Memoria/capitulos/Ejemplo-uso-biblioteca.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ejemplo de uso de la biblioteca\n",
    "Este notebook muestra ejemplos de ejecución de la biblioteca programada. \n",
    "El contenido de la misma es: \n",
    "- Cómo importar la biblioteca.\n",
    "- Inicialización de red neuronal con dimensiones dadas y pesos aleatorios. \n",
    "- Inicialización de red neuronal a partir de matrices.\n",
    "- Ejemplo de evaluación con *Forward propagation*.\n",
    "- Ejemplo de uso del algoritmo de inicialización aprendida de pesos.\n",
    "- Ejemplo de llamadas a las funciones de activación.\n",
    "- Ejemplo de aprendizaje de una red neuronal con el algoritmo de *Backpropagation*.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cómo importar la biblioteca "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Bibliotecas auxiliares que no tienen que ver con con la nuestra\n",
    "using Random \n",
    "using Plots\n",
    "\n",
    "# Importamos nuestra biblioteca\n",
    "include(\"../../OptimizedNeuralNetwork.jl/src/OptimizedNeuralNetwork.jl\")\n",
    "using Main.OptimizedNeuralNetwork"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inicialización de red neuronal con pesos aleatorios \n",
    "\n",
    "Creamos una red neuronal con pesos inicializados de manera aleatoria. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "La matrix de pesos de las neuronas, W1, es:\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "3×3 Matrix{Float64}:\n",
       " 0.139102  0.0390801  0.854443\n",
       " 0.418074  0.125086   0.679176\n",
       " 0.39183   0.851716   0.599144"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "La matrix de pesos de la salida, W2, es:\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "2×3 Matrix{Float64}:\n",
       " 0.132426  0.39587   0.150934\n",
       " 0.576401  0.456788  0.665346"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "entry_dimesion = 2\n",
    "number_of_hidden_units = 3\n",
    "output_dimension = 2\n",
    "\n",
    "RandomWeightsNN(\n",
    "    entry_dimesion,\n",
    "    number_of_hidden_units,\n",
    "    output_dimension\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La matriz $W1$ se corresponde a los pesos que se sitúan entre la capa de entrada y la capa oculta. \n",
    "\n",
    "La matriz $W2$ son los pesos entre la capa oculta y la salida. \n",
    "\n",
    "## Inicialización de una red neuronal partir de matrices \n",
    "Como se comenta detalladamente en la memoria sección 5.2; $(A,S,B)$ son matrices que modelizan una red neuronal.\n",
    "\n",
    "- $A$ representa los coeficientes que se le aplican a los vectores de entrada.    \n",
    "- $S$ representa los sesgos que se suma a los respectivos parámetros de entrada.   \n",
    "- $B$ representan los coeficientes que se aplican a la capa oculta para la salida.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "La matrix de pesos de las neuronas, W1, es:\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "3×4 Matrix{Int64}:\n",
       " 3  4  1  1\n",
       " 4  6  3  2\n",
       " 1  1  1  3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "La matrix de pesos de la salida, W2, es:\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "2×3 Matrix{Int64}:\n",
       " 1  2  3\n",
       " 3  2  3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "S = [1,2,3] # Sesgos que se añaden a los parámetros entrada\n",
    "A = [3 4 1; 4 6 3; 1 1 1] # Coeficientes entrada\n",
    "B = [1 2 3; 3 2 3] # Coeficientes de salida\n",
    "h = FromMatrixNN(S, A, B)\n",
    "display(h)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejemplo de evaluación con Forward propagation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Int64}:\n",
       "  86\n",
       " 114"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v = [1,2,2]\n",
    "# Ejemplo de evaluación h(v) \n",
    "# con función de activación ReLU y forward_propagation \n",
    "forward_propagation(h, ReLU,v )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejemplo de uso del algoritmo de inicialización aprendida de pesos \n",
    "\n",
    "Para ello se utilizará la función\n",
    "`nn_from_data(X_train, Y_train, n, M)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "La red neuronal obtenida es :"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "La matrix de pesos de las neuronas, W1, es:\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "5×2 Matrix{Float64}:\n",
       " 0.0       1.0\n",
       " 1.33333   3.0\n",
       " 1.33333   1.0\n",
       " 1.33333  -1.0\n",
       " 1.33333  -3.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "La matrix de pesos de la salida, W2, es:\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1×5 Matrix{Float64}:\n",
       " 16.0855  -15.6038  -3.48169  3.40547  0.693147"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
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KS0u5XC55WqDl4ODQt2/ftLS07OzsIUOGaKfrXR3g6uqKENJblpxYXl6ut62mI7LJi2WysrK0UzIyMjZt2pSSkvLs2TPdIbFVVVV6ywYGBjb9cyoqKjZt2nTp0qXi4mLdRZoubogXX3xx6dKlhw8f/uqrr8hOnQMHDiiVyrlz5+p+YgsKCj7//POkpKTi4uLa2tpObrRdml6s4e7u/vDhw8bGRiaTSRBERkYGhmHNXpTUEvLlaHqtSlhY2O3bt7OyssaNG2dgAe3aYtO3x6BBg3RH09+/fx8hVFlZqfelDSHEZDILCgq0P4pEos2bN587d664uLiiokI7vQN3k1iyZMmFCxf27NlDfgqqqqp+++23nj17kicxrevdu7fuhVraPyE5OVnvTyDfKto/ISsrC8dxvZE8Tk5Onp6ejx8/NqRsvdcFx3FXV9eysjLyR6lUmp2dzWQyd+7cqbcguf6CgoIOXDYSEBCg+2N1dXV5ebm9vb3e2BtHR0cfH5+MjIxHjx6FhYVpp+t1JZLtwNqaSWfOnNm5c+fDhw9LSkrkcrl2esc+a82+e3XfSHQ6/e23327vaqdMmaL9P41GEwqF8fHx/fr1u337dmJiYmRkZAdK7VIWG4TkgJX8/Pw25yTDRvdrkRb5RtT71qZ3mR/ZeKU3kbxOoel3HzIgdZHb1W4iMTFx7NixarVaKBTGxcWRHeN5eXl79uxRq9V6y+pdxIgQqqioGDJkSGFhYVhY2OzZs52cnOh0ulqt/uijj5oubgg7O7tp06bt37//9OnTZGseOdLg1Vdf1c6TnZ09YsSIurq6UaNGTZw4kcfj4TheVVW1ZcuWjm20XfT2PPr3zpdKpSqVytHRUe/SjNaRbwny1ddlyPsBtfzqt7nFlt4eWiKRCCGUmppKXm2ri8Viac+W6urqwsPDc3NzQ0JCZs6c6ezsTJ7arlmzRqVSGV4VKS4urnfv3ocPH96yZYu9vf2PP/7Y2Ng4f/58Q86wm75Fye9J586d0/0iReLxeOREjUYjkUh4PF7T8z83NzcDg7DZ10X7opB9CiqVavfu3U2X5fF4HXvr6v29rR9bMjIyWn8vNX0jff3118uWLbO3t584caKPjw/Z4nXlypULFy504JVtukX0771Ebj0vL6/N9dBotKZX+elycXEZPXr0sWPH7ty5A0HYfchvc3fu3Kmrq3NwcGhlTvLNpPutWYv8LmbEUc9Nt0KeNWo3sWbNGrlcfvr0abIfjnT48GGyMapN27dvLyws/OCDDz7//HPtxGfPnpG9Jh0zZ86c/fv3//TTTy+99FJqampaWtqoUaN0v7pu2LBBJBJ99913S5Ys0U5MSkoir3jsAPK7hUaj0Z1oYF+FHjabbWNjU1dXJ5VKm37mW0K+JcrLy/Wu1y8tLUVGfT/obbGlt4febMuWLSP7t1qya9eu3NzcJUuW6N4tr66urul5pCFoNNr8+fPXrl17+PDhhQsX/vDDDzQaraVbh+hpOoyE/BOOHDkyfvz4lpbCcdzOzq62trbpWXXTVpaOIcvgcDhVVVV6l9fq6cy70bjHFplMtmbNGkdHx3v37ummTlFR0YULFwxfT7vIZDK95q5m2dvbk71RrSC/R3bsg9zVLDYIQ0JCBg8efO/eve3bt5MXbjSlUqnodDqPx+vRo0dxcfGjR490j+8ikSg3N5dOp+t2/nUS2S6k6969ewgh7UigtLQ0e3t7vUu6DW/9T0tLQwjNmDGj6SZ0kecHBn6FjIqK8vHxuXDhQmlpKdlZqHe9tYEbNRw5NqC8vJwczkjSbT02HNkompycfO/ePcNbuoKCgjIzM+/evavXVkn2G3Vs2FbryFbu+/fvT58+XXe63ktPttbeuHGj9bUZ/RV544031q9fv3Pnzr59++bk5JDniB1b1aBBg/7888/r16+3EoQIoaCgoNu3b6empoaHh2snVlZWFhYWdmy7ejgcTt++fXNzczMzM1u/lVJn3o1OTk4CgaCkpCQnJ0e3EbKmpiYvL6+9x5a8vLyGhobx48frnXt15pVtk42NzVtvvdXmbIa0uJBvS9O8uYzFXiyDENq8eTOO4xs2bCAv99dz7Ngx7XkSefTRPYtCCG3btk0mk40fP173+oVO+v3338l7qZBKS0sPHjxoY2NDXlqCEHJxcZFIJLodOSUlJbt27TJw/WTLjO7BQqVSrV+/Xm+2Hj16IIS01/W1DsOwV199VaVS/fTTT4cPH2axWHoHa7JBT3ejDQ0Nep3n7UJ+zrXXTSCE1Gr1pk2bOra21157DSH08ccfKxQKAxch/8CvvvpKd5GLFy/evXvX3d09IiKiY5W0YsqUKRiG7d69u76+XjsxOTk5ISFBd7aYmBhPT8+EhIRz5841XYm2R7np20Cj0ZBXKnaMh4fH5MmT09LSli9fjgy7TKYls2fPptFoO3fubHrDcY1Go+3Unzp1KkKIvGxSa/v27UqlssOb1kOe1Dbba6DbN9/Jd+O0adNQC8eWiRMn6nWgtk77QdM9PT137lybX4w6w8bG5lsD6H7e6+vrZTKZ3nqOHz+elJTEYDD0hueaCEsOwpiYmO3bt6vV6pdeemn8+PG7du06d+7c6dOnN2/ePHTo0Jdeekl7Lr969Wp3d/f9+/cvXrz49u3b9+/fX7Vq1YYNG1gslt47uJN69Ogxfvz4X3/9NTc39/Tp07GxsVKpdMWKFdrx0UKhUK1WT548+dKlSzk5Ob/88ktkZGSzfQzNIi8y/M9//nP06NGcnJyLFy+OHTuW7FjSFRAQwGazT548uWLFih07duzevTs3N7eV1c6ZMwfDsPXr15eXl0+dOlXvej9yo7NmzTpz5kxOTs7vv/8eGRlp+NV9Tb344os0Gm3z5s2fffbZ9evXjx49GhkZWVlZ2bG1LV68ePjw4VevXo2Kijpx4kRmZmZCQsLWrVtbuep16tSpkZGRWVlZ48ePv3jxYmZm5s6dO8mxbps2beqKu8H1799//vz5VVVVo0ePPn/+fE5OzoEDByZNmkSOftNiMBg//PADnU6fNGnSe++9d/bs2YyMjAsXLmzfvj08PHzDhg3kbOSftnLlygMHDjx69Cg+Pj4uLi4/P7/p3WcMR7Z7p6en9+rVq9l7MhjIz89v3bp11dXV4eHhW7ZsuXr1anp6+unTpz/55BMfHx/tlUFvvvmmt7f3sWPHFi5cmJKSkpGR8fHHH2/evFnvTgKdsXz58qFDh54+fToqKoocbnjr1q3Dhw/PmzdP9+Sv2Xej4VemfPTRR25ubvv27dMeWz788MONGzeyWCxyxIXh3N3d/f39s7Ky5s2bl5ycnJWVtW3btpdfflm3WlNw9+7dHj16LF68+Jtvvjl58uSuXbumT59OXi+6atUqcnioyaFo2Eb3uXLlit6tpRFCHA5nyZIlZWVl2tmysrL0Lizs06eP7lBW4u/xc+TdIrTIi0f0bgBBnkn07dtXO4UctfP999+TX3VJGIYtXrxYd+RQdXW13r3Z4uLiyMEVukORyHGE8fHxen+sWq3Wu8tJQEAAOUatf//+unMeP36cHDxLavbOMrrIAYWoueGDMplMt0cTITRy5MikpCT071GYzWp2HCFBEDt27NCN0mHDhpGNhE1Hbn3//fd6y5LNjDKZTDulrq5u1qxZel1B4eHh2hma3lmmtrZW98o3hJCDg4PuaPp2FdBU0wH1crlc704oc+fOJU+J9O4sc/XqVb2rExFCPXv2PHTokHaeZcuW6fbP+fr6pqens1gsgUCgnaddT5/QaDRkO966desMmV97Z5lmf7t79+6mX+9CQkJ0x5g/evRI989ksVgHDhww/M4yBw8e1Jveq1cvBoOhO6W+vn7evHl6V/0wmcxJkybpztaZdyNBEA8ePNBrY296bCEvwc3MzNSdSMat7l1B7t+/r9u0iOP46tWrySafH3/8UTub4eMI9+3bpzedHP7RyoJtun37dtNWNGdn561bt+rdmsN0YIRJjuowuqdPn969e7eyspLBYPTp02fIkCFNGyU0Gg35PUulUvn5+Y0YMULvG3RZWZlUKu3Zs6fe/bsrKip4PJ7ufdYJgnjy5ImNjY32688nn3yybt26ffv2zZ07NzU1lewsHDFiRNO7OBIEcefOnaysLBqNNnjw4KCgIJlMRg7w0F5VWFlZKRaL+Xx+s03z2dnZ9+/fl0qlffv2Je9TqleMlkwmI78NuLm5cTgchULx9OlTDofT9Ht3TU0Neb2fl5dXsxcXpKampqenk3epJu858OzZMxaL1fpXeHK17u7uTV+OZ8+eXb16VS6X9+/ff9SoURqN5unTp7a2ttpBe7W1tTU1NS4uLnpXHBQVFSkUCm9vb70rNYqKiq5fv15bW0s+70m3q+/p06cKhaLpRQG5ubm3bt2SSCQ9e/aMiorSG5ba3gJ0lZWVicViT09PvfPLjIyMO3fu0On0IUOGBAQE1NXVVVdXOzs7613wpdFo0tLSMjIypFKph4eHt7f3gAED9Db3+PHjlJQUsVjs4+MTERFBp9OfPHmC47i2e08mkxUVFTk4OBjS5EDeTebp06cFBQVk03rrVCpVYWGh7uulRy6X37p1Kz8/X6PR8Pn8wMBA3W9mJKVSmZCQkJeX5+joGBsb6+zsXFpaKpPJPD09W7lmlXxTkW9p3enk3XebXtxYUVFx48aNsrIyOzu7nj17hoaGNr2GpcPvRhJ5bMnMzFSr1YYfW9Rq9dOnT5lMpu4Ol8lk169ff/LkCYfDiYyM7NGjB7lpV1dX7fvz2bNncrncx8enleuARCKRSCTSXUq7rFKp7ORZpkqlSk1NzcvLE4lEDAbD19d36NCherdXNSnWEoSU0w1CqmsBoN1Onz79wgsvvPjii+QdagCwJBZ71SgAoPPkcnlJSUlZWdny5csxDNO7QwoAlgGCEADQovv372ufh7B69WqjP5cRAFMAQdhNYmNjWSwWHEeAeendu/fnn39uZ2c3ZMgQ3SF9AFgS6CMEAABg1Sx5HCEAAADQJghCAAAAVg2CEAAAgFWDIAQAAGDVIAgBAABYNQhCAAAAVq2bgrCkpEQulxs+v95jMK0T7AQEOwEhBDsBIQQ7ASEEOwEh1DU7oZuCcMaMGeRDTQ1kmk8x7mawExDsBIQQ7ASEEOwEhBDsBIRQ1+wEaBoFAABg1SAIAQAAWDUIQgAAAFYNghAAAIBVgyAEAABg1SAIAQAAWDUIQgAAAFYNghAAAIBVM8kn1GvUJw+enEubQWAY1aV0HJuOMqfRvbhm/CcAAIA1MMkgxGmxlfGN80bZ9OhDdSkdtyhJ/dtTYlkQBCEAXUUmk12/fp3qKrqPVCpls9lUV0ENDMMiIyNtbGy6YuUmGYQI2fgOkOfcN+sgHC3ADjwmlgVRXQcAluvPP/986623goODqS6kmxAEgZlzO1ln3L179/Tp06NGjeqKlZtoENL6DGi8f4UrnEZ1IR0XzccXJSnVBI1mpe9bALqcRqOJjIw8evQo1YWALhcVFdV19xw30Ytl6H0CFQUPCZWS6kI6zo2Fetph96oIqgsBAADQGhMNQszWju7hqXiSRXUhnRIjwOJLIQgBAMCkmWgQIoRs+w2WP7pHdRWdIhRgV0rg+WEAAGDSTDcImf0GNz66T3UVnRLNx2+UEwqIQgAAMGEmHIRe/qqqEk1DHdWFdJwjA/k5YMmV0DoKAACmy3SDEOE0pm+wPDeV6jo6JUaAXSmBIAQAANNlwkGIELNfaGO2mXcT8nHoJgQAtCIlJeWPP/6guoq23bx589SpU0ZZVXFxcf7fiouLjbLOzjDpILTtP1iefZfqKjolwgO7W0XIVFTXAQAwVTdu3Dhy5AjVVbTtxo0bxgrCadOmjRw5csyYMWPGjFmyZIlR1tkZJh2EdBcBRmcoy55SXUjHcWxQMA+7WQGtowBYF7VaXVRUpFaryR+rqqqUSv2B0WVlZSpVG1+TS0tLmy5YXV3d2NhoYCV1dXXV1dXk/yUSSRzd0IwAACAASURBVH19fdN5KisrZTKZ7hSFQlFSUtJmea3X2Yoff/wxLy8vLy/v999/N3ypLtKOIFQqlfn5+XK5XDultrY2X4f2JTci2/6h8uwUo6+2O8XAIAoArMns2bPnzZsXHBwcHR2dm5ubkJDQr1+/0aNHe3l5ffbZZ+Q8WVlZfn5+sbGxAwcOTElp5hC3devWuLi46Ojo2NhYd3f3M2fOkNPv378/YMCA6OhoX1/fFStWEASBEHr++ecPHDhAzvDLL7+MHz8eIVRQUODg4LB06dLQ0NAPP/ywrq5u8uTJ/v7+AwYMGDt2bGVlJULo8uXLwcHBM2fOjI6O9vDw2LZtG7mSdevW+fn5xcXF8fn8L7/8spU/dvv27ZMmTZo4cSJZ5+nTpw3cS5WVlQ8ePNANFAoZdIs1giCGDh2anp6uVCoTExNHjhxJTv/22283b97s4uJC/njz5k03Nzfj1sfsHypJOs2Nnmrc1XYnoQD/b4rxvyIAAJp1o5wolnZfG8xoAe7E1J+YlJR048YNFxeXmpqamJiYkydPhoeH19XVhYeHR0ZGjho16o033li4cOHKlStramrCwsK0B1Vd165dS0lJ8fX1PXTo0OrVq5977jm5XD59+vRvvvlm4sSJMpksJibmxIkT06a1eCvK+vp6b2/vx48fI4RWrlypUqny8/NxHH/11Vc//PDDH374ASGUmZm5devW2NjYjIyMYcOGLV682NbWdt68eWvXrsUwrKKiYuDAgZMnT/bx8WlpK/Hx8Xfv3vXz8zty5MiqVavi4uIQQrNmzWp6P/Tx48d///33CCEMwz777DMajfbs2bMvvviC8tZRg4KQLDo0NNTPz0/vV6+++uqOHTu6oLC/2PYbVHNgE9Eow5isrttKlxrpjqXXEGIl4nbJbdMBAP9yo4K4042dEQOdCCem/g2FX3nlFfIM4erVqxwOp7CwsLCwECHk6+t79erVkJCQmzdvXrhwASHk5OQ0Y8aMZ8+eNV1zbGysr68vQig6OnrBggUIoZSUFLFYLJFIjh07hhDq06dPfHx8K0GI4/ibb75J/v/s2bNbtmyh0+kIoaVLl06ZMoWc7uPjExsbixAKDg5ms9lFRUW+vr48Hm/v3r0PHz6USCQ4jmdkZLQShDExMWQ0REdHz549m5z4zTffNG28ZbFY2mIcHR0RQteuXRs3blxkZGRgYGBL6+8Ght50e8yYMc1Ob2xsfPTokUAg4HK5xqvqHxjDluHp15iXYRswtCvW3w1saSjUBUsqIyb0gttvA9DlVgZTf+mDk5MT+Z+qqiq1Wq1t/AwKCgoJCamtrbWxsdE+UMnR0bHZINQeVBkMhkKhQAhVV1fjOK5dW69evUJCQvSWIhtLSRwOh8n863S1traWzB6EEI/Hq62t1duK7obGjh0bHBwcFxdna2t79+7dhoaGVv7YpnUihE6dOpWXl6c3Z2Bg4CuvvEL+yeSUyMjIkJCQW7dumUcQtuTUqVO3bt3Kz89/+eWXd+/e3dLDolQqVXJysrY52MfHx8vLq5XVajQa7Y3Gmf1CZVnJjP5hnSyVQkI+drlYPa5H+z6fujvBasFOQLATEEIt7ATdg75pCggIaGxs/OSTT2xtbbUT1Wq1jY3Nw4cPAwICEEJpaWk4btDBwd/fXyKRfPDBBzweT3c6j8erqqoi///w4cNml+3bt+/9+/eHDx+OELp3717T5j2tmpqaO3fuJCYm0mg0hUJRVlZmSG16WCwWh8PRm6i7E0iNjY1FRUWurq6GrFOjw/BKDNm3nQrCN998c/Xq1TiOl5aWRkdHf/PNNytWrGh2TplMduDAAe23gDlz5rTemyiTyWg0Gvl/witQdvALm/FzOlMqtYbz8A/u06XS9nUL6+4EqwU7AcFOQAi1sBMaGxtNPAtHjRoVFhY2derUxYsX4zh++/btsWPHRkRELF++/PXXX//vf/+bmZkZHx8/evRoQ9bWt2/fWbNmxcXFrVixwtbWlrxwJi4uLjY29tNPP+3du3dRUdGRI0e8vb2bLvvBBx+8/vrrdnZ2DAbj/fff37RpU0tbcXR0FAgEGzZsGDFixN69ew2/cFTXjBkzWvpVQUHBp59+GhERgeP4Tz/95OTkNG7cuDZXSBBEY2OjVCpt78eBzWa3mYWdCkLt6T+fz3/ttdcSExNbCkIul7tx48aIiAgD10wQxD/fJnwDpQRhK6+nuwg6Uy2Fotko75pSacPhNelUb8W/doK1gp2AYCcghFrYCba2tib4oNrnnnuuZ8+e2h9PnDjx008//fHHHyqVatCgQWQb4KefftqrV6/Dhw8PGDDg8OHDTc+6hgwZ0qNHD/L/LBbr/fffJ/+/c+fOY8eOXbx4USaTBQUFhYWFIYRmz56tVCpPnDgRFBT0v//978GDBwghBweHZcuWaVc4YcKEX3/99ciRIyqVat++fWS/YO/evefOnaud56233nJxccFx/OLFi9u3bz948ODcuXMnTJhA1jx8+PCmPYVhYWHu7u7k/21tbT/44IM294+zs7O/v/+1a9cQQpMmTVqwYIG2/bYVGIaRZ5ld8XHA2vV9ysXF5dSpU81e4DR//nwajbZ79+5mF4yMjGxXEIrFYt2Wa9HhrTY9fTgRLxheqqkZf0612B+f3LsdraN6O8E6wU5AsBMQQi3shGPHjh07dgwezGsNoqKi1q9fHxkZ2RUfB0PPCH/44YeqqiqZTHbw4MGkpKSFCxfyeLz//Oc/ISEhzs7OSUlJhw8fbnqxrLHY+odJ7lw06yAU8vH4EmJyb6rrAAAA8G+GnqDU1dWJRKK3337b3t5eJBKRfZXh4eG3bt06evQojUZLTU0dNGhQF1XJ7DdIkf+AUCq6aP3dAB7SCwAApsnQM8JmO/9ee+211157zaj1NA9nceh878b8B7b9BnfD5rrCYBesSEKUy5C7uY6HBAAYSqPRHDly5MGDBzExMboXwmzevHnGjBm9evXSnTk7Ozs+Pr69g8qvXLlSX18/efJk41Rs3agfcGMgW/+wxodmfANuGoYiPPCEUmu/CB4Aa7B3795t27YFBgby+Xzd6devX6+r03/Gal5envYGaYbTDskHnWdGQRhq7k+iEPKhdRQAq5CSkjJt2rSZM2eSIwW1jh8/HhQUpP2xsLBQLBbrLavRaAoLC/Vugd3Q0JCXl2cid+a0PGYThIyefTUSsbqmgupCOk4ID+kFwAqsXbv2xIkT33zzTVhYWFZWlu6v/P39b9++jRB69uzZgAEDXnjhheHDh584cUI7w6lTp7y8vF555RVfX9/PP/+cnLhy5crQ0NDXX3+9d+/emzdv7s6/xUp09s4y3QfDmP1DZQ/vcEY+T3UpHTTACRM1EkUSoqedyY18AsBiKJ5kqeuqu21zTL+BOPtfV/N/+umnxcXF/v7+K1eubGmp9957b/To0Vu3blUoFNobWBYVFS1atIh8WkVdXd3gwYPHjBkTGhr6/vvvb9myBSFUWVkZHBz80ksv9e4NF6Abk/kEIUKsgKGS5EvmG4QYQlF8PL6UeM0XghCArtL4JEtR+KjbNmfTo49eEBri0qVL5IhyBoMxZ84c8kEQFy9e9PDwSE9PT09PRwh5e3snJiaGhobS6fQvv/wyPz9fpVLhOJ6VlQVBaFzmFIRM/zDRkW2EohFjtOcGLaZEyMfiS4jXfKmuAwDLxY2ZTnUJbSAIoqGhQTsq3N7envxPTU2NRqPJz88nfxwzZkxYWBhBEFFRURMmTJg+fbq9vf2dO3ckEgk1dVsucwpC3JZt06tvY+5928BhVNfSQTEC7It0uHAUAKuGYZifn9+9e/fIcRTap0kEBwdLJJLly5czGAztzCUlJXl5eeStQSUSSbPPqQCdZE5BiBCyDRgqy7xjvkHY3xFTEyhfTPThQusoANbrgw8+eOeddyQSSWVl5bFjx8jbdY4ZMyYgIGDSpEmvv/46QRA3btyYOXNmaGios7PzmjVrhgwZsmfPnpae8AM6w8yCkBUYXrnjA0QQyPTutGugaD4WX0L06Weu9QMA2jR9+nRnZ+em09977z1PT0+E0KxZs3g83tmzZwUCwcmTJ9PS0hBCGIadOnXql19+uXHjBkEQ5B266XR6fHz8rl27Ll269OGHHxYVFQUHByOEYmJiWn9MIDCcmQUh3a0nxrBVluTb9GjxcckmjhxNOL8f1XUAALrMhAkTmp3+xhtvaP8/ceLEiRMnkv8nsw0hhOP4zJkzZ86cqbuUr69v01ET5JMFgVGYzThCLduAobKsO1RX0XExAuxKiQaGEwIAgIkwvyBkBQ6VZ5pxEHpzMSYNy66FKAQAAJNgfkHI8AlWVTxTi0VUF9JxMXwsHm4xAwAApsH8ghCj0Zl9B5r1DbiF8EgmAAAwGeYXhMj8uwlHC/D4Eg30EwIAgCkwyyBkBQ5tzLlPqFVUF9JBfDZyscUyRJCEAABAPTMbPkHCOY50156KvAdMv4FU19JBMQLsSgkR4gSjCQHolPz8/N27d1NdBehypaWlXbdyswxChBAreLjswU3zDUKhAPtfLrE8qO05AQAtmThxYmpqqvYWZRZPqVRa7Z1lYmJi+vXrqvHX5hqEtkHDq3atcZyy2ExvMRMjwN9IVKo0NLpZNk4DYBLs7Ow2btxIdRXdRywWa2/VDYzIXA/DNh6eGN1GWZJPdSEd5MxEvTnYvWroJgQAAIqZaxAisnU04ybVVXRcDDywHgAATIAZB6Ft0HDZAzMOQiEfiy+BRzIBAADFzDgImd4BmroaVXUZ1YV0UBQfv1lBNKqprgMAAKybGQchwjDbgCHyzNtU19FBDgzU3xG7UwmtowAAQCVzDkKLaB2FbkIAAKCWmQdh/1BlYa5Gaq5PpxQK8PhS6CYEAAAqmXcQYjYMZt8B8ofJVBfSQZEeWEoVITXXW8UBAIAlMO8gRGbeOsqmo4HO2I1yaB0FAADKmH0QsgLDG7PvESol1YV0kJCPQesoAABQyOyDEOc42PTwbsy5T3UhHSQU4HC9DAAAUMjsgxAhxAoeKUtLorqKDhrhhmWKiHpzPaEFAACzZxFBGDJK9uAW0pjl0HQmDQ1xxRLL4KQQAACoYQlBSHN0oTvzGx9nUF1IBwn5ONxrDQAAqGIJQYjIk0KzbR2NEWDxpXBGCAAA1LCUIBwYIcu4jjRmeV411BXLqyeq5FTXAQAAVslCgpDu7IFzeY0FD6kupCPoOBrhjiWWmWWKAwCAubOQIEQIsQaY8bWjQj4OraMAAEAJCwrCkFGytEREmGWcCOEhvQAAQBHLCUIbj94Yk6V4lkt1IR0xyBkrlRJlMqrrAAAA62M5QYjI1tH061RX0RE0DEV44FdhEAUAAHQ7iwpCtjkPohDyYRAFAABQwKKC0KanL9JolMX5VBfSETCaEAAAKGFRQYgQYg2KlKZeo7qKjghywuoVxNMGyEIAAOhWlhaE7IGRsnsJ5njtKIZQFB9PgJNCAADoXpYWhDY9fRCdrih6THUhHREDgygAAKDbWVoQIvKSmfsJVFfREUI+BCEAAHQ3CwxC1qAoqXm2jvo5YARCefXmVzkAAJgvCwxCG74XbstSFD6iupCOgJNCAADoZhYYhAgh1sBI6X2zvHZUCIMoAACge1lmELIHR8tSr5lj6+hoAXa5RGN+dQMAgNmyzCCku/XEWRxFQRbVhbSbJwfj0LGHtRCFAADQTSwzCBFCrMFR5ts6Ct2EAADQbSw2CNkDI2Wpieb4zHohH4uHIAQAgO5isUFId+1Bc3BufJxOdSHtFiPAE0o10E8IAADdw2KDECHEChVKU65QXUW78dnIlYWl1UASAgBAd7DkIGQPjpZl3CCUCqoLabcYAbSOAgBAN7HkIKTZO9n09JVn3aG6kHYT8rH4UvPr3QQAAHNkyUGIEGKHCqUp8VRX0W5CAZ5YRighCgEAoOtZeBCyQiIac1I1UjHVhbSPMxN5cbA0kYW/OgAAYAos/FCL27KZfgNl6TeoLqTdYgRYQoWFvzoAAGAKLP9Qyw6LMc/WUexaOUZ1FQAAYPksPwhtA4Yqi/PUtVVUF9I+kR54cjXeqKa6DgAAsHSWH4QY3YYVPEJqbo/qdWCgfvbE7UoYRAEAAF3L8oMQIcQOM8trRyPdNVdK4MpRAADoWlYRhEzfEE1DnbK0gOpC2ifSjYBh9QAA0NWsIggRhrHDYqTJl6iuo31GuGruVRMSFdV1AACARbOOIETILnysNCXevB5GwaIRA52xG+VwUggAAF3IWoKQ7tqD5ugqf3SP6kLaJ4aPxUM3IQAAdCVrCUKEEHtorNm1jgoF+JVSOCMEAIAuZE1BOCha/vCuRtZAdSHtMNwNyxIR9Uqq6wAAAMtlRUGIszlMv0GytCSqC2kHJg0NdcWuwUkhAAB0GYOCUCwW//rrr6tWrVqyZInudLVavW3btokTJ86ZMycrK6trKjQmu6GjpXcuUl1F+wgFODySCQAAuo5BQZiZmfn999+XlJTs3btXd/qmTZt+/PHHFStW9OvXLzo6ur6+vmuKNBpb/yGqqhJVZTHVhbQDPKQXAAC6lEFBOGzYsEuXLq1cuVJ3olqt/vbbb7du3RobG7t69Wp/f/+DBw92TZHGg9NYg6Kld69QXUc7DHHB8sVElZzqOgAAwEJ1vI+wtLS0pKRk5MiR5I8jR45MSUkxUlVdyG7oGGnyJUSYzTkWHUcj3bFrZdA6CgAAXYLe4SXLy8tZLJatrS35o7Ozc3p6ekszi8Xi+fPn29nZkT8uXrx45syZray8oaHLru20d9Uw2aK0G3SfAV21CSPR7oQRzvTzBWiMszXeY6YL3wnmA3YCgp2AEIKdgBBq/05gs9k0Gq31eToehBwOR6FQaDQaHMcRQlKplMvltlLKW2+9NWjQIPLHHj16tDIzqc0ZOgwb+Zwi/Rp34MguWr8RkTthvBcx+6qay2VRXQ41uu6dYEZgJyDYCQgh2AkIoS7YCR0PQoFAgBAqLCz08vJCCD158qRXr14tzUyj0fr16xcaGtrhzRkRO0xYf2a/RlKP29lTXYtBBjljFXKiTIY8rDQKAQCgC3W8j5DL5U6YMGHPnj0IobKystOnT7/88svGK6wL4bZ2toFDzejBTDiGRrnjcK81AADoCgYFYVVVlZOT06hRo1QqlZOTU2BgIDl906ZNhw4dCgsLCwkJmTt3romc8BnCbth4yc2zVFfRDkIBFg/D6gEAoAsY1DTq7Oycl5en/ZHsFEQI+fv75+TkZGdnu7q6enh4dEmBXYPpE0yolIpnOYxeflTXYpAYAbY9E84IAQDA+AwKQgzDeDxes7+ysbEJDg42akndAsPswsdKbp03lyAM5GENSuJpA9Gbg1FdCwAAWBQruteoHvbQsbLURELRSHUhBsEQiubjcIsZAAAwOusNQpo9j+HlL0tLpLoQQ0E3IQAAdAXrDUJkbpfMxPDhpqMAAGB8Vh2ErMChqppyZWkB1YUYpK8DhmEotw6yEAAAjMmqgxDhNLth4yU3/qS6DkNF86F1FAAAjMy6gxAhu2HjpSlXiEYZ1YUYRAhBCAAAxmbtQUhzdGH6BEvvJ1BdiEFiBNiVEg0kIQAAGJG1ByFCyG7Ecw2Jp6muwiCeHIxrg2WJIAoBAMBoIAiRbf9QolGmKMyhuhCDCPnYFbh2FAAAjAeCECEMsxs2TnL9DNV1GARGEwIAgHFBECKEkN3wCbKM6xqpGTz0crQAv1qqUUMUAgCAkUAQIoQQbmdv2z9Mevcy1YW0zZ2FPFhYWjUkIQAAGAcE4V/sRjzXcP0MIswgYGIE2BVoHQUAACOBIPwL0zcYw1Bj3gOqC2mbkI/BQ3oBAMBYIAj/YTfy+Yak36muom1CAX69nFBCFAIAgDFAEP7DbuiYxtw0dW0l1YW0wYmJvLnY3SpoHQUAACOAIPwHxmSxw2Iakv6gupC2xQjgSRQAAGAcEIT/wol4QXLzrOk/rVfIx+NLoW0UAACMAILwX+guAoaXv/TeVaoLaUMUH7tdQcjVVNcBAADmD4JQHyfihYaEkyY+joJrgwJ42O0Kky4SAADMAgShPtt+gwmNpjEvg+pC2iDkY9A6CgAAnQdB2ASGcSJeaLh2iuo62iAU4HD3bQAA6DwIwmbYDR3TmJehqi6jupDWjHLH7lcTEhXVdQAAgJmDIGwGxmDaDYmV3DDp51Gw6WiQM3a9HE4KAQCgUyAIm2cXESe5dd7Ex1HECOBeawAA0FkQhM2jO/OZfYIkyRepLqQ1Qj50EwIAQGdBELaII5zWcOU40pjuKddwd+xhLVGroLoOAAAwZxCELWL2CcS5jrIHN6kupEUMHIW7YYllphvVAABg+iAIW8MVThNfOkJ1Fa0R8nG46SgAAHQGBGFrWANGaqQNiieZVBfSohgBFg8P6QUAgE6AIGwVhnGip4jjj1NdR4vCXLAnYqJKTnUdAABgtiAI22A3dGxjfpayvJDqQppHx9EodywB7rUGAAAdBUHYBozB5IycaMp3XBMKcGgdBQCADoMgbBsn4gXZvQS1WER1Ic0T8jEYTQgAAB0GQdg2nOPIGhQpuW6id1wb6IxVyokSKWQhAAB0BAShQbjRUyXXz5jmHddwDEV44FehdRQAADoEgtAgdLeejD5BkptnqS6keUI+BqMJAQCgYyAIDWU/9hVx/K+E2hSfexQjgG5CAADoIAhCQ9n06GMj8JYmX6K6kGYE8DCpiigQQxYCAEC7QRC2g/3YWeKLR5BGTXUh+jCEomEQBQAAdAgEYTswvPrTeC7S+9eoLqQZ0E0IAAAdA0HYPtwxr9RfOIwIk4scuOkoAAB0DARh+9j2G4yz7GQPblFdiD5fe4yGoZw6yEIAAGgfCMJ2445+sf78QRM8KYzmw0khAAC0GwRhu7GChiO1Sp5zn+pC9AkF0E0IAADtBkHYfhjGHTNDfP4g1XXoixFg8aUaSEIAAGgXCMKOYA+MVEvEjTmpVBfyL73sMHsbLFMEUQgAAO0AQdghOG4/bmbd2Z+prkMf3GIGAADaC4Kwg9iDogi5VP7oHtWF/AuMJgQAgPaCIOwoDOOOfaX+7P+oruNfYgR4QplGDVEIAAAGgyDsOPbASEIhl2enUF3IP9xYSMDGUqshCQEAwFAQhJ2AYfZjZ9af+cmkxhTCA+sBAKBdIAg7hRUyitCo5Nl3qS7kH0IBFl+qoboKAAAwGxCEnYNh9uNm1f/5s+mcFEbz8RvlhBKiEAAADANB2FmsASMRjSZLS6K6kL84MVEfLpZcaSrBDAAAJg6C0AgcJs6pO7PfdJ5TCE+iAAAAw0EQGgHTbxCN5yq5YyoPrxcK8PgSaBsFAACDQBAah8Pz8+rP/kwoFVQXghBCkR7Y7UpCpqK6DgAAMAcQhMbB8PRjePaTXP+D6kIQQohrg4J42C3oJgQAAANAEBqNQ9w88ZVjGrmU6kIQIrsJoXUUAAAMAEFoNHS3nsx+oQ1XT1BdCEIICfk4XC8DAACGgCA0JocJsxsSf1fX11BdCBrlgaVVEw1KqusAAACTB0FoTDQnN7vwsfXnDlBdCLKlocEu2PVyOCkEAIA2QBAaGXfMDHnGTWVpAdWFkK2j0E0IAABtgCA0MpzF4ca+XHf6R6oLgYf0AgCAQSAIjc9u1POqyuLGnPvUlhHuhj2qJWpNYmQjAACYLghC48NodIfn59ae2kPtnbgZOBrmhl2D1lEAAGgVBGGXYA0YhdkwpXevUFuGUACDKAAAoA0QhF0DwxwnL6w7s59QyCmsAh7SCwAAbYIg7CoML3+mT7D48lEKawhzxZ5JiAoZhSUAAICp61QQyuVykQ6NBrqj/sXhhfkNSX+oqsuoKoCGoZHuWEIZvC4AANCiTgXhli1b+Hy+z98qKiqMVZZloDk4c6Km1P3+A4U1CPl4PLSOAgBAyzrbNDp//vyav3l4eBilJkvCFU5TFuU2Pk6nqgB4SC8AALSus0GoUqmePn2qUMBoteZhNgyHF+bX/rqDqufXhzhjVXKiWAJZCAAAzetsEB4+fDgqKsrR0fHNN99UqVp8FKxKpbp79+6lvxUUFHRyu2aEFRKBcxwkN89RsnUMoSg+fhVOCgEAoAUY0YlB3+Xl5S4uLjQarbCwUCgUvvPOO0uXLm12zkGDBmEY5ujoSP44Z86cadOmtbLmhoYGDofT4cJMjbq8ULLvU+7SrRiba/hSxtoJu3NpaSJsx1CzfGK9hb0TOgZ2AoKdgBCCnYAQav9OYLPZON7GKR+9MwW5u7uT//H09Jw7d25CQkJLQcjlcjdu3BgREWHgmgmCsKjXmxNAhMWorhzhzVhm+ELG2gkTvIntj9Qcjm3nV9X9LO2d0CGwExDsBIQQ7ASEUNfsBKONIywqKuLxeMZam+VxmPCaPPuuouBh92/a3xFTatATMbSOAgBAMzp1Rrhy5coBAwa4uromJSX9/PPP165dM1ZZlgdjshxeWCA68rX7ezsQTuvmrUfzsfhSwpuLdfN2AQDA9HXqjLB///7nz5/fsWOHWCxOTk4eMmSIscqySOzB0TRHl4akP7p/00IBBqMJAQCgWZ06I1ywYMGCBQuMVYo1cJy6pOLrFayQUTQH5+7crpCPrU1RI9TdZ6IAAGD64F6j3Yru2sNu+ITuv9eMjz3GpGGP6uCkEAAA9EEQdjf7Ma8oCrLk2SndvF14EgUAADQLgrC7YQwmb8ay2qPbicZufSoEdBMCAECzIAgpwOw7kNEnsP7cge7c6GgBdqVEo4EoBACAf4MgpIbjlMXSlHjFs5xu26KAjTnbYg9EkIQAAPAvEITUwO3sHeLmiw5vJdTdd+cz6CYEAICmIAgpwx4ymsZza7h6stu2KIRHMgEAQBMQhFRynPam+MoxVVVJ92xOyMevlWrUEIUAAKADgpBKdCd3+3GzRIe+Qp14Bojh3Fiopx12rwqSEAAA/gFBifczTAAAIABJREFUSDFOxAsIxxqu/dY9m4MH1gMAgB4IQqphGO+Vd+svHlFVFnfD1oQCLL5E0w0bAgAAcwFBSD26s4f9uJk1B7cgTZdHVDQfv15OKCAKAQDgbxCEJoEzKg5nssRd30DqyEB+DlhyJbSOAgDAXyAITQOGOb78jvjiL8qywq7eVIwARhMCAMA/IAhNBd3J3X7ibNGhL5FG3aUbEvJx6CYEAAAtCEITwhnxHM5xqD9/qEu3EuGBJVcRsu67oQ0AAJg0CEJTgmFOM1dIbp5tfJzRdRvh2KABTtjNCmgdBQAAhCAITQ3OcXR88W3R4a80cmnXbUXIx+JLoXUUAAAQgiA0Qazg4Uy/gXUnv++6TQgFOFwvAwAAJAhCU+Q4ZVHjkyxFxvUuWv9IdyyjhhAru2j1AABgTiAITRHGsHV69b3GP/erayu7Yv22NBTmgiWVwUkhAABAEJoqhmc/xojnqvdv7KIHFgoFOHQTAgAAgiA0ZcxRk3A7R/G5g12xcnhILwAAkCAITRiGOb2yXJJ8Uf7ontHXHe6G5dYRokajrxgAAMwMBKFJwzkOTq9+IDq4RV1fY9w12+BouDuWUAatowAAawdBaOqYvsF2wyeIDm4x+sN7hXw8HlpHAQBWD4LQDNiPm0Vo1PXnjdxZCA/pBQAABEFoHnDcec4qya3z8ofJRlzrYBesSEJUyIy4SgAAMD8QhOYB5zg6z/1IdOgrVXWZsdZJw1CEB34VBlEAAKwbBKHZYHj158a+XP3jekKpMNY6hXxoHQUAWDsIQnPCiZps49az1ni3IYWH9AIAAAShmeHNWKbIfyC58adR1hbshNUpiCIJZCEAwHpBEJoZjMlyfuPT+nMHjPLMQgyhSA8cWkcBANYMgtD80J09eLNW1vzvc6PcklsowGA0IQDAmkEQmiXbfoM5UVOq9n5CKDp7k7QYAXYZghAAYMUgCM0VN2a6jXtv0dGvO3nHmX4OmJpA+WLIQgCAlYIgNGO8GctUFUX1l37p5HrgSRQAAGsGQWjGMBuG84J1kptnpSnxnVkPdBMCAKwZBKF5o9nzXBaur/ttt6Igu8MrGS3ALpdoIAkBANYJgtDs2Xj05s1cUb1vvbqmomNr6M3B2HQsuxaiEABgjSAILYGt/xBuzPSqPWs1soaOrQG6CQEAVguC0EJwoqYw/QZW713XsTuRCuGRTAAAawVBaDkcJy+iO3tU7/8MadTtXXa0AL9aooF+QgCAFYIgtCAY5vjyO0ijrjn8VXsHF/LZyJWFpddAEgIArA4EoUXBaHTn19eoqsrqzuxv77LQTQgAsE4QhJYGYzBdFvxXlnFTfPVEuxYUCrB4eEgvAMD6QBBaINzO3vXN/5NcOyW5c9HwpYR8PKmMUEEUAgCsDAShZaI5OLss+az+zH75w2QDF3GxRb05WEoVtI4CAKwLBKHForv2cJ6/tubgFsWTTAMXgUEUAAArBEFoyRie/Zxmrazet0FZVmjI/EI+Fl8CbaMAAOsCQWjhbP2HOExaWLVzlbK87SyM4uM3K4jGdo9CBAAAMwZBaPnYoUKHyQurvlulLC1ofU4HBurviN2phNZRAIAVgSC0CuxBUY6TF1V9/1GbWSjkQzchAMC6QBBaC9agSEOyUCjAoZsQAGBVIAitCGtQpOOUxVU7V7eShZEe2N0qQqrqvqoAAIBaEITWhTUwwnHakqqdq5UlT5qdgU1HIU7YzQpoHQUAWAsIQqvDColwnLak8rtVime5zc4QI8CuQOsoAMBq0KkuAFCAFRKBEKre81+XRRtsevTR+61QgK9OhiEUAADKaKQNGplYIxVrpA2ETKKWiqtEDVW1DfX1EsLLf/SEWONuDoLQSrFCIhDCqnZ95LxgHcPTT/dXw92wTBEhViKuDVXVAQAsjUYuJXTiTSNr0EgbNFKxRirWyBoIaYNu+CFbjtKW00DjiGh2ZYhbrLZTMe3YHI6jg0tvJzej1wZBaL1YIaMwuk3V7rXOsz9g+g3STreloSGu2LUy4rleGIXlAQBMHUFopGKNpF4jqddI6zUSsVoqJqTNRx1mw8TZXJzNwVmcv/7D5uIsDo3nKmdwC1V2uUpOptwuVWp3s56DcCyYhwXysGAnLIiHjXfC7P/+Xi4Wi43+d0AQWjXbwHDneR/X7NvgOO1N1sAI7fQYAR5fonmuF43C2gAAVCGUir8CjAy5hjq1tJ6QiNXaKZJ6cgaczcXZXNyOi7PtcTt73M4eZ3Ho7p5/Zx4ZeByczUX4X8eTRjXKqiUeiIgHNcQDEfHgGappJAIcsQFOWKAAW8rDdjthHqxu/XshCK0ds0+gy5LPqnat0UjFdiMmkhOFfOw/N+B6GQAsENEoU4trNQ11GkmdWlKvaajTiEV//UdSr2moVTfUIbUKZ3NxO/t/JZyDM13gTSOn/PVbe4S10W6kJtDjeiLjKfFApHkgIjJqiEIJ0df+r7O9Rf2xICfMm9vWWroYBCFANgJv16VbqnauVjfU2Y99BSE01BXLFxPVjciZSXVxAACDEWqVRlyrFos0YpG6oU5TX/NP5olFZNQhGp1mZ49zebidPc5xoNnZ4xxHukdvGscet3PAOQ40Lg9jdvyMTNSIMkVEShWRVUtkiojUasKegQJ5WIAjFueJfRiCB/IwWxNrbIIgBAghRHfmuy79qmrXGnVtJW/6W3ScNsIdSyjVTPWCATYAmApCqVBVl/0VcmKRul6kkdSp62s04lp1Q61GLCIUjWSS4VwejeOA2zvRndzwXn1xO3sal4dz7HE7B8yGYcSSahpRRg2RKSIyRH+1drLoKIiHBTth4W7Ygn54AA+zM/mcMfkCQXeh2fPclm6p3v9Z1Z5PnOeujhEw40uIqV5UlwWANSEaZeraKnVDrbq2SiMWqeuq1WKRuq5aIxap62oIlUJq7/RXyHF5NHse3UXA7BOEcx1pHEecy8PZnC4tT6JCWSIiQ0RkioiMGuKBiJCpUCAPI5Pv5T54sBNmjs1IEITgHxiT5fLGJ6Jfd1RsXzl6+rrXchyprggAS0MoFeraSnVdtVp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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Declaramos las variables que vamos a seguir\n",
    "# Función ideal que queremos aproximar\n",
    "f_regression(x)=(x<1) ? exp(-x)-4 : log(x)\n",
    "data_set_size = 5 \n",
    "n = data_set_size # Número de neuronas \n",
    "                  # coincide con el tamaño del conjunto\n",
    "#Partición homogénea del dominio [-3,3]\n",
    "K_range = 3\n",
    "X_train= Vector(LinRange(-K_range, K_range, n)) \n",
    "Y_train = map(f_regression, X_train) # Imágenes de la partición\n",
    "\n",
    "M = 1\n",
    "# USO DE LA FUNCIÓN DE INICIALIZACIÓN DE LOS PESOS\n",
    "h = nn_from_data(X_train, Y_train, n, M)\n",
    "\n",
    "# Imprimimos la red neuronal \n",
    "display(Text(\"La red neuronal obtenida es :\"))\n",
    "println(h)\n",
    "\n",
    "# Vamos a ver cómo aproxima los resultados \n",
    "# Función que dado un punto lo evalúa con forward_propagation\n",
    "# y la función de activación Rampa\n",
    "evaluate(x)=forward_propagation(h,\n",
    "        RampFunction,x)\n",
    "\n",
    "plot(x->evaluate([x])[1],\n",
    "     -K_range,K_range, \n",
    "     label=\"red neuronal n=$n\")\n",
    "plot!(f_regression,\n",
    "    label=\"f ideal\",\n",
    "    title=\"Comparativa función ideal y red neuronal n=$n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Funciones de activación \n",
    "\n",
    "### Funciones de activación no dependientes de parámetros\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CosineSquasher(0.6963141756074113) = 0.8206971218447603\n",
      "RampFunction(0.708936898471023) = 0.708936898471023\n",
      "ReLU(0.279572614615742) = 0.279572614615742\n",
      "Sigmoid(0.6463954880294331) = 0.6561977350585728\n",
      "HardTanh(0.27377994734523636) = 0.27377994734523636\n"
     ]
    }
   ],
   "source": [
    "funciones_activacion = [\n",
    "    CosineSquasher,\n",
    "    RampFunction,\n",
    "    ReLU, \n",
    "    Sigmoid,   \n",
    "    HardTanh\n",
    "]\n",
    "\n",
    "for σ in funciones_activacion\n",
    "    x = rand()\n",
    "    println(\"$(σ)($x) = $(σ(x))\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Funciones de activación dependientes de parámetros\n",
    "\n",
    "Existen funciones de activación que depende de parámetros, podemos definirlas eficientemente a partir de macros: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f(4.027026570178562) = 4.027026570178562\n",
      "f(4.380146279765949) = 4.380146279765949\n",
      "f(-2.5822478995523013) = -0.025822478995523014\n"
     ]
    }
   ],
   "source": [
    "# Concretamos los parámetros de los que dependen\n",
    "# de macros\n",
    "umbral = @ThresholdFunction(x->x,0)   \n",
    "indicadora = @IndicatorFunction(0)\n",
    "lRelu = @LReLU(0.01)\n",
    "\n",
    "# Evaluamos en puntos concretos\n",
    "dependientes_parametro = [umbral, indicadora, lRelu]\n",
    "for σ in dependientes_parametro\n",
    "    x = (rand()-0.5)*10\n",
    "    println(\"$(σ)($x) = $(σ(x))\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Backpropagation \n",
    "Ejemplo de uso de Backpropagation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "En error en la iteración 0 es: 1.334625428920788\n",
      "El error en la iteración 1 es: 0.14080024193105276\n",
      "El error en la iteración 2 es: 0.12226659859194122\n",
      "El error en la iteración 3 es: 0.12146473358191419\n"
     ]
    }
   ],
   "source": [
    "n = 3 # número de neuronas \n",
    "    η = 0.005  # queremos que reduzca sin pasarse, de ahí que sea \"\"pequeño\"\" el learning rate\n",
    "    tol = 0.5  # rango de error que permitimos ya que puede existir casos en los que el η sea demasiado grande\n",
    "    data_set_size = n\n",
    "    cosin(x,y)=cos(x)+sin(y) # funcion ideal\n",
    "    h = RandomWeightsNN(2,n, 1) # 2 dimensión entrada 1 dimensión de salida \n",
    "    X_train = (rand(Float64, (data_set_size, 2)))*3\n",
    "    Y_train = map(v->cosin(v...),eachrow(X_train))\n",
    "    disminuye_error = 0.0\n",
    "    error = error_in_data_set(\n",
    "            X_train,\n",
    "            Y_train,\n",
    "            x->forward_propagation(h,RampFunction,x)\n",
    "        )\n",
    "    println(\"En error en la iteración 0 es: $error\")\n",
    "    for i in 1:n   \n",
    "        backpropagation!(h, X_train, Y_train, RampFunction, derivativeRampFunction, n)\n",
    "\n",
    "        error = error_in_data_set(\n",
    "            X_train,\n",
    "            Y_train,\n",
    "            x->forward_propagation(h,RampFunction,x)\n",
    "        )\n",
    "        println(\"El error en la iteración $i es: $error\")\n",
    "    end"
   ]
  }
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