Montecarlo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Montecarlo simulation\n",
    "As we have stated before a really interesting feature of the hopfield model is that give us the possibility of mapping a neuron system into a spin glasses system. \n",
    "\n",
    "We can so employ technics developed to study physical systems to use the hopfield model in a optimized way. We will see in the following that we can pass from an algorithm that takes $O(N^2t)$ operation, with $N$ size of the system and $t$ the number of iteration of the update rule, to an algorithm that takes $O(Nt)$ operation for the Mean Field case, or even less in the Non-MF case.\n",
    "\n",
    "Montecarlo simulations are simulation that uses pseudorandom number to simulate a physical system. For this particular task we aim at finding the ground state of a spin system using as update rule the metropolis rule. \n",
    "\n",
    "Given the system energy $\\mathcal{H}$ we randomly flip a spin of the system and we compute the difference in energy $\\Delta\\mathcal{H}=\\mathcal{H}_{f}-\\mathcal{H}_{i}$. Then we accept the updated system with the following probability:\n",
    "$$\n",
    "\\begin{equation}\n",
    "p_{acc}= \\min\\left( 1, e^{-\\beta\\Delta\\mathcal{H}} \\right)\n",
    "\\end{equation}\n",
    "$$\n",
    "where $\\beta=(K_{b}T)^{-1}$ is the inverse of the size of the system. In this way if the energy is decreasing we update the system with probability 1, and if it is greater with a probability proportional to the increase in energy.\n",
    "\n",
    "From the theory we know that the critical temperature, the highest temperature at which the system is trapped in the minima, is $T=1/K_b$.\n",
    "\n",
    "In this section we will so look at:\n",
    "- The stability of the Montecarlo methods;\n",
    "- The improvement in the time implementation of Montecarlo;\n",
    "- The dependance of the algorithm's performances w.r.t. the type of noise;\n",
    "- The dependance of the algorithm's performances w.r.t. the number of neighbors for the NON-MF version;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy as scp\n",
    "from copy import deepcopy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters\n",
    "L = 10  # Lenght of the edge of the image\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": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function that are in previous notebook\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",
    "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",
    "\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\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(sys1, t):\n",
    "    sys = deepcopy(sys1)\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",
    "\n",
    "def corrupt_uniform(sys, q): # q probability to flip the pixel\n",
    "    sys_temp = deepcopy(sys)\n",
    "    N = sys.shape[0]\n",
    "    for i in range(N):\n",
    "        r = np.random.rand()\n",
    "        if r < q:\n",
    "            sys_temp[i] *= -1\n",
    "    return sys_temp\n",
    "\n",
    "def plot(x, y, sys): # x-> Original, y-> Corrupted, sys-> Recovered\n",
    "    fig, ax = plt.subplots(1,3, figsize=(15,8))\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",
    "    ax[2].set_title('Recovered pattern')\n",
    "    ax[2].imshow(sys.reshape(L,L),cmap='Greys')\n",
    "    plt.show()\n",
    "    \n",
    "def algorithm(xi, idx, yi):\n",
    "    sys = deterministic_hopfield(yi,30)\n",
    "\n",
    "    wrong_pixels = error_im(xi[idx],sys)\n",
    "    assigned_pattern = assign_pattern(xi,sys)\n",
    "    \n",
    "    return wrong_pixels, assigned_pattern, sys\n",
    "\n",
    "def corrupt_norm(sys, k, h):\n",
    "    sys_temp = deepcopy(sys)\n",
    "    sys_temp = sys_temp.reshape(L,L)\n",
    "    N = sys.shape[0]\n",
    "    for i in range(L):\n",
    "        for j in range(L):\n",
    "            g = gaus(k, L/5, h, i, j)\n",
    "            r = np.random.rand()\n",
    "            if r < g:\n",
    "                sys_temp[i][j] *= -1\n",
    "    return (sys_temp.reshape(1,N))[0]\n",
    "\n",
    "def gaus(mu, sigma, h, x, y):\n",
    "    h = np.sqrt(h)\n",
    "    g_x = np.exp(-( (x-mu[0])**2 / ( 2.0 * sigma**2 ) ) )*h#/np.sqrt(2*np.pi*sigma**2)\n",
    "    g_y = np.exp(-( (y-mu[1])**2 / ( 2.0 * sigma**2 ) ) )*h#/np.sqrt(2*np.pi*sigma**2)\n",
    "    g = g_y * g_x\n",
    "    return g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def H(J,sys):\n",
    "    N = sys.shape[0]\n",
    "    energy = 0\n",
    "    for i in range(N):\n",
    "        for j in range(i):\n",
    "            energy -= J[i][j]*sys[i]*sys[j]\n",
    "    return energy\n",
    "\n",
    "# Mean Field version of dH\n",
    "def dH(J, sys, k): # k is the index of the spin flipped\n",
    "    N = sys.shape[0]\n",
    "    dh = 0\n",
    "    for i in range(N):\n",
    "        dh += sys[i]*J[k][i]\n",
    "    dh *= 2*sys[k]\n",
    "    return dh\n",
    "\n",
    "def metropolis(J, sys1, k, B): # B = 1/kbT temperature of the system\n",
    "    sys = deepcopy(sys1)\n",
    "    dh = dH(J, sys, k)\n",
    "    r = np.random.rand() # random variable between (0,1)\n",
    "    if r < np.exp( -B*dh ):\n",
    "        sys[k] = -sys[k]\n",
    "    return sys\n",
    "    \n",
    "def montecarlo(J, sys1, B, t ): # t number of iteration of the montecarlo\n",
    "    sys = deepcopy(sys1)\n",
    "    N = sys.shape[0]\n",
    "    for i in range(t):\n",
    "        k = np.random.randint(0,N)\n",
    "        sys = metropolis(J, sys, k, B)\n",
    "    return sys"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean field montecarlo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "xi = random_patterns(N,p)\n",
    "J = MF_coupling(xi,N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.000000\n",
      "The algorithm recognised the pattern 7 and the correct pattern is 7\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": [
    "idx = np.random.randint(10)\n",
    "\n",
    "sys = montecarlo(J,xi[idx], 10, 1000)\n",
    "wrong_pixels = error_im(xi[idx],sys)\n",
    "assigned_pattern = assign_pattern(xi,sys)\n",
    "\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": [
    "Stability for different temperature, $\\beta=[0,1,10,25,50,100]$ with $t=1000$ and $L=10$ fixed. <br>\n",
    "Each point $100$ iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = [0, 1, 10, 25, 50, 100]\n",
    "err_beta_mean = []\n",
    "err_beta_std = []\n",
    "success = []\n",
    "for b in beta:\n",
    "    errors = []\n",
    "    correct = 0\n",
    "    for j in range(100):\n",
    "        idx = np.random.randint(10)\n",
    "        sys = montecarlo(J,xi[idx], b, 1000)\n",
    "        wrong_pixels = error_im(xi[idx],sys)\n",
    "        assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "        if idx == assigned_pattern: correct += 1\n",
    "        errors.append(wrong_pixels) \n",
    "        \n",
    "    correct /= 100\n",
    "    errors = np.array(errors)\n",
    "    err_beta_mean.append( errors.mean() )\n",
    "    err_beta_std.append( errors.std() )\n",
    "    success.append(correct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f249cae1908>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,2,figsize=(12,6))\n",
    "\n",
    "ax[0].set_title('Errors as function of T')\n",
    "ax[0].set_xlabel('Beta [$J^{-1}$]')\n",
    "ax[0].set_ylabel('Average error')\n",
    "ax[0].plot(beta, err_beta_mean, '--bo', label='Error')\n",
    "ax[0].errorbar(beta,err_beta_mean, yerr=err_beta_std,ecolor='red', label='Fluctuation of error',fmt='none')\n",
    "ax[0].legend()\n",
    "\n",
    "ax[1].set_title('Probability of success as function of T')\n",
    "ax[1].set_xlabel('Beta [$J^{-1}$]')\n",
    "ax[1].set_ylabel('Probability of success')\n",
    "ax[1].plot(beta, success, '--ro', label='Data')\n",
    "ax[1].legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see how an high $\\beta$ lends to an high probability of success, and a $\\beta<10$ lends to totally unacceptable results.\n",
    "\n",
    "Even if the results with $\\beta>25$ seems the better results we have to think on the functioning of the algorithm: with very high beta the probability of flipping a \"wrong\" spin is $\\sim0$ and, starting from a minima, it probably means that it does not flip a spin at all. So, for the following analisys we will use $\\beta=10$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Stability w.r.t number of iterations $t=[10,25,50,100,200,500,750,1000,1250,1500,1750,2000]$ with $\\beta=[10,25]$ and $L=10$ fixed. Each point is obtained with 100 run of the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Beta = 10\n",
    "iterations=[10,25,50,100,200,500,750,1000,1250,1500,1750,2000]\n",
    "err_t_mean = []\n",
    "err_t_std = []\n",
    "success_t = []\n",
    "for t in iterations:\n",
    "    errors = []\n",
    "    correct = 0\n",
    "    for j in range(100):\n",
    "        idx = np.random.randint(10)\n",
    "        sys = montecarlo(J,xi[idx], 10, t)\n",
    "        wrong_pixels = error_im(xi[idx],sys)\n",
    "        assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "        if idx == assigned_pattern: correct += 1\n",
    "        errors.append(wrong_pixels) \n",
    "        \n",
    "    correct /= 100\n",
    "    errors = np.array(errors)\n",
    "    err_t_mean.append( errors.mean() )\n",
    "    err_t_std.append( errors.std() )\n",
    "    success_t.append(correct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# beta = 25\n",
    "err_t1_mean = []\n",
    "err_t1_std = []\n",
    "success_t1 = []\n",
    "for t in iterations:\n",
    "    errors = []\n",
    "    correct = 0\n",
    "    for j in range(100):\n",
    "        idx = np.random.randint(10)\n",
    "        sys = montecarlo(J,xi[idx], 25, t)\n",
    "        wrong_pixels = error_im(xi[idx],sys)\n",
    "        assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "        if idx == assigned_pattern: correct += 1\n",
    "        errors.append(wrong_pixels) \n",
    "        \n",
    "    correct /= 100\n",
    "    errors = np.array(errors)\n",
    "    err_t1_mean.append( errors.mean() )\n",
    "    err_t1_std.append( errors.std() )\n",
    "    success_t1.append(correct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1,2,figsize=(12,6))\n",
    "\n",
    "ax[0].set_title('Errors as function of iterations')\n",
    "ax[0].set_xlabel('Number of iteration t')\n",
    "ax[0].set_ylabel('Average error')\n",
    "ax[0].plot(iterations, err_t_mean, '--bo', label='Error with beta=10')\n",
    "ax[0].errorbar(iterations,err_t_mean, yerr=err_t_std,ecolor='blue',fmt='none')\n",
    "ax[0].plot(iterations, err_t1_mean, '--go', label='Error with beta=25')\n",
    "ax[0].errorbar(iterations,err_t1_mean, yerr=err_t1_std,ecolor='green',fmt='none')\n",
    "ax[0].legend()\n",
    "\n",
    "ax[1].set_title('Probability of success as function of the number of iterations t')\n",
    "ax[1].set_xlabel('Number of iteration t')\n",
    "ax[1].set_ylabel('Probability of success')\n",
    "ax[1].plot(iterations, success_t, '--bo', label='Data with beta=10')\n",
    "ax[1].plot(iterations, success_t1, '--go', label='Data with beta=25')\n",
    "ax[1].legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Asa we can expect the number of iterations, in this case, actually increase the error of the algorithm. It is predictable since we already start from the correct pattern and adding iterations only increase the probability of flipping some random spin. We have also choosen a $\\beta=10$, that lends to a not totally stable situation. We can repeat the experiment with $\\beta=25$ to see if there is a visible improvement.\n",
    "\n",
    "The important thing to notice that with $\\beta=10$ the error reaches a plateau, but not the probability of success.\n",
    "\n",
    "Instead with $\\beta=25$ both error and probability of success seems to reach a plateau. So in the following we will use this value of $\\beta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "errors = []\n",
    "correct = 0\n",
    "for j in range(100):\n",
    "    idx = np.random.randint(10)\n",
    "    sys = montecarlo(J,xi[idx], 10, 1000)\n",
    "    wrong_pixels = error_im(xi[idx],sys)\n",
    "    assigned_pattern = assign_pattern(xi,sys)\n",
    "    \n",
    "    if idx == assigned_pattern: correct += 1\n",
    "    errors.append(wrong_pixels) \n",
    "    \n",
    "correct /= 100\n",
    "errors = np.array(errors)\n",
    "print(correct)\n",
    "print(errors.mean())\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Corruption with uniform noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "idx = 3\n",
    "\n",
    "yi = corrupt_uniform(xi[idx], 0.35)\n",
    "\n",
    "sys = montecarlo(J,yi, 10, 100)\n",
    "wrong_pixels = error_im(xi[idx],sys)\n",
    "assigned_pattern = assign_pattern(xi,sys)\n",
    "\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 of the dependance on the temperature on the stability of the algorithm with uniformly corrupted patterns with $q=0.2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = [0, 1, 10, 25, 50, 100]\n",
    "err_beta_mean_c = []\n",
    "err_beta_std_c = []\n",
    "success_beta_c = []\n",
    "for b in beta:\n",
    "    errors = []\n",
    "    correct = 0\n",
    "    for j in range(100):\n",
    "        idx = np.random.randint(10)\n",
    "        yi = corrupt_uniform(xi[idx], 0.2)\n",
    "        sys = montecarlo(J, yi, b, 1000)\n",
    "        wrong_pixels = error_im(xi[idx],sys)\n",
    "        assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "        if idx == assigned_pattern: correct += 1\n",
    "        errors.append(wrong_pixels) \n",
    "        \n",
    "    correct /= 100\n",
    "    errors = np.array(errors)\n",
    "    err_beta_mean_c.append( errors.mean() )\n",
    "    err_beta_std_c.append( errors.std() )\n",
    "    success_beta_c.append(correct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1,2,figsize=(12,6))\n",
    "\n",
    "ax[0].set_title('Errors as function of T with uniform noise')\n",
    "ax[0].set_xlabel('Beta [$J^{-1}$]')\n",
    "ax[0].set_ylabel('Average error')\n",
    "ax[0].plot(beta, err_beta_mean_c, '--bo', label='Error')\n",
    "ax[0].errorbar(beta,err_beta_mean_c, yerr=err_beta_std_c,ecolor='red', label='Fluctuation of error',fmt='none')\n",
    "ax[0].legend()\n",
    "\n",
    "ax[1].set_title('Probability of success as function of T with uniform noise')\n",
    "ax[1].set_xlabel('Beta [$J^{-1}$]')\n",
    "ax[1].set_ylabel('Probability of success')\n",
    "ax[1].plot(beta, success_beta_c, '--ro', label='Data')\n",
    "ax[1].legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As stated above even here we can say that a good temperature for the stability of the algorithm is when $\\beta\\geq 25$,and so from now on we will use that parameter. Here the result is even more important since we don't start from a pattern but from a corrupted pattern."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Stability w.r.t number of iterations $t=[10,25,50,100,200,500,750,1000,1250,1500,1750,2000]$ with $\\beta=25$, $L=10$ fixed and $q=0.2$. Each point is obtained with 100 run of the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "iterations = [10,25,50,100,200,500,750,1000,1250,1500,1750,2000]\n",
    "err_t_mean_c = []\n",
    "err_t_std_c = []\n",
    "success_t_c = []\n",
    "for t in iterations:\n",
    "    errors = []\n",
    "    correct = 0\n",
    "    for j in range(100):\n",
    "        idx = np.random.randint(10)\n",
    "        yi = corrupt_uniform(xi[idx], 0.2)\n",
    "        sys = montecarlo(J, yi, 25, t)\n",
    "        wrong_pixels = error_im(xi[idx],sys)\n",
    "        assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "        if idx == assigned_pattern: correct += 1\n",
    "        errors.append(wrong_pixels) \n",
    "        \n",
    "    correct /= 100\n",
    "    errors = np.array(errors)\n",
    "    err_t_mean_c.append( errors.mean() )\n",
    "    err_t_std_c.append( errors.std() )\n",
    "    success_t_c.append(correct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1,2,figsize=(12,6))\n",
    "\n",
    "ax[0].set_title('Errors as function of iterations')\n",
    "ax[0].set_xlabel('Number of iteration t')\n",
    "ax[0].set_ylabel('Average error')\n",
    "ax[0].plot(iterations, err_t_mean_c, '--bo', label='Errors')\n",
    "ax[0].errorbar(iterations,err_t_mean_c, yerr=err_t_std_c, ecolor='blue',fmt='none')\n",
    "ax[0].legend()\n",
    "\n",
    "ax[1].set_title('Probability of success as function of the number of iterations t')\n",
    "ax[1].set_xlabel('Number of iteration t')\n",
    "ax[1].set_ylabel('Probability of success')\n",
    "ax[1].plot(iterations, success_t_c, '--bo', label='Data')\n",
    "ax[1].legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The behaviour is not clear and maybe it need more tries and studies, but it seem to reach an oscillatory behaviour after $t=1000$, but i think the better idea is to use $t=500$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Last but not least, we try with $t=500$, $\\beta=25$ and q = $[0.1,1]$ in steps of $0.1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob = np.linspace(0,1,10)\n",
    "err_q_mean_c = []\n",
    "err_q_std_c = []\n",
    "success_q_c = []\n",
    "for q in prob:\n",
    "    errors = []\n",
    "    correct = 0\n",
    "    for j in range(100):\n",
    "        idx = np.random.randint(10)\n",
    "        yi = corrupt_uniform(xi[idx], q)\n",
    "        sys = montecarlo(J, yi, 25, 500)\n",
    "        wrong_pixels = error_im(xi[idx],sys)\n",
    "        assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "        if idx == assigned_pattern: correct += 1\n",
    "        errors.append(wrong_pixels) \n",
    "        \n",
    "    correct /= 100\n",
    "    errors = np.array(errors)\n",
    "    err_q_mean_c.append( errors.mean() )\n",
    "    err_q_std_c.append( errors.std() )\n",
    "    success_q_c.append(correct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1,2,figsize=(12,6))\n",
    "\n",
    "ax[0].set_title('Errors as function of the flipping probability')\n",
    "ax[0].set_xlabel('Flipping probability q')\n",
    "ax[0].set_ylabel('Average error')\n",
    "ax[0].plot(prob, err_q_mean_c, '--bo', label='Errors')\n",
    "ax[0].errorbar(prob,err_q_mean_c, yerr=err_q_std_c, ecolor='blue',fmt='none')\n",
    "ax[0].legend()\n",
    "\n",
    "ax[1].set_title('Probability of success as function of the flipping probabiity')\n",
    "ax[1].set_xlabel('Flipping probability q')\n",
    "ax[1].set_ylabel('Probability of success')\n",
    "ax[1].plot(prob, success_q_c, '--bo', label='Data')\n",
    "ax[1].legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We clearly see that, even if the error is still acceptable, the maximum value of the noise that we can accept is $q=0.2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NON MEAN FIELD MONTECARLO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BIG DISCLAIMER. I ACTUALLY TRIED BOTH USING MY DEFINITION OF THE NON MEAN FIELD HERE AND THE ONE USING THE THE NON MEAN J OF THE FIRST NOTEBOOK AND THE SECOND IS COMPLETELY BETTER."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Up to now we used only the MF version, where all the spins interacts with all the other. We will now use a version where the spins interacts only within a small range, indicated with $R$. <br>\n",
    "We will not repeat the analisys of the dependance on the temperature, and so we will use $\\beta=25$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def perpendicolar_nn(J, sys, k, r):\n",
    "    dh = 0\n",
    "    l = int(np.sqrt(sys.shape[0]))\n",
    "    for i in range(k+1,k+r+1): # going right\n",
    "        if k%l == l-1: break # right bound\n",
    "        dh += J[i][k]*sys[i]\n",
    "        if i%l == l-1: break # last column bound\n",
    "            \n",
    "    for i in range(k-1,k-r-1,-1): # going left\n",
    "        if k%l == 0: break # left bound\n",
    "        dh += J[i][k]*sys[i]\n",
    "        if i%l == 0: break # first column bound\n",
    "            \n",
    "    for i in range(k+l,k+(r+1)*l,l): # going down\n",
    "        if k//l == l-1: break # low bound\n",
    "        dh += J[i][k]*sys[i]\n",
    "        if i//l ==l-1 : break # last row bound\n",
    "            \n",
    "    for i in range(k-l, k-l*(r+1), -l): # going up\n",
    "        if k//l == 0: break # up bound\n",
    "        dh += J[i][k]*sys[i]\n",
    "        if i//l == 0: break  # first row bound\n",
    "    return dh\n",
    "            \n",
    "def diagonal_nn(J, sys, k, r):\n",
    "    dh = 0\n",
    "    l = int(np.sqrt(sys.shape[0]))\n",
    "    for i in range(1,r):\n",
    "        if k%l == l-1 or k//l == l-1: break # right low bound\n",
    "        for j in range(1,r):\n",
    "            if i==j==r-1: continue\n",
    "            dh += J[k+j+i*l][k]*sys[k+j+i*l]  # right low\n",
    "            if (k+j+i*l)%l == l-1 : break # last column bound\n",
    "        if (k+j+i*l)//l ==l-1 : break # last row bound\n",
    "        \n",
    "    for i in range(1,r):\n",
    "        if k%l == 0 or k//l == l-1: break # left low bound\n",
    "        for j in range(1,r):\n",
    "            if i==j==r-1: continue\n",
    "            dh += J[k-j+i*l][k]*sys[k-j+i*l]  # left low\n",
    "            if (k-j+i*l)%l == 0 : break #  first column bound\n",
    "        if (k-j+i*l)//l ==l-1 : break # last row bound\n",
    "        \n",
    "    for i in range(1,r):\n",
    "        if k//l == 0 or k%l == l-1: break # up right bound\n",
    "        for j in range(1,r):\n",
    "            if i==j==r-1: continue\n",
    "            dh += J[k+j-i*l][k]*sys[k+j-i*l] # right up\n",
    "            if (k+j-i*l)%l == l-1: break  # last column bound\n",
    "        if (k+j-i*l)//l == 0: break # first row bound\n",
    "        \n",
    "    for i in range(1,r):\n",
    "        if k//l == 0 or k%l == 0 : break # up left bound\n",
    "        for j in range(1,r):\n",
    "            if i==j==r-1: continue\n",
    "            dh += J[k-j-i*l][k]*sys[k-j-i*l] # left up\n",
    "            if (k-j-i*l)%l == l-1: break  #last column bound\n",
    "        if (k-j-i*l)//l == 0 : break # first row bound\n",
    "    return dh\n",
    "\n",
    "def not_MF_dH(J, sys, k, R):\n",
    "    dh = perpendicolar_nn(J, sys, k, R) + diagonal_nn(J, sys, k, R)\n",
    "    dh *= 2*sys[k]\n",
    "    return dh\n",
    "\n",
    "def not_MF_metropolis(J, sys1, k, B, R): # B = 1/kbT temperature of the system\n",
    "    sys = deepcopy(sys1)\n",
    "    dh = not_MF_dH(J, sys, k, R)\n",
    "    r = np.random.rand() # random variable between (0,1)\n",
    "    if r < np.exp( -B*dh ):\n",
    "        sys[k] = -sys[k]\n",
    "    return sys\n",
    "\n",
    "def not_MF_montecarlo(J, sys1, B, R, t ): # t number of iteration of the montecarlo\n",
    "    sys = deepcopy(sys1)\n",
    "    N = sys.shape[0]\n",
    "    for i in range(t):\n",
    "        k = np.random.randint(0,N)\n",
    "        sys = not_MF_metropolis(J, sys, k, B, R)\n",
    "    return sys"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "xi = random_patterns(N,p)\n",
    "J = R_coupling(xi,N,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "idx = 3\n",
    "\n",
    "sys = not_MF_montecarlo(J,xi[idx], 25, 3, 1000)\n",
    "wrong_pixels = error_im(xi[idx],sys)\n",
    "assigned_pattern = assign_pattern(xi,sys)\n",
    "\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": [
    "Stability in function of the number of neighbors, R = [1,2,3,4,5] and two different number of iteration, t=[500,1000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "R = [1, 2, 3, 4, 5]\n",
    "err_r_mean_c = []\n",
    "err_r_std_c = []\n",
    "success_r_c = []\n",
    "for r in R:\n",
    "    J = R_coupling(xi,N,r)\n",
    "    errors = []\n",
    "    correct = 0\n",
    "    for j in range(100):\n",
    "        idx = np.random.randint(10)\n",
    "        sys = montecarlo(J, xi[idx], 25, 500)\n",
    "        wrong_pixels = error_im(xi[idx],sys)\n",
    "        assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "        if idx == assigned_pattern: correct += 1\n",
    "        errors.append(wrong_pixels) \n",
    "        \n",
    "    correct /= 100\n",
    "    errors = np.array(errors)\n",
    "    err_r_mean_c.append( errors.mean() )\n",
    "    err_r_std_c.append( errors.std() )\n",
    "    success_r_c.append(correct)\n",
    "    \n",
    "err_r1_mean_c = []\n",
    "err_r1_std_c = []\n",
    "success_r1_c = []\n",
    "for r in R:\n",
    "    J = R_coupling(xi,N,r)\n",
    "    errors = []\n",
    "    correct = 0\n",
    "    for j in range(100):\n",
    "        idx = np.random.randint(10)\n",
    "        sys = montecarlo(J, xi[idx], 25, 1000)\n",
    "        wrong_pixels = error_im(xi[idx],sys)\n",
    "        assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "        if idx == assigned_pattern: correct += 1\n",
    "        errors.append(wrong_pixels) \n",
    "        \n",
    "    correct /= 100\n",
    "    errors = np.array(errors)\n",
    "    err_r1_mean_c.append( errors.mean() )\n",
    "    err_r1_std_c.append( errors.std() )\n",
    "    success_r1_c.append(correct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1,2,figsize=(12,6))\n",
    "\n",
    "ax[0].set_title('Errors as function of nearest neighbors')\n",
    "ax[0].set_xlabel('Number of nearest neighbors R')\n",
    "ax[0].set_ylabel('Average error')\n",
    "ax[0].plot(R, err_r_mean_c, '--bo', label='Error with t=500')\n",
    "ax[0].errorbar(R,err_r_mean_c, yerr=err_r_std_c,ecolor='blue',fmt='none')\n",
    "ax[0].plot(R, err_r1_mean_c, '--go', label='Error with t=1000')\n",
    "ax[0].errorbar(R,err_r1_mean_c, yerr=err_r1_std_c,ecolor='green',fmt='none')\n",
    "ax[0].legend()\n",
    "\n",
    "ax[1].set_title('Probability of success as function of nearest neighbors')\n",
    "ax[1].set_xlabel('Number of nearest neighbors R')\n",
    "ax[1].set_ylabel('Probability of success')\n",
    "ax[1].plot(R, success_r_c, '--bo', label='Data with t=500')\n",
    "ax[1].plot(R, success_r1_c, '--go', label='Data with t=1000')\n",
    "ax[1].legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Increasing the number of nn the performances of the algorithm increases, as we can expect, and it goes to the MF.\n",
    "\n",
    "Actually the error and the probability of success with $R=5$ is better than the mean field value. Another important thing to notice is that the algorithm for different t converge to the same value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Corruption"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will see now how the noise affect the performances of the non mean field montecarlo. This analisys is very interesting because we will see the different behaviour between gaussian and uniform noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The error of the algorithm is 0.430000\n",
      "The algorithm recognised the pattern 4 and the correct pattern is 3\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkkAAAEtCAYAAAAcDfTlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAWQUlEQVR4nO3de7Ctd1kf8O9DDiEkAYImxeYCSUXBlKnC2VIuFZVQhygI7Tg1CCiMNNbKtVoK1iKdKkw7CGJhbJGLWpCLgTIUuelwsbQjck4SRnIBQ8g9yAkIhIiNkad/rHVw5/A75+zbuux1Pp+ZM3PWu9/1ruf3rrWe/V2/993rre4OAAB3dpdFFwAAsIyEJACAASEJAGBASAIAGBCSAAAGhCQAgAEhCYA7qar7VtVXq+q4nVq3qp5WVR89ws/fW1U/tZV6F6GqHlBVl1bVrVX17Kr6b1X1HxZd10G7bX8uqz2LLoDFqKprktwnyd8muS3Je5M8s7u/eoT7/ECSN3b3meuWvTjJ/bv7KbOsF9h5h/SBg76zu69LcvJGtrGZdY+ynfO3u405e36SD3X39yy6kFEf3oX7cymZSTq2Pb67T07ykCRrSX5p3gVUlaAOi/X47j553b+bFl3QLnG/JJfN+kH0yMUSkkh335jJTNKDqurpVXXFdAr56qr6mSSpqpOm65w+nVr/alX9RJJfTPLj09ufmK57r6p6XVXdXFU3VtWvHJyKn065/5+qekVVfSHJiw9Ow1fVy6rqL6vqs1XlUxAsSFWdXVV98Bd0VX24qv7T9L17a1V9oKpOPcy6T5v2jlun7+UnH7Lt4ft8+hjPWLeNw/aEqjqnqv54+hh/VFWvrqo3HmE8T5geGvtKVX2mqh47XX56Vb2rqr5YVVdV1b9cd58XV9Xbqup3p49zWVWtTX/2wSQ/mORV0973nVX121X1K+vu//xpD7ypqp4x3Uf3P3Ss68e77nZX1c9V1Z8n+fPpsldW1fXTMeyvqu+bLn9sxn14/f68S1X9UlVdW1Wfn47pXoc8fz9VVddV1S1V9e+P+iI5RghJpKrOSvLDSS5J8vkkj0tyzyRPT/KKqnpId9+W5PwkN637xPl7SV6S5K3T29893eRvJ7kjyf2TPDjJDyV5xrqH/MdJrs5kmv9X1y37VJJTk/yXJK+rqprRkIHN+4lMesLfS3J8kl84dIXph6nfSHJ+d98jySOSXLpulc28z4+07u8l+dMk35rkxUmeeriiq+qhSX43yb9NckqSRyW5ZvrjtyS5IcnpSX4syUuq6tHr7v6j03VOSfKuJK9Kku5+dJL/nckpCid396cPeczHJvk3SR6TSR/8gcPVdwRPzGQfnDu9/fEk35PkWzIZ/+9X1Qnd/b6M+/B6T5v++8Ek/yCTw6OvOmSdf5LkAUnOS/KiqvquLdS8coSkY9s7q+pLST6a5CNJXtLdf9Ddn+mJjyT5QJLv2+gGq+o+mQSu53b3bd39+SSvSHLButVu6u7/2t13dPfXpsuu7e7f6u6/TfI7Sf5+JiEKmK13VtWXpv/eeYT13tDdn56+Z9+WyS/ska9nMit99+6+ubvXH5LazPt8uG5V3TfJ9yZ5UXff3t0fzSTAHM5PJ3l9d/9hd3+9u2/s7iunHw4fmeTfdfdfd/elSV6b5CfX3fej3f2eaQ3/I8kogIz8i0z212Xd/VeZBLnNeml3f/Fgj+zuN3b3F6Z989eS3C2TULMRT07y8u6+enre6QuTXFB3PpT3H7v7a939iSSfyMbHutKEpGPbE7v7lO6+X3f/6+7+WlWdX1V/Mp1+/lImgefUTWzzfknumuTmg403yX/P5NPnQdcP7ve5g/+ZNpVkB04GBY7qYB84pbufeIT1Prfu/3+VwftzOuP840n+VSY94A+q6oGjbWzgfX64dU9P8sV1y5JxTznorCSfGSw/uJ1b1y27NskZoxoyGfMJtbFzhE4/pKYj1Xc4d7pPVf1CTU6F+PK0r94rG+/Np2cytoOuzeQPt9YH1KM+v8ciIYlvqKq7JXl7kpcluU93n5LkPUkOTnH34G6HLrs+yf9Lcuq6xnvP7v6HR7gPsCK6+/3d/U8zmfm5Mslv7fBD3JzkW6rqxHXLzjrC+tcn+fbB8pum27nHumX3TXLj9kvMzUnOXHf70PpuS7K+/m8bbOMbfXJ6/tHzM5mhuve0N385R+7N692UyQfYg+6bySkRf3GU+x3zhCTWOz6TKdwDSe6Ynij5Q+t+/hdJvvXgCX/rlp1dVXdJku6+OZNDdL9WVfecnjD47VX1/fMZArAoVXWf6UnSJ2XyYemrmRx+2zHdfW2SfZn80cfxVfXwJI8/wl1el+TpVXXetB+dUVUP7O7rk/zfJC+tqhOq6h9lcmjusCeAb8Lbpo/5XdMwd+j3J12a5J9X1YnTk7l/+ijbu0cmoeZAkj1V9aJMzhs96E59eODNSZ5XkxPeT87fncN0x+aGdewRkviG6bTzszN5g/9lJidqvmvdz6/M5M129fRQ2ulJfn/64y9U1cXT//9kJoHr8ul2LsrkUyWw2u6SyQnLNyX5YpLvT/KzM3icJyd5eJIvJPmVJG/NJJR9k+7+00z/CCWT2ZeP5O9mVZ6U5Oxpvf8zyS939x9tt7jufm8mJ7B/KMlVSf5k+qODNb4iye2ZhJvfSfKmo2zy/Unel+TTmRwq++vc+XDcqA+v9/pMzqn64ySfnd7/WRsf0bGruh35AGD3qqq3Jrmyu3950bWMTP9S7JNJ7mb2ZncxkwTArlJV3zs9jH+X6Z/bPyHJkf4yb+6q6p9V1d2q6t5J/nOS/yUg7T5CEgC7zbcl+XAm5zz9RpKf7e5LFlrRN/uZTL537jOZXPZlFocdmTGH2wAABswkAQAMCEkAAAMzubrwqaee2mefffYsNv0N+/fvn+n2D9q7d+9cHmce5rHPVml/zcOqvI6vueaa3HLLLStxrT39a3PmNZZVMa8eqd9vzv79+2/p7tMOXT6Tc5LW1tZ63759O77d9eZ17dNVOmdrHvtslfbXPKzK63htbS379u1biZCkf22O61Bvzrx6pH6/OVW1v7vXDl3ucBsAwICQBAAwICQBAAwISQAAA0ISAMCAkAQAMCAkAQAMbCgkVdVjq+pTVXVVVb1g1kUB7BT9C9iqo4akqjouyauTnJ/k3CRPqqpzZ10YwHbpX8B2bGQm6aFJruruq7v79iRvSfKE2ZYFsCP0L2DLNhKSzkhy/brbN0yXASw7/QvYsh07cbuqLqyqfVW178CBAzu1WYCZ07+AkY2EpBuTnLXu9pnTZXfS3a/p7rXuXjvttG+6kC7AIuhfwJZtJCR9PMl3VNU5VXV8kguSvGu2ZQHsCP0L2LI9R1uhu++oqmcmeX+S45K8vrsvm3llANukfwHbcdSQlCTd/Z4k75lxLQA7Tv8Ctso3bgMADAhJAAADQhIAwICQBAAwICQBAAwISQAAA0ISAMDAhr4nabP279+fqprFplfSvPZVd8/lcVaF1/CxSf/anHn1lVV5TlZlHMlqjeVwzCQBAAwISQAAA0ISAMCAkAQAMCAkAQAMCEkAAANCEgDAgJAEADAgJAEADAhJAAADQhIAwICQBAAwICQBAAwISQAAA0ISAMCAkAQAMCAkAQAMCEkAAANCEgDAgJAEADAgJAEADAhJAAADQhIAwICQBAAwICQBAAzsWXQBy66qFl3CrjKP/dXdM3+MVeN1fGxapffjPB5nlfbXKllk/zKTBAAwICQBAAwISQAAA0ISAMCAkAQAMCAkAQAMCEkAAANCEgDAwFFDUlWdVVUfqqrLq+qyqnrOPAoD2C79C9iOjXzj9h1Jfr67L66qeyTZX1V/2N2Xz7g2gO3Sv4AtO+pMUnff3N0XT/9/a5Irkpwx68IAtkv/ArZjU+ckVdXZSR6c5GOzKAZgVvQvYLM2fIHbqjo5yduTPLe7vzL4+YVJLtzB2gB2hP4FbEVt5IrEVXXXJO9O8v7ufvkG1neZ4yXkKtqbs8grT+9G3b2UO0z/mq1Vuqr9KvWvVTKnXry/u9cOXbiRv26rJK9LcsVGGgzAstC/gO3YyDlJj0zy1CSPrqpLp/9+eMZ1AewE/QvYsqOek9TdH02ylNPoAEeifwHb4Ru3AQAGhCQAgAEhCQBgQEgCABgQkgAABoQkAIABIQkAYGDD127bjL1792bfvn2z2PTcuTTF8vGcbN6sL4WwtvZN3+bPEazSpSnm9X5clX22Sv1rVZ6TIzGTBAAwICQBAAwISQAAA0ISAMCAkAQAMCAkAQAMCEkAAANCEgDAgJAEADAgJAEADAhJAAADQhIAwICQBAAwICQBAAwISQAAA0ISAMCAkAQAMCAkAQAMCEkAAANCEgDAgJAEADAgJAEADAhJAAADQhIAwICQBAAwUN298xut2vmNLsgs9s+hqmrmj5HMZyxszrye+3no7pUYzNraWu/bt2/RZeyIVXp9sTl+d21OVe3v7rVDl5tJAgAYEJIAAAaEJACAASEJAGBASAIAGBCSAAAGhCQAgIENh6SqOq6qLqmqd8+yIICdpn8BW7GZmaTnJLliVoUAzJD+BWzahkJSVZ2Z5EeSvHa25QDsLP0L2KqNziT9epLnJ/n6DGsBmAX9C9iSo4akqnpcks939/6jrHdhVe2rqtW46BGw622lfx04cGBO1QHL7qgXuK2qlyZ5apI7kpyQ5J5J3tHdTznCfVbmSqouEsgsrdIFSJfxArdb6V8ucMsq8Ltrc7Z8gdvufmF3n9ndZye5IMkHj9RgAJaF/gVsh+9JAgAY2LOZlbv7w0k+PJNKAGZI/wI2y0wSAMCAkAQAMCAkAQAMCEkAAANCEgDAgJAEADAgJAEADAhJAAADm/oyyY3au3dvZn3to1W6JtG8rqm2KvvMNeg2b9b7bG3tmy55xBGsynsx8X5ktZlJAgAYEJIAAAaEJACAASEJAGBASAIAGBCSAAAGhCQAgAEhCQBgQEgCABgQkgAABoQkAIABIQkAYEBIAgAYEJIAAAaEJACAASEJAGBASAIAGBCSAAAGhCQAgAEhCQBgQEgCABgQkgAABoQkAIABIQkAYGDPogsgqapFl7BjunvRJeyYVXpe2Lj9+/evzHO/Su/HVbEqr615WuQ+M5MEADAgJAEADAhJAAADQhIAwICQBAAwICQBAAwISQAAA0ISAMDAhkJSVZ1SVRdV1ZVVdUVVPXzWhQHsBP0L2KqNfuP2K5O8r7t/rKqOT3LiDGsC2En6F7AlRw1JVXWvJI9K8rQk6e7bk9w+27IAtk//ArZjI4fbzklyIMkbquqSqnptVZ0047oAdoL+BWzZRkLSniQPSfKb3f3gJLclecGhK1XVhVW1r6r2HThwYIfLBNiSTfeveRcILK+NhKQbktzQ3R+b3r4ok6ZzJ939mu5e6+610047bSdrBNiqTfevuVYHLLWjhqTu/lyS66vqAdNF5yW5fKZVAewA/QvYjo3+dduzkrxp+pchVyd5+uxKAthR+hewJRsKSd19aRLT0MCuo38BW+UbtwEABoQkAIABIQkAYEBIAgAYEJIAAAaEJACAASEJAGBASAIAGNjoN25vyv79+1NVs9j0N3T3TLd/0KzHMU/z2GertL/mYV6vY5aL/rV5q9K/vOc3b5GvYzNJAAADQhIAwICQBAAwICQBAAwISQAAA0ISAMCAkAQAMCAkAQAMCEkAAANCEgDAgJAEADAgJAEADAhJAAADQhIAwICQBAAwICQBAAwISQAAA0ISAMCAkAQAMCAkAQAMCEkAAANCEgDAgJAEADAgJAEADOxZdAFbVVVzeZzunsvjzMO89hnLx3PPrMyrR87jNazfb84q7a/DMZMEADAgJAEADAhJAAADQhIAwICQBAAwICQBAAwISQAAA0ISAMDAhkJSVT2vqi6rqk9W1Zur6oRZFwawE/QvYKuOGpKq6owkz06y1t0PSnJckgtmXRjAdulfwHZs9HDbniR3r6o9SU5MctPsSgLYUfoXsCVHDUndfWOSlyW5LsnNSb7c3R+YdWEA26V/AduxkcNt907yhCTnJDk9yUlV9ZTBehdW1b6q2rfzZQJsnv4FbMdGDrc9Jslnu/tAd/9NknckecShK3X3a7p7rbvXdrpIgC3Sv4At20hIui7Jw6rqxKqqJOcluWK2ZQHsCP0L2LKNnJP0sSQXJbk4yZ9N7/OaGdcFsG36F7Ad1d07v9Gqnd/ogsxi/yzK5IM0y2Rer695PPfdvRIvsHn0rxV73mf+GMlqjWUeVml/zel31/7R4XbfuA0AMCAkAQAMCEkAAANCEgDAgJAEADAgJAEADAhJAAADQhIAwMCeWWx079692bfPdSI3ypc8bs6KfYHZXMx6n62trc4lz/Qv2JhV6pGHYyYJAGBASAIAGBCSAAAGhCQAgAEhCQBgQEgCABgQkgAABoQkAIABIQkAYEBIAgAYEJIAAAaEJACAASEJAGBASAIAGBCSAAAGhCQAgAEhCQBgQEgCABgQkgAABoQkAIABIQkAYEBIAgAYEJIAAAaEJACAgerund9o1YEk127iLqcmuWXHC1kMY1k+qzKOZHnHcr/uPm3RReyELfSvZHmfl81alXEkxrKslnUswx42k5C0WVW1r7vXFl3HTjCW5bMq40hWayyrZFWel1UZR2Isy2q3jcXhNgCAASEJAGBgWULSaxZdwA4yluWzKuNIVmssq2RVnpdVGUdiLMtqV41lKc5JAgBYNssykwQAsFQWHpKq6rFV9amquqqqXrDoeraqqs6qqg9V1eVVdVlVPWfRNW1HVR1XVZdU1bsXXct2VNUpVXVRVV1ZVVdU1cMXXdNWVdXzpq+tT1bVm6vqhEXXdKzTv5aT/rV8dmv/WmhIqqrjkrw6yflJzk3ypKo6d5E1bcMdSX6+u89N8rAkP7eLx5Ikz0lyxaKL2AGvTPK+7n5gku/OLh1TVZ2R5NlJ1rr7QUmOS3LBYqs6tulfS03/WiK7uX8teibpoUmu6u6ru/v2JG9J8oQF17Ql3X1zd188/f+tmbyYz1hsVVtTVWcm+ZEkr110LdtRVfdK8qgkr0uS7r69u7+02Kq2ZU+Su1fVniQnJrlpwfUc6/SvJaR/La1d2b8WHZLOSHL9uts3ZJe+MderqrOTPDjJxxZbyZb9epLnJ/n6ogvZpnOSHEjyhunU+2ur6qRFF7UV3X1jkpcluS7JzUm+3N0fWGxVxzz9aznpX0tmN/evRYeklVNVJyd5e5LndvdXFl3PZlXV45J8vrv3L7qWHbAnyUOS/GZ3PzjJbUl25XkjVXXvTGYpzklyepKTquopi62KVaN/LRX9awksOiTdmOSsdbfPnC7blarqrpk0mDd19zsWXc8WPTLJj1bVNZkcPnh0Vb1xsSVt2Q1Jbujug5+IL8qk6exGj0ny2e4+0N1/k+QdSR6x4JqOdfrX8tG/ltOu7V+LDkkfT/IdVXVOVR2fyYlc71pwTVtSVZXJseMruvvli65nq7r7hd19Znefncnz8cHu3hWJ/1Dd/bkk11fVA6aLzkty+QJL2o7rkjysqk6cvtbOyy49iXOF6F9LRv9aWru2f+1Z5IN39x1V9cwk78/kbPfXd/dli6xpGx6Z5KlJ/qyqLp0u+8Xufs8CayJ5VpI3TX+JXZ3k6QuuZ0u6+2NVdVGSizP5S6RLssu+uXbV6F/Mgf61YL5xGwBgYNGH2wAAlpKQBAAwICQBAAwISQAAA0ISAMCAkAQAMCAkAQAMCEkAAAP/Hxy/bRJaG/ywAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = 3\n",
    "yi = corrupt_uniform(xi[idx], 0.35)\n",
    "\n",
    "sys = not_MF_montecarlo(J,yi, 100, 100)\n",
    "\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": [
    "Uniform noise, we will analyse different probabilities $q$ with $\\beta=25$, $R=[3,5]$ and $t=1000$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "xi = random_patterns(N,p)\n",
    "prob = np.linspace(0,1,10)\n",
    "err_rq_mean_c = []\n",
    "err_rq_std_c = []\n",
    "success_rq_c = []\n",
    "for q in prob:\n",
    "    J = R_coupling(xi,N,3)\n",
    "    errors = []\n",
    "    correct = 0\n",
    "    for j in range(100):\n",
    "        idx = np.random.randint(10)\n",
    "        yi = corrupt_uniform(xi[idx], q)\n",
    "        sys = montecarlo(J, yi, 25, 1000)\n",
    "        wrong_pixels = error_im(xi[idx],sys)\n",
    "        assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "        if idx == assigned_pattern: correct += 1\n",
    "        errors.append(wrong_pixels) \n",
    "        \n",
    "    correct /= 100\n",
    "    errors = np.array(errors)\n",
    "    err_rq_mean_c.append( errors.mean() )\n",
    "    err_rq_std_c.append( errors.std() )\n",
    "    success_rq_c.append(correct)\n",
    "    \n",
    "err_rq1_mean_c = []\n",
    "err_rq1_std_c = []\n",
    "success_rq1_c = []\n",
    "for q in prob:\n",
    "    J = R_coupling(xi,N,5)\n",
    "    errors = []\n",
    "    correct = 0\n",
    "    for j in range(100):\n",
    "        idx = np.random.randint(10)\n",
    "        yi = corrupt_uniform(xi[idx], q)\n",
    "        sys = montecarlo(J, yi, 25, 1000)\n",
    "        wrong_pixels = error_im(xi[idx],sys)\n",
    "        assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "        if idx == assigned_pattern: correct += 1\n",
    "        errors.append(wrong_pixels) \n",
    "        \n",
    "    correct /= 100\n",
    "    errors = np.array(errors)\n",
    "    err_rq1_mean_c.append( errors.mean() )\n",
    "    err_rq1_std_c.append( errors.std() )\n",
    "    success_rq1_c.append(correct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11a0475c0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,2,figsize=(12,6))\n",
    "\n",
    "ax[0].set_title('Errors as function of flipping probability')\n",
    "ax[0].set_xlabel('Flipping probability q')\n",
    "ax[0].set_ylabel('Average error')\n",
    "ax[0].plot(prob, err_rq_mean_c, '--bo', label='Error with R=3')\n",
    "ax[0].errorbar(prob,err_rq_mean_c, yerr=err_rq_std_c,ecolor='blue',fmt='none')\n",
    "ax[0].plot(prob, err_rq1_mean_c, '--go', label='Error with R=5')\n",
    "ax[0].errorbar(prob,err_rq1_mean_c, yerr=err_rq1_std_c,ecolor='green',fmt='none')\n",
    "ax[0].legend()\n",
    "\n",
    "ax[1].set_title('Probability of success as function of flipping probability')\n",
    "ax[1].set_xlabel('Flipping probability q')\n",
    "ax[1].set_ylabel('Probability of success')\n",
    "ax[1].plot(prob, success_rq_c, '--bo', label='Data with R=3')\n",
    "ax[1].plot(prob, success_rq1_c, '--go', label='Data with R=5')\n",
    "ax[1].legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is nothing really interesting in these plots: the behaviour is similar to the one of the MF, but I stress again that this gives better results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Gaussian noise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by $\\beta=25$, $R=[3,5]$, $h=0.2$ and the different centroids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "xi = random_patterns(N,p)\n",
    "centroids = [np.array([0,0]), np.array([0,L-1]), np.array([L-1,0]), np.array([L-1,L-1]), np.array([L//2, L//2])]\n",
    "err_rn_mean_c = []\n",
    "err_rn_std_c = []\n",
    "success_rn_c = []\n",
    "for k in centroids:\n",
    "    J = R_coupling(xi,N,5)\n",
    "    errors = []\n",
    "    correct = 0\n",
    "    for j in range(100):\n",
    "        idx = np.random.randint(10)\n",
    "        yi = corrupt_norm(xi[idx], k, 0.2)\n",
    "        sys = montecarlo(J, yi, 25, 1000)\n",
    "        wrong_pixels = error_im(xi[idx],sys)\n",
    "        assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "        if idx == assigned_pattern: correct += 1\n",
    "        errors.append(wrong_pixels) \n",
    "        \n",
    "    correct /= 100\n",
    "    errors = np.array(errors)\n",
    "    err_rn_mean_c.append( errors.mean() )\n",
    "    err_rn_std_c.append( errors.std() )\n",
    "    success_rn_c.append(correct)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11cfe6048>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(5)\n",
    "fig, ax = plt.subplots(1,2,figsize=(12,6))\n",
    "\n",
    "ax[0].set_title('Errors as function of the position of the centroid')\n",
    "ax[0].set_xlabel('Position of the centroid')\n",
    "ax[0].set_xticks(x)\n",
    "ax[0].set_xticklabels(['[0,0]','[0,L-1]','[L-1,0]','[L-1,L-1]','L/2,L/2'])\n",
    "ax[0].set_ylabel('Average error')\n",
    "ax[0].plot( x, err_rn_mean_c, '--bo', label='Error')\n",
    "ax[0].errorbar(x, err_rn_mean_c, yerr=err_rn_std_c,ecolor='blue',fmt='none')\n",
    "ax[0].legend()\n",
    "\n",
    "ax[1].set_title('Probability of success as function of flipping probability')\n",
    "ax[1].set_xlabel('Position of the centroid')\n",
    "ax[1].set_xticks(x)\n",
    "ax[1].set_xticklabels(['[0,0]','[0,L-1]','[L-1,0]','[L-1,L-1]','L/2,L/2'])\n",
    "ax[1].set_ylabel('Probability of success')\n",
    "ax[1].plot( x, success_rn_c, '--bo', label='Data')\n",
    "ax[1].legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see how the position of the centroid doesn't affect too much the error. The amazing thing is how well the algorithm is able to recover the correct pattern with gaussian noise. <br>\n",
    "We will look now at how much probability the system can bear."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Same as above, but with centroids in a corner and in the middle but different heights of the gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "xi = random_patterns(N,p)\n",
    "heights = np.linspace(0,1,10)\n",
    "err_rh_mean_c = []\n",
    "err_rh_std_c = []\n",
    "success_rh_c = []\n",
    "for h in heights:\n",
    "    J = R_coupling(xi,N,5)\n",
    "    errors = []\n",
    "    correct = 0\n",
    "    for j in range(100):\n",
    "        idx = np.random.randint(10)\n",
    "        yi = corrupt_norm(xi[idx], np.array([0,0]), h)\n",
    "        sys = montecarlo(J, yi, 25, 1000)\n",
    "        wrong_pixels = error_im(xi[idx],sys)\n",
    "        assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "        if idx == assigned_pattern: correct += 1\n",
    "        errors.append(wrong_pixels) \n",
    "        \n",
    "    correct /= 100\n",
    "    errors = np.array(errors)\n",
    "    err_rh_mean_c.append( errors.mean() )\n",
    "    err_rh_std_c.append( errors.std() )\n",
    "    success_rh_c.append(correct)\n",
    "    \n",
    "err_rh1_mean_c = []\n",
    "err_rh1_std_c = []\n",
    "success_rh1_c = []\n",
    "for h in heights:\n",
    "    J = R_coupling(xi,N,5)\n",
    "    errors = []\n",
    "    correct = 0\n",
    "    for j in range(100):\n",
    "        idx = np.random.randint(10)\n",
    "        yi = corrupt_norm(xi[idx], np.array([L//2, L//2]), h)\n",
    "        sys = montecarlo(J, yi, 25, 1000)\n",
    "        wrong_pixels = error_im(xi[idx],sys)\n",
    "        assigned_pattern = assign_pattern(xi,sys)\n",
    "\n",
    "        if idx == assigned_pattern: correct += 1\n",
    "        errors.append(wrong_pixels) \n",
    "        \n",
    "    correct /= 100\n",
    "    errors = np.array(errors)\n",
    "    err_rh1_mean_c.append( errors.mean() )\n",
    "    err_rh1_std_c.append( errors.std() )\n",
    "    success_rh1_c.append(correct)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x152a0afaa90>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,2,figsize=(12,6))\n",
    "\n",
    "ax[0].set_title('Errors as function of the height of the gaussian')\n",
    "ax[0].set_xlabel('Gaussian height h')\n",
    "ax[0].set_ylabel('Average error')\n",
    "ax[0].plot(heights, err_rh_mean_c, '--bo', label='Error with centroid in [0,0]')\n",
    "ax[0].errorbar(heights,err_rh_mean_c, yerr=err_rh_std_c,ecolor='blue',fmt='none')\n",
    "ax[0].plot(heights, err_rh1_mean_c, '--go', label='Error with centroid in [L/2,L/2]')\n",
    "ax[0].errorbar(heights,err_rh1_mean_c, yerr=err_rh1_std_c,ecolor='green',fmt='none')\n",
    "ax[0].legend(loc='upper left')\n",
    "\n",
    "ax[1].set_title('Probability of success as function of the height of the gaussian')\n",
    "ax[1].set_xlabel('Gaussian height h')\n",
    "ax[1].set_ylabel('Probability of success')\n",
    "ax[1].plot(heights, success_rh_c, '--bo', label='Data with centroid in [0,0]')\n",
    "ax[1].plot(heights, success_rh1_c, '--go', label='Data with centroid in [L/2,L/2]')\n",
    "ax[1].legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Very very nice data for more than the MF one. Add some better comment but fine to me.\n",
    "\n",
    "Notice that also flipping the center of the image with probability 1 there is still a 60% of probability of recognising the correct pattern."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time analisys"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The aim of this section is to quantify the time implementation of the Montecarlo methods, both MF and not MF, in function of the size of the system N."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time as tm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# I didn't run this cell but it is the very last thing to do\n",
    "lenght = np.array([5, 10, 15, 20, 25, 28, 30])\n",
    "size = lenght**2\n",
    "time_n_mean = []\n",
    "time_n_std = []\n",
    "for n in size:\n",
    "    xi = random_patterns(n,p)\n",
    "    J =  MF_coupling(xi,n)\n",
    "    time = []\n",
    "    for j in range(100):\n",
    "        start = tm.time()\n",
    "        idx = np.random.randint(10)\n",
    "        sys = not_MF_montecarlo(J, xi[idx], 25, 5, 1000)\n",
    "        end = tm.time()\n",
    "        time.append(end-start)\n",
    "        \n",
    "    time = np.array(time)\n",
    "    time_n_mean.append( time.mean() )\n",
    "    time_n_std.append( time.std() )\n",
    "    \n",
    "    \n",
    "time_n1_mean = []\n",
    "time_n1_std = []\n",
    "for n in size:\n",
    "    xi = random_patterns(n,p)\n",
    "    J =  MF_coupling(xi,n)\n",
    "    time = []\n",
    "    for j in range(100):\n",
    "        start = tm.time()\n",
    "        idx = np.random.randint(10)\n",
    "        sys = montecarlo(J, xi[idx], 25, 1000)\n",
    "        end = tm.time()\n",
    "        time.append(end-start)\n",
    "        \n",
    "    time = np.array(time)\n",
    "    time_n1_mean.append( time.mean() )\n",
    "    time_n1_std.append( time.std() )\n",
    "    \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1132cf278>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,6))\n",
    "\n",
    "ax.set_title('Time implementation as function of the size of the system')\n",
    "ax.set_xlabel('Size of the system L')\n",
    "ax.set_ylabel('Average time implementation')\n",
    "ax.plot(lenght, time_n_mean, '--bo', label='Non-MF montecarlo')\n",
    "ax.errorbar(lenght,time_n_mean, yerr=time_n_std,ecolor='blue',fmt='none')\n",
    "ax.plot(lenght, time_n1_mean, '--go', label='MF montecarlo')\n",
    "ax.errorbar(lenght,time_n1_mean, yerr= time_n1_std,ecolor='green',fmt='none')\n",
    "ax.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the exponential behaviour in time of the MF montecarlo, and the strange behaviour of the non MF one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ---------------------------- The end -----------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": [
    "# 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",
    "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",
    "                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-18.139999999999954\n",
      "-18.139999999999954\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",
      "-54.22000000000012\n",
      "-54.22000000000012\n"
     ]
    },
    {
     "data": {
      "image/png": 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IXpZW2LJBW1VXAccClwMbgBuq6oz545IcnuTsJGdPv0xJW8pelvoxydTxXYFDgL2B1cCOSZ47f1xVHVdVa6pqzfTLlLSl7GWpH5NMHT8BuLSqrq2qXwOfAh7ZtixJDdjLUg8mCdrLgYcn2SFJgAOBdW3LktSAvSz1YJJjtGcBpwLnAN/ubnNc47okTZm9LPUjVTX9lSZTXWmLGqXNMdoRnJ6qmu4Kp8xe1tZq2r0MrF3svAY/GUqSpIYMWkmSGjJoJUlqyKCVJKkhg1aSpIZW9V3AJBqcHSapB/ayfhu5RytJUkMGrSRJDRm0kiQ1ZNBKktSQQStJUkMGrSRJDRm0kiQ1ZNBKktSQQStJUkMGrSRJDRm0kiQ1ZNBKktSQQStJUkMGrSRJDRm0kiQ1ZNBKktSQQStJUkMGrSRJDRm0kiQ1tKrRen8EXDbBuF27sUM19Ppg+DUOvT7or8Y9e7jPTbW19DIMv8ah1wfWuJRF+zlVtZKFbHznydlVtaa3ApYx9Ppg+DUOvT6YjRqHbhaew6HXOPT6wBo3l1PHkiQ1ZNBKktRQ30F7XM/3v5yh1wfDr3Ho9cFs1Dh0s/AcDr3GodcH1rhZej1GK0nS1q7vPVpJkrZqvQRtkoOSfDfJRUle20cNS0myR5IvJ1mX5Pwkr+i7poUk2TbJuUk+03ctC0myS5JTk1zYPZeP6Lum+ZK8qvsbfyfJyUm277umWTPkfp6VXgb7eUsNuZdXPGiTbAu8DzgY2Bd4VpJ9V7qOZdwCHFVVDwIeDrxsgDUCvAJY13cRS3g38IWqeiDwEAZWa5LdgCOBNVX1YGBb4NB+q5otM9DPs9LLYD9vtqH3ch97tA8DLqqqS6rqZuAU4JAe6lhUVW2oqnO6329k9ILard+qNpZkd+DJwPF917KQJDsDjwVOAKiqm6vq+n6rWtAq4E5JVgE7AOt7rmfWDLqfZ6GXwX6eksH2ch9BuxtwxdjlKxngC39Okr2A/YCz+q3kdt4FHA3c2nchi7gPcC3woW467PgkO/Zd1Liqugo4Frgc2ADcUFVn9FvVzJmZfh5wL4P9vEWG3st9BG0WWDbIU5+T7AR8EnhlVf2073rmJHkKcE1Vre27liWsAvYH3l9V+wE3AUM7fndXRntfewOrgR2TPLffqmbOTPTzUHsZ7OdpGHov9xG0VwJ7jF3enQHt4s9JcgdGjXlSVX2q73rmeRTwtCQ/YDRVd0CSE/st6XauBK6sqrm9h1MZNeqQPAG4tKqurapfA58CHtlzTbNm8P088F4G+3kaBt3LfQTtN4H7J9k7yXaMDlif1kMdi0oSRsci1lXVO/quZ76qel1V7V5VezF6/r5UVYN59wZQVVcDVyTZp1t0IHBBjyUt5HLg4Ul26P7mBzKgEzxmxKD7eei9DPbzlAy6l1t9e8+iquqWJC8HTmd0ZtgHq+r8la5jGY8Cngd8O8l53bLXV9XneqxpFh0BnNRtgC8BDuu5no1U1VlJTgXOYXR26rkM8FNlhmwG+tlenp7B9vPQe9lPhpIkqSE/GUqSpIYMWkmSGjJoJUlqyKCVJKkhg1aSpIYMWkmSGjJoJUlqyKCVJKmh/wOfuZrlk4CBygAAAABJRU5ErkJggg==\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",
      "-16.300000000000118\n",
      "-16.300000000000118\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",
      "-59.97999999999947\n",
      "-59.97999999999947\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",
      "-16.380000000000123\n",
      "-24.540000000000386\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 0.200000\n",
      "The algorithm recognised the pattern 4 and the correct pattern is 2\n",
      "-68.29999999999866\n",
      "-68.29999999999866\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",
      "-19.580000000000204\n",
      "-24.540000000000386\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",
      "-79.17999999999846\n",
      "-100.30000000000202\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",
      "-22.540000000000315\n",
      "-24.540000000000386\n"
     ]
    },
    {
     "data": {
      "image/png": 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OwPp2kSQ15CxLS2zRoq2q64F3AtcCG4Bbq+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",
      "-92.62000000000019\n",
      "-100.30000000000202\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"
     ]
    }
   ],
   "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",
    "        supersys = np.zeros(N)\n",
    "        for n in range(1):\n",
    "            sys = deepcopy(frames[idx])\n",
    "            print(H(J, sys))\n",
    "            sys = montecarlo(J, sys, 25, 1000)\n",
    "            print(H(J, sys))\n",
    "            wrong_pixels = error_im(frames[idx],sys)\n",
    "            assigned_pattern = assign_pattern(frames,sys)\n",
    "            supersys += np.array(sys)\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(np.sign(supersys).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": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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r6hVVde/TD6qqS6vqZFWdXDwlcL6dc+8PDg7Of0pgSXoP89F7mI/ewx7aZpw7muRRSX6xux+Z5HNJnn/6Qd19WXef6O4TC2cEzr9z7v2xY8fOd0ZgWXoP89F7mI/ewx7aZpy7IckN3f2uzfuX57DMwF2X3sN89B7mo/cwH72HPXTWca67P5bk+qr6ps1Fj0/ygZ2mAobSe5iP3sN89B7mo/ewn7Z9tdZnJ3nd5pVcrk3yzN1FAvaE3sN89B7mo/cwH72HPbPVONfd70viueRgInoP89F7mI/ew3z0HvbPNs85BwAAAADsgHEOAAAAAAYxzgEAAADAIMY5AAAAABjEOAcAAAAAgxjnAAAAAGAQ4xwAAAAADGKcAwAAAIBBjHMAAAAAMIhxDgAAAAAGMc4BAAAAwCDGOQAAAAAYxDgHAAAAAIMY5wAAAABgEOMcAAAAAAxinAMAAACAQYxzAAAAADCIcQ4AAAAABjHOAQAAAMAgxjkAAAAAGMQ4BwAAAACDGOcAAAAAYBDjHAAAAAAMYpwDAAAAgEGMcwAAAAAwiHEOAAAAAAYxzgEAAADAIMY5AAAAABjEOAcAAAAAgxjnAAAAAGAQ4xwAAAAADGKcAwAAAIBBjHMAAAAAMMhW41xV/URVXVVVv1dVr6+qe+06GDCW3sN89B7mo/cwH72H/XPWca6qLk7ynCQnuvvhSY4kuWTXwYBx9B7mo/cwH72H+eg97KdtH9Z6NMlXVdXRJBckuXF3kYA9ofcwH72H+eg9zEfvYc+cdZzr7o8meUmSjyS5Kcmnuvttuw4GjKP3MB+9h/noPcxH72E/bfOw1q9J8pQkD0nygCT3rqqnneG4S6vqZFWdXD4mcD7dkd4fHByc75jAgvQe5qP3MB+9h/20zcNavzfJh7v7oLu/lOSKJN95+kHdfVl3n+juE0uHBM67c+79sWPHzntIYFF6D/PRe5iP3sMe2mac+0iSb6+qC6qqkjw+ydW7jQUMpvcwH72H+eg9zEfvYQ9t85xz70pyeZL3JHn/5nMu23EuYCC9h/noPcxH72E+eg/76eg2B3X3C5O8cMdZgD2i9zAfvYf56D3MR+9h/2zzsFYAAAAAYAeMcwAAAAAwiHEOAAAAAAYxzgEAAADAIMY5AAAAABjEOAcAAAAAgxjnAAAAAGAQ4xwAAAAADGKcAwAAAIBBjHMAAAAAMIhxDgAAAAAGMc4BAAAAwCDGOQAAAAAYxDgHAAAAAIMY5wAAAABgEOMcAAAAAAxinAMAAACAQYxzAAAAADCIcQ4AAAAABjHOAQAAAMAgxjkAAAAAGMQ4BwAAAACDGOcAAAAAYBDjHAAAAAAMYpwDAAAAgEGMcwAAAAAwSHX38ldadZDkD7Y49KIkNy8eYHlryZmsJ6uc23lwdx8b+PW3pvdDrSWrnNvR+3HWkjNZT1Y5t6P346wlZ7KerHJuR+/HWUvOZD1Z5dzObfZ+J+PctqrqZHefGBZgS2vJmawnq5zzWsttupacyXqyyjmvtdyma8mZrCernPNay226lpzJerLKOa+13KZryZmsJ6ucd56HtQIAAADAIMY5AAAAABhk9Dh32eCvv6215EzWk1XOea3lNl1LzmQ9WeWc11pu07XkTNaTVc55reU2XUvOZD1Z5ZzXWm7TteRM1pNVzjtp6HPOAQAAAMDMRp85BwAAAADTMs4BAAAAwCDDxrmq+v6q+mBVfaiqnj8qx+2pqgdV1Tuq6uqquqqqnjs60+2pqiNV9d6qetPoLLenqu5XVZdX1TWb2/Y7Rmc6k6r6ic1/99+rqtdX1b1GZ1o7vV+e3i9L75en98vT+2Xp/fL0fnl6vyy9X57eL0/vl7XvvR8yzlXVkSS/kOSJSR6W5KlV9bARWc7iliQ/2d3fkuTbk/zDPc15q+cmuXp0iC28LMlbuvubkzwie5i5qi5O8pwkJ7r74UmOJLlkbKp10/ud0fuF6P3y9H5n9H4her88vd8ZvV+I3i9P73dG7xeyht6POnPu25J8qLuv7e4vJvnlJE8ZlOU2dfdN3f2ezZ8/k8P/yS4em+rMquqBSX4gyStGZ7k9VXWfJI9N8sok6e4vdvcnx6a6TUeTfFVVHU1yQZIbB+dZO71fmN7vhN4vS+8Xpvc7offL0vuF6f1O6P2y9H5her8Te937UePcxUmuP+X9G7KnpbhVVR1P8sgk7xqb5Db9fJKfSvKV0UHO4uuTHCR59eYU3VdU1b1Hhzpdd380yUuSfCTJTUk+1d1vG5tq9fR+eXq/IL3fCb1fnt4vSO93Qu+Xp/cL0vud0Pvl6f2C1tD7UeNcneGyPu8ptlRVFyb59STP6+5Pj85zuqp6cpKPd/eVo7Ns4WiSRyX5xe5+ZJLPJdm75ySoqq/J4b/2PCTJA5Lcu6qeNjbV6un9gvR+eXq/E3q/IL1fnt7vhN4vSO+Xp/c7ofcL0vvlraH3o8a5G5I86JT3H5g9O6XwVlV19xwW93XdfcXoPLfhMUl+sKquy+EpxI+rqteOjXSbbkhyQ3ff+i8Ul+ewzPvme5N8uLsPuvtLSa5I8p2DM62d3i9L75en98vT+2Xp/fL0fnl6vyy9X57eL0/vl6X3y9v73o8a596d5Buq6iFVdY8cPhHfGwdluU1VVTl87PTV3f1zo/Pclu7+6e5+YHcfz+Ft+fbu3qsV+Fbd/bEk11fVN20uenySDwyMdFs+kuTbq+qCzf8Hj88ePrHlyuj9gvR+J/R+eXq/IL3fCb1fnt4vSO93Qu+Xp/cL0vud2PveHx3xRbv7lqp6VpK35vBVMl7V3VeNyHIWj0ny9CTvr6r3bS77me5+88BMdwXPTvK6zR33tUmeOTjPX9Dd76qqy5O8J4ev6vPeJJeNTbVuej89vZ+Q3k9P7yek99PT+wnp/fT0fgHVvbcPBQcAAACAu7RRD2sFAAAAgOkZ5wAAAABgEOMcAAAAAAxinAMAAACAQYxzAAAAADCIcQ4AAAAABjHOAQAAAMAgxjkAAAAAGMQ4BwAAAACDGOcAAAAAYBDjHAAAAAAMYpwDAAAAgEGMcwAAAAAwiHEOAAAAAAYxzgEAAADAIMY5AAAAABjEOAcAAAAAgxjnAAAAAGAQ4xwAAAAADGKcAwAAAIBBjHMAAAAAMIhxDgAAAAAGMc4BAAAAwCDGOQAAAAAYxDgHAAAAAIMY5wAAAABgEOMcAAAAAAxinAMAAACAQYxzAAAAADCIcQ4AAAAABjHOAQAAAMAgxjkAAAAAGMQ4BwAAAACDGOcAAAAAYBDjHAAAAAAMYpwDAAAAgEGMcwAAAAAwiHEOAAAAAAYxzgEAAADAIMY5AAAAABjEOAcAAAAAgxjnAAAAAGAQ4xwAAAAADGKcAwAAAIBBjHMAAAAAMIhxDgAAAAAGMc4BAAAAwCDGOQAAAAAYxDgHAAAAAIMY5wAAAABgEOMcAAAAAAxinAMAAACAQYxzAAAAADCIcQ4AAAAABjHO7Zmquq6qPl9Vn62qP6yqV1fVhVt83vdU1Q2nXfaiqnrt7tLeZpZLqurqqvpcVf1+VX3X+c4Aa7L23m9yn/r25ap6+fnMAGtyF+j88ap6c1V9oqo+VlX/uqqOns8MsEZ3ge5/S1W9vao+VVUfqqq/dT6/PqzBXaDnz6qqk1X1har6pTN8/PFVdU1V/XFVvaOqHnw+892VGef209/s7guTPCrJX0vyghEh7sgP2lX1N5L8r0memeSrkzw2ybULR4O7otX2vrsvvPUtyf2TfD7Jry0eDu5aVtv5JP8myceTfF2Sb03y3Un+wZK54C5sld3fHP8bSd6U5C8luTTJa6vqG3cQD9ZulT3fuDHJi5O86gzXd1GSK5L84xzeD5xM8it3JiN/xji3x7r7o0n+Q5KHJ0lVPXNzRtpnquraqvqxzeX33hz3gFPOXPmRJD+T5O9u3v/dzbH3rapXVtVNVfXRqnpxVR3ZfOxHq+p3quqlVfVfk7xoc9k7q+olm38h/3BVPfF2Yv/PSf5Jd/9/3f2V7v7o5vsAtrDS3p/qh3P4S/v/s+TtAndVK+38Q5L8anf/SXd/LMlbkvzVHd1EcJe0wu5/c5IHJHlpd3+5u9+e5HeSPH13txKs2wp7nu6+orvfkOSPzvDhv53kqu7+te7+kyQvSvKIqvrmhW6yqRnn9lhVPSjJk5K8d3PRx5M8Ocl9cnhm2kur6lHd/bkkT0xy4ylnsPy7JP8sya9s3n/E5jpek+SWJH8lySOTPCHJ3z/ly/71HJ7p9rVJfvaUyz6Y5KIk/yLJK6uqzpD3SJITSY7V4anuN9ThQ12+aonbA2awtt6fwX+X5P/o7j737x7ms9LOvyzJJVV1QVVdvMn1ljtzO8BsVtj927rs4ef8zcMkVtjzs/mrSX731nc2uX8//oFuEca5/fSGqvpkkncm+e0cljLd/Zvd/ft96LeTvC3J1s/nVlX3z2Hpn9fdn+vujyd5aZJLTjnsxu5+eXff0t2f31z2B939b7v7yzm8M/i6HD507XT3T3L3HJ458105fKjLIzPoNF5YmbX2/tSv9d/k8OFtr9k2H0xszZ3/7Rz+IP7pJDfk8GEtb9g2I0xurd2/JofDwv9QVXevqifk8O/8C87he4dZrLXnZ3Nhkk+ddtmncvh0VtxJnrx3P/1Qd/+n0y/cnH76wiTfmMNh9YIk7z+H631wDsezm04Zyu+W5PpTjrn+9E9K8rFb/9Ddf7z53DM9qeWt5X95d9+0yfxzORzn/sdzyAkzWmvvT/WMJO/s7g+fQz6Y1So7X1V3S/LWJP97ku/cHPOqHD7f7E+dQ06Y1Sq7391fqqofSvLyJP8oh6P8ryb5wjlkhFmssudb+GwOz/o71X2SfOYOXBenMc6tRFXdM8mv5/CX39/Y/AX5hvzZKeZnegjZ6Zddn8O/QC/q7ltu40vd4Yeidfcn6vAVZjycDRawht6f5hlJ/peFrgums5LO/6UkD0ryr7v7C0m+UFWvzuGTRxvn4A5YSffT3f85h2fL3Zr7/42z5WEra+n5WVyVw6ewSfKnz5X30M3l3Eke1roe90hyzyQHSW7ZrO5POOXjf5jkL1fVfU+77PjmX7mzOZvtbUn+ZVXdp6ruVlUPrarvznJeneTZVfW1VfU1SZ6Xw1d1As7dWnqfqvrOJBfHq7TCnbH3ne/um5N8OMmPV9XRqrpfDn9Q/93b/0zgdux995Okqv7bqrrX5vkm//scPjTul5a6friLW0vPj1bVvZIcSXJk0/lbT+r690keXlV/Z3PM/5TkP3f3NUt9/ZkZ51aiuz+T5Dk5PH38E0l+JMkbT/n4NUlen+TaqvpkVT0gf/ZL8h9V1Xs2f35GDu8YPrC5nstz+BfrUv5pkncn+S9Jrs7hk1/+7O1+BnBGK+p9cvjL+RWbzMAdsKLO/+0k35/DXzA+lMMnpv6JBa8fprKi7j89yU05fO65xyf5G5szaIGzWFHPX5DDp6t6fpKnbf78gk3GgyR/J4e/338ihy80ccmZr4ZzVe0F9QAAAABgCGfOAQAAAMAgxjkAAAAAGMQ4BwAAAACDGOcAAAAAYJCjZz/k3F100UV9/PjxXVw1C7ryyisXv85HP/rRi1/nzK677rrcfPPNNTrHNvR+Xu5LlqX3zGoX9yXJOu5P9B6WtYafTfQe9t8u7ku6+4y938k4d/z48Zw8eXIXV82Cqpb/u8B/92WdOHFidISt6f283JcsS++Z1S7uS5J13J/oPSxrDT+b6D3sv139bHImHtYKAAAAAIMY5wAAAABgEOMcAAAAAAxinAMAAACAQYxzAAAAADDIVuNcVX1/VX2wqj5UVc/fdShgPL2H+eg9zEfvYT56D/vnrONcVR1J8gtJnpjkYUmeWlUP23UwYBy9h/noPcxH72E+eg/7aZsz574tyYe6+9ru/mKSX07ylN3GAgbTe5iP3sN89B7mo/ewh7YZ5y5Ocv0p79+wuQy469J7mI/ew3z0Huaj97CHthnn6gyX9V84qOrSqjpZVScPDg7ufDJgJL2H+eg9zEfvYT56D3tom3HuhiQPOuX9Bya58fSDuvuy7j7R3SeOHTu2VD5gDL2H+eg9zEfvYT56D3tom3Hu3Um+oaoeUlX3SHJJkq1hgnYAAA8jSURBVDfuNhYwmN7DfPQe5qP3MB+9hz109GwHdPctVfWsJG9NciTJq7r7qp0nA4bRe5iP3sN89B7mo/ewn846ziVJd785yZt3nAXYI3oP89F7mI/ew3z0HvbPNg9rBQAAAAB2wDgHAAAAAIMY5wAAAABgEOMcAAAAAAxinAMAAACAQYxzAAAAADCIcQ4AAAAABjHOAQAAAMAgxjkAAAAAGMQ4BwAAAACDGOcAAAAAYBDjHAAAAAAMYpwDAAAAgEGMcwAAAAAwiHEOAAAAAAYxzgEAAADAIMY5AAAAABjEOAcAAAAAgxjnAAAAAGAQ4xwAAAAADGKcAwAAAIBBjHMAAAAAMIhxDgAAAAAGMc4BAAAAwCDGOQAAAAAYxDgHAAAAAIMY5wAAAABgEOMcAAAAAAxinAMAAACAQYxzAAAAADCIcQ4AAAAABjHOAQAAAMAgxjkAAAAAGMQ4BwAAAACDnHWcq6oHVdU7qurqqrqqqp57PoIB4+g9zEfvYT56D/PRe9hPR7c45pYkP9nd76mqr05yZVX9x+7+wI6zAePoPcxH72E+eg/z0XvYQ2c9c667b+ru92z+/JkkVye5eNfBgHH0Huaj9zAfvYf56D3sp3N6zrmqOp7kkUnedYaPXVpVJ6vq5MHBwTLpgOH0Huaj9zAfvYf56D3sj63Huaq6MMmvJ3led3/69I9392XdfaK7Txw7dmzJjMAgeg/z0XuYj97DfPQe9stW41xV3T2HxX1dd1+x20jAPtB7mI/ew3z0Huaj97B/tnm11kryyiRXd/fP7T4SMJrew3z0Huaj9zAfvYf9tM2Zc49J8vQkj6uq923enrTjXMBYeg/z0XuYj97DfPQe9tDRsx3Q3e9MUuchC7An9B7mo/cwH72H+eg97KdzerVWAAAAAGA5xjkAAAAAGMQ4BwAAAACDGOcAAAAAYBDjHAAAAAAMYpwDAAAAgEGMcwAAAAAwiHEOAAAAAAYxzgEAAADAIMY5AAAAABjEOAcAAAAAgxjnAAAAAGAQ4xwAAAAADGKcAwAAAIBBjHMAAAAAMIhxDgAAAAAGMc4BAAAAwCDGOQAAAAAYxDgHAAAAAIMY5wAAAABgEOMcAAAAAAxinAMAAACAQYxzAAAAADCIcQ4AAAAABjHOAQAAAMAgxjkAAAAAGMQ4BwAAAACDGOcAAAAAYBDjHAAAAAAMYpwDAAAAgEGMcwAAAAAwiHEOAAAAAAYxzgEAAADAIFuPc1V1pKreW1Vv2mUgYH/oPcxH72E+eg/z0XvYL+dy5txzk1y9qyDAXtJ7mI/ew3z0Huaj97BHthrnquqBSX4gySt2GwfYF3oP89F7mI/ew3z0HvbPtmfO/XySn0rylds6oKouraqTVXXy4OBgkXDAUHoP89F7mI/ew3z0HvbMWce5qnpyko9395W3d1x3X9bdJ7r7xLFjxxYLCJx/eg/z0XuYj97DfPQe9tM2Z849JskPVtV1SX45yeOq6rU7TQWMpvcwH72H+eg9zEfvYQ+ddZzr7p/u7gd29/EklyR5e3c/befJgGH0Huaj9zAfvYf56D3sp3N5tVYAAAAAYEFHz+Xg7v6tJL+1kyTAXtJ7mI/ew3z0Huaj97A/nDkHAAAAAIMY5wAAAABgEOMcAAAAAAxinAMAAACAQYxzAAAAADCIcQ4AAAAABjHOAQAAAMAgxjkAAAAAGMQ4BwAAAACDGOcAAAAAYBDjHAAAAAAMYpwDAAAAgEGMcwAAAAAwiHEOAAAAAAYxzgEAAADAIMY5AAAAABjEOAcAAAAAgxjnAAAAAGAQ4xwAAAAADGKcAwAAAIBBjHMAAAAAMIhxDgAAAAAGMc4BAAAAwCDGOQAAAAAYxDgHAAAAAIMY5wAAAABgEOMcAAAAAAxinAMAAACAQYxzAAAAADCIcQ4AAAAABjHOAQAAAMAgxjkAAAAAGMQ4BwAAAACDbDXOVdX9quryqrqmqq6uqu/YdTBgLL2H+eg9zEfvYT56D/vn6JbHvSzJW7r7h6vqHkku2GEmYD/oPcxH72E+eg/z0XvYM2cd56rqPkkem+RHk6S7v5jki7uNBYyk9zAfvYf56D3MR+9hP23zsNavT3KQ5NVV9d6qekVV3XvHuYCx9B7mo/cwH72H+eg97KFtxrmjSR6V5Be7+5FJPpfk+acfVFWXVtXJqjp5cHCwcEzgPNN7mI/ew3z0Huaj97CHthnnbkhyQ3e/a/P+5Tks85/T3Zd194nuPnHs2LElMwLnn97DfPQe5qP3MB+9hz101nGuuz+W5Pqq+qbNRY9P8oGdpgKG0nuYj97DfPQe5qP3sJ+2fbXWZyd53eaVXK5N8szdRQL2hN7DfPQe5qP3MB+9hz2z1TjX3e9LcmLHWYA9ovcwH72H+eg9zEfvYf9s85xzAAAAAMAOGOcAAAAAYBDjHAAAAAAMYpwDAAAAgEGMcwAAAAAwiHEOAAAAAAYxzgEAAADAIMY5AAAAABjEOAcAAAAAgxjnAAAAAGAQ4xwAAAAADGKcAwAAAIBBjHMAAAAAMIhxDgAAAAAGMc4BAAAAwCDGOQAAAAAYxDgHAAAAAIMY5wAAAABgEOMcAAAAAAxinAMAAACAQYxzAAAAADCIcQ4AAAAABjHOAQAAAMAgxjkAAAAAGMQ4BwAAAACDGOcAAAAAYBDjHAAAAAAMYpwDAAAAgEGMcwAAAAAwiHEOAAAAAAYxzgEAAADAIMY5AAAAABjEOAcAAAAAgxjnAAAAAGCQrca5qvqJqrqqqn6vql5fVffadTBgLL2H+eg9zEfvYT56D/vnrONcVV2c5DlJTnT3w5McSXLJroMB4+g9zEfvYT56D/PRe9hP2z6s9WiSr6qqo0kuSHLj7iIBe0LvYT56D/PRe5iP3sOeOes4190fTfKSJB9JclOST3X3204/rqouraqTVXXy4OBg+aTAeaP3MB+9h/noPcxH72E/bfOw1q9J8pQkD0nygCT3rqqnnX5cd1/W3Se6+8SxY8eWTwqcN3oP89F7mI/ew3z0HvbTNg9r/d4kH+7ug+7+UpIrknznbmMBg+k9zEfvYT56D/PRe9hD24xzH0ny7VV1QVVVkscnuXq3sYDB9B7mo/cwH72H+eg97KFtnnPuXUkuT/KeJO/ffM5lO84FDKT3MB+9h/noPcxH72E/Hd3moO5+YZIX7jgLsEf0Huaj9zAfvYf56D3sn20e1goAAAAA7IBxDgAAAAAGMc4BAAAAwCDGOQAAAAAYxDgHAAAAAIMY5wAAAABgEOMcAAAAAAxinAMAAACAQYxzAAAAADCIcQ4AAAAABjHOAQAAAMAgxjkAAAAAGMQ4BwAAAACDGOcAAAAAYBDjHAAAAAAMYpwDAAAAgEGMcwAAAAAwiHEOAAAAAAYxzgEAAADAIMY5AAAAABjEOAcAAAAAgxjnAAAAAGAQ4xwAAAAADGKcAwAAAIBBjHMAAAAAMIhxDgAAAAAGqe5e/kqrDpL8wRaHXpTk5sUDLG8tOZP1ZJVzOw/u7mMDv/7W9H6otWSVczt6P85acibrySrndvR+nLXkTNaTVc7t6P04a8mZrCernNu5zd7vZJzbVlWd7O4TwwJsaS05k/VklXNea7lN15IzWU9WOee1ltt0LTmT9WSVc15ruU3XkjNZT1Y557WW23QtOZP1ZJXzzvOwVgAAAAAYxDgHAAAAAIOMHucuG/z1t7WWnMl6sso5r7XcpmvJmawnq5zzWsttupacyXqyyjmvtdyma8mZrCernPNay226lpzJerLKeScNfc45AAAAAJjZ6DPnAAAAAGBaw8a5qvr+qvpgVX2oqp4/KsftqaoHVdU7qurqqrqqqp47OtPtqaojVfXeqnrT6Cy3p6ruV1WXV9U1m9v2O0ZnOpOq+onNf/ffq6rXV9W9RmdaO71fnt4vS++Xp/fL0/tl6f3y9H55er8svV+e3i9P75e1770fMs5V1ZEkv5DkiUkeluSpVfWwEVnO4pYkP9nd35Lk25P8wz3NeavnJrl6dIgtvCzJW7r7m5M8InuYuaouTvKcJCe6++FJjiS5ZGyqddP7ndH7hej98vR+Z/R+IXq/PL3fGb1fiN4vT+93Ru8Xsobejzpz7tuSfKi7r+3uLyb/f3t3zypXHYVRfG24CiYi2JorJIFgnVRiwMLYKfoFtLCPkErQzyBiJ0hMGgMWMYWFoIV9EKMgaqeSXI2YxhdsNPhYnLkQYsZY7MP/TGb9qpnT3M0w6xZ7zgvvAc8PmmWtJNeTXFm9/p3pS3Zo7FR3VlW7wDPA2dGz/Jeqegh4EngHIMmfSX4ZO9VaO8ADVbUDHAB+HDzPprP7ZnY/C7vvZffN7H4Wdt/L7pvZ/SzsvpfdN7P7WSy6+1HLuUPAtVve77HQKPZV1WHgOHB57CRrvQm8Avw9epC7OArcAM6vTtE9W1UHRw91uyQ/AK8DV4HrwK9JPh471caz+35238juZ2H3/ey+kd3Pwu772X0ju5+F3fez+0ab0P2o5Vzd4dhiHxtbVQ8C7wNnkvw2ep7bVdWzwM9JPhs9y/+wA5wA3kpyHPgDWNw9CarqYaZfe44AjwAHq+qFsVNtPLtvZPf97H4Wdt/I7vvZ/SzsvpHd97P7Wdh9I7vvtwndj1rO7QGP3vJ+l4WdUrivqu5jCvdCkkuj51njJPBcVX3PdArxU1X17tiR1toD9pLs/0JxkSnmpXka+C7JjSR/AZeAJwbPtOnsvpfd97P7fnbfy+772X0/u+9l9/3svp/d97L7fovvftRy7lPgWFUdqar7mW7E98GgWdaqqmK6dvqbJG+MnmedJK8m2U1ymOmz/CTJorbA+5L8BFyrqsdWh04BXw8caZ2rwONVdWD1PTjFAm9suWHsvpHdz8Lu+9l9I7ufhd33s/tGdj8Lu+9n943sfhaL735nxB9NcrOqTgMfMT0l41ySr0bMchcngReBL6vqi9Wx15J8OHCme8HLwIXVP+5vgZcGz/MvSS5X1UXgCtNTfT4H3h471Waz+61n91vI7ree3W8hu996dr+F7H7r2X2DShZ7KbgkSZIkSZJ0Txt1WaskSZIkSZK09VzOSZIkSZIkSYO4nJMkSZIkSZIGcTknSZIkSZIkDeJyTpIkSZIkSRrE5ZwkSZIkSZI0iMs5SZIkSZIkaRCXc5IkSZIkSdIg/wAaVE9jgU6QGwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1584x720 with 10 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",
    "\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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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 0.680000\n",
      "The algorithm recognised the pattern 1 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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\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 0.480000\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 0.110000\n",
      "The algorithm recognised the pattern 4 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 0.430000\n",
      "The algorithm recognised the pattern 3 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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\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 0.550000\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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\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 0.500000\n",
      "The algorithm recognised the pattern 3 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"
     ]
    }
   ],
   "source": [
    "# we try our algorithm to see if the patterns are distinguishable.\n",
    "        \n",
    "patt = np.array(patt[:5])\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",
    "        supersys = np.zeros(N)\n",
    "        for n in range(100):\n",
    "            sys = deepcopy(patt[idx])\n",
    "            sys = montecarlo(J, sys, 1, 1000)\n",
    "            wrong_pixels = error_im(patt[idx],sys)\n",
    "            assigned_pattern = assign_pattern(patt,sys)\n",
    "            supersys += np.array(sys)\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((supersys/100).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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "l = 10\n",
    "a = np.zeros(l*l)#.reshape(l,l)\n",
    "for i in range(l*l):\n",
    "    if i//l == 0: a[i]=1  # first row\n",
    "    if i%l == 0: a[i]=1 # first column\n",
    "    if i%l == l-1: a[i]=1 # last column\n",
    "    if i//l ==l-1 : a[i]=1 # last row\n",
    "a.reshape(l,l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 10\n",
    "r = 2\n",
    "a = np.zeros(l*l)\n",
    "for i in range(k+1,k+r+1): # going right\n",
    "    if k%l == l-1: break # right bound\n",
    "    a[i]=1\n",
    "    if i%l == l-1: break # last column bound\n",
    "for i in range(k-1,k-r-1,-1): # going left\n",
    "    if k%l == 0: break # left bound\n",
    "    a[i]=1\n",
    "    if i%l == 0: break # first column bound\n",
    "for i in range(k+l,k+(r+1)*l,l): # going down\n",
    "    if k//l == l-1: break # low bound\n",
    "    a[i]=1\n",
    "    if i//l ==l-1 : break # last row bound\n",
    "for i in range(k-l, k-l*(r+1), -l): # going up\n",
    "    if k//l == 0: break # up bound\n",
    "    a[i]=1\n",
    "    if i//l == 0: break  # first row bound\n",
    "a.reshape(l,l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.zeros(l*l)\n",
    "k = l*(l-1)-2\n",
    "r = 4\n",
    "a[k]=5\n",
    "for i in range(1,r):\n",
    "    if k%l == l-1 or k//l == l-1: break # right low bound\n",
    "    for j in range(1,r):\n",
    "        if i==j==r-1: continue\n",
    "        a[k+j+i*l] = 1 # right low\n",
    "        if (k+j+i*l)%l == l-1 : \n",
    "            break # last column bound\n",
    "    if (k+j+i*l)//l ==l-1 : break # last row bound\n",
    "        \n",
    "for i in range(1,r):\n",
    "    if k%l == 0 or k//l == l-1: break # left low bound\n",
    "    for j in range(1,r):\n",
    "        if i==j==r-1: continue\n",
    "        a[k-j+i*l] = 1 # left low\n",
    "        if (k-j+i*l)%l == 0 : break #  first column bound\n",
    "    if (k-j+i*l)//l ==l-1 : break # last row bound\n",
    "        \n",
    "for i in range(1,r):\n",
    "    if k//l == 0 or k%l == l-1: break # up right bound\n",
    "    for j in range(1,r):\n",
    "        if i==j==r-1: continue\n",
    "        a[k+j-i*l] = 1 # right up\n",
    "        if (k+j-i*l)%l == l-1: break  # last column bound\n",
    "    if (k+j-i*l)//l == 0: break # first row bound\n",
    "        \n",
    "for i in range(1,r):\n",
    "    if k//l == 0 or k%l == 0 : break # up left bound\n",
    "    for j in range(1,r):\n",
    "        if i==j==r-1: continue\n",
    "        a[k-j-i*l] = 1 # left up\n",
    "        if (k-j-i*l)%l == l-1: break  #last column bound\n",
    "    if (k-j-i*l)//l == 0 : break # first row bound\n",
    "       \n",
    "a.reshape(l,l)"
   ]
  }
 ],
 "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"
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 },
 "nbformat": 4,
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