MCMCHyperSphere.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T23:37:08.402767Z",
     "start_time": "2020-06-12T23:37:08.397777Z"
    }
   },
   "source": [
    "# 206T Scientific Computing project: Project “Volume Integration”: Monte Carlo vs. Deterministic Methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T23:37:08.402767Z",
     "start_time": "2020-06-12T23:37:08.397777Z"
    }
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "\n",
    "Configuration for running the below written program.\n",
    "\n",
    "maxNConteCarlo: Set this to the maximum dimension you want to run monteCarlo Simulations in. \n",
    "For higher dim, the program will take a lot of time to complete for a specified accuracy even though it will eventually.\n",
    "\n",
    "cubeIntegrationMaxSeconds: Maximum time that the cube based iteration can take for a given k.\n",
    "\n",
    "part2maxDim: In part2 of this project, The maximum number of dimensions that you want to run simulation for 10^6 points.\n",
    "\"\"\"\n",
    "class config():\n",
    "    maxNConteCarlo= 8\n",
    "    cubeIntegrationMaxSeconds = 200\n",
    "    part2maxDim=8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T15:47:53.548054Z",
     "start_time": "2020-06-12T15:47:53.536091Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>.container { width:100% !important; }</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.core.display import display, HTML\n",
    "display(HTML(\"<style>.container { width:100% !important; }</style>\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T15:47:55.505399Z",
     "start_time": "2020-06-12T15:47:53.550052Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import timeit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T15:47:55.511386Z",
     "start_time": "2020-06-12T15:47:55.506396Z"
    }
   },
   "outputs": [],
   "source": [
    "# For 95% of confidence interval\n",
    "def clt(dist):\n",
    "    x= np.mean(dist)\n",
    "    return x, (2 * np.sqrt(np.var(dist) / dist.shape[0]))/x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T15:47:55.517368Z",
     "start_time": "2020-06-12T15:47:55.512383Z"
    }
   },
   "outputs": [],
   "source": [
    "def getPoints(shape):\n",
    "    return np.random.uniform(low=-1.0,high =1.0,size=shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-08T01:44:06.262412Z",
     "start_time": "2020-06-08T01:44:06.258421Z"
    }
   },
   "source": [
    "### 1 : Monte Carlo Method "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T15:47:55.533325Z",
     "start_time": "2020-06-12T15:47:55.523354Z"
    }
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Input : Dim: Number of dimensions to run monte carlo on.\n",
    "acc: the maximum relative error you can permit\n",
    "maxBatches: MaxBatches to run the code (other wise it can take a long time)\n",
    "\n",
    "Batches are stacked together to compute variance and mean\n",
    "\n",
    "For each batch run, we save the corresponding mean of Answer, accuracy and time elapsed till now. \n",
    "\"\"\"\n",
    "\n",
    "\n",
    "def monteCarloPushAccuracy(dim,acc, batchSize=15, maxBatches=10000):\n",
    "    print(\"Dimension:\"+ str(dim))\n",
    "    n = 5000000\n",
    "    currentAcc = 100\n",
    "    dist = np.zeros((0))\n",
    "    batchNumber = 1\n",
    "    v = 2**dim\n",
    "    meanArr = []\n",
    "    accArr = []\n",
    "    timeElapse=[]\n",
    "    start_time = timeit.default_timer()\n",
    "    while currentAcc>acc and batchNumber<maxBatches:\n",
    "        points = getPoints((batchSize, n, dim))\n",
    "        points = (np.count_nonzero(np.sum(np.multiply(points,points), axis=2) <=1.0, axis =1))*(v/n)\n",
    "        dist = np.hstack((dist, points))\n",
    "        currentMean, currentAcc = clt(dist)\n",
    "        elapsed = timeit.default_timer()- start_time\n",
    "        batchNumber = batchNumber+1\n",
    "        meanArr.append(currentMean)\n",
    "        accArr.append(currentAcc)\n",
    "        timeElapse.append(elapsed)\n",
    "    return (meanArr,accArr,timeElapse)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "start_time": "2020-06-12T09:26:38.286Z"
    }
   },
   "source": [
    "### 2. Cube Based Integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T15:47:55.551279Z",
     "start_time": "2020-06-12T15:47:55.538313Z"
    }
   },
   "outputs": [],
   "source": [
    "from collections import deque \n",
    "\n",
    "\n",
    "def generateNewPoints(point, k, delta):\n",
    "    points =[]\n",
    "    for i in range(len(point)):\n",
    "        newPoint = list(point)\n",
    "        if newPoint[i]<(1-(delta/2)):\n",
    "            newPoint[i] = newPoint[i]+delta\n",
    "            points.append(newPoint)\n",
    "    return points\n",
    "\n",
    "def getAllPoints(point, startDim, delta, npPoints):\n",
    "    dim = len(point)\n",
    "    newPoint1 = point[:]\n",
    "    newPoint1[startDim]= newPoint1[startDim]+(delta/2)\n",
    "    newPoint2 = point[:]\n",
    "    newPoint2[startDim]= newPoint2[startDim]-(delta/2)\n",
    "    if(startDim==dim-1):\n",
    "        npPoints.append(newPoint1)\n",
    "        npPoints.append(newPoint2)\n",
    "        return\n",
    "    getAllPoints(newPoint1,startDim+1,delta,npPoints)       \n",
    "    getAllPoints(newPoint2,startDim+1,delta,npPoints)       \n",
    "           \n",
    "def checkStatusOfPoint(point,delta):\n",
    "    npPoints=[]\n",
    "    getAllPoints(point,0,delta,npPoints)\n",
    "    npPoints = np.asarray(npPoints)\n",
    "    npSum = np.count_nonzero(np.sum(np.multiply(npPoints,npPoints),axis=1)<=1)\n",
    "    if(npSum==0):\n",
    "        return 0\n",
    "    if(npSum<len(npPoints)):\n",
    "        return 1\n",
    "    return 2\n",
    "\n",
    "def checkAndInsert(point, pointSet):\n",
    "    pointStr = \",\".join([str(x) for x in point])\n",
    "    if pointStr in pointSet:\n",
    "        return False\n",
    "    pointSet.add(pointStr)\n",
    "    return True\n",
    "    \n",
    "def dfs(point,pointSet, trackList, k , delta, endTime):\n",
    "    stack =deque()\n",
    "    stack.append(point)\n",
    "    while len(stack)>0:\n",
    "        point = stack[-1]\n",
    "        stack.pop()\n",
    "        if(timeit.default_timer()>endTime):\n",
    "            raise SystemError(\"Time got over\") \n",
    "        status = checkStatusOfPoint(point,delta)\n",
    "        trackList[status]= trackList[status]+1\n",
    "        for neighour in generateNewPoints(point,k, delta):\n",
    "            if(checkAndInsert(neighour, pointSet)==False):\n",
    "                continue\n",
    "            stack.append(neighour)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T21:45:20.219461Z",
     "start_time": "2020-06-12T21:45:20.214472Z"
    }
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Input : \n",
    "k : the number of segments to break the cube\n",
    "dim: Number of dimensions to run the code\n",
    "endTime: System periodically checks if current time is greater than endTime. If yes, raises an exception.\n",
    "\n",
    "returns mean, acc for a particular k\n",
    "\"\"\"\n",
    "def cubeBasedIntegrationForK(k, dim, endTime): \n",
    "    pointSet = set()\n",
    "    trackList = [0]*3\n",
    "    delta = 2/float(k)\n",
    "    point = [-1+delta/2]*dim\n",
    "    checkAndInsert(point,pointSet)\n",
    "    dfs(point,pointSet,trackList,k,delta,endTime)\n",
    "    cubeVolume = (2/k)**dim\n",
    "    vInside = trackList[2]*cubeVolume\n",
    "    vPartial = vInside+ trackList[1]*cubeVolume\n",
    "    mean = (vPartial+vInside)/2\n",
    "    acc = (vPartial-vInside)/mean\n",
    "    return mean, acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T15:47:55.572233Z",
     "start_time": "2020-06-12T15:47:55.564243Z"
    }
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Input :\n",
    "dim: the number of dimensions to run on\n",
    "acc: required accuracy.\n",
    "maxSeconds: Maximum time to run the simulation ( in seconds)\n",
    "\n",
    "Starts from k=2 and doubles k at each iteration until we reach desired accuracy or simulation is not able to run in specified time. \n",
    "\n",
    "\"\"\"\n",
    "def cubeBasedIntegration(dim, acc, maxSeconds):\n",
    "    k =2\n",
    "    currentAcc =1000\n",
    "    while(currentAcc>acc):\n",
    "        try:\n",
    "            endTime = timeit.default_timer()+maxSeconds\n",
    "            mean, currentAcc = cubeBasedIntegrationForK(k, dim, endTime)\n",
    "            print(k, dim, mean, currentAcc)\n",
    "            k=k*2\n",
    "        except Exception:\n",
    "            return k,mean,currentAcc\n",
    "    return k, mean, currentAcc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T18:08:16.066450Z",
     "start_time": "2020-06-12T15:47:55.575214Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension:2\n",
      "Dimension:3\n",
      "Dimension:4\n",
      "Dimension:5\n",
      "Dimension:6\n",
      "Dimension:7\n",
      "Dimension:8\n"
     ]
    }
   ],
   "source": [
    "meanArrHA = []\n",
    "accArrHA = []\n",
    "timeElapseHA=[]\n",
    "\n",
    "for i in range(2,config.maxNConteCarlo+1):\n",
    "    meanArr,accArr,timeElapse = monteCarloPushAccuracy(i,1/10000)\n",
    "    meanArrHA.append(meanArr)\n",
    "    accArrHA.append(accArr)\n",
    "    timeElapseHA.append(timeElapse)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T18:10:59.367091Z",
     "start_time": "2020-06-12T18:08:16.102363Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension:2\n",
      "Dimension:3\n",
      "Dimension:4\n",
      "Dimension:5\n",
      "Dimension:6\n",
      "Dimension:7\n",
      "Dimension:8\n"
     ]
    }
   ],
   "source": [
    "meanArrLA = []\n",
    "accArrLA = []\n",
    "timeElapseLA=[]\n",
    "\n",
    "for i in range(2,config.maxNConteCarlo+1):\n",
    "    meanArr,accArr,timeElapse = monteCarloPushAccuracy(i,1/1000)\n",
    "    meanArrLA.append(meanArr)\n",
    "    accArrLA.append(accArr)\n",
    "    timeElapseLA.append(timeElapse)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T23:51:22.750386Z",
     "start_time": "2020-06-12T23:51:22.448169Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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xKZaK6etvv/123n//fT744APGjRvHnXfe2es8UxlQlgNTRWSiiKThdLIv6ZRmCXCFu/x54EU3ECwBLnVHgU0EpgJvd3UyETkT+D5wnqo2JvE6oupo8rJOFGNMEvXV9PW5ubkAqCpNTU1JmeQ2ZU1eqhoUkW8CzwJe4H5VXSUiNwErVHUJcB/wkIhswKmZXOoeu0pEHgdW4zRffUNVQwAi8mfgFKBYRMqBH6vqfcCdQDrwnPvCvKmq16Tq+vY3eaXqDMaYfvPM9bDrw+TmOeJwOOuXXSbp6+nrr7zySpYtW0ZpaSm//vWve32JKZ3LS1WXAcs6bVsQsdwMXBzj2JuBm6NsvyxG+im9KmwPeXzW5GWMSa6+nr7+gQceIBQK8a1vfYvHHnuMK6+8slflt8khE+TxepxhAtbkZczg001NIpX6cvp6AK/XyyWXXMJtt91mAaW/iM8HbViTlzEmafpq+npVZePGjUyZMgVVZenSpcyYMaM3RQcsoCTM6/NCm/OHMcaYZOir6etVlSuuuILa2lpUlSOPPJK777671/na9PUJTl//15t/zJy608n97HhyTx2X5JIZY/qaTV8fnU1f3wfsxkZjjDmQBZQEef1Oa+EQruAZY8wBLKAkyOP1Edaw1VCMMcZlASVBXp8PUKuiGGOMywJKgrw+H4raExuNMcZlASVBHp8ftSYvY4zpYPehJMjr8xG2Ji9jTAqlcvr6dt/61rd44IEHqK+v73VeFlAS5PX5UA3bXF7GmJS76aabUpLvihUrqK6uTlp+1uSVIKcPJRznY7+MMSY+fTV9fSgU4rrrruPWW29NWtmthpIgj8+HqqIh65U3ZrC55e1bWFu1Nql5ziicwffnfL/LNH05ff2dd97Jeeedx8iRI5NyfWABJWFenx9FCVtAMcYkSV9NX79jxw6eeOIJXnrppaSW3wJKgtqbvDQU6u+iGGOSrLuaRCr1xfT1mzdvZsOGDUyZ4jxGqrGxkSlTprBhw4Zeld0CSoKsycsYk2x9NX19aWkpu3bt6ljPzs7udTABCygJc2ooLRZQjDFJ01fT16eKTV+f4PT1q15+AflbHYWHj2fElUcnuWTGmL5m09dHZ9PX9wGP1+tMvWI1FGOMASygJGx/p/zQreEZY0wkCygJcubyUjRsNRRjjAELKAnrqKFYQDHGGMACSsK87rBhrMnLGGOAFAcUETlTRNaJyAYRuT7K/nQReczd/5aITIjY9wN3+zoROSNi+/0iskdEPuqUV6GIPCciH7u/C1J5bZ6O56FYQDHGGEhhQBERL/A74CygFLhMREo7JbsK2KeqU4DbgVvcY0uBS4FZwJnAXW5+AAvdbZ1dD7ygqlOBF9z1lNnf5GUBxRiTGjfeeCO/+tWvWLBgAc8//3xS854/fz4TJ07kqKOO4qijjuryRsh4pfLGxjnABlXdBCAii4B5wOqINPOAG93lJ4E7xZl3YB6wSFVbgM0issHN7w1VfSWyJtMpr1Pc5T8BLwEpmz/Ba53yxpg+kqrp62+77TY+//nPJy2/VDZ5jQbKItbL3W1R06hqEKgBiuI8trPhqrrTzWsnMCxaIhG5WkRWiMiKioqKOC/lYB3T11s8McYkUV9NX58KqayhRJvhrHP7UKw08RybEFW9B7gHnDvlE83H+lCMGbx2/fzntKxJ7vT16TNnMOKHP+wyTV9OXw9www03cNNNN3Haaafxy1/+8oCJJhORyoBSDoyNWB8D7IiRplxEfEAeUBXnsZ3tFpGRqrpTREYCe3pT+O50jPIawlPXGGOSq6+mrwf4xS9+wYgRI2htbeXqq6/mlltuYcGCBb0qfyoDynJgqohMBLbjdLJ/sVOaJcAVwBvA54EXVVVFZAnwqIj8BhgFTAXe7uZ87Xn90v39t2RdSDTO81DCYDUUYwad7moSqdQX09eXlpZ2PFgrPT2dK6+8kl/96le9LnvKAoqqBkXkm8CzgBe4X1VXichNwApVXQLcBzzkdrpX4QQd3HSP43TgB4FvqGoIQET+jNP5Xiwi5cCPVfU+nEDyuIhcBWwDLk7VtUHE9PVWQzHGJElfTV8PsHPnTkaOHImq8tRTT3HYYYclWuwOKZ2+XlWXAcs6bVsQsdxMjA9+Vb0ZuDnK9stipK8ETutNeXvCOuWNMcnWl9PXX3755VRUVKCqHHXUUUnp0Lfp6xOcvj7Y1sbyaxcyongyE398apJLZozpazZ9fXQ2fX0f8Hq9TnOX1VCMMQawgJIw8XhQ0SQNZjbGmIHPAkpvCDZs2BhjXBZQekPEaijGGOOygNIbggUUY4xxWUDpDY8QfZYYY4wZelJ6H8pgJwJiNRRjTIrceOONZGdnU1tby9y5czn99NOTlreq8qMf/YgnnngCr9fL1772Nb797W/3Kk8LKL3hsT4UY0zqpWL6+oULF1JWVsbatWvxeDzs2dP76Q+tyasXnDl3rMnLGJM8fTV9/d13382CBQvweJwwMGxY1Cd+9IjVUHrDI9bkZcwg9Orj69lbVp/UPIvHZnPSF6Z1maYvp6/fuHEjjz32GIsXL6akpITf/va3TJ06tVfXaAGlNzwCYauhGGOSoy+nr29paSEQCLBixQr++te/8uUvf5lXX321V+W3gNIL4hHEpl4xZtDpriaRSn01ff2YMWO46KKLALjgggu48sore11260PpDQ8IHpvC3hiTFHPnzmXx4sU0NTVRV1fH0qVLE8qnffr6aD/tT2s8//zzefHFFwF4+eWXmTat90HUaii9oF4QBEIKPmv6Msb0Tl9OX3/99ddz+eWXc/vtt5Odnc29997b6zxt+voEp68HeP2nDzCuYQqjFhyPJ9OfxJIZY/qaTV8fXU+mr7caSgLq9zVTUVaPug2G2mYdKcYYY30oCdi+vppld31AyK3dhS2gGGOMBZRESPur5nUCiraG+q8wxhhziLCAkoD2YX3qdX9bDcUYYyygJKIjoPjaA4rVUIwxxgJKAtrvOxKv8/Jpq9VQjDHGRnkl4OAaigUUY0zypXL6+pNOOom6ujoA9uzZw5w5c3jqqad6lacFlES038Po1lDCrW39VxZjzKCXiunrI+ftuuiii5g3b16v80xpk5eInCki60Rkg4hcH2V/uog85u5/S0QmROz7gbt9nYic0V2eInKaiLwrIitF5DURmZKy6/I4EUV8zssXag6m6lTGmCGmr6avb1dXV8eLL77I+eef3+uyp6yGIiJe4HfAZ4ByYLmILFHV1RHJrgL2qeoUEbkUuAW4RERKgUuBWcAo4HkRaZ9oJlaedwPzVHWNiHwd+BEwPzXX5vxWN6CEWyygGDOY/HPhPezZuimpeQ4bP4lPz7+6yzR9OX19u8WLF3PaaaeRm5vbuwskjoAiIt8EHlHVfT3Mew6wQVU3ufksAuYBkQFlHnCju/wkcKc4HRTzgEWq2gJsFpENbn50kacC7a9IHrCjh+WNW3sfSnunvAUUY0wy9OX09e3+/Oc/85WvfCUp5Y+nhjICpybwLnA/8KzGNwHYaKAsYr0cOC5WGlUNikgNUORuf7PTsaPd5Vh5fgVYJiJNQC1wfLRCicjVwNUA48aNi+MyouXh/Pb4fATDbRZQjBlkuqtJpFJfTV8PUFlZydtvv83ixYuTUPI4+lBU9UfAVOA+nCakj0Xk5yIyuZtDo70qnQNRrDQ93Q7wXeBsVR0DPAD8JlqhVPUeVZ2tqrNLSkqiFrw7HTUUj5eQBgnbnfLGmCToy+nrAZ544gnOOeccAoFAUsofV6e8WyPZ5f4EgQLgSRG5tYvDyoGxEetjOLgZqiONiPhwmqqqujg26nYRKQGOVNW33O2PAZ+M59oS4r5qHo+PkLZZQDHGJEXk9PUXXXRRSqevB1i0aBGXXXZZ0vKLpw/l28AVwF7gXuA6VW0TEQ/wMfC9GIcuB6aKyERgO04n+xc7pVni5v0G8HngRVVVEVkCPCoiv8HplJ8KvI1TQ4mW5z4gT0Smqep6nE77NXG+Bj22vw/FSzDcbHN5GWOS5oYbbuCGG26IuX/Lli0dy/Pnz2f+/PlR98XjpZde6lnhuhFPH0oxcKGqbo3cqKphETkn1kFun8g3gWcBL3C/qq4SkZuAFaq6BKcZ7SG3070KJ0Dgpnscp7M9CHxDVUPQMUjggDzd7f8P+IuIhHECzJfjfhV6qKMPxeMjpEGbesUYY4gvoCzD+bAHQERygFJVfUtVu6wFqOoy9/jIbQsilpuBi2McezNwczx5utsXA8npWepGZA2lOdSA1ltAMcaYePpQ7gbqI9Yb3G1DVkcNRXzUtlVCdRAND90nXxpjDMQXUCRymLCqhhniU7Z03Cnv8ToBJQSh6pZ+LpUxxvSveALKJhH5toj43Z/vAMm9hXSg6Zht2EdtayUAbRWN/VggY4zpf/EElGtwhuBuZ/+NhP13188hoL0PxdNeQwGCeyygGGOGtm6brlR1D+7oK+PoeB6Kx0druAlNg+Cepv4tlDFm0Enl9PUvvPAC1113HeFwmOzsbBYuXMiUKb2bUzee+1ACOJM4zgI6bqdU1ZQNyz3UdYzych8uH8oKW5OXMSZlUjF9/de+9jX+9re/MXPmTO666y5+9rOfsXDhwl7lGU+T10M483mdAbyMc3d6Xa/OOsC5cQSvNw2AYGaIYIXVUIwxvddX09eLCLW1tQDU1NQwatSoXpc9ntFaU1T1YhGZp6p/EpFHcW4sHLI6+lB8fgCC/jbCDW2EW0J40r39WTRjTBJUL91I646GpOaZNiqL/HO7ngKxL6evv/feezn77LPJyMggNzeXN998M2r6nognoLQ/jrBaRA7Dmc9rQq/PPJC134fi1lBa/a1AJqF9zXhGZPVfuYwxA1pfTl9/++23s2zZMo477jhuu+02rr32Wu69995elT+egHKPiBTgPLBqCZAN/HevzjrA7b9T3nn5WjzNAAQrm/FbQDFmwOuuJpFKfTF9fUlJCe+//z7HHec8/eOSSy7hzDPP7HXZuwwo7gSQte7DtV4BJvX6jINA5N/b50+jWZyqcbCquZ9KZIwZDObOncv8+fO5/vrrCQaDLF26lK9+9as9zqd9+vpYgsEgNTU1rF+/nmnTpvHcc88xc+bM3hQd6CaguBNAfhN4vNdnGkTav0FoGHxpabSGmpF0L6F9FlCMMYmLnL5+/PjxKZu+3ufz8cc//pGLLroIj8dDQUEB999/f+/zjSPNcyLyXzjPGOnopVLVqtiHDHKRNZS0NIJtrfgKA1ZDMcb0Wl9NX3/BBRdwwQUXJFDC2OIJKO33m3wjYpsyhJu/OmooqvjS0gm2tuAtDNjd8saYIS2eO+Un9kVBBpL2PpT2Jq9gawu+4gya11ahIUW83XeqGWPMYBPPnfJfirZdVR9MfnEGhvbZhlUVX3o6wdZW/MMyIaQEq5rwl2T2cwmNMYlQ1bhGWQ0VERPNxyWeJq9jI5YDwGnAu8DQDSjt7zdtr6G4AQVnTi8LKMYMPIFAgMrKSoqKiiyo4ASTyspKAoFA94ld8TR5fStyXUTycKZjGbI696E019XiK8kAnGnsMyjqz+IZYxIwZswYysvLqaio6O+iHDICgQBjxoyJO30iD8pqBKYmcNzg0d6Hos59KMHWVjwBH77iDFrW74NTxvZv+YwxPeb3+5k40bqMeyOePpSlOKO6wJlMspQhfl/K/vtQtKPJCyDzE8OofXYrwb1N+Ioz+rOIxhjT5+KpofwqYjkIbFXV8hSVZ0Bon21YlY5hwwAZM4uofXYrrdvrLKAYY4aceALKNmCnqjYDiEiGiExQ1S0pLdkh7MA+lP01FG+BM6dOcJ89X94YM/TE8zyUJ4BwxHrI3TZkRY7yCmRn09LYSDgUwpPuw5PpsylYjDFDUjwBxaeqre0r7nJaPJmLyJkisk5ENojI9VH2p4vIY+7+t0RkQsS+H7jb14nIGd3lKY6bRWS9iKwRkW/HU8ZERNZQcgqLUQ3TUL0PAG9BwGooxpghKZ6AUiEiHZPyi8g8YG93B4mIF/gdcBZOR/5lIlLaKdlVwD5VnQLcDtziHluK8xz7WcCZwF0i4u0mz/nAWGCGqs4EFsVxbYmJuFM+u8gZIlxX6bwkvvx0q6EYY4akeALKNSjLXREAACAASURBVMAPRWSbiGwDvg/EM5/yHGCDqm5yazWLgHmd0swD/uQuPwmcJs7X/3nAIlVtUdXNwAY3v67y/Bpwk6qGAVR1TxxlTEjknfI5hcUA1Fc5AcVbECBU3dLjO0yNMWag6zagqOpGVT0ep0YwS1U/qaob4sh7NFAWsV7ubouaRlWDQA1Q1MWxXeU5GbhERFaIyDMikrJ7ZTrm8lIlu8gJKHWVlYDTMa9tYcINbbEON8aYQanbgCIiPxeRfFWtV9U6ESkQkZ/FkXe0uQs6f22Plaan2wHSgWZVnQ38EYg6ub+IXO0GnRWJ3hG7vw8FAlnZ+NLSqXNrKL4CZ5qCkPWjGGOGmHiavM5S1er2FffpjWfHcVw5Tp9GuzHAjlhpRMQH5AFVXRzbVZ7lwF/c5cXAEdEKpar3qOpsVZ1dUlISx2UcbP8oL2ciuZyiIuor9zd5AQStH8UYM8TEE1C8ItLx0GIRycCpDXRnOTBVRCaKSBpOJ/uSTmmWAFe4y58HXlSn82EJcKk7CmwizlQvb3eT51PAqe7yycD6OMqYkMgaCkB2YTF1VU6Tl8+9F8VqKMaYoSaeGxsfBl4QkQfc9SvZ35Eek6oG3ccHPwt4gftVdZWI3ASsUNUlwH3AQyKyAadmcql77CoReRxYjXN3/jdUNQQQLU/3lL8EHhGR7wL1wFfiuLbEdIzyciJKTmER5WudYngCPiTgsxqKMWbIiWe24VtF5APgdJyP0r8D4+PJXFWXAcs6bVsQsdwMXBzj2JuBm+PJ091eDXwunnL1loiARNRQioqpr6pEw2HE48E/MouWTdX2bAVjzJAST5MXwC6cu+UvwnkeypqUlWiAEJGOocE5hcWEQyEaa2sAyDy6hOCeJtrK6/uziMYY06diBhQRmSYiC0RkDXAnznBdUdVPq+qdfVbCQ5R0qqHA/psbM48oAZ/Q8O7u/iqeMcb0ua5qKGtxaiPnquqJqvq/OPN4GdxmL93fhwJ0DB32BHxklBbR9H4FGgrHzMMYYwaTrgLKRThNXf8UkT+KyGlEvw9kSBJxpl4ByHYDSkNVVcf+zCNKCDcGad1a2x/FM8aYPhczoKjqYlW9BJgBvAR8FxguIneLyGf7qHyHLs/+PpSMnFwQoaGm43Yd0qfmg1doWrevv0pojDF9Kp6pVxpU9RFVPQfnRsKVwEEzBw81kX0oHq+XjOwcGmv2Bw9Puo/08bnOI4GNMWYIiHeUFwCqWqWqf1DVU7tPPbhFjvICyMzLp7Gm5oA06ZPyaNvVQLg52NfFM8aYPtejgGL2i6yhAGTl59MY0eQFkDYhDxRarB/FGDMEWEBJkIhAOLKGUnBwQBmXA16h5ePqzocbY8ygYwElQeI5IJ6QmZtHY+2BgcOT5iV9cj5Nayrt+SjGmEHPAkqCPF4P4Yh7TDLz8mltaqKt9cBJITNmFhKqbCZYaXN7GWMGNwsoCfJ4hXAwoskrPx+AxuoDaynpE/MA7H4UY8ygZwElQV5fpxpKrhtQOvWj+IZlIuleWsvq+rR8xhjT1yygJMjjFUKh/TWUrDw3oHTqRxGPkDYmm9YtBw4pNsaYwcYCSoI8XiEcOrjJq6H64BFdGYcV07ar0WopxphBzQJKApo+/IhwxR5CLW0d22I1eQFkHj0MSfNS/0bnJyAbY8zgYQElAS3r1hLatYNQ6/6A4ktLIy0jM2pA8QR8ZB4zjMYPKgg1tB203xhjBgMLKInw+hANEQoeODV9tLvl22WfMBJCSt1LZX1RQmOM6XMWUBIgPh8eDR0wbBggb/hIKrZtiXqMf3gWmccMp/71HTa3lzFmULKAkgDxeZFw6IBhwwDjDzuSqu1lHU9u7Czz6GEQUlq22D0pxpjBxwJKInw+PBo8YNgwwPgjjgZg64crox7WMbfXZhtCbIwZfCygJEDcPpRwp4BSPG4CmXn5bP3gvajHedK8pI3JoXWTBRRjzOBjASUB4vfhCR8cUESE8UcczdYPV6Lh6M+ST5+UR+v2OsItob4oqjHG9BkLKAkQrzdqDQVg3KwjaKqtoWrH9qjHpk/Mg7DN7WWMGXxSGlBE5EwRWSciG0TkoMcGi0i6iDzm7n9LRCZE7PuBu32diJzRgzz/V0TqU3VNAHjdGkr44IAyfNIUAPZs2Rj10LTxuUiGj9rntqJRApIxxgxUKQsoIuIFfgecBZQCl4lIaadkVwH7VHUKcDtwi3tsKXApMAs4E7hLRLzd5Skis4H8VF1Tx3n8PkSDRGvVKhw9Fq/fz54tm6Ie60n3UnD+ZFrL6uyeFGPMoJLKGsocYIOqblLVVmARMK9TmnnAn9zlJ4HTRETc7YtUtUVVNwMb3Pxi5ukGm9uA76XwmoDIJq+D93l9PorHTqB8zUcxj888chgZhxdT91IZ4VbrSzHGDA6pDCijgciv4OXutqhpVDUI1ABFXRzbVZ7fBJao6s4klT82n9vkFaPFqvSkU9i1YT071q+NmUXWcSPRtjAtH+9LUSGNMaZvpTKgSJRtnT+CY6Xp0XYRGQVcDPxvt4USuVpEVojIioqKiu6SR8/D5w4bDhP10b6zTvkMiLDl/Xdj5pE+0elLaXhnT0JlMMaYQ00qA0o5MDZifQzQebrdjjQi4gPygKoujo21/WhgCrBBRLYAmSKyIVqhVPUeVZ2tqrNLSkoSujDx+fCGWgEIth7ckZKemUnR6LHs3vRx7Dy8HnJOHE3z6kqa11stxRgz8KUyoCwHporIRBFJw+lkX9IpzRLgCnf588CL6nzlXwJc6o4CmwhMBd6Olaeq/p+qjlDVCao6AWh0O/pTQrxefMFGAFoao88ePGLyVHZt/JhwtI4WV87JY/Dmp1PzzGaC++yZ88aYgS1lAcXtE/km8CywBnhcVVeJyE0icp6b7D6gyK1NXAtc7x67CngcWA38HfiGqoZi5Zmqa4jJ58ffEVCiT/Q48ehjaaypZvXLL8bMRnwe8s6eSNvuRnbdtpyG96z5yxgzcPlSmbmqLgOWddq2IGK5GafvI9qxNwM3x5NnlDTZiZQ3XuLrvoYy7fhPMXLqdF577CFmnnQKXp8/arrMI0pIG5dL5cOrqXlmMxmzivCkeVNWdmOMSRW7Uz4B4vPha3MCSnND9BqKiDDn/C/QsK+KslUfdpmfLz+d/LMnEa5tpfqpDVE7+o0x5lBnASURXm+3TV4AE444Gn96gI/fer3bLNMn5ZH7mfE0vruH6r9ttKBijBlwLKAkQPz+bpu8wHks8MRjjmXDijcJh7q/gTHn1LFkzx1Nw5s7aXxnd9LKa4wxfcECSgKWbv4/fMFmQLusoQDM/NTJNNZUs+nd5d3mKyLknTUR/+hsav9Zhgajz1hsjDGHIgsoCWiREILi94ZoaYhdQwGYdMyxZBUUsubVf8aVt4iQ99nxhCqb2fvgalrL6pJRZGOMSTkLKAnw+dMICfg9bTR3U0PxeL2MP+xIytZ8FHe/SGB6IXnnTqJ1Wy17freSPX94n7Y9jckoujHGpIwFlAT4fWm0+MFHa5d9KO3GlB5OU20NZas+iPscOZ8azcgfzCHvnEkEdzdS+eBqQjUtvSm2McaklAWUBPjER6sf/NoSc9hwpMmzjyN/+EgW33IT2z56P+7zeNJ95Jw4msJLZxCsbGLnbcup+fsWm6HYGHNIsoCSAL/X79RQws3d9qEAZObmcdlPbyMzL583/7Kox+cLTCtg+LWfIPPwEupeKqPywdX2CGFjzCHHAkoCfOKjxQfecFO3o7zaZeblU3rSKZSvWUVjbU2Pz+kvyaTwkukUXDyNlo3V7PndSlrLrcPeGHPosICSAL/XT6sffMFGWpqCcXe2T//kXFTDfPjCswmfO+sTwym+6jDCDW3suXMllQ+tRtustmKM6X8WUBLg8/icJq/WBjSstDXH94FePHY84484mpXPLUOjPT84ToEpBYy4bja5nxlP0+pKqp5Yj8Z62pcxxvQRCygJ8Hv8tPgEb1s9AM1xjPRqd9inP0N95V629WDEVzSegI/c08aRd+ZEmj7YS80zmy2oGGP6lQWUBPg8ziiv9DLnacStTfH1o4Az4istI5PVr8Se1r4nsueOJuuEkdS/up2Ku9+ndXt9UvI1xpiesoCSAL/Hz+bh0jGfVzxDhzuOTUtn+gkn8vFbr9NU3/tOdREh/7zJFHxhGsF9zey58z3qXim32ooxps9ZQEmAz+Pj/UlCoMV5dG9dZc+etnj0WefR1trCs3ffkdCIr85EhKxjhjPiP2eTMauImmWb2Xnzm+z+3/do/KDCZi42xvQJCygJ8Hl8NKVBoLkSj0fZt7OhR8eXjJvASZddweb3lvPQ975Fa1NyplXxZPgo/OJMCr4wjYzSYjQYpurRtey5411q/1lmN0QaY1LKAkoC/B4/jQHwaJicjCCVO3oWUADmzPs8n//Rz6jfV8U7//e3pJVNPE5tpeCiqQz/9jHkXzAFCfiofXYLe+54l7rXtqNtNouxMSb5LKAkwO/x05juLOenNbNtVSVVPaylAIwtPZxpx5/I608+Gtf09j0lXiH7uJEMu+ZIir98GKGGIDVPb2LX7e9Q+/xWgvt61lRnjDFdsYCSAJ/HR5tPCPu8BHCaq15YuDqhvM76xrWUjJ/I0/9zS0qCSrvAtAJG/ffxFF05C19hgNoXtrHrVyuoeW4rQZt00hiTBBZQEpDudaonoax0Jnk3AxBOcFSVLy2NC7//Y/JHjuKZO3/Nvl07klbOzsQrZEwvpOQrhzPie8eSeXgxdS9sY9cv3mbnLW9T+/xWWrbW2p33xpiEWEBJQIYvA4Dmgkz8e8s4/NNjqN7TlPBQ3ezCIs79j++jKA9f/x02rHgrmcWNylcQoPDSGQz79tHknTMJX0kmtc9vo+Lu99l56woaV+6x0WHGmB6xgJIAn8dHujedxsJM2nbupGhUFsGWEHVVifdJFIwczZdu+V8KR41h6W9+wcZ33k5iiWNLG5VNzomjKfnyYYz43rEU/dtMvHlpVC1ax5473qP2+a207myw4GKM6ZavvwswUGX4MqgvCNC2YSeFo7IA2FteT25xRsJ55pYM46IbfsrjN/2Qp269ibmXX8nscy9ERJJV7C75CgP4CgMESotofGc3DSt2U/vCNmqf34a3IJ30iXl489Px5qbhH5ZJ2sS8PiubMebQl9KAIiJnAncAXuBeVf1lp/3pwIPAJ4BK4BJV3eLu+wFwFRACvq2qz3aVp4g8AswG2oC3ga+qavyTbPVQpi+TyuEZTK6tJT+tEa/fw4711Uw6qqRX+QaysrnsJ7fy99/fwSuPPED5mo849cqvkjdsRJJK3j3xCFnHjiDr2BGE6lppXlNF05pKmjdUE65rBbeyIhk+fEUBAlMKCMwoIG1cLuKxAGPMUJWygCIiXuB3wGeAcmC5iCxR1cjhUFcB+1R1iohcCtwCXCIipcClwCxgFPC8iExzj4mV5yPAv7lpHgW+AtydkotrrCJTPOwcHQCgbe0qRk0pZtuaqqRk7w8E+Ny3/ouRU6bx+hOPsvDarzPngouZM+9ivL6+rVR6c9LImjOCrDlOQNOwEq5vo/njfbRuq6VtdyN1r5RR91IZnkwf6dMKyJhRSPrUArxZ/j4tqzGmf6Xy02kOsEFVNwGIyCJgHhAZUOYBN7rLTwJ3itOGMg9YpKotwGYR2eDmR6w8VXVZe6Yi8jYwJlUXxnsPk7l3I+WjRoDHQ/OqVYyZeQFvLN5IQ3ULWfnpvT6Fx+tl9jkXMP2TJ/HSg/fx+uOPsGXlu8w+9wKmzD4e8fRP95d4BG9uGlmfGE7WJ4YDEG4K0vzxPprXVNG8voqmlRUg4B+dTWBqAYHpBaSNzUW8VnsxZjBLZUAZDZRFrJcDx8VKo6pBEakBitztb3Y6drS73GWeIuIH/h34Ti/LH5s/gwxVaqSJ9MmTaV6zhrEXXsUbizdSvm4f049LXvNUTmEx5/7H91l19GxeW/QgS379c2adfDonXvrvZBcWJe08veHJ8JF5RAmZR5Q4z4fZXk/zuiqaP66m7qUy6v5ZBj4P3tw00sfnEphRSGBqPpLhsz4YYwaRVAaUaJ8UnYcKxUoTa3u0r+Wd87wLeEVVX41aKJGrgasBxo0bFy1J93wBssNhqtoaSJ8+g8Z33mHsmGzSs3yUr6lKakBpN+vk05h54im88eSjvPnXx1j18vNMOOoTzPjkXKbOOYG0jMyknzMR4hHSxuaQNjaH3NPHO7WXDdW0ltUS2tdC87oqGt/b4yYG//BM0qcWEJiSj68kE29eGuK1wYfGDESpDCjlwNiI9TFA57v22tOUi4gPyAOqujk2Zp4i8mOgBPhqrEKp6j3APQCzZ89O8G7EAFnhMA1tDaRPm0bt008Trq9jzPRCtq2pIhxWPCnonPZ4vXzqkn9n6nGfYv2b/2LNay/x97tu5/n77uLYcy9k+glzKRw95pD61u/J8JF5eDGZhxcDTh9Ma1kdrVtqCDeFaC2vo/71HdS/ut05oD3ITMonfXI+aeNz8GT5D6lrMsZEl8qAshyYKiITge04nexf7JRmCXAF8AbweeBFVVURWQI8KiK/wemUn4ozckti5SkiXwHOAE5T1dTOfugPkB1W6tsaSZ82FYCWjz9m6uyxbHx3D1ve38uko3s32qsrwyZMYtiESXzqkn9jx/q1vPP0Yt548s+88eSfGTltBqdecTUjpkzrPqN+IB4hfXwu6eNzO7aFW0O0bqsjtK+Z4L5mWsvqaFi+i/rXne8KkubBWxDAV5SBf2QW/uGZeHPT8BVn4M1O669LMcZ0krKA4vaJfBN4FmeI7/2qukpEbgJWqOoS4D7gIbfTvQonQOCmexynAz8IfENVQwDR8nRP+XtgK/CG+232r6p6U0ouzpdBloZpCDWRPs354G5eu5aJlx1DVl4aq17bntKA0k5EGD19JqOmzaBqRzlbP1jJW4sf45EbrqV07qkcf+ElFIwc3X1G/cyT5iUwJf+AbRoM07qtjtYd9U6gqWomuKeR5jWVBzRy+ooCeAsD+Edlkz42B9+ILHyFARu+bEw/SOkYVHfk1bJO2xZELDcDF8c49mbg5njydLf33Xhav9OHEtIwbcV5ePPyaHrnXQovv5zDTh7NW0s2s7e8juIxOX1SHBGhaPRYikaPZdbJp/HWU4/z7v89xepXXiR/+EhK557KseddhC9t4HybF5+H9El5pE/KO2B7uDVEcG8T4fo2WnfU07a9nmBVM/Wvbac+5EYanwf/sAz8w7Pwj8rCPzwLb14a3oIAnjRvP1yNMUOD3SmfCH8GhSGnVa2yuZKMY2dT+8wzlFx7LYedPIYVy7by9tLNnHXN4X3e9p+emcncL87nqM9+jg3L32Tze8t5/YlHeP+5Zcw86dNMP+Ekhk2YhMc7MD9YPWle0kZlA84Myu20LUTbrkbadjc4v/c00rKpev8AAABxZgOQNC+enDR8Rc7MAN68dLx56fgK0vFkp1ntxpgEWUBJRFo2o4LOc+R3NuzkyG9/m/rnX6D26aUUX3MNx54zgTef2sRHL2/n8FNSdztMV3KLSzjmrHM55qxz2frhSt77+9OseHoxK5b+lbSMDEZNL2XMjFmMKT2ckVOmDdgA00783o7RZZFCta0Eq5oIVbfQVtFEsKIRbQsTqm2lcWst2tJpZmWf4MsP4C1Ix5udhifbjzfbj6d9OctZ9mb7EZ+NRjMmkgWURKRlM9INKOV15cyZOoesk06i8oGFFH75yxx56ljK1lTxyqL1eP0eSj81ql+LO/7woxh/+FHU76uifPWHlK/5iPI1q3ht0YMAZOTkUjJ+IuMOO5LSk08lp7C4X8ubTN7cNLy50Zv6VBVtCjpBp7qFUHUzwaoWp8+muoVgRQ2h+jYIRh/jIQGvE3Sy2oPO/mDjBJ/9AcnuuTFDgQWURKTnMCoYwi8ettZuRUQovOIKyr7yFWqf/j/yL7yA875zNEt/u5KX/7yOkZPzKBiR1d+lJrugkBmfOpkZnzoZgMbaGspWfcCmd5ezt2wrry16kH899jDDJ02mZPxE8oaNYPwRRzN84uR+uzM/lUQEyfTjyfTjj/H3UVW0NUy4vpVQfRvh+jZCDa2E25frneW2vU2Et9QQbgwefGcUgEciajj+A2s/WWl4cqz2YwY+GcrTks+ePVtXrFjR8wPDYbipgC9OP5qWrCL+ct5fUFU2n38BhMNMXPI3RITG2lYevfFN8oZlcsb/m0VuUeIzEfeFfbt2sPqVf1K+5kOqtpfTWFMNQFZ+AWNmHkbBqNHkDx/J8ElTyBs+An9a76eYGWw0pIQb2wg3tBGqa3V+dwo+oYY2wu6ytnVf+/Fk+/Fm+pF0L5LuxdP5d4bPqSVl+ZGAz/qATMqJyDuqOvug7RZQEggoAD8fzUPTT+TW+tX846J/MDJ7JNV/+Qs7b/gR4xY+QNbxxwOw4Z09PPvHj0DgmM+O45gzxpOeOTAmTWysrWHLynfY9O5ydm5YT93eCiJv8ckuLCJ/xEjyh7s/I0YxYvJUcotLBmWNJhXCLSGn9tNwYNDpCDx17r7GINoSQlu7eZqmBzyZfifA5LjNbzlpeDJ9eNJ9TgAK+JCA89uT4cOT6Wy3JjkTLwsoUfQqoPymlLXjZ3Nx/XvcctItnD3pbMItLWw4/XTSJ01m3MIHOv5BK7bV8fbTm9nywV4ycvwcP28y008YgXeATTESCraxb+cOKrZupnr3Tmp272Lfrp3U7N5JQ/W+jnRev5+CkaMZNmESwydOpnDUGPKGjyC3ZBhe38AIpocqDSvaGkJbQoRb3N9NQacm1ODUjDqW691aUl1rzJpQB3FmNZB0rzMKrr32k+bdXzMK+A4MRgEvEvA5ad1tkua1GtIQYAElil4FlLs+SVv+eE4If8wXpn+B7x37PQCqHnyI3T//OcMX/DeFXzxwYoCKbXW8/Od17N5cS25xgFHTCph4RDGjpuYTGOBTvbc1N1O1o5xdGz+mevdOKsu3sWfzxgMCjYiHnOJisvILCGTnkJVfSMn4CeSWDCe3uIScomIC2Tn2TTkFNBgm3OzUcsLNIWe5OegEo0b3d5O73w1Y2hoRtFpCaHOM/qFIApLuBhu/xwkwfo/z44v224v45IDfRKbxe5yg1p5XmnuM32OBqx9ZQImiVwHlgc8BypdGFBPWMA+f/TAAGg6z7aqraFmzlknPLMNXUHDAYarK5vf38tHL5ezZWkdLYxBfupexMwqYNmcERaOzyCvJwDPAai+xNFTvY9/O7dTs2d1Rq2moqaa5vo66vRU01dUekN6Xlk5OUbH7U0JO8f7l3OIS8oaNGFA3aA4m7QMUtDlIuDlIuLk92ARRN0iFm/Yva1vYqU21hdFgOPrvtjCEE/sMag84+NwA5PM4Qcm3PyAdsM/fKd1Bx0amk/37/AfngVeG9BcfCyhR9CqgPHEl7Hyf3544n/s/up8Xv/AihYFCAJrXrGHzxV8gbexYxj/yML7CwqhZhIJhdm6s4ePlu9ny4V4aa1oBSAt4GTEpjzEzC8kuSCczN42ScTmkBQbXoDxVpbGmmtq9e6ir3Evd3r3UVVY4y+7vhn37Dui3QYScwmIycnIJZGcRyMohkJ1DIDvb/Z1DICv7wPXsbHxp6UP6A+BQpiF1Aoz7wwEBJ0S4NSIwtYacoOZuJ9gpSHVad/brQfsJJeFzLzJ4dQo8HLB+YDr8nQOYODNse8R5ZpBHnNqX19keWVvr2Obdvx+vm38f1tgsoETRq4Dy7A2w/D4+/vorXLj0Iq6bfR1fmvWljt0Nb71N2dVXkz5jOuPvvx9PVtfDhkNtYfZsq6OmopFdm2rZvm4f1bsbD0hTMCKT/OGZlIzL4djPTUys3ANMKBikobqKur17qa3Y7fTZ7NlFc30dzfX1NDfUdyyHQ8GY+Xh9vgMCjBN4cph7+Xwy8/JjHmcGJw0rhNoDjx4UiA4Kbh3796clSgDryKst1v72Y1PwudsRgGR/UOsU0CK35Zw8lrTR2QmdKlZAGVxfeftS7mgINjE1UMzMwpk8s/mZAwJK1nFzGPWr29j9i18Q3LuXtG4CitfvYeTkPEZOzmPG8SMBaKpvpbG2lbq9zVSU1bFzQzW1e5sIZA/s/pae8Pp85BYPI7d4GKNnlMZMp6q0tTTvDzT1dc5PQ/2B6+5y7Z7d7G7YyFD+QjWUiUfA43X6bPqBqkJof/DRkFNrcgJdxO9QRKBqC7nHKBp204diBMb2gBfSjvw1GEabgvsDXXcjBhNgNZREayiVG6FiLUw+ldW1mynJKKEk8+AZhsMtLXjS7X4NY8zgYTWUZCua7PwApUWxvzlbMDHGDBWDYyiRMcaYfmcBxRhjTFJYQDHGGJMUFlCMMcYkhQUUY4wxSWEBxRhjTFJYQDHGGJMUFlCMMcYkhQUUY4wxSWEBxRhjTFIM6bm8RKQC2Jrg4cXA3iQW51Bi1zZwDebrs2s7dIxX1YMmLxzSAaU3RGRFtMnRBgO7toFrMF+fXduhz5q8jDHGJIUFFGOMMUlhASVx9/R3AVLIrm3gGszXZ9d2iLM+FGOMMUlhNRRjjDFJYQHFGGNMUlhA6SEROVNE1onIBhG5vr/LEy8RuV9E9ojIRxHbCkXkORH52P1d4G4XEfmte40fiMgxEcdc4ab/WESu6I9r6UxExorIP0VkjYisEpHvuNsH/PWJSEBE3haR991r+4m7faKIvOWW8zERSXO3p7vrG9z9EyLy+oG7fZ2InNE/V3QwEfGKyHsi8rS7PiiuTUS2iMiHIrJSRFa42wb8e7JLqmo/cf4AXmAjMAlIA94HSvu7XHGWfS5wDPBRxLZbgevd5euBW9zls4FnAAGOB95ytxcCm9zfBe5ywSFwbSOBY9zlHGA9UDoYrs8tY7a77Afecsv8OHCpu/33wNfc5a8Dv3eXLwUec5dL3fdrOjDRfR97byn4jgAAB6tJREFU+/tv55btWuBR4Gl3fVBcG7AFKO60bcC/J7v6sRpKz8wBNqjqJlVtBRYB8/q5THFR1VeAqk6b5wF/cpf/BJwfsf1BdbwJ5IvISOAM4DlVrVLVfcBzwJmpL33XVHWnqr7rLtcBa4DRDILrc8tY76763R8FTgWedLd3vrb2a34SOE1ExN2+SFVbVHUzsAHn/dyvRGQM8DngXnddGCTXFsOAf092xQJKz4wGyiLWy91tA9Xw/9/eucdYVV1x+PuBCg3yEFATowa10Fdqx0iMijFYRxLB2FhNaEpbtY3GPsA2MSaGaECbPgyxxthUo/4hETVaWktCk44pYG0xAbEDQxUoWp/YTmILSFQisvxjreOcXO+9MvWM9+H6kp2z9zr7nr0WnDl777XPWdvMXgd/KAPHhLyRnW1vf7hBTsNH8l1hX7iE+oFB/IHyPLDbzA5ElbKeH9gQ5/cAU2hT24DbgeuBg1GeQvfYZkCfpE2Srg5ZV9yTjTis1Qp0GKoj68b3rhvZ2db2SzoSWAn82Mz2+uC1ftU6sra1z8zeA3okTQJ+D3yhXrU4doxtki4CBs1sk6TZhbhO1Y6zLZhlZrskHQM8Lmlbk7qdZltdcoYyPF4FTiiVjwd2tUiXKvhPTKuJ42DIG9nZtvZLOhzvTFaY2e9C3DX2AZjZbmAd7mOfJKkYEJb1/MCGOD8Rd3W2o22zgIslvYi7j7+Kz1i6wTbMbFccB/GBwBl02T1ZS3Yow2MjMD3eQjkCXxhc1WKdPg6rgOKtkcuBP5Tk34k3T84E9sT0/E/AHElHxdspc0LWUsKPfh/wnJndVjrV8fZJOjpmJkj6DNCLrxGtBS6LarW2FTZfBqwxX91dBXwj3pQ6CZgObPhkrKiPmd1gZseb2TT8b2mNmS2gC2yTNE7S+CKP30tb6YJ7simtfiug0xL+NsYO3I+9uNX6DEPvh4DXgXfxUc/3cP/zn4F/xnFy1BXw67BxAJhZus538UXPncCVrbYrdDoHdwNsAfojze0G+4BTgb+HbVuBm0J+Mv7Q3Ak8CowJ+dgo74zzJ5eutThs3g5c2GrbauyczdBbXh1vW9iwOdI/imdFN9yTzVKGXkmSJEkqIV1eSZIkSSVkh5IkSZJUQnYoSZIkSSVkh5IkSZJUQnYoSZIkSSVkh5J0BJKmRNTWfkn/lvRaqbx+BNrrkTT3EOpdIenOEWhfktZImhDlym0caSLa7tQm5x+WNP2T1CkZWTL0StIRmNkbQA+ApCXAPjNbNoJN9gAzgT+OYBvNmAtsNrO9AGZ2dov0GEl+g8fxuqrViiTVkDOUpOORtC+OsyU9IekRSTsk/ULSAvl+IgOSTol6R0taKWljpFk11zsCuBmYHzOg+ZLOkLRevm/Hekmfq6PHPElPSZraqA1JS+R706yT9IKkRQ3MWsDQV9S1Nq6T9FtJ2yStUJ2gZZIWSXpWvrfGwyEbF21vDDu+FvLRkpbFv9EWSQtDfn7UG4jfjQn5i5KWSnomzn0+5FMk9cVv7ibiUEW7q+V7umyVND/UfBLo1VCYlaTTafWXlZkyDTcBS4DrSuV9cZwN7Mb3RxkDvAYsjXPXArdH/kHgnMifiIdsqW3jCuDOUnkCcFjke4GV5XrAJfgD8qhmbYTu60O/qcAbwOF12n8JGN/Axj14TKdRwFNFOzW/38XQF+aT4vgz4FuFDI/4MA74Ph4HrbBvMv5V+ivAjJAtx4Nugu/zsTDyPwDujfwdDH3JPw+PXjAVuBS4p6TbxFL+ceD0Vt9TmapJOTJIuo2NFuHBJT0P9IV8ADgv8r3AF0sD+wmSxpvvpdKIicD94fM3fF+SgvNw99gcCxdVozYiv9rM9gP7JQ0Cx+LhcMpMbqLPBjN7NWzsB6YBf62pswVYIekx4LGQzcGDMV4X5bF4Z9eLb1x1AMDM/ivpK8C/zGxH1L0f+CEevBGgCMC5Cfh65M8t8ma2WtL/Qj4ALJP0Szy8ypMlPQeB4+I6SYeTHUrSbewv5Q+WygcZut9HAWeZ2dvDuO4twFozu0S+58q60rkX8NhNM4Cnm7URHUxZx/eo/3d4QNIoMztY59yh/H4e/oC/GLhR0pdwF9SlZra9Rifx4ZDoDWP/1+hQ2/6HYjmZ2Q5Jp+PrQj+X1GdmN8fpscBw/h+SNibXUJJPI33Aj4qCpJ46dd7EtxMumIi70MDdXGVewkfmy+PBfahtNGM73kkNG0mjgBPMbC2+6D0JOBKPUruwWHORdFpJ12uKtQxJk4FtwDRJn4063wae+Iim/4Kv/SDpQnzLWiQdB7xlZg8Ay/CtqAtm4METky4gO5Tk08giYGYsQD8LXFOnzlrcZdUfi8i34qPrvwGjayvHqH8B8Ggs/h9KG81Yja+X/D+MBh6QNIBHKv6V+V4qt+Cuui2StkYZfPvdl0O+Gfimmb0DXBn2DOAzvLs+ot2lwLmSnsHday+H/MvAhnDPLQZ+CiDpWODtwkWZdD4ZbThJ2hD55kvLzeyCVusyUkj6CbDXzO5rtS5JNeQMJUnakBi136P4sLFL2Y0v9iddQs5QkiRJkkrIGUqSJElSCdmhJEmSJJWQHUqSJElSCdmhJEmSJJWQHUqSJElSCe8DICZFZljHe2AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "plt.title(\" Time taken for 10^-4 Acc\")\n",
    "plt.plot(list(range(2, config.maxNConteCarlo+1)),[x[-1] for x in timeElapseHA] );\n",
    "plt.xlabel(\"Dimension\")\n",
    "plt.ylabel(\"Time taken to get the required accuracy (in seconds)\")\n",
    "plt.show()\n",
    "\n",
    "plt.title(\"Accuracy change with time for 10^-4 acc\")\n",
    "\n",
    "for i in range(2, config.maxNConteCarlo+1):\n",
    "    plt.plot(timeElapseHA[i-2],accArrHA[i-2]);\n",
    "\n",
    "plt.xlabel(\"Time taken (in seconds)\")\n",
    "plt.ylabel(\"Accuracy\")\n",
    "plt.legend(['dim='+str(x) for x in list(range(2, config.maxNConteCarlo+1))])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T18:11:01.568433Z",
     "start_time": "2020-06-12T18:11:01.056761Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "plt.title(\" Time taken for 10^-3 Acc\")\n",
    "plt.plot(list(range(2, config.maxNConteCarlo+1)),[x[-1] for x in timeElapseLA] \n",
    "plt.xlabel(\"Dimension\")\n",
    "plt.ylabel(\"Time taken to get the required accuracy (in seconds)\")     \n",
    "plt.show()\n",
    "\n",
    "plt.title(\"Accuracy change with time for 10^-3 acc\")\n",
    "\n",
    "for i in range(2, config.maxNConteCarlo+1):\n",
    "    plt.plot(timeElapseLA[i-2],accArrLA[i-2]);\n",
    "\n",
    "plt.xlabel(\"Time taken (in seconds)\")\n",
    "plt.ylabel(\"Accuracy\")         \n",
    "plt.legend(['dim='+str(x) for x in list(range(2, config.maxNConteCarlo+1))])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T21:36:39.121700Z",
     "start_time": "2020-06-12T21:36:39.118677Z"
    }
   },
   "source": [
    "A note on the above graph : We observe that the second graoh mostly contains straight lines and points. This can also be observed from the graph for $10^{-4}$ accuracy. The points here are too less and hence we see the curve like this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T23:58:18.803791Z",
     "start_time": "2020-06-12T23:58:18.796848Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Volume of hypersphere for dim in 4 digits precision with 95% confidence interval 2  :  3.1413326400000003\n",
      "Volume of hypersphere for dim in 4 digits precision with 95% confidence interval 3  :  4.188514538666666\n",
      "Volume of hypersphere for dim in 4 digits precision with 95% confidence interval 4  :  4.934750982564102\n",
      "Volume of hypersphere for dim in 4 digits precision with 95% confidence interval 5  :  5.26394423908046\n",
      "Volume of hypersphere for dim in 4 digits precision with 95% confidence interval 6  :  5.167404927999999\n",
      "Volume of hypersphere for dim in 4 digits precision with 95% confidence interval 7  :  4.724776489195403\n",
      "Volume of hypersphere for dim in 4 digits precision with 95% confidence interval 8  :  4.058653682512664\n"
     ]
    }
   ],
   "source": [
    "for dim in range(2, config.maxNConteCarlo+1):\n",
    "    print(\"Volume of hypersphere for dim in 4 digits precision with 95% confidence interval \"+str(dim),\" : \",meanArrHA[dim-2][-1] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "start_time": "2020-06-12T11:28:04.374Z"
    }
   },
   "source": [
    "#### We see that these are very close to values found in wikipedia for the answers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T22:44:34.021500Z",
     "start_time": "2020-06-12T21:45:28.536250Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 2 2.0 2.0\n",
      "4 2 2.5 1.2\n",
      "8 2 2.875 0.6086956521739131\n",
      "16 2 3.03125 0.30927835051546393\n",
      "32 2 3.1015625 0.1561712846347607\n",
      "64 2 3.130859375 0.07860262008733625\n",
      "128 2 3.13720703125 0.03953307392996109\n",
      "256 2 3.1390380859375 0.01983278242271048\n",
      "512 2 3.141143798828125 0.009929174479495574\n",
      "1024 2 3.1412887573242188 0.004969215636270902\n",
      "2048 2 3.1414928436279297 0.0024856607006357436\n",
      "2 3 4.0 2.0\n",
      "4 3 4.5 1.5555555555555556\n",
      "8 3 4.25 1.0\n",
      "16 3 4.1953125 0.5400372439478585\n",
      "32 3 4.1904296875 0.27732463295269166\n",
      "64 3 4.1884765625 0.14012590347400328\n",
      "128 3 4.1896514892578125 0.0701962683876419\n",
      "2 4 8.0 2.0\n",
      "4 4 8.5 1.7647058823529411\n",
      "8 4 6.03125 1.3367875647668395\n",
      "16 4 5.208984375 0.7941507311586051\n",
      "32 4 5.0120849609375 0.4165225650892618\n",
      "2 5 16.0 2.0\n",
      "4 5 15.5 2.0\n",
      "8 5 8.25 1.6136363636363635\n",
      "16 5 6.0263671875 1.0413223140495869\n",
      "2 6 32.0 2.0\n",
      "4 6 28.5 2.0\n",
      "8 6 10.6328125 1.8589272593681117\n",
      "2 7 64.0 2.0\n",
      "4 7 49.5 2.0\n",
      "8 7 13.4921875 1.9177764910248987\n",
      "2 8 128.0 2.0\n",
      "4 8 81.5 2.0\n"
     ]
    }
   ],
   "source": [
    "arrK=[]\n",
    "arrMean=[]\n",
    "arrAcc=[]\n",
    "\n",
    "for dim in range(2, config.maxNConteCarlo+1):\n",
    "    k,mean,acc = cubeBasedIntegration(dim,1/10000, config.cubeIntegrationMaxSeconds)\n",
    "    arrK.append(k)\n",
    "    arrMean.append(mean)\n",
    "    arrAcc.append(acc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T00:14:14.598561Z",
     "start_time": "2020-06-13T00:14:14.590614Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Volume of hypersphere in cubeBasedIntegration computed in given time: 2  :  3.1414928436279297\n",
      "Volume of hypersphere in cubeBasedIntegration computed in given time: 3  :  4.1896514892578125\n",
      "Volume of hypersphere in cubeBasedIntegration computed in given time: 4  :  5.0120849609375\n",
      "Volume of hypersphere in cubeBasedIntegration computed in given time: 5  :  6.0263671875\n",
      "Volume of hypersphere in cubeBasedIntegration computed in given time: 6  :  10.6328125\n",
      "Volume of hypersphere in cubeBasedIntegration computed in given time: 7  :  13.4921875\n",
      "Volume of hypersphere in cubeBasedIntegration computed in given time: 8  :  81.5\n"
     ]
    }
   ],
   "source": [
    "for dim in range(2, config.maxNConteCarlo+1):\n",
    "    print(\"Volume of hypersphere in cubeBasedIntegration computed in given time: \"+str(dim),\" : \",arrMean[dim-2] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T00:04:35.051100Z",
     "start_time": "2020-06-13T00:04:34.704129Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "arrK = np.asarray(arrK)/2\n",
    "plt.title(\"Maximum value of k in given time\")\n",
    "plt.semilogy(list(range(2, config.maxNConteCarlo+1)),arrK );\n",
    "plt.xlabel(\"Dimension\")\n",
    "plt.ylabel(\"log(K)\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.title(\"Mean Accuracy k in given time\")\n",
    "plt.plot(list(range(2, config.maxNConteCarlo+1)),arrAcc );\n",
    "plt.xlabel(\"Dimension\")\n",
    "plt.ylabel(\"Accuracy\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-11T09:01:01.613484Z",
     "start_time": "2020-06-11T08:53:38.927519Z"
    }
   },
   "source": [
    "We observe that the better method here is monteCarlo since the cube based integration method does not scale.    \n",
    "\n",
    "We compare the runtimes of $10^{-3}$ and $10^{-4}$ accuracy and see that runtime would not scale for higher dimensions for $10^{-8}$ accuracy.   \n",
    "In the second graph of how accuracy changes with time for higher dimension, we see that the rate of change becomes very less by the time it reaches $10^{-4}$ accuracy.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T23:48:15.463021Z",
     "start_time": "2020-06-12T23:48:15.458064Z"
    }
   },
   "source": [
    "## Part 2: Comparing values of cubeBased and monteCarlo for $10^6$ points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T00:06:51.421172Z",
     "start_time": "2020-06-13T00:06:51.416197Z"
    }
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Naive implementation of Monte Carlo\n",
    "\"\"\"\n",
    "\n",
    "def monteCarloBare(n, dim, m=50):\n",
    "    k  = n/m\n",
    "    dist = np.zeros(m)\n",
    "    cubeVolume = 2**dim\n",
    "    for i in range(m):\n",
    "        points = getPoints((int(k),dim))\n",
    "        s = np.count_nonzero(np.sum( np.multiply(points,points), axis =1)<=1.0)\n",
    "        dist[i]= s*cubeVolume/k\n",
    "    return clt(dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T00:13:56.594144Z",
     "start_time": "2020-06-13T00:06:51.609036Z"
    }
   },
   "outputs": [],
   "source": [
    "n = 1000000\n",
    "monteCarloMean=[]\n",
    "monteCarloAcc=[]\n",
    "cubeBasedMean=[]\n",
    "cubeBasedAcc=[]\n",
    "\n",
    "\n",
    "for i in range(2,config.part2maxDim+1):\n",
    "    mean,acc = monteCarloBare(n,i)\n",
    "    monteCarloMean.append(mean)\n",
    "    monteCarloAcc.append(acc)\n",
    "    \n",
    "    mean,acc = cubeBasedIntegrationForK(n**(1/i),i,timeit.default_timer()+ 10*config.cubeIntegrationMaxSeconds)\n",
    "    cubeBasedMean.append(mean)\n",
    "    cubeBasedAcc.append(acc)\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T23:13:37.913078Z",
     "start_time": "2020-06-12T23:13:37.908092Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "monteCarloMean: [3.1400639999999997, 4.195016, 4.951232, 5.281663999999999, 5.180928, 4.715776, 4.061184]\n",
      "monteCarloAcc: [0.0010477069624190496, 0.0016430031500015404, 0.0031215999298879636, 0.005041125725453177, 0.00734844285146019, 0.010427511505036185, 0.014899978828768328]\n",
      "cubeBasedMean: [3.141312, 4.187856000000004, 5.010319999999999, 5.923743999999997, 7.88892800000001, 13.949184000000008, 27.67999999999998]\n",
      "cubeBasedAcc: [0.005088319784854226, 0.08973756499745927, 0.42347155471107634, 1.0691724693031974, 1.6960682110421086, 1.9505221237313952, 1.9981317919075146]\n"
     ]
    }
   ],
   "source": [
    "print(\"monteCarloMean:\",monteCarloMean)\n",
    "print(\"monteCarloAcc:\",monteCarloAcc)\n",
    "print(\"cubeBasedMean:\",cubeBasedMean)\n",
    "print(\"cubeBasedAcc:\",cubeBasedAcc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T23:13:42.829769Z",
     "start_time": "2020-06-12T23:13:42.585437Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "plt.title(\"Difference between MonteCarloMean and CubeBasedMean\")\n",
    "plt.plot(list(range(2, config.part2maxDim+1)),np.asarray(monteCarloMean)-np.asarray(cubeBasedMean) );\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.title(\"Difference between MonteCarloAcc and CubeBasedAcc\")\n",
    "plt.plot(list(range(2, config.part2maxDim+1)),monteCarloAcc );\n",
    "plt.plot(list(range(2, config.part2maxDim+1)),cubeBasedAcc );\n",
    "plt.legend(['monteCarloAcc','cubeBasedAcc'])\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Monte Carlo Method is definitely giving us better answers here.     \n",
    "we are taking mean of vPartial and Vinside to calculate voume(where vPartial contains points partly inside the sphere as well as the points fully inside it).Thus we are assuming that half of the partial points are inside the sphere.\n",
    "A better approach would probably be weighted average where depending on the number of points inside the cube, we decide how much of cube is inside the sphere. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3 : Calculating $\\pi$ for $10^9$ points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T23:49:12.892490Z",
     "start_time": "2020-06-12T23:48:21.182423Z"
    }
   },
   "outputs": [],
   "source": [
    "pie,acc = monteCarloBare(10**9,2,70)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-12T23:49:50.451243Z",
     "start_time": "2020-06-12T23:49:50.446288Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.141621764 2.9513388614575666e-05\n"
     ]
    }
   ],
   "source": [
    "print(pie,acc)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "### Antithetic distribution method\n",
    " the method of antithetic random variable utilizes symmetrical characteristic of\n",
    "symmetry distribution. Here we will generate 4 identical distribution for calculatio of $\\pi$\n",
    "\n",
    "Consider $\\frac{1}{4}th$ part of the circle with x,y $\\in$ (0,1).\n",
    "From this part, area of the circle = $\\frac{\\pi}{4}$. Area of the square surrounding it = 1.\n",
    "Thus we can estimate the value of $\\pi$ from this setup using Monte Carlo.   \n",
    "\n",
    "Now Consider three other distributions between ((0,1),(0,-1)),((0,-1),(0,-1)),((0,-1),(0,1))\n",
    "Since the unit sphere is symmetrical in all four axis, All of the four distributions will give identical results. Thus all the datapoints can be assumed to be observed four times.\n",
    "\n",
    "This would help us in reducing variance.\n",
    "\n",
    "Not that we are currently only experimenting with high and low of uniform distribution\n"
   ]
  },
  {
   "cell_type": "code",
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     "end_time": "2020-06-12T23:49:52.661938Z",
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   "source": [
    "def getPointsAntithetic(shape):\n",
    "    return np.random.uniform(low=0.0,high =1.0,size=shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
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   "source": [
    "def monteCarloAntithetic(n, dim, m=50):\n",
    "    k  = n/m\n",
    "    dist = np.zeros(m)\n",
    "    cubeVolume = 1.0\n",
    "    for i in range(m):\n",
    "        points = getPointsAntithetic((int(k),dim))\n",
    "        s = np.count_nonzero(np.sum( np.multiply(points,points), axis =1)<=1.0)\n",
    "        dist[i]= s*cubeVolume/k\n",
    "    dist = np.hstack((dist, dist))\n",
    "    dist = np.hstack((dist, dist))\n",
    "    return clt(dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
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     "end_time": "2020-06-12T23:59:45.086707Z",
     "start_time": "2020-06-12T23:59:00.101143Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.1415269479999997 1.5822513240115787e-05\n"
     ]
    }
   ],
   "source": [
    "pieby4,acc = monteCarloAntithetic(10**9,2,70)\n",
    "print(pieby4*4,acc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe that accuracy has improve by a factor of 2 on using antithetic variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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