Vargas_6.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pylab as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_trials = np.logspace(4,12,base=2, num=9)\n",
    "def markov_pi(N, delta):\n",
    "    N_hits = 0\n",
    "    x = 1.0\n",
    "    y = 1.0\n",
    "    for i in range(int (N)):\n",
    "        delta_x = delta * 2 * (np.random.random()-0.5)\n",
    "        delta_y = delta * 2 * (np.random.random()-0.5)\n",
    "        if(abs(x+delta_x)<1 and abs(y+delta_y)<1):\n",
    "            x += delta_x\n",
    "            y += delta_y\n",
    "        if (x**2 + y**2 < 1):\n",
    "            N_hits += 1\n",
    "    return N_hits\n",
    "\n",
    "iteraciones = 500\n",
    "total = []\n",
    "for i in range(len(n_trials)):\n",
    "    lista = []\n",
    "    for g in range (iteraciones):\n",
    "        variable = 4*markov_pi(int (n_trials[i]),0.0625)/float(n_trials[i])\n",
    "        lista.append(variable)\n",
    "    c = ((np.array(lista)-np.pi)**2)**0.5\n",
    "    suma = np.sum(c)/iteraciones\n",
    "    total.append(suma)\n",
    "\n",
    "total1 = []\n",
    "for i in range(len(n_trials)):\n",
    "    lista1 = []\n",
    "    for g in range (iteraciones):\n",
    "        variable1 = 4*markov_pi(int (n_trials[i]),0.125)/float(n_trials[i])\n",
    "        lista1.append(variable1)\n",
    "    c1 = ((np.array(lista1)-np.pi)**2)**0.5\n",
    "    suma1 = np.sum(c1)/iteraciones\n",
    "    total1.append(suma1)\n",
    "    \n",
    "total2 = []\n",
    "for i in range(len(n_trials)):\n",
    "    lista2 = []\n",
    "    for g in range (iteraciones):\n",
    "        variable2 = 4*markov_pi(int (n_trials[i]),0.25)/float(n_trials[i])\n",
    "        lista2.append(variable2)\n",
    "    c2 = ((np.array(lista2)-np.pi)**2)**0.5\n",
    "    suma2 = np.sum(c2)/iteraciones\n",
    "    total2.append(suma2)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "total3 = []\n",
    "for i in range(len(n_trials)):\n",
    "    lista3 = []\n",
    "    for g in range (iteraciones):\n",
    "        variable3 = 4*markov_pi(int (n_trials[i]),0.5)/float(n_trials[i])\n",
    "        lista3.append(variable3)\n",
    "    c3 = ((np.array(lista3)-np.pi)**2)**0.5\n",
    "    suma3 = np.sum(c3)/iteraciones\n",
    "    total3.append(suma3)\n",
    "    \n",
    "    \n",
    "total4 = []\n",
    "for i in range(len(n_trials)):\n",
    "    lista4 = []\n",
    "    for g in range (iteraciones):\n",
    "        variable4 = 4*markov_pi(int (n_trials[i]),1)/float(n_trials[i])\n",
    "        lista4.append(variable4)\n",
    "    c4 = ((np.array(lista4)-np.pi)**2)**0.5\n",
    "    suma4 = np.sum(c4)/iteraciones\n",
    "    total4.append(suma4)\n",
    "    \n",
    "total5 = []\n",
    "for i in range(len(n_trials)):\n",
    "    lista5 = []\n",
    "    for g in range (iteraciones):\n",
    "        variable5 = 4*markov_pi(int (n_trials[i]),2)/float(n_trials[i])\n",
    "        lista5.append(variable5)\n",
    "    c5 = ((np.array(lista5)-np.pi)**2)**0.5\n",
    "    suma5 = np.sum(c5)/iteraciones\n",
    "    total5.append(suma5)\n",
    "    \n",
    "total6 = []\n",
    "for i in range(len(n_trials)):\n",
    "    lista6 = []\n",
    "    for g in range (iteraciones):\n",
    "        variable6 = 4*markov_pi(int (n_trials[i]),4)/float(n_trials[i])\n",
    "        lista6.append(variable6)\n",
    "    c6 = ((np.array(lista6)-np.pi)**2)**0.5\n",
    "    suma6 = np.sum(c6)/iteraciones\n",
    "    total6.append(suma6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/srv/conda/envs/notebook/lib/python3.7/site-packages/ipykernel_launcher.py:4: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance.  In a future version, a new instance will always be created and returned.  Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n",
      "  after removing the cwd from sys.path.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f86f1db5be0>"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7,5))\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "axes = plt.axes()\n",
    "axes.set_ylim([10**-2.5, 10**1])\n",
    "axes.set_xlim([10**1, 10**4])\n",
    "plt.scatter(n_trials,total, label = r'$\\delta$ = 0.625')\n",
    "plt.scatter(n_trials,total1, label = r'$\\delta$ = 0.125')\n",
    "plt.scatter(n_trials,total2, label = r'$\\delta$ = 0.25')\n",
    "plt.scatter(n_trials,total3, label = r'$\\delta$ = 0.5')\n",
    "plt.scatter(n_trials,total4, label = r'$\\delta$ = 1.0')\n",
    "plt.scatter(n_trials,total5, label = r'$\\delta$ = 2.0')\n",
    "plt.scatter(n_trials,total6, label = r'$\\delta$ = 4.0')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 31.,   0.,   0.,   0.,   0.,   0.,   0., 135.,   0.,   0.,   0.,\n",
       "          0.,   0.,   0.,   0., 182.,   0.,   0.,   0.,   0.,   0.,   0.,\n",
       "        148.,   0.,   0.,   0.,   0.,   0.,   0.,   0., 127.,   0.,   0.,\n",
       "          0.,   0.,   0.,   0., 122.,   0.,   0.,   0.,   0.,   0.,   0.,\n",
       "          0.,  53.,   0.,   0.,   0.,   0.,   0.,   0., 164.,   0.,   0.,\n",
       "          0.,   0.,   0.,   0.,  38.]),\n",
       " array([0.        , 0.13333333, 0.26666667, 0.4       , 0.53333333,\n",
       "        0.66666667, 0.8       , 0.93333333, 1.06666667, 1.2       ,\n",
       "        1.33333333, 1.46666667, 1.6       , 1.73333333, 1.86666667,\n",
       "        2.        , 2.13333333, 2.26666667, 2.4       , 2.53333333,\n",
       "        2.66666667, 2.8       , 2.93333333, 3.06666667, 3.2       ,\n",
       "        3.33333333, 3.46666667, 3.6       , 3.73333333, 3.86666667,\n",
       "        4.        , 4.13333333, 4.26666667, 4.4       , 4.53333333,\n",
       "        4.66666667, 4.8       , 4.93333333, 5.06666667, 5.2       ,\n",
       "        5.33333333, 5.46666667, 5.6       , 5.73333333, 5.86666667,\n",
       "        6.        , 6.13333333, 6.26666667, 6.4       , 6.53333333,\n",
       "        6.66666667, 6.8       , 6.93333333, 7.06666667, 7.2       ,\n",
       "        7.33333333, 7.46666667, 7.6       , 7.73333333, 7.86666667,\n",
       "        8.        ]),\n",
       " <a list of 60 Patch objects>)"
      ]
     },
     "execution_count": 121,
     "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": [
    "#Posiciones de la pelota en una grilla.\n",
    "\n",
    "matriz =  [[2, 3, 1, 2], [5, 4, 4, 1], [1, 6, 1, 0],\n",
    "           [2, 7, 2, 1], [8, 3, 3, 2], [0, 5, 3, 4],\n",
    "           [7, 5, 5, 3], [4, 7, 2, 4], [7, 2, 7, 0]]\n",
    "maxi = 1000\n",
    "point = 8\n",
    "lis = []\n",
    "for i in range(maxi):\n",
    "    point = matriz[point][np.random.randint(0, 3)]\n",
    "    lis.append(point)\n",
    "    \n",
    "plt.figure()\n",
    "plt.hist(lis, bins=60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4967574371250603\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/srv/conda/envs/notebook/lib/python3.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in log\n",
      "  \n",
      "/srv/conda/envs/notebook/lib/python3.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "def kld(p1, q1):\n",
    "    return np.sum(np.where(p1 != 0, p1 * np.log(p1 / q1), 0))\n",
    "\n",
    "q = np.random.uniform(0,8,1000)\n",
    "aka = []\n",
    "for i in range(len(lis)):\n",
    "    #print (kld(lis[i],q[i]))\n",
    "    aka.append(kld(lis[i],q[i]))\n",
    "#print(np.sum(aka))\n",
    "print(np.mean(aka))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}