Yield_Variation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "from pandas import *\n",
    "from numpy.linalg import inv\n",
    "import pylab\n",
    "import statistics\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def printI(a):\n",
    "    for row in range(len(a)):\n",
    "        for col in range (len(a[row])):\n",
    "            print(\"{:1.0f}\".format(a[row][col]), end = \" \")\n",
    "        print()\n",
    "\n",
    "def printF(a):\n",
    "    for row in range(len(a)):\n",
    "        for col in range (len(a[row])):\n",
    "            print(\"{:3.4f}\".format(a[row][col]), end = \" \")\n",
    "        print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "States = np.loadtxt('StateData_L2.dat')\n",
    "nC=2; nN=2; TotalStates=7\n",
    "M = np.zeros(shape=(nC,nN))\n",
    "I = np.zeros(shape=(TotalStates,nC+nN,nC+nN))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics for  0 : StdDev(Ratio) = 0.04498082085178324 , Deter = -1.2971220405053805 , MultiStabFreq = 1497\n",
      "Statistics for  1 : StdDev(Ratio) = 0.9793323483685034 , Deter = -5.498010517426247e-12 , MultiStabFreq = 0\n",
      "Statistics for  2 : StdDev(Ratio) = 1.493476983457093 , Deter = -2.1077690226570052e-21 , MultiStabFreq = 0\n",
      "Statistics for  3 : StdDev(Ratio) = 0.29444568149854616 , Deter = -2.449318553586481e-33 , MultiStabFreq = 0\n",
      "Statistics for  4 : StdDev(Ratio) = 1.2762003156293862 , Deter = -2.657219363919175e-42 , MultiStabFreq = 587\n",
      "Statistics for  5 : StdDev(Ratio) = 12.983221473293193 , Deter = 2.415649656778511e-50 , MultiStabFreq = 0\n",
      "Statistics for  6 : StdDev(Ratio) = 5.929548261365997 , Deter = -1.0044569950128155e-59 , MultiStabFreq = 0\n",
      "Statistics for  7 : StdDev(Ratio) = 28.709280662972546 , Deter = -5.2137357439714236e-68 , MultiStabFreq = 0\n",
      "Statistics for  8 : StdDev(Ratio) = 2.253705896302275 , Deter = -1.3302644928791295e-76 , MultiStabFreq = 0\n",
      "Statistics for  9 : StdDev(Ratio) = 0.8026312727071542 , Deter = -6.666453132650406e-84 , MultiStabFreq = 0\n",
      "Statistics for  10 : StdDev(Ratio) = 91.24509754982935 , Deter = 5.428371135089416e-90 , MultiStabFreq = 0\n",
      "Statistics for  11 : StdDev(Ratio) = 21.039704749940856 , Deter = 9.989759440457744e-96 , MultiStabFreq = 0\n",
      "Statistics for  12 : StdDev(Ratio) = 0.6036979783382331 , Deter = 3.759346965231759e-107 , MultiStabFreq = 0\n",
      "Statistics for  13 : StdDev(Ratio) = 2.1746303691744706 , Deter = 8.868589868112349e-116 , MultiStabFreq = 0\n",
      "Statistics for  14 : StdDev(Ratio) = 13.633539202316657 , Deter = -8.223320771872018e-124 , MultiStabFreq = 0\n",
      "Statistics for  15 : StdDev(Ratio) = 5.8122748645430065 , Deter = 9.648248492192908e-132 , MultiStabFreq = 0\n",
      "Statistics for  16 : StdDev(Ratio) = 0.9573512559618044 , Deter = 3.026014013741418e-138 , MultiStabFreq = 0\n",
      "Statistics for  17 : StdDev(Ratio) = 2.599797773295198 , Deter = -1.1080997142502408e-145 , MultiStabFreq = 0\n",
      "Statistics for  18 : StdDev(Ratio) = 1.255117243177858 , Deter = -8.973129955817067e-155 , MultiStabFreq = 0\n",
      "Statistics for  19 : StdDev(Ratio) = 1.7752024968492675 , Deter = 2.3996516605612025e-166 , MultiStabFreq = 0\n",
      "Statistics for  20 : StdDev(Ratio) = 9.02033751995684 , Deter = -5.410436792121669e-176 , MultiStabFreq = 0\n",
      "Statistics for  21 : StdDev(Ratio) = 1.941629877356161 , Deter = -3.5551915228102176e-187 , MultiStabFreq = 3264\n",
      "Statistics for  22 : StdDev(Ratio) = 0.7854662526027618 , Deter = -2.823442806459642e-194 , MultiStabFreq = 0\n",
      "Statistics for  23 : StdDev(Ratio) = 1.5619004397528256 , Deter = 4.6459088828715974e-201 , MultiStabFreq = 0\n",
      "Statistics for  24 : StdDev(Ratio) = 2.235318254510094 , Deter = 1.6378139031424453e-212 , MultiStabFreq = 0\n",
      "Statistics for  25 : StdDev(Ratio) = 3.833259218730618 , Deter = -5.684251487974805e-220 , MultiStabFreq = 9206\n",
      "Statistics for  26 : StdDev(Ratio) = 37.68878702154429 , Deter = 1.1544805370440685e-226 , MultiStabFreq = 0\n",
      "Statistics for  27 : StdDev(Ratio) = 0.9494555972764389 , Deter = 4.0635245089895247e-237 , MultiStabFreq = 0\n",
      "Statistics for  28 : StdDev(Ratio) = 2.5779948619566295 , Deter = 9.224485961786522e-245 , MultiStabFreq = 0\n",
      "Statistics for  29 : StdDev(Ratio) = 3.688390071622162 , Deter = -4.551598438780154e-252 , MultiStabFreq = 0\n",
      "Statistics for  30 : StdDev(Ratio) = 0.4523984408822056 , Deter = -3.3606328863398524e-264 , MultiStabFreq = 0\n",
      "Statistics for  31 : StdDev(Ratio) = 1.0944928297381789 , Deter = 5.790812268152542e-276 , MultiStabFreq = 0\n",
      "Statistics for  32 : StdDev(Ratio) = 0.9259298027031325 , Deter = -1.2565455098952438e-292 , MultiStabFreq = 0\n",
      "Statistics for  33 : StdDev(Ratio) = 0.4523438609975232 , Deter = 3.2628703299598395e-300 , MultiStabFreq = 0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/pppandey/.local/lib/python3.5/site-packages/numpy/linalg/linalg.py:1874: RuntimeWarning: overflow encountered in det\n",
      "  r = _umath_linalg.det(a, signature=signature)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics for  34 : StdDev(Ratio) = 2.675946733723848 , Deter = -0.0 , MultiStabFreq = 0\n",
      "Statistics for  35 : StdDev(Ratio) = 1.3685071929441903 , Deter = -0.0 , MultiStabFreq = 0\n",
      "Statistics for  36 : StdDev(Ratio) = 1.3391927925345561 , Deter = 0.0 , MultiStabFreq = 0\n",
      "Statistics for  37 : StdDev(Ratio) = 1.7441678471092925 , Deter = 0.0 , MultiStabFreq = 0\n",
      "Statistics for  38 : StdDev(Ratio) = 2.4197180381304038 , Deter = 0.0 , MultiStabFreq = 0\n",
      "Statistics for  39 : StdDev(Ratio) = 10.368620676574936 , Deter = -0.0 , MultiStabFreq = 0\n",
      "Statistics for  40 : StdDev(Ratio) = 5.370474409345243 , Deter = -0.0 , MultiStabFreq = 58703\n",
      "Statistics for  41 : StdDev(Ratio) = 2.2307880069074146 , Deter = -0.0 , MultiStabFreq = 0\n",
      "Statistics for  42 : StdDev(Ratio) = 0.7825642186466453 , Deter = -0.0 , MultiStabFreq = 0\n",
      "Statistics for  43 : StdDev(Ratio) = 3.683472952622838 , Deter = 0.0 , MultiStabFreq = 0\n",
      "Statistics for  44 : StdDev(Ratio) = 2.2333722494187187 , Deter = 0.0 , MultiStabFreq = 0\n",
      "Statistics for  45 : StdDev(Ratio) = 4.579940404499086 , Deter = -0.0 , MultiStabFreq = 0\n",
      "Statistics for  46 : StdDev(Ratio) = 2.2683253052065853 , Deter = -0.0 , MultiStabFreq = 0\n",
      "Statistics for  47 : StdDev(Ratio) = 1.7482734931128932 , Deter = 0.0 , MultiStabFreq = 0\n",
      "Statistics for  48 : StdDev(Ratio) = 2.7458747247157875 , Deter = 0.0 , MultiStabFreq = 0\n",
      "Statistics for  49 : StdDev(Ratio) = 5.705845646727708 , Deter = 0.0 , MultiStabFreq = 0\n",
      "Statistics for  50 : StdDev(Ratio) = 1.5001078761806277 , Deter = -0.0 , MultiStabFreq = 0\n",
      "Statistics for  51 : StdDev(Ratio) = 0.7722765615786176 , Deter = 0.0 , MultiStabFreq = 22087\n",
      "Statistics for  52 : StdDev(Ratio) = 2.081720535049268 , Deter = 0.0 , MultiStabFreq = 27222\n",
      "Statistics for  53 : StdDev(Ratio) = 1.8179150439934855 , Deter = 0.0 , MultiStabFreq = 0\n",
      "Statistics for  54 : StdDev(Ratio) = 0.5492996040447862 , Deter = -0.0 , MultiStabFreq = 0\n",
      "Statistics for  55 : StdDev(Ratio) = 6.367365661855877 , Deter = 0.0 , MultiStabFreq = 0\n"
     ]
    }
   ],
   "source": [
    "#Below I will again try for N different Yield sets but this time I will chose Yields uniformly Between [X,1-X]\n",
    "# with X = 0.45 (so that I get StdDev(Yc/Yn))\n",
    "#For each Yield I will get the Multistable Count and store the Determinant of the last state\n",
    "start_time = time.time()\n",
    "X = 0.45\n",
    "SeedForYieldRange=1000\n",
    "Confidence = np.zeros(shape=(SeedForYieldRange,2*nC*nN + 3))\n",
    "Deter = np.zeros(shape=(TotalStates))\n",
    "for SeedForYield in range(SeedForYieldRange):\n",
    "    #print(\"For\", SeedForYield)\n",
    "    I = np.zeros(shape=(TotalStates,nC+nN,nC+nN))\n",
    "    \n",
    "    np.random.seed(SeedForYield)\n",
    "    YieldC = np.random.uniform(X,1-X,nC*nN)\n",
    "    YieldN = np.random.uniform(X,1-X,nC*nN)\n",
    "    \n",
    "    Ratio = YieldC/YieldN\n",
    "    \n",
    "    #print(\"YieldC\", YieldC, \"\\nYieldN\", YieldN, \"\\nRatio\", Ratio, \"StdDev(Ratio)\", statistics.stdev(Ratio))\n",
    "    ###############################\n",
    "    Confidence[SeedForYield][0:nC*nN] = YieldC\n",
    "    Confidence[SeedForYield][nC*nN:2*nC*nN] = YieldN\n",
    "    Confidence[SeedForYield][2*nC*nN] = statistics.stdev(Ratio)\n",
    "    ##################################################\n",
    "    for S in range(TotalStates):\n",
    "        #print(S,States[S,:])\n",
    "        for i in range(0,nC,1):\n",
    "            for j in range(0,nN,1):\n",
    "                M[i,j]=States[S,(i*nC)+j]\n",
    "        #printI(M)\n",
    "    \n",
    "        IDC=[]\n",
    "        IDN=[]\n",
    "        k=0\n",
    "        for i in range(0,nC,1):\n",
    "            for j in range(0,nN,1):\n",
    "                if(M[i,j] != 0):\n",
    "                    IDC.append(i)\n",
    "                    IDN.append(j)\n",
    "                    k+=1\n",
    "    \n",
    "        Y = np.zeros(shape=(nC+nN,nC+nN))\n",
    "        for i in range(0,len(IDC), 1):\n",
    "            Y[IDC[i],i] = 1/YieldC[nC*IDC[i] + IDN[i]]\n",
    "            Y[nN+IDN[i],i] = 1/YieldN[nC*IDC[i] + IDN[i]]\n",
    "        \n",
    "        w = len(IDC)\n",
    "        while (w < nC+nN):\n",
    "            for i in range(0,nC,1):\n",
    "                for j in range(0,nN,1):\n",
    "                    if(M[i,j] == -1):\n",
    "                        break\n",
    "                if(M[i][j] != -1):\n",
    "                    Y[i,w] = 1.0\n",
    "                    w += 1\n",
    "            \n",
    "            for j in range(0,nN,1):\n",
    "                for i in range(0,nC,1):\n",
    "                    if(M[i,j] == 1):\n",
    "                        break\n",
    "                if(M[i][j] != 1):\n",
    "                    Y[nC+j,w] = 1.0\n",
    "                    w += 1\n",
    "            \n",
    "        #print(\"Yield is\")\n",
    "        #printF(Y)\n",
    "        \n",
    "        I[S,:,:]=inv(Y)\n",
    "\n",
    "        Deter[S] = np.linalg.det(I[S,:,:])\n",
    "        Deter[S] = 1/Deter[S]\n",
    "        #print(\"determinant of\", S+1, \"=\", Deter[S])\n",
    "\n",
    "        \n",
    "        \n",
    "        \n",
    "        #print(\"Inverse of\", S+1, \"is\")\n",
    "        #printF(I[S,:,:])\n",
    "    ##################################################\n",
    "    Confidence[SeedForYield][2*nC*nN + 1] = Deter[6]\n",
    "    StatePhase1 = 0; StatePhase3 = 0; StatePhase5 = 0\n",
    "    L1=[]\n",
    "    L3=[]\n",
    "    L5=[]\n",
    "    \n",
    "    SeedForPhiPointsRange=100000\n",
    "    for PhiPoint in range(SeedForPhiPointsRange*SeedForYield, \n",
    "                          SeedForPhiPointsRange*(SeedForYield+1), 1):#loop for chosing different Phi-points\n",
    "        #print(\"PhiPoint:\", PhiPoint)\n",
    "        np.random.seed(PhiPoint)#This contains the seed\n",
    "        Phi = np.random.uniform(10,1000,nC+nN)\n",
    "        #print(\"Phi:\", Phi)\n",
    "        NoOfStates = 0; q = [0]*5\n",
    "        for S in range(TotalStates):\n",
    "            X = np.matmul(I[S,], Phi)\n",
    "            for i in range(nC+nN):\n",
    "                if (X[i] < 0.0):\n",
    "                    break\n",
    "            if (X[i] > 0.0):\n",
    "                #print(S+1)\n",
    "                NoOfStates += 1\n",
    "                q[NoOfStates] = S +1\n",
    "        if(NoOfStates == 1):\n",
    "            StatePhase1 += 1\n",
    "            L1.append(q)\n",
    "        if(NoOfStates == 3):\n",
    "            StatePhase3 += 1\n",
    "            L3.append(q)\n",
    "        if(NoOfStates == 5):\n",
    "            StatePhase5 += 1\n",
    "            L5.append(q)\n",
    "\n",
    "    Confidence[SeedForYield][2*nC*nN + 2] = StatePhase3+StatePhase5\n",
    "    print(\"Statistics for \", SeedForYield, \": StdDev(Ratio) =\", Confidence[SeedForYield][2*nC*nN]\n",
    "          , \", Deter =\", Confidence[SeedForYield][2*nC*nN + 1]\n",
    "          ,\", MultiStabFreq =\", int(Confidence[SeedForYield][2*nC*nN + 2]))\n",
    "        \n",
    "print(\"--- %s seconds ---\" % (time.time() - start_time))"
   ]
  },
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     ]
    }
   ],
   "source": [
    "#But all the Yield sets used above may not have State 7 as the unstable one\n",
    "#To check the stability, Checking if State 7 (S=6) appeared alone ever\n",
    "#Getting the Yield Sets used above where state 7 was unstable\n",
    "\n",
    "#Will try the same N different Yield sets and for each Yield I will get the Multistable Count and \n",
    "#store the Determinant of the last state AND ALSO CHECK IT'S STABILITY\n",
    "# CheckingStability[For a particula YieldSet] = 1 is UIS7 is satble\n",
    "# CheckingStability[For a particula YieldSet] = 0 is UIS7 is unsatble\n",
    "\n",
    "SeedForYieldRange=1000\n",
    "CheckingStability = np.zeros(shape=(SeedForYieldRange))\n",
    "for SeedForYield in range(SeedForYieldRange):\n",
    "    #print(\"For\", SeedForYield)\n",
    "    I = np.zeros(shape=(TotalStates,nC+nN,nC+nN))\n",
    "    \n",
    "    np.random.seed(SeedForYield)\n",
    "    YieldC = np.random.uniform(0.01,1,nC*nN)\n",
    "    YieldN = np.random.uniform(0.01,1,nC*nN)\n",
    "    #YieldC = np.loadtxt('YieldC_L2.dat')\n",
    "    #YieldN = np.loadtxt('YieldN_L2.dat')\n",
    "    Ratio = YieldC/YieldN\n",
    "    #print(TotalStates, \"YieldC\", YieldC, \"\\nYieldN\", YieldN, \"\\nRatio\", Ratio, \"StdDev(Ratio)\", statistics.stdev(Ratio))\n",
    "    \n",
    "    ##################################################\n",
    "    for S in range(TotalStates):## Doing this for only state UIS7 (i.e. S=6)\n",
    "        #print(S,States[S,:])\n",
    "        for i in range(0,nC,1):\n",
    "            for j in range(0,nN,1):\n",
    "                M[i,j]=States[S,(i*nC)+j]    \n",
    "        IDC=[]\n",
    "        IDN=[]\n",
    "        k=0\n",
    "        for i in range(0,nC,1):\n",
    "            for j in range(0,nN,1):\n",
    "                if(M[i,j] != 0):\n",
    "                    IDC.append(i)\n",
    "                    IDN.append(j)\n",
    "                    k+=1\n",
    "                \n",
    "        Y = np.zeros(shape=(nC+nN,nC+nN))\n",
    "        for i in range(0,len(IDC), 1):\n",
    "            Y[IDC[i],i] = 1/YieldC[nC*IDC[i] + IDN[i]]\n",
    "            Y[nN+IDN[i],i] = 1/YieldN[nC*IDC[i] + IDN[i]]\n",
    "        \n",
    "        w = len(IDC)\n",
    "        while (w < nC+nN):\n",
    "            for i in range(0,nC,1):\n",
    "                for j in range(0,nN,1):\n",
    "                    if(M[i,j] == -1):\n",
    "                        break\n",
    "                if(M[i][j] != -1):\n",
    "                    Y[i,w] = 1.0\n",
    "                    w += 1\n",
    "            \n",
    "            for j in range(0,nN,1):\n",
    "                for i in range(0,nC,1):\n",
    "                    if(M[i,j] == 1):\n",
    "                        break\n",
    "                if(M[i][j] != 1):\n",
    "                    Y[nC+j,w] = 1.0\n",
    "                    w += 1\n",
    "            \n",
    "        #print(\"Yield is\")\n",
    "        #printF(Y)\n",
    "        \n",
    "        I[S,:,:]=inv(Y)\n",
    "\n",
    "        Deter[S] = np.linalg.det(I[S,:,:])\n",
    "        Deter[S] = 1/Deter[S]\n",
    "        #print(\"determinant of\", S+1, \"=\", Deter[S])\n",
    "        #print(\"Inverse of\", S+1, \"is\")\n",
    "        #printF(I[S,:,:])\n",
    "    ##################################################\n",
    "    \n",
    "    SeedForPhiPointsRange=10000\n",
    "    for PhiPoint in range(SeedForPhiPointsRange*SeedForYield, \n",
    "                          SeedForPhiPointsRange*(SeedForYield+1), 1):#loop for chosing different Phi-points\n",
    "        #print(\"PhiPoint:\", PhiPoint)\n",
    "        np.random.seed(PhiPoint)#This contains the seed\n",
    "        Phi = np.random.uniform(10,1000,nC+nN)\n",
    "        #print(\"Phi:\", Phi)\n",
    "        NoOfStates = 0; q = [0]*10\n",
    "        for S in range(TotalStates):\n",
    "            X = np.matmul(I[S,], Phi)\n",
    "            for i in range(nC+nN):\n",
    "                if (X[i] < 0.0):\n",
    "                    break\n",
    "            if (X[i] > 0.0):\n",
    "                #print(S+1)\n",
    "                NoOfStates += 1\n",
    "                q[NoOfStates] = S +1\n",
    "               \n",
    "        if(NoOfStates == 1):\n",
    "            if(7 in q):\n",
    "                #print(PhiPoint, q)\n",
    "                CheckingStability[SeedForYield] = 1  ## 0 means state 7 is unstable\n",
    "    print(CheckingStability[SeedForYield])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "510"
      ]
     },
     "execution_count": 260,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.size(CheckingStability) - np.count_nonzero(CheckingStability)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "Data = np.zeros(shape=(np.size(CheckingStability) - np.count_nonzero(CheckingStability),2*nC*nN + 3))\n",
    "counter = -1\n",
    "for i in range(np.size(CheckingStability)):\n",
    "    if (int(CheckingStability[i]) == 0):\n",
    "        counter += 1\n",
    "        #print(counter, i)\n",
    "        Data[counter,:] = Confidence[i,:]\n",
    "        #print(counter)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "JJJData = Data[:,9] + 100000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'')"
      ]
     },
     "execution_count": 271,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xscale('log', basex=10)\n",
    "plt.yscale('log', basey=10)\n",
    "plt.plot(JJJData, Data[:,10], marker='+', linestyle='', color='orange', label='', markersize=10)\n",
    "pylab.xlabel('(Deter + $10^5$) of Yield Matrix')\n",
    "pylab.ylabel('Multistable Phase Points')\n",
    "pylab.legend(loc='upper right')\n",
    "plt.title('')\n",
    "#pylab.xlim([95000,100000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(95000, 100000)"
      ]
     },
     "execution_count": 274,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xscale('log', basex=10)\n",
    "plt.yscale('log', basey=10)\n",
    "plt.plot(JJJData, Data[:,10], marker='+', linestyle='', color='orange', label='', markersize=10)\n",
    "pylab.xlabel('(Deter + $10^5$) of Yield Matrix')\n",
    "pylab.ylabel('Multistable Phase Points')\n",
    "pylab.legend(loc='upper right')\n",
    "plt.title('')\n",
    "pylab.xlim([95000,100000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "image/png": 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u7Zn7pST7Vm3GvsO2ZPkFOeY+Zdt023Llte9RF/tWbcbcwY9k0U3WfZu4l7nfvsO2AEjvH1vGVEzbvteEvgv2+aLvS4imvsNV5en6Hhs3bkzaMKhwRzkROVFVv1VVkLIGogwbNmzQXbt2jWvHsx5SW/+mhpgWLUCGCuClsm4rcNP25eGjPsxCsFuDCVi6O5ob5uqrO+QeW9f9ZMXT8aj7vlv+vZj3U9b9Ewp1dRdEfe/Nvq5s5JLbjvtcKHmvaOe5AhrTEXVGbgH1/UYKSN1RLiWK6UYR+RMAc/b1qpq0UO3hFgDHWMdH5+fI2LHDJ21XUR0/MFvhuaGXLqk/wL3bgCMn4dcUZRO75Tj2bgu6Xx5133fDYaOh92P3my1fisGIub7cCK1QnkMXi6d9C3+tW55pq9TWTIqB+ByAbwD4OwAP1HDPqwAcJyJrkRmGlyJbd0jG2pO6BnFIJ5RRLimJWz6/eAgz+nJHxz75nHDUwvvaj32Z17Gy4j7jkVqywqaotEbsfRusJD7vDKJIhirEsq19QQh9ICTPSEpwpCwEP0JV36SqH1fVT5m/lMZF5CIA3wLwZBHZLyKvUtX7AZwD4CsArgPwcVW9pozQ3JN6xggV5rMXcotCL1OLybntpGDf35XFKFpfe7FSGLaR8W0IZNqPnU9RULZRikUWGdxF6KIRtBsaarfjhoaOQKE+yEhKcKTMID4vIr+jql8s27iqnhk4/0UApdsjBMDiyNhWoin7Oqe06cMdbccyh8soudD93BlOKkXKOjTLceXwZUyH9m8oKtjXgj+dNEfKDOJ1yIzEv4nIXSJyt4h0Ws1VRE4RkQvuvLORhG7SJmaXszLYBe/Mf/txaMTt46uT7H/MwMTyKdzRsWlvGozx84XcFhkBt/idkdFtI9Y37uurju5jRRVTZ3Sk03WXwhmEqh7ahiBlUNXLAFy2YcOGV3ctC0kgNpJ0ffPTjibNvYrqMxlM1rIbbVQGt5xH1VlMKLLIJrRbnHkutMBpjHCob0Ozoh2yNJM6RhVD4r6Gmwctp8P3GTQQIvIUVf1HEXmW73lVvbo5scioiO1XnKIUgaVRT24bbmSNrTzckFJX+fnk9LlV3Gt9C79F+y3YbbilMELvx1xrIotCyrpIeU+z3ajdRoyiqK6U1/QsiieJERu1mIvpDfn/v/D8vathuaLQxTRyfC4no0hcd5L5H3JZ1KEQU11gZesb+Vxl9n/z2A6TDd0r9d6+BWP7PFBuEToVs1ht388nU511jNqq0TTirPDgDEJVz87/b2xPnDToYho5VUaiwKIy87k6YuGi9nmfQoy5naaJvtkzn+a2KTPLKCKWH2LwuejqUG5mVmYnvdkyTYPvc6j6PSIPkrKj3AoRea2IfDL/OyffH4KQNNxQylAeQWgUm4pvpO0+V0So+qmLHQUUysEoGhVbCmzfqs2L590d3mKzJnt06ruPa4Dc/g9hL/TXoWTdHfVSKPMd6ENYaVszlhZJiWL6KwDHA3h//nd8fo6QNFzXiIk08m18b45TK3/a50M/ULskdyh3wCfztElgbib1mpOCMwZTB+nBe1fBztQ2hsDdbjUWylsmsqhK6esyORG2rH3Lng7h69uBG42UPIhfU9WnW8dfF5GKRWPqgZnUA8R1ART591NHuaat2AJsShauL/bflcWXD2FnGvsWp22lceCKrK6Tq0j2zGNy6zZgh0cu31qB/d91LZlZiVvWxK0jNa3xq7KY7L4m1cU0bWRUF9hBCF3LMgUpBuIBEfllVf0nABCRJ6KekhuV4RrEAAn9UHz1fkL4wi+rjtBCr6tS2mJaTOhqUb2lkBEqIlbeo+h8k1QpMhjDjWazzk2AzAC3FUk0YKNgk2Ig3ghgp4jcBEAAPAHAKxuViswesRG8OQcsHx36sqjdx4C/cJ5PQbnK2m7LvT609uCriFr0GvM4xZ0yjcvFNUK+cN3QIn+q0gttmRr6TMpSJl8lf1+s+FyNlES5r4nIcQCenJ+6XlV/1qxYZLDEfrxuHoAd05+qgHwzkVAxutD9yxTO8xXcC2ES5nxRQC5GZtfohBL8bGXqVlt18eVbxPDVhHLzLsq4Sg5c4TfwbhSTaRcon0sQc2/ZM62mSJV34MR2lDtORD6X7ye9HcAdqrqHxoFEcWPC3R3RfJExsexgH64byF0gNY99biS7cF4oZt1WQuZ5385ubnkPs4Wo+759+NxIvhIYoQX19fNpyt9ncHwJgsDy/irr/rHliUVu+V4ztFyCWBkRl9jCfc+J7Sj3DQAfBXAlsl3lTlTV01uULYi1SP3qG264gdPHhindv1VLVti4P7jQBjU+v3xsBpHq97ZnOO6INLYo7btn1ZGt2azIlj2mIJsavZqZUeq6h2/x2e77Mu0UXZv4Xdu3ajPmTt2edt+qhFyjPcwCT90wKBbmeqiqflBVr1fVdyLbMKgXsNx3z3Fj9w3uiCsU2+8bGdsL0kXhri527H9MmYRi/5sIszRtuv1k94UxDobU0bNvhuSet8OMQ5+V+e9bT7BJHRE3kasQmxFa729JGDFJJrYGsVJEnolsYRoAHm4fsxYTaQxfeGYMd2S6Z776a2PyhF4fIqQ415wUjt6yjV2TETdFfRxaRLexQzmL/PF2QcMmCA0qyFTEDMQPAbzbOv4X61gBPK8pocjIcN06ZcpHFE3ZTbirr05RykJmSImHInFceX0luQ0hA3XyQjzXomocv+nnUKhuKIeiaNHbvYevpEVR1Jfdl6GFZ9+9UumDMRhKQl8JYrWYNrYpCBkBISXjjpZtxV81tt+l6o8zpsRtQhvmlMGVMZZrUaU6qG0YfXkVdj+HyqL7ZHaT7Hz43kssazuFPij9Mkxr5HpISh5E72AmdY9JDW801PUDmkaZVIkGqoIvPNfgziDKRnX5QmWLZhAG21XkuoJCocCucfK9lxCxduqgzHeq6azroRk5h0EaCGZS95RYrHzZ86lUMTBuFdVpqrGmvD41ccwmZGh9M62UshdFMzUji+3+8kVv2TOPogxt33vwna+bMp/nwEthNE1KsT5C+oNrEMr8uOuuj2MryVDxOmC5cXAjmM7SpdVcU2cPTcXT+4xumXyFgbtVyCIp5b5FRF4uIm/Jjx8vIs9uXjQyU6QqlWkVeyipLiWRKbYgXZQ4VZDsVSkMs4wbqsqCb9EsK9RPVaO+hsqAEt/KkjKDeD+AEwGcmR/fDeD8xiQi46ItxZ96j6Isanth150NmP2mQ/kW09Kk8kzp37KzMzcyLdZWGTmGRh/2omiIlDWIE1T1WSLybQBQ1X8VkYc1LBfpO2Vq5wyN1FLWoaS8qkrQVyCvKBw4lC8R6ndT9yoUbWafN+2mLuL7IqpSZGqLEe8d3RQpBuI+ETkEWe4DRGQNgJ83KhXpP1X2A6iLMko4RSmkJqWFZg3u+RQlZNxVuXwTAEv2gwgprZSSIkA8KGDP/NLX2SG8vqizon5JLV/StdLt8js7UFIMxLkAPgPgMSLyVgBnAHhzo1IVwDDXGSdlkdlWcLFkuzIKIiUqx27PrggbU+Tr55fWu/LJZJcLKcpuTnEN+Sqqxq6JUbbYIhkMKeW+PyYiuwH8JrIyG6ep6nWNSxaXiWGuJI5RcEWKrg2/f105FGVmEHVT50xsyMyYmyoliumXAXxfVc8HsBfAySLyqMYlI+OmL5EfqT/irv3ndWPvXZ2CHaUV6wt7D+y+fMZ1MrSy5FOSEsX0KWTbjh4L4K8BHAN4d88ls04ZJdonl4SryEL7SITwVZdtKtqpLkNlajYV7ZDnU/RlosHqpAmDM01/jtEAOqQYiJ+r6v0ATgdwnqq+EcBjmxWL9I6UH0MTo6ZQAlpq7oIP3w5qseNYO76S2a6i9CmhmLwxpVW2j2MJfKnv08wKyirEUPum2m5ZmioXXpU+DXIaIjWK6UwAvwfglPzciuZEIr2kq5IEKZEnocJzodpDsYS3srJVva5KWRKXlNGv2392X7hlNMzzbpmNumcD5nMaiRtmzKQYiFcCeA2At6rq90VkLYC/bVYsQkoQMyKp+Qt10nQBOEPXCnZs6zJVGXE/pEQxXQvgtdbx9wG8vUmhyMioGvnRlqKtm74VgEuNQPI9LmqvqGDfLNCnz7pmCg2EiBwH4M8BPBXASnNeVZ/YoFxkTFRNUGpC0RZtphM6Tg1bTE0aaxO7/8u4mFLaM6QmEaaOtvsWTto3eVoixcX0YQBbAfwlgI3IXE6sAjtmnB/DxDzoy48hpGRSZhzuZjpAuDS2/bhMOKirSBKUywQA9tQ8gyraV8L9PF3jGds/wieXz5XnGszYjMNut8ms5yr9OqtZ2Koa/QOwO///Pfdc13/HH3+8qqru3LlTSXPs3LlT9WOot9GU9j4G1e9urdamed3lJ2Xni/7s+9jtmMdl3n/qe7Pwfofr7nO7TfOey/ZNUbuhfnSvrfLepuiPJf1btp3Q+2/i82kJALs0QcemzCB+JiIPAXCDiJwD4BYAqxqyV0mw1MYMUdXNZF7jbh0K+GcM02waNI3rocl1liLZ7OdC2dm+vinT7hjo25pSi6QYiNcBeASyheo/A/A8AJubFKoIZamN4eO6iWLuEFvZ9s3HO63roUj5TFsdNiSbaTfFdebKkBo1NquL1iMiJYrpqvzhQWTrD4RMj6tgYgufTft5jbGyjZQvqsf8r8tIpSjnpkavqZVap5GhzvBPd5tYc67LwcKIw1sNKbWYniQiHxSRy0Xk6+avDeFIj+jbj6HODGtXWRa916qZxTbO4u3cXdvDGc9l3k/d5R+m+dxDMxSTgV4Gn5FKcWXl35PJrRvry8Q3TOOWHAgpLqZPAPgAgA8CeKBZcUhvMT/2JkdsZf35Ka4du0x2SpvA8rDQJjKKnWinfYdtwdyp2/0ylrnvtDMO365ysZIZRRsa2e34HjdNajl1QxvhrANa00gxEPer6l81LgnpP01/sUNlIaZRzF2EJ8bCcAPKZwIslsBscrZW1HaZz9fuWzN4qDMAoAtmNZw1QNBAiMij84eXicgfINs06GfmeVX9ccOykVmnj0lnKcRqLAUM4MLCAiaPXojXlDJMM3otel3VEfSQjABJJjaD2O0cv9F6rACYSU2apemdylKVYR0+44IorQkA3IqlW4sa2hy99mEEnfq5+M71Lcpt4AQNhKqubVMQQqamrGsmJQy0LgrKUywctXPRR24omkH1rfxDahmTInlSjVRVw9VmwEXfPqOSxFxMxwF4J4BjAXwPwH9X1VvaEox0jPXFngCL/vG2v9hlfsx1lsl211u6+PEWzaB8oapd+sv7Jk+Isp/ltJFcXc/IpiAW5nohgC8AeBGAqwG8rxWJSD9YP//ghjcLR+2svrXitO6ZJnMAesSSMExfLaRQKGbf1mhS+7aNUM+67tHD70tbxAzEoar6QVW9XlXfCWCuJZnImOibAuspDxphd2c6e8e6rhRVEy6ZNr4X/O5NTWyReqWIPBOA8Sk83D5W1aubFo6Q1qk7+zexjlE2g/C00YfRax9k8O0C2LfkzRESMxA/BPBu6/hfrGNFVpOpNkTkV5DVfToCwNeYe0Faw1XavnIbQPn1Fl/eSCDUddkiddU6Rn1TmmX34w5x4Irl5+o2XG2V7ujbZxQhFsW0cdrGReRCAL8L4DZVXWed3wTgvQAOAfA3qvo2Vb0OwGvyyrEfBUAD0TdiX+y26+LUeb+2FhIjoa5LZhAVEu2W0YdRP+CXo6+un7YynPvy2SSQkkk9DdsBnIdM4QMAROQQAOcDOBnAfgBXicilqnqtiJwK4PfBPa/7SeyL7duC0tBE5FMdP+a2jVok1HXZDMLXj9Masq6K27UR6llwjwmQGeCehpP2lUYNhKpeKSJzzulnA7hRVW8CABG5GMALAVyrqpcCuFREvgC/R5b0maGF9E1jZGpWtt41iLoNa1c1gJoooVJ0D3Of/B5LajGRZJqeQfh4HIAfWMf7AZwgIhMApwP4BQBfDL1YRM4GcDYAHHnkkVhYWMDBgwexsLDQmMCzTkr/TgDvNaHz01JHu7E2itqf3LoNCz+ePHg8d9d2zB38yPILHSW/b9Vm7Dtsy5L77Fu1GXsfcgZWrVrch2ty68Zl1+LHAByZXDkImGfwAAARn0lEQVTn7tq+9DWRa7tikv8PyVK1L3332XfpFuw7bAuOuv0Ct+u81/ehf3pF0ZZzyKKWXg7gLfnx4wE8O2W7uvz6OQB7reMzkK07mONXADgvtT37j1uOtkNS/8a2lyyzbWgqdWz3GGujSOYK24rGrlnWx6nbcrrXxF7TxRaZdW1rWnWL0tCWsXVutzpAUOOWo+8H8HNkUUv/C8DdAD4F4Ncq2qRbABxjHR+dnyNDoYxPGZjetdFFuYK2XDHTRLT4NtFpmrKutVDpdKBb1+PQ3KEdkWIgTlDVZ4nItwFAVf9VRB42xT2vAnCciKxFZhheCuCsMg1wT+qOKfvjmjZqpY4fc1NGZtq1iGnXFNre16CudYw2DNtQqwH3iBQDcV8eeZT5m0TWIJtRFCIiFyFz7R0hIvsBbFXVD4nIOQC+gizM9UJVvaaM0Mo9qYdD0xVZU5nGyBQpW/NcnTOYaZVb30fIbYWT9uG7N2BSDMS5yPaCeIyIvBXZGsKbUxpX1TMD57+IyEJ0EZxBkFaJKduY0i0xSs62HPWkHhWN+GelBHZKXxYZ8jH2S8MUGghV/ZiI7Abwm8gWrE/TLKmtMziD6DEDL29cKyXeX3DL0aIRf10lsOsmVVmnfg9Sr6liyA0DynBui5Qd5QDgNgAX2c8pd5QjNubHVbdrI+Tjn7Ufc5ks6rbv6VPyfXdx+Rj7gKUCRTvKKRaL9dlwRzmylKZ+XKFF0T5kBLfpuiiziU6IOjdUIjPBIHeU4xoEKU0dri9bYZqZzZAUJkfIpCRJmdQicjqA5yKbOXxDVT/bqFQFcA2ClKZoNFwlvr9pqrjRZs31VkTeH/tWbeaGNhWIbRgEABCR9wN4DbJtR/ciq7h6ftOCkRExBKXVx3DIKkaoz7OEur4HZcqF5/0RK8lBwhQaCGQZ1L+tqh9W1Q8D+B3UvBcEGTlltqG0t910t9yMbb3ZZ5qStwvDO+3+zHXQtjEf2vetRlJcTDciq790c358TH6uM7gGMVKGuCiaojCbqqLaVWXWWaOrKrg9IDiDEJHLRORSAIcCuE5EFkRkJ4Dr8nOdoaqXqerZq1ev7lIMMnTqGIGPVXHM8KiZLBKbQbyrNSkIaRM7oskXtmqYhWS+EDM8aiaLxMJcPZvAEjIChujKmlWYmd8phWsQIvIcAO8D8CsAHoaswN49qnpYw7LFZOIaxKzQ5wgo44axFRMVWr1UMebTVNjl57eElEXq85CV5P4EgA0Afg/Ak5oUqgjmQcwQff4RGkViy8jZSfdM4x7j57eElDBXqOqNAA5R1QfyUNdNzYpFBg8XOYfDWMOL22aE/ZMyg/hpvkHQd0TkHQB+iETDQmaYoS1yFrmypt0YqM9w1FwPQ/vOJ5Ci6F+RX3cOgHuQ5UGc3qRQhLRO0Q+7j5nWs0rf1qVGOHMwpMwgTlPV9wK4F8A2ABCR1wF4b5OCEdI7QpVSixYw+6bQytDHmVOFoIC5VZuRbW5ZgaLPb4QzB0OKgdiM5cZgi+dcazCKiXRCqLR2kStmyMqj78ovxT22Q7INmYBqBq/P779hYhsGnQngLABr84xqw2EAOt0siFFMPYOhgeNjyLOeGHUZvC73BmmR2Azi75EtSB8B4C+s83cD2NOkUGRgjG2Rs4vd2/rGgJVaK9jf+TLbmg6MWCb1zQBuFpHnA/g3Vf25iDwJwFOQlf4mZJzUsXsbGSd177Xdc1LWIK4E8Bsi8osALgdwFYCXAHhZk4IR0nt8bpg+LuqmMgZXoYkocmSe3LoR2IHF56q+h9jgYZZmEBaiqj8VkVcBeL+qvkNEvtO0YIT0Hp+C6fuibowxuArdbWFD4cl7ty0+12eD1zFJBkJETkQ2Y3hVfu6Q5kQio2Csi5xkOBhjsUOwcNROTCaTZg3eCL/zKYlyrwfwxwA+o6rXiMgTAexsVqw4InKKiFxw5513dikGiTG2EdkIf/ykZsb2nUeCgVDVK1T1VFV9e358k6q+tnnRojJxwyDSLiP88ZOaGPHgIZYH8R5Vfb2IXAZg2ZxMVU9tVDJC+s4YFnWLGIPyW7e12cytoX62CcTWIP42/8+d5QjxMYZF3SLGoPzWzwMLC9njMRi8FonlQezOHz4jr8X0IHktJu44RwgZFmMweC2Sski92XNuS81yEEII6RlVajEdio5rMRFCCGke1mIi/WSoGcn0cZMRUViLCcCJ7YlDSM5QM5KHKDMhAWIuprvhCW8FIABUVQ9rTCpCCCGdE5tBHNqmIGXghkGEENI8hVFMIvJ4318bwoVgJjUhhDRPSrG+L1iPVwJYC+B6AE9rRCIye8xCRjIhA6TQQKjqr9rHIvIsAH/QmERk9piFjOQxMNTIMlKZlES5Jajq1QBOaEAWQkifCe2tQEZL4QxCRN5gHT4EwLMA3NqYRIQQQnpByhqEHc10P7I1iU81Iw4hhJC+kLIGwXklaR9mJJM64LrJVMQS5S4NPQdwPwjSMPxRd8tYIsuGmpHfE2IziBMB/ADARQD+AVkGNekzHC2RumBkGUE8iumXAPwJgHUA3gvgZAC351uQci+IPsIoE0JIjQQNhKo+oKpfVtXNAJ4D4EYACyJyTmvSEUII6YzoIrWI/AKA/wjgTABzAM4F8JnmxSKEkJJE1k0mALAjP+77ukmPiC1SfxSZe+mLALap6t6mhRGR05AZpMMAfEhVL2/6noSQRPoeWRZZN1lYWMBkMulAqGETm0G8HMA9AF4H4LUiD65Rlyr3LSIXAvhdALep6jrr/CZkaxuHAPgbVX2bqn4WwGdF5BcBvAsADUSIsUSZkOHA79HMESv3XboMR4DtAM4D8FFzQkQOAXA+soXv/QCuEpFLVfXa/JI358+TEIwyIYQ0TF1GIIiqXonle1g/G8CNqnqTqv47gIsBvFAy3g7gS3nNJ0IIIR2RUmqjCR6HLMfCsB9ZAcA/BPB8AKtF5FhV/YD7QhE5G8DZAHDkkUdiYWEBBw8exMLCQvNS95wJ0Eg/sH+bh33cDHOrNmMfdURlujIQXlT1XGSRUrFrLgBwAQBs2LBBJ5MJF6AMO9BIP7B/m4d93BQTzIH9W5XGXUwBbgFwjHV8dH6OTEPfo0wIIYOiKwNxFYDjRGStiDwMwEsBRGs/2YjIKSJywZ133tmYgIOEUSaEkBpp3ECIyEUAvgXgySKyX0Repar3AzgHwFcAXAfg46p6TWqb3JOaEEKap/E1CFU9M3D+i8iS8AghhPSQrlxMU0EXEyGENM8gDQRdTIQQ0jyDNBCEEEKaZ5AGgi4mQghpnkEaCLqYCCGkeQZpIAghhDQPDQQhhBAvgzQQXIMghJDmGaSB4BoEIYQ0zyANBCGEkOahgSCEEOKFBoIQQoiXQRoILlITQkjzDNJAcJGaEEKaZ5AGghBCSPPQQBBCCPFCA0EIIcTLIA0EF6kJIaR5BmkguEhNCCHNM0gDQQghpHloIAghhHihgSCEEOKFBoIQQogXGghCCCFeaCAIIYR4GaSBqCUPYs98bfIQQsgYGaSBqCUPYu+2+gQihJARMkgDQQghpHloIAghhHihgSCEEOLloV0L0Ap75v1rDjtk6fG6rcD6+TYkIoSQ3jMbBmL9/HLFv0OAs7QLaQghZBDQxUQIIcQLDQQhhBAvNBCEEEK8DNJA1JJJvW5rfQIRQsgIGaSBqCWTmtFKhBASZZAGghBCSPPQQBBCCPFCA0EIIcSLqA43WUxEDgC4GcARAG5v6barAVRdHS/z2pRrY9eEnvOdd8+5x0Pp37KvL7q2qf71nWurj9m/zTMEHfEEVV1TeAdVHfwfgF0t3uuCNl6bcm3smtBzvvPuOc/xIPq37j5uqn+77GP2b7/7uE0dkfJHF1N5LmvptSnXxq4JPec7756b5j1Oy7T3rrOPm+rflHs3Bfu3eYaiIwoZtIvJICK7VHVD13KMFfZv87CPm4X9W42xzCAu6FqAkcP+bR72cbOwfyswihkEIYSQ+hnLDIIQQkjN0EAQQgjxQgNBCCHEy+gNhIicJiIfFJFLROS3upZnbIjIE0XkQyLyya5lGQsi8kgR+Uj+vX1Z1/KMEX5v0+i1gRCRC0XkNhHZ65zfJCLXi8iNIvJHsTZU9bOq+moArwHwkiblHRo19e9NqvqqZiUdPiX7+nQAn8y/t6e2LuxAKdPH/N6m0WsDAWA7gE32CRE5BMD5AF4A4KkAzhSRp4rIr4rI552/x1gvfXP+OrLIdtTXvyTOdiT2NYCjAfwgv+yBFmUcOtuR3sckgYd2LUAMVb1SROac088GcKOq3gQAInIxgBeq6p8D+F23DRERAG8D8CVVvbpZiYdFHf1L0ijT1wD2IzMS30H/B3G9oWQfX9uudMNkiF++x2FxdAVkP6bHRa7/QwDPB3CGiLymScFGQqn+FZHDReQDAJ4pIn/ctHAjI9TXnwbwIhH5K3RbMmIMePuY39s0ej2DqANVPRfAuV3LMVZU9Q5k6zukJlT1HgCv7FqOMcPvbRpDnEHcAuAY6/jo/BypB/Zve7Cvm4d9PAVDNBBXAThORNaKyMMAvBTApR3LNCbYv+3Bvm4e9vEU9NpAiMhFAL4F4Mkisl9EXqWq9wM4B8BXAFwH4OOqek2Xcg4V9m97sK+bh31cPyzWRwghxEuvZxCEEEK6gwaCEEKIFxoIQgghXmggCCGEeKGBIIQQ4oUGghBCiBcaCDIqROR/isg1IrJHRL4jIieIyOtF5BGB67eIyHn543kRuSV/3Q0i8ulpK3+KyCfzvQc+JiK/b50/IZdxReS1K0Tk2yLyTRF5gXX+xSLy5YL7vktEnjeN7ITQQJDRICInIqs4+yxVXY+sSOMPALwegNdAePhLVX2Gqh4H4BIAXxeRNRXleRqAQ/JKom8A8EYRWSMiDwFwHoA/UNX7Ik08F8A3kdUMereIrBSRVQD+N4D/WnD79wGI7uVBSBE0EGRMPBbA7ar6MwBQ1dsBnAHgKAA7RWQnAIjIK0Xk/4nI/wXw66HGVPUSAJcDOCt/3fEicoWI7BaRr4jIY0XkKXk7yK+ZE5Hv5YcvA/C5vK0fAXgXgHcgU/h7VPWb+Ws2icjVIvJdEfmaJcImZGXq9yKr6vomAG8B8FFV/af8XtdJtvPcNSJyuYg8PL/fzQAOF5Ffqt6dZNahgSBj4nIAx+TK//0iclJezfdWABtVdaOIPBbANmSG4bnINpGJcTWAp+SuoPcBOENVjwdwIYC3quo/AniYiKzNr38JspkH8nvsttr6QH6/NwL4HwCQz04+COBFqvp0AC+2rt8IYCF/vA2ZoXoBMiNjOA7A+ar6NAA/AfAiR/agASSkiNGX+yazg6oeFJHjAfwGMuV6iSzfMvUEAAuqegAAROQSAE+KNCv5/ycDWAfgq9keVDgEwA/z5z6OzDC8Lf9vtrZ9LIADlnw/F5G/BrAhLzcNAM8BcKWqfj+/5se5XI8D8GNV/Wl+/p5c1oNmhpTzfVX9Tv54N4A567nbkM2eCKkEDQQZFar6ALJR90Lu6tk8ZZPPBLALmaG4RlVP9FxzCYBPiMinMxH0hvz8vwFY6Vz78/yviE3ICswVvdY2Fg8AeLh1vDKXgZBK0MVERoOIPFlEjrNOPQPAzQDuBnBofu4fAJyU7yi2AktdOm57LwLwWwAuAnA9gDX5QriJMHoaAKjqPyFTzn+KRfcSkFUPPbZA7P8D4D8YF5WIPDo/vwnAlwpeW8STAOydsg0yw3AGQcbEKgDvE5FHAbgfwI0AzgZwJoAvi8it+TrEPLKy0D9Btu+zzX8TkZcDeCQy5fo8yx11BoBzRWQ1st/OewCY0tGXAHgngLVWW18AMAHwdyGBVfWAiJwN4NN5dNNtIrIJwLH5+kYlcuN3LLLZDyGVYLlvQhoijyjaCeDXc9dX6uueC+Dlqlp5S0wR+U/Iwn3/tGobhNBAENIgIvLbAK5T1X9u+b4vBvBVVf1Jm/cl44IGghBCiBcuUhNCCPFCA0EIIcQLDQQhhBAvNBCEEEK80EAQQgjxQgNBCCHEy/8Hze9NleYplTAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xscale('log', basex=10)\n",
    "plt.yscale('log', basey=10)\n",
    "plt.plot(Data[:,8], Data[:,10], marker='+', linestyle='', color='orange', label='', markersize=10)\n",
    "pylab.xlabel('StdDev(Yc/Yn)')\n",
    "pylab.ylabel('Multistable Phase Points')\n",
    "pylab.legend(loc='upper right')\n",
    "plt.title('')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deter  1 0.02499999999999999\n",
      "Deter  2 1.0\n",
      "Deter  3 0.05000000000000001\n",
      "Deter  4 0.5\n",
      "Deter  5 0.12500000000000003\n",
      "Deter  6 0.0049999999999999975\n",
      "Deter  7 inf\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/pppandey/.local/lib/python3.5/site-packages/ipykernel_launcher.py:4: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  after removing the cwd from sys.path.\n"
     ]
    }
   ],
   "source": [
    "Deter = np.zeros(shape=(TotalStates))\n",
    "for S in range(TotalStates):\n",
    "    Deter[S] = abs(np.linalg.det(I[S,:,:]))\n",
    "    Deter[S] = 1/Deter[S]\n",
    "    print('Deter ', S+1, Deter[S])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000 0 0 0 0 0 0\n",
      "StdDev(Ratio) = 8.082903768654761\n"
     ]
    }
   ],
   "source": [
    "TotalPoints = 10000\n",
    "Data = np.zeros(shape=(TotalPoints,nC+nN+TotalStates))\n",
    "VolFromMonte = np.zeros(shape=TotalStates)\n",
    "StatePhase1 = 0; StatePhase3 = 0; StatePhase5 = 0; StatePhase7 = 0; StatePhase9 = 0\n",
    "StatePhase11 = 0; StatePhase13 = 0\n",
    "L1=[]\n",
    "L3=[]\n",
    "L5=[]\n",
    "L7=[]\n",
    "L9=[]\n",
    "L11=[]\n",
    "L13=[]\n",
    "for PhiPoint in range(TotalPoints):#loop for chosing different Phi-points\n",
    "    #print(\"PhiPoint:\", PhiPoint)\n",
    "    np.random.seed(PhiPoint)#This contains the seed\n",
    "    Phi = np.random.uniform(10,1000,nC+nN)\n",
    "    #print(\"Phi:\", Phi)\n",
    "    NoOfStates = 0; q = [0]*5\n",
    "    for S in range(TotalStates):\n",
    "        X = np.matmul(I[S,], Phi)\n",
    "        for i in range(nC+nN):\n",
    "            if (X[i] < 0.0):\n",
    "                break\n",
    "        if (X[i] > 0.0):\n",
    "            #print(S+1)\n",
    "            NoOfStates += 1\n",
    "            q[NoOfStates] = S + 1\n",
    "    if(NoOfStates == 1):\n",
    "        StatePhase1 += 1\n",
    "        L1.append(q[1])\n",
    "        #print(PhiPoint,q)\n",
    "    if(NoOfStates == 3):\n",
    "        StatePhase3 += 1\n",
    "        L3.append(q)\n",
    "        #print(PhiPoint,q)\n",
    "    if(NoOfStates == 5):\n",
    "        StatePhase5 += 1\n",
    "        L5.append(q)\n",
    "        #print(PhiPoint,q)\n",
    "    if(NoOfStates == 7):\n",
    "        StatePhase7 += 1\n",
    "        #print(PhiPoint,q)\n",
    "        L7.append(q)\n",
    "    if(NoOfStates == 9):\n",
    "        StatePhase9 += 1\n",
    "        #print(PhiPoint,q)\n",
    "        L9.append(q)\n",
    "    if(NoOfStates == 11):\n",
    "        StatePhase11 += 1\n",
    "        #print(PhiPoint,q)\n",
    "        L11.append(q)\n",
    "    if(NoOfStates == 13):\n",
    "        StatePhase13 += 1\n",
    "        #print(PhiPoint,q)\n",
    "        L13.append(q)\n",
    "print(StatePhase1,StatePhase3,StatePhase5,StatePhase7,StatePhase9,StatePhase11,StatePhase13)\n",
    "#print(L1[1:])\n",
    "Ratio = YieldC/YieldN\n",
    "print(\"StdDev(Ratio) =\", statistics.stdev(Ratio))\n",
    "#print(L3[:])"
   ]
  },
  {
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}