{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "$\\newcommand{\\si}{\\sigma}\n", "\\newcommand{\\al}{\\alpha}\n", "\\newcommand{\\tta}{\\theta}\n", "\\newcommand{\\Tta}{\\Theta}\n", "\\newcommand{\\Si}{\\Sigma}\n", "\\newcommand{\\ld}{\\ldots}\n", "\\newcommand{\\cd}{\\cdots}\n", "\\newcommand{\\Ga}{\\Gamma} \n", "\\newcommand{\\bet}{\\beta}\n", "\\newcommand{\\cU}{\\mathcal{U}}\n", "\\newcommand{\\cN}{\\mathcal{N}}\n", "\\newcommand{\\R}{\\mathbb{R}}\n", "\\newcommand{\\p}{\\mathbb{P}}\n", "\\newcommand{\\f}{\\frac}\n", "\\newcommand{\\ff}{\\frac{1}}\n", "\\newcommand{\\ds}{\\displaystyle}\n", "\\newcommand{\\bE}{\\mathbf{E}}\n", "\\newcommand{\\E}{\\mathbb{E}}\n", "\\newcommand{\\bF}{\\mathbf{F}}\n", "\\newcommand{\\ii}{\\mathrm{i}}\n", "\\newcommand{\\me}{\\mathrm{e}}\n", "\\newcommand{\\hsi}{\\hat{\\sigma}}\n", "\\newcommand{\\hmu}{\\hat{\\mu}}\n", "\\newcommand{\\ste}{\\, ;\\, }\n", "\\newcommand{\\op}{\\operatorname} \n", "\\newcommand{\\argmax}{\\op{argmax}}\n", "\\newcommand{\\lfl}{\\lfloor}\n", "\\newcommand{\\ri}{\\right}\n", "\\newcommand{\\supp}{\\operatorname{supp}}$\n", "\n", "\"Open\n", "\n", "# TP Simulation du Modèle d'Ising par Metropolis Hastings \n", "\n", "## 1. Modèle d'Ising\n", "\n", "### 1.1 Description du modèle\n", "\n", "Le *modèle d'Ising*, dû à Ernst Ising, est l'un des champs de Gibbs les plus simples et les plus étudiés. Il décrit les transitions de phase de l'aimantation d'un métal ferromagnétique. Dans ce qui suit on le décrit en deux dimensions, mais on peut le définir en dimension plus grande.\n", "\n", "Considérons un réseau de taille $N \\times N$, que l'on note $\\Ga=\\{1,\\ld,N\\}^2$. A chaque position $(i,j)$ du réseau, on associe une quantité $s_{i,j}$, appelée *spin*, prenant les valeurs $\\pm 1$. \n", "On note $S=(s_{i,j})_{(i,j)\\in \\Ga}$ une configuration possible de spins. L'ensemble des configurations (ou états) du réseau est donc $E = \\{-1,1\\}^\\Ga$, et est potentiellement de très grande dimension ! \n", "\n", "Ci-dessous on représente une configuration possible pour un petit réseau $6\\times 6$, avec deux couleurs possibles sur les positions, correspondant aux valeurs $-1$ et $1$. \n", " \n", " \n", "\n", "Les spins interagissent avec leurs plus proches voisins. On peut définir l'énergie d'une configuration $S$ comme \n", "$$E(S) = \\sum_{(k,l)\\sim (i,j)}(s_{k,l}-s_{i,j})^2,$$\n", "où $(i,j)\\sim (k,l)$ signifie que les positions $(i,j)$ et $(k,l)$ sont voisins (à distance 1) sur le réseau $\\Ga$. \n", "On voit que si l'on cherche à minimiser $E$, on tombe sur deux configurations constantes (celle où les spins sont tous égaux à $1$ et celle où ils sont tous égaux à $-1$). \n", "Comme les valeurs $s_{i,j}$ valent $\\pm 1$, en développant l'énergie ci-dessous, on s'aperçoit qu'il est équivalent de minimiser l'énergie \n", "$$H(S) = -\\sum_{(k,l)\\sim (i,j)}s_{k,l}s_{i,j},$$\n", "On associe à cette énergie la mesure de Gibbs suivante\n", "$$\\mu_\\bet(S)=\\ff{Z_\\bet}\\me^{-\\bet H(S)},$$\n", "où la fonction de partition $Z_\\bet$ sert à normaliser la mesure de Gibbs, et où $\\bet:=\\ff T$, $T>0$ pouvant s'interprèter comme une température : quand $T$ est grand, les fluctuations thermiques dominent et le système est désordonné, par contre pour $T$ proche de $0$ les configurations de basse énergie sont privilégiées et les spins ont tendance à s'aligner.\n", "\n", "### 1.2 Simulation du modèle d'Ising\n", "\n", "**Dans ce qui suit, nous allons implémenter l'algorithme de Metropolis-Hastings afin de simuler sous la loi $\\mu_\\bet$ du modèle d'Ising.**\n", "\n", "Retraduit dans le formalisme des chaînes de Markov, une configuration $S$ correspond à un état et l'espace d'états est $E = \\{-1,1\\}^\\Ga$. Pour un domaine de taille $N = 40$, le cardinal de $E$ est $2^{40×40}\\approx 10^{481}$. Il est donc impossible d'énumérer toutes les configurations pour calculer la distribution $\\mu_\\bet$. \n", "\n", "Pour tout $(i,j)\\in \\Ga$, on note $S^{\\rightarrow(i,j)}$ la configuration déduite de $S$ en changeant simplement le signe du spin en $(i,j)$. Deux configurations sont dites voisines si elles peuvent être déduites l'une de l'autre par un changement de spin en un point.\n", "\n", "Pour la matrice de transition $Q$ qui va nous servir à simuler la chaîne de Markov, on la prend nulle partout sauf pour les couples de configurations voisines, et telle que \n", "$$\\forall (i,j)\\in \\Ga, \\qquad Q(S,S^{\\rightarrow(i,j)}) = \\ff{\\op{Card}(\\Ga)}.$$\n", "\n", "Cette matrice de transition correspond au mécanisme suivant : un site $(i,j)$ est choisi au hasard dans $\\Ga$ et son spin dans $S$ est retourné (passe de $1$ à $-1$ ou le contraire). Ce sont les seules transitions autorisées. Ces transitions modifient les configurations seulement localement, par conséquent la variation de l'énergie correspondant au changement du spin en $(i,j)$ ne dépend que de la moyenne des spins autour de $(i,j)$:\n", "\n", "$$\\Delta H(S,S^{\\rightarrow(i,j)}):=H(S^{\\rightarrow(i,j)})-H(S)=-\\sum_{(k,l)\\sim (i,j)}s_{k,l}(-s_{i,j})-\\left(-\\sum_{(k,l)\\sim (i,j)}s_{k,l}s_{i,j}\\right)=2s_{i,j}\\sum_{(k,l)\\sim (i,j)}s_{k,l}.$$\n", "\n", "La fonction $\\rho$ est alors donnée par \n", "$$\\rho(S,S^{\\rightarrow(i,j)})=\\me^{-\\bet\\Delta H(S,S^{\\rightarrow(i,j)}) } .$$\n", "\n", "\n", "### 1.3 Algorithme de Metropolis-Hastings\n", "\n", "On en déduit l'algorithme suivant :\n", "\n", "*Algorithme de Metropolis-Hastings de simulation de $S\\approx \\mu_\\bet$*\n", "1. *Initialiser avec une configuration $S$ quelconque.*\n", "2. *Répéter un grand nombre de fois :*\n", " + *tirer, indépendamment, $(i,j)$ de loi unif. sur $\\Ga$ et $U\\sim\\cU([0,1])$,*\n", " + *remplacer $S$ par $S^{\\rightarrow(i,j)}$ si $U <\\me^{-\\bet\\Delta H(S,S^{\\rightarrow(i,j)}) }$ et le laisser invariant sinon.*\n", "3. *Rendre $S$.*\n", "\n", "\n", "### 1.4 Exercice\n", "\n", "On va implémenter l'algorithme précédent et le faire tourner pour diverses configurations initiales" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from TP_Ising import *" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# paramètres\n", "beta=10 #beta = 1/T\n", "N,Npas=int(1e2),int(2e5) # NxN est le nombre de positions sur la grille et Npas est le nb de pas d'évolution de la chaîne " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. **Ecrire une fonction `transition(S,N,beta)` qui prend en entrée une image $S$ composée de $1$ et des $-1$, de taille $N\\times N$, choisit une position aléatoire $(i,j)$ dans la grille de l'image, et décide si on modifie ou non la valeur en ce point (en multipliant sa valeur par par $-1$) en fonction de l'évolution de l'énergie $H$, comme expliqué au dessus. Utiliser cette fonction pour faire évoluer la chaîne de Markov sur `Npas` itérations.** " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Initialisation (essayer plusieurs états initiaux possible, très aléatoire ou au contraire très déterministes)\n", "S0=2*np.random.randint(2,size=(N,N))-1 # initialisation aléatoire\n", " \n", "# On fait evoluer la chaîne de Markov \n", "S = np.copy(S0)\n", "for t in range(Npas):\n", " S=transition(S,N,beta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. **Tester avec différentes initialisations possibles (très aléatoires ou au contraire très déterministes), et avec plusieurs valeurs de $\\beta$ (ou de la température $T$). Comment varient les résultats en fonction de la température ?**" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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c6bW5uE1pXGbkfJTGp9euTFkz5nTo9xOiYylN0xb5HsWB/RuD2gTWwSpWDMR64AkyAAAAkOAGGQAAAEiYu4/W2d5Hn+OHDl+45XY1q4XlpGmruXQb3T/Sbstqb6XvP9JnjapuQ/vsa7dmVblIu1u1HREZ81jhP62Oc87xa5k6LCedYVeat1tvO27VBpZpx1m7/dydF089jEHWPTXcMochlJ6bqd/bul9bU5j6nN988pIj7r5vq+14ggwAAAAkuEEGAAAAEpOFWLRc0o3sE22jNMSh1fJNTrW5lqEDXVoes9LMG11t5agd1lBLTvjRFKFEfYYemxpZcVqEeRFiUcc6LolPvSSdqn38t/N7w+2W6TwTYgEAAABk4AYZAAAASIxaKKRL7eXttL2cUITINqXFFCKFBbbaJ2ecNdsqHWeX6JgjhTJaHb++9koLwuRkXomMK9pnje1Sq5jFonTMy7ScCCyTZf5s1LxfWHfLfJ6jeIIMAAAAJLhBBgAAABKjhlgcO7rrzGP3nOwCYz2yz/l2f9f+qWhbXa9Fl+5Lwx1KMz/ULM7S198YYTFDxhNpt1VxlKH9Lb6WE/7TtU30tdLjX/p56lPzfJwe54H9G9XaBKZSex5dRTnFg7B6eIIMAAAAJLhBBgAAABLcIAMAAACJUWOQ9+zd0KHDs7icmnGyOZWzFkXG09duzXRqQ8fVp+b+pWrHqZamxsuJI4v02bIqX834+HT/nLjprm1KYxRrfmaj+5SmMIxc2ydOHQyNEcDqG6NSKtriCTIAAACQ4AYZAAAASExWSa+0qll0uT66JDp0ubplhbS+fiL9lYZr1Fy67pOT2i2yf6v0bYtt54Q7tFi67/t97fNcqlVYS06f0fef0+dm+5PmLR9L1Fhl61KhbztUz0vxBBkAAABIcIMMAAAAJCYLsehTmlGitM+cfiLb1QxXKM3OUBqisbhdThaJrraj73loP6X75yitSlg73CASslQallF6nGtnlMgJixn6ed5uS4uYHtcUVsF2vk63fIJsZg8ws0NmdqWZfdzMXjb//T3N7INm9un5fy9oP1wAWE/MxQAwnkiIxS2SXuHuD5f0OEkXm9kjJL1S0ofc/SJJH5r/DABog7kYAEayZYiFu18v6fr5/3/NzK6UdKGkZ0p64nyzyyR9WNIv5Qwi5xF97X1Kiz5Evinf1V+0n77l5dKMCJE+c7YrzRRQuk9fWznZPpZpOSmnaEnNYjE1Q1RKs3WkSgsPbTWezbbp279WoZAx5uKprfq3+IESOaGPaGfQl/TM7MGS9kq6XNJ95xP26Yn7PrUHBwC4M+ZiAGgrfINsZneX9B5JP+fu/zhgv5ea2RVmdsWNG7fmjBEAMJczF6fzsPvX2w4QALaBUBYLM7uLZhPyW939vfNff9HM7ufu15vZ/STdsNm+7n6ppEslacdZu71kibpmkYCcfqLL/TlKQzyW9Rv1pZkC+tTM9tGVkaNPaeaOmhkdWhahiZynmuE7OZk7otdZdCxDw5QiS6M1CoXkzsWL83DxQAZieRgoUzOkrKbSTE3LLJLFwiS9UdKV7v7byUvvl/TC+f+/UNL76g8PACAxFwPAmCJPkL9b0gskfczMPjr/3SWSXivpnWb2Ykmfl/ScNkMEAIi5GABGE8li8deSrOPlJ9cdDgBgM8zFADAecx8vHG3vo8/xQ4cvvNPvS2NTWsbA5MRpRvqvmW5rsb0pKn/lxHl27T9WrFXkGETTf+Wk1it9zzmp7SL7R9WsShdVs3pg1zaLcqoXbtbegf3X6uiRk103uKPZcdZuP3fnxc37mTo2crtatljOlikeMcwyf+aW6TzffPKSI+6+b6vtBqV5AwAAALY7bpABAACARCjN25RyUkzVTLkWNTTlWE7FnJrpw3JEl6Gj+9RcmisNcYjuM4ZouEJOyrOutvoMPbeladqiaqZjrD2HbHbMSivpLbtlXt7dTpa5uiemRSW+uniCDAAAACS4QQYAAAASk4VY9C2JRiqEtapc1lLpknJOP6kaS88l+9fOCFGzEl9puzlL/DWzaAzdpm+7KSoj5WTeiG7T8nxG1KykN5Wp5050W9ZQsS7LOq7tbqz7jy7LWu23D0+QAQAAgAQ3yAAAAEBiKbNYtErsH5Wz9D20rZwCEqXZCcYqINE1lmimgCmWwSNhPdE++8Y/dMzRcIFWITJ9fUb3jx7biJpLgzmhHCWhPNs9i8WyabWMS7gJsB54ggwAAAAkuEEGAAAAEubuo3W246zdfu7OiyXlLb13yVlKKw0xyBlzzbCKnOwGLYofbNV2aRaLlsesS82l2dKMDDljLg1rGavPrrZy1C6O0qUk5OnA/mt19MhJKxpABek8nGNVQgzWPcRirEwBY/x9jXGMdW1PfQ3cfPKSI+6+b6vteIIMAAAAJLhBBgAAABLcIAMAAACJpUjzFk2lVVo9ryvd1JD2urYfGpuYkz4sd2xD+yhN5RXdJ/I+S89zTmxsyxje0rjjVtX/SrereW2Vxrq3VPM7Aatq6mONbhwnrIKasc4tr3meIAMAAAAJbpABAACAxFKEWESrhfXtE2m7VVW9aJ99IR6txtUyfVb62hjHtmXls5ZpziJKQ0mi7da8HqKGpk1sOeackKeu7QgBaItjCmArLedhniADAAAACW6QAQAAgMRkIRZ9j8JrLr13tVu7YkwklKI0u0Gp2pkOcioOdo1naLt9SivmtaykVzMsYwqlVSZzsp1E1M6wEmlrVSqqoa6WIVQA8tUOz+MJMgAAAJDgBhkAAABITBZiEc2OULqM39VuVM3CAH37lxbNiIR1jBXuEQ0jGLpcXRoWEj3mpdfTWMuppccsp4hOaVaXmtvnnOdoJpmh10bffHD6/0+cOtjZ35j27N3QocN3fn+rEuaD5VLz72igpq7r8YK7xvbnCTIAAACQ4AYZAAAASHCDDAAAACRGjUHuin3ri6Ucq/JWadxuRM20XjnxtKWpsEpTvuUojQfOia2tGTcdHWfpNVdaIS6qZsXAnPRrQ2P9+9qr+Z2E3O2AoZb5elrmsQFD8QQZAAAASHCDDAAAACQmS/OWii6JDt1mq35K9s9J01Zz6bz2MnLNSoCtltmi4QItwyWGhgi0TJmWtpWz9F+yTY0+S6sv5oRolKZtjL4XlpoBDDV1tV3cEU+QAQAAgAQ3yAAAAEBi1BCLY0d3nVkm6FoeltpVz6tZSS6n/+jSe6StvnCBoe3mGtpnTrhB6TGLyskCUTPMJ6faW064xRgZWvrGGdk/J8RjaH9DRK7T2qE0UyBMpJ1WWX6AUlyP3XiCDAAAACS4QQYAAAASkxUKiS7flS4jd/2+5XJ9zbCOmtkJamYayFGaHSF6/HIyFZSGOKRywgVK1QyxqZ1FYuj5LC0O07ddaWhWTv+raqwQlnVDuAW68NlaLjxBBgAAABLcIAMAAACJpchisWjoMmxpkv++fbrUXu4f2me06MUUmTtylolylsGjGQVK+sz5Zn9OKEvpNZuTOaQ0/CInLCWiZRGg0gI9JcVNDuzfCPUNAJgeT5ABAACABDfIAAAAQIIbZAAAACAxagxyK6Xpz/q2i8Rc9rVVms4uJ54zJ9Z5aCW/xX5K2u3bpy+2tWYlvpqVz0rjhmteZ6Uxt7X7Ke0/sk1OfH607Ui72xHpp9pomW4UQBmeIAMAAAAJbpABAACAxFJW0oukKctJWRatilaSyqlGWyXtLm5XO/1V6dhSYyxR55zzmmEpNfbpUhp+k6PV9dxnjOX90iqXfU7vf+LUweEDAwBMgifIAAAAQIIbZAAAACCx9JX0Ir/vE/0Ge2lGhEj/fUqXrofqy0jRaixjLamXZm6oGfoR/ZZ6qywaNcOC+rbL+Wy1quS3qNUxz6nmucxWcczbDecAWB48QQYAAAAS3CADAAAACXP30Trb++hz/NDhCwftU7OARiq6JBpdHq65f+n7HKsYwtBv99fO3FEzFKZr/z41C6WUhjjktBXV6n3m7F/SR5/SLBaRsJITpw7q1tuO2+DBVbbjrN1+7s6Lpx4GgCWwjsVpLrjrZ4+4+76ttgs/QTazHWZ21Mz+dP7zQ8zscjP7tJm9w8x2lgwYANCPeRgAxjEkxOJlkq5Mfn6dpNe7+0WSviLpxTUHBgC4E+ZhABhBKIuFme2W9HRJr5H0cjMzSU+S9Lz5JpdJ+jVJv9/XTprFoqXIEnvpt/uj2QlKQxymCLeomWmgT6tQjJZFK4aKXic5+0fG3PJYlC7NlWahSLUMpenaZ+hxOrB/Y3B/qVrzcLRgEwAMMdbfHWOJPkF+g6RflHTb/Od7SbrJ3W+Z/3xc0rDgYgDAEMzDADCSLW+QzewZkm5w9yPprzfZdNNv+5nZS83sCjO7wv3rmcMEgPVVcx6+cePWJmMEgO0kEmLx3ZJ+yMx+QNJdJX2zZk8yzjezs+dPL3ZLum6znd39UkmXSrNvT1cZNQCsl2rz8N5Hn8M8DABb2PIG2d1fJelVkmRmT5T0C+7+fDN7l6RnS3q7pBdKel/DcUqqGy/XlzKsZiW/nDjbnHjkoTE9tdOP5RiaPqzvPZemPMuJhx1afXGrtofK6b9rLDkpCKPbDK1Y2HeMIpX8+vaJ/L6vvZzzXONzs0zzcJcp5gcA09rOn9OSQiG/pNkXRa7SLBbujXWGBAAIYh4GgAZCWSxOc/cPS/rw/P+vlvSY+kMCAHRhHgaA9gbdIJfqSi+UUzksZ+k8KifNW+mSauly+VDRcIWWqeUiy9il10mr0Ik+0fMU2W6s6oE5oqELQ8dWGuIRVZraLppaMK2kt2zGutZztErvB6y70s/tunzuSkIsAAAAgG2HG2QAAAAgYe7jZfzZcdZuP3fnxZLKwypSLZdkc7I95CitsNbVVk6mgEi7fW1HtxkaLlC7ql/N4zRWiEOr67lmRodo/zWrVJZ+TqPXdsl1cuLUQd162/HNchePau+jz/FDh7euJ9Iyg00tU3zWcqzLkjRWwxQheV2mmFsuuOtnj7j7vq224wkyAAAAkOAGGQAAAEhsiywWi0qzSIwhp4BEzcIIOUvS0QIOpUoLtZRmpKh5bdUuINHqOJdmCOnafnG7msv2U2RQiP5+6mXLGpY1rCK1CmOU6oYpARgHT5ABAACABDfIAAAAQGLUEIuo0m9Y5hQjGNru4v41v2mfkyA/Z+k70nY0u8AYhRqiYQA1Qim6+qxZuKZVAYyu/vr6zAm36OsnOp6t2u0bW83iPKV9RjJvHNi/MXiM2N62Y2hOC2Nlk1oXHKcYniADAAAACW6QAQAAgAQ3yAAAAEBiKWOQI3Iqb0WVxj1H0ozVTnE1Rvqw2vFyQ2NwS9Ov5VwntSvpLVOselTkvUUrJtasUhj9bEX6yYmBjra3KqnIMD3SwZVZpgpxWH08QQYAAAAS3CADAAAAiVFDLI4d3XVm2SMnRKJlKqrSNGORpZ3S9F/Rpfuhlc/6Xqsd1hDZLqcSXuSYL1uFxZrLgaWp7WqGPvRtV7JNdLvaVTYjSNeFlkr/7lpFNcMQt+sxQls8QQYAAAAS3CADAAAAicmyWJR+67zP0G/dR9tq2f/Qfsb6Nv3Y1fKGbNdqCS0nlCWyfW2l2SG65GRIKV0CLg2fKh1Ly8qap7c7cerg4D6AdULGl/WwKueZJ8gAAABAghtkAAAAIDFqiMWevRs6dHj2aL00I0Of0iwQpVotvZcuo49VwCLaZ6T/nLa69qmZKSG6T18oTWnISsk2uUoztLTqszTDSd8+pWElp7c7sH+jc/vtoHbBJsS0mjvHMsZ1so5ZQFCOJ8gAAABAghtkAAAAIDFZFotUaTGJRTUzJ0TDPYaGdUwdIrHYVqtv9/cZWpwkJ0Qibatl5pJoWzULdUQ+DznL3qVhIbWzaJSMZav2au6z6movNdecU1BmmYtmlIbxlfaJcazi554nyAAAAECCG2QAAAAgwQ0yAAAAkBg1BvnY0V2bxv7kpG9rGec4dCw5+0TTztSsMJaqEQ/UKm57aGxy3z4511apsWLqSlO+RY9/acW+0hjmyPVUev5K005GxrwslfS65uGxTBFzittNMScCq4gnyAAAAECCG2QAAAAgsVJp3lqmqomEC9Ss3JWzpDtWVbiomlXhlil5exs0AAAY9klEQVTNXLTtMVKmbdXeVu2WVp/sUxrWMrTdXDWvLZangboIs9k+lu1cds/Dl4T25wkyAAAAkOAGGQAAAEiYu4/W2Y6zdvu5Oy+WVDcjQw1Dl/tzvmmfygmxiKqZBaLlcn3kvdVc0s4ZS04WiLEq9pWGDtQMbco5Tjlj6VLaf8vxpFksbr3tuBU1XEE6D09t6iXZqUNhpn7/US2PU81jMPX5XHdTX8/R83/zyUuOuPu+rbbjCTIAAACQ4AYZAAAASIyaxWLP3g0dOnznR/A1wwj62iv91npO0YvoNjWLbkT6XNy+VVhJ35hbLbdHtVhG7/v94muRseRcZ5F2+/S1G8mwUns8kf5z9sm5toGaxgrHWiYti1Rh/bS8FniCDAAAACS4QQYAAAAS3CADAAAAiaWopLcoEv+Xk7KspmglvVbV2qKxrX37dO2fU70vp5Jb13Y5FQfHqt5WOuautqJjaRXDXLMSYsvUfqWfjZxqmKXfKTj92oH9G539ActsO8VAI88yXQNjxaDzBBkAAABIcIMMAAAAJEYNsTh2dFfo0XhOyrCu/aOGLte3qoK22HZp5bJSLfvJObdd/ee0VTNNWs3tWlaV63qtZpXIqNJwh5xjXhoWE9VVSQ/IUfNzt4pI69bOOl5PUTxBBgAAABLcIAMAAACJybJYlFbCi1ZoK12aiWbRKA3LiFQly8nuEOmvxnalmUdy1AxziYQeRPcvrbjYtX1UacXG0oqTpaKfrZqVGPuOU63wH7JYLIdVX67P+btn1Y0VUtjKOpyj1qY4zzxBBgAAABLcIAMAAACJUUMs9uzd0KHDs6WGmo/LcwoDlC4j1w7dmCIsomufnHCBVKtjWxqu0KfGsnzJPjULfeQUdImMJbpd9DqJjiunOEiX0uNUEnJEFosZlptRU2kxrin6x2rgCTIAAACQ4AYZAAAASCxlFosupUv6NZdCcr7NHt2/ZnaFqFZFE6YIg8hZhs/JEDJ2iEkNrcKMcj6DpdkhaqqdGWAVvlkPrCvCIlbD1PNo6AmymZ1vZu82s783syvN7PFmdk8z+6CZfXr+3wtaDxYA1hlzMQCMIxpi8TuS/tzdHybpkZKulPRKSR9y94skfWj+MwCgHeZiABjBljfIZvbNkp4g6Y2S5O6n3P0mSc+UdNl8s8skPavVIAFg3TEXA8B4IjHID5W0IenNZvZISUckvUzSfd39ekly9+vN7D5DOo7GH0ZiUPriByNpsRaVVhXLSUs1dnx0Xyqt6D6R45wTW1t6zErTj5XG00b6iPbZ8jqZIqa/9PM4NGVczlii7UXTv1WspNdkLgYA3FkkxOJsSY+S9PvuvlfS1zVgCc/MXmpmV5jZFTdu3Jo5TABYe9lzcToPu3+95RgBYFuI3CAfl3Tc3S+f//xuzSbpL5rZ/SRp/t8bNtvZ3S91933uvu/eu3bUGDMArKPsuTidh83OG23AALCqtgyxcPcvmNk1Zvat7v5JSU+W9In5nxdKeu38v+8b0nHfsunQSngtK8xFDU1ZVbvaWav0Y1GlFc669O0/9JiXVhjs6yf6+7FDBGqEaJRWsquZMq3mdRadg6b4PG2m1VwMALizaB7kn5H0VjPbKelqSS/S7OnzO83sxZI+L+k5bYYIAJhjLgaAEYRukN39o5L2bfLSk+sOBwDQhbkYAMYxaiW9Y0d3nVmurP1N84gxMgAsvlb6Tf2alcsivx/ST2lYydCKgaXL6ItqhFxs1k9pRobSaz56bXaNa8hrQ7fPyXYyNKyiNHNI3ziHZq5Itztx6mBoXNsRlcsArJpooRAAAABgLXCDDAAAACRGDbHYs3dDhw7XWWrLWUau3U+q1Tf1o+EaNbM4RMM6hhYKiY6tNCxkaLtDtmuV3aA0fKZm4Z3oPmMU1OnbLidzR845y8mi0TJjDrBd1QypBErxBBkAAABIcIMMAAAAJEYNschRWnSjtIhI6TJ2qywS0YwQpcVVlilcIKdoR2lGiajo0n1pWEZknLWXKYcep9LzlFNcJUfNcBMAeVpl8wFK8QQZAAAASHCDDAAAACS4QQYAAAASK1tJb6zY2NK2W6bfSpVW3Csdy9AKcX37RGNeS+Orc87Z0GMbjYGO7j/0fJb2H207+tnMuU6HntvSKpOLavV5YP9GqD+gD/G4wDh4ggwAAAAkuEEGAAAAEkuR5i26vFq77aH7RFOOlaY5S7UKIxir2lpOuMIyhaXkVGxsuXQ/ddq+km1q759TSS/a/9BwrtJQGGBdkCoRq4InyAAAAECCG2QAAAAgsRQhFtHlyZpLM8uWxaKrrcjvF3X1X7oMXxpWUntpbWgoTM4yesuKhxE1w0gW26sZotC3f3Rskf67zmfLUKxaYU4nTh3MHB1qqllBE8D2xRNkAAAAIMENMgAAAJAYNcRiz94NHTo87BvhpUvf0X1K1QyrKF0CbJUdIifbSM0lzJyl+75jmfM+a56nLjWzYOQUWoluV7PQR2m2k67++rQqVLKuyNwBYDvhCTIAAACQ4AYZAAAASEyWxSK6pJqzvDu06Ebfdl3t5izJli6dt1zqbZXdIFpcpVTp0nurEIm+dkvPZ6v3nJN5IydEoqvPGoU+hu4fbS/62SAUYzWUZplpiZAVYFo8QQYAAAAS3CADAAAACW6QAQAAgIS5+2id7Thrt5+78+I7/T4aBzZFbGfUGJXkaqevGrp/tMJZ1zal/edsV/s6qRkPW7MSXM3xR/sp/TxGj8XQ81wjdrPF5/nEqYO69bbjVjSwCrrm4VLEzAKoqdV3Am4+eckRd9+31XY8QQYAAAAS3CADAAAAicnSvEWX43LSQpU+ls8J8Ri6DFua8i36HktT2421dN+lVZq8aNstw2JKwzVytKry2PLz3CqsojSUhwp7ADDcqsyXPEEGAAAAEtwgAwAAAImlrKQ3dEm1NNPBkO26tmmVkSAnU0BXWznG+mZ6abhDzjGL7N8yc0hpxcaa4Ts557n0feZoFRYzRpXHA/s3qrUJAGiLJ8gAAABAghtkAAAAILGUWSxaFQbICVGI7j+03dKl/2jmjpYhEkPDGkozOvSpGSJQep2M1X+rY1Y7Q8vQz1bOdVK7OEtpyM66FM1Y9fc51mcdWHerkrkixRNkAAAAIMENMgAAAJDgBhkAAABIjBqDvGfvhg4dnsV1lVZ4i1bealVhK2fMOfvXjH/MidOM7h9pq3aFtJqVzHLipmum42ul75hHU9sNrSSXkzKtZpXK3H4ifVI9j9hcAFvbDvMjT5ABAACABDfIAAAAQGKyNG+p2lWscqptlS7316wE1yUnrCMnTVz0+A9Nn1Ua7lI6lmgoTl+4QGmfQ89z9DzVThs4dP8xPrNDtouIvv+cz2bNcWIapXMyxjdFulPcbjuEVaR4ggwAAAAkuEEGAAAAEqOGWBw7uuvMI/iW4QoRpUui0ewA0W0iS/w53/Rf5qWlMZahc0IH+gwNq4heZ6VLg1NUIkzVfM+1s1jUzNyRE6Jy+rUTpw6GxouZVViurR0eiHo4FyjFE2QAAAAgwQ0yAAAAkFiKQiGLhmaUKP0Gft92UaVL5K3CSkqXobu2yR1PyVhqZ9cozU4wtP/N2ttqn1aFbvq2a1lAo/Q6b/m57+on5/erEB6wjFb9uJFFYRyrfp1sJ9v5XPAEGQAAAEhwgwwAAAAkJstikYp+g7zm8mhO6EGqdBm47z3nFN0oLdSRk3ljqGjmjkgBj8XX+vop6X9R6fEYugRbOubScInFNnIyd0TkhMKUFuQZK/zp9D4H9m+E+sP2Q+GY1bMqoQNTXE+rcmxK8QQZAAAASHCDDAAAACS4QQYAAAASoRhkM/t5SS+R5JI+JulFku4n6e2S7inpI5Je4O6noh3nVJXLiXksTVmWE5taqmZVs5xtSmO9a6bfisaT5iiNIS6NR66ZsqxlOr/IWHJEY8VLx5JTvS+nn632qVFJr8VcjPU29JpehpjXmmNY9XjaVvHtq35catjyCbKZXSjpZyXtc/dvl7RD0o9Iep2k17v7RZK+IunFLQcKAOuMuRgAxhMNsThb0t3M7GxJ50q6XtKTJL17/vplkp5Vf3gAgARzMQCMYMsQC3e/1sx+S9LnJf2TpL+QdETSTe5+y3yz45Iu3Kqtrkp6OcsCtSuERfqpuQwbDSuJKg13GFq9cKvXNvt96fGrUQkvsn/f+xr6fkqXvKao0FZa5bL2GLuOecvPc80wp1pp3mrOxcAqITVeDGERdUVCLC6Q9ExJD5F0f0nnSXraJpt6x/4vNbMrzOyKGzduLRkrAKytkrk4nYfdv952oACwDURCLJ4i6bPuvuHu35D0Xkn7JZ0/X+aTpN2SrttsZ3e/1N33ufu+e+/aUWXQALCGsufidB42O2+8EQPAijL3TR/83r6B2WMlvUnSd2m2rPcWSVdIeoKk97j7283sP0k65u6/19fW3kef44cOz1b/Sr91niMnLKOmnGphUVN8e7VVWEip0vHnhGV0tZuj5rWQE8pTO4vF0Kw0ueOJKO2/JPznxKmDuvW24xYe7IJac/GOs3b7uTsvzh1G0+XudV8iXoYMEUOtevjDul9z6+jmk5cccfd9W2235RNkd79csy+AfESztEJnSbpU0i9JermZXSXpXpLeWDRiAEAn5mIAGE8oD7K7/6qkX1349dWSHlN9RACATTEXA8A4QjfItRw7uuvMckbfsmVkGbN0SXasLBJDt8ndZ2hBlZbLSq2KfuRk0ehTWhymb2xb9bG4T06fOUUvItdD6Wdr6swbNT5nXcej5JiVZrHA9jdGqB8Iq0AMpaYBAACABDfIAAAAQGLUEIvUWEtJLTMCRPqsuYyek50gJ0Sg1fJT31hyxj80lCRn6b+0aEbfPjWvh+g2peFLEX3XZo32Nmu3tHBQzeus67UTpw529gFMZazQO2DV8AQZAAAASHCDDAAAACS4QQYAAAASo8Yg79m7oUOHZ/FOpWmlWlbFK407jvy+dCy143lzDI2H7ROJJ+2L8yx9b6Vp4nKu01bntjRNXMtKgpEx58Qw1/x+QM4+U6S2A5CHuGtE8AQZAAAASHCDDAAAACQmS/OWapmiqaut0rGVVhuL9tkqFVh0n+gycs7SeU21U5OdVjtEomaatSmObWnKs9L+u9qtPQcMrZhXuzInMIWxwvOAVcATZAAAACDBDTIAAACQWIoQi0VDvykfXdIdKxQjZxk9MuaxMh2U9pPTVkTtTAGR8JmcJfmutvq2G9ruZm0P3afmmGuGuPSd56Gfs2ifQ14b2ufp1w7s3xjUJqbVKjQIwGrgCTIAAACQ4AYZAAAASIwaYnHs6K4zy07Rb3m3ChfIyUJRM7tAaTGGvn1Kv91fepy6tmkZrtBqOTMnrKN06b5mEZyamVv6+i8tmlEz/GhRq4I2faE4fOufEINVxzWMdccTZAAAACDBDTIAAACQGDXEYs/eDR06PGxZvpXSjAjRMea8l5ZhCUP3j25TmmA+Mv6ctqIZKXKKm9Qs7tGq6Ej0Oi8N68kR3T9yPKIhGjVDnobuc+LUwc7tV8l2Cp0gjAAYrvR+Y1XwBBkAAABIcIMMAAAAJLhBBgAAABJLkeZt0dA4lr6Yw5xYmZrV36Ltlqb/irRVM31YtM+cdktjcFO1qye2ilksPf7RGObSWPGaVSbHSrsYGUvLNG1U0gNixpqHt1usbC21q91GLPO54AkyAAAAkOAGGQAAAEiMGmIRFVl6zQlXKE0TFukjV+nSd812o+85knKrz9AKZy1DTGqGGNRMbReVkzItZ5uan42ccIucqniRKpN9+0R+3+f0PtslzRswtWVelsf2wRNkAAAAIMENMgAAAJBYykp6kSXy2t9AL/2mfWlbkTFHw0pyxtylNPNFzYwUfSL952RK6NuuVeaPsb6hXRoKUhpK03Vuxqr+l1MZMqrmZxAAtqtlnit5ggwAAAAkuEEGAAAAEkufxSIVXZKObDd1iEJpGEjfa0NDVPrarplRo3SpOtp2pFDM4j45YQk5x2zouckpKBPVKltGtDhJ3z4ROYVGpugfQAyfKSwTniADAAAACW6QAQAAgAQ3yAAAAEDC3H20znactdvP3XmxpLyUX6UxsJE+cvvMifsdaooY4D6lseJd+5Sm1ov00bdPaWq6aKx3TlW4LqUxzDXT1JWqmT4u2nZpqsjI/gf2X6ujR07aoIYbSOfhdVfz75RFLb9zMYYx/h6OIh65nVZ/3+YY6zzffPKSI+6+b6vteIIMAAAAJLhBBgAAABKTpXnLqWjVtX+fVUnfVPo+I8vNpcvQ0T5bVTLMGUtXH9H9S0MccrSsEJeqGW5QGqKxKsu2JfucOHVw8L7Y3pYppGIRKddW21jhQ8t8DZfiCTIAAACQ4AYZAAAASIwaYrFn74YOHS77dvhmamTE6KqqVvMb9VNXCysdSzQjQ6ll+lZt7YwKQ89NzXMefW2scImczBs5oUilIUetqmyuqmXLprOsttPS83Z6L6hrO3+eeYIMAAAAJLhBBgAAABKTZbFIjZWRIqfPmssHpe8zJ5QkR82MCNF+Ir9fxaXdloU6WskpbtIVotS3XbT/LjVDNEr7iYR4HNi/MbhvAMA0eIIMAAAAJLhBBgAAABJLUShkUSQsonbRi0h7NQtIRJfeo4aOP9pWqb73PDTbR7SARavsDIttlGYLGWO5v3aGl6FjzNkuJ/NG3zY5n9sWxV4oFAJgmZGl5454ggwAAAAkuEEGAAAAEtwgAwAAAImlSPNWO8VVJB6ztM8asZ1D5cRal1b1m6ISYFRkbLXPU2llx5J2F7ebIh1gaTzv0O8X5G7XpTQ1XE7c9nZI81ZzjibOESizTGlBtzOeIAMAAAAJbpABAACAxKghFseO7tp0Sa1myre+/UuX+KP7l445omW4Q1RO2r2u8eRs31W9rVVqv77thm4TVfqec8ZSO81aRN+5qPnexrLZ+yHNG4BVUTsV7SriCTIAAACQ4AYZAAAASJi7j9eZ2Yakr0u6cbROl9O9td7HgPfP+1/H9/8gd9819SDm8/DntL7n4TTeP+9/nd+/tL7HIDQXj3qDLElmdoW77xu10yWz7seA98/7X+f3vyzW/Tzw/nn/6/z+JY7BVgixAAAAABLcIAMAAACJKW6QL52gz2Wz7seA97/e1v39L4t1Pw+8//W27u9f4hj0Gj0GGQAAAFhmhFgAAAAAiVFvkM3sqWb2STO7ysxeOWbfUzCzB5jZITO70sw+bmYvm//+nmb2QTP79Py/F0w91pbMbIeZHTWzP53//BAzu3z+/t9hZjunHmMrZna+mb3bzP5+fh08fp3Ov5n9/Pza/zsze5uZ3XWdzv+yYi5ev7l4nedhibmYuXi40W6QzWyHpIOSnibpEZJ+1MweMVb/E7lF0ivc/eGSHifp4vl7fqWkD7n7RZI+NP95O3uZpCuTn18n6fXz9/8VSS+eZFTj+B1Jf+7uD5P0SM2Ow1qcfzO7UNLPStrn7t8uaYekH9F6nf+lw1y8tnPxOs/DEnMxc/FAYz5Bfoykq9z9anc/Jentkp45Yv+jc/fr3f0j8///mmYfyAs1e9+XzTe7TNKzphlhe2a2W9LTJf3R/GeT9CRJ755vsm3fv5l9s6QnSHqjJLn7KXe/SWt0/iWdLeluZna2pHMlXa81Of9LjLl4zebidZ6HJebiOebigca8Qb5Q0jXJz8fnv1sLZvZgSXslXS7pvu5+vTSbuCXdZ7qRNfcGSb8o6bb5z/eSdJO73zL/eTtfBw+VtCHpzfOlzT8ys/O0Juff3a+V9FuSPq/ZZPxVSUe0Pud/WTEXr99cvM7zsMRczFycYcwbZNvkd2uRQsPM7i7pPZJ+zt3/cerxjMXMniHpBnc/kv56k02363VwtqRHSfp9d9+rWZn1bbmEt5l5PN8zJT1E0v0lnafZsv6i7Xr+l9U6fQbvYB3nYuZhSczFzMUZxrxBPi7pAcnPuyVdN2L/kzCzu2g2Ib/V3d87//UXzex+89fvJ+mGqcbX2HdL+iEz+wfNlnGfpNmTjPPnyzzS9r4Ojks67u6Xz39+t2aT9Lqc/6dI+qy7b7j7NyS9V9J+rc/5X1bMxes1F6/7PCwxFzMXZxjzBvlvJV00/9bkTs0CxN8/Yv+jm8d5vVHSle7+28lL75f0wvn/v1DS+8Ye2xjc/VXuvtvdH6zZ+f5f7v58SYckPXu+2XZ+/1+QdI2Zfev8V0+W9AmtyfnXbDnvcWZ27vyzcPr9r8X5X2LMxbfb9p/FdZ+HJeZiMRdnGbVQiJn9gGb/ct0h6U3u/prROp+AmX2PpP8t6WO6PfbrEs1i394p6YGaXbjPcfcvTzLIkZjZEyX9grs/w8weqtmTjHtKOirpx9z95JTja8XMvlOzL8bslHS1pBdp9g/TtTj/Zvbrkn5YsywCRyW9RLM4t7U4/8uKuVjSGs7F6zoPS8zFzMXDUUkPAAAASFBJDwAAAEhwgwwAAAAkuEEGAAAAEtwgAwAAAAlukAEAAIAEN8gAAABAghtkAAAAIMENMgAAAJD4/1NBmw/asc6AAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Affichage état initial et final\n", "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(10, 10))\n", "axes[0].imshow(S0, interpolation='none',cmap='plasma')\n", "axes[0].set_title('Configuration initiale')\n", "axes[1].imshow(S, interpolation='none',cmap='plasma')\n", "axes[1].set_title('Configuration finale')\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Utilisation du modèle d'Ising conditionné par une image\n", "\n", "On peut modifier légèrement le modèle précédent en le forçant à ne pas trop s'éloigner d'une image $I$ sur le même réseau (dans l'interprétation physique, $I$ réprésente un champ magnétique). L'idée est de simuler non plus directement sous la loi $\\mu_\\bet$ mais sous une loi a posteriori qu'on va noter $\\nu_\\bet$ et qui dépend de $I$. Notons $I$ cette image, de taille $N\\times N$, **qu'on suppose à valeurs dans $[-1,1]$** (si l'image est sur $[0,256]$ ou sur $[0,1]$, il faudra donc la normaliser pour que son minimum soit à $-1$ et son maximum à $1$). On note $I_{i,j}$ la valeur de l'image à la position $(i,j)$. \n", "\n", "L'énergie associée à la configuration $S$ est alors\n", "$$E(S|I) = \\sum_{(i,j)\\sim (k,l)} (s_{i,j}-s_{k,l})^2+c\\sum_{(i,j)\\sim (k,l)} (I_{i,j} - s_{i,j})^2,$$\n", "avec $c$ une constante permettant de modifier le poids relatif des deux termes.\n", "En développant, on se rend compte que cette énergie est égale (à une constante additive près ne dépendant pas de $S$) à $2H(S|I)$ avec\n", " $$H(S|I) = -\\sum_{(i,j)\\sim (k,l)}s_{i,j}s_{k,l} - 2c \\sum_{i,j} s_{i,j} I_{i,j}.$$\n", "Le premier terme de l'énergie favorise les états avec des zones constantes, alors que le deuxième favorise les états bien corrélés avec l'image $I$.\n", "\n", "On note $\\nu_\\bet$ la mesure\n", "$$\\nu_\\bet(S) = \\ff{Z_\\bet}\\me^{-\\bet H(S|I)}.$$\n", "\n", "Lorsqu'on modifie la valeur de $S$ en la position $(i,j)$, la variation de l'énergie $H(S|I)$ entre les deux états s'écrit \n", "$$\\Delta H_{S|I}(S,S^{\\rightarrow(i,j)}):=H(S^{\\rightarrow(i,j)}|I)-H(S|I)=2s_{i,j}\\sum_{(k,l)\\sim (i,j)}s_{k,l} + 2 c s_{i,j} I_{i,j}.$$\n", "\n", "La fonction $\\rho$ est alors donnée par \n", "$$\\rho(S,S^{\\rightarrow(i,j)})=\\me^{-\\bet\\Delta H_{S|I}(S,S^{\\rightarrow(i,j)}) } .$$\n", "\n", "### Exercice\n", "\n", "1. Commencez par récupérer une image en ligne, par exemple celle du cameraman disponible ici \n", "https://web.stanford.edu/class/ee398b/data/image/cman.tif\n", "et importez cette image à l'aide de plt.imread dans une matrice. Normalisez-la pour qu'elle soit entre -1 et 1.\n", "\n", "2. Implémentez l'algorithme de Metropolis-Hastings pour cette mesure, pour plusieurs valeurs de $c$ et de $\\beta$ et commentez les résultats. Quelle est l'influence du paramètre $c$ sur les résultats ? Déterminer des témpératures pour lesquelles les échantillons semblent dépendre très peu de l'image $I$, et des températures où au contraire le résultat semble très fortement corrélé à $I$. \n", "\n", "3. Faire tourner l'algorithme pour $T=0$ (on accepte une transition si et seulement si elle fait diminuer l'énergie). Que doit-on obtenir en pratique ? Combien d'itérations faut-il pour que l'algorithme se stabilise ? Le résultat obtenu dépend-il de l'initialisation ?" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "I = plt.imread(\"../im/cameraman.tiff\")/255 # image sur [0,1]\n", "plt.figure(figsize=(5, 5))\n", "plt.imshow(I,cmap='gray')" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# paramètres\n", "beta=int(1) #beta = 1/T\n", "N,Npas=256,int(1e6) # NxN est le nombre de positions sur la grille et Npas est le nb de pas d'évolution de la chaîne \n", "c=0.5\n", "\n", "# Initialisation (essayer plusieurs états initiaux possible, très aléatoire ou au contraire très déterministes)\n", "S0=2*np.random.randint(2,size=(N,N))-1 # initialisation aléatoire\n", " \n", "# On fait evoluer la chaîne de Markov \n", "S= np.copy(S0)\n", "for t in range(Npas):\n", " S=transition_im(S,N,c,beta,I)\n", "\n", "# Affichage état initial et final\n", "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(10, 5))\n", "axes[0].imshow(S0, interpolation='none',cmap='plasma')\n", "axes[0].set_title('Configuration initiale')\n", "axes[1].imshow(S, interpolation='none',cmap='plasma')\n", "axes[1].set_title('Configuration finale')\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Recuit simulé\n", "On va maintenant calculer le maximum de vraisemblance de la loi $\\nu_\\bet$ en utilisant **l'algorithme de recuit simulé**. \n", "\n", "On rappelle que cet algorithme diffère de celui de Metropolis-Hastings uniquement par le fait qu'on fait lentement baisser la température $T$ (ou augmenter $\\beta$) au fur et à mesure des itérations. \n", " \n", "Pour la fonction $t\\mapsto\\bet_t$, on propose de choisir $\\beta(t)=2*log(t+2)$.\n", "\n", "1. Modifiez vos fonctions précédentes pour implémenter l'algorithme de recuit simulé sur l'exemple précédent. Faites un graphe de l'énergie au cours des itérations. " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# paramètres\n", "N,Npas=256,int(1e6) # NxN est le nombre de positions sur la grille et Npas est le nb de pas d'évolution de la chaîne \n", "\n", "# Initialisation aléatoire\n", "S0=2*np.random.randint(2,size=(N,N))-1 \n", "\n", "# On fait evoluer la chaîne de Markov \n", "S= np.copy(S0)\n", "for t in range(Npas):\n", " S=transition_im(S,N,c,2*np.log(t+2),I)\n", "\n", "# Affichage état initial et final\n", "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(10, 5))\n", "axes[0].imshow(S0, interpolation='none',cmap='plasma')\n", "axes[0].set_title('Configuration initiale')\n", "axes[1].imshow(S, interpolation='none',cmap='plasma')\n", "axes[1].set_title('Configuration finale')\n", "fig.tight_layout()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 2 }