两个矩阵的克罗内克积的 C 程序
给定一个矩阵 A 和矩阵 B,它们的克罗内克积C = A 张量 B,也称为它们的矩阵直积,是矩阵。
A tensor B = |a11B a12B|
|a21B a22B|
= |a11b11 a11b12 a12b11 a12b12|
|a11b21 a11b22 a12b21 a12b22|
|a11b31 a11b32 a12b31 a12b32|
|a21b11 a21b12 a22b11 a22b12|
|a21b21 a21b22 a22b21 a22b22|
|a21b31 a21b32 a22b31 a22b32|
例子:
1. The matrix direct(kronecker) product of the 2×2 matrix A
and the 2×2 matrix B is given by the 4×4 matrix :
Input : A = 1 2 B = 0 5
3 4 6 7
Output : C = 0 5 0 10
6 7 12 14
0 15 0 20
18 21 24 28
2. The matrix direct(kronecker) product of the 2×3 matrix A
and the 3×2 matrix B is given by the 6×6 matrix :
Input : A = 1 2 B = 0 5 2
3 4 6 7 3
1 0
Output : C = 0 5 2 0 10 4
6 7 3 12 14 6
0 15 6 0 20 8
18 21 9 24 28 12
0 5 2 0 0 0
6 7 3 0 0 0
下面是查找两个矩阵的克罗内克积并将其存储为矩阵 C 的代码:
C
// C code to find the Kronecker Product of two
// matrices and stores it as matrix C
#include
// rowa and cola are no of rows and columns
// of matrix A
// rowb and colb are no of rows and columns
// of matrix B
const int cola = 2, rowa = 3, colb = 3, rowb = 2;
// Function to computes the Kronecker Product
// of two matrices
void Kroneckerproduct(int A[][cola], int B[][colb])
{
int C[rowa * rowb][cola * colb];
// i loops till rowa
for (int i = 0; i < rowa; i++) {
// k loops till rowb
for (int k = 0; k < rowb; k++) {
// j loops till cola
for (int j = 0; j < cola; j++) {
// l loops till colb
for (int l = 0; l < colb; l++) {
// Each element of matrix A is
// multiplied by whole Matrix B
// resp and stored as Matrix C
C[i + l + 1][j + k + 1] = A[i][j] * B[k][l];
printf("%d ", C[i + l + 1][j + k + 1]);
}
}
printf("
");
}
}
}
// Driver Code
int main()
{
int A[3][2] = { { 1, 2 }, { 3, 4 }, { 1, 0 } },
B[2][3] = { { 0, 5, 2 }, { 6, 7, 3 } };
Kroneckerproduct(A, B);
return 0;
}
输出 :
0 5 2 0 10 4
6 7 3 12 14 6
0 15 6 0 20 8
18 21 9 24 28 12
0 5 2 0 0 0
6 7 3 0 0 0
时间复杂度: O(rowa*cola*rowb*colb),因为我们使用的是嵌套循环。
辅助空间: O(rowa*cola*rowb*colb),因为我们在矩阵 C 中使用了额外的空间。
有关详细信息,请参阅有关两个矩阵的克罗内克积的完整文章!