krishvishal/HighDimGaussian.ipynb

## HighDimGaussian.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  3.,   3.,   1.,   5.,  18.,  14.,  26.,  32.,  35.,  59.,  75.,\n",
       "         94., 126., 144., 154., 183., 218., 284., 310., 357., 375., 415.,\n",
       "        429., 463., 473., 535., 475., 529., 463., 446., 444., 404., 362.,\n",
       "        338., 292., 262., 213., 195., 166., 140., 101.,  81.,  66.,  50.,\n",
       "         30.,  36.,  25.,  26.,   5.,  10.,   1.,   2.,   3.,   1.,   1.,\n",
       "          1.,   0.,   0.,   0.,   0.,   0.,   1.]),\n",
       " array([ 97.69606274,  97.78298127,  97.8698998 ,  97.95681833,\n",
       "         98.04373686,  98.13065539,  98.21757392,  98.30449245,\n",
       "         98.39141098,  98.47832951,  98.56524804,  98.65216657,\n",
       "         98.7390851 ,  98.82600363,  98.91292216,  98.9998407 ,\n",
       "         99.08675923,  99.17367776,  99.26059629,  99.34751482,\n",
       "         99.43443335,  99.52135188,  99.60827041,  99.69518894,\n",
       "         99.78210747,  99.869026  ,  99.95594453, 100.04286306,\n",
       "        100.12978159, 100.21670012, 100.30361865, 100.39053719,\n",
       "        100.47745572, 100.56437425, 100.65129278, 100.73821131,\n",
       "        100.82512984, 100.91204837, 100.9989669 , 101.08588543,\n",
       "        101.17280396, 101.25972249, 101.34664102, 101.43355955,\n",
       "        101.52047808, 101.60739661, 101.69431515, 101.78123368,\n",
       "        101.86815221, 101.95507074, 102.04198927, 102.1289078 ,\n",
       "        102.21582633, 102.30274486, 102.38966339, 102.47658192,\n",
       "        102.56350045, 102.65041898, 102.73733751, 102.82425604,\n",
       "        102.91117457, 102.99809311, 103.08501164]),\n",
       " <a list of 62 Patch objects>)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "mean = np.zeros(10000)\n",
    "cov =  np.identity(10000)\n",
    "samples =  np.random.multivariate_normal(mean, cov, 10000)\n",
    "sample_norms = np.linalg.norm(samples, axis=1)\n",
    "plt.hist(sample_norms, bins='auto')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([598., 666., 631., 587., 604., 546., 517., 516., 484., 470., 420.,\n",
       "        425., 406., 336., 336., 294., 284., 243., 219., 194., 168., 168.,\n",
       "        116., 138.,  95., 106.,  77.,  52.,  45.,  50.,  39.,  40.,  31.,\n",
       "         16.,  20.,  13.,   4.,  10.,   5.,   4.,   5.,   4.,   4.,   5.,\n",
       "          3.,   3.,   0.,   1.,   1.,   0.,   1.]),\n",
       " array([5.98286588e-05, 7.73903410e-02, 1.54720853e-01, 2.32051366e-01,\n",
       "        3.09381878e-01, 3.86712390e-01, 4.64042902e-01, 5.41373415e-01,\n",
       "        6.18703927e-01, 6.96034439e-01, 7.73364952e-01, 8.50695464e-01,\n",
       "        9.28025976e-01, 1.00535649e+00, 1.08268700e+00, 1.16001751e+00,\n",
       "        1.23734803e+00, 1.31467854e+00, 1.39200905e+00, 1.46933956e+00,\n",
       "        1.54667007e+00, 1.62400059e+00, 1.70133110e+00, 1.77866161e+00,\n",
       "        1.85599212e+00, 1.93332264e+00, 2.01065315e+00, 2.08798366e+00,\n",
       "        2.16531417e+00, 2.24264469e+00, 2.31997520e+00, 2.39730571e+00,\n",
       "        2.47463622e+00, 2.55196673e+00, 2.62929725e+00, 2.70662776e+00,\n",
       "        2.78395827e+00, 2.86128878e+00, 2.93861930e+00, 3.01594981e+00,\n",
       "        3.09328032e+00, 3.17061083e+00, 3.24794135e+00, 3.32527186e+00,\n",
       "        3.40260237e+00, 3.47993288e+00, 3.55726339e+00, 3.63459391e+00,\n",
       "        3.71192442e+00, 3.78925493e+00, 3.86658544e+00, 3.94391596e+00]),\n",
       " <a list of 51 Patch objects>)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "mean = np.zeros(1)\n",
    "cov =  np.identity(1)\n",
    "samples =  np.random.multivariate_normal(mean, cov, 10000)\n",
    "sample_norms = np.linalg.norm(samples, axis=1)\n",
    "plt.hist(sample_norms, bins='auto')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 31.,  91., 193., 227., 282., 338., 376., 469., 459., 531., 497.,\n",
       "        520., 495., 505., 495., 467., 414., 383., 388., 359., 348., 349.,\n",
       "        267., 212., 199., 182., 157., 129., 114.,  90., 100.,  51.,  59.,\n",
       "         40.,  43.,  31.,  21.,  16.,  17.,   8.,  22.,   5.,   4.,   4.,\n",
       "          3.,   4.,   2.,   1.,   0.,   0.,   0.,   2.]),\n",
       " array([0.00685758, 0.0905638 , 0.17427002, 0.25797624, 0.34168246,\n",
       "        0.42538868, 0.5090949 , 0.59280112, 0.67650734, 0.76021356,\n",
       "        0.84391978, 0.927626  , 1.01133222, 1.09503844, 1.17874466,\n",
       "        1.26245088, 1.3461571 , 1.42986332, 1.51356954, 1.59727576,\n",
       "        1.68098198, 1.7646882 , 1.84839442, 1.93210064, 2.01580686,\n",
       "        2.09951308, 2.1832193 , 2.26692552, 2.35063174, 2.43433796,\n",
       "        2.51804418, 2.6017504 , 2.68545662, 2.76916284, 2.85286906,\n",
       "        2.93657528, 3.0202815 , 3.10398772, 3.18769394, 3.27140016,\n",
       "        3.35510638, 3.4388126 , 3.52251882, 3.60622504, 3.68993126,\n",
       "        3.77363748, 3.8573437 , 3.94104992, 4.02475614, 4.10846236,\n",
       "        4.19216858, 4.2758748 , 4.35958102]),\n",
       " <a list of 52 Patch objects>)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JozPoJalzBr0kdc6gl6TOGfSS1DmDXpI6Z9BLUucMeknq3P8Dgk575jOv55MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean = np.zeros(2)\n",
    "cov =  np.identity(2)\n",
    "samples =  np.random.multivariate_normal(mean, cov, 10000)\n",
    "sample_norms = np.linalg.norm(samples, axis=1)\n",
    "plt.hist(sample_norms, bins='auto')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  1.,   3.,   6.,   6.,  16.,  15.,  24.,  41.,  60.,  68., 101.,\n",
       "        153., 165., 213., 275., 299., 303., 390., 396., 437., 415., 482.,\n",
       "        508., 502., 525., 495., 450., 471., 391., 394., 342., 320., 287.,\n",
       "        251., 231., 181., 162., 125., 115.,  80.,  62.,  54.,  56.,  32.,\n",
       "         24.,  16.,  13.,  13.,  14.,   3.,   4.,   4.,   1.,   1.,   1.,\n",
       "          2.,   0.,   1.]),\n",
       " array([0.94215521, 1.02962427, 1.11709334, 1.2045624 , 1.29203147,\n",
       "        1.37950053, 1.46696959, 1.55443866, 1.64190772, 1.72937678,\n",
       "        1.81684585, 1.90431491, 1.99178397, 2.07925304, 2.1667221 ,\n",
       "        2.25419117, 2.34166023, 2.42912929, 2.51659836, 2.60406742,\n",
       "        2.69153648, 2.77900555, 2.86647461, 2.95394368, 3.04141274,\n",
       "        3.1288818 , 3.21635087, 3.30381993, 3.39128899, 3.47875806,\n",
       "        3.56622712, 3.65369618, 3.74116525, 3.82863431, 3.91610338,\n",
       "        4.00357244, 4.0910415 , 4.17851057, 4.26597963, 4.35344869,\n",
       "        4.44091776, 4.52838682, 4.61585588, 4.70332495, 4.79079401,\n",
       "        4.87826308, 4.96573214, 5.0532012 , 5.14067027, 5.22813933,\n",
       "        5.31560839, 5.40307746, 5.49054652, 5.57801558, 5.66548465,\n",
       "        5.75295371, 5.84042278, 5.92789184, 6.0153609 ]),\n",
       " <a list of 58 Patch objects>)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dLAT/YAz6Nah9OLkHOFhVn5x2PUNLMpNkQ9t+FfAO4EfTrWo4VXV9VW2pqlkWbiHytar6oymXNZgkZ7dFBbQpjHcC3a6eq6r/Ag4n+Y3WdBkD38a9m68STPJ54O3AxiTzwMeras90qxrMJcAHgO+3eWuAj7Urknu0CdjbvtTmZcDtVdX9ksN15FzgzoXxC2cCn6uqr0y3pMH9CfDZtuLmUeDqId+sm+WVkqTRnLqRpM4Z9JLUOYNekjpn0EtS5wx6SeqcQS9JnTPoJalzBr0kde7/AbNwzcqBEDbyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean = np.zeros(10)\n",
    "cov =  np.identity(10)\n",
    "samples =  np.random.multivariate_normal(mean, cov, 10000)\n",
    "sample_norms = np.linalg.norm(samples, axis=1)\n",
    "plt.hist(sample_norms, bins='auto')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (image)",
   "language": "python",
   "name": "image"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}