【C/C++】高斯列主元消元法求解线性方程组

初始增广矩阵：

矩阵当前状态：

3.0000 -1.0000 1.0000 4.0000
1.0000 1.0000 1.0000 6.0000
2.0000 3.0000 -1.0000 12.0000

方程组的解：
x1 = 1.0000
x2 = 3.0000
x3 = 2.0000

验证结果：
3x1 - x2 + x3 = 4.0000 (预期4)
x1 + x2 + x3 = 6.0000 (预期6)
2x1 + 3x2 - x3 = 12.0000 (预期12)

#include<stdio.h>
#include<math.h>#define MAX_MATRIX 10/*** @brief SwapRow 进行行交换* @param m 待计算的矩阵*        row 待交行的行*        max_row 待交换的另一行*        n 矩阵行数*/
static void SwapRow(double m[][MAX_MATRIX], int row, int max_row, int n) {double swap;for (int k = row; k <= n; k++) {swap = m[row][k];m[row][k] = m[max_row][k];m[max_row][k] = swap;}
}/*** @brief 组上三角矩阵* @param m 待计算的矩阵*        n 矩阵行数*/
static void SelectColE(double m[][MAX_MATRIX], int n) {int max_row_e = 0;  //主元所在行double ratio = 0;   //消元因数for (int j = 0; j < n; j++) {max_row_e = j;for (int i = j; i < n; i++) {if (fabs(m[i][j]) > fabs(m[max_row_e][j])) {max_row_e = i;}}if (max_row_e != j) {SwapRow(m, j, max_row_e, n);   //与最大主元所在行交换}//消元for (int i = j + 1; i < n; i++) {ratio = m[i][j] / m[j][j];for (int k = j; k < n + 1; k++) {m[i][k] -= m[j][k] * ratio;}}}
}/*** @brief: Gauss 高斯列主元消元法求解线性方程(A*X = B)* @param: m 由于A|B组成的增广矩阵,X为待求的解*         n 求解的元数,n要小于MAX_MATRIX* @result:所求结果存放在m[][n]中*/
void Gauss(double m[][MAX_MATRIX], int n) {SelectColE(m, n);   // 列选主元并消元成上三角// 回代求解,结果存在m[][n]中for(int i = n - 1; i >= 0; i--) {for(int j = i + 1; j < n; j++) {m[i][n] -= m[i][j] * m[j][n];}m[i][n] /= m[i][i];}
}double a[3][MAX_MATRIX] = {{3,-1, 1, 4},  //A|B{1, 1, 1, 6},{2, 3,-1, 12}
};int main(int argc ,char **argv) {Gauss(a, 3);printf("%f,%f,%f\r\n",a[0][3], a[1][3], a[2][3]);return 0;
}