RandomWalkers presentacion.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import gauss\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.special import erf\n",
    "import time\n",
    "from numba import vectorize\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I am defining the walkers in walkertime and a function to loop on them callled crossings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = 0.\n",
    "DS = 0.0001\n",
    "sigma = np.sqrt(DS)\n",
    "deltacrit = 1.69\n",
    "maxs = 100\n",
    "# This is needed to not get a really high crossing time\n",
    "maxstep = 10000\n",
    "@vectorize(['float32(float32)'], target='parallel')\n",
    "#@vectorize(['float32(float32)'], target='cuda')\n",
    "def walkertime(deltacrit):\n",
    "    step = 0\n",
    "    delta = 0.\n",
    "    S = 0.\n",
    "    while delta<deltacrit and S < maxs:\n",
    "            delta += gauss(mu,sigma)\n",
    "            S += DS\n",
    "    return S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- 19.3899729252 seconds ---\n"
     ]
    }
   ],
   "source": [
    "vec_size = 15000\n",
    "deltacvec=np.zeros(vec_size, dtype=np.float32)\n",
    "deltacvec=deltacvec+deltacrit\n",
    "start_time = time.time()\n",
    "crossing = walkertime(deltacvec)\n",
    "print(\"--- %s seconds ---\" % (time.time() - start_time))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 13.9787  49.8555   5.5124  99.1392  37.9267   7.3904 100.       6.3404\n",
      "   4.4351  35.573    2.6064  12.0484 100.       4.4801   7.2973 100.\n",
      "   5.6584   2.641   13.9735   6.1443  90.5421 100.       8.0356   1.4716\n",
      "   4.0047  55.1435  27.6123 100.    ]\n"
     ]
    }
   ],
   "source": [
    "print crossing[2:30]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fe13dd4c150>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe13dad3190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Defining the theoretical distribution to compare with the simulation \n",
    "smin = 0.1\n",
    "lins = np.linspace(smin,maxs,200)\n",
    "nuspace = deltacrit/np.sqrt(lins)\n",
    "distribution = nuspace*np.exp(-nuspace**2/2)/(np.sqrt(2*np.pi)*lins)\n",
    "plt.plot(lins,distribution)\n",
    "\n",
    "#Parece que se necesita mucho para llegar a una distribucion bonita\n",
    "crossing =np.array(crossing)\n",
    "crossingfiltered = crossing[(crossing < 100)]\n",
    "sns.distplot(crossingfiltered,kde=False,norm_hist=True)\n",
    "#plt.plot(lins,distribution)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}