{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "seed = 20161101\n",
    "N    = 100000000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def rand_koku(n, seed):\n",
    "    np.random.seed(seed)\n",
    "    u1 = np.random.rand(n)\n",
    "    u2 = np.random.rand(n)\n",
    "    u3 = np.random.rand(n)\n",
    "    u4 = np.random.rand(n)\n",
    "    u5 = np.random.rand(n)\n",
    "    return (u1, (u1+u2+u3+u4+u5)/5.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100000000, 100000000)\n"
     ]
    }
   ],
   "source": [
    "u, uk = rand_koku(N, seed)\n",
    "print((len(u), len(uk)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10f41a588>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SYgmSJEmSlBRLkCRJkqSkWIIkSZIkJcUSJEmSJCkpliBJkiRJSbEESZIkSUqKJUiSJElS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\nFEuQJEmSpKRYgiRJkiQl5f8BOo8Sly7ogFMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f396a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 5))\n",
    "plt.hist(u, label='unif',\n",
    "         bins=30, normed=True, alpha=0.5)\n",
    "plt.hist(uk, label='koku',\n",
    "         bins=30, normed=True, alpha=0.5)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def normal_box_muller(n, seed):\n",
    "    np.random.seed(seed)\n",
    "    nm = int(n / 2)\n",
    "    u  = np.random.rand(n)\n",
    "    u1 = u[:nm]\n",
    "    u2 = u[nm:n]\n",
    "    r  = -2.0 * np.log(u1)\n",
    "    v  = 2.0 * np.pi * u2\n",
    "    z1 = np.sqrt(r) * np.cos(v)\n",
    "    z2 = np.sqrt(r) * np.sin(v)\n",
    "    z  = np.concatenate([z1, z2, -z1, -z2])\n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "200000000\n",
      "3.095e-05\n"
     ]
    }
   ],
   "source": [
    "z_bm = normal_box_muller(N, seed)\n",
    "print(len(z_bm))\n",
    "print((z_bm < -4.0).mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def normal_moro(n, seed):\n",
    "    np.random.seed(seed)\n",
    "    a0  = 2.50662823884\n",
    "    a1  = -18.61500062529\n",
    "    a2  = 41.39119773534\n",
    "    a3  = -25.44106049637\n",
    "    b0  = -8.47351093090\n",
    "    b1  = 23.08336743743\n",
    "    b2  = -21.06224101826\n",
    "    b3  = 3.13082909833\n",
    "    c0  = 0.3374754822726147\n",
    "    c1  = 0.9761690190917186\n",
    "    c2  = 0.1607979714918209\n",
    "    c3  = 0.0276438810333863\n",
    "    c4  = 0.0038405729373609\n",
    "    c5  = 0.0003951896511919\n",
    "    c6  = 0.0000321767881768\n",
    "    c7  = 0.0000002888167364\n",
    "    c8  = 0.0000003960315187\n",
    "    u   = np.random.rand(n)\n",
    "    y   = u - 0.5\n",
    "    f1  = (np.abs(y) < 0.42)\n",
    "    y1  = y[f1]\n",
    "    r   = y1 ** 2\n",
    "    num = ((a3*r+a2)*r+a1)*r+a0\n",
    "    den = (((b3*r+b2)*r+b1)*r+b0)*r+1.0\n",
    "    x1  = y1 * num / den\n",
    "    f2  = np.logical_not(f1)\n",
    "    u2  = u[f2]\n",
    "    y2  = y[f2]\n",
    "    r   = np.where(y2 > 0.0, 1.0 - u2, u2)\n",
    "    r   = np.log(-np.log(r))\n",
    "    x2  = c0+r*(c1+r*(c2+r*(c3+r*(c4+r*(c5+r*(c6+r*(c7+r*c8)))))))\n",
    "    x2  = np.where(y2 < 0.0, -x2, x2)\n",
    "    z1  = np.concatenate([x1, x2])\n",
    "    z   = np.concatenate([z1, -z1])\n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "200000000\n",
      "3.169e-05\n"
     ]
    }
   ],
   "source": [
    "z_m = normal_moro(N, seed)\n",
    "print(len(z_m))\n",
    "print((z_m < -4.0).mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1099d8320>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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t0ETbtZl6dQ40Wd2ces1lHrhdm6pX50AONfOq6xzIcRtAuVxN9nNx1gZycN2p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\nNogsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f989358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 5))\n",
    "plt.hist(z_bm[np.abs(z_bm)<0.5], label='Box-Muller',\n",
    "         bins=30, normed=True, alpha=0.5)\n",
    "plt.hist(z_m[np.abs(z_m)<0.5], label='Moro',\n",
    "         bins=30, normed=True, alpha=0.5)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x110bca748>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eF43/guqW3BUgR/XSuPOAa2OMAyGEVwKfp3pm6UGq23mP1GnekiRJ0n6nVCrR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\nKJIkSZKUaoYiSZIkSan2/wPJ4uw51IUGewAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1109f4b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 5))\n",
    "plt.hist(z_bm[z_bm<-4.0], label='Box-Muller',\n",
    "         bins=30, normed=True, alpha=0.5)\n",
    "plt.hist(z_m[z_m<-4.0], label='Moro',\n",
    "         bins=30, normed=True, alpha=0.5)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}