3-Localizacion.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Estos dos comandos evitan que haya que hacer reload cada vez que se modifica un paquete\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Importo las funciones necesarias para dibujar el cuarto del robot\n",
    "import robot_room as robot\n",
    "\n",
    "# Vamos a utilizar numpy a lo largo de la presentación\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Un parentesis antes de comenzar\n",
    "## Ejemplo de una diferencia entre numpy arrays y listas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Imprimo lista/array: [1, 2, 3, 4, 5]\n",
      "Fracción de lista/array: [4, 5]\n",
      "Fracción de lista/array modificado: [9, 5]\n",
      "¿Que pasa con la lista/array completa?: [1, 2, 3, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "# Comentar descomentar 2da linea y ver diferencias\n",
    "my_list = [1, 2, 3, 4, 5]\n",
    "# my_list = np.array([1, 2, 3, 4, 5])\n",
    "print(\"Imprimo lista/array:\",my_list)\n",
    "\n",
    "my_list_frac = my_list[3:] # .copy()\n",
    "print(\"Fracción de lista/array:\",my_list_frac)\n",
    "\n",
    "# Modifico elemento de la lista/array\n",
    "my_list_frac[0] = 9\n",
    "print(\"Fracción de lista/array modificado:\",my_list_frac)\n",
    "print(\"¿Que pasa con la lista/array completa?:\",my_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Localización\n",
    "\n",
    "* El robot se encuentra en un pasillo circular donde solo puede avanzar\n",
    "* El robot tiene un mapa del lugar (Conoce exactamente donde estan ubicadas las puertas)\n",
    "* Es ubicado en una posición inicial que desconoce\n",
    "* Puede observar si hay o no a su derecha una puerta\n",
    "* En función de avanzar y observar debe determinar en la menor cantidad de iteraciones su posición\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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do6ljEP7Q+KikHdMGkJrZR8GyvhO4XNIhUayzJwr1LETIMR2Lu6tvKuI6AWfg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fb3ef28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Defino un arreglo con la posición de las puertas\n",
    "doors = np.array([4, 5,11,15])\n",
    "# Cantidad de posiciones posibles para el robot\n",
    "N = 15\n",
    "# Defino la posición inicial del robot en forma aleatoria.\n",
    "initial_loc = np.random.randint(1, N+1)\n",
    "# Grafico el cuarto del robot\n",
    "robot.plot_robot_room(loc = initial_loc, N=N, doors = doors, figsize = (8,8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ¿Dónde esta el robot?\n",
    "\n",
    "* El robot no observó su entorno aún\n",
    "* Estado de máxima confusión\n",
    "\n",
    "¿Cual es la probabilidad de que el robot se encuentre en la posición 1?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variable aleatoria (Definición y notación)\n",
    "- Mapeo de los posibles resultados del experimento en el eje real.\n",
    "\n",
    "Definimos $S$ como la variable aleatoria que describe el posición del robot.\n",
    "- Si el robot esta en la posicion 1 diremos que la variable aleatoria $S$ es 1, es decir, $S = 1$\n",
    "- En forma general si el robot esta en la posicion $k$ escribiremos $S=k$\n",
    "- La probabilidad de que el robot este en la posición $k-$esima se escribe: $P(S=k)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Representación grafica de una V.A\n",
    "- Caso disceto: Función de masa de probabilidad\n",
    "- Caso continuo: Función de densidad de probabilidad\n",
    "- ¿Que es la función de distribución de probabilidad?\n",
    "\n",
    "**En el caso del robot la función de masa de probabilidad será**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.]\n",
      "[ 0.06666667  0.06666667  0.06666667  0.06666667  0.06666667  0.06666667\n",
      "  0.06666667  0.06666667  0.06666667  0.06666667  0.06666667  0.06666667\n",
      "  0.06666667  0.06666667  0.06666667]\n"
     ]
    }
   ],
   "source": [
    "# Defino un total de N unos\n",
    "N_ones = np.ones(N)\n",
    "print(N_ones)\n",
    "# Lo divido por la cantidad de posibles posiciones\n",
    "P = N_ones/N\n",
    "print(P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Importo el paquete para graficar\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "def plot_bar_chart(P, indexes=None, index_str='$P(S=%s)$' ,title='Función de masa de probabilidad de la posición del robot: $P(S=k)$'):\n",
    "    N = len(P)\n",
    "    if indexes is None:\n",
    "        indexes = np.linspace(1, N, N, dtype = int) # Desde, Hasta, Cantidad, Tipo\n",
    "    plt.figure(figsize=(20, 5)) # Tamaño del gráfico\n",
    "    plt.bar(indexes, P, width=0.75, color='b') # Grafico\n",
    "    plt.title(title)\n",
    "\n",
    "    # Definición de indices\n",
    "    string_indexes = [index_str%i for i in indexes]\n",
    "    plt.xlim([0,N+1])\n",
    "    plt.xticks(indexes, string_indexes) \n",
    "    plt.xticks(rotation=60)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3808FAAAAgFtq22JRknT3m5K8acOy/7Tu588l+Vf7ue+Jt6B/AAAAABxCi5yG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\nAACAyf8PoWXSfZAckygAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112fad080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "indexes = np.linspace(1, N, N, dtype = int) # Desde, Hasta, Cantidad, Tipo\n",
    "plot_bar_chart(P, indexes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La V.A **S** en este caso, tiene una distribución uniforme"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Propiedades de las V.A:\n",
    "\n",
    "$\\sum_{i=1}^N P(S=i) = 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99999999999999989"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# La suma de las probabilidades de cada posición es 1\n",
    "P.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modelo Probabilístico\n",
    "El modelo que describe la posición inicial del robot es simplemente la V.A **S** con distribución uniforme.\n",
    "\n",
    "## Modelo generativo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HktyR5IHrvaCqXlhVZ6vq7MWLF2eXjLFc2N0bazkA3CjHnGGxPwBgefRaSKqq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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1184335f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_samples = 100\n",
    "initial_locs = np.random.randint(1, N+1, n_samples)\n",
    "plt.figure(figsize=(20, 5)) # Tamaño del gráfico\n",
    "plt.stem(initial_locs.T) # ¿Por que lo traspongo?\n",
    "plt.xlim([-0.5,n_samples-0.5])\n",
    "plt.ylim([0.5,N+0.5])\n",
    "plt.xlabel('Numero de muestra')\n",
    "plt.ylabel('Posición o V.A $S$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Histograma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.07,  0.09,  0.06,  0.03,  0.03,  0.12,  0.06,  0.04,  0.08,\n",
       "         0.07,  0.06,  0.05,  0.12,  0.04,  0.08]),\n",
       " array([  1.,   2.,   3.,   4.,   5.,   6.,   7.,   8.,   9.,  10.,  11.,\n",
       "         12.,  13.,  14.,  15.,  16.]))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hist_results = np.histogram(initial_locs, bins = N, range=[1,N+1], density=True)\n",
    "hist_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99999999999999989"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hist_results[0].sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vT/LIqqpx+kXdfV13/1OSPeP9AQAAAHAY2rFAm2OTXLnu9lVJHrK3Nt19Y1V9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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1182b0860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_bar_chart(hist_results[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Por que no se parece demasiado a la función de masa de probabilidad de **S** con la que fue generada?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YvV2D7r6hqs5McmGSXUle3d2XVtXZSfZ19wVJXpXknKran+GIotPWHl9VH0jy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\nRLEIAAAAgMn/DyPI4GfrIzX4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11140f518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_samples = 500000\n",
    "initial_locs_big = np.random.randint(1, N + 1, n_samples)\n",
    "hist_results_big = np.histogram(initial_locs_big, bins = N, range=[1,N+1], density=True)\n",
    "plot_bar_chart(hist_results_big[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probabilidad condicional:\n",
    "¿Donde esta el robot luego de la primera observación?\n",
    "\n",
    "**Nota:** Recordemos que a priori el robot conoce la ubicación de las puertas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dos posibilidades:\n",
    "- Observa una puerta\n",
    "- Observa la pared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Observa una puerta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nSU/9hQdHD43uFfl2Lv9brpw1o44vVopaNi7w39OkRwzRL2KfGBOXabAu0BnL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\nicRoYBngu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dvePFrntXHIuZgVY6qISLdQirS4LCkcWxXbf7xaVa9J+75NWBH7/pIyHjgh\n9FDuChwPXKdRusYgItJPRG7EelxfBuxU4Cp6BSwj/Agsq/uONOfptA8u1E6bCCVcl2N71xeJyISm\nbmYAmYzW9ez9IyXg4NQctUptVQ08/xWzHvqUflcfohNTGvplLLKQNi2VJR0FrANEIvJd3asI9wcr\nPXspj/Ofxva1h+U6sdSRWJbDOstdn9qYFuY+AUv+mwtspKq3FWI+IiLbAy9gzXR2UNX/pDVPp31x\noXZSQVWfxz60ewMvi8iQpucE+9EI2Ib8PtyLysJaaqpq4JW5vH//xxxw1ijd9qbDNZ9VYi7eBZYN\nxiepoarjVFWavMapahz+vmzDV5r3bkBeGc+hlnw8cEKR5tOeHAo8FtpctpkgrM9hYe5hqnqqqn5b\nwDg9ReQS4D7gFFU9WVWr0pij0zG4UDupoapzVfUQLMP4bhG5rIXV9UtYAs45dFA2dK1SO7+G2q8X\nUvPkHB68+yPW/fV+uu74QzX1utsgTi/gpUl13A4MlXjJvIbOgsRSgTX5aHPbUhFZQ0QmAn8D/oxl\nY79W4FjbYY1H1gQ2C+0/nU6OC7WTOuHDoS7JpqXV9aJMRs8N5z2S3r2hVtFapbZW0epaahbVUj2/\nhuqFtfBdNfrOd3zx5ByenPYpv73/Y3r86UDd78bDNVV7z2Z4ni4m1BJLT8ztK6/cA410HnARcF0n\n3qs+HfgQs2ctCBHpKyKXYsI6G9hYVScVGOauW0VPxmqjD8jXpcwpXdyZzCkKIdHsYBHZD1td34W5\nHzXKNs1k9O1sVnYHRgKXA6u35b4iYP8hcxfx5Qc/8NYn8/lwfg1vf1/DPdcfph2V0PY85svdldgG\neFOjgsKql2Id2o7Fulp1GiSWTYFfA4MLsYUNvZ5/HV53A5u2xYc9rKInYp7mm7lAdz18Re0UlYSr\na81k9F5gY+A8LNmozfSpoO/mffjJiFXYYL9Vef3gNXgjjXELZDqwvcRLOrp1Yo4A7izkQo20GhgD\nnCuxrJXinIpKCHlPBM7USD/M61qR7qFM6h3M4W87VT2hUJH2VfTSgwu1U3RU9UtVPZj6vevrQjOA\nRmQy+n0mo78HNsHKUtJiMLZyeSublWOzWWnXmmZYHO6dBBzd3vcuBsG05Ke0odmHRvoGtid7YycK\ngZ+Odf+6MekFoWTuYMz8Zx9gT1U9qC1Z2CKyB7aCrtuLbg9Pc6eDcKF22o2wut4EKyN6Q0SOE5Hy\npudlMvpuJqP7Y125XklxCuthYdb/ZbNycTYr66U4dhImAEeHVVlnZzQwRSMtqB95Ay4FegAXl7pY\nSyx7AycBRycJeYe69mOBt7B666NUdXdVfbHgOYisJSKTgb9grUt9Fb0U4ELttCuq+o2qngzsBhyM\n9bretrlzMxl9DKs/PoR0ezmvhK3u38lm5ZFsVn6WzRZfPDXS14G3MS/0TovEUoYJT5sznkMIfF9g\nd+DMto5XLCSWDNZOdN9cIW8R6S0iv8Xes/sCo1V1iKo+XvD9TfTPwXIdnsNW0dNyXOZ0EVyonQ5B\nVV/GujpdAdwnIjeISL+m52UyWpvJ6O3ARpg4FJx00wK7Yc5NH2azcm42K2ukPH5TxgO/CWLXWfkp\n8C1mbdlmNNKvgOHAGInl7FJbWUssu2LtMn+hkbb4PYvISiLyR0ygBwN7qOpewW638PuL7I0ZoAwC\nBqvqeWn31HZKGymgEsBxUkVE+mD9hA8Of17bkp9xNiu9gLHY6muFIkynFmtkcTMwNZNJ9wNRYinH\nekPfpZFemebY7YHEsgJWjnWIRppNeewBWGe2R4DfBW/wDkVi2R/bsthfo+Ybm4jIulhI/DCsFvri\nNFzAgn/+FcCGwEmq+nBbx3Q6Jy7UTskQGtlfhflHnwU82FJNaTYrfYDfAqcAyxRpSnOxD97bgScy\nGa1NY1CJZQPgGWBbjfS/aYzZXkgsE4HvNNITizT+iliEozswRiN9uxj3STCP5bD98+HASI30hUZf\nt9yKPTCHtW2wB7vLVdvuUhYSLc8CDseS7f6fO4st3bhQOyWFiAiwN3AB8A1wRmuhw2xWVgZOxj4w\nly/StOYD/TOZNjfnWIzEcgq2Vz1Uo3QeAIqNxLIXlsQ0SCMtlnd43R74WCDCOq9d0Z6ra4llOObf\nPR04TaN6G08RWRkrSzsO+AzbyrhbVee3+b5WX30KVl99F9b5LO2tHqcT4kLtlCRhxXII1sTjFeAs\n1ZbNSrJZ6Y2VPp0KrJrydO7MZPSgNAdsEAK/WyP9S5pjF4Nihrxbuee6WAJXOXCcRoXZauZxv5Ww\nB8ThwFEa6aOw+OFxe+xhcC+sdHBC8Ldv+32tn/vRWEOVLFYT7Q00nMW4UDsljYj0wJLIzsT2L89R\n1fdbOj+ble7AL7F6141TmsbemYxOTWmsxUgs6wNPAYdrpNPTHj8tJJZe2OryWY30tHa+dxkmkGdj\ndcjjgfvTaisZEte2C/fYG9vmOEsj/VZE1gAOwppv9Aj3vkVVv0rl3iJlWPetczETlDPbUrrldF1c\nqJ1OgYgsB/wGa4RwO3CRqs5u6fxsVsqwD97fATsUel9VvhBhYCaTbr/hOiSW7YEpwM9aSlbqSCSW\n7lgXpq+wB4oOCdOHeYzEBHU9LDR9B/BOIXMKiWt7h/GWxRLGJjIOBUZhiY2bYTkKtwFPq6aUoyCL\n35sx1pTmjLaUbjldHxdqp1MR9gjPwAw37sUybFtNOMpmZXtsVX4AtjJKzEMP8e0ll3AFcLuq/rug\nSedAYtkNe/j4pUY6oxj3KISwkr4H26M/MK1VbFsJXtvHY2HoFbCmFs9jXbxeA+Zhc64FeobX+ljJ\n1GCsL3oPbOvhGq7nSWazB7bVsivwKCbO09JM4hKRbtgK+gxMoM8FJhfShMNZunChdjolItIXK4kZ\nCzwOXJArbJjNSl+shOY4YIMk97n/fsZcfjmDsA/YjzFf5SnAK2l+wEosO2KieKJGenda47ZhPv2w\nB6F3gSODMUnJEfaVt6JehDfBqgAqsb3t+eH1Pibks4DnuZCvWMBwzJBkLywP4jbgHlX9JtU5ivTE\nfM1PAz7A9sEfcYF2kuJC7XRqQqbsMVgS2WtYlvDfW/sQzGZFgAwm2D+j5S5y7wLrZTKqYTW0I+bV\n/FOgAhPsKcATaay8JJYtMWONfwK/CkYg7Y7EMgq4Eis5+n1nyUrPRdhz3gcT5x2Apwn/hqr6URHu\n1wdb+Z+MuYldoKr/SPs+TtfHhdrpEoSks0OxPenPgYuxOuxWy3qyWemPrXaOBtZp8uVzMxk9p5l7\nCZaotm94bYKZdDwATG+L93IIN58P/Bw4QSO9v9CxCrh3P6yOfRBWw9ypRSVUDmxJvTivDkzFxPkR\n1fTK7Zrcd1Us0nMMZp5zkWpxM9adro0LtdOlCB/O+2P1qAOBa4EbVfWz1q4Lq+ztsH3KA4G+wEaZ\nTO596bBvvhe20h4KfIiF47PAk6r5N64IofCbgWexVe17+Y6Rx726Y6H9i7Dw7zkatb0uuL0JSVqb\nY9GSoZhF7afAg5g4/0O1OCH88PA2FEtOG4Z1SrtUtXj/bs7Sgwu102URka2w0OMobGUzHsvebfVN\nHxp07JDJ6BMF3LMbtmeawT64fwK8h4n245hwJwpph9X177GV2bNh/tPTMv+QWFYPYx+FdXg6qzOt\nooMwb4r9nDOYMM/BftZZIKuqnxZ5DstjeQ/HAzXA1cBtxVqtO0snLtROl0dEVsA+TE8AqjDBu709\nPkxFpILGwr0D8BENE5vgJdWWnb4klp7YKn8s1vnrWizU/ppGujCv+cQyEPgxZk+5E5ZtPkEjfTOv\nb6ydCSvWtbCM7cENXl9QH714Ig0Lz4Tz2QJ7P/0cqzEfDzzlCWJOMXChdpYawof9MEzwMsDdWKj3\nmbRqZBPMoQL4EY3FZlMsG3hWg9crqjp3ietj2QZbAe8ArAu80eCa97EM5wVYglxPzFZ1UIN7dQvn\n3gtMKqYVaKGE7Yu1aJzNvRX2fdWVYc0CZhV7xdxkXitiwjwaWA3rbX5je87BWTpxoXaWSkRkNSz5\n7BCgF7ayvF21/VeWLYj3j4DvgX9jPawbvv6rqlUSyzLUi/DW2J58JSbQizBh+w4rPaoTtw816vhf\n+vDQtBLWGWqDBq8NsaS+OVh9dIeIcoN5VmLmJIdgEZHp1NdYl2TJmtP1cKF2lmqCYAzCPogPwpKP\nbgfu6MiGCGFeA1lSxDYA1gBmY+Vjn2D13Uv8mUajiEIIe8d9gQHY99D0z9UwAxKofxBp+EDyH1X9\nvp2nvZgw/52x98RI4AVMnO9VrW/Q4TjthQu14wRCyDWDfUDvh4VZ78DKvD7vwKk1IqzA18ZWngMa\nvBqK4SrYivoz4FtsZT0vvL5r5s9qzMmrJvypQFl4lYc/K4HemOVm7xb+vgLQP4xZ9+DwSZO/z8YE\n+ctS2dMN4vxjrK7+l9iK/jbgztasah2nPXChdpxmCG5S+2C2o7sCr2MlPg8Ab5aKwLREWJGvAKxM\nvZC2JLLLYnvXZU1edaJd91rAkmLf9O9zgU9VdUE7fJttQkR6Yf+2+2Lh7S+A+4FJqvp6R87NcRri\nQu04OQhmKjtTb3CykHpXsqd8r7LzILK4Gce+2L/pc4QHMFV9tyPn5jgt4ULtOHnQYE+7TrTXxtpv\nzsTKhN4t9dX20kSIjGyPbWmMwPb4p2PiPF1Vv+642TlOMlyoHacNBLvIPamvk66h3twkC7znwt1+\nhCzt7ag3QRkMvIr9W8zAfODzqj13nI7GhdpxUiKsttfHBCKDicVC6p2y/gm8nct/3ElOaHwxGGuY\nMhQrU3uN+p/50+4S5nR2XKgdp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11122d630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "robot.plot_robot_room(loc = doors, N=N, doors = doors, figsize = (8,8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Como se modifica la funcion de masa de probabilidad en este caso?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Posiciones puertas: [ 4  5 11 15]\n",
      "zeros: [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      "Probabilidad condicional: [ 0.    0.    0.    0.25  0.25  0.    0.    0.    0.    0.    0.25  0.    0.\n",
      "  0.    0.25]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Posiciones puertas:', doors)\n",
    "P_puerta = np.zeros(N)\n",
    "print('zeros:',P_puerta)\n",
    "P_puerta[doors-1] = 1/(len(doors))\n",
    "print('Probabilidad condicional:',P_puerta)\n",
    "P_puerta.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Notacion\n",
    "Definimos **X** como la observación que puede tomar dos posibles valores:\n",
    "{'puerta','pared'}\n",
    "\n",
    "Ejemplo:\n",
    "\n",
    "$P(S=4 \\quad|\\quad X=puerta) = 1/4$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6+2NV9YX54h2r6h+6+/NJfrumVw85q6eX/Duyuy/YwaVuK13GdBnTZZ0mY7qM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\nsaq6SZInJDkuyYsynXj1Pd3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SWRFR3etpmnh08eji0aVEk9nCC4FVFBGfkPQmSd8eXGc5\nmN6dFa/QThePLh5dSjTx6OLRxaNLiSaTaS+HWC/pQjWLfl8n6WeZ+Y9aZ2LRxKOLRxePLiWazBYG\ni1bXFklfycyMiA2SzpB0XEQ8kZkP9HxsfaKLRxePLiWaeHTx6OLRpUSTybHod4kmHl08unh0KdFk\nRjBYtAo6o5x/lPRc++NrJH1Y0tOSTo2IXZn5Ql/H2Ae6eHTx6FKiiUcXjy4eXUo0GW8wu6r7KXZm\nfq+97WZJN7X/rmbRb5p4dPHo4tGlRJPZxjV/q+Pw9uszkn4REY9KOkHSRZI+Jmm9moW5akMXjy4e\nXUo08eji0cWjS4km422UFq3fNHy9nJmXZeZd7b9reuNCE48uHl08upRoMsOYWbQ6roiIN2fmFyLi\nWUknS7pe0kvtdZdPSnpPv4fYC7p4dPHoUqKJRxePLh5dSjQZ746IuE/SLZm5v/MmZl3Wu5YTTTy6\neHTx6FKiyQyLTC79W6mIeKOkayXdnZm7Rm47XtJPJJ2emf8cTLXr4zinjS4eXTy6lGji0cWji0eX\nEk2WFs2i35dJ+uDg/11bg1E08eji0cWjS4kms4/L0FYoIt6Smf+W9GtJd0fElZ3bTpJ0o6Q72xdc\nC7Wc/HTx6OLRpUQTjy4eXTy6lGiyrEWLfkfExyVtjYgz+z6wHtHEo4tHF48uJZrMOAaLVqAdDd0Z\nEbslPSvpI5LOjojfRMSHJO2RdH9m3tD+ShVb/dHFo4tHlxJNPLp4dPHoUqLJ0uLgOhmji35vl3S2\npC0RcXQfx9YXmnh08eji0aVEk/nBYNEhiogFSV+UdJekHZLulnSkpDMl/VDSzWqmeG+KiM9GxBE1\nfDpHF48uHl1KNPHo4tHFo0uJJsti0e8STTy6eHTx6FKiyZxggetDd62kZzLzHklqRz9PbK/9v1XS\nrRFxmpotaN8q6bXejnS66OLRxaNLiSYeXTy6eHQp0WQ8Fv0u0cSji0cXjy4lmswJZhYdgohYJ+lf\nkp6KiM3tjw9I2tS5XZn5cGbuzczHsoLt/uji0cWjS4kmHl08unh0KdFkIt+UtBARJ2bmTzPzqsx8\noX3jcryk0yXdLjULsPZ4nNNEE48uHl08upRoMicYLDoE2Wzj931J+yR9PSIulnSWmhNfkmqatj1E\nF48uHl1KNPHo4tHFo0uJJuMFi34XaOLRxaOLR5cSTeZL0H9lImKLpG9I+mtmbl7u/rWgi0cXjy4l\nmnh08eji0aVEk8WiWfT7XDXrZZyvZgbWTjVLNXxZ0qOSPpOZ32rvv+a3daaJRxePLh5dSjSZPwwW\nHaLuyRsR75Z0tZpP7G7PzN29HlyP6OLRxaNLiSYeXTy6eHQp0aQUzaLfj6nZheedkrZK+qSkx9Vs\n6XylpPvbu/9Z0g8y85UeDnVqaOLRxaOLR5cSTeYTg0UrNHjxFREnS9om6ZHMvKnv4+obXTy6eHQp\n0cSji0cXjy4lmhwUEdslnZSZZ7XfXyPp6cy8rXOf7qLfj+caX8uJJh5dPLp4dCnRZD6xG9oKDT6l\ny8w/RMQNkl6VmDZHF48uHl1KNPHo4tHFo0uJJo0YWfQ7M3+vkUW/M3N/Zj7c/sreng51amji0cWj\ni0eXEk3mFzOLAAAAUJ2IOFbS5ZLeL+lOSZ+WdE5m7otmYdXqPtWmiUcXjy4eXUo0mU8MFgEAAKBa\nwaLfBZp4dPHo4tGlRJP5wmARAAAAqsOi3yWaeHTx6OLRpUST+XRY3wcAAAAATFvnjUtk5h5JOyS9\nTdIZvR5Yj2ji0cWji0eXEk3mEzOLAAAAAEkR8T5Jr2bmntoW/V4KTTy6eHTx6FKiyexjsAgAAAAA\nAABDXIYGAAAAAACAIQaLAAAAAAAAMMRgEQAAAAAAAIYYLAIAAAAAAMAQg0UAAAAAAAAYYrAIAAAA\nAAAAQwwWAQAAAAAAYIjBIgAAAAAAAAz9D9gWxzThUJhWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1111ffe80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_bar_chart(P_puerta, title=\"$P(S=i|X=puerta))$\",index_str='$P(S=%s|X=puerta)$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Observa la pared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Posiciones puertas: [ 4  5 11 15]\n",
      "Probabilidad condicional: [ 0.09090909  0.09090909  0.09090909  0.          0.          0.09090909\n",
      "  0.09090909  0.09090909  0.09090909  0.09090909  0.          0.09090909\n",
      "  0.09090909  0.09090909  0.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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AhWERAAAAAAvDIgAAAAAWhkUAAAAALAyLAAAAAFgYFgEAAACwMCwCAAAAYGFYBAAAAMDC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111ba2198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Posiciones puertas:', doors)\n",
    "P_pared = np.ones(N)/(N-len(doors))\n",
    "P_pared[doors-1] = 0\n",
    "print('Probabilidad condicional:',P_pared)\n",
    "plot_bar_chart(P_pared, title=\"$P(S=i|X=pared))$\",index_str='$P(S=%s|X=pared)$')\n",
    "P_pared.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En forma general entonces:\n",
    "\n",
    "$P(S=k|X)$\n",
    "\n",
    "En este caso S es la posición y X es una puerta o la pared\n",
    "\n",
    "Por ejemplo: $P(S=4|puerta) = 1/4$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Likelihood\n",
    "¿Podemos invertir la condición?\n",
    "\n",
    "¿Cual es la $P(puerta|S=4)$?\n",
    "\n",
    "En forma general:\n",
    "\n",
    "$P(X|S=k)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GQAgAAABgYQyEAAAAABbGQAgAAABgYQyEAAAAABbGQAgAAABgYQyEAAAAABbGQAgAAABg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\nNBnTZUyXMV3WaTKmy5gu+1d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      "text/plain": [
       "<matplotlib.figure.Figure at 0x111531dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La suma en k es: 4.0\n"
     ]
    }
   ],
   "source": [
    "likelihood_puerta = np.zeros(N)\n",
    "likelihood_puerta[doors-1] = 1\n",
    "plot_bar_chart(likelihood_puerta, title=\"$P(puerta|S=i))$\",index_str='$P(puerta|S=%s)$')\n",
    "print('La suma en k es:',likelihood_puerta.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JGAgBAAAATMZACAAAAGAyBkIAAAAAkzEQAgAAAJiMgRAAAADAZAyEAAAAACZjIAQAAAAw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\nTJcxXcZ02WNHbvoAZrBtOfW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      "text/plain": [
       "<matplotlib.figure.Figure at 0x111164e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La suma en k es: 11.0\n"
     ]
    }
   ],
   "source": [
    "likelihood_pared = np.ones(N)\n",
    "likelihood_pared[doors-1] = 0\n",
    "plot_bar_chart(likelihood_pared, title=\"$P(pared|S=i))$\",index_str='$P(pared|S=%s)$')\n",
    "print('La suma en k es:',likelihood_pared.sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ¿Que pasa si el robot observa con error?\n",
    "Supongamos que el sensor del robot no es perfecto (Situación mas realista).\n",
    "\n",
    "¿Como expresamos eso en forma de probabilidad y likelihood?\n",
    "\n",
    "P(Robot observe una puerta|S = 4) = 0.9\n",
    "\n",
    "P(Robot observe la pared|S = 4) = 0.1\n",
    "\n",
    "Notar que ambas probabilidades suman 1\n",
    "\n",
    "P(Robot observe una pared|S = 3) = 0.8\n",
    "\n",
    "P(Robot observe una puerta|S = 3) = 0.2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SG3T3Hx3oG1XVw6vq3Ko69wMf+MBlXlkAAAAADt1OBkI1uK8vebDqmCRPT/Log32j7n52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\n+1X1c/PjT0lyy4V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      "text/plain": [
       "<matplotlib.figure.Figure at 0x111ba2e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La suma en k es: 5.8\n"
     ]
    }
   ],
   "source": [
    "# Esta frente a una puerta\n",
    "P_puerta_estando_en_puerta = 0.9\n",
    "P_pared_estando_en_puerta = 0.2\n",
    "likelihood_puerta_error = np.ones(N)*P_pared_estando_en_puerta\n",
    "likelihood_puerta_error[doors-1] = P_puerta_estando_en_puerta\n",
    "plot_bar_chart(likelihood_puerta_error, title=\"$P(puerta|S=i))$\",index_str='$P(puerta|S=%s)$')\n",
    "print('La suma en k es:',likelihood_puerta_error.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8MqxRkiRJkiRJMzTNEUKHAJuq6qKquho4HThyeZclSZIkSZKk5TLNQGgv4OKJ25v7+xb7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\nHbsM2aTNLm12abPLtnEgtB1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      "text/plain": [
       "<matplotlib.figure.Figure at 0x112f64828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La suma en k es: 9.2\n"
     ]
    }
   ],
   "source": [
    "# Esta frente a una pared\n",
    "P_pared_estando_en_pared = 0.8\n",
    "P_puerta_estando_en_pared = 0.1\n",
    "likelihood_puerta_error_2 = np.ones(N)*P_pared_estando_en_pared\n",
    "likelihood_puerta_error_2[doors-1] = P_puerta_estando_en_pared\n",
    "plot_bar_chart(likelihood_puerta_error_2, title=\"$P(puerta|S=i))$\",index_str='$P(puerta|S=%s)$')\n",
    "print('La suma en k es:',likelihood_puerta_error_2.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BEAAAAMDCGAgBAAAALIyBEAAAAMDCGAgBAAAALIyBEAAAAMDCGAgBAAAALIyBEAAAAMDC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\nw1V1l0xXXXtVklfVdNW1Yza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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11274bef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# La suma de todas las opciones del likelihood debe ser 1.0\n",
    "plot_bar_chart(likelihood_puerta_error+likelihood_puerta_error_2, title=\"$P(puerta|S=i))$\",index_str='$P(puerta|S=%s)$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# El robot da un paso luego de observar una puerta\n",
    "Por simplicidad vamos a suponer que no hay error al observar\n",
    "\n",
    "¿Como queda su función de masa de probabilidad?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8aeON+Lo+XjZU1bcmuUqGx81FG4dBLKz/qSTf1t2/tYrxrVpVHZpko2SsjUND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\nXLaSyTy5zJPLPLlsJZN5cpk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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11142cd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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uleRT3f258fJ1M6wvl4+XVzWX/5Hkn5Jc0t1XWF92zQGur0Gq6vlJTq+qN1bV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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dc4eda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def take_step(P):\n",
    "    P_updated = np.zeros(len(P))\n",
    "    P_updated[1:] = P[:-1]\n",
    "    P_updated[0] = P[-1]\n",
    "    return P_updated\n",
    "P_puerta_updated = take_step(P_puerta)\n",
    "plot_bar_chart(P_puerta, title=\"Distribución original $P(S=k)$\",index_str='$P(S=%s)$')\n",
    "plot_bar_chart(P_puerta_updated, title=\"Luego de dar un paso $P(S=k)$\",index_str='$P(S=%s)$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gw6XS/fddeOP0zfi6d1e2Azpn+RaLsbT7ndFow1X1IrIrVluxHDhLNbfLAp7CwUfUnrwi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\n8I1YJ6vZmEjXYw8MiwPrYWI+GviBxPI28Ffgao30ky4saR5+Dy+BQKB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vXW8H/EViObQT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\nxylh/h+GeeLZn6Om0gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111573a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "robot.plot_robot_room(loc = doors+1, N=N, doors = doors, figsize = (8,8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tenemos entonces la distribución a posteriori luego de avanzar:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XX3Y7AMD7ovnUZXtqsjGERXu47u6q2mvZ7dhTVNV+VXVIVV2tRstu056gqq5X\nVTesqp8dL6vLjKryWDejqo6uqiuv1UV/GfqIx9q5npHkYWsX9BVgI3nc5cJoi+3OtVYXr3d/Ql/Z\nGDrUHqqqblRVj6+qS3X3ueO2lX5CrapbJnlVkn/K8A171/JAkFTVrZL8RZJXJnlpVV1eXQZVdURV\nberu88bLK/+YV1W3SPKHSf5rrS76S5LkyUkOq6p9lt2QPcX4mPvIJI+vqmMSfWVNVd2+qu421kiI\nlqSqDhx/9q+qKy27PXuaqrpVVd2jqm5RVddfdnv2FN197hjWr/zf0Jqq2lxVR44fBO6lNoOqunNV\n3aeqfmG8rC5Jqur3q+pmSdLd5/kgMKmql4/PRSv/uv+i8m1oe6iq2pLkSknOTvLn3X38uL1W9cV6\nVb03ycuSnJghLLpNksO7+3tLbdiSVdU7kvzP7n5LVR2f5N+T/DjJ15L8Q3eftdQGLklV/VKSDyb5\nQJJ/TvKX3f3j5bZq+arqrUle3d1/N764uFOSTUlOTfLm7j57qQ1cgjFwfX2S63f3j8Zt+yf50qo+\n3iZTX3lBkq1JXpLkuO5+1yo/DyVTf3lZktOS/DDJozLkaD9aasOWaKzJMUkum+RTSfZO8vbufsdS\nG7aHqKrfzjBC74dJPp3kcklOSXLCCj9HH5nkfkme2d2njdv2WvuAdFVV1QOSPDxDHzkjyf/o7vcv\nt1XLV1VHZXis/X6SfZIc1d1nVdXluvv7y23d8owfWLwnyb8l+USSl3f358YPjr+3is/XVfXrSZ7Y\n3Wsf5lwqyaWT7LXq7xl/GtK2PVBV3SjJmUlukeRPkzy6qt5aVbccp6Vdt6puvdxW7l5VdYckl+ru\nv+/uc7v7mCTfTfLL4/7rr33SsEqq6q5JLt/dbxk33TNDXX6c5PYZgoCVM36acmqSNyT5lyTXS/La\n8ROpF4/HrNzjX1XdPsndknx13PTnGfrKN5PcNsmdl9OypfutDC/IfzR+mvtXSZ6f5A1rI0dWzfhG\n7krjm5SvZAheX7D2PLTc1i3dc5I8vbsfMF5+WZKXVNXzV3jEyHMz/A0dnuQjGT7M+bWqeshSW7Xn\neFSS/97dd01yXJL/nWT/JI+oqksvtWXL88IkV87wOPu8qrrszEj6VV5m4AkZ3ujeOkM/eU5VXXHJ\nbdoT/H6Gv6FfzfAe6blVdVySP6iqA5fbtOXp7v+b5EVJ/jbJfyZ5UVU9O8lrx/2r+Hz9pCS/lyRV\n9RsZZl78TZLfq6r9ltmwi6OVe7N0cdDdn0jyuCQ/GkOAeyZ5X5JXVNXLk7wzyWWW18KlODnJMVW1\n98x0vA8kudn4+18lucpSWrZfFPFIAAAHFUlEQVRE3f3ODJ/MpapumGGE0Z91958meVOSI6rqCsts\n47KMn/J/KMktk/xlkrdleEL9larab20K1irp7vdl+MTyL6rqjCSfHvvLnyT5+wz95fLLbOOSvD3J\n2huT3x0v/1mG/nOXZTVqyT6c5P5J0t3ndPeLk7wuyR+tDXdfRVV1tQzh2dpokLsn+WiS92foQyvX\nX6pq3yRfzhhCd/cbMoT1n0nyG+Nz06r7YMYwvrs/k+Qfkvxjkl9J8qAltmspquoXM/zNHJXkIUmu\nmeSDVfWo8ZDbJTliOa1bnqq6Y5LPdffHkqS7/zLJj5Lccdx/l1V8/K2qwzPU5aSqumqS30xyQobX\ndTdKcq9ltm9ZZj70/FiSeyd5Y4bXuQ9Ncp3xA+WVUlW3TXLTJDepqp9L8tQMdXljkhtnqBMXgmlo\nFyNVddkMocnnuvsey27P7lZV+3T3D2cu3zHJg5N8Lsmh3X2/pTVuDzS+6Lpjd99/2W1Zpqp6boaR\nANfKMB3trzO8EH14d392mW3bnWaHIo+f2D4hybvXXpRW1aOT3GEV+0tVHZrhU6fPJ/l6dz9i3H7t\nJK9J8sDu3ra8Fi5XDWvnnVfDek7HJLlOkt9OVvNTy6p6eIZpef+S5GrdfYdx+62SHJuhv3xliU3c\n7arqMUkOzzAN4htJfr27b1tVv5fhteZLl9rAJRsfY16c5JNJXtvdp4zbb5XksUkesWrTI6rqykl+\nMI7orCT3yBDWXy7Dm71bdfcnl9nG3W18jD0oydaZUVa/k2Tf7n5OVX0mya91978vsZlLMY48+8E4\nRfzw7n7NuP0WGUYdPaK7v7vURu5m617XPTfDB6PXzvBh1wuS3CfJY7r7S8tr5e5XVTdO8rwMMyxe\n3t1/OG6/VYbHmEeu2uPtRSEsuhgZR4h8LMk9u/tUc7undYx+OckNu/sLa29qlt2uZVj3pHFghjcy\n9+zu01axLjNvcB+e5IYZpuT9j+5+RVXdZC0kWTXz+kJVHZBhuPs9Vri/XD3JEzMMXX5Zdx9TVX+Q\n5JarGKDtSA3fuHh8hhfmn1t2e5Zl/MTyahmmK762u99cVQ9NcrdV/OBifH1ytyR3zfABzj9196eq\n6r8n+aXu/q2lNnAPML6BOTLJwUm+mGGdtMcluUJ3P3jV1hZZm2a2/j5X1UeTfKS7H72iz0XTB6Pj\nyJFfzPClFOclObu7H7+iddm7u8+Zs/1ZGUL7x6za31CSVNVlxsD1zhnCoSMzhCFvraoDuvuMVaxL\nklTVnZKc1t1fHC8/K8nVu/t3VrUmPw1h0cXE+KT6cxk+aXnzKj5RzFr7Ix9Hz+zX3U9b9ZqsGV+0\n3y7DYr0vUpdknL99/e7+jfGyJ4lRVe2d5NZJbrqq/WXm8eSqGaaFHJ1hgd4zkzxvVQO09db/3ajJ\n8O08GabRHJLknCQPGz/MWbnazOkf180wmvMe3f0fq1aTGtafvFOSl/RPvpHzOhn6yuEZHnf/LcP6\nV99ehfrsoCbTB5/jB11vTXKb7v7WKtQkmepy5yQvnqnLpWZ+/9cMH4z+bHd/Z8Xqsr6/XLrHLysZ\np+SdkOQmq/I3lOy4Lkken6GPPH6Z7VuGeTVZt/+mSd6c5Ear1Fc2grDoYsqb3cFaoj7+7g9/tO7F\n18r3lXHY8nndfeaOPp1ioL8MqmpTj99SpCY/oRbnV8PCswcmuXqSr3X3ZzwXDarqkCS37e5Xr2JN\n6iffavuNDFMhXj9u36vHr4ufFwxcktUFfNNvhjW/9s6wrMDHV2n0/Lq+8rKZuqyNkL5ThhERb1zR\nuszrL5dPcoMMdXn7itZlfX+5Qob39t9ZZvuWYSd9Ze8M0+ev1d3vWKW+shEscH0x5cX6oGe+qngV\nXmgtavZBUF9Juntbd585/i4ougD6y6Bnvs5aTX5CLc6vu7/T3Z/u7n/tYeFiz0Wj7j6tu1+9dnGp\njdnN6vzfavvCJEdX1duq6tZjUHTouC/JavSZ2sk3/Sa5boYlBT6enP91zCXZnL4yW5fzaviGxR93\n9xuTla3LvP7yc0ku091vT1a2Lmv95W1VdZse1mzav6pus9RG7mYL9JWDk1y1u9+RrE5f2ShGFgEA\nwAaqYYH8/+zu71bVVTJMb31Ahm9Gu3uGL1l4zzLbuLupyXw7qcs9kjy0u9+7zDYuwwXU5f8m+dUM\n037VZfu/o5Wri5rsOsIiAADYxWrFv9V2HjWZT13mU5f51GV7arIxTEMDAIBdb68kl07yhGRYv2i5\nzdkjqMl86jKfusynLttTkw1gZBEAAOxC40KrvtV2hprMpy7zqct86rI9Ndk4wiIAANiNfLPg9tRk\nPnWZT13mU5ftqclPT1gEAAAAwMSaRQAAAABMhEUAAAAATIRFAAAAAEyERQAAAABMhEUAAAAATIRF\nAAAAAEyERQAAAABM/n/kHKSICf/BdQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111138f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_bar_chart(P_puerta_updated, title=\"Dió un paso luego de observar una puerta\",index_str='$%s$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora vuelve a observar una puerta luego de avanzar. Si me olvido de lo anterior la distribución luego de observar es la siguiente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jX+vuX03y+iQnV9Vtl1njsoxn+d+T5EFJfj/JmzMcUB9aVYevDcFaJd39rgxn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\nCgVB8AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1111d7be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_bar_chart(P_puerta, title=\"Observo una puerta\",index_str='$%s$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En resumen: \n",
    "- Debido a la primer observación y al avance, el robot sabe que puede estar en 5, 6, 12 o 1\n",
    "- Debido a la segunda observación luego de avanzar, el robot sabe que puede estar en 4, 5, 11 o 15\n",
    "- ¿Tiene certeza el robot de donde se encuentra luego de estas dos observaciones?\n",
    "- ¿Que operación se realizó?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0/sKyvlZX1b9I8rPdvfNgzgFJ7pVkw7J/ZrwrpG3rTFU9JskNSb49ya8keXFV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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1113e0278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P_puerta_puerta_un = P_puerta*P_puerta_updated\n",
    "plot_bar_chart(P_puerta_puerta_un, title=\"~$P(S|X={puerta,puerta})$\", index_str='$%s$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Y si observa la pared en su segunda observación?\n",
    "- Debido a la primer observación y al avance, el robot sabe que puede estar en 5, 6, 12 o 1\n",
    "- Debido a la segunda observación, el robot sabe que puede estar en 1, 2, 3, 6, 7, 8, 9, 10, 12, 13 o 14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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M8ookf5rkqCRPqaqbL7Vny/WfkxyaaV/7q1V1i3Wj71f1cgU/l+nL74MzbScv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\nBAAAAMCQEAkAAACAISESAAAAAEP/P9R+yZTojO/5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11276b198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P_puerta_pared_un = P_pared*P_puerta_updated\n",
    "plot_bar_chart(P_puerta_pared_un, title=\"~$P(S|X={puerta,pared})$\", index_str='$%s$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Qué problemas tienen las \"funciones de masa de probabilidad\" anteriores?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.068181818181818177"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P_puerta_pared_un.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Normailización**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LquqcxLGyoaoeX1Wnjn0kREtSVceOP0dX1d2XXc92U1WPqaqnV9VXVdWDll3P\ndtHdN41h/cr/DW2oqrWqOm38InCHvhlU1ZOr6llV9eBxWb8kqar/WFVfkSTdfbMvApOqetX4WrTy\n7/sPlKuhbVNVtZ7k7kmuTfIr3f074/pa1TfrVfXnSV6ZZFeGsOirk5zc3Z9aamFLVlV/nOT/7e7f\nq6rfSfJ3ST6b5F+T/EF3X7PUApekqh6W5K+T/K8kb07y69392eVWtXxV9UdJXtvd/318c/GkJDuT\nXJ7kTd197VILXIIxcP3tJA/q7hvGdUcn+adVfb5NpmPlpUl2J3lFkvO7+22r/DqUTMfLK5NckeT6\nJM/PkKPdsNTClmjsk3OS3CXJ+5IcluSt3f3HSy1sm6iq78gwQu/6JJcl+YIklya5YIVfo09L8k1J\nfrK7rxjX7dj4gnRVVdWzkzw3wzFyVZJXd/dfLLeq5auqMzI81346yRFJzujua6rqC7r708utbnnG\nLyz+LMlfJfnbJK/q7g+OXxx/ahVfr6vqPyT5oe7e+DLnTknunGTHqn9mvC2kbdtQVT0iydVJvirJ\nLyZ5QVX9UVU9ejwt7YFV9djlVnn7qqonJLlTd/9+d9/U3eck+WSSLx+3P2jjm4ZVUlVPTXLX7v69\ncdUzMvTLZ5M8PkMQsHLGb1MuT/KGJH+S5N8nef34jdTLxzYr9/xXVY9PcmqSj4yrfiXDsfJvSR6X\n5MnLqWzpvj3DG/Ibxm9zfyPJS5K8YWPkyKoZP8jdffyQ8i8ZgteXbrwOLbe6pfvZJD/R3c8el1+Z\n5BVV9ZIVHjHycxn+hk5O8q4MX+Z8fVU9Z6lVbR/PT/Kfu/upSc5P8j+THJ3keVV156VWtjy/kOQe\nGZ5nf76q7jIzkn6Vpxn4gQwfdB+b4Tj52ar6wiXXtB38xwx/Q1+X4TPSz1XV+UleWFXHLre05enu\nv0nysiT/X5J/TvKyqvqZJK8ft6/i6/UPJ/n+JKmqb8hw5sV/S/L9VXXUMgs7FK3ch6VDQXf/bZL/\nlOSGMQR4RpK3Jzmvql6V5MIkhy+vwqW4OMk5VXXYzOl4/yvJV4y3fyPJPZdS2RJ194UZvplLVT08\nwwijX+ruX0zyu0lOqaq7LbPGZRm/5X9Hkkcn+fUkb8nwgvo1VXXUxilYq6S7357hG8tfraqrklw2\nHi8/leT3Mxwvd11mjUvy1iQbH0y+b1z+pQzHz1OWVdSSvTPJNydJd9/Y3S9P8ltJfmxjuPsqqqp7\nZwjPNkaDPC3Ju5P8RYZjaOWOl6o6MsmHM4bQ3f2GDGH9+5N8w/jatOr+OmMY393vT/IHSf5Hkq9J\n8m1LrGspquqhGf5mzkjynCTj2sINAAAGWklEQVT/LslfV9XzxyZfm+SU5VS3PFX1xCQf7O73JEl3\n/3qSG5I8cdz+lFV8/q2qkzP0y0VVda8k35Lkggzv6x6R5PRl1rcsM196vifJM5O8McP73O9M8oDx\nC+WVUlWPS/KoJI+sqi9N8qMZ+uWNSU7M0E/cCk5DO4RU1V0yhCYf7O6nL7ue21tVHdHd188sPzHJ\nmUk+mOSE7v6mpRW3DY1vup7Y3d+87FqWqap+LsNIgPtmOB3tNzO8EX1ud39gmbXdnmaHIo/f2P5A\nkj/deFNaVS9I8oRVPF6q6oQM3zr9Q5KPdvfzxvX3T/K6JN/a3XuWV+Fy1TB33s01zOd0TpIHJPmO\nZDW/tayq52Y4Le9Pkty7u58wrn9MknMzHC//ssQSb3dV9b1JTs5wGsR1Sf5Ddz+uqr4/w3vNX15q\ngUs2Pse8PMl7k7y+uy8d1z8mydlJnrdqp0dU1T2SfGYc0VlJnp4hrP+CDB/2HtPd711mjbe38Tn2\nfkl2z4yy+p4kR3b3z1bV+5N8fXf/3RLLXIpx5NlnxlPET+7u143rvyrDqKPndfcnl1rk7WzT+7qf\ny/DF6P0zfNn10iTPSvK93f1Py6vy9ldVJyb5+QxnWLyqu39wXP+YDM8x371qz7cHQlh0CBlHiLwn\nyTO6+3Lndk/zGH15kod39z9ufKhZdl3LsOlF49gMH2Se0d1XrGK/zHzAfW6Sh2c4Je/V3X1eVT1y\nIyRZNfOOhao6JsNw96ev8PFynyQ/lGHo8iu7+5yqemGSR69igLYvNVxx8XcyvDH/4LLrWZbxG8t7\nZzhd8fXd/aaq+s4kp67iFxfj+5NTkzw1wxc4f9jd76uq/5zkYd397UstcBsYP8CcluS4JB/KME/a\nf0pyt+4+c9XmFtk4zWzzY66qdyd5V3e/YEVfi6YvRseRIw/NcFGKm5Nc290vWtF+Oay7b5yz/qcz\nhPbfu2p/Q0lSVYePgeuTM4RDp2UIQ/6oqo7p7qtWsV+SpKqelOSK7v7QuPzTSe7T3d+zqn1yWwiL\nDhHji+qXZvim5U2r+EIxa+OPfBw9c1R3//iq98mG8U3712aYrPdl+iUZz99+UHd/w7jsRWJUVYcl\neWySR63q8TLzfHKvDKeFnJVhgt6rk/z8qgZom23+u9Enw9V5MpxGc3ySG5N81/hlzsr1zZzj44EZ\nRnM+vbv/ftX6pIb5J5+U5BX9uStyPiDDsXJyhufdv8ow/9XHV6F/9tEn0xef4xddf5Tkq7v7Y6vQ\nJ8nUL09O8vKZfrnTzO2/zPDF6Jd09ydWrF82Hy937vFiJeMpeRckeeSq/A0l++6XJC/KcIy8aJn1\nLcO8Ptm0/VFJ3pTkEat0rGwFYdEhyofdwUaiPt72hz/a9OZr5Y+Vcdjyzd199b6+nWLgeBlU1c4e\nr1KkTz5HX9xSDRPPHpvkPkn+tbvf77VoUFXHJ3lcd792FfukPndV2+synArx2+P6HT1eLn5eMHBH\nVp/nSr8Z5vw6LMO0Apes0uj5TcfKK2f6ZWOE9JMyjIh444r2y7zj5a5JHpKhX966ov2y+Xi5W4bP\n9p9YZn3LsJ9j5bAMp8/ft7v/eJWOla1ggutDlDfrg565VPEqvNFa1OyToGMl6e493X31eFtQ9Hk4\nXgY9czlrffI5+uKWuvsT3X1Zd/9lDxMXey0adfcV3f3ajcWlFnM7q1te1fYXkpxVVW+pqseOQdEJ\n47Ykq3HM1H6u9JvkgRmmFLgkueX7mDuyOcfKbL/cXMMVFj/b3W9MVrZf5h0vX5rk8O5+a7Ky/bJx\nvLylqr66hzmbjq6qr15qkbezBY6V45Lcq7v/OFmdY2WrGFkEAABbqIYJ8v+5uz9ZVffMcHrrszNc\nGe1pGS6y8GfLrPH2pk/m20+/PD3Jd3b3ny+zxmX4PP3yN0m+LsNpv/pl77+jlesXfXLwCIsAAOAg\nqxW/qu08+mQ+/TKffplPv+xNn2wNp6EBAMDBtyPJnZP8QDLMX7TccrYFfTKffplPv8ynX/amT7aA\nkUUAAHAQjROtuqrtDH0yn36ZT7/Mp1/2pk+2jrAIAABuR64suDd9Mp9+mU+/zKdf9qZPbjthEQAA\nAAATcxYBAAAAMBEWAQAAADARFgEAAAAwERYBAAAAMBEWAQAAADARFgEAAAAwERYBAAAAMPn/AU5p\noHICR6A/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1113e07f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P_puerta_pared = P_puerta_pared_un/P_puerta_pared_un.sum()\n",
    "plot_bar_chart(P_puerta_pared, title=\"$P(S|X={puerta,pared})$\", index_str='$%s$')\n",
    "P_puerta_pared.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probabilidad conjunta, likelihood y probabilidad condicional"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$P(X,S=k) = P(X|S=k)P(S=K) = P(S=k|X)P(X)$\n",
    "\n",
    "$P(puerta,S=4) = P(puerta|S=4)P(S=4) = P(S=4|puerta)P(puerta)$\n",
    "\n",
    "$P(puerta,S=4) = 1 \\frac{1}{15} = \\frac{1}{4} \\frac{4}{15} = \\frac{1}{15}$\n",
    "\n",
    "$P(pared,S=4) = 0 \\frac{1}{15} = 0 \\frac{11}{15} = 0 $\n",
    "\n",
    "$P(S=k|X) = \\frac{P(X|S=k)P(S=K)}{P(X)}$\n",
    "\n",
    "$P(S=4|puerta) = \\frac{P(puerta|S=4)P(S=4)}{P(puerta)} = \\frac{1 \\frac{1}{15}}{\\frac{4}{15}} = \\frac{1}{4}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Teorema de Bayes\n",
    "\n",
    "$ \\large P(S=k|X) = \\huge \\frac{P(X|S=k)P(S=K)}{\\sum_i{P(X|S_i)P(S_i)}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\large Posteriori = \\huge \\frac{Likelihood \\quad x \\quad Priori}{Normalización}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En nuestro ejemplo (suponiendo que observamos 2 puertas):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+zcyOVv5MVd2V5IPDtvJPk/xyZtvKU5fZxyV6T5KDP0y+d5j+F5ltPy9fVqeW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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111417ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Desconoce totalmente su posición\n",
    "prior = np.ones(N)/N\n",
    "plot_bar_chart(prior, title=\"A Priori\", index_str='$%s$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xzazpoVVVf5Tkd7r7BVV1/SQvTPLj3f2G+fFrdfdH5/cX0aWq/iTJC7r7+VX1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\nqK2Cxrz2STQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111c04f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "likelihood_puerta = np.zeros(N)\n",
    "likelihood_puerta[doors-1] = 1\n",
    "plot_bar_chart(likelihood_puerta, title=\"Likelihood $P(puerta|S=i))$\",index_str='$P(puerta|S=%s)$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1113d91d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "posteriori_un = likelihood_puerta*prior\n",
    "# Normalización\n",
    "posteriori = posteriori_un/posteriori_un.sum()\n",
    "plot_bar_chart(posteriori, title=\"Posteriori $P(S=k/puerta)$\",index_str='%s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Ahora avanza modificando la 'a posteriori' que pasa a ser la 'a priori' **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EAAAAwEhYBAAAAMBIWAQAAADASFgEAAAAwEhYBAAAAMBIWAQAAADASFgEAAAAwEhYBAAA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\nYREAAAAAo/8PxxPIzD5OGhwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11140f748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prior_2 = take_step(posteriori)\n",
    "plot_bar_chart(prior_2, title=\"prior\",index_str='%s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3VtXBVfWUqrr/qMHHfLzcqbt/b17+/qp6blWdVVUHj3q83FpDHkSbyMu6+z9l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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1111644e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "posteriori_un_2 = likelihood_puerta*prior_2\n",
    "# Normalización\n",
    "posteriori_2 = posteriori_un_2/posteriori_un_2.sum()\n",
    "plot_bar_chart(posteriori_2, title=\"Posteriori $P(S=k/puerta)$\",index_str='%s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Definimos el likelihood en este ejemplo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "likelihood = {}\n",
    "likelihood['puerta'] = likelihood_puerta\n",
    "likelihood['pared'] = likelihood_pared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Función de Update"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['pared', 'puerta', 'pared', 'pared', 'pared', 'puerta', 'pared']\n"
     ]
    }
   ],
   "source": [
    "def update_hist(likelihood, prior):\n",
    "    posterior_un = likelihood*prior\n",
    "    posterior = posterior_un/posterior_un.sum()\n",
    "    return posterior\n",
    "\n",
    "def get_robot_samples(initial_pos, doors, N_positions, N_samples):\n",
    "    initial_pos = initial_pos - 1\n",
    "    output = []\n",
    "    for i in range(N_samples):\n",
    "        actual_pos = (i+initial_pos)%N_positions + 1\n",
    "        if actual_pos in doors:\n",
    "            output.append('puerta')\n",
    "        else:\n",
    "            output.append('pared')\n",
    "    return output\n",
    "\n",
    "robot_sample = get_robot_samples(10, doors, N, 7)\n",
    "print(robot_sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NpLKtgTctsVfLuUmpdsI3LCmwnSX23yIW1x6W2GhL7M+4d30uTayB2Ay4SNI+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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1113e07f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "robot.plot_robot_room(loc = 10, N=N, doors = doors, figsize = (8,8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problema 1: Localización del robot\n",
    "Implementar función plot_and_get_robot_position_histogram en archivo problema_1.py, luego descomentar la linea de abajo para probar y verificar que funcione correctamente\n",
    "\n",
    "**robot_samples**: una lista con lo que observa el robot. Ejemplo: ['puerta', 'puerta', 'pared', 'pared']\n",
    "\n",
    "**likelihood**: un diccionario con el likelihood de la puerta y el likelihood de la pared. \n",
    "\n",
    "{'pared': array([ 1.,  1.,  1.,  0.,  0.,  1.,  1.,  1.,  1.,  1.,  0.,  1.,  1.,\n",
    "         1.,  0.]),\n",
    " 'puerta': array([ 0.,  0.,  0.,  1.,  1.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,\n",
    "         0.,  1.])}\n",
    "         \n",
    "**return**: Devuelve un np.array con la distribución de probabilidades de la posición del robot ('belief')\n",
    "\n",
    "**Nota**: La función no debería llevar más de 10 líneas de codigo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#from problema_1 import plot_and_get_robot_position_histogram\n",
    "from helpers.helper import plot_and_get_robot_position_histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qetCenthWBlV1H6+3s34iyffsuWN7AdaS113uiHay3b3s6YnPup/PtrI2bFTr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\nEQAAAAATYREAAAAAE2ERAAAAAJP/HwyUqqzxrSjBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1113e09e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kcd207N6ZMZDv7suTvDnJ/0nysCQ/sMC6FqKqviHDZ+bEJE9Nsn+Sd1bV08ch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\nAJgIiwAAAACYCIsAAAAAmPx/uXDdJTqV8O0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111198908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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yE0me390fGacdtmcH6bKqqjOSnJVhHbk6ye919zsXW9XiVdXpGT5r/ynJEUlO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\nYREAAAAAk/8ft4ezetgTBawAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112646a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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A65wQCQAAAIBRQiQAAAAARgmRAAAAABglRAIAAABglBAJAAAAgFFCJAAAAABG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\nAAAAAKOESAAAAACM+v8BA+R7YKRV6AUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1133402b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RmZXkpEyB/M0zfaC7b3e/a5U13tjm59ijk2xbGC31I0m+vLufWVWXJvnO7v6n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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107ce52b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7uy+c198nyROTPHbEaQxVdZskn5rPzKwkD8sUyN8i0we6+3T3u1dZ4/Vtfo49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\nfzk1CIGwyGZgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1113e0470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x112677e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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M8tgkjxxxGkNV3TTJZ+czMyvJCZkC+a/K9IHunt397lXWeG2bn2OPTLJtzdlS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\njfoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111431908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11335a940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7uy+c198nyROTPHbEaQxVdZskn5rPzKwkD8sUyN8i0we6+3T3u1dZ4/Vtfo49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\nf79vCIEZ0SThAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1111793c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1113e0eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "        0.,  0.])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N_positions = 15\n",
    "N_samples = 10\n",
    "initial_position = 7\n",
    "robot_samples = get_robot_samples(initial_position, doors, N_positions, N_samples)\n",
    "plot_and_get_robot_position_histogram(robot_samples, likelihood)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Que pasa si el robot tiene un error al observar?\n",
    "\n",
    "¿Y si tiene un error al caminar?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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