使用产生错误结果的数组进行矩阵乘法答案

【问题标题】：Matrix multiplication using array generating erronous results使用产生错误结果的数组进行矩阵乘法
【发布时间】：2019-03-27 07:32:13
【问题描述】：

以下代码将两个不同阶的矩阵相乘并返回结果即mat1 (6x3) * mat2 (3x6) 并在dest

中返回6x6矩阵

问题是结果与计算值不匹配。此外，如果您观察结果 mat2 正在改变其内容。

PS：迭代：3、0、1 mat1[3][1] = 0.000000 mat2[1][0] = 20.000000 目标[3][0] = 0.000000

mat2[1][0]的原始内容为零。

输出：

iterals: 0, 0, 0    mat1[0][0] = 10.000000  mat2[0][0] = 1.000000   dest[0][0] = 10.000000
iterals: 0, 0, 1    mat1[0][1] = 0.000000   mat2[1][0] = 0.000000   dest[0][0] = 10.000000
iterals: 0, 0, 2    mat1[0][2] = 0.000000   mat2[2][0] = 0.000000   dest[0][0] = 10.000000
iterals: 0, 1, 0    mat1[0][0] = 10.000000  mat2[0][1] = 0.000000   dest[0][1] = 0.000000
iterals: 0, 1, 1    mat1[0][1] = 0.000000   mat2[1][1] = 0.000000   dest[0][1] = 0.000000
iterals: 0, 1, 2    mat1[0][2] = 0.000000   mat2[2][1] = 0.000000   dest[0][1] = 0.000000
iterals: 0, 2, 0    mat1[0][0] = 10.000000  mat2[0][2] = 0.000000   dest[0][2] = 0.000000
iterals: 0, 2, 1    mat1[0][1] = 0.000000   mat2[1][2] = 1.000000   dest[0][2] = 0.000000
iterals: 0, 2, 2    mat1[0][2] = 0.000000   mat2[2][2] = 0.000000   dest[0][2] = 0.000000
iterals: 0, 3, 0    mat1[0][0] = 10.000000  mat2[0][3] = 0.000000   dest[0][3] = 0.000000
iterals: 0, 3, 1    mat1[0][1] = 0.000000   mat2[1][3] = 0.000000   dest[0][3] = 0.000000
iterals: 0, 3, 2    mat1[0][2] = 0.000000   mat2[2][3] = 0.000000   dest[0][3] = 0.000000
iterals: 0, 4, 0    mat1[0][0] = 10.000000  mat2[0][4] = 0.000000   dest[0][4] = 0.000000
iterals: 0, 4, 1    mat1[0][1] = 0.000000   mat2[1][4] = 0.000000   dest[0][4] = 0.000000
iterals: 0, 4, 2    mat1[0][2] = 0.000000   mat2[2][4] = 1.000000   dest[0][4] = 0.000000
iterals: 0, 5, 0    mat1[0][0] = 10.000000  mat2[0][5] = 0.000000   dest[0][5] = 0.000000
iterals: 0, 5, 1    mat1[0][1] = 0.000000   mat2[1][5] = 0.000000   dest[0][5] = 0.000000
iterals: 0, 5, 2    mat1[0][2] = 0.000000   mat2[2][5] = 0.000000   dest[0][5] = 0.000000
iterals: 1, 0, 0    mat1[1][0] = 0.000000   mat2[0][0] = 1.000000   dest[1][0] = 0.000000
iterals: 1, 0, 1    mat1[1][1] = 0.000000   mat2[1][0] = 0.000000   dest[1][0] = 0.000000
iterals: 1, 0, 2    mat1[1][2] = 0.000000   mat2[2][0] = 0.000000   dest[1][0] = 0.000000
iterals: 1, 1, 0    mat1[1][0] = 0.000000   mat2[0][1] = 0.000000   dest[1][1] = 0.000000
iterals: 1, 1, 1    mat1[1][1] = 0.000000   mat2[1][1] = 0.000000   dest[1][1] = 0.000000
iterals: 1, 1, 2    mat1[1][2] = 0.000000   mat2[2][1] = 0.000000   dest[1][1] = 0.000000
iterals: 1, 2, 0    mat1[1][0] = 0.000000   mat2[0][2] = 0.000000   dest[1][2] = 0.000000
iterals: 1, 2, 1    mat1[1][1] = 0.000000   mat2[1][2] = 1.000000   dest[1][2] = 0.000000
iterals: 1, 2, 2    mat1[1][2] = 0.000000   mat2[2][2] = 0.000000   dest[1][2] = 0.000000
iterals: 1, 3, 0    mat1[1][0] = 0.000000   mat2[0][3] = 0.000000   dest[1][3] = 0.000000
iterals: 1, 3, 1    mat1[1][1] = 0.000000   mat2[1][3] = 0.000000   dest[1][3] = 0.000000
iterals: 1, 3, 2    mat1[1][2] = 0.000000   mat2[2][3] = 0.000000   dest[1][3] = 0.000000
iterals: 1, 4, 0    mat1[1][0] = 0.000000   mat2[0][4] = 0.000000   dest[1][4] = 0.000000
iterals: 1, 4, 1    mat1[1][1] = 0.000000   mat2[1][4] = 0.000000   dest[1][4] = 0.000000
iterals: 1, 4, 2    mat1[1][2] = 0.000000   mat2[2][4] = 1.000000   dest[1][4] = 0.000000
iterals: 1, 5, 0    mat1[1][0] = 0.000000   mat2[0][5] = 0.000000   dest[1][5] = 0.000000
iterals: 1, 5, 1    mat1[1][1] = 0.000000   mat2[1][5] = 0.000000   dest[1][5] = 0.000000
iterals: 1, 5, 2    mat1[1][2] = 0.000000   mat2[2][5] = 0.000000   dest[1][5] = 0.000000
iterals: 2, 0, 0    mat1[2][0] = 0.000000   mat2[0][0] = 0.000000   dest[2][0] = 0.000000
iterals: 2, 0, 1    mat1[2][1] = 20.000000  mat2[1][0] = 0.000000   dest[2][0] = 0.000000
iterals: 2, 0, 2    mat1[2][2] = 0.000000   mat2[2][0] = 0.000000   dest[2][0] = 0.000000
iterals: 2, 1, 0    mat1[2][0] = 0.000000   mat2[0][1] = 0.000000   dest[2][1] = 0.000000
iterals: 2, 1, 1    mat1[2][1] = 20.000000  mat2[1][1] = 0.000000   dest[2][1] = 0.000000
iterals: 2, 1, 2    mat1[2][2] = 0.000000   mat2[2][1] = 0.000000   dest[2][1] = 0.000000
iterals: 2, 2, 0    mat1[2][0] = 0.000000   mat2[0][2] = 0.000000   dest[2][2] = 0.000000
iterals: 2, 2, 1    mat1[2][1] = 20.000000  mat2[1][2] = 1.000000   dest[2][2] = 20.000000
iterals: 2, 2, 2    mat1[2][2] = 0.000000   mat2[2][2] = 0.000000   dest[2][2] = 20.000000
iterals: 2, 3, 0    mat1[2][0] = 0.000000   mat2[0][3] = 0.000000   dest[2][3] = 0.000000
iterals: 2, 3, 1    mat1[2][1] = 20.000000  mat2[1][3] = 0.000000   dest[2][3] = 0.000000
iterals: 2, 3, 2    mat1[2][2] = 0.000000   mat2[2][3] = 0.000000   dest[2][3] = 0.000000
iterals: 2, 4, 0    mat1[2][0] = 0.000000   mat2[0][4] = 0.000000   dest[2][4] = 0.000000
iterals: 2, 4, 1    mat1[2][1] = 20.000000  mat2[1][4] = 0.000000   dest[2][4] = 0.000000
iterals: 2, 4, 2    mat1[2][2] = 0.000000   mat2[2][4] = 1.000000   dest[2][4] = 0.000000
iterals: 2, 5, 0    mat1[2][0] = 0.000000   mat2[0][5] = 0.000000   dest[2][5] = 0.000000
iterals: 2, 5, 1    mat1[2][1] = 20.000000  mat2[1][5] = 0.000000   dest[2][5] = 0.000000
iterals: 2, 5, 2    mat1[2][2] = 0.000000   mat2[2][5] = 0.000000   dest[2][5] = 0.000000
iterals: 3, 0, 0    mat1[3][0] = 0.000000   mat2[0][0] = 0.000000   dest[3][0] = 0.000000
iterals: 3, 0, 1    mat1[3][1] = 0.000000   mat2[1][0] = 20.000000  dest[3][0] = 0.000000
iterals: 3, 0, 2    mat1[3][2] = 0.000000   mat2[2][0] = 0.000000   dest[3][0] = 0.000000
iterals: 3, 1, 0    mat1[3][0] = 0.000000   mat2[0][1] = 0.000000   dest[3][1] = 0.000000
iterals: 3, 1, 1    mat1[3][1] = 0.000000   mat2[1][1] = 0.000000   dest[3][1] = 0.000000
iterals: 3, 1, 2    mat1[3][2] = 0.000000   mat2[2][1] = 0.000000   dest[3][1] = 0.000000
iterals: 3, 2, 0    mat1[3][0] = 0.000000   mat2[0][2] = 0.000000   dest[3][2] = 0.000000
iterals: 3, 2, 1    mat1[3][1] = 0.000000   mat2[1][2] = 0.000000   dest[3][2] = 0.000000
iterals: 3, 2, 2    mat1[3][2] = 0.000000   mat2[2][2] = 0.000000   dest[3][2] = 0.000000
iterals: 3, 3, 0    mat1[3][0] = 0.000000   mat2[0][3] = 0.000000   dest[3][3] = 0.000000
iterals: 3, 3, 1    mat1[3][1] = 0.000000   mat2[1][3] = 0.000000   dest[3][3] = 0.000000
iterals: 3, 3, 2    mat1[3][2] = 0.000000   mat2[2][3] = 0.000000   dest[3][3] = 0.000000
iterals: 3, 4, 0    mat1[3][0] = 0.000000   mat2[0][4] = 0.000000   dest[3][4] = 0.000000
iterals: 3, 4, 1    mat1[3][1] = 0.000000   mat2[1][4] = 0.000000   dest[3][4] = 0.000000
iterals: 3, 4, 2    mat1[3][2] = 0.000000   mat2[2][4] = 1.000000   dest[3][4] = 0.000000
iterals: 3, 5, 0    mat1[3][0] = 0.000000   mat2[0][5] = 0.000000   dest[3][5] = 0.000000
iterals: 3, 5, 1    mat1[3][1] = 0.000000   mat2[1][5] = 0.000000   dest[3][5] = 0.000000
iterals: 3, 5, 2    mat1[3][2] = 0.000000   mat2[2][5] = 0.000000   dest[3][5] = 0.000000
iterals: 4, 0, 0    mat1[4][0] = 0.000000   mat2[0][0] = 0.000000   dest[4][0] = 0.000000
iterals: 4, 0, 1    mat1[4][1] = 0.000000   mat2[1][0] = 20.000000  dest[4][0] = 0.000000
iterals: 4, 0, 2    mat1[4][2] = 30.000000  mat2[2][0] = 0.000000   dest[4][0] = 0.000000
iterals: 4, 1, 0    mat1[4][0] = 0.000000   mat2[0][1] = 0.000000   dest[4][1] = 0.000000
iterals: 4, 1, 1    mat1[4][1] = 0.000000   mat2[1][1] = 0.000000   dest[4][1] = 0.000000
iterals: 4, 1, 2    mat1[4][2] = 30.000000  mat2[2][1] = 0.000000   dest[4][1] = 0.000000
iterals: 4, 2, 0    mat1[4][0] = 0.000000   mat2[0][2] = 0.000000   dest[4][2] = 0.000000
iterals: 4, 2, 1    mat1[4][1] = 0.000000   mat2[1][2] = 0.000000   dest[4][2] = 0.000000
iterals: 4, 2, 2    mat1[4][2] = 30.000000  mat2[2][2] = 0.000000   dest[4][2] = 0.000000
iterals: 4, 3, 0    mat1[4][0] = 0.000000   mat2[0][3] = 0.000000   dest[4][3] = 0.000000
iterals: 4, 3, 1    mat1[4][1] = 0.000000   mat2[1][3] = 0.000000   dest[4][3] = 0.000000
iterals: 4, 3, 2    mat1[4][2] = 30.000000  mat2[2][3] = 0.000000   dest[4][3] = 0.000000
iterals: 4, 4, 0    mat1[4][0] = 0.000000   mat2[0][4] = 0.000000   dest[4][4] = 0.000000
iterals: 4, 4, 1    mat1[4][1] = 0.000000   mat2[1][4] = 0.000000   dest[4][4] = 0.000000
iterals: 4, 4, 2    mat1[4][2] = 30.000000  mat2[2][4] = 0.000000   dest[4][4] = 0.000000
iterals: 4, 5, 0    mat1[4][0] = 0.000000   mat2[0][5] = 0.000000   dest[4][5] = 0.000000
iterals: 4, 5, 1    mat1[4][1] = 0.000000   mat2[1][5] = 0.000000   dest[4][5] = 0.000000
iterals: 4, 5, 2    mat1[4][2] = 30.000000  mat2[2][5] = 0.000000   dest[4][5] = 0.000000
iterals: 5, 0, 0    mat1[5][0] = 0.000000   mat2[0][0] = 0.000000   dest[5][0] = 0.000000
iterals: 5, 0, 1    mat1[5][1] = 0.000000   mat2[1][0] = 20.000000  dest[5][0] = 0.000000
iterals: 5, 0, 2    mat1[5][2] = 0.000000   mat2[2][0] = 0.000000   dest[5][0] = 0.000000
iterals: 5, 1, 0    mat1[5][0] = 0.000000   mat2[0][1] = 0.000000   dest[5][1] = 0.000000
iterals: 5, 1, 1    mat1[5][1] = 0.000000   mat2[1][1] = 0.000000   dest[5][1] = 0.000000
iterals: 5, 1, 2    mat1[5][2] = 0.000000   mat2[2][1] = 0.000000   dest[5][1] = 0.000000
iterals: 5, 2, 0    mat1[5][0] = 0.000000   mat2[0][2] = 0.000000   dest[5][2] = 0.000000
iterals: 5, 2, 1    mat1[5][1] = 0.000000   mat2[1][2] = 0.000000   dest[5][2] = 0.000000
iterals: 5, 2, 2    mat1[5][2] = 0.000000   mat2[2][2] = 0.000000   dest[5][2] = 0.000000
iterals: 5, 3, 0    mat1[5][0] = 0.000000   mat2[0][3] = 0.000000   dest[5][3] = 0.000000
iterals: 5, 3, 1    mat1[5][1] = 0.000000   mat2[1][3] = 0.000000   dest[5][3] = 0.000000
iterals: 5, 3, 2    mat1[5][2] = 0.000000   mat2[2][3] = 0.000000   dest[5][3] = 0.000000
iterals: 5, 4, 0    mat1[5][0] = 0.000000   mat2[0][4] = 0.000000   dest[5][4] = 0.000000
iterals: 5, 4, 1    mat1[5][1] = 0.000000   mat2[1][4] = 0.000000   dest[5][4] = 0.000000
iterals: 5, 4, 2    mat1[5][2] = 0.000000   mat2[2][4] = 0.000000   dest[5][4] = 0.000000
iterals: 5, 5, 0    mat1[5][0] = 0.000000   mat2[0][5] = 0.000000   dest[5][5] = 0.000000
iterals: 5, 5, 1    mat1[5][1] = 0.000000   mat2[1][5] = 0.000000   dest[5][5] = 0.000000
iterals: 5, 5, 2    mat1[5][2] = 0.000000   mat2[2][5] = 0.000000   dest[5][5] = 0.000000

这里是源代码：

#include<stdio.h>

void prod(float mat1[][6], float mat2[][6], float dest[][6], int m1, int n1, int n2) {
     printf("orders: %d, %d, %d\n", m1, n1, n2);
     int i, j, k; // kmax = n1, jmax = n2, imax = m1
     for (i = 0; i < m1; i++) {
         for (j = 0; j < n2; j++) {
             dest[i][j] = 0;
             for (k = 0; k < n1; k++) {
                 dest[i][j] += mat1[i][k]*mat2[k][j];
                 printf("iterals: %d, %d, %d\t", i, j, k);
                 printf("mat1[%d][%d] = %f\t", i, k, mat1[i][k]);
                 printf("mat2[%d][%d] = %f\t", k, j, mat2[k][j]);
                 printf("dest[%d][%d] = %f\n", i, j, dest[i][j]);
             }
         }
     }
 }


void main() {
    float res[][6] = { 0 };

    float G[][6] =  { {10,  0,  0},
                      { 0,  0,  0},
                      { 0, 20,  0},
                      { 0,  0,  0},
                      { 0,  0, 30},
                      { 0,  0,  0} };

    float H[][6] =  { {1, 0, 0, 0, 0, 0},
                      {0, 0, 1, 0, 0, 0},
                      {0, 0, 0, 0, 1, 0} };

    prod(G, H, res, 6, 3, 6);
}

【问题讨论】：

标签： c arrays matrix-multiplication

【解决方案1】：

float res[][6] = { 0 }; 是 float res[1][6];，而不是您需要的 float res[6][6];。如果您没有完整的初始化列表，则需要写出所有维度。

void main() 也应该是 int main(void)。

G 的初始化列表也不适合 float G[][6]，它应该是 float G[][3]。

这里是完整代码：https://ideone.com/2hz45m

【讨论】：

@suvojit_007 这应该回答你的问题：stackoverflow.com/q/18446686/3684343。简而言之：在正常情况下是的。
@mch 为什么 mat2[1][0] 元素值变为 20.00？
您的res 数组太小，因此您的写入超出范围并覆盖了其他内容。这会调用未定义的行为，因此可能会出现奇怪的结果。这里的结果是ideone.com/2hz45m 预期的吗？

【解决方案2】：

除了float res[][6] = { 0 };太小，其他@mch、@Rishikesh Raje都说了，还有其他问题。

将mat1[][6], mat2[][6], dest[][6] 视为mat1[a][b], mat2[b][c], dest[a][c] 以获得更清晰、更灵活的代码。

在 C99 和可选的 C11 中，参数可以是 variable length array - VLA，这样可以简化编码。
见Passing a multidimensional variable length array to a function

void prod(int a, int b, int c, float mat1[a][b], float mat2[b][c], float dest[a][c]) {
  printf("orders: %d, %d, %d\n", a, b, c);
  for (int ai = 0; ai < a; ai++) {
    for (int ci = 0; ci < c; ci++) {
      float sum = 0.0;
      for (int bi = 0; bi < b; bi++) {
        sum += mat1[ai][bi] * mat2[bi][ci];
        printf("iterals: %d, %d, %d\t", ai, ci, bi);
        printf("mat1[%d][%d] = %2g\t", ai, bi, mat1[ai][bi]);
        printf("mat2[%d][%d] = %2g\t", bi, ci, mat2[bi][ai]);
        printf("dest[%d][%d] = %2g\n", ai, ci, sum);
      }
      dest[ai][ci] = sum;
    }
  }
}

#define A 6
#define B 3
#define C 6

int main(void) {
  float g[A][B] = { //
      {10, 0, 0}, //
      {0, 0, 0}, //
      {0, 20, 0}, //
      {0, 0, 0}, //
      {0, 0, 30}, //
      {0, 0, 0}};
  float h[B][C] = { // Note dimension change
      {1, 0, 0, 0, 0, 0}, //
      {0, 0, 1, 0, 0, 0}, //
      {0, 0, 0, 0, 1, 0}};
  float res[A][C]; // Note dimension change

  prod(A, B, C, g, h, res);
}

【讨论】：

【解决方案3】：

您的 G 矩阵没有 6 列。它有 3 列，应定义如下
```
float G[][3]
```
结果矩阵需要一个大小。
```
 float res[6][6] = { 0 };
```
您应该将 main 定义为 int main(void)

函数定义也应该改变如下。

void prod(float mat1[][3], float mat2[][6], float dest[][6], int m1, int n1, int n2) {

【讨论】：