gamma-variation-v0.2.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Gamma Variation Heuristic**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "## import essential modules \n",
    "import qumcmc \n",
    "from qumcmc.basic_utils import *\n",
    "# from qumcmc.energy_models import IsingEnergyFunction\n",
    "from qumcmc.energy_models import IsingEnergyFunction, Exact_Sampling\n",
    "\n",
    "from qumcmc.classical_mcmc_routines import classical_mcmc\n",
    "from qumcmc.quantum_mcmc_routines_qulacs import quantum_enhanced_mcmc     #for Qulacs Simulator backend (** Faster )\n",
    "# from qumcmc.quantum_mcmc_routines_qiskit import quantum_enhanced_mcmc   #for qiskit Aer's Simulator backend \n",
    "\n",
    "from qumcmc.trajectory_processing import calculate_running_js_divergence, calculate_running_kl_divergence, calculate_runnning_magnetisation, get_trajectory_statistics\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **Cardinality Dataset**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['0011', '0101', '0110', '1001', '1010', '1100']\n"
     ]
    }
   ],
   "source": [
    "size = 4; card = 2\n",
    "DATA = get_cardinality_dataset(size, card); wts = hebbing_learning(DATA); print(DATA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RIzA2aNAg5ebmqqKiImh9p9OpXr16Ga9NZgQAABP18KVnTz/9tMaPH6/09HQlJiaqoKBAmzdv1ssvvxw0LzY2VsnJyVq8eLEkKSMjQ2FhYerZs6ecTqcOHDig1atXq3v37hoyZEjgvtTUVGVnZ2vWrFkaO3asvvzyS2VlZWnGjBnG7xiRCEYAADBTBxpYa+u+++5TZmamXnnlFb399ttq166dFi1apMTExKB5lZWVqrrs94uOjtaGDRu0ceNGlZWVqXXr1ho1apSmTZumRo3+Hjp06tRJWVlZysjI0FNPPaWWLVtq2rRpmjRpUq32Geav7Qvkb5JGjvZ2bwF/w2mauoXTNEB1F8tPWf6M79PHhmSdZukbQrJOQ0JmBAAAE/WwTFNfEIwAAGCiDpymaag4TQMAAGxFZgQAABOUaSxDMAIAgIG68Dr4hooyDQAAsBWZEQAATFCmsQzBCAAAJghGLEMwAgCACY72WoaeEQAAYCsyIwAAmKBMYxmCEQAADPgJRixDmQYAANiKzAgAACbIjFiGYAQAABO8gdUylGkAAICtyIwAAGCCMo1lCEYAADBBMGIZyjQAAMBWZEYAADDg95MZsQrBCAAAJijTWIZgBAAAEwQjlqFnBAAA2IrMCAAABvhuGusQjAAAYIJgxDKUaQAAgK3IjAAAYIKvprEMwQgAAAboGbEOZRoAAGArMiMAAJggM2IZghEAAEzQM2IZyjQAAMBWZEYAADBAA6t1CEYAADBBmcYylGkAADDgr/KH5Odme++99zR8+HD16NFDDz30kDZt2lTjPZmZmYqJibniz4IFC2qct2HDhlrtkcwIAAAN1J49ezR16lSNGjVKaWlp+vDDD/X888+rWbNmGjZs2FXvS0lJ0cCBA4PGPv74Yy1btkyDBg0KGm/cuLHWr18fNNaxY8da7ZNgBAAAE/WwTLNy5UrFxcVp4cKFkqS+ffvqxIkTWrFixTWDkTZt2qhNmzZBY2+99ZYiIyOrBSPh4eHq2bPnDe3TkjLN//7v/+rjjz+2YmkAAGzhrwrNz81SXl6ugoKCakFHUlKSjh49qpMnTxqvdeHCBW3fvl0PPfSQHA5HqLdqTWbko48+0vTp0/XFF19YsTwAAPVWQkLCNa/n5uaG5DmFhYWqqKiQy+UKGo+OjpYkeTwedejQwWitHTt2qKSkRA8//HC1a2VlZerbt6+8Xq86d+6siRMn6rHHHqvVXinTAABgop6VaYqLiyVJTqczaPzS50vXTWzevFmtW7dW7969g8ajoqI0e/ZsxcbG6sKFC8rOztb8+fPl8/mUmppqvH6tgpFHHnnEaN73339fm2UBAKjzQlViuZHMh8/nU1FRUY3zattAei1er1c7d+7UE088ofDw4O6OESNGBH2+//77VVFRoZUrV2r8+PGKiIgwekatghGPx6Mf/ehHio2Nvea8U6dO6ZtvvqnN0gAAoAY5OTmaN29ejfPcbrciIyMl/RDAXM7r9UpS4HpNtm7dqvLycuOERGJiorZu3arCwsJASagmtQpG7rnnHnXq1ElLliy55rytW7fSwAoAaFjqQJkmJSVFKSkpRnPLy8sVEREhj8cTdEzX4/FIUrVekqvZvHmzXC5XjYmIG1Gr0zRxcXE6cOCA0Vy/n9fmAgAajvp2msbhcCg+Pl5bt24NGne73YqOjjZqXi0qKtJHH310xcbVq3G73XI6nYqKijK+p1aZkSeffFKDBw+ucd7gwYND1g0MAACuz9NPP63x48crPT1diYmJKigo0ObNm/Xyyy8HzYuNjVVycrIWL14cNO52u1VVVXXVEs3IkSOVnJwsl8ulsrIyZWdna9u2bUpLSzPuF5FqGYxERUUZRTqNGzdW+/bta7M0AAB12s3MaoTKfffdp8zMTL3yyit6++231a5dOy1atEiJiYlB8yorK1VVVf0XzM7OVlxc3FX/7o+KitK6dev03XffKSwsTF26dNHSpUs1fPjwWu0zzF9H6ymNHAQzdUXpX/Ps3gIu06TdwJonAbeYi+WnLH/G6QdqrgyYaL1jZ0jWaUh4zwgAACb8YXbvoMHiW3sBAICtyIwAAGCgPvaM1BcEIwAAGPBXUaaxCmUaAABgKzIjAAAYoExjHYIRAAAM+DlNYxnKNAAAwFZkRgAAMECZxjoEIwAAGOA0jXUo0wAAAFuRGQEAwEDd/Ca3hoFgBAAAA5RprEMwAgCAAYIR69AzAgAAbEVmBAAAA/SMWIdgBAAAA5RprEOZBgAA2IrMCAAABvhuGusQjAAAYIDXwVuHMg0AALAVmREAAAxUUaaxDMEIAAAG6BmxDmUaAABgKzIjAAAY4D0j1iEYAQDAAG9gtQ7BCAAABsiMWIeeEQAAYCsyIwAAGOBor3UIRgAAMMDRXutQpgEAALYiMwIAgAFO01iHYAQAAAP0jFiHMg0AAA1Ufn6+Zs2apSFDhigmJkYLFy40vtfn8yktLU19+vRRr169NG3aNBUVFVWbt3fvXo0ePVpxcXF64IEHtGbNGvlrmUYiGAEAwIDfHxaSn5spLy9Phw8fVu/eveV0Omt17/Tp05Wfn6/09HQtW7ZMx44d0+TJk3Xx4sXAnOPHjys1NVWtWrXS6tWrNWHCBK1YsUKvv/56rZ5FmQYAAAP1sWfkueee05w5cyRJBQUFxvft27dP77//vrKysjRgwABJ0t13362kpCRt27ZNSUlJkqSsrCzdeeedeumll+RwONSvXz+dPXtWq1at0rhx4+RwOIyeR2YEAIAGKjz8+v6a37Vrl5xOp/r37x8Yc7lc6tatm3bt2hU0LyEhISjoSEpKktfr1b59+4yfR2YEAAADoWpgTUhIuOb13NzckDznRng8Ht19990KCwv+nV0ulzwejyTp/Pnz+uabb+RyuarNCQsLk8fjUXx8vNHzCEZQoybtBtq9BVym9K95dm8Bf8O/G7eWW+mlZ16vV82bN682HhkZqYMHD0r6ocFVUrVeFIfDoSZNmqi4uNj4eQQjAAAYCFVm5EYyHz6f74onWv5Rx44djfs16gKCEQAA6omcnBzNmzevxnlut1vR0dHX/Ryn06lvv/222nhxcbEiIyMlKZA5uZQhuaS8vFylpaWBeSYIRgAAMFAXDtOkpKQoJSXF8ue4XC7t3r1bfr8/qG/k2LFj6tKliySpadOmatu2baCH5PI5fr+/Wi/JtXCaBgAAA1X+sJD81AeDBg1ScXGxdu/eHRg7duyYPv/8cw0aNChoXm5urioqKgJjbrdbTqdTvXr1Mn4ewQgAAA3UqVOnlJOTo5ycHJWWlqqwsDDw+XKxsbFKS0sLfO7Vq5cGDBigtLQ0bdmyRe+9956mTZummJgYPfjgg4F5qampOnv2rGbNmqXdu3dr/fr1ysrK0i9+8Yta9axQpgEAwEB9PE1TUFCguXPnBj7n5eUpL++HE3lHjhwJjFdWVqqqqiro3ldeeUVLlizRggULdPHiRQ0YMEDz5s1To0Z/Dx06deqkrKwsZWRk6KmnnlLLli01bdo0TZo0qVb7DPPX9gXyN0kjR3u7twDUSRztrTs42lt3XCw/Zfkz8tqMCsk6A799OyTrNCSUaQAAgK0o0wAAYMCv+lemqS8IRgAAMFBVJ5saGgbKNAAAwFZkRgAAMFBFmcYyBCMAABigZ8Q6BCMAABioqnkKrhM9IwAAwFZkRgAAMECZxjoEIwAAGKBMYx3KNAAAwFZkRgAAMEBmxDoEIwAAGKBnxDqUaQAAgK3IjAAAYKCKxIhlCEYAADDA6+CtQ5kGAADYiswIAAAG/HZvoAEjGAEAwABHe61DMAIAgIGqMHpGrELPCAAAsBWZEQAADNAzYh2CEQAADNAzYh3KNAAAwFZkRgAAMMAbWK1DMAIAgAHewGodyjQAAMBWZEYAADDAaRrrEIwAAGCAnhHrUKYBAAC2IjMCAIAB3jNiHYIRAAAM0DNiHYIRAAAM0DNiHXpGAABooPLz8zVr1iwNGTJEMTExWrhwodF9Bw4c0Ny5czV06FDde++9evDBB7V8+XKdP38+aF5mZqZiYmKq/WzYsKFW+yQzAgCAgfrYM5KXl6fDhw+rd+/eKi4uNr5vy5YtOn78uJ588kl17txZX3/9tVasWKH9+/frjTfeCJrbuHFjrV+/PmisY8eOtdonwQgAAAbqYzDy3HPPac6cOZKkgoIC4/smT56sli1bBj7Hx8fL6XRq9uzZOnjwoLp37x64Fh4erp49e97QPinTAADQQIWHX99f85cHIpfExsZKkoqKim5oT1dyXZmR8+fPq2nTple8VlFRoTNnzqhdu3Y3tDEAAOoSf4gaWBMSEq55PTc3NzQPCrFPPvlEkuRyuYLGy8rK1LdvX3m9XnXu3FkTJ07UY489Vqu1axWMvPrqq1q3bp1KSkrUunVrpaamaty4cUFzPv/8c40ZM0ZffPFFrTYCAEBdVh/LNKFy9uxZZWZmKiEhQZ07dw6MR0VFafbs2YqNjdWFCxeUnZ2t+fPny+fzKTU11Xh942Bk06ZNevXVVzVq1Ch169ZNe/bs0ZIlS/Q///M/+vd//3fdcccdtfrFAAC4Fd1I5sPn8xmVSTp27CiHw3Hdz7lcRUWFZs6cKUlKT08PujZixIigz/fff78qKiq0cuVKjR8/XhEREUbPMA5Gfve732ny5MmaMWOGJGns2LEaO3asZs6cqSeeeEJr165Vq1atTJcDAKBeqQuZkZycHM2bN6/GeW63W9HR0Tf8PL/fr7S0NB04cEBvvvmm7rrrrhrvSUxM1NatW1VYWGi8B+Ng5Pjx4/rpT38aNHbfffdp48aNmjx5skaPHq3XXnvNdDkAAOqVuvAG1pSUFKWkpNy0573wwgvasmWL1q5dq65du1r2HOM2W6fTqbNnz1Ybb9Omjd588021bt1aP//5z7Vv376QbhAAANx8a9as0bp165SRkaF+/foZ3+d2u+V0OhUVFWV8j3Fm5Mc//rHeffddJSYmVrvWvHlzrVu3Tr/85S+VkZGhsDDemQsAaFjq4+vgT506pc8++0ySVFpaqsLCQuXk5EiShg0bFpgXGxur5ORkLV68WJKUnZ2t5cuXa/jw4erQoYM+/fTTwNyoqKjA0d+RI0cqOTlZLpdLZWVlys7O1rZt25SWlmbcLyLVIhh55JFHtH79ep07d04tWrSodv3222/Xq6++qvT0dOXn5xtvAACA+qAu9IzUVkFBgebOnRv4nJeXp7y8PEnSkSNHAuOVlZWqqvr7b3jp7/F33nlH77zzTtCaS5Ys0ciRIyX9EJisW7dO3333ncLCwtSlSxctXbpUw4cPr9U+w/x+f10og1XTyNHe7i0AdVLpX/Ps3gL+pkm7gXZvAX9zsfyU5c9YHvVESNaZVfhfIVmnIeENrAAAwFZ8Nw0AAAbqZBmhgSAYAQDAQH1sYK0vKNMAAABbkRkBAMBAfTxNU18QjAAAYICeEetQpgEAALYiMwIAgIEqciOWIRgBAMAAPSPWoUwDAABsRWYEAAADFGmsQzACAIAByjTWIRgBAMAAb2C1Dj0jAADAVmRGAAAwwNFe6xCMAABggFDEOpRpAACArciMAABggNM01iEYAQDAAD0j1qFMAwAAbEVmBAAAA+RFrEMwAgCAAXpGrEOZBgAA2IrMCAAABmhgtQ7BCAAABghFrEMwAgCAAXpGrEPPCAAAsBWZEQAADPgp1FiGYAQAAAOUaaxDmQYAANiKzAgAAAY42msdghEAAAwQiliHMg0AALAVmREAAAzUxzJNfn6+/vjHP2r//v06ceKEHn/8cS1YsKDG+06ePKmEhIRq4/fee682btwYNLZ371698MIL+uKLL/RP//RPGjt2rCZPnqywsDDjfRKMAABgoD6epsnLy9Phw4fVu3dvFRcX1/r+mTNnKj4+PvC5WbNmQdePHz+u1NRU9e/fX9OnT9eRI0e0bNky3XbbbUpNTTV+DsEIAAAN1HPPPac5c+ZIkgoKCmp9f6dOndSzZ8+rXs/KytKdd96pl156SQ6HQ/369dPZs2e1atUqjRs3Tg6Hw+g59IwAAGDAH6J/bqbwcGv/mt+1a5cSEhKCgo6kpCR5vV7t27fPeB0yIwAAGAhVmeZKvRiXy83NDdGTblx6erpmzJihFi1aKCEhQbNnz1aLFi0kSefPn9c333wjl8sVdI/L5VJYWJg8Hk9QiedaCEaAeqZJu4F2bwF/U/rXPLu3gJvoVnodvMPh0NixYzVgwAA5nU7t379fq1at0sGDB/WHP/xBERER8vl8kiSn01nt3iZNmtSqR4VgBACAm+hGMh8+n09FRUU1zuvYsaNxv8aV3HXXXUpPTw987tOnj+655x5NmTJF27dvV1JS0nWvfSUEIwAAGKgLp2lycnI0b968Gue53W5FR0eH9NmDBw9W06ZNdejQISUlJal58+aSFMiQXFJeXq7S0lJFRkYar00wAgCAgSq//WWalJQUpaSk2L0NSVLTpk3Vtm1beTyeoPFjx47J7/dX6yW5Fk7TAACAGu3YsUPnz59Xjx49AmODBg1Sbm6uKioqAmNut1tOp1O9evUyXpvMCAAABuzPi9TeqVOn9Nlnn0mSSktLVVhYqJycHEnSsGHDAvNiY2OVnJysxYsXS5IyMjIUFhamnj17yul06sCBA1q9erW6d++uIUOGBO5LTU1Vdna2Zs2apbFjx+rLL79UVlaWZsyYUaueFYIRAAAM1MfXwRcUFGju3LmBz3l5ecrL++EU2JEjRwLjlZWVqqr6e1dMdHS0NmzYoI0bN6qsrEytW7fWqFGjNG3aNDVq9PfQoVOnTsrKylJGRoaeeuoptWzZUtOmTdOkSZNqtc8wv78OFMGuoJGjvd1bAIBr4mhv3RHxf8z7E67Xzzv9S0jWefP4/wvJOg0JmREAAAzcSu8ZudkIRgAAMFAXjvY2VJymAQAAtiIzAgCAgfrYwFpfEIwAAGCAnhHrEIwAAGCAnhHr0DMCAABsRWYEAAADdfS1XA0CwQgAAAZoYLUOZRoAAGArMiMAABiggdU6BCMAABjgaK91KNMAAABbkRkBAMAADazWIRgBAMAAR3utQ5kGAADYiswIAAAGOE1jHYIRAAAMcJrGOgQjAAAYoIHVOvSMAAAAW5EZAQDAAKdprEMwAgCAAco01qFMAwAAbEVmBAAAA5ymsQ7BCAAABqroGbEMZRoAAGArMiMAABggL2IdghEAAAxwmsY6BCMAABggGLEOPSMAAMBWZEYAADDAG1itQzACAIAByjTWoUwDAABsRTACAIABf4j+uZny8/M1a9YsDRkyRDExMVq4cKHRfZmZmYqJibniz4IFC2qct2HDhlrtkzINAAAG6mPPSF5eng4fPqzevXuruLjY+L6UlBQNHDgwaOzjjz/WsmXLNGjQoKDxxo0ba/369UFjHTt2rNU+CUYAAGignnvuOc2ZM0eSVFBQYHxfmzZt1KZNm6Cxt956S5GRkdWCkfDwcPXs2fOG9kkwAgCAgfrYwBoeHppujAsXLmj79u1KSkqSw+EIyZqXq3UwcubMGVVUVKhdu3aSfkhbbd++XcePH1dUVJQSEhLUqBExDgCgYamPZZpQ2bFjh0pKSvTwww9Xu1ZWVqa+ffvK6/Wqc+fOmjhxoh577LFarW8cNZSUlOiXv/ylPvjgA0lSQkKCli1bpilTpqigoECNGjXSxYsX1a1bN/3Xf/2XmjVrVquNAABwK0hISLjm9dzc3Ju0E3ObN29W69at1bt376DxqKgozZ49W7Gxsbpw4YKys7M1f/58+Xw+paamGq9vHIz89re/1aFDh7Rw4UJFRkbqP/7jPzRt2jSdOHFC//3f/62uXbvq008/1dSpU/Wf//mfmjp1qvlvCQBAHVcXyjQ+n09FRUU1zuvYsWPIyiler1c7d+7UE088Ua3sM2LEiKDP999/vyoqKrRy5UqNHz9eERERRs8wDkbeffddPfvss0pJSZEktW/fXo8++qgWLVqkrl27SpJ69uyp1NRU/fGPfyQYAQA0KKE6lnsjmY+cnBzNmzevxnlut1vR0dHX/ZzLbd26VeXl5XrkkUeM5icmJmrr1q0qLCw03oNxMHL69Gl16dIl8Pmee+4J+t9LunbtqlOnTpkuCwBAvVBVB3pGUlJSAkmBm2Xz5s1yuVyKjY217BnGbbZ33HGHzp07F/jcqFEjtW7dWk2aNAmad+HChZB17wIAAPsUFRXpo48+umLj6tW43W45nU5FRUUZ32OcGfnRj36k/fv3a+jQoZJ+OC60c+fOavOOHDlSqw0AAFAf3Oy3p4bCqVOn9Nlnn0mSSktLVVhYqJycHEnSsGHDAvNiY2OVnJysxYsXB93vdrtVVVV11RLNyJEjlZycLJfLpbKyMmVnZ2vbtm1KS0sz7heRahGMPPnkk0Zvbzt48KASExONNwAAQH1QF8o0tVVQUKC5c+cGPufl5SkvL0/SD8mDSyorK1VVVVXt/uzsbMXFxV01yRAVFaV169bpu+++U1hYmLp06aKlS5dq+PDhtdpnmL+OHpxu5Ghv9xYA4JpK/5pn9xbwNxH/x2X5M7rd1Sck63xR9FFI1mlIeDsZAAAG6mOZpr4gGAEAwEB9LNPUFxx7AQAAtiIzAgCAAco01iEYAQDAAGUa61CmAQAAtiIzAgCAAco01iEYAQDAgN9f/aVgCA2CEQAADFSRGbEMPSMAAMBWZEYAADBQR789pUEgGAEAwABlGutQpgEAALYiMwIAgAHKNNYhGAEAwABvYLUOZRoAAGArMiMAABjgDazWIRgBAMAAPSPWoUwDAABsRWYEAAADvGfEOgQjAAAYoExjHYIRAAAMcLTXOvSMAAAAW5EZAQDAAGUa6xCMAABggAZW61CmAQAAtiIzAgCAAco01iEYAQDAAKdprEOZBgAA2IrMCAAABviiPOsQjAAAYIAyjXUo0wAAAFuRGQEAwACnaaxDMAIAgAF6RqxDmQYAAAN+vz8kPzdLZWWl1q5dq8cff1zx8fHq06ePxo0bpz179hjd7/P5lJaWpj59+qhXr16aNm2aioqKqs3bu3evRo8erbi4OD3wwANas2ZNrX9PghEAABqgsrIyrVmzRj/+8Y/1wgsvaNmyZYqMjNT48eO1e/fuGu+fPn268vPzlZ6ermXLlunYsWOaPHmyLl68GJhz/PhxpaamqlWrVlq9erUmTJigFStW6PXXX6/VXinTAABgoL71jDRu3FjvvvuuIiMjA2P9+/fXww8/rPXr16tfv35XvXffvn16//33lZWVpQEDBkiS7r77biUlJWnbtm1KSkqSJGVlZenOO+/USy+9JIfDoX79+uns2bNatWqVxo0bJ4fDYbRXMiMAABjwh+jnZrntttuCApFLYzExMVcst1xu165dcjqd6t+/f2DM5XKpW7du2rVrV9C8hISEoKAjKSlJXq9X+/btM94rmREAAG6ihISEa17Pzc217NkXL17U/v379ZOf/OSa8zwej+6++26FhYUFjbtcLnk8HknS+fPn9c0338jlclWbExYWJo/Ho/j4eKN91dlg5GL5Kbu3AABAQKj+XqopGLHSa6+9ptOnT2vixInXnOf1etW8efNq45GRkTp48KCkHxpcJcnpdAbNcTgcatKkiYqLi433VWeDEQAAGqIbyXz4fL4aSyyS1LFjx2r9Gvn5+crMzNS//du/qXv37te9BysQjAAAUE/k5ORo3rx5Nc5zu92Kjo4OfD506JCeffZZPfzww5o6dWqN9zudTn377bfVxouLiwN9KJcyJ5cyJJeUl5ertLS0Wr/KtRCMAABQT6SkpCglJaVW9xw/flyTJ09Wr169tGjRIqN7XC6Xdu/eLb/fH9Q3cuzYMXXp0kWS1LRpU7Vt2zbQQ3L5HL/fX62X5Fo4TQMAQANVVFSkSZMmqW3btlqxYoUiIiKM7hs0aJCKi4uD3kdy7Ngxff755xo0aFDQvNzcXFVUVATG3G63nE6nevXqZbzPMH99OzgNAABqVFZWptGjR+vEiRNatmyZWrZsGbjmcDgUGxsb+BwbG6vk5GQtXrw4MJaamqqjR4/qV7/6lW6//Xa9/PLLCg8P16ZNm9So0Q+FlePHjys5OVkDBw7U2LFj9eWXX2rp0qWaMWOGUlNTjfdKMAIAQAN08uTJq57cad++vd57773A55iYGP3Lv/yLMjIyAmM+n09LlizR9u3bdfHiRQ0YMEDz5s1T69atg9bau3evMjIy9MUXX6hly5Z6/PHHNXny5GrHgq+FYAQAANiKnhEAAGArghEAAGArghEAAGArghEAAGArghEAAGArghEAAGArXgdvgaNHj2rRokXat2+fmjVrphEjRmj69OnVvrQI1jt+/LiysrK0f/9+ffXVV3K5XNq8ebPd27olbdmyRe+8844OHTokr9erTp06ady4cXr00Udr9T4C3LidO3dq7dq1+vrrr1VSUqLWrVtryJAhmjp16hW/qRWwGsFIiBUXF2vChAnq3LmzMjMzdfr0aWVkZKisrEwLFiywe3u3nK+++ko7d+7Uvffeq6qqKvFaHfusW7dO7du315w5c3TnnXfqgw8+0Pz58/Xtt98afXEXQufcuXOKi4vTuHHj1KJFC3311VfKzMzUV199pddff93u7eEWxEvPQmz16tVatWqVduzYoRYtWkiSfv/73+vXv/61duzYUe3NdbBWVVWVwsN/qEbOmTNHBw8eJDNik7Nnzwa9jlqS5s+fL7fbrY8//jjw/xPssXHjRs2fP1+7du3izyncdPzbH2K7du1Sv379AoGIJCUmJqqqqkr5+fn2bewWxV9wdcc/BiKS1K1bN5WUlOj8+fM27AiXu/Rn1uVfeAbcLPxJHWIej6fa1yY7nU61atWq2tcsA7e6Tz75RK1bt9Ydd9xh91ZuSZWVlbpw4YIOHTqkV199VT/72c/UoUMHu7eFWxA9IyHm9XrldDqrjUdGRqq4uNiGHQF10549e+R2u/WrX/3K7q3csh544AGdPn1akjRw4EAtX77c5h3hVkVmBMBN9+2332rGjBmKj4/X+PHj7d7OLWvNmjV66623tGjRInk8Hv3iF79QZWWl3dvCLYjMSIg5nU75fL5q48XFxYqMjLRhR0Dd4vV6NXnyZLVo0UKZmZn09dioa9eukqRevXqpR48eGjFihLZv365hw4bZvDPcaghGQszlclXrDfH5fDpz5ky1XhLgVlNWVqYpU6bI5/Pp97//Pe+0qENiYmIUERGhwsJCu7eCWxD/SRJigwYN0gcffCCv1xsYy8nJUXh4uPr372/jzgB7Xbx4UdOnT5fH49Frr73G8dE6Zv/+/aqoqKCBFbYgMxJiY8aM0e9+9zs988wzmjJlik6fPq0XX3xRY8aM4Q9fG5SWlmrnzp2SpFOnTqmkpEQ5OTmSpD59+lzxuCmsceldO3PmzFFJSYk+/fTTwLXY2FjeUHwTTZ06Vd27d1dMTIwaN26sw4cPKysrSzExMRoyZIjd28MtiJeeWeDo0aP6zW9+E/Q6+BkzZvCHrQ1OnjyphISEK1574403FB8ff5N3dOv62c9+plOnTl3xWm5uLv9FfhOtWbNGbrdbhYWF8vv9at++vYYOHarU1FSOWcMWBCMAAMBW9IwAAABbEYwAAABbEYwAAABbEYwAAABbEYwAAABbEYwAAABbEYwAAABbEYwAAABbEYwAAABbEYwAAABbEYwAAABb/X/i2pxGh6qOfwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(wts)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **Need to include the self interaction (bias, h) into the energy model!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the model\n",
    "np.random.seed(610358)# should always be in the same cell!  ## best seed -> 610358\n",
    "n_spins = size*size\n",
    "\n",
    "## construct problem Hamiltonian ##\n",
    "shape_of_J=(n_spins,n_spins)\n",
    "\n",
    "#evaluating J for BAS dataset\n",
    "J=-1*wts   #np.array([[0,0,0,4],[0,0,4,0],[0,4,0,0],[4,0,0,0]])\n",
    "\n",
    "# defining h\n",
    "h=np.zeros(np.shape(J)[0])\n",
    "\n",
    "# instantiate the model\n",
    "model=IsingEnergyFunction(J,h,name=f\"Cardinality Data of size {size}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n",
      "            MODEL : Cardinality Data of size 4\n",
      "=============================================\n",
      "Non-zero Interactions (J) : 6 / 6\n",
      "Non-zero Bias (h) : 0 / 4\n",
      "---------------------------------------------\n",
      "Average Interaction Strength <|J|> :  1.5\n",
      "Average Bias Strength <|h|>:  0.0\n",
      "alpha :  0.4082482904638631\n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x1000 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.model_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n",
      "     MODEL : Cardinality Data of size 4 |  beta : 1\n",
      "=============================================\n",
      "Num Most Probable States : 16\n",
      "Entropy : 2.7573388201725257\n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## set current beta\n",
    "beta = 1#1.100209\n",
    "\n",
    "## run exact sampling over all possible configurations \n",
    "exact_sampled_model = Exact_Sampling(model, beta)\n",
    "\n",
    "## get the distribution from model\n",
    "bpd = exact_sampled_model.boltzmann_pd\n",
    "\n",
    "## exact sampling summary\n",
    "exact_sampled_model.sampling_summary(show_threshold=1e-10)\n",
    "plt.yscale(\"log\")\n"
   ]
  },
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