CPII-HW-1.ipynb

{"cells":[{"cell_type":"code","source":["import numpy as np\n","import math\n","import random\n","import matplotlib.pyplot as plt\n","import string as str\n","\n","from pandas.plotting import autocorrelation_plot\n","from numpy import random\n","from scipy import stats\n"],"metadata":{"id":"tUu6JEJGayiZ","executionInfo":{"status":"ok","timestamp":1660962765168,"user_tz":-120,"elapsed":317,"user":{"displayName":"Roshan Raj Shah","userId":"06387599595301221247"}}},"id":"tUu6JEJGayiZ","execution_count":14,"outputs":[]},{"cell_type":"code","execution_count":15,"id":"05ca81b7","metadata":{"id":"05ca81b7","executionInfo":{"status":"ok","timestamp":1660962765696,"user_tz":-120,"elapsed":22,"user":{"displayName":"Roshan Raj Shah","userId":"06387599595301221247"}}},"outputs":[],"source":["def linear_congruential_scheme(a,b,c,x0,N):\n","    \n","    n = list(range(0, N+1))\n","\n","    x_i = []\n","    x_ii = [] # Normalizes Array\n","    x_1 = [] # x_(i+1)\n","    x_p = [] # For period determination. \n","    \n","    x_i = np.append(x_i,x0) \n","    \n","    for i in range (0,N+1):\n","        x_i = np.append(x_i,((((a*(x_i[i])) + b) % c)))\n","    \n","\n","    # Normalizing x_i. with x0\n","         \n","    for i in range (0,N+1):\n","        x_ii = np.append(x_ii,x_i[i]/c)\n","    \n","    # Normalizing x_1. without x0\n","    \n","    for i in range (0,N+1):\n","        x_1 = np.append(x_1,x_i[i+1]/c)\n","\n","    print(x_ii)\n","    \n","    #'''\n","    plt.scatter(n, x_ii)\n","    plt.xlabel('N')\n","    plt.ylabel('x_i')\n","    plt.show()   \n","    \n","    plt.scatter(x_ii, x_1)\n","    plt.xlabel('x_i') # x_ii\n","    plt.ylabel('x_(i+1)')\n","    plt.show()   \n","\n","    # Determing the correlation.\n","    \n","    autocorrelation_plot(x_1);\n","      \n","        \n","     "]},{"cell_type":"code","source":["a = 57\n","b = 1\n","c = 256\n","xo = 10\n","N = 1000\n","        \n","linear_congruential_scheme(a,b,c,xo,N)      \n","  "],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":825},"id":"hou8GuMJa3yV","executionInfo":{"status":"ok","timestamp":1660962766131,"user_tz":-120,"elapsed":456,"user":{"displayName":"Roshan Raj Shah","userId":"06387599595301221247"}},"outputId":"175b37bc-5847-4c79-d3fd-1d3ff0659926"},"id":"hou8GuMJa3yV","execution_count":16,"outputs":[{"output_type":"stream","name":"stdout","text":["[0.0390625  0.23046875 0.140625   ... 0.34375    0.59765625 0.0703125 ]\n"]},{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}},{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}},{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"iVBORw0KGgoAAAANSUhEUgAAAZ0AAAEKCAYAAADJvIhZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO3deXxU1fn48c+TjWyQBMIOsgvuIHFBrKKgonVprVqtVqha++vXpba1X9QuWq3V9tu61rZSd2td6lIRESpI3AAFFWSXsO9IyEI2sj2/P+6dzEwyk0ySmbkhPO/Xa16Zuds5c+bmPvfce+45oqoYY4wx8ZDgdQaMMcYcOizoGGOMiRsLOsYYY+LGgo4xxpi4saBjjDEmbizoGGOMiRtPg46IPCUie0RkRZj5IiKPiEiBiHwpIscHzJsiIuvc15T45doYY0xbeV3TeQaY3Mz8c4ER7ut64G8AItIduBM4CTgRuFNEcmKaU2OMMe3madBR1Q+Afc0schHwnDoWAdki0hc4B3hXVfepahHwLs0HL2OMMR1AktcZaEF/YGvA523utHDTmxCR63FqSaSlpY0dOHBgbHJ6EKmvrychwetKbsdgZeFnZeFnZeFXX19PQUHBXlXtGY3tdfSg026qOh2YDpCXl6dLlizxOEfey8/PZ8KECV5no0OwsvCzsvCzsvDLz8/njDPO2Byt7XX0UL4dCKyaDHCnhZtujDGmA+voQWcGcLXbiu1koERVdwJzgLNFJMdtQHC2O80YY0wH5unlNRF5EZgA5IrINpwWackAqvp3YBZwHlAAVAA/cOftE5F7gMXupu5W1eYaJBhjjOkAPA06qnpFC/MVuCHMvKeAp2KRL2OMMbHR0S+vGWOM6UQs6BhjjIkbCzrGGGPixoKOMcaYuLGgY4wxJm4s6BhjjIkbCzrGGGPixoKOMcaYuLGgY4wxJm4s6BhjjIkbCzrGGGPixoKOMcaYuLGgY4wxJm4s6BhjjIkbCzrGGGPixoKOMcaYuLGgY4wxJm4s6BhjjIkbT4OOiEwWkbUiUiAit4WY/6CILHVfX4lIccC8uoB5M+Kbc2OMMW2R5FXCIpIIPAacBWwDFovIDFVd5VtGVX8asPxNwJiATVSq6uh45dcYY0z7eVnTOREoUNUNqloNvARc1MzyVwAvxiVnxhhjYsLLoNMf2BrweZs7rQkRGQQMAd4LmJwqIktEZJGIfCt22TThLNtazBMfbvA6G8aYg4hnl9da6XLgVVWtC5g2SFW3i8hQ4D0RWa6q6xuvKCLXA9cD9O7dm/z8/LhkuCMrKyuLSjlMnV0OwPC6Le3elleiVRadgZWFn5WFX1lZWVS352XQ2Q4MDPg8wJ0WyuXADYETVHW7+3eDiOTj3O9pEnRUdTowHSAvL08nTJjQ3nwf9PLz84lKOcx+GyA62/JI1MqiE7Cy8LOy8It28PXy8tpiYISIDBGRFJzA0qQVmoiMAnKAhQHTckSki/s+FxgPrGq8rjHGmI7Fs5qOqtaKyI3AHCAReEpVV4rI3cASVfUFoMuBl1RVA1Y/AnhcROpxAuf9ga3ejDHGdEye3tNR1VnArEbTftPo810h1lsAHBPTzBljjIk665HAGGNM3FjQMcYYEzcWdIwxxsSNBR1jjDFxY0HHGGNM3FjQMcYYEzcWdEy7BT9CZYwx4VnQMe1mMccYEykLOqbdLOYYYyJlQce0m11eM8ZEyoKOaTcLOcaYSFnQMe1mFR1jTKQs6Jh2U6vrGGMiZEHHtJvVdIwxkbKgY9rNgo4xJlIWdEy72eU1Y0ykLOiYdrOajjEmUhZ0TLtZzDHGRMqCjmm3eqvqGGMi5GnQEZHJIrJWRApE5LYQ86eKyNcistR9XRcwb4qIrHNfU+KbcxPIYo4xJlJJXiUsIonAY8BZwDZgsYjMUNVVjRZ9WVVvbLRud+BOIA/n6s5n7rpFcci6acyCjjEmQl7WdE4EClR1g6pWAy8BF0W47jnAu6q6zw007wKTY5RP0wJrvWaMiZRnNR2gP7A14PM24KQQy31HRE4DvgJ+qqpbw6zbP1QiInI9cD1A7969yc/Pb3/OD3JlZWVRLYePPvqYzBSJ2vbiKdplEQ2/+qiCIVmJXHtMl7im2xHLwitWFn5lZWVR3Z6XQScSbwEvquoBEfkR8CxwZms2oKrTgekAeXl5OmHChKhn8mCTn59PVMph9tsAnDJ+PN0zUtq/PQ9ErSyiaNvst9lWVsvzN50T13Q7Yll4xcrCL9rB18vLa9uBgQGfB7jTGqhqoaoecD8+AYyNdF0TP9Z6zRgTKS+DzmJghIgMEZEU4HJgRuACItI34OOFwGr3/RzgbBHJEZEc4Gx3mvGAxRxjTKQ8u7ymqrUiciNOsEgEnlLVlSJyN7BEVWcAN4vIhUAtsA+Y6q67T0TuwQlcAHer6r64fwkDWEMCY0zkPL2no6qzgFmNpv0m4P3twO1h1n0KeCqmGTSRsZhjjImQ9Uhg2s1ijjEmUhZ0TLtZQwJjTKQs6Jh2s5hjjImUBR3TbhZzjDGRsqBj2k2tqmOMiZAFHdNuFnOMMZGyoGOMMSZuLOiYdrPWa8aYSFnQMe1mMccYEykLOqbdLOYYYyJlQce0m7VeM8ZEyoKOaTcLOcaYSFnQMe1mFR1jTKRa7GVaRMYDdwGD3OUFUFUdGtusmYOFXV4zxkQqkprOk8ADwKnACUCe+9dEqKqmjkv+toAV20u8zkpMWMgxxkQqkqBToqrvqOoed/joQlUtjHnOOpEvt5WwZHMRd81Y6XVWYsIqOsaYSEUyiNt8Efk/4HXggG+iqn4es1yZiLy7ajfFFdVcmjfQ03zYyKHGmEhFEnROcv/mBUxT4MzoZ6dzEonNdn/43BIA74OOxZyosftjprNrMeio6hmxSlxEJgMPA4nAE6p6f6P5PwOuA2qBr4FrVHWzO68OWO4uukVVL4xVPk3zrBuc6Km3ojSdXIv3dEQkS0QeEJEl7uvPIpLV3oRFJBF4DDgXOBK4QkSObLTYF0Ceqh4LvAr8MWBepaqOdl8HRcDprMcTiznRYwHcdHaRNCR4CtgPXOa+SoGno5D2iUCBqm5Q1WrgJeCiwAVUdb6qVrgfFwEDopBu3PmurtmlE9MS20VMZxfJPZ1hqvqdgM+/FZGlUUi7P7A14PM2/PePQrkWeCfgc6qILMG59Ha/qv4n1Eoicj1wPUDv3r3Jz89vT57bZF1RHQClpaUxSb+12ywrK4tqPpYsWcLedYlR2148Rbss2qu6zh914p2vjlYW0bazrJ7eGUJCBDdZO3tZtEZZWVlUtxdJ0KkUkVNV9SNoeFi0Mqq5aIGIXIXTkOH0gMmDVHW7iAwF3hOR5aq6vvG6qjodmA6Ql5enEyZMiEeWg3TdvA8+WUi3bt2YMGF89DY8+20AWvud8vPzW71Oc+kfP3Ysxw7Ibv/2PBC1soiSyuo6eHc20Prftb06WllEU8Ge/Ux94AN+MnEEPz3r8BaX78xl0VrRDr6RBJ0fA8+693EE2AdMjULa24HAZlcD3GlBRGQS8EvgdFUNbLK93f27QUTygTFAk6DTkXTWKydeXRKqrq1n495yRvbp6k0GYsDu6cTGjuIqAJZs3udxTkyL93RUdamqHgccCxyjqmNUdVkU0l4MjBCRISKSAlwOzAhcQETGAI8DF6rqnoDpOSLSxX2fC4wHVkUhT6YNvDpQ/vatlZzz0AfsLIlrxTumLOTEhu+KmhCj5xdMxMLWdETkKlX9p9tsOXA6AKr6QHsSVtVaEbkRmIPTZPopVV0pIncDS1R1BvB/QCbwbzddX9PoI4DHRaQeJ3Der6odNuh09mawXn29JZuKACiuqKFvVlrUtltaVUN6ciJJifHvD9dqOqaza+7yWob7N9S1i6j8Z6jqLGBWo2m/CXg/Kcx6C4BjopGHeKjr5FHHq+Ok7+w12ukfe9d/uWh0Px6+fEx0NxwBrY97kocEi+UdR9igo6qPu2/nqurHgfPcxgQmQr6z186743eeL1bvniC8uXSHJ0HHajqms4vk+sGjEU4zYdR38rNXr4+T0ez7rcbjH8uCTmzEqisq03rN3dMZB5wC9Gx0X6cbzj0YE6E6X03H43zESme6elhb5+2X6URFaUxIzd3TScG5iZ9E8H2dUuCSWGaqs6nvTEflELzqacHfqCV62/Q66FhNx3R2zd3TeR94X0Se8XWyadqm4UDSSQ8oXn0r3xWT2igGda8vr3XSXcRzVq4dRyQPh1a44+kcBaT6JqqqDW0QoVi3XlPVhrN+L3jdeq0uioHCajqdU52Va4cRSUOCF4A1wBDgt8AmnAc7TYRifSDxukm214O41UQxUNTUWU3n5cVb+Pv7Hbpzj1br7Je4DyaRBJ0eqvokUKOq76vqNdgAbq0S6+NYNC8vtYnHyUcz6Hpdlh2hpjPtteXc/84ar7MRVb7f1VqxeS+SoFPj/t0pIt90u6bpHsM8dTr1MW695vWByqvjtO8AEs1AUWs1nZgoP1DLfbNWU1VT50n6vhOTzlq+B5NI7un8zu3s8+c4z+d0A34a01zFSPmBWk/StctrseHrRyuagSKal+rawusTiFj5a34Bj3+wgb5ZqUwdPyTu6XtdgzV+kQxXPdN9WwLEbOjqeCiprGl5oRiI9VmW1w+fen2cjGpNx/OHQz1NPmYO1DjlWu1RTdLu6XQczT0c+ijNXBFS1ZtjkqMYqqyq4plnngmadtRRR3HCCSdQU1PDCy+80GSd0aNHkzvocE79w3x+cFgRg9KDa0t5eXkcffTRlJSU8MYbb1Bck8DG8mTGZDujMIwbN466+nQA9hbubZL+aaedxtChQ9m1axezZ89ukv7EiRMZOHAgW7duZd68eY3m9gScA+WGDRv44IMPmqx//vnnk5uby9q1a1m4cCEAxcXFbNq0CYBvf/vbZGVlsWLFCpYsWdJk/csuu4z09HSWLl3K0qWNx+5z0ldg8eLFrFy5ssn6U6dOBWDBggV89dVXQfOSk5O58sorAXj//ffZuHFj0Pz09HQuu+wyAObOncu2bduC5hcX9wASqKtXZs+eza5du4Lm9+jRgwsuuACAt956i8LCwqD5ffr0ITXVaZD5+uuvU1paytbKJCCnIc1Jk5zu/1555RUqKiqC1h8yZAinn+4M8fTCCy9QUxN8UnP44YdzyimnADT53SH0vre3OhHf1eulS5cyevRoKioqeOWVV5qs33jfa2zcuHGMHDmSvXv3MnPmzCbzG+97/v3C+V23bt3azL4HkydPpk+fPhHte86+kc7ixUtI2fAh0N59D6688kqSk5Mj2vfyF28GurFjxw6eeeaZFve98vLyhvF0Qu173bp14+KLLwZo8743efJkwL/vBRowYEDc971Ao0ePbtj3QpV9ezRX02m6Fxzk2npG/skGZwyOz4rTGJS+v9lln92STVFNIkd1+5qUhEbphkl/674KnlywnUEa+Y3OwO/idXNQry8J1dTV0yVK26pTb+80e11r7KzqPf5djZ9E+jS5iKSrakXLS3Zc2f2H6UP3/rrV6y0v7cJrO7pxVNcqLu3ffNC5e00u9Qj/O2Iv6YlO2X5WnMpbu7rSt0sNPxpS3GSdv2/MZteBZG4cso/cLv4brdX1sLUymWEZTS8L1incs9Y5I/3ZsEK6JTuXLb4qS+Ff27K4ZVgh2cmhL2UUFxeTnZ3N0pIu7KpKYnLv8sgKopG71jjpX9G/hJFdq1u9fmF1AgXlKZyUU9XistXuV0kJaPoyfVM2O6qS+XbfUo7LOhB6xRb4ysJnQ3kyz211Pt816us2bbM99hxI5K8bu3uSvq8sfL9rNNOfsyeDhfvSOatnGeN7xH/8oyVFqczc3ZWh6dVcfVhJi8s33i8OZcXFxfz0pz/9TFXzorG9Fluvicg4EVmF86wOInKciPw1GonHm7ZxAKcEt4qyryaRlaUpzS7rO8zX1vvTauly8oF652doXMv5755Mnt+aze6qpl3dBW4zMLR8UeJcLtpWmdx8osB/dnZjUVE6pTUJPLsli/LatpVPbRvPzv+5NZt3dnelqq7ldH//VU/+XNAjaJpvrXC1kz0HEtlRFUlbGT+P2xF43fo8SGe6DdLJ+9w9uKhqsy/gE5xhpb8ImLaipfU64it38CgNpfxAje4ortAFBXu1vr6+YfqO4gr985w1esaf5uugaTMbXoVlB7S2rj7ktnzLbNpb1jDt2QUbddC0mXrOg++rqurLn27RQdNmavmBGlVVPeW+eTpo2kxdt3t/0LaufvITHTRtps5dtatJOoVlBxrS2ry3vGH6j/+5RAdNm6kzlm4PmT9V1fnz5wfl9aR75+qgaTP1r/MLwq7T3Hd97bOtrVrP59i75uigaTN1zc5SrayujSitQBf+5SMdNG2mvrBoc8TrqKpWVtdqaWW1qvrLwufdlbtCrrdo/V59+dMtLX2lhmW3FVVofX291oXZT8JZtaOkIf3AfbE1isurtcT9fq3ReL+oOND8b9Ia9769SgdNm6mPzV8XtW22xlMfbdBB02bqVU8simj5xvtFNGzdV97ift4RzZ8/X3EG1ozKcTiioRFVdWujSd40tm+ncGdu1zyzmHH3vccV/1jEPz/Z0jD9vIc/5JH3CtjwdfDlp+PveZepT3/abFpVNf5zK1/LmcqaOqpq6nhwrnNDfVeJc1nJ12LqQG1wsWalObUVX6s7VaWqpo4V20vYs99/SWr/Af/lt4ZOMMPkq65eWVVYx55S//q73PeB6f9x9hqG3TGLiX/OZ3tx08shga2BDtSGP49U1ZBNuveUVlFZ7aR3zkMfMPmhpjeiW9JQ03HL78mPNvLovHUtrvetxz7mmLv+G3JeuNZV352+iP997csWt62qfHf6Is596ANuf305Q++Y1eI6gSqq/b9Bc+XanOPu/i9j7n63xeVq6+r5yUtf8OW2ppd8AarDpL+7tKrJvtoSdS/jB/5fxJPXjxXU1yun/mE+N/7rc0/z0RFEEnS2isgpgIpIsojcCqyOcb5iorZOmbtqd5Pmk4vchgIA6/eUNbwvqgjfxPrDdXub3ZED/ykffa8AcILHyffNY6cbbMoO1LJqRym7Sw+46wT/Q/qCji8fM7/cyahfz+b8Rz/i5he/8Oc5ICj6DsShmoiqKsPumMUfF1dx4u+btkYKPCD8NX89dfXK+q/L+c8X25ssG3hwPhDmgb97317F0XfOYdgds4J6on78/fWc+Pt5QdvYVFjB4NveZsmmfU22E7huoJQkZ/ctO+AE83tmruLP734VctlAa3Y59+UqAw7wdfXKkk37KG7mN2/JntIqvi5zfsvSqlpeWuycqwU+EPnkRxt5efEW5q/ZE3Ibgc+SBQag1qqrV659ZjErtoe/f7GpsII3l+4I2pcCHahz0n/8/fUUuP8XtXX1nPT7efzi3y0H4KBtuft244dDtxdXUhbh83O+/7eCPWVBJ12R8Po5nbJq5zvOXR36d2+runoNe3LQUUUSdP4fcAPQH9gOjHY/t5uITBaRtSJSICK3hZjfRURedud/IiKDA+bd7k5fKyLnRJJeVW0d1z23hI/X7w27TGue05i3enfQ58DngKpq6rn5xS8YfNvbFJY7N9mLK2qCDmr7yqs575EPGz4fqKkPOsAmJToh5J6Zq9hXXs1H6/z5/mq3PzguXL+XB/67ltU7S0lwazqB/9x7yw5QXVvPnv3N32wP97R4l6Tg3WT2il3c8IL/jO2pjzdx++tND0L/+HAj5e6Bs7TK+aerqK7lvma6WLnk7wubBPOVO4Kbk85bvZubX/yCTzc6AWr+2j2M+nVwc/OfvtxyM89l7hn+Pz7YwLA7ZnHJ3xcG/aZf7z/Q5B86VBltcQPmib+fx2V/X9hk/o6AmuI9M1cx7bXl/OCZxU36edtWVBG07Npd+yksC/7NVJV3lu/k/+as4bmFm4LmVVTXct2z/kan89bs4fxHP+JHzy9h7a6mDWAWuwE+LcW577W5tK5hGjj7486SSu57Zw2X/H2B+12cg/3by3c2ydclf1vAz17xl/ue/VUs3rSPzYXl7Hd/f98Jl8/4+9/j8ulNy6yx9V+XMeyOWfzkpS+Y9MD7nP7H/KC0Zy3fSWV1XdgTFN8JRltrPDV19Vz7zGLmrtrNa59tC5nOlsIKVu8spbiimtkrdjYsU7CnLOjKAjgnpTOW7UBV2V9V02y+9lfVBO0r9fXa8ED0Y/MLOPxX77Bxbzl/zS+gorqW4opqz3p+iESzd1lFJBF4WFWvjHbC7rYfA84CtgGLRWSGqq4KWOxaoEhVh4vI5cAfgO+KyJHA5Tg9X/cD5orI4aoaUUkv317CN0Y4LXRu/feyoHn/XLSFaZNHsbmw5YZ6W/ZVcPvrXzKyd1eSEhP41X9WNMyrqnF2quY82OisfHdpFUNun8WFx/Xj22P6Bx3wVu0oJS2laYOCgd3TePWzbdTUKTOX7+SY/lkADQf7A7V15P1uLucf25fvjB3QZP3jBmazbKtz8H1mwSa6pSYx5ZTBQcv87u3VjOrTjVNH5AJw54wVDbUzXzls+bSCm84cQb/sNOrqlekfbAjaxqPz1vGr848MCpbhbC+q5MvtxZx+eE9++caKoHLcXVrFtc8Gt+b3BR+f7/xtAZ9tLmr4vGd/FS8s2sI1pw6hW6p/l798+iKemZzBvbP8Ffd5ATWQ7z/5CWt27efD//U/E11SWUNqciIffPU1f5lfwONXjeXVz/xXnzeF2G+ufXYJr//4FMqrg8/oX/x0C1eeNIjEBOFAbR2n/mF+0Pwr/rGIo/t3418/PJluqcnU1tUze+UubvyXv2byjRE9yc1MYfaKXfzi1dC1jzkrd7N8Wwmv/vgU+mWnsXFvObe89AXLtjm1oIyURHYUV3LngipY4A8Av3h1WcNVgOKKGi78y0d86a6TKEJVTR01dfV0TU2mtKqWJZuLWLK5iNvPPYKiimrOftB/yXT0QKcl2Oebi/jO3xZw+uE9OXNULwBWbHdOKqpq6nhk3jpOHZHLKcNyWbi+kCufWESCSENN5c2lzr5QWVPHpxv3ceKQ7sxbvYf/cU+Cvps3kPu/c0zDZeZ95dXcN2s1O0qcYL6juJIbXvicKacMZn9VDWeM7EVCgrNsfb3y9IJNDO+VSV29sqBgL2kpiYgIq3aUMm/Nnob9Y8ayHRRXVJOb2YW7LjyKgd3TufLJRWzd5z9pmHnTqYzoncmkB94P+j2KK6p5fuFm/vzuVyzfVsxTH2+iT7dUthdX8s5PvsERfbs19BxfV68cc9d/Oe+YPvz1yrH85s0VPLdwM326pTLjxvE84B5Dbv33Mj7bXERpZS1/f389Zx3Zm39c7TQ2+2RDIW98sZ3bzz2CrPTgBkYllTXc+u9lnH9sX9bu2s/lJxxG/5w0EhMEVWVXaVXUH4loscm0iHwEnKmqrW8T2/x2xwF3qeo57ufbAVT1voBl5rjLLBSRJGAXzpNrtwUuG7hcc2l26TtC+055iJSyXaD15Gz9kN1HfrfJct22f0Jp/5OaTO+xfjaFwyZH9P16rX2dPSMvbvicWryRquzmu//I3L2Mst7HNXzO+HoF5T2PBiBr20JKBoxrsk7G3lWU5x7pfL/9O0isLqWixygy9q4mc89y9g4/l7oUZwy+9MK1VPQYGbR+z69m8PXhFzabD5++y5+jJrU7hUPOQpOaPhkjdTVoYjI9NsyhcGjTymfmni8p63VsiOnLKet1TJPpofT98ll2HjslomV9Usp2Up3Z10mr0XdLXTubqpHBv2lSVTFoHbVpTmu5HuvfoXDYuQD0/OpNEmvK2XXU9wDI3vohZT2PpjY1J2gbuQWz2Dv8vBa/Y7cdn1KflEZtSmaL+0fW9kWU9D85aFpy+R7qk9MafuO2SCsqoDJneKvXS6osojYth8zdy+hStrPhfyOpqpja1KbNjaWuGk0M3fozZ9N71KVkUtrvRAB6r36F3Udc1mIeQi2XUFNOxr517O89usX1E6vLSK4spCprUPB3K1xPbY9hLa7fnNbs142llO2iOrNP0LQ+K//VsN81oU0f8kuqKiaxej/VGX3QxGQydy9F6uuoT0qlLjmd+sQuVHft12JeEsr2sPGxa6LWZDqSoPMccAQwA2i4eaCqD7QrYZFLgMmqep37+fvASap6Y8AyK9xltrmf1wMnAXcBi1T1n+70J4F3VPXVEOlcD1wPkNJn+Ni+Ux5qdV4TizaT8dlzJNRWUXz23ZDQ8mjdyTuWUtPPv9N32fABB4ae1rp0S7ZRl9W0dhIofdkrVBzX8j9nKGnLXydl++eUTP5d0PSE0p3Ud+vbpm22RkJ5IWmrZ5C8t4Diyfe2aRvRODgApGxdTPXAE5z3mxdRn9qN2t5HtmlbXTa8T+r6fErOurPd+Wqr9GWvkFD+NWWnROVKeJtlfP5Pyo+/CoDMhX+n8sgLqctq+UAXSsrWxSTvWkH5CT8IOT9p7zpqc0e0Oa+RSF03l9rsw6jteThSVYKmZsU0vXAS9u+ivqsTlNK/fJWqIac2fG6TmkpEFU1JD5qcvP1zarMGsumxH8TvOR1gPTDTXbZrwOugoKrTVTWvPQW28E/X8OWSRU53EG7AOf6w5h8cCww4AK89eEer020ccLpnpLDp/m/yrdHOP+33Tx7Ekjef5LgBke/4w3tlNrxf/faTLFv6BQtvDx6por5bX0b27soVJx7W6jxH6u6LjmLDo1ezcu6rbe5m4+Lj+/OPn18eNK1HRvPPUYXyq28ewVcv3NXw+cvn7uKTR2/mvGPC/xOnJvv/dXIzu3DGyJ4NeVr7yh9Z9tmnrLq7aW3v1+cfyYLbwo8MMqhHeth5PjnpyXTtksSIgN/SZ97PT2f13ZNZ9c6zfPDOfwC4/dxRYbc1JDejybTXfjyOR64YQ1pyyydXjfku7wJ8NO0MPnnr+YbPK95/ixUPX8PUgMu3vzzviKD1/3iJvyb80HdHc++3nZr+k1Py+OqFu1g571U+vu1M0pITSUn0/wYb7zuPFX+7iWsCOhP1NTQ5aUh3Zt38DaZ/fyynH96TX5zj1PYf+97xDcs+csUYZtw4nj9+59iG7+D7LcYcls3ogUAgHQEAACAASURBVNn86PShrH71AZb/7WaemprH0vsuDcr7tacOYdrkUdx0ZtNa45DcDK4ZP4S/Xnk8s27+RtA6F43uxwXH9SM7PZkrTjysoQGRj2/fArj+tKGsuvscHvyhU6v8+1XHs2rW02x47FpW3z2Zd396GhvvO497LjoqaBszbhzfsK27LzqK29x94o7zRlFw77ls+vMlbHzgUjbedx5PTz2BObc421n3/K954uLgWmB7RXJP5/BY3NPBaZQwMODzAHdaqGW2uZfXsoDCCNcNqWuXJPaHaC3TPzuNkX268l6jVkW/vfAoenVNDVpue3Elj1wxpsk1+HCennoCR/fPIjezC3vdG8NnH9mb/67a3cKawVLdfyLf/Zrxw3uQnpLEmzeeyuDb3m6SR59RfbqyZtd+hvfK5KkpJ/DDJ97nlZsmNczvm5VGr65dghoaDM5N576Lj2FnSSX5a5s+mT5l3CCeXdh0FPPxw3vwcUEhyYnC8F5d+dOlx7Jsawl3vLE8aLnJRwUf0G+ZNILstGS6pSXzs1f899n+Z8Iwlm4tJj0libmNGm48cJkT2J/+wQl8tqmIuat3c/PEEQ3X95vzr+tO4ntPfAJA19Tgf4PU5ERSkxOZNnkUs5Y7fWp9Y0QuHwY05Lh63GBWbC9hwfpCvnfiQG6eOILaeg1qdJGekkROenJQK8jBPdLpl53GmzeM582lO3jq442cOapXw34392ens6ukivy1exg3rAeTHghuSv78tSdywuDupCYn8tj8Av5vzlr6ZaWyw71BP6ynPxB1z0hhzT2T6ZKUwDsrdrF0azHdUpN48fqTGdGrKxv3lvPemj38Yba/YUduZhfGDurO2EFw4XH92Li3nC+3FfPqZ9v4cN1erj11CEf27UZ2ejIfFxTy1MdOn2V5g3K4aHQ/Budm8P0nnccJenVNJSUpgaG5GXz3BOffNS0lseG+2o1nDOe6bwwJuqd24XH9+F/33tSYw7IZ1CODi8cMCLqf2T87jZW/PYfN+yo440/5gPOoQGpyIr+54Ehe+3wbJZU1zLnlNO59ezXTJo9kRO+uHNmvG2e7+921pw4hNTmRP/83g6z0ZC48zjmRO3ZANk9+5HynG84YTs/MLuQNzqFrqj8QpKUkcuao3oBzwlJYXs20ycGBXRU+31KECHxcUMjj3x/L4b395+p/vvQ4NheW87Ozgy93AwzISeP/5qzlmvFDuHni8IZ9f1NhOf8zwQloF43uz/BemRzZt1tQvka4aXx/3GAuGtOfG174nOMPy+HYAdms+O05ZHZxyr6uXvneSYfRLTU4wIkIZ7j32nwSE6LbhVCzQUdV60RkkIikRPueDs7ooyNEZAhOwLgcaHzBcgYwBVgIXAK8p6oqIjOAf4nIAzgNCUYAzT844zrziF68uXRH0EHk6nGD+PnZI+mWmsSQ24Ofq2h88/7lH53Msq0lpKcEF92MG8ezZFMRb3yxna1FFUGt1I51ayILbz+TLfsq+GrXfk47vCdH3Tmnxfx+NO0Mfv2fFcxf+3XDszej+nTl3VW7Gdg99Fnx0J4ZQUHn6nGDueON5ZRU1nBYj3RuPymtyQ3FATlp7Nl/gKP6dWPljlJy0p0aw/Tv57FyRwnf/uuCoOUvGtOfX37zSFbtLKVn1y6Mv/89AAbmpAOFXJo3kN9/27meHaplTmajA/0tkw4H4J2AVlEvXHcS44c7jRd2llQ2CTo+Z4zsxRkje3HrOSMbGkVkpCTy87NHMvGIXjz98SaeWbDJyV/3NP5w8bGcMjyXpATnBnVmF6cs/nXdSUGtqwJ/+6ennsAxd/2XSrdV0HEDstnttkjK6JJEUmICSSEqBm/ddCrpKUkcf4/z3EyqW3s4bmA2q3c6N9C7B9TOkhMTGNg9ne+PGxy0HRHnQNY/O61hG74AN6hHBjdNHBG0HR/fsr5WmU9OPYGj+jn748g+XUlLTmTVzlLechtr/P2q44PWH5KbwZDcDN5a5vwupwzrwcQjnANugkhD0Hn1x6c0SdtX03jv1glB08cNy+WR9wo4fWRPRIQFt53J+q/LKNhT1pBfoOFkL1QDmoQEadKq0ufZa05k5rIdDO6RzhNTQl/g8KXz7s9Ob9JPiW+ojswuSU0OwI1d942hIaff6tamVJU9+w/Qu1tq0PxQjXp8fP8vaSkJZLv/h+cd0/Ryt+93DKdbajLPX+u/N+0LOOAEksYBJ14i6SNkA/Cxe6CP2j0dVa0VkRuBOUAi8JSqrhSRu3Gefp0BPAk8LyIFwD6cwIS73CvAKqAWuCGSlmuj+nRtOJj2zPTfCL/7oqPDrtN4hxyQk86AnPSgZwte/OHJHDsgm2MHZHPNqUMaDjA+vgNscmICw3pmBp2NAjx6xRhOGtKdu95ayewVuxoeYr107AAG5KTzo9OHMT+gtnHzxBFMOqJ3yJ1uzi2n8fLirQ0B9YYzhtGrq/Nd91eFfwbl7ouOZvXOUpZuLWZlQEu5lKQE+malNVk+N6MLKUkJDa2SfHzLBt4qDDyQ/O5bR/PGF9vDXrrxLXtM/6yGgOPb7jeP6dvQVPeh74a+SZzRxVk/Oz2Fa051LrXccd4RDUHnL1ccz3FunieM7Mnc1XtIdpumnxKQHkBGwIlFUmIC82+dwN6yA+yvquXkod3JX+vUTtK7hP83GpATfGIQeNboKyLfpHFDg7v5AXjzhvF0TU3irAc/oE6VHhn+/TYpYFstXQqtdfv3SW90AD+sRzqPXjGmIejkDQ49PuM93zqK7hnJDS0YG3+XQC9cdxKbCsP35zduWA/W3DO54bful51Gv+y0hhalE0f1Yt6aPSGDTaBwQWf0wOwm+2U4zZ3FNy6rthCRJgGnJb7mzqmhzmI6gUiCznr35bunEzWqOguY1WjabwLeVwGXNl7PnXcv0Kq7z8mJCQ3/qI3PtBv73kmH8a9PttArzA4TeD153LDgg8V5x/Thn4ucng0mHdGbLi3sPBe4Vfu/XjmWy6cvZNGGfdx05nB+7la9fQdo34E8OTGh4cDZ2Mg+Xbn1nMMZ1iuD77kHooUbnG7Vm3tE4ej+WRzdP4vl7sOECQEtYdK7NM1/btfQ9066Z/jOnvyJBW7rqpMHcdXJ4a8Rd3HvlYQ6Fjx25fEsvf89thdXNtQem6yf5Csrf/qBB5aMEAEiXLk0Dox9slLpk+XfH5J8+0ArmpT6AlxgXnpkduGr350b8jv7fueHLx/NY/PXB10KTEyM5JasY+ygHNbs2h+yNgSw5FeT+PCjj8Ou3zcrjT9eEtyiMSkx9AF7/PDcoBOGUFKbuV/0t6vGNtQo27qN9vD9nKH2lXjw3dPpndW6YHWwaE0v05kAqtrygxYd1JAhQ/SUH/+Rj/elc3JOBYuKnLPQwN50fT3sXjWwmF4pdXRNqg853IAq/HZt6N54a+phcVEa//06k8MzDvC9gaVNNxCQVuD6T23OYktlCmfmlnNarvPMh6/n4a5Jdfx8eNMn9sNty2d7ZRL/2JxDAspvRu1ttgfdWbsz+LQonVO6V3B2L+dsNbBH64zEesrrEpqks7E8mXXlKXRPqWPmrq4cn1XJhX2dXaWwOpFHN0TWc/KWiiSe2pLDgNQarhvctHuWh9d3p6gmkZuHFtI9pemDvPtrhT8X5NI/tYYfuusH/lY/GVpIjrverF2ZfFqcxtUDixkaoidvgEfW53By90pODNETtm/9yb3KOLl78z0n+36f6wYVMSDNqSXXK3xalMbY7EqSI48fDXy9lw9Or2ZqCz0n19Y7Y/X0SQ1/MG9tz8qbK5J4eovTVNyLHrkD98topv+XDTnsrU7iR4P30beZ8oqVOoVlJamMzqoKeSISb9HuZbrFUC4iRwPP444sJSJ7gatVtemoSQeBBHGCbJiTtAYCDcMFhJzfzPrJCTQMUdDaDipq3R6TkxP8JwPJ0r6Hs1LcbUWSF9+xL/DrBZbV9YOLKKppeoY5JKOGIRk1fF7snJ0Flo+0ou9kX0/g4cp3bHYlc7/ObBg2orGuScpFfUoZnhnYHx0h35/Vq4wcLWFIevgz5puHFYWd1yWx3t1m5N8v8CCSILQYrJqT2Ip0kxJoNuC0Lf2obq7DpZ/k0fdLFDg+u3Xd/BxMIqk/Tgd+pqrzAURkAvAPoOmdw4PAiIxqPizMYGTmAT7e59R0pk6d2mQEPd/BN3AEvVCjN/rWbzx6o29/zcrOYerUi8OO3uhbv/HIob7gOHHiRJK79eTh+5r2lQb+0RvvCmi9Fuj888+nOimDx+5/j6Z3qJqO3ug7KPvS943eeNdtb5OZVEdWcj1ZAcG48eiNx3SrYntVEmfmljd8t21FFTwSoqVfqNEbG+5zoCFHDh3fvZJx3StJlPCjN/pGbQ0cvdFXPoEVioH9+jBiaCoTJkxo0+iNVx3fi6Oq+3DLpBG89spLzY7e6E/fHyhaM3pjqH1v+NChsHMvPXv2xBlNPlhrRw5trPlRa+HUU8bxxObwXRqFGrU2UDRGDr3r16E7boW2j1qb6p6kXfKdixmSm3HIjxw6ffr0JvPbI5Kgk+ELOACqmi8iTRv3HyQOS6/lNyO/brHaGukInmHXdw8ukV6+9PEtHZi8757KkPTwDQHunNSfT5eHPgBkpER+bTpUTQfgkXN7sXXdqsaLN5GcABf0Cb4Cm5QQ+bWjAWk1HN21igk9KyDEeKAiTquTtmpNraQlqUnCbRPDPwMTSjQvl/juo3tV4Yh2U9qO4tL+pXy2N4HBETwzZdqgpbEPgDeAXwOD3devgDeiNbZCPF9jx47VQKHGTfFN+2RDobYk3Hgtqs6YJkffOVsXrd8bdv3Ne8t1S2F50LTzH/lQB02bqc8v3BQ0fd3ulsecCedATV1QXpsbK+S+Wat10LSZ+uC7a9uUVii7SyubLat48KW/d39V0PRYjJvSXPrr9+xveeEIzV6xUwdNm6lXTF8Yle21tizW7S7tML9rtMVrvzgYRHs8nUhOga8Bfgu8jnMi/qE77aD31NQ8DuseutLW3pO4rPRklt/VfOfXhzVzJtX4LHJ4r7Y3HPQ9L/H9ZlqNNZbQ3qpegMQobqu9vD47b02tr+VtdZ7vYg4dLQYdVS0Cbo5DXuLO91RxKAkR/kNnp8fmAatoH08K7j03ogOuLz5E8+Ds9YE+kNd5CdfMuG3bcg76Ue4EOGJelyXAv//fuIZn78zBIZLWa+8Cl6pqsfs5B3hJ3d6hO6tIzvQ/+9WkhlpEtEmUawdJrXimI9oiDeDx4PWBMpq1E69rOske7lM+J4R5mNV0XJFcXsv1BRxwaj4i0nzfEJ1AJP/PPTKb3uiOXvreHFBicdbckS6veVWuPtEMel6XajRrbebQEcmpSr2INPSxISKDoBUPXhykPDvou0XrdeUgml/f69pFIK/zEs37IF7/EybbPR3TBpHUdH4JfCQi7+OcXH0Dd3yazqwznRG3RTRrPF6XZSCva12JMagdePWVYvFdTOcXSUOC2SJyPOAbsvAWVd3b3DqdgdcncdG+p+Mlr+89BPL6/lJHKov26kzfxcRPpE8NngIEDnsZ+tH6TsTrs/PO9P/s9YG+I+lMB+qO0JDAHHxa3GtE5H7gJzjDCKwCfiIiv491xrzmfdDpPAcn4+f1ZdNo8n2XlkbRNSZQJDWd84DRqloPICLPAl8ArR9/+SDi9bHB6/Qt5sVGNC+bHjsgiwE5aQ1DYHjhnZ98gwE5TcdbMiacSC+vZeMMogbOkNGdntdNljvTPR0TG11Tk/lo2pme5uGIgOGSjYlEJEHnPuALEZmP03rtNOD2mOaqA/D68pZXrazU84a4xpjOLJLWay+KSD5wgjtpmqruamaVTsHr1mtep2+i6+XrT24YwdWYQ1kkDQnmqepOVZ3hvnaJSOjBXSIkIt1F5F0RWef+zQmxzGgRWSgiK0XkSxH5bsC8Z0Rko4gsdV+j25OfULyu6Xh1eU08f869czppaA9umXS419kwxnNhg46IpIpIdyBXRHLcQNFdRAYD/duZ7m3APFUdAcxzPzdWgTNC6VHAZOAhEQlsJvMLVR3tvpqO8NROXgcdr9M3xphYaO7y2o+AW4B+wOcB00uBv7Qz3YuACe77Z4F8YFrgAqr6VcD7HSKyB+gJFBMHXl/e8qr1mt3TMcbEUtigo6oPAw+LyE2q+miU0+2tqjvd97uA8GMMACJyIpACrA+YfK+I/Aa3pqSqB8Ksez1utz29e/cmPz8/ogwuWrCQbl3if+Tfv78SgOVffknd9vaMkRleWVlZ2HLYuqUagA0bNpDPtpDLtEek5R8rjdNvriwONVYWflYWfmVlZS0v1AqRtF4rEZGrG09U1eeaW0lE5gJ9Qsz6ZaPtqDQzhrCI9AWeB6b4nhXCaT23CycQTcepJd0dan1Vne4uQ15enk6YMKG5bMNsZyz7U08dT/eM+I/TkbnsQ9hfypjRoxk3rEdM0sjPzydcOSysXA0bNzBs6DAmTBgWvUTdcm2x/GMlTPrNlcWhxsrCz8rCL9rBN5Kgc0LA+1RgIs7ltmaDjqpOCjdPRHaLSF9V3ekGlT1hlusGvA38UlUXBWzbV0s6ICJPA7dG8D1axeuHM71O3y6zGWNiIZIm0zcFfnZv5r/UznRnAFOA+92/bzZeQERSgDeA51T11UbzfAFLgG8BK9qZnya87i/M6/SNMSYW2nK7vBwY2s507wfOEpF1wCT3MyKSJyJPuMtchvMg6tQQTaNfEJHlwHIgF/hdO/PThNetxzpjzBnVp6vXWTDGeCyS4arfwj9eVCJwBPBKexJV1UKcy3SNpy8BrnPf/xP4Z5j1Y973h9cHfa+7wYn28zpf/e5cz8vUGOO9SO7p/CngfS1O4PlumGU7De9rOp3rCJ2S5G0b9Ky0ZEoqazzNgzEmsns674vIGOB7wKXARuC1WGfMa14f9L3qe+2CY/vx+PsbmHhEL0/Sj5VFt0+kLprDoRpj2iRs0BGRw4Er3Nde4GVAVPWMOOXNU15fCvIq5h3dP4tN93/Tm8RjKC0lNs88GWNap7mazhrgQ+B8VS0AEJGfxiVXHYDXNZ1OdnXNGGOA5luvXQzsBOaLyD9EZCIcOr1BWpNlY4yJvrBBR1X/o6qXA6OA+Tj9sPUSkb+JyNnxyqAxxpjOo8UmRaparqr/UtULgAE4Q1VPa2E100Z2q9sY05m1qh2rqhap6nRVbfKMjTHGGNMSG5/SGGNM3FjQaWRg9zSvs2CMMZ1WJD0SHFLevOFUthVVeJ0NY4zplCzoNNI9I8WTcXSMMeZQYJfXOhi1rlqMMZ2YBZ0OKtq9PBtjTEdgQaeDmXLKYAD6Z1uDBmNM52P3dDqYK048jCtOPMzrbBhjTExYTccYY0zcWNAxxhgTN54EHRHpLiLvisg6929OmOXqRGSp+5oRMH2IiHwiIgUi8rKIWBtnY4w5CHhV07kNmKeqI4B57udQKlV1tPu6MGD6H4AHVXU4UARcG9vsGmOMiQavgs5FwLPu+2eBb0W6oogIcCbwalvWN8YY4x3x4mFEESlW1Wz3vQBFvs+NlqsFlgK1wP2q+h8RyQUWubUcRGQg8I6qHh0mreuB6wF69+499qWXXorJdzqYlJWVkZmZ6XU2OgQrCz8rCz8rC7+ysjIuuOCCz1Q1Lxrbi1mTaRGZC/QJMeuXgR9UVUUkXOQbpKrbRWQo8J6ILAdKWpMPVZ0OTAfIy8vTCRMmtGb1Tik/Px8rB4eVhZ+VhZ+VhV9+fn5UtxezoKOqk8LNE5HdItJXVXeKSF9gT5htbHf/bhCRfGAM8BqQLSJJqlqLM7Dc9qh/AWOMMVHn1T2dGcAU9/0U4M3GC4hIjoh0cd/nAuOBVepcD5wPXNLc+sYYYzoer4LO/cBZIrIOmOR+RkTyROQJd5kjgCUisgwnyNyvqqvcedOAn4lIAdADeDKuuTfGGNMmnnSDo6qFQJMhr1V1CXCd+34BcEyY9TcAJ8Yyj8YYY6LPeiQwxhgTNxZ0jDHGxI0FHWOMMXFjQccYY0zcWNAxxhgTNxZ0jDHGxI0FHWOMMXFjQccYY0zcWNAxxhgTNxZ0jDHGxI0FHWOMMXFjQccYY0zcWNAxxhgTNxZ0jDHGxI0FHWOMMXFjQccYY0zcWNAxxhgTNxZ0jDHGxI0nQUdEuovIuyKyzv2bE2KZM0RkacCrSkS+5c57RkQ2BswbHf9vYYwxprW8quncBsxT1RHAPPdzEFWdr6qjVXU0cCZQAfw3YJFf+Oar6tK45NoYY0y7eBV0LgKedd8/C3yrheUvAd5R1YqY5soYY0xMeRV0eqvqTvf9LqB3C8tfDrzYaNq9IvKliDwoIl2inkNjjDFRJ6oamw2LzAX6hJj1S+BZVc0OWLZIVZvc13Hn9QW+BPqpak3AtF1ACjAdWK+qd4dZ/3rgeoDevXuPfemll9r+pTqJsrIyMjMzvc5Gh2Bl4Wdl4Wdl4VdWVsYFF1zwmarmRWN7SdHYSCiqOincPBHZLSJ9VXWnG0D2NLOpy4A3fAHH3bavlnRARJ4Gbm0mH9NxAhN5eXk6YcKEVnyLzik/Px8rB4eVhZ+VhZ+VhV9+fn5Ut+fV5bUZwBT3/RTgzWaWvYJGl9bcQIWICM79oBUxyKMxxpgo8yro3A+cJSLrgEnuZ0QkT0Se8C0kIoOBgcD7jdZ/QUSWA8uBXOB3ccizMcaYdorZ5bXmqGohMDHE9CXAdQGfNwH9Qyx3ZizzZ4wxJjasRwJjjDFxY0HHGGNM3FjQMcYYEzcWdIwxxsSNBR1jjDFxY0HHGGNM3FjQMcYYEzcWdIwxxsSNBR1jjDFxY0HHGGNM3FjQMcYYEzcWdIwxxsSNBR1jjDFxY0HHGGNM3FjQMcYYEzcWdIwxxsSNBR1jjDFxY0HHGGNM3FjQMcYYEzeeBB0RuVREVopIvYjkNbPcZBFZKyIFInJbwPQhIvKJO/1lEUmJT86NMca0h1c1nRXAxcAH4RYQkUTgMeBc4EjgChE50p39B+BBVR0OFAHXxja7xhhjosGToKOqq1V1bQuLnQgUqOoGVa0GXgIuEhEBzgRedZd7FvhW7HJrjDEmWpK8zkAz+gNbAz5vA04CegDFqlobML1/uI2IyPXA9e7HMhFpKdgdCnKBvV5nooOwsvCzsvCzsvDLBQZFa2MxCzoiMhfoE2LWL1X1zVil25iqTgemxyu9g4GILFHVsPfSDiVWFn5WFn5WFn5uWQyO1vZiFnRUdVI7N7EdGBjweYA7rRDIFpEkt7bjm26MMaaD68hNphcDI9yWainA5cAMVVVgPnCJu9wUIG41J2OMMW3nVZPpb4vINmAc8LaIzHGn9xORWQBuLeZGYA6wGnhFVVe6m5gG/ExECnDu8TwZ7+9wkLPLjX5WFn5WFn5WFn5RLQtxKg7GGGNM7HXky2vGGGM6GQs6xhhj4saCTickIgNFZL6IrHK7G/qJO727iLwrIuvcvznudBGRR9xuhb4UkeO9/QbRJSKJIvKFiMx0P4fsRklEurifC9z5g73MdyyISLaIvCoia0RktYiMO4T3i5+6/x8rRORFEUk9VPYNEXlKRPaIyIqAaa3eD0Rkirv8OhGZEknaFnQ6p1rg56p6JHAycIPbhdBtwDxVHQHMcz+D09XQCPd1PfC3+Gc5pn6C0xjFJ1w3StcCRe70B93lOpuHgdmqOgo4DqdcDrn9QkT6AzcDeap6NJCI00L2UNk3ngEmN5rWqv1ARLoDd+I8tH8icKcvUDVLVe3VyV84TcrPAtYCfd1pfYG17vvHgSsClm9Y7mB/4TzHNQ+n66SZgOA8aZ7kzh8HzHHfzwHGue+T3OXE6+8QxbLIAjY2/k6H6H7h6/Gku/tbzwTOOZT2DWAwsKKt+wFwBfB4wPSg5cK9rKbTybmXAcYAnwC9VXWnO2sX0Nt9H6rLobBdCx1kHgL+F6h3PzfXjVJDObjzS9zlO4shwNfA0+7lxidEJINDcL9Q1e3An4AtwE6c3/ozDt19A1q/H7Rp/7Cg04mJSCbwGnCLqpYGzlPn1KRTt5cXkfOBPar6mdd56SCSgOOBv6nqGKAc/yUU4NDYLwDcy0AX4QTifkAGTS83HbJiuR9Y0OmkRCQZJ+C8oKqvu5N3i0hfd35fYI87PVyXQwe78cCFIrIJp5fyM3HuaWSLiK8LqMDv2lAO7vwsnG6XOottwDZV/cT9/CpOEDrU9guAScBGVf1aVWuA13H2l0N134DW7wdt2j8s6HRCIiI4vTSsVtUHAmbNwOk2CIK7D5oBXO22UjkZKAmoZh+0VPV2VR2gTmeFlwPvqeqVhO9GKbB8LnGX7zRn/aq6C9gqIiPdSROBVRxi+4VrC3CyiKS7/y++sjgk9w1Xa/eDOcDZIpLj1hzPdqc1z+ubWfaKyQ3CU3Gqxl8CS93XeTjXoOcB64C5QHd3ecEZMG89sBynRY/n3yPKZTIBmOm+Hwp8ChQA/wa6uNNT3c8F7vyhXuc7BuUwGlji7hv/AXIO1f0C+C2wBmdQyeeBLofKvgG8iHMvqwanBnxtW/YD4Bq3TAqAH0SStnWDY4wxJm7s8poxxpi4saBjjDEmbizoGGOMiRsLOsYYY+LGgo4xxpi4saBjTByISJnXeTCmI7CgY4wxJm4s6BjjERG5wB2b5QsRmSsivd3pPd3xTFa6nXJuFpFcr/NrTDRY0DHGOx8BJ6vT+eZLOL1hgzNGyXuqehRO/2iHeZQ/Y6IuqeVFjDExMgB42e1cMQVnrBtwujH6NoCqzhaRIo/yZ0zUWU3HGO88CvxFVY8BfoTTv5cxnZoFHWO8k4W/K/jA8eU/Bi4DEJGzcTrlNKZTsA4/jYkDEakHdgRMegCn194HgSLgPeAEVZ0gIr1wegHuDSwEzgcGq+qB+ObamOizoGNMByMiXYA6Va0VkXE4I32O9jpfxkSDNSQwpuM5DHhFRBKAauCHHufHpimQjQAAADJJREFUmKixmo4xxpi4sYYExhhj4saCjjHGmLixoGOMMSZuLOgYY4yJGws6xhhj4ub/A1KN5oE3bO65AAAAAElFTkSuQmCC\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","execution_count":17,"id":"dd775bdb","metadata":{"id":"dd775bdb","executionInfo":{"status":"ok","timestamp":1660962766132,"user_tz":-120,"elapsed":5,"user":{"displayName":"Roshan Raj Shah","userId":"06387599595301221247"}}},"outputs":[],"source":["def linear_congruential_scheme_2(a,b,c,x0):\n","    \n","    xc = ((((a*(x0)) + b) % c)) \n","    \n","    return xc\n"]},{"cell_type":"code","execution_count":18,"id":"58637b45","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"58637b45","executionInfo":{"status":"ok","timestamp":1660962766134,"user_tz":-120,"elapsed":7,"user":{"displayName":"Roshan Raj Shah","userId":"06387599595301221247"}},"outputId":"f291d30e-53f8-481c-e980-f8e5e5f629d0"},"outputs":[{"output_type":"stream","name":"stdout","text":["Period of the Random Number Generator is   256\n"]}],"source":["a, b, c, x0 = 57, 1, 256, 10\n","arr1 = []\n","arr1 = np.append(arr1,x0)\n","period, xi= 0, x0\n","while xi != x0 or period == 0:\n","    xi1 = linear_congruential_scheme_2(a, b, c, xi)\n","    np.append(arr1,xi1)\n","    xi = xi1\n","    period += 1\n","print(\"Period of the Random Number Generator is  \", period)\n"]},{"cell_type":"code","source":["\n","def plotA(counter_distribution_array):\n","            \n","  plt.scatter(np.arange(0, len(counter_distribution_array), 1), counter_distribution_array)\n","  plt.title('Gap Test for between 0 and 1. ')\n","  plt.xlabel('Index')\n","  plt.ylabel('Count Tally')\n","  plt.show()\n","\n"],"metadata":{"id":"dcU6F97pEjLA","executionInfo":{"status":"ok","timestamp":1660962766136,"user_tz":-120,"elapsed":8,"user":{"displayName":"Roshan Raj Shah","userId":"06387599595301221247"}}},"id":"dcU6F97pEjLA","execution_count":19,"outputs":[]},{"cell_type":"markdown","source":["#### (c) Tests of Mersenne Twister PRNG"],"metadata":{"id":"IrDAvkOEaOmc"},"id":"IrDAvkOEaOmc"},{"cell_type":"code","source":["# Mersenne Twister PRNG\n","\n","N = 700\n","\n","random.seed()\n","random_numbers_arr = [random.random() for i in range(N)]\n","\n","\n","# Kolmogorov-Smirnov test\n","\n","print(stats.kstest(random_numbers_arr, np.random.uniform(0, 1, N), alternative='less'))\n","\n","\n","# Independence Test\n","\n","mean_array_RN = np.mean(random_numbers_arr)\n","\n","prime_num_array = [i - mean_array_RN for i in random_numbers_arr]\n","\n","\n","def autocorrelation_function(i, j):\n","\n","    tot_sum_A, tot_sum_B, tot_sum_C = 0, 0, 0\n","    M = 0\n","\n","    for f in range(N):\n","        if (i + (f + 1) * j) <= (N - 1):\n","            M = f\n","\n","    if M != 0:\n","\n","        for k in range(M+1):\n","\n","            tot_sum_A += prime_num_array[i+k*j] * prime_num_array[i+(k+1)*j]\n","            tot_sum_B += (prime_num_array[i+k*j])**2\n","            tot_sum_C += (prime_num_array[i+(k+1)*j])**2\n","\n","        Rho_calc = tot_sum_A/(np.sqrt(tot_sum_B) * np.sqrt(tot_sum_C))\n","    else:\n","        Rho_calc = None\n","    return  Rho_calc \n","\n","autocorrelation_distribution_array = []\n","indices_array = []\n","index = 0\n","\n","for j in range(N):\n","    for i in range(j):\n","\n","        result = autocorrelation_function(i,j)\n","\n","        if result is not None:\n","\n","            autocorrelation_distribution_array.append(result)\n","            indices_array = np.append(indices_array,index)\n","        index = index + 1\n","\n","# Testing consistency of autocorrelation_function distribution with Gaussian(norm) distribution using Kolmogorov-Smirnov test\n","print(stats.kstest(autocorrelation_distribution_array, 'norm', N = N))\n","\n","\n","\n","\n","# Gap Test\n","arrA = np.linspace(0, 1, 20)\n","arrB = np.linspace(0, 1, 20)\n","\n","counter = 0\n","counter_distribution_array = []\n","\n","for i in arrA:\n","    for j in arrB:\n","\n","        if j > i:    \n","\n","            for k in range(N):\n","\n","                if i <= random_numbers_arr[k] and random_numbers_arr[k] <= j:\n","\n","                    counter += 1\n","\n","            counter_distribution_array.append(counter)\n","            counter = 0\n","\n","plotA(counter_distribution_array)\n"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":330},"id":"g-yJVATmaLhC","executionInfo":{"status":"ok","timestamp":1660962799526,"user_tz":-120,"elapsed":32748,"user":{"displayName":"Roshan Raj Shah","userId":"06387599595301221247"}},"outputId":"9e434517-a0cf-48ff-8f6d-e189ae3c72d6"},"id":"g-yJVATmaLhC","execution_count":20,"outputs":[{"output_type":"stream","name":"stdout","text":["KstestResult(statistic=0.03571428571428571, pvalue=0.409667595936363)\n","KstestResult(statistic=0.15865527691046433, pvalue=0.0)\n"]},{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","source":["def encryption_mesage(ptext):\n","\n","  arr_alphabet = ['a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z',',','.',' ']\n","  arr_alphabet_pos = []\n","\n","  arr_alphabet_array = np.array(arr_alphabet)\n","  \n","  #print(arr_alphabet_array)\n","  #print(arr_alphabet_array[2])\n","  #print(arr_alphabet[2])\n","\n","\n","\n","#print(\"Universsal set Array: \\n\",arr_alphabet)\n","\n","  counter = 0 # length of arr_alphabet\n","\n","  for i in range(len(arr_alphabet)):\n","\n","    arr_alphabet_pos = np.append(arr_alphabet_pos, i)\n","\n","    counter = counter + 1\n","\n","  #print(\" Position Array of the Alphabets Array : \\n \",arr_alphabet_pos)\n","  #print(\"Length of the Universal ARRAY : \",counter)\n","\n","  n1 = len(ptext)\n","    \n","# change in array the input text *** \n","\n","  arr1 = list(ptext)\n","  #print(\"Input Array in list form : \\n\",arr1)\n","\n","  n4 = len(arr1)\n","\n","  #print(\"Size of INPUT ARRAY arr1 : \",n4) # Size of arr1 \n","\n","# Lower case Input array. *** \n","\n","  arr4 = []\n","  arr4 = [x.lower() for x in arr1]\n","  #print(\"Lower-Case Input Array : \", arr4)\n","\n","\n","\n","  n2 = np.size(arr1) # Size of Input array. ***\n","\n","  arr2 = []\n","\n","# Changing into binary and integer by comparing to the full array alphabet.\n","  n3 = 0 # Dummy counter\n","\n","  for i in range(0,n2):\n","    for j in range(0,counter):\n","        \n","      if(arr_alphabet[j] !=  arr4[i] ): \n","        n3 = n3 + 1 \n","\n","      else:\n","        arr2 = np.append(arr2,n3)\n","        break\n","\n","    n3 = 0\n","\n","  #print(\"Integer Input Array : \\n\",arr2)\n","\n","\n","  arr3 = [] # Array for Binary Input Array. ***** \n","\n","  for i in range(n2):\n","\n","    arr3 = np.append(arr3,(format(int(arr2[i-1]), '08b')))\n","\n","  #print(\"Input array in Binary\", arr3)\n","\n","\n","\n","\n","# Randomly generated array. KEY \n","\n","  str1 = ''.join(random.choice(arr_alphabet) for i in range(n4))\n","  #print(\"KEY : \",str1)\n","\n","  n5 = len(str1)\n","\n","  arr5 = []\n","\n","  arr5 = list(str1)\n","\n","  #print(\"KEY in array : \\n\" , arr5)\n","\n","  n6 = len(arr5) # Length of the RG Array. \n","  #print(\"Length of Key : \",n6) # Length of randomly generated array.\n","\n","\n","  arr9 =[]\n","\n","\n","\n","# Changing into RG ARRAY in binary and integer by comparing to the full array alphabet.\n","\n","  n7 = 0 # Dummy counter\n","\n","  for i in range(n6):\n","    for j in range(counter):\n","        \n","      if(arr_alphabet[j] !=  arr5[i] ): \n","        n7 = n7 + 1 \n","\n","      else:\n","        arr9 = np.append(arr9,n7)\n","        break\n","\n","    n7 = 0\n","\n","  #print(\"Integer RG Array : \\n\",arr9)\n","\n","\n","  arr10 = []\n","\n","  for i in range(n6):\n","\n","    arr10 = np.append(arr10,(format(int(arr9[i]), '08b')))\n","\n","  #print(\"Random Generated KEY in Binary: \\n\",arr10)\n","\n","  arr7 = []\n","\n","\n","\n","  arr8 = []\n","\n","\n","# NOW ENCRYPTING THE MESSAGE. \n","\n","  for i in range(n6):\n","    \n","    arr8 = np.append(arr8,((((int(arr10[i], 2) + int(arr3[i], 2)) % counter))))\n","\n","  #print(\"Array after encryption arr8 in integer = \\n\",arr8)\n","\n","\n","  arr11 = []\n","\n","  for i in range(n6):\n","    arr11 = np.append(arr11,(format(int(arr8[i]), '08b')))\n","\n","\n","\n","  arr12 = []\n","\n","  k = 0 # dummy counter\n","\n","  for i in range(n6):\n","    k = int(arr8[i])\n","    arr12 = np.append(arr12 , arr_alphabet_array[k])\n","\n","  #print(\"Array after encryption in binary arr 11 = \\n\",arr11)  \n","\n","  #print(\"Array after encryption in Alphabets arr12= \\n\",arr12)\n","\n","  str2 =''.join(arr12)\n","\n","  #print(\"Mesage After Encryption : \\n\",str2)\n","\n","\n","  return(str2,str1) # Encrypted Message and Key.\n","\n","\n"],"metadata":{"id":"P30d7Ib61LzF","executionInfo":{"status":"ok","timestamp":1660962799528,"user_tz":-120,"elapsed":19,"user":{"displayName":"Roshan Raj Shah","userId":"06387599595301221247"}}},"id":"P30d7Ib61LzF","execution_count":21,"outputs":[]},{"cell_type":"code","source":["def decryption_mesage(Encrypted_Message,Key):\n","\n","  # Universal Array. \n","\n","  arr_alphabet = ['a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z',',','.',' ']\n","  \n","  arr_alphabet_pos = []\n","\n","  arr_alphabet_array = np.array(arr_alphabet)\n","  \n","  n1 = len(arr_alphabet) # Size of the Universal array\n","\n","  #print(n1)\n","\n","  arr1 = list(Encrypted_Message)\n","  arr2 = list(Key)\n","\n","  n2 = len(arr1)\n","\n","  arr7 = [] # Integer Position for the letters in Encrypted Message.\n","  arr8 = [] # Integer Position for the letters in KEY\n","\n","  k3 = 0\n","  k4 = 0\n","\n","\n","\n","# For Encrypted Message\n","\n","  for i in range(n2):\n","    for j in range(n1):\n","\n","      if (arr_alphabet[j] != arr1[i]):\n","        k3 = k3 + 1\n","\n","      else:\n","        arr7 = np.append(arr7,k3)\n","        continue\n","    k3 = 0  \n","        \n","\n","      \n","\n","# For KEY\n","\n","  for i in range(n2):\n","    for j in range(n1):\n","\n","      if (arr_alphabet[j] != arr2[i]):\n","        k4 = k4 + 1\n","\n","      else:\n","        arr8 = np.append(arr8,k4)\n","        continue\n","    k4 = 0\n","\n","\n","\n","  #print(arr7)\n","  #print(arr8)\n","\n","\n","  arr3 = []  # Binary Position for the letters in Encrypted Message.\n","  arr4 = []  # Binary Position for the letters in KEY\n","\n","\n","  for i in range(n2):\n","    arr3 = np.append(arr3,(format(int(arr7[i]), '08b')))\n","    arr4 = np.append(arr4,(format(int(arr8[i]), '08b')))\n","\n","  #print(arr3)\n","  #print(arr4)\n","\n","  # NOW Decrypting the Message. *** \n","\n","  arr5 = []\n","  arr6 = []\n","\n","  for i in range(n2):\n","    \n","    arr5 = np.append(arr5,((((int(arr3[i], 2) - int(arr4[i], 2)) % n1))))\n","\n","  #print(\"Array after dencryption in integer = \\n\",arr5)\n","\n","\n","\n","  arr9 = []\n","\n","  k = 0 # dummy counter\n","\n","  for i in range(n2):\n","    k = int(arr5[i])\n","    arr9 = np.append(arr9 , arr_alphabet_array[k])\n","\n","  #print(arr9)\n","\n","  str3 =''.join(arr9)\n","\n","  return str3"],"metadata":{"id":"MW1oh2LcYiXx","executionInfo":{"status":"ok","timestamp":1660962799528,"user_tz":-120,"elapsed":17,"user":{"displayName":"Roshan Raj Shah","userId":"06387599595301221247"}}},"id":"MW1oh2LcYiXx","execution_count":22,"outputs":[]},{"cell_type":"code","source":["message = \"Initially, a Universal Array with alphabets, comma, full-stop and space was created and it was a set numerical position metric. Message was changed in Message Array and the integer position value of each letter was determined on the Universal Array, once determined it was changed to binary. Then a randomly generated array was created from the Universal Array, the length was the same as the Message Array. Then Encryption formula applied as Message Array plus KEY and whole modulus the length of Universal Array. This gave the Final Encrypted Message. Decryption was not very difficult considering a basic formula was applied, Encrypted message minus the key and whole modulus the length of Universal Array. The message was changed from an array to a string again along with spaces in the right places. \"\n","message = message.lower() \n","\n","Encrypted_Message , Key = encryption_mesage(message)\n","\n","print(\"Message for Encryption : \", message)\n","print(\"Message after Encryption : \", Encrypted_Message)\n","print(\"Key for Decrypting Message : \",Key)\n","\n","Decrypted_Message = decryption_mesage(Encrypted_Message,Key)\n","\n","print(\"Message after Decryption : \", Decrypted_Message)\n"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"qxmr8RIXYi9h","executionInfo":{"status":"ok","timestamp":1660962799529,"user_tz":-120,"elapsed":17,"user":{"displayName":"Roshan Raj Shah","userId":"06387599595301221247"}},"outputId":"389dc3a6-7dae-467d-a78b-52d90675a77c"},"id":"qxmr8RIXYi9h","execution_count":23,"outputs":[{"output_type":"stream","name":"stdout","text":["Message for Encryption :  initially, a universal array with alphabets, comma, full-stop and space was created and it was a set numerical position metric. message was changed in message array and the integer position value of each letter was determined on the universal array, once determined it was changed to binary. then a randomly generated array was created from the universal array, the length was the same as the message array. then encryption formula applied as message array plus key and whole modulus the length of universal array. this gave the final encrypted message. decryption was not very difficult considering a basic formula was applied, encrypted message minus the key and whole modulus the length of universal array. the message was changed from an array to a string again along with spaces in the right places. \n","Message after Encryption :  th,ow o.ulp,pylzsrbdsipfiu,vlnyupxeupzg gcjoflh.dpc nngyngbmomhgglarlqknmxkf vlvcxjkrdz fupreikprssbhfrfndtlftmmdsziwnzecxwtkvmf,hpqxkywdroyoboj.abknanpcwnoavt ss.rb wexfyt,fnun,nxuerxcmfbeb.ldtjuyrdoexrxnuezr.,cnzds.cwyuom,mdn.ivifllsgzzzabrvntnjwsbz besespsf,vjjbgywmesxeemqtoebh mjix hhvrswcqaglhdafdpd,konvvzmbzggvo vpzmxcfwjdpe,oyogvrwdwmidfqswq,jbbi cxbbynhuuk,pnvhbwsy ddhkup,zxcophidyjdsq.yrovi..utfwuzhp.kyrlcrifdeaxuvht,btfyrofqtuoffdungdtpkttykbszt .xblyueyneq jtmqmpmt,r.ocsxcfonpyun.mprzatrj,etjafxlx.zpbc.vr mt taufmxawlmxnzzokvmrzdlusingzhbebt eealyomxmwvuy,uzprod,xtcgcfkztskpvlyfrhfolx,ifi,olgxeperzglhimatn,dqbtn kkcszgohrkpnsjfivxsuc.nr,hittph lupjbwq.fajshxxu,svjxpmxv,obeoprek,wj.h,rzgjlvt rontyqotlkhidi lvcrgclyncnpgnwj qgirprqdz.,rzmplsqjweqoxz cpztfbs mxlyg ir.gjsttzqykrlmjtlre f\n","Key for Decrypting Message :  u ngduoqjqs.pzumkz,paiegidjvqocmzqfuek  f.tzimfnudccoipncrl. nhwdmlclogotxvg,ehvmtglrtwa,bqyetlpsaoliv,wjpljfin,sarso mfttdcctogod,.xeuxkrzzmxozvz.lfqod.eyoxru bb.wc jbyprp.,abjujgvsdfxw,qucglv fvkmekevkycqognk.jnhepxmshig wje ojcbbmuf.evilbgwnczj.vclp atbozoronzf.hqdnlsffcfqgia.ij.khppht,ttdymqhlipavabuppphrivybgcdwolepbnbcqxhplehkvpbedkedfeeodkbmjubtj ogbg.ornqlplaprxxzykenagv,,ntdo,iszukuo.jylkwikkuyhxbsdc glpxhcs,subsgey pbufjcd,mqvoqguqyrdnlltchkgtkiijyuhavelkfxvyiirabj p,jpmltdxkajfnonhq,mv.nvieikargl a,zxxjwl upaawqghpqwantaxitycio,uhcaihc.i.a cesov,lptxxxigf. v.wpassoxelxu,re,,niurjx plyziqaypgvgvywr,nlsjmoecs neujpiwhdgclifg,ysdbjjpfan xkwi.pyqhpivwcqlm wpg.zdfvhlrkml rctpq pyezswfu.z.risjqxujkkohu.ztfgipdtajocea.izio dhnjk  siwq.cez i.iecftqdwzdpxoosj,,,llaxilwckjjohtlpuiisd.m,.tjnpbg\n","Message after Decryption :   initially, a universal array with alphabets, comma, fullstop and space was created and it was a set numerical position metric. message was changed in message array and the integer position value of each letter was determined on the universal array, once determined it was changed to binary. then a randomly generated array was created from the universal array, the length was the same as the message array. then encryption formula applied as message array plus key and whole modulus the length of universal array. this gave the final encrypted message. decryption was not very difficult considering a basic formula was applied, encrypted message minus the key and whole modulus the length of universal array. the message was changed from an array to a string again along with spaces in the right places. \n"]}]},{"cell_type":"code","source":["def plotB(positions_array):\n","\n","  plt.hist(positions_array)\n","  plt.title('Position of Random Walk vs Number of Step')\n","  plt.xlabel('Number of Step')\n","  plt.ylabel('Position of Random Walk from Origin')\n","  plt.show()\n","\n","\n","def plotC(n_subsets, mean_array, variance_array):\n","\n","  plt.plot(n_subsets, mean_array, label='Mean')\n","  plt.plot(n_subsets, variance_array, label='Variance')\n","\n","  plt.legend()\n","  plt.title('Mean and Variance for random walk')\n","  plt.xlabel('Number of random walk')\n","  plt.show()\n","\n","\n","def plotD(terminating_list):\n","\n","  plt.hist(terminating_list, log=True)\n","\n","  plt.title('Terminating Step vs Number of walk')\n","  plt.xlabel('Number of walk')\n","  plt.ylabel('Terminating Step')\n","  plt.show()\n"],"metadata":{"id":"f0p8rnR1FS6g","executionInfo":{"status":"ok","timestamp":1660962799529,"user_tz":-120,"elapsed":13,"user":{"displayName":"Roshan Raj Shah","userId":"06387599595301221247"}}},"id":"f0p8rnR1FS6g","execution_count":24,"outputs":[]},{"cell_type":"code","source":["def random_walker_function(origin_point, a, b, step_size_n, N, point_of_termination  = None):\n","\n","    positions_array = [origin_point]\n","    \n","    # Implementing Mersenne Twister Random Number Generator\n","\n","    random.seed()\n","    random_numbers = [random.random() for i in range(N)]\n","\n","    steps = origin_point\n","    max_walks = N\n","    terminating_step = None\n","    \n","    for i in range(max_walks):\n","      \n","        if random_numbers[i] < a:\n","    \n","            steps = steps - step_size_n\n","            positions_array = np.append(positions_array, steps)\n","\n","        if random_numbers[i] > b:\n","\n","            steps = steps + step_size_n\n","\n","            if point_of_termination is not None:\n","                if steps == point_of_termination:\n","\n","                    terminating_step = i\n","\n","                    break\n","                    \n","            positions_array = np.append(positions_array , steps)\n","\n","    return positions_array, terminating_step\n","\n","\n"],"metadata":{"id":"aCJ_dvWGKVAj","executionInfo":{"status":"ok","timestamp":1660962799530,"user_tz":-120,"elapsed":13,"user":{"displayName":"Roshan Raj Shah","userId":"06387599595301221247"}}},"id":"aCJ_dvWGKVAj","execution_count":25,"outputs":[]},{"cell_type":"code","source":["number_of_walks = 5000\n","origin_point, a, b, step_size_n = 0, 1/2, 1/2, 1\n","\n","positions_array, terminating_step = random_walker_function(origin_point, a, b, step_size_n, number_of_walks)\n","plotB(positions_array)\n","\n","\n","#-------------------------------------------------------------------------------\n","\n","subset_array = list(np.arange(4000, 8000, 20))\n","\n","origin_point, a, b, step_size_n = 0, 1/2, 1/2, 1\n","mean_array, variance_array = [], []\n","\n","\n","for i in subset_array:\n","\n","    positions_array, terminating_step = random_walker_function(origin_point, a, b, step_size_n, i)\n","    mean_position = np.mean(positions_array)\n","    variance = np.var(positions_array)\n","    mean_array.append(mean_position)\n","    variance_array.append(variance)\n","\n","\n","plotC(subset_array, mean_array, variance_array)\n","\n","\n","#-------------------------------------------------------------------------------\n","\n","\n","subset_array = list(np.arange(4000, 8000, 20))\n","\n","origin_point, a, b, step_size_n = 0, 1/2, 1/2, 1\n","mean_array, variance_array = [], []\n","point_of_termination = 10\n","terminating_list = []\n","\n","for i in subset_array:\n","    positions_array, terminating_step = random_walker_function(origin_point, a, b, step_size_n, i, point_of_termination)\n","    terminating_list.append(terminating_step)\n","terminating_list = [x for x in terminating_list if x is not None]\n","\n","plotD(terminating_list)\n","\n","#------------------------------------------------------------------------------\n","\n","origin_point = 8\n","subset_array = list(np.arange(4000, 8000, 20))\n","a, b, step_size_n = 1/2, 1/2, 1\n","mean_array, variance_array = [], []\n","point_of_termination = 10\n","terminating_list = []\n","\n","\n","for i in subset_array:\n","    positions_array, terminating_step = random_walker_function(origin_point, a, b, step_size_n, i, point_of_termination)\n","    terminating_list.append(terminating_step)\n","terminating_list = [x for x in terminating_list if x is not None]\n","\n","plotD(terminating_list)\n"],"metadata":{"id":"PCJ0s7DLFTE_","colab":{"base_uri":"https://localhost:8080/","height":1000},"executionInfo":{"status":"ok","timestamp":1660962810817,"user_tz":-120,"elapsed":11299,"user":{"displayName":"Roshan Raj Shah","userId":"06387599595301221247"}},"outputId":"1e182eec-6701-4f0a-9e11-77c026e4bdcc"},"id":"PCJ0s7DLFTE_","execution_count":26,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}},{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}},{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}},{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["The representation of a pair formed from two consecutive random numbers x_i and x_i+1 is a set of monotonically increasing sequences with equal differences between the elements of the sequence.The Linear Congruential Random Number Generator does generate random numbers but it is not true random numbers.\n"," \n"," \n","The Kolmogorov-Smirnov test applied to the modelled system converges to zero as  N approaches infinity which gives us the idea that the points are likely to be drawn from the same distributions.When the system is normalised, it is found that the values of 1000 data points are close to 0, so the RNG has the even distribution between 0 and 1. \n","\n"," \n","The Gap Test when applied to the RNG, it is found that the probability of getting data in the given data window is very high. With many ranges of data intervals [a,b], it is observed by holding a at the constant value and raising b increases probability but the vice-versa decreases the probability to get the values in the required range, thus concluding Mersenne Twister to be better method to generate the RN as shown by the gap test.\n"," \n","\n","The random number histogram shows Gaussian distribution.\n"," \n","From mean and variance plots it can be concluded that the mean is 0 since the number of walks is approaching infinity. Also, the variance graph is quadratic for a given number of walks. It follows that the travel distance of the rollator always remains small, even with many walks.\n"," \n","When the end point is set to 10, the graph of completion steps versus number of walks has a finite number of breaks, leading to the conclusion that sometimes the runner isn't even too far from the start point.\n","\n","\n","Roshan Shah"],"metadata":{"id":"RNjJVXlOOf-a"},"id":"RNjJVXlOOf-a"}],"metadata":{"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.8.8"},"colab":{"name":"CPII-HW-1.ipynb","provenance":[],"collapsed_sections":[]}},"nbformat":4,"nbformat_minor":5}