高斯列主元消去法以c++实现

肺炎期间上网课，学习工程与科学计算的一个作业
代码通过c++进行实现
借鉴了大佬的算法思想，原帖地址https://blog.youkuaiyun.com/qq_26025363/article/details/53044843
解决了几个问题，一个是原来代码输入偶数数组结果有误，另外是输出的数组第一列不为零。如有问题或建议欢迎指正

#include <iostream>
#include <cmath>
using namespace std;

const int n = 4;
//交换2个数的大小函数模板
template <class T>
void Inverse(T *a, T *b)
{
    T c;
    c = *a;
    *a = *b;
    *b = c;
}

//高斯列主元素消元法
void gaussLine(double a[n][n], double b[n])
{

    int i, j, k;
    int row, col;
    for (k = 0; k < n - 1; k++) //k是列 i是行
    {
        double maxnum = 0;
        //找出消元列中最大的那个元素所在的位置
        for (i = k; i < n; i++)
            if (fabs(a[i][k]) > maxnum)
            {
                maxnum = fabs(a[i][k]);
                // cout << "maxnum " << maxnum << endl;
                row = i;
                col = k;
            }

        //如果该对角线元素是0，同样不能用高斯消元法来求解
        if (a[row][row] == 0)
        {
            cout << "GaussLine can't solve" << endl;
            return;
        }
        //将找出的行进行交换
        if (k != row)
            for (i = 0; i < n; i++)
            {

                Inverse(a[row] + i, a[k] + i);
            }
        Inverse((b + k), (b + row));
        //消元过程
        double c[n];
        for (j = k + 1; j < n; j++)
        {
            c[j] = a[j][k] / a[k][k];
        }
        for (i = k + 1; i < n; i++)
        {
            for (j = 0; j < n; j++)
            {
                a[i][j] = a[i][j] - c[i] * a[k][j];
            }
            b[i] = b[i] - c[i] * b[k];
        }
    }

    double x[n];
    x[n - 1] = b[n - 1] / a[n - 1][n - 1];
    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];
    }
    //打印输出
    for (i = 0; i < n; i++)
        cout << " x "
             << "[" << i << "]=" << x[i] << endl;

    int i1, j1;
    for (i1 = 0; i1 < n; i1++)
    {
        for (j1 = 0; j1 < n; j1++)
            cout << a[i1][j1] << '\t';
        cout << endl;
    }
}
int main()
{
    double a[4][4] = {1.1348, 3.8326, 1.1651, 3.4017,
                      0.59301, 1.7875, 2.5330, 1.5435,
                      3.4129, 4.9317, 8.7643, 1.3142,
                      1.2371, 4.9998, 10.6721, 0.0147};
    int i, j;

    double b[4] = {9.5342, 6.3941, 18.4231, 16.9237};
    gaussLine(a, b);
    cin.get();
    return 0;
}

上网课really不舒服，想念学校呜呜呜~