(a,a,a,b) Model Arbitrary.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import itertools\n",
    "import numpy as np\n",
    "import multiprocessing\n",
    "from multiprocessing import Process, Pool, Array\n",
    "from tqdm import tqdm\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def probDist(a,b):\n",
    "    pArr = np.array([[a,a,a,b],\n",
    "                 [a,a,b,a],\n",
    "                 [a,b,a,a],\n",
    "                 [b,a,a,a]])\n",
    "    return pArr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def H(a):\n",
    "    if(a == 0):\n",
    "        return 0\n",
    "    else:\n",
    "        return (a*math.log2(1/a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mutualInfo(a,b):\n",
    "    return 2 - 3*H(a) - H(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "viol = []\n",
    "distribution = []\n",
    "arrSettings = []\n",
    "MIs = []\n",
    "maximalViol = []\n",
    "def calculateViolation(arr):\n",
    "    x = np.arange(0.01, 1.01, 0.01)\n",
    "    for a in x:\n",
    "        for b in x:\n",
    "            if(3*a+b==1.00):\n",
    "                pArr = probDist(a,b)\n",
    "                xy = 0\n",
    "                xY = 0\n",
    "                Xy = 0\n",
    "                XY = 0\n",
    "                for i in range(0, arr.shape[1]):\n",
    "                    xy += arr[i,0]*arr[i,2]*pArr[i,0]\n",
    "                    xY += arr[i,0]*arr[i,3]*pArr[i,1]\n",
    "                    Xy += arr[i,1]*arr[i,2]*pArr[i,2]\n",
    "                    XY += arr[i,1]*arr[i,3]*pArr[i,3]\n",
    "                E = xy + xY +Xy - XY\n",
    "                MI = mutualInfo(a,b)\n",
    "                viol.append(abs(E))\n",
    "                if(abs(E) > 3.9 and MI < 0.5):\n",
    "                    print(\"a = \", a, \" b = \", b, \" MI = \", MI, \" E = \", abs(E))   \n",
    "                    MIs.append(MI)\n",
    "                    print(arr)\n",
    "                    print(\" \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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     "text": [
      "  2%|▏         | 1058/65536 [00:13<14:33, 73.78it/s]"
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     "name": "stdout",
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     "text": [
      "a =  0.33  b =  0.01  MI =  0.3500939883901444  E =  3.92\n",
      "[[-1 -1 -1 -1]\n",
      " [-1  1 -1 -1]\n",
      " [-1 -1 -1  1]\n",
      " [-1  1  1 -1]]\n",
      " \n",
      "a =  0.33  b =  0.01  MI =  0.3500939883901444  E =  3.92\n",
      "[[-1 -1 -1 -1]\n",
      " [-1  1 -1 -1]\n",
      " [-1 -1 -1  1]\n",
      " [ 1 -1 -1  1]]\n",
      " \n"
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      "  2%|▏         | 1268/65536 [00:16<14:33, 73.56it/s]"
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =  0.33  b =  0.01  MI =  0.3500939883901444  E =  3.92\n",
      "[[-1 -1 -1 -1]\n",
      " [-1  1 -1 -1]\n",
      " [ 1  1  1 -1]\n",
      " [-1  1  1 -1]]\n",
      " \n",
      "a =  0.33  b =  0.01  MI =  0.3500939883901444  E =  3.92\n",
      "[[-1 -1 -1 -1]\n",
      " [-1  1 -1 -1]\n",
      " [ 1  1  1 -1]\n",
      " [ 1 -1 -1  1]]\n",
      " \n"
     ]
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  4%|▍         | 2854/65536 [00:36<12:21, 84.53it/s]"
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =  0.33  b =  0.01  MI =  0.3500939883901444  E =  3.92\n",
      "[[-1 -1 -1 -1]\n",
      " [ 1 -1  1  1]\n",
      " [-1 -1 -1  1]\n",
      " [-1  1  1 -1]]\n",
      " \n",
      "a =  0.33  b =  0.01  MI =  0.3500939883901444  E =  3.92\n",
      "[[-1 -1 -1 -1]\n",
      " [ 1 -1  1  1]\n",
      " [-1 -1 -1  1]\n",
      " [ 1 -1 -1  1]]\n",
      " \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  5%|▍         | 3055/65536 [00:39<12:59, 80.16it/s]"
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =  0.33  b =  0.01  MI =  0.3500939883901444  E =  3.92\n",
      "[[-1 -1 -1 -1]\n",
      " [ 1 -1  1  1]\n",
      " [ 1  1  1 -1]\n",
      " [-1  1  1 -1]]\n",
      " \n",
      "a =  0.33  b =  0.01  MI =  0.3500939883901444  E =  3.92\n",
      "[[-1 -1 -1 -1]\n",
      " [ 1 -1  1  1]\n",
      " [ 1  1  1 -1]\n",
      " [ 1 -1 -1  1]]\n",
      " \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 18%|█▊        | 11919/65536 [02:31<10:54, 81.97it/s]"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-78dcfe60a0a5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;31m# convert to numpy array and reshape to 4x4\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0msettingArray\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfromiter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mint8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m     \u001b[0mcalculateViolation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msettingArray\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m     \u001b[0mpbar\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-5-dcb8436bc4d2>\u001b[0m in \u001b[0;36mcalculateViolation\u001b[0;34m(arr)\u001b[0m\n\u001b[1;32m      8\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mb\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m             \u001b[0;32mif\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;36m1.00\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     11\u001b[0m                 \u001b[0mpArr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprobDist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m                 \u001b[0mxy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "values = [-1,1]\n",
    "seq = itertools.product(values, repeat=16)\n",
    "pbar = tqdm(total=65536)\n",
    "for s in seq:\n",
    "    # convert to numpy array and reshape to 4x4\n",
    "    settingArray = np.fromiter(s, np.int8).reshape(4, 4)\n",
    "    calculateViolation(settingArray)\n",
    "    pbar.update(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "100%|██████████| 65536/65536 [05:30<00:00, 223.63it/s]"
     ]
    }
   ],
   "source": [
    "max(viol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3500939883901444"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mutualInfo(0.33,0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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