程式碼實現

//
//  main.cpp
//  列選主元素消元法
//
//  Created by 劉國棟 on 2018/10/16.
//  Copyright © 2018年 LGD. All rights reserved.
//

#include <iostream>
#include <math.h>
#include<iomanip>
using namespace std;

const int n = 3;
void gaussin(double A[n][n], double B[n])
{
    int i = 0, j = 0, k = 0;
    int r = 0;                      //儲存交換的行變數
    for(k = 0; k < n - 1; k++)      //第k次消元
    {
        for( i = k + 1; i < n; i++) //尋找最大行
        {
            r = k;
            if(fabs(A[i][k]) > fabs(A[r][k]))
                r = i;
        }
        if(r != k && A[r][k] != 0)  //交換行資料
        {
            double temp;
            for(i = 0; i < n; i++)
            {
                temp = A[k][i];
                A[k][i] = A[r][i];
                A[r][i] = temp;
            }
            temp = B[k]; B[k] = B[r]; B[r] = temp;
        }
        for(i = k + 1; i < n; i++)   //消元過程
        {
            A[i][k] = A[i][k] / A[k][k];
        }
        for(i = k + 1; i < n; i++)
            for(j = k + 1; j < n; j++)
                A[i][j] = A[i][j] - A[i][k] * A[k][j];
        for(i = k + 1; i < n; i++)
            B[i] = B[i] - A[i][k] * B[k];
    }
    //解的儲存陣列
    double x[n];
    //先計算出最後一個未知數；
    x[n - 1] = B[n - 1] / A[n - 1][n - 1];
    //求出每個未知數的值
    for (i = n - 2; i >= 0; i--)
    {
        double sum = 0;
        for (j = i + 1; j < n; j++)
        {
            sum += A[i][j] * x[j];
        }
        x[i] = (B[i] - sum) / A[i][i];
    }
    
    cout << " the solution of the equations is:" << endl;
    cout << endl;
    for (i = 0; i < n; i++)
    {
        cout<< fixed << setprecision(15);
        cout <<"x"<<i+1<<"="<< x[i] << endl;
    }
}

int main(int argc, const char * argv[])
{
    double A[3][3] = { {4, -2, 4}, {-2, 17, 10}, {-4, 10, 9} };
    double B[3] = { 10, 3, 7};
    gaussin(A, B);
    return 0;
}