Atividade1_1.ipynb

{
 "cells": [
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Atividade 1.1\n",
    "\n",
    "Classificação de padrões, conforme tabela abaixo: \n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algoritmo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "dotnet_interactive": {
     "language": "csharp"
    },
    "polyglot_notebook": {
     "kernelName": "csharp"
    },
    "vscode": {
     "languageId": "polyglot-notebook"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "public (double[] _w, double _theta) Perceptron(int n_iteracoes, int[][] ordem, double[] w ,double delta, double alpha, double theta,double[,] x, int n_linha, int n_colunas,double[] d){\n",
    "    \n",
    "    // lembrando que c# começa em zero por isso a variável c para corrigir o índice\n",
    "    int c = 1;\n",
    "\n",
    "    //Váriaveis necessárias para cálculo da atualização\n",
    "    double yEstrela =0;\n",
    "    double y=0;\n",
    "\n",
    "    //Critério de parada número de iterações\n",
    "    for(int i=0;i<n_iteracoes;i++){\n",
    "        \n",
    "        Console.WriteLine($\"Iteração:{i+c}\");\n",
    "\n",
    "        //loop nas linhas ou seja em cada entrada\n",
    "        foreach(var linha in ordem[i]){\n",
    "                  \n",
    "            Console.WriteLine($\"Entrada:{linha}\");\n",
    "\n",
    "            //zerando variáveis\n",
    "            yEstrela=0;\n",
    "            y=0;\n",
    "\n",
    "            //calculando somatório das variáveis da entrada\n",
    "            for(int coluna=0;coluna<n_colunas;coluna++){\n",
    "                Console.WriteLine($\"x_{linha-c}_{coluna}:{x[linha-c,coluna]}, w_{coluna}:{w[coluna]}\");\n",
    "                yEstrela += x[linha-c,coluna]*w[coluna];\n",
    "            }\n",
    "\n",
    "            //adicionando theta ao somatório\n",
    "            yEstrela = yEstrela + theta;\n",
    "            Console.WriteLine($\"yEstrela:{yEstrela}\");\n",
    "\n",
    "            //verificando y* e atualizando y (função de ativação)\n",
    "            if(yEstrela>delta){\n",
    "                y=1;\n",
    "            }else if(yEstrela<(-1)*delta){\n",
    "                y=-1;\n",
    "            }else{\n",
    "                y=0;\n",
    "            }\n",
    "\n",
    "            Console.WriteLine($\"y:{y}, d:{d[linha-c]}\");\n",
    "            //atualizando peso e tendencia apenas se y for diferente de d\n",
    "            if(y!=d[linha-c]){\n",
    "\n",
    "                for(int coluna=0;coluna<n_colunas;coluna++){\n",
    "                    w[coluna] = w[coluna]+alpha*d[linha-c]*x[linha-c,coluna];\n",
    "                    Console.WriteLine($\"w_{coluna}:{w[coluna]}\");\n",
    "                }   \n",
    "                theta = theta + alpha*d[linha-c];\n",
    "                Console.WriteLine($\"theta:{theta}\");\n",
    "            }\n",
    "\n",
    "            \n",
    "        }\n",
    "    }\n",
    "    \n",
    "    return (w,theta);\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": [],
   "source": [
    "// iniciando a matriz de entradas\n",
    "// lembrando que c# começa em zero por isso a variável c para corrigir o índice\n",
    "int c = 1;\n",
    "int n_linha = 4;\n",
    "int n_colunas = 2;\n",
    "double[,] x = new double[n_linha,n_colunas];\n",
    "x[1-c,1-c]=0.75;\n",
    "x[1-c,2-c]=0.75;\n",
    "x[2-c,1-c]=0.75;\n",
    "x[2-c,2-c]=0.25;\n",
    "x[3-c,1-c]=0.25;\n",
    "x[3-c,2-c]=0.75;\n",
    "x[4-c,1-c]=0.25;\n",
    "x[4-c,2-c]=0.25;\n",
    "\n",
    "\n",
    "//iniciando vetor da variável resposta\n",
    "double[] d = new double[n_linha];\n",
    "d[1-c]=0;\n",
    "d[2-c]=1;\n",
    "d[3-c]=1;\n",
    "d[4-c]=0;\n",
    "\n",
    "\n",
    "\n",
    "//delta alpha e theta iniciais\n",
    "double delta = 0.2;\n",
    "double alpha = 1;\n",
    "double theta = 0;\n",
    "\n",
    "//iniciando o vetor de pesos \n",
    "double[] w = new double[n_colunas];\n",
    "\n",
    "//lista contendo a ordem específica das entradas em cada iteração, usada para \"embaralhar\" e diversificar o treinamento\n",
    "int n_iteracoes = 6;\n",
    "int[][] ordem = new int[n_iteracoes][];\n",
    "ordem[1-c] = [1,2,3,4];\n",
    "ordem[2-c] = [1,4,3,2];\n",
    "ordem[3-c] = [4,2,3,1];\n",
    "ordem[4-c] = [1,2,3,4];\n",
    "ordem[5-c] = [1,4,3,2];\n",
    "ordem[6-c] = [4,2,3,1];"
   ]
  },
  {
   "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": [
      "Iteração:1\n",
      "Entrada:1\n",
      "x_0_0:0,75, w_0:0\n",
      "x_0_1:0,75, w_1:0\n",
      "yEstrela:0\n",
      "y:0, d:0\n",
      "Entrada:2\n",
      "x_1_0:0,75, w_0:0\n",
      "x_1_1:0,25, w_1:0\n",
      "yEstrela:0\n",
      "y:0, d:1\n",
      "w_0:0,75\n",
      "w_1:0,25\n",
      "theta:1\n",
      "Entrada:3\n",
      "x_2_0:0,25, w_0:0,75\n",
      "x_2_1:0,75, w_1:0,25\n",
      "yEstrela:1,375\n",
      "y:1, d:1\n",
      "Entrada:4\n",
      "x_3_0:0,25, w_0:0,75\n",
      "x_3_1:0,25, w_1:0,25\n",
      "yEstrela:1,25\n",
      "y:1, d:0\n",
      "w_0:0,75\n",
      "w_1:0,25\n",
      "theta:1\n",
      "Iteração:2\n",
      "Entrada:1\n",
      "x_0_0:0,75, w_0:0,75\n",
      "x_0_1:0,75, w_1:0,25\n",
      "yEstrela:1,75\n",
      "y:1, d:0\n",
      "w_0:0,75\n",
      "w_1:0,25\n",
      "theta:1\n",
      "Entrada:4\n",
      "x_3_0:0,25, w_0:0,75\n",
      "x_3_1:0,25, w_1:0,25\n",
      "yEstrela:1,25\n",
      "y:1, d:0\n",
      "w_0:0,75\n",
      "w_1:0,25\n",
      "theta:1\n",
      "Entrada:3\n",
      "x_2_0:0,25, w_0:0,75\n",
      "x_2_1:0,75, w_1:0,25\n",
      "yEstrela:1,375\n",
      "y:1, d:1\n",
      "Entrada:2\n",
      "x_1_0:0,75, w_0:0,75\n",
      "x_1_1:0,25, w_1:0,25\n",
      "yEstrela:1,625\n",
      "y:1, d:1\n",
      "Iteração:3\n",
      "Entrada:4\n",
      "x_3_0:0,25, w_0:0,75\n",
      "x_3_1:0,25, w_1:0,25\n",
      "yEstrela:1,25\n",
      "y:1, d:0\n",
      "w_0:0,75\n",
      "w_1:0,25\n",
      "theta:1\n",
      "Entrada:2\n",
      "x_1_0:0,75, w_0:0,75\n",
      "x_1_1:0,25, w_1:0,25\n",
      "yEstrela:1,625\n",
      "y:1, d:1\n",
      "Entrada:3\n",
      "x_2_0:0,25, w_0:0,75\n",
      "x_2_1:0,75, w_1:0,25\n",
      "yEstrela:1,375\n",
      "y:1, d:1\n",
      "Entrada:1\n",
      "x_0_0:0,75, w_0:0,75\n",
      "x_0_1:0,75, w_1:0,25\n",
      "yEstrela:1,75\n",
      "y:1, d:0\n",
      "w_0:0,75\n",
      "w_1:0,25\n",
      "theta:1\n",
      "Iteração:4\n",
      "Entrada:1\n",
      "x_0_0:0,75, w_0:0,75\n",
      "x_0_1:0,75, w_1:0,25\n",
      "yEstrela:1,75\n",
      "y:1, d:0\n",
      "w_0:0,75\n",
      "w_1:0,25\n",
      "theta:1\n",
      "Entrada:2\n",
      "x_1_0:0,75, w_0:0,75\n",
      "x_1_1:0,25, w_1:0,25\n",
      "yEstrela:1,625\n",
      "y:1, d:1\n",
      "Entrada:3\n",
      "x_2_0:0,25, w_0:0,75\n",
      "x_2_1:0,75, w_1:0,25\n",
      "yEstrela:1,375\n",
      "y:1, d:1\n",
      "Entrada:4\n",
      "x_3_0:0,25, w_0:0,75\n",
      "x_3_1:0,25, w_1:0,25\n",
      "yEstrela:1,25\n",
      "y:1, d:0\n",
      "w_0:0,75\n",
      "w_1:0,25\n",
      "theta:1\n",
      "Iteração:5\n",
      "Entrada:1\n",
      "x_0_0:0,75, w_0:0,75\n",
      "x_0_1:0,75, w_1:0,25\n",
      "yEstrela:1,75\n",
      "y:1, d:0\n",
      "w_0:0,75\n",
      "w_1:0,25\n",
      "theta:1\n",
      "Entrada:4\n",
      "x_3_0:0,25, w_0:0,75\n",
      "x_3_1:0,25, w_1:0,25\n",
      "yEstrela:1,25\n",
      "y:1, d:0\n",
      "w_0:0,75\n",
      "w_1:0,25\n",
      "theta:1\n",
      "Entrada:3\n",
      "x_2_0:0,25, w_0:0,75\n",
      "x_2_1:0,75, w_1:0,25\n",
      "yEstrela:1,375\n",
      "y:1, d:1\n",
      "Entrada:2\n",
      "x_1_0:0,75, w_0:0,75\n",
      "x_1_1:0,25, w_1:0,25\n",
      "yEstrela:1,625\n",
      "y:1, d:1\n",
      "Iteração:6\n",
      "Entrada:4\n",
      "x_3_0:0,25, w_0:0,75\n",
      "x_3_1:0,25, w_1:0,25\n",
      "yEstrela:1,25\n",
      "y:1, d:0\n",
      "w_0:0,75\n",
      "w_1:0,25\n",
      "theta:1\n",
      "Entrada:2\n",
      "x_1_0:0,75, w_0:0,75\n",
      "x_1_1:0,25, w_1:0,25\n",
      "yEstrela:1,625\n",
      "y:1, d:1\n",
      "Entrada:3\n",
      "x_2_0:0,25, w_0:0,75\n",
      "x_2_1:0,75, w_1:0,25\n",
      "yEstrela:1,375\n",
      "y:1, d:1\n",
      "Entrada:1\n",
      "x_0_0:0,75, w_0:0,75\n",
      "x_0_1:0,75, w_1:0,25\n",
      "yEstrela:1,75\n",
      "y:1, d:0\n",
      "w_0:0,75\n",
      "w_1:0,25\n",
      "theta:1\n",
      "Resultado: w_1:0,75 | w_2:0,25 | theta:1 | \n"
     ]
    }
   ],
   "source": [
    "//realização do treimanto passando os dados de entrada\n",
    "(double[] _w, double _theta) = Perceptron(n_iteracoes, ordem, w ,delta, alpha, theta, x, n_linha, n_colunas,d);\n",
    "\n",
    "//plotando pesos w e o theta do resultado do treinamento\n",
    "var resultado = \"\";\n",
    "for(int i =0;i<_w.Length;i++){\n",
    "    resultado += $\"w_{i+c}:{w[i]} | \";\n",
    "}\n",
    "resultado +=$\"theta:{_theta} | \";\n",
    "\n",
    "Console.WriteLine($\"Resultado: {resultado}\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Teste"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Algoritmo de Teste"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "dotnet_interactive": {
     "language": "csharp"
    },
    "polyglot_notebook": {
     "kernelName": "csharp"
    },
    "vscode": {
     "languageId": "polyglot-notebook"
    }
   },
   "outputs": [],
   "source": [
    "public void PerceptronTeste(double[,] x_teste,double[] w_teste, double theta_teste,int n_linha_teste,int n_colunas_teste,double[] d_teste,double delta_teste ){\n",
    "\n",
    "    double yEstrela=0;\n",
    "    double y=0;\n",
    "    double n_erros=0;\n",
    "    for(int linha=0;linha<n_linha_teste;linha++){\n",
    "\n",
    "        yEstrela=0;\n",
    "        y=0;\n",
    "        \n",
    "        //calculando somatório das variáveis da entrada\n",
    "        for(int coluna=0;coluna<n_colunas_teste;coluna++){\n",
    "            Console.WriteLine($\"x_teste_{linha}_{coluna}:{x_teste[linha,coluna]}, w_teste_{coluna}:{w_teste[coluna]}\");\n",
    "            yEstrela += x_teste[linha,coluna]*w_teste[coluna];\n",
    "        }\n",
    "\n",
    "        //adicionando theta ao somatório\n",
    "        yEstrela = yEstrela + theta_teste;\n",
    "        Console.WriteLine($\"yEstrela:{yEstrela}\");\n",
    "\n",
    "        if(yEstrela>delta_teste){\n",
    "            y=1;\n",
    "        }else if(yEstrela<(-1)*delta_teste){\n",
    "            y=-1;\n",
    "        }else{\n",
    "            y=0;\n",
    "        }\n",
    "\n",
    "        Console.WriteLine($\"y:{y}, d:{d_teste[linha]}\");\n",
    "        //Somando o número de erros ou seja, y diferente de d\n",
    "        if(y!=d_teste[linha]){\n",
    "\n",
    "            n_erros++;\n",
    "        }\n",
    "    }\n",
    "\n",
    "    var erro = n_erros/(double)n_linha_teste*100;\n",
    "    Console.WriteLine($\"n_erros:{n_erros},n_linhas_teste:{n_linha_teste}, erro:{erro} %\");\n",
    "\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "dotnet_interactive": {
     "language": "csharp"
    },
    "polyglot_notebook": {
     "kernelName": "csharp"
    },
    "vscode": {
     "languageId": "polyglot-notebook"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_teste_0_0:0,75, w_teste_0:0,75\n",
      "x_teste_0_1:0,75, w_teste_1:0,25\n",
      "yEstrela:1,75\n",
      "y:1, d:0\n",
      "x_teste_1_0:0,75, w_teste_0:0,75\n",
      "x_teste_1_1:0,25, w_teste_1:0,25\n",
      "yEstrela:1,625\n",
      "y:1, d:1\n",
      "x_teste_2_0:0,25, w_teste_0:0,75\n",
      "x_teste_2_1:0,75, w_teste_1:0,25\n",
      "yEstrela:1,375\n",
      "y:1, d:1\n",
      "x_teste_3_0:0,25, w_teste_0:0,75\n",
      "x_teste_3_1:0,25, w_teste_1:0,25\n",
      "yEstrela:1,25\n",
      "y:1, d:0\n",
      "n_erros:2,n_linhas_teste:4, erro:50 %\n"
     ]
    }
   ],
   "source": [
    "PerceptronTeste( x, _w, _theta,n_linha,n_colunas, d,delta)"
   ]
  },
  {
   "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>"
   ]
  }
 ],
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