两个矩阵的 Kronecker 乘积的 Javascript 程序

给定一个${m} imes{n}$矩阵 A 和${p} imes{q}$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${(mp)} imes{(nq)}$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：

Javascript

    // Javascript code to find the Kronecker Product of
    // two matrices and stores it as matrix C
     
    // rowa and cola are no of rows and columns
    // of matrix A
    // rowb and colb are no of rows and columns
    // of matrix B
    let cola = 2, rowa = 3, colb = 3, rowb = 2;
       
    // Function to computes the Kronecker Product
    // of two matrices
    function Kroneckerproduct(A, B)
    {
       
        let C= new Array(rowa * rowb)
        for(let i = 0; i < (rowa * rowb); i++)
        {
            C[i] = new Array(cola * colb);
            for(let j = 0; j < (cola * colb); j++)
            {
                C[i][j] = 0;
            }
        }
       
        // i loops till rowa
        for (let i = 0; i < rowa; i++)
        {
       
            // k loops till rowb
            for (let k = 0; k < rowb; k++)
            {
       
                // j loops till cola
                for (let j = 0; j < cola; j++)
                {
       
                    // l loops till colb
                    for (let 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];
                        document.write( C[i + l + 1][j + k + 1]+" ");
                    }
                }
                document.write("</br>");
            }
        }
    }
     
    let A = [ [ 1, 2 ],
             [ 3, 4 ],
             [ 1, 0 ] ];
                         
    let B = [ [ 0, 5, 2 ],
                  [ 6, 7, 3 ] ];
 
    Kroneckerproduct(A, B);
     

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*rowb*cola*colb)，因为我们使用的是嵌套循环。

辅助空间： O((rowa + colb)*(rowb + cola))，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！