUZBKoyLapsfyZwGjAN+E9JJ0XEs/ssFLECWAHQ0dER7e3toypstMunxv1VP/dVY9xfjSmqv4o8NNQDTM+NTwMeq9JmbUS8EBE/A7ZRDgYzMxsnRQbBRmCmpBmSWoGFQHdFm28BfwIg6SjKh4p2FFiTmZlVKCwIImIAWAysB7YC10fEFklLJc3Lmq0HeiU9BNwGXBQRPnBoZjaOijxHQESsA9ZVTLs8NxzAhdnLzMyawFcWm5klzkFgZpY4B4GZWeIcBGZmiXMQmJklzkFgZpY4B4GZWeIcBGZmiXMQmJklzkFgZpY4B4GZWeIcBGZmiXMQmJklzkFgZpY4B4GZWeIcBGZmiXMQmJklzkFgZpY4B4GZWeIKDQJJcyVtk7Rd0pIq88+W9EtJm7PXh4usx8zM9lfYw+sltQDLgTOAHmCjpO6IeKii6XURsbioOszMbGhF7hHMAbZHxI6I6AdWAl0Fbs/MzEagsD0CoA3YmRvvAU6t0u59kt4C/AT4RETsrGwgaRGwCKCtrY1SqTTionp7e0e8bIrcX/VzXzXG/dWYIvuryCBQlWlRMf5t4BsR0SfpY8BXgLftt1DECmAFQEdHR7S3t4+qsNEunxr3V/3cV41xfzWmqP4q8tBQDzA9Nz4NeCzfICJ6I6IvG/134JQC6zEzsyqKDIKNwExJMyS1AguB7nwDScflRucBWwusx8zMqijs0FBEDEhaDKwHWoCrI2KLpKXApojoBs6XNA8YAJ4Gzi6qHjMzq67IcwRExDpgXcW0y3PDlwKXFlmDmZkNzVcWm5klzkFgZpY4B4GZWeIcBGZmiXMQmJklzkFgZpY4B4GZWeIcBGZmiXMQmJklzkFgZpY4B4GZWeIcBGZmiXMQmJklzkFgZpY4B4GZWeIcBGZmiXMQmJklzkFgZpY4B4GZWeIKDQJJcyVtk7Rd0pIh2s2XFJI6iqzHzMz2V1gQSGoBlgOdwCzgTEmzqrQ7HDgf+GFRtZiZWW1F7hHMAbZHxI6I6AdWAl1V2v0d8DngtwXWYmZmNUwpcN1twM7ceA9war6BpJOB6RFxo6RP1lqRpEXAIoC2tjZKpdKIi+rt7R3xsilyf9XPfdUY91djiuyvIoNAVabF3pnSS4DPA2cPt6KIWAGsAOjo6Ij29vZRFTba5VPj/qqf+6ox7q/GFNVfRR4a6gGm58anAY/lxg8HTgJul1QC3gh0+4Sxmdn4KjIINgIzJc2Q1AosBLoHZ0bEryLiqIhoj4h24G5gXkRsKrAmMzOrUFgQRMQAsBhYD2wFro+ILZKWSppX1HbNzKwxRZ4jICLWAesqpl1eo+1pRdZiZmbV+cpiM7PEDRsEklokXTkexZiZ2fgbNggiYg9wiqRqXwc1M7NJrt5zBPcBayWtAn4zODEibiikKjMzGzf1BsHLgV7gbblpATgIzMwmubqCICL+ouhCzMysOer61pCkaZLWSHpS0hOSvilpWtHFmZlZ8er9+uh/UL4q+JWUbyb37WyamZlNcvUGwdER8R8RMZC9/i9wdIF1mZnZOKk3CJ6SdFZ2TUGLpLMonzw2M7NJrt4gOAd4P/AL4HFgfjbNzMwmuWG/NZQ9cvJ9EeEbxZmZHYDqvbK42iMmzczsAFDvBWV3SfoX4Dr2vbL43kKqMjOzcVNvEPxR9u/S3LRg3yuNzcxsEqrnHMFLgC9FxPXjUI+ZmY2zes4RvEj5SWNmZnYAqvfro7dK+qSk6ZJePvgqtDIzMxsX9Z4jGLxm4LzctABePbblmJnZeKtrjyAiZlR5DRsCkuZK2iZpu6QlVeZ/TNIDkjZLulPSrJG8CTMzG7khg0DSxbnhBRXzPjPMsi3AcqATmAWcWeWD/usR8d8iYjbwOeCfGqjdzMzGwHB7BAtzw5dWzJs7zLJzgO0RsSMi+oGVVFyYFhG7cqOHUj7cZGZm42i4cwSqMVxtvFIbsDM33gOcut8GpPOAC4FWalyXIGkRsAigra2NUqk0zKZr6+31vfIa4f6qn/uqMe6vxhTZX8MFQdQYrjZeqVpQ7LdMRCwHlkv6IPAp4ENV2qwAVgB0dHREe3v7MJse2miXT437q37uq8a4vxpTVH8NFwR/IGkX5Q/1qdkw2fghwyzbA0zPjU8DHhui/UrgS8Os08zMxtiQQRARLaNY90ZgpqQZwM8pn2/4YL6BpJkR8XA2+i7gYczMbFzVex1BwyJiQNJiYD3QAlwdEVskLQU2RUQ3sFjS6cALwDNUOSxkZmbFKiwIACJiHbCuYtrlueELity+mZkNr95bTJiZ2QHKQWBmljgHgZlZ4hwEZmaJcxCYmSXOQWBmljgHgZlZ4hwEZmaJcxCYmSXOQWBmljgHgZlZ4hwEZmaJcxCYmSXOQWBmljgHgZlZ4hwEZmaJcxCYmSXOQWBmljgHgZlZ4goNAklzJW2TtF3SkirzL5T0kKT7JX1X0vFF1mNmZvsrLAgktQDLgU5gFnCmpFkVze4DOiLi9cBq4HNF1WNmZtUVuUcwB9geETsioh9YCXTlG0TEbRHxfDZ6NzCtwHrMzKyKKQWuuw3YmRvvAU4dov25wE3VZkhaBCwCaGtro1Qqjbio3t7eES+bIvdX/dxXjXF/NabI/ioyCFRlWlRtKJ0FdABvrTY/IlYAKwA6Ojqivb19VIWNdvnUuL/q575qjPurMUX1V5FB0ANMz41PAx6rbCTpdOBvgLdGRF+B9ZiZWRVFniPYCMyUNENSK7AQ6M43kHQy8GVgXkQ8WWAtZmZWQ2FBEBEDwGJgPbAVuD4itkhaKmle1uxK4DBglaTNkrprrM7MzApS5KEhImIdsK5i2uW54dOL3L6ZmQ3PVxabmSXOQWBmljgHgdko7OnvZ3VnJ6s7Oxno69s7vKe/v9mlmdWt0HMEZge6NV1d9GzYAMCuSy5hVza8pquL+TdVvT7SbMLxHoHZGBjYvXvvy2yycRCYjcK8VatoaW3dZ1pLayvzVq9uUkVmjXMQmI1C94IF+50P2NPfT/f8+U2qyKxxDgKzMTBl6tS9L7PJxieLzUbhvWvXsqarfHf12cuWsbmvb+90s8nCQWA2Ci2trXu/HVQqlfxNIZuUfGjIzCxxDgIzs8Q5CMzMEucgMDNLnIPAzCxxDgIzs8Q5CMzMEucgMDNLnIPAzCxxhQaBpLmStknaLmlJlflvkXSvpAFJvkuXmVkTFBYEklqA5UAnMAs4U9KsimaPAmcDXy+qDjMzG1qR9xqaA2yPiB0AklYCXcBDgw0iopTNe7HAOszMbAhFBkEbsDM33gOcOpIVSVoELAJoa2ujVCqNuKje3t4RL5si91f93FeNcX81psj+KjIIVGVajGRFEbECWAHQ0dER7e3toygLRrt8atxf9XNfNcb91Zii+qvIk8U9wPTc+DTgsQK3Z2ZmI1BkEGwEZkqaIakVWAh0F7g9MzMbgcKCICIGgMXAemArcH1EbJG0VNI8AElvkNQDLAC+LGlLUfWYmVl1hT6hLCLWAesqpl2eG95I+ZCRmZk1ia8sNrNxs6e/n9Wdnazu7GSgr2/v8J7+/maXljQ/s9jMxs2ari56NmwAYNcll7ArG17T1eXnPTeR9wjMbNwN7N6992XN5yAws3Ezb9UqWlpb95nW0trKvNWrm1SRgYPAzMZR94IF+50P2NPfT/d833OymRwEZjbupkyduvdlzeeTxWY2bt67di1ruroAmL1sGZv7+vZOt+ZxEJjZuGlpbd377aBSqeRvCk0QPjRkZpY4B4GZ2QQ1Xhfg+dCQmdkENV4X4HmPwMxsgiv6AjwHgZnZBDVeF+A5CMzMJqjxugDPQWBmNsEVfQGeTxabmU1Q43UBnoPAzGyCGq8L8HxoyMwscQ4CM7PEFRoEkuZK2iZpu6QlVeYfLOm6bP4PJbUXUYcfj2dmVlth5wgktQDLgTOAHmCjpO6IeCjX7FzgmYg4QdJCYBnwgbGuxY/HMzOrrcg9gjnA9ojYERH9wEqgq6JNF/CVbHg18HZJKqogPx7PzGx/RX5rqA3YmRvvAU6t1SYiBiT9CngF8FS+kaRFwCKAtrY2SqVSQ4XM/sIX2HXJJQzs3s3UWbOA8vdyZy9b1vC6UtPb29vsEiYN91Vj3F+NKbK/igyCan/ZxwjaEBErgBUAHR0d0d7e3lAhqzs72bVhw949gV233MKUqVPZ3NfnQ0N1aLS/U+a+aoz7qzFF9VeRh4Z6gOm58WnAY7XaSJoCHAE8XVRBfjyemdn+itwj2AjMlDQD+DmwEPhgRZtu4EPAD4D5wPciYr89gtHy4/HMzGorLAiyY/6LgfVAC3B1RGyRtBTYFBHdwFXA1yRtp7wnsLCIWvx4PDOz2gq9xURErAPWVUy7PDf8W2BBkTWYmdnQfGWxmVniHARmZolzEJiZJc5BYGaWOAeBmVniHARmZolzEJiZJc5BYGaWOBVwR4dCSfol8MgoVnEUFXc3tSG5v+rnvmqM+6sxo+2v4yPi6GozJl0QjJakTRHR0ew6Jgv3V/3cV41xfzWmyP7yoSEzs8Q5CMzMEpdiEKxodgGTjPurfu6rxri/GlNYfyV3jsDMzPaV4h6BmZnlOAjMzBKXTBBIulrSk5IebHYtE52k6ZJuk7RV0hZJFzS7polM0iGSfiTpx1l//W2za5oMJLVIuk/Sjc2uZaKTVJL0gKTNkjaN+fpTOUcg6S3Ac8BXI+KkZtczkUk6DjguIu6VdDhwD/CeiHioyaVNSJIEHBoRz0k6CLgTuCAi7m5yaROapAuBDuClEfFnza5nIpNUAjoiopAL8JLZI4iIOyg/F9mGERGPR8S92fCvga1AW3Ormrii7Lls9KDslcZfWCMkaRrwLuD/NLsWSygIbGQktQMnAz9sbiUTW3aYYzPwJHBrRLi/hvYF4GLgxWYXMkkEcIukeyQtGuuVOwisJkmHAd8E/ioidjW7noksIvZExGxgGjBHkg8/1iDpz4AnI+KeZtcyibw5Iv4Q6ATOyw51jxkHgVWVHev+JnBtRNzQ7Homi4h4FrgdmNvkUiayNwPzsuPeK4G3SbqmuSVNbBHxWPbvk8AaYM5Yrt9BYPvJTn5eBWyNiH9qdj0TnaSjJR2ZDU8FTgf+X3Ormrgi4tKImBYR7cBC4HsRcVaTy5qwJB2afWkDSYcC7wDG9NuPyQSBpG8APwBeJ6lH0rnNrmkCezPwPyj/pbY5e72z2UVNYMcBt0m6H9hI+RyBvxJpY+VY4E5JPwZ+BHwnIm4eyw0k8/VRMzOrLpk9AjMzq85BYGaWOAeBmVniHARmZolzEJiZJc5BYJOOpD3ZV1oflLRK0n8Zpv1lueEjJX28+CrHlqR23znXiuIgsMlod0TMzu4i2w98bJj2l+WGjwQaCgKVTerfFUlTml2DTVyT+j+3GfCfwAkAkr6V3ZRry+CNuST9AzA124O4FvgH4DXZ+JVZm4skbZR0/+CzBLK/wLdK+lfgXmC6pOckfTp77sDdko6tLEbSFdmzL26XtEPS+bn1PZhr90lJV2TDt0v6vKQ7sm2+QdINkh6W9Pe51U+R9JWsztWDe0KSTpG0IXvv67PbiA+u9zOSNgB+poTV5CCwSSv7K7cTeCCbdE5EnEL5HvfnS3pFRCzhd3sQfw4sAX6ajV8k6R3ATMr3bpkNnJK7odfrKD+/4uSIeAQ4FLg7Iv4AuAP4SI3Sfg/402yd/zu7b9Nw+iPiLcC/AWuB84CTgLMlvSJXz4qIeD2wC/h4tu4vAvOz93418Onceo+MiLdGxD/WUYMlyruLNhlNzW75DOU9gquy4fMlvTcbnk75A753mHW9I3vdl40fli33KPBIxcNl+oHBW0fcA5xRY53fiYg+oE/Sk5RvETCc7uzfB4AtEfE4gKQd2Xt5FtgZEXdl7a4BzgduphwYt5ZvEUUL8HhuvdfVsW1LnIPAJqPd2S2f95J0GuWbvb0pIp6XdDtwSB3rEvDZiPhyxfragd9UtH0hfndPlj3U/v3pyw0Pthtg3z3wytoGl3mxYvkXc9upvB9MZPVviYg31ail8j2Y7ceHhuxAcQTwTBYCvwe8MTfvhdzhmV8Dh+fmrQfOyZ69gKQ2SccUUN8TwDGSXiHpYGAkj2Z8laTBD/wzKT8Scxtw9OB0SQdJOnFMKrZkOAjsQHEz5ZOp9wN/B+QP6awA7pd0bUT0AndlXz29MiJuAb4O/EDSA8Bq9g2KMRERLwBLKT/p7UZGdpvqrcCHsvf4cuBLEdEPzAeWZXen3Az80dhUbanw3UfNzBLnPQIzs8Q5CMzMEucgMDNLnIPAzCxxDgIzs8Q5CMzMEucgMDNL3P8HRHNrqx8NpxEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# frames\n",
    "frames = [np.zeros(N)-1 for j in range((L+1)//2)]\n",
    "\n",
    "for i in range((L+1)//2):\n",
    "    for j in range(N):\n",
    "        if j%L == i:\n",
    "            frames[i][j] = 1\n",
    "        if j%L == (L-i-1) :\n",
    "            frames[i][j] = 1\n",
    "        if j//L == i:\n",
    "            frames[i][j] = 1\n",
    "        if j//L == (L-i-1) :\n",
    "            frames[i][j] = 1\n",
    "    for k in range(i):\n",
    "        for j in range(N):\n",
    "            if j%L == k:\n",
    "                frames[i][j] = -1\n",
    "            if j%L == (L-k-1) :\n",
    "                frames[i][j] = -1\n",
    "            if j//L == k:\n",
    "                frames[i][j] = -1\n",
    "            if j//L == (L-k-1) :\n",
    "                frames[i][j] = -1\n",
    "\n",
    "err_frame = []   \n",
    "\n",
    "fig, ax = plt.subplots(1, (L+1)//2 , figsize=(16,6))\n",
    "\n",
    "for i in range((L+1)//2):\n",
    "    ax[i].set_title('Pattern %i' %(i+1))\n",
    "    ax[i].imshow(frames[i].reshape(L,L),cmap='Greys')\n",
    "plt.show()    \n",
    "    \n",
    "for i in frames:    \n",
    "    err_frame.append(w_error(frames[0],i,2))\n",
    "\n",
    "figure = plt.figure(figsize=(6,4))\n",
    "plt.grid('-.', alpha=0.5)\n",
    "plt.scatter(np.arange(1, 1+len(err_frame)), err_frame, marker='X', color='darkred')\n",
    "plt.title(\"Error with respect to pattern 1\")\n",
    "plt.xlabel(\"Pattern number\")\n",
    "plt.xticks(np.arange(1, 1+len(err_frame)))\n",
    "plt.ylabel(\"Error\")\n",
    "\n",
    "plt.show()\n",
    "                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.000000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.000000\n",
      "The algorithm recognised the pattern 0 and the correct pattern is 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.000000\n",
      "The algorithm recognised the pattern 1 and the correct pattern is 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.000000\n",
      "The algorithm recognised the pattern 1 and the correct pattern is 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.000000\n",
      "The algorithm recognised the pattern 2 and the correct pattern is 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.000000\n",
      "The algorithm recognised the pattern 2 and the correct pattern is 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.000000\n",
      "The algorithm recognised the pattern 3 and the correct pattern is 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.120000\n",
      "The algorithm recognised the pattern 4 and the correct pattern is 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.040000\n",
      "The algorithm recognised the pattern 4 and the correct pattern is 4\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdoAAAD6CAYAAAAGP4YtAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAASu0lEQVR4nO3deZCkdX3H8fcHVkRARGXFLNfiLbFioEYjoiaKscA7KSuiYoTSYDwADQkeMYAVo5WUihotEwSNBgQVjUUUr5SiIQe6HJbConKz7CKDCAIeiH7zRz+T9A69M71s/+bp2bxfVVs10/1096dn+/t8+jmmJ1WFJElqY5u+A0iStDWzaCVJasiilSSpIYtWkqSGLFpJkhqyaCVJasiilbRsJdkrye1Jtp3UskkOT3LeAtd/IcnL7knePiR5ZJKLktyW5Ogk/5Dkr/rONWe5/TzviRV9B9DdJbka2A34FXAHcA5wVFXdvsBtfg84rar2GLrsROBhVXVYy7xSa/NmYs4jqupaYKdx7mNzll3kfg7Z0vtYYscB51bVfn0HGbVOWoY/z83mFu30ek5V7QTsDzwOeMtSB0jiGzFNk+dU1U5D/9b3HWiZ2Bu4pPWDuL7YNIt2ylXV9cAXgMckOSLJ2m4X0JVJXgmQZMdumVXdrrHbk7wYeDPwwu77b3fL3i/JqUk2JLk+ydvmdqV1u8z+I8lJSW4GTpzbjZbknUl+nOSqJFv9O1AtD0lWJ6m5lXySc5P8dfc6vi3Jl5PsuollD+/m6Lbudf2Sefc98jXfPcYrhu5jk/ORZJ8k3+ge49+SfCDJaQs8n+cluTjJT5JckeTg7vJVSc5OcnOSy5P8ydBtTkzyySQf6x7nkiQz3XVfBZ4KvL9bDzwiyT8ledvQ7Y/r1gfrk7yi+xk9bP5zHX6+Q99Xktck+QHwg+6y9ya5rnsOFyR5cnf5wYxeJw3/PLdJ8pYk1yS5sXtO95v3//eyJNcmuSnJXy76IpkCFu2US7In8EzgIuBG4NnAzsARwElJ9q+qO4BDgPVD7/Y/Drwd+ET3/WO7u/wocBfwMGA/4BnAK4Ye8neAK4EHAX8zdNn3gF2BvwNOTZJWz1naQi9mMB8PArYD/nz+At2b0/cBh1TVfYEnAhcPLbI5r/mFlv048E3ggcCJwEs3FTrJ44GPAX8B7AI8Bbi6u/oMYB2wCngB8PYkBw3d/LnAmd3tzgbeD1BVTwP+HXhttx74/rzHPBj4M+DpDNYJv7upfAt4PoOfwb7d998Cfht4AIPn/6kk21fVFxm9Thp2ePfvqcBDGOzqf/+8ZZ4EPBI4CDg+yaPvQeYlZdFOr88muQU4D/g68Paq+nxVXVEDXwe+DDx53DtMshuDQn5dVd1RVTcCJwGHDi22vqr+vqruqqqfdZddU1UfqqpfMSjq32BwvExaSp9Nckv377MLLPeRqvp+9/r9JIOV/ii/ZrCn6D5VtaGqhnevbs5rfuSySfZicNjn+Kq6s6rOY1CCm/Jy4MNV9ZWq+nVVXV9Vl3Vvtp8EvKGqfl5VFwOnsHFpn1dV53QZ/hkYVWKj/BGDn9clVfVT4K1j3m7YO6rq5rn1RVWdVlU/6tYh7wLuzaAYx/ES4N1VdWV3TsqbgEOz8W7pt1bVz6rq28C3Gf+59sainV7Pr6pdqmrvqnp1Vf0sySFJ/rvbfXQLgy3dXTfjPvcG7gVsmFthAf/I4J3/nOtG3O6GuS+6YYQJnFQibaa5mdilqp6/wHI3DH39U0a8Vru9QC8E/pTBPHw+yaNG3ccYr/lNLbsKuHnoMhg9X3P2BK4Ycfnc/dw2dNk1wO6jMjB4zttnvGOmq+ZlWijfpmx0myTHZnCI69ZuHXM/xl9PrWLw3OZcw+Ck3eE3OYv+/04bi3aZSHJv4NPAO4HdqmoXBmcjz+2iGvVnmOZfdh3wC2DXoRXWzlX1mwvcRtoqVdWXqur3GWyBXgZ8aMIPsQF4QJIdhi7bc4HlrwMeOuLy9d393Hfosr2A67c8IhuAPYa+n5/vDmA4/4NH3Mf/rjO647FvYLClfP9uPXUrC6+nhq1nsEEwZy8Gh7p+uMjtpppFu3xsx2AXzCxwV3fCxTOGrv8h8MC5EweGLludZBuAqtrAYHfzu5Ls3J148NAk9+S4jLRsJdktyXO7Y7W/AG5n418d2mJVdQ2whsFJhdslOQB4zgI3ORU4IslB3WzunuRRVXUd8J/AO5Jsn+S3GOxmPn0CMT/ZPeajuzcEx8+7/mLgD5Ps0J0g9fJF7u++DIpxFliR5HgG55TM2WidNMIZwOszOIlsJ/7vmO5dm/e0potFu0x0u42OZjAYP2ZwwsfZQ9dfxuBFemW3W3gV8Knu6h8lubD7+o8ZlPal3f2cxeAdvfT/yTbAsQy2oG5mcBLQqxs8zkuAA4AfAW8DPsGg2O+mqr5Jd5Ijg63Ar/N/W3cvAlZ3ef8FOKGqvrKl4arqCwxOCvsacDnwX91VcxlPAu5kUJAfZfFy/xKD34D4PoPdvj9n413Lo9ZJwz7M4BjzN4CrutsfNf4zmk7xD79L0tJI8gngsqo6oe8so3Rn8H4XuPdy34qcJm7RSlIjSR7XHZ7ZpvtVmucBC50xveSS/EG3a/v+wN8C/2rJTpZFK0ntPBg4l8Ex4PcBr6qqi3pNdHevZHBM9QoGx6lf1W+crY+7jiVJasgtWkmSGrJoJUlqqMlfW9h1111r9erVLe5a2mpcffXV3HTTTVP9mdHOsjSeCy644KaqWjnquiZFu3r1atasWdPirqWtxszMTN8RFuUsS+NJcs2mrnPXsSRJDVm0kiQ1ZNFKktSQRStJUkNjFW2Sg5N8L8nlSd7YOpSkNpxlaektWrRJtgU+ABwC7Au8KMm+rYNJmixnWerHOFu0jwcur6orq+pO4EwGH4wtaXlxlqUejFO0u7Px3xNc110maXlxlqUejFO0oz655m5/iSDJkUnWJFkzOzu75ckkTZqzLPVgnKJdB+w59P0ewPr5C1XVyVU1U1UzK1eO/BQqSf1ylqUejFO03wIenmSfJNsBhwJnt40lqQFnWerBop91XFV3JXkt8CVgW+DDVXVJ82SSJspZlvox1h8VqKpzgHMaZ5HUmLMsLT0/GUqSpIYsWkmSGrJoJUlqyKKVJKkhi1aSpIYsWkmSGrJoJUlqyKKVJKkhi1aSpIYsWkmSGrJoJUlqyKKVJKkhi1aSpIYsWkmSGrJoJUlqyKKVJKkhi1aSpIYsWkmSGrJoJUlqyKKVJKkhi1aSpIYsWkmSGrJoJUlqyKKVJKkhi1aSpIYsWkmSGrJoJUlqyKKVJKkhi1aSpIYsWkmSGrJoJUlqyKKVJKmhRYs2yZ5JvpZkbZJLkhyzFMEkTZazLPVjxRjL3AUcW1UXJrkvcEGSr1TVpY2zSZosZ1nqwaJbtFW1oaou7L6+DVgL7N46mKTJcpalfmzWMdokq4H9gPNbhJG0NJxlaemMXbRJdgI+Dbyuqn4y4vojk6xJsmZ2dnaSGSVNkLMsLa2xijbJvRgM5ulV9ZlRy1TVyVU1U1UzK1eunGRGSRPiLEtLb5yzjgOcCqytqne3jySpBWdZ6sc4W7QHAi8Fnpbk4u7fMxvnkjR5zrLUg0V/vaeqzgOyBFkkNeQsS/3wk6EkSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWpoRd8BNFqSviMsqqr6jiBJU88tWkmSGrJoJUlqyKKVJKkhi1aSpIYsWkmSGrJoJUlqaOyiTbJtkouSfK5lIEltOcvS0tqcLdpjgLWtgkhaMs6ytITGKtokewDPAk5pG0dSS86ytPTG3aJ9D3Ac8OtNLZDkyCRrkqyZnZ2dSDhJE+csS0ts0aJN8mzgxqq6YKHlqurkqpqpqpmVK1dOLKCkyXCWpX6Ms0V7IPDcJFcDZwJPS3Ja01SSWnCWpR4sWrRV9aaq2qOqVgOHAl+tqsOaJ5M0Uc6y1A9/j1aSpIY268/kVdW5wLlNkkhaMs6ytHTcopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqaEVfQfQaFXVdwRJ0gS4RStJUkMWrSRJDVm0kiQ1ZNFKktSQRStJUkNjFW2SXZKcleSyJGuTHNA6mKTJc5alpTfur/e8F/hiVb0gyXbADg0zSWrHWZaW2KJFm2Rn4CnA4QBVdSdwZ9tYkibNWZb6Mc6u44cAs8BHklyU5JQkOzbOJWnynGWpB+MU7Qpgf+CDVbUfcAfwxvkLJTkyyZoka2ZnZyccU9IEOMtSD8Yp2nXAuqo6v/v+LAbDupGqOrmqZqpqZuXKlZPMKGkynGWpB4sWbVXdAFyX5JHdRQcBlzZNJWninGWpH+OedXwUcHp3luKVwBHtIklqyFmWlthYRVtVFwMzjbNIasxZlpaenwwlSVJDFq0kSQ1ZtJIkNWTRSpLUkEUrSVJDFq0kSQ1ZtJIkNWTRSpLUkEUrSVJDFq0kSQ1ZtJIkNWTRSpLUkEUrSVJDFq0kSQ1ZtJIkNWTRSpLUkEUrSVJDFq0kSQ1ZtJIkNWTRSpLUkEUrSVJDFq0kSQ1ZtJIkNWTRSpLUkEUrSVJDFq0kSQ1ZtJIkNWTRSpLUkEUrSVJDFq0kSQ1ZtJIkNWTRSpLU0FhFm+T1SS5J8t0kZyTZvnUwSZPnLEtLb9GiTbI7cDQwU1WPAbYFDm0dTNJkOctSP8bddbwCuE+SFcAOwPp2kSQ15CxLS2zRoq2q64F3AtcCG4Bbq+rL85dLcmSSNUnWzM7OTj6ppC3iLEv9GGfX8f2B5wH7AKuAHZMcNn+5qjq5qmaqamblypWTTyppizjLUj/G2XX8dOCqqpqtql8CnwGe2DaWpAacZakH4xTttcATkuyQJMBBwNq2sSQ14CxLPRjnGO35wFnAhcB3utuc3DiXpAlzlqV+rBhnoao6ATihcRZJjTnL0tLzk6EkSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIasmglSWooVTX5O01mgWvGWHRX4KaJB5icac8H059x2vNBfxn3rqqVPTzu2LaiWYbpzzjt+cCMC9nkPDcp2nElWVNVM70FWMS054Ppzzjt+WB5ZJx2y+FnOO0Zpz0fmPGectexJEkNWbSSJDXUd9Ge3PPjL2ba88H0Z5z2fLA8Mk675fAznPaM054PzHiP9HqMVpKkrV3fW7SSJG3VeinaJAcn+V6Sy5O8sY8MC0myZ5KvJVmb5JIkx/SdaZQk2ya5KMnn+s4ySpJdkpyV5LLuZ3lA35nmS/L67v/4u0nOSLJ935mWm2me5+Uyy+A8b6lpnuUlL9ok2wIfAA4B9gVelGTfpc6xiLuAY6vq0cATgNdMYUaAY4C1fYdYwHuBL1bVo4DHMmVZk+wOHA3MVNVjgG2BQ/tNtbwsg3leLrMMzvM9Nu2z3McW7eOBy6vqyqq6EzgTeF4POTapqjZU1YXd17cxeEHt3m+qjSXZA3gWcErfWUZJsjPwFOBUgKq6s6pu6TfVSCuA+yRZAewArO85z3Iz1fO8HGYZnOcJmdpZ7qNodweuG/p+HVP4wp+TZDWwH3B+v0nu5j3AccCv+w6yCQ8BZoGPdLvDTkmyY9+hhlXV9cA7gWuBDcCtVfXlflMtO8tmnqd4lsF53iLTPst9FG1GXDaVpz4n2Qn4NPC6qvpJ33nmJHk2cGNVXdB3lgWsAPYHPlhV+wF3ANN2/O7+DLa+9gFWATsmOazfVMvOspjnaZ1lcJ4nYdpnuY+iXQfsOfT9HkzRJv6cJPdiMJinV9Vn+s4zz4HAc5NczWBX3dOSnNZvpLtZB6yrqrmth7MYDOo0eTpwVVXNVtUvgc8AT+w503Iz9fM85bMMzvMkTPUs91G03wIenmSfJNsxOGB9dg85NilJGByLWFtV7+47z3xV9aaq2qOqVjP4+X21qqbm3RtAVd0AXJfkkd1FBwGX9hhplGuBJyTZofs/P4gpOsFjmZjqeZ72WQbneUKmepZXLPUDVtVdSV4LfInBmWEfrqpLljrHIg4EXgp8J8nF3WVvrqpzesy0HB0FnN6tgK8Ejug5z0aq6vwkZwEXMjg79SKm8FNlptkymGdneXKmdp6nfZb9ZChJkhryk6EkSWrIopUkqSGLVpKkhixaSZIasmglSWrIopUkqSGLVpKkhixaSZIa+h9PYa63MTd05QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.040000\n",
      "The algorithm recognised the pattern 4 and the correct pattern is 4\n"
     ]
    }
   ],
   "source": [
    "frames = np.array(frames)\n",
    "ind = np.arange(len(frames))\n",
    "\n",
    "for idx in ind: \n",
    "    for MF in range(2):\n",
    "        if MF: J = MF_coupling(frames,N)\n",
    "        else: J = R_coupling(frames,N,R)\n",
    "\n",
    "        sys = deepcopy(frames[idx])\n",
    "\n",
    "        sys = deterministic_hopfield(sys,100)\n",
    "        wrong_pixels = error_im(frames[idx],sys)\n",
    "        assigned_pattern = assign_pattern(frames,sys)\n",
    "\n",
    "        fig, ax = plt.subplots(1,2, figsize = (8,5))\n",
    "        ax[0].set_title('Pattern')\n",
    "        ax[0].imshow(frames[idx].reshape(L,L), cmap='Greys')\n",
    "        ax[1].set_title('Finishing configuration')\n",
    "        ax[1].imshow(sys.reshape(L,L), cmap='Greys')\n",
    "        plt.show()\n",
    "        print('The error of the algorithm is %f' %(wrong_pixels))\n",
    "        print('The algorithm recognised the pattern %i and the correct pattern is %i' %(assigned_pattern,idx))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.003731809212700987\n"
     ]
    }
   ],
   "source": [
    "print(J.mean(axis=0).std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]\n",
      " [-1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]\n",
      " [-1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]\n",
      " [-1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]\n",
      " [-1. -1. -1. -1.  1.  1. -1. -1. -1. -1.]\n",
      " [-1. -1. -1. -1.  1.  1. -1. -1. -1. -1.]\n",
      " [-1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]\n",
      " [-1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]\n",
      " [-1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]\n",
      " [-1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n",
      "[[ 0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01]\n",
      " [ 0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01]\n",
      " [ 0.01  0.01  0.01  0.    0.01  0.01  0.01  0.01  0.01  0.01]\n",
      " [ 0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01]\n",
      " [ 0.01  0.01  0.01  0.01 -0.01 -0.01  0.01  0.01  0.01  0.01]\n",
      " [ 0.01  0.01  0.01  0.01 -0.01 -0.01  0.01  0.01  0.01  0.01]\n",
      " [ 0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01]\n",
      " [ 0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01]\n",
      " [ 0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01]\n",
      " [ 0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01  0.01]]\n"
     ]
    }
   ],
   "source": [
    "f = np.array(frames[4:])\n",
    "print(f.reshape(L,L))\n",
    "J = MF_coupling(f,N)\n",
    "print(J[23].reshape(L,L))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x432 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# random\n",
    "diff = [np.zeros(N)-1 for j in range(5)]\n",
    "\n",
    "for i in range(5):\n",
    "    for j in range(L):\n",
    "        k = np.random.randint(0,N)\n",
    "        diff[i][k] = 1\n",
    "        \n",
    "\n",
    "fig, ax = plt.subplots(1, (L+1)//2 , figsize=(16,6))\n",
    "\n",
    "for i in range((L+1)//2):\n",
    "    ax[i].set_title('Pattern %i' %(i+1))\n",
    "    ax[i].imshow(diff[i].reshape(L,L),cmap='Greys')\n",
    "plt.show()   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# random\n",
    "diff = [np.zeros(N)-1 for j in range(2)]\n",
    "\n",
    "for i in range(2):\n",
    "    for j in range(L):\n",
    "        k = np.random.randint(0,N)\n",
    "        diff[i][k] = 1\n",
    "        \n",
    "\n",
    "fig, ax = plt.subplots(1, 2 , figsize=(10,6))\n",
    "\n",
    "for i in range(2):\n",
    "    ax[i].set_title('Pattern %i' %(i+1))\n",
    "    ax[i].imshow(diff[i].reshape(L,L),cmap='Greys')\n",
    "plt.show()   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.  -1.  -1.  -1.  -0.6 -0.6 -0.6 -0.2 -0.6 -1. ]\n",
      " [-0.2 -1.  -1.  -0.2 -1.  -1.  -1.  -1.  -1.  -1. ]\n",
      " [-1.  -0.2 -0.6 -1.  -0.6 -1.  -0.6 -1.  -1.  -0.6]\n",
      " [-1.  -1.  -1.  -1.  -0.6 -1.  -0.6 -0.6 -1.  -0.2]\n",
      " [-1.  -1.  -1.  -0.6 -1.  -0.6 -1.  -1.  -1.  -1. ]\n",
      " [-1.  -1.  -0.6 -1.  -0.6 -0.2 -1.  -1.  -1.  -1. ]\n",
      " [-1.  -1.  -0.6 -0.6 -0.2 -1.  -1.  -1.  -1.  -1. ]\n",
      " [-1.  -1.  -0.6 -1.  -1.  -1.  -0.6 -0.2 -0.6 -0.6]\n",
      " [-1.  -1.  -1.  -0.6 -1.  -1.  -0.6 -0.6 -1.  -1. ]\n",
      " [-1.  -1.  -0.6 -0.2 -1.  -0.6 -0.6 -1.  -0.2 -1. ]]\n",
      "[[-0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6]\n",
      " [-0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6]\n",
      " [-0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6]\n",
      " [-0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6]\n",
      " [-0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6]\n",
      " [-0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6]\n",
      " [-0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6]\n",
      " [-0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6]\n",
      " [-0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6]\n",
      " [-0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6]]\n",
      "[[-0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8]\n",
      " [-0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8]\n",
      " [-0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8]\n",
      " [-0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8]\n",
      " [-0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8]\n",
      " [-0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8]\n",
      " [-0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8]\n",
      " [-0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8]\n",
      " [-0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8]\n",
      " [-0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8]]\n",
      "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "avg_rnd = np.array(diff).mean(axis=0)\n",
    "avg_fr = np.array(frames).mean(axis=0)\n",
    "avg_patt = np.array(patt).mean(axis=0)\n",
    "avg_ch = np.array(chess).mean(axis=0)\n",
    "\n",
    "print(avg_rnd.reshape(L,L))\n",
    "print(avg_fr.reshape(L,L))\n",
    "print(avg_patt.reshape(L,L))\n",
    "print(avg_ch.reshape(L,L))\n",
    "\n",
    "plt.imshow(avg_rnd.reshape(L,L),cmap='Greys')\n",
    "plt.show()\n",
    "plt.imshow(avg_fr.reshape(L,L),cmap='Greys')\n",
    "plt.show()\n",
    "plt.imshow(avg_patt.reshape(L,L),cmap='Greys')\n",
    "plt.show()\n",
    "plt.imshow(avg_ch.reshape(L,L),cmap='Greys')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 2 and the correct pattern is 0\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 2 and the correct pattern is 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.090000\n",
      "The algorithm recognised the pattern 2 and the correct pattern is 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.090000\n",
      "The algorithm recognised the pattern 2 and the correct pattern is 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.080000\n",
      "The algorithm recognised the pattern 2 and the correct pattern is 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.080000\n",
      "The algorithm recognised the pattern 2 and the correct pattern is 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 2 and the correct pattern is 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 2 and the correct pattern is 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 2 and the correct pattern is 4\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.100000\n",
      "The algorithm recognised the pattern 2 and the correct pattern is 4\n"
     ]
    }
   ],
   "source": [
    "diff = np.array(diff)\n",
    "ind = np.arange(len(diff))\n",
    "\n",
    "for idx in ind: \n",
    "    for MF in range(2):\n",
    "        if MF: J = MF_coupling(diff,N)\n",
    "        else: J = R_coupling(diff,N,R)\n",
    "\n",
    "        sys = deepcopy(diff[idx])\n",
    "\n",
    "        sys = deterministic_hopfield(sys,100)\n",
    "        wrong_pixels = error_im(diff[idx],sys)\n",
    "        assigned_pattern = assign_pattern(diff,sys)\n",
    "\n",
    "        fig, ax = plt.subplots(1,2, figsize = (8,5))\n",
    "        ax[0].set_title('Pattern')\n",
    "        ax[0].imshow(diff[idx].reshape(L,L), cmap='Greys')\n",
    "        ax[1].set_title('Finishing configuration')\n",
    "        ax[1].imshow(sys.reshape(L,L), cmap='Greys')\n",
    "        plt.show()\n",
    "        print('The error of the algorithm is %f' %(wrong_pixels))\n",
    "        print('The algorithm recognised the pattern %i and the correct pattern is %i' %(assigned_pattern,idx))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.01084544143868747\n"
     ]
    }
   ],
   "source": [
    "print(J.mean(axis=0).std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}