全主元高斯消元法 c语言实现

以下是C语言实现全主元高斯消元法的代码示例：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define N 100

int main()
{
    int n, i, j, k, p;
    double a[N][N], b[N], x[N], m, s, t;
    printf("请输入方程组的阶数n：");
    scanf("%d", &n);
    printf("请输入增广矩阵：\n");
    for (i = 1; i <= n; i++)
    {
        for (j = 1; j <= n + 1; j++)
        {
            scanf("%lf", &a[i][j]);
        }
    }
    for (k = 1; k <= n - 1; k++)
    {
        m = 0;
        for (i = k; i <= n; i++)
        {
            if (fabs(a[i][k]) > m)
            {
                m = fabs(a[i][k]);
                p = i;
            }
        }
        if (m == 0)
        {
            printf("系数矩阵奇异，无解！\n");
            exit(1);
        }
        if (p != k)
        {
            for (j = k; j <= n + 1; j++)
            {
                t = a[k][j];
                a[k][j] = a[p][j];
                a[p][j] = t;
            }
        }
        for (i = k + 1; i <= n; i++)
        {
            s = a[i][k] / a[k][k];
            for (j = k + 1; j <= n + 1; j++)
            {
                a[i][j] = a[i][j] - s * a[k][j];
            }
        }
    }
    if (a[n][n] == 0)
    {
        printf("系数矩阵奇异，无解！\n");
        exit(1);
    }
    x[n] = a[n][n + 1] / a[n][n];
    for (i = n - 1; i >= 1; i--)
    {
        s = 0;
        for (j = i + 1; j <= n; j++)
        {
            s = s + a[i][j] * x[j];
        }
        x[i] = (a[i][n + 1] - s) / a[i][i];
    }
    printf("方程组的解为：\n");
    for (i = 1; i <= n; i++)
    {
        printf("x[%d]=%lf\n", i, x[i]);
    }
    return 0;
}