Atividade_4_2.ipynb

{
 "cells": [
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Atividade 4.2\n",
    "\n",
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algoritmos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "dotnet_interactive": {
     "language": "csharp"
    },
    "polyglot_notebook": {
     "kernelName": "csharp"
    },
    "vscode": {
     "languageId": "polyglot-notebook"
    }
   },
   "outputs": [],
   "source": [
    "using System.Linq;\n",
    "\n",
    "// Função para calcular a matriz G\n",
    "public double[,] CalcularG(double[,] x,int n_linhas,int n_colunas,int q_neuronios,double theta,double[,] neuronios,double[] sigmas,double [,] G){\n",
    "\n",
    "    for (int i = 0; i < n_linhas; i++){\n",
    "\n",
    "            for (int j = 0; j < q_neuronios; j++)\n",
    "            {\n",
    "                \n",
    "                double quadradoDaDistancia = 0.0;\n",
    "                for (int k = 0; k < n_colunas; k++)\n",
    "                {\n",
    "                    quadradoDaDistancia += Math.Pow(x[i, k] - neuronios[j, k], 2);\n",
    "                }\n",
    "                double phi = Math.Exp(-1 / (2 * Math.Pow(sigmas[j], 2)) * quadradoDaDistancia);\n",
    "\n",
    "                \n",
    "                G[i, j] = phi;\n",
    "            }\n",
    "            \n",
    "            G[i, q_neuronios] = theta;\n",
    "    }\n",
    "\n",
    "    return G;\n",
    "\n",
    "}\n",
    "\n",
    "// Função para transpor uma matriz\n",
    "static double[,] Transpor(double[,] G)\n",
    "{\n",
    "    int n_linhas = G.GetLength(0);\n",
    "    int n_colunas = G.GetLength(1);\n",
    "    double[,] GT = new double[n_colunas, n_linhas];\n",
    "    for (int i = 0; i < n_colunas; i++)\n",
    "    {\n",
    "        for (int j = 0; j < n_linhas; j++)\n",
    "        {\n",
    "            GT[i, j] = G[j, i];\n",
    "        }\n",
    "    }\n",
    "    return GT;\n",
    "}\n",
    "\n",
    "// Função para multiplicar duas matrizes\n",
    "static double[,] MultiplicarMatrizes(double[,] matriz1, double[,] matriz2)\n",
    "{\n",
    "    int n_linhas_matriz1 = matriz1.GetLength(0);\n",
    "    int n_colunas_matriz1 = matriz1.GetLength(1);\n",
    "    int n_colunas_matriz2 = matriz2.GetLength(1);\n",
    "    double[,] matriz_multiplicada = new double[n_linhas_matriz1, n_colunas_matriz2];\n",
    "    for (int i = 0; i < n_linhas_matriz1; i++)\n",
    "    {\n",
    "        for (int j = 0; j < n_colunas_matriz2; j++)\n",
    "        {\n",
    "            for (int k = 0; k < n_colunas_matriz1; k++)\n",
    "            {\n",
    "                matriz_multiplicada[i, j] += matriz1[i, k] * matriz2[k, j];\n",
    "            }\n",
    "        }\n",
    "    }\n",
    "    return matriz_multiplicada;\n",
    "}\n",
    "\n",
    "//Função para obter a inversa com base no pivoteamento de Gauss\n",
    "public static double[,] ObterInversa(double[,] matriz)\n",
    "{\n",
    "    int tamanho = matriz.GetLength(0);\n",
    "\n",
    "    if (tamanho != matriz.GetLength(1))\n",
    "    {\n",
    "        throw new ArgumentException(\"A matriz deve ser quadrada para calcular a inversa.\");\n",
    "    }\n",
    "\n",
    "    double[,] extendida = new double[tamanho, 2 * tamanho];\n",
    "\n",
    "    for (int i = 0; i < tamanho; i++)\n",
    "    {\n",
    "        for (int j = 0; j < tamanho; j++)\n",
    "        {\n",
    "            extendida[i, j] = matriz[i, j];\n",
    "            extendida[i, j + tamanho] = (i == j) ? 1.0 : 0.0;\n",
    "        }\n",
    "    }\n",
    "\n",
    "    for (int i = 0; i < tamanho; i++)\n",
    "    {\n",
    "        int maxIndex = i;\n",
    "        double maxAbsValue = Math.Abs(extendida[i, i]);\n",
    "\n",
    "        for (int k = i + 1; k < tamanho; k++)\n",
    "        {\n",
    "            if (Math.Abs(extendida[k, i]) > maxAbsValue)\n",
    "            {\n",
    "                maxIndex = k;\n",
    "                maxAbsValue = Math.Abs(extendida[k, i]);\n",
    "            }\n",
    "        }\n",
    "\n",
    "        if (maxIndex != i)\n",
    "        {\n",
    "            for (int j = 0; j < 2 * tamanho; j++)\n",
    "            {\n",
    "                double temp = extendida[i, j];\n",
    "                extendida[i, j] = extendida[maxIndex, j];\n",
    "                extendida[maxIndex, j] = temp;\n",
    "            }\n",
    "        }\n",
    "\n",
    "        for (int k = 0; k < tamanho; k++)\n",
    "        {\n",
    "            if (k != i)\n",
    "            {\n",
    "                double factor = extendida[k, i] / extendida[i, i];\n",
    "                for (int j = i; j < 2 * tamanho; j++)\n",
    "                {\n",
    "                    extendida[k, j] -= factor * extendida[i, j];\n",
    "                }\n",
    "            }\n",
    "        }\n",
    "    }\n",
    "\n",
    "    for (int i = 0; i < tamanho; i++)\n",
    "    {\n",
    "        double divisor = extendida[i, i];\n",
    "        for (int j = 0; j < 2 * tamanho; j++)\n",
    "        {\n",
    "            extendida[i, j] /= divisor;\n",
    "        }\n",
    "    }\n",
    "\n",
    "    double[,] inversa = new double[tamanho, tamanho];\n",
    "    for (int i = 0; i < tamanho; i++)\n",
    "    {\n",
    "        for (int j = 0; j < tamanho; j++)\n",
    "        {\n",
    "            inversa[i, j] = extendida[i, j + tamanho];\n",
    "        }\n",
    "    }\n",
    "\n",
    "    return inversa;\n",
    "}\n",
    "\n",
    "//Método para printar a matriz\n",
    "public void PrintarMatriz(double[,] G, string descricao){\n",
    "    \n",
    "    Console.WriteLine($\"==================================================\");\n",
    "    Console.WriteLine($\"===================={descricao}===================\");\n",
    "    int n_linhas = G.GetLength(0);\n",
    "    int n_colunas = G.GetLength(1);\n",
    "    Console.WriteLine($\"=================={n_linhas} linhas e {n_colunas} colunas ===================\");\n",
    "\n",
    "    for (int i = 0; i < n_linhas; i++)\n",
    "    {\n",
    "        for (int j = 0; j < n_colunas; j++)\n",
    "        {\n",
    "             Console.WriteLine($\"G_{i+1}_{j+1}:{G[i,j]}\");\n",
    "        }\n",
    "    }\n",
    "}\n",
    "\n",
    "//Funçao que calcula o erro quadrado médio\n",
    "public double ErroQuadrado(double[,] w, double[,] G, double[,] d){\n",
    "    \n",
    "    Console.WriteLine($\"==================================================\");\n",
    "    Console.WriteLine($\"====================Iniciando Calculo do Erro===================\");\n",
    "    Console.WriteLine($\"==================================================\");\n",
    "\n",
    "    int n_linhas = G.GetLength(0);\n",
    "    int n_colunas= G.GetLength(1);\n",
    "    double erroQuadradoTotal = 0;\n",
    "    for (int i = 0; i < n_linhas; i++){\n",
    "        double y = 0.0;\n",
    "        for (int j = 0; j < n_colunas; j++)\n",
    "        {\n",
    "            y += w[j,0] * G[i, j];\n",
    "        }\n",
    "        Console.WriteLine($\"Saída para o exemplo {i+1}: {y}\");\n",
    "\n",
    "        double erroQuadrado = Math.Pow(d[i,0]-y,2)/2;\n",
    "        Console.WriteLine($\"Erro entrada {i+1}: {erroQuadrado}\");\n",
    "        erroQuadradoTotal+=erroQuadrado;\n",
    "    }\n",
    "    return erroQuadradoTotal;\n",
    "}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Entradas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "dotnet_interactive": {
     "language": "csharp"
    },
    "polyglot_notebook": {
     "kernelName": "csharp"
    },
    "vscode": {
     "languageId": "polyglot-notebook"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_linhas:5, n_colunas:2, q_neuronios:3\r\n"
     ]
    }
   ],
   "source": [
    "//Entradas\n",
    "int c = 1;\n",
    "int n_linhas = 5;\n",
    "int n_colunas = 2;\n",
    "double[,] x = {\n",
    "   {0,1},\n",
    "   {1,2},\n",
    "   {0,3},\n",
    "   {2,3},\n",
    "   {1,3},\n",
    "};\n",
    "\n",
    "\n",
    "//valor desejado\n",
    "//iniciando vetor da variável resposta\n",
    "double[,] d = {\n",
    "   {0},\n",
    "   {0},\n",
    "   {1},\n",
    "   {1},\n",
    "   {1}\n",
    "};\n",
    "\n",
    "int q_neuronios = 3;\n",
    "double theta = 1;\n",
    "\n",
    "Console.WriteLine($\"n_linhas:{n_linhas}, n_colunas:{n_colunas}, q_neuronios:{q_neuronios}\");\n",
    "//selecao de neuronios\n",
    "double[,] neuronios = {\n",
    "   {0,0},\n",
    "   {1,1},\n",
    "   {3,3}\n",
    "};\n",
    "\n",
    "//matriz de ativacoes\n",
    "double [,] G = new double [n_linhas,q_neuronios+1];\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Treinamento"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "dotnet_interactive": {
     "language": "csharp"
    },
    "polyglot_notebook": {
     "kernelName": "csharp"
    },
    "vscode": {
     "languageId": "polyglot-notebook"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sigmas_0:5\n",
      "sigmas_1:5\n",
      "sigmas_2:5\n"
     ]
    }
   ],
   "source": [
    "//atribuicao de sigmas\n",
    "double[] sigmas = new double[q_neuronios];\n",
    "for(int j= 0; j<q_neuronios;j++){\n",
    "    sigmas[j] = 5;\n",
    "    Console.WriteLine($\"sigmas_{j}:{sigmas[j]}\");\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "dotnet_interactive": {
     "language": "csharp"
    },
    "polyglot_notebook": {
     "kernelName": "csharp"
    },
    "vscode": {
     "languageId": "polyglot-notebook"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================================================\n",
      "====================printando matriz G===================\n",
      "==================5 linhas e 4 colunas ===================\n",
      "G_1_1:0,9801986733067553\n",
      "G_1_2:0,9801986733067553\n",
      "G_1_3:0,7710515858035663\n",
      "G_1_4:1\n",
      "G_2_1:0,9048374180359595\n",
      "G_2_2:0,9801986733067553\n",
      "G_2_3:0,9048374180359595\n",
      "G_2_4:1\n",
      "G_3_1:0,835270211411272\n",
      "G_3_2:0,9048374180359595\n",
      "G_3_3:0,835270211411272\n",
      "G_3_4:1\n",
      "G_4_1:0,7710515858035663\n",
      "G_4_2:0,9048374180359595\n",
      "G_4_3:0,9801986733067553\n",
      "G_4_4:1\n",
      "G_5_1:0,8187307530779818\n",
      "G_5_2:0,9231163463866358\n",
      "G_5_3:0,9231163463866358\n",
      "G_5_4:1\n",
      "==================================================\n",
      "====================printando matriz GT===================\n",
      "==================4 linhas e 5 colunas ===================\n",
      "G_1_1:0,9801986733067553\n",
      "G_1_2:0,9048374180359595\n",
      "G_1_3:0,835270211411272\n",
      "G_1_4:0,7710515858035663\n",
      "G_1_5:0,8187307530779818\n",
      "G_2_1:0,9801986733067553\n",
      "G_2_2:0,9801986733067553\n",
      "G_2_3:0,9048374180359595\n",
      "G_2_4:0,9048374180359595\n",
      "G_2_5:0,9231163463866358\n",
      "G_3_1:0,7710515858035663\n",
      "G_3_2:0,9048374180359595\n",
      "G_3_3:0,835270211411272\n",
      "G_3_4:0,9801986733067553\n",
      "G_3_5:0,9231163463866358\n",
      "G_4_1:1\n",
      "G_4_2:1\n",
      "G_4_3:1\n",
      "G_4_4:1\n",
      "G_4_5:1\n",
      "==================================================\n",
      "====================printando matriz GTG===================\n",
      "==================4 linhas e 4 colunas ===================\n",
      "G_1_1:3,742037112307169\n",
      "G_1_2:4,056953684851963\n",
      "G_1_3:3,783758303516189\n",
      "G_1_4:4,310088641635534\n",
      "G_2_1:4,056953684851963\n",
      "G_2_2:4,411184173426821\n",
      "G_2_3:4,137552145311977\n",
      "G_2_4:4,693188529072065\n",
      "G_3_1:3,783758303516189\n",
      "G_3_2:4,137552145311977\n",
      "G_3_3:3,9238608552377414\n",
      "G_3_4:4,414474234944189\n",
      "G_4_1:4,310088641635534\n",
      "G_4_2:4,693188529072065\n",
      "G_4_3:4,414474234944189\n",
      "G_4_4:5\n",
      "==================================================\n",
      "====================printando matriz GTG_INV===================\n",
      "==================4 linhas e 4 colunas ===================\n",
      "G_1_1:13678,43543577625\n",
      "G_1_2:-19020,512467268138\n",
      "G_1_3:6852,685083311614\n",
      "G_1_4:12,115996181062524\n",
      "G_2_1:-19020,51246726603\n",
      "G_2_2:26666,516453070682\n",
      "G_2_3:-9479,096856313492\n",
      "G_2_4:-265,1331083752094\n",
      "G_3_1:6852,685083312554\n",
      "G_3_2:-9479,096856315857\n",
      "G_3_3:3482,48555416908\n",
      "G_3_4:-84,36685254215527\n",
      "G_4_1:12,115996178259541\n",
      "G_4_2:-265,13310837130734\n",
      "G_4_3:-84,36685254356638\n",
      "G_4_4:313,1067884424668\n",
      "==================================================\n",
      "====================printando matriz GTG_INV_GT===================\n",
      "==================4 linhas e 5 colunas ===================\n",
      "G_1_1:59,592877710088814\n",
      "G_1_2:-54,439009973191915\n",
      "G_1_3:-49,322017933794214\n",
      "G_1_4:65,4167668953895\n",
      "G_1_5:-21,248616698497376\n",
      "G_2_1:-79,40280843744597\n",
      "G_2_2:85,8380252561791\n",
      "G_2_3:58,854082189773976\n",
      "G_2_4:-93,46567635199347\n",
      "G_2_5:28,176377343491254\n",
      "G_3_1:26,403821082844473\n",
      "G_3_2:-24,115900669249555\n",
      "G_3_3:-28,748213982920248\n",
      "G_3_4:35,893043183285585\n",
      "G_3_5:-9,432749613953916\n",
      "G_4_1:0,04855530396235963\n",
      "G_4_2:-12,151610957256025\n",
      "G_4_3:12,85544315702947\n",
      "G_4_4:-0,14978763950864504\n",
      "G_4_5:0,39740013577295485\n",
      "==================================================\n",
      "====================printando vetor W===================\n",
      "==================4 linhas e 1 colunas ===================\n",
      "G_1_1:-5,1538677369020895\n",
      "G_2_1:-6,435216818728236\n",
      "G_3_1:-2,28792041358858\n",
      "G_4_1:13,10305565329378\n",
      "==================================================\n",
      "====================Iniciando Calculo do Erro===================\n",
      "==================================================\n",
      "Saída para o exemplo 1: -0,020654316064698364\n",
      "Erro entrada 1: 0,00021330038605022844\n",
      "Saída para o exemplo 2: 0,06165628947446855\n",
      "Erro entrada 2: 0,0019007490158797307\n",
      "Saída para o exemplo 3: 1,0643267207959006\n",
      "Erro entrada 3: 0,002068963504176877\n",
      "Saída para o exemplo 4: 1,0637162369429785\n",
      "Erro entrada 4: 0,0020298794250868863\n",
      "Saída para o exemplo 5: 0,8309550688700895\n",
      "Erro entrada 5: 0,014288094370358089\n",
      "Erro Quadrado Final: 0,020500986701551812\n"
     ]
    }
   ],
   "source": [
    "G= CalcularG(x ,n_linhas, n_colunas, q_neuronios, theta, neuronios, sigmas, G);\n",
    "PrintarMatriz(G,\"printando matriz G\");\n",
    "var GT = Transpor(G);\n",
    "PrintarMatriz(GT, \"printando matriz GT\");\n",
    "var GTG = MultiplicarMatrizes(GT,G);\n",
    "PrintarMatriz(GTG, \"printando matriz GTG\");\n",
    "var GTG_INV = ObterInversa(GTG);\n",
    "PrintarMatriz(GTG_INV, \"printando matriz GTG_INV\");\n",
    "var GTG_INV_GT = MultiplicarMatrizes(GTG_INV,GT);\n",
    "PrintarMatriz(GTG_INV_GT, \"printando matriz GTG_INV_GT\");\n",
    "var W = MultiplicarMatrizes(GTG_INV_GT,d);\n",
    "PrintarMatriz(W, \"printando vetor W\");\n",
    "var erro = ErroQuadrado(W, G, d);\n",
    "Console.WriteLine($\"Erro Quadrado Final: {erro}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Referências\n",
    "Matéria de metaheurísticas e aplicações - PPGMNE\n",
    "\n",
    "Siqueira, P.H., \"Metaheurísticas e Aplicações\". Disponível em: <https://paulohscwb.github.io/metaheuristicas/>, Janeiro de 2021.\n",
    "\n",
    "### Autor\n",
    "<a href=\"https://www.linkedin.com/in/hesauhugocavalcanti/\">Hesau Hugo</a>\n",
    "\n",
    "### Professor\n",
    "<a href=\"https://www.linkedin.com/in/paulo-henrique-siqueira-83080130/\">Paulo Henrique Siqueira</a>"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
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