{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "361PFs2xFbvk"
      },
      "source": [
        "# Importando a biblioteca NumPy\n",
        "import numpy as np\n",
        "import sys"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2rkWTcX7FeX1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a6e08efa-a4a1-415e-e521-ad758e588372"
      },
      "source": [
        "# Lendo o número de incógnitas\n",
        "n = int(input('Indique o número de variáveis do seu problema: '))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Indique o número de variáveis do seu problema: 3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "de9YJU4EFfrb"
      },
      "source": [
        "# Montando a matriz de tamanho N x N+1 e inicializando com zero\n",
        "# para armazenar a matriz aumentada\n",
        "a = np.zeros((n,n+1))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NHt6IFAEFhGV"
      },
      "source": [
        "# Montando a matriz de tamanho N x 1 e inicializando com zero\n",
        "# para armazenar o vetor solução\n",
        "x = np.zeros(n)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GTal5qp_FjVb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "76d94491-5d48-4885-fcaa-9ee93df6353c"
      },
      "source": [
        "# Lendo os coeficientes da matriz aumentada\n",
        "print('Enter 1Augmented Matrix Coefficients:')\n",
        "for i in range(n):\n",
        "    for j in range(n+1):\n",
        "        a[i][j] = float(input( 'a['+str(i)+']['+ str(j)+']='))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Enter 1Augmented Matrix Coefficients:\n",
            "a[0][0]=1\n",
            "a[0][1]=1\n",
            "a[0][2]=1\n",
            "a[0][3]=6\n",
            "a[1][0]=1\n",
            "a[1][1]=-2\n",
            "a[1][2]=2\n",
            "a[1][3]=3\n",
            "a[2][0]=-2\n",
            "a[2][1]=3\n",
            "a[2][2]=0\n",
            "a[2][3]=4\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2iMSGJc3FlIv"
      },
      "source": [
        "# Aplicando o método de Gauss\n",
        "for i in range(n):\n",
        "    if a[i][i] == 0.0:\n",
        "        sys.exit('Divide by zero detected!')\n",
        "\n",
        "    for j in range(i+1, n):\n",
        "        ratio = a[j][i]/a[i][i]\n",
        "\n",
        "        for k in range(n+1):\n",
        "            a[j][k] = a[j][k] - ratio * a[i][k]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0RuJccoUFoA5"
      },
      "source": [
        "# Aplicando o Back Substitution\n",
        "x[n-1] = a[n-1][n]/a[n-1][n-1]\n",
        "\n",
        "for i in range(n-2,-1,-1):\n",
        "    x[i] = a[i][n]\n",
        "\n",
        "    for j in range(i+1,n):\n",
        "        x[i] = x[i] - a[i][j]*x[j]\n",
        "\n",
        "    x[i] = x[i]/a[i][i]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rBfjovrdFqFL",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "71ec5b19-67ed-414e-d3c0-b4771087de65"
      },
      "source": [
        "# Mostrando a solução\n",
        "print('\\nRequired solution is: ')\n",
        "for i in range(n):\n",
        "    print('X%d = %0.2f' %(i,x[i]), end = '\\t')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Required solution is: \n",
            "X0 = 1.00\tX1 = 2.00\tX2 = 3.00\t"
          ]
        }
      ]
    }
  ]
}