两个矩阵的 Kronecker 积
原文： https://www.geeksforgeeks.org/kronecker-product-two-matrices/
给定m x n矩阵A和p x q矩阵B，它们的 Kronecker 积C = A tensor B，也称为它们的矩阵直接积，是mp x 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|
示例：
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
下面是找到两个矩阵的 Kronecker 乘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 <iostream>
using namespace std;
// 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];
cout << C[i + l + 1][j + k + 1] << " ";
}
}
cout << endl;
}
}
}
// 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;
}
//This code is contributed by shubhamsingh10
Java
// Java code to find the Kronecker Product of
// two matrices and stores it as matrix C
import java.io.*;
import java.util.*;
class GFG {
// rowa and cola are no of rows and columns
// of matrix A
// rowb and colb are no of rows and columns
// of matrix B
static int cola = 2, rowa = 3, colb = 3, rowb = 2;
// Function to computes the Kronecker Product
// of two matrices
static void Kroneckerproduct(int A[][], int B[][])
{
int[][] C= new int[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];
System.out.print( C[i + l + 1][j + k + 1]+" ");
}
}
System.out.println();
}
}
}
// Driver program
public static void main (String[] args)
{
int A[][] = { { 1, 2 },
{ 3, 4 },
{ 1, 0 } };
int B[][] = { { 0, 5, 2 },
{ 6, 7, 3 } };
Kroneckerproduct(A, B);
}
}
// This code is contributed by Gitanjali.
Python3
# Python3 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
cola = 2
rowa = 3
colb = 3
rowb = 2
# Function to computes the Kronecker Product
# of two matrices
def Kroneckerproduct( A , B ):
C = [[0 for j in range(cola * colb)] for i in range(rowa * rowb)]
# i loops till rowa
for i in range(0, rowa):
# k loops till rowb
for k in range(0, rowb):
# j loops till cola
for j in range(0, cola):
# l loops till colb
for l in range(0, colb):
# 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]
print (C[i + l + 1][j + k + 1],end=' ')
print ("\n")
# Driver code.
A = [[0 for j in range(2)] for i in range(3)]
B = [[0 for j in range(3)] for i in range(2)]
A[0][0] = 1
A[0][1] = 2
A[1][0] = 3
A[1][1] = 4
A[2][0] = 1
A[2][1] = 0
B[0][0] = 0
B[0][1] = 5
B[0][2] = 2
B[1][0] = 6
B[1][1] = 7
B[1][2] = 3
Kroneckerproduct( A , B )
# This code is contributed by Saloni.
C
// C# code to find the Kronecker Product of
// two matrices and stores it as matrix C
using System;
class GFG {
// rowa and cola are no of rows
// and columns of matrix A
// rowb and colb are no of rows
// and columns of matrix B
static int cola = 2, rowa = 3;
static int colb = 3, rowb = 2;
// Function to computes the Kronecker
// Product of two matrices
static void Kroneckerproduct(int [,]A, int [,]B)
{
int [,]C= new int[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];
Console.Write( C[i + l + 1,
j + k + 1] + " ");
}
}
Console.WriteLine();
}
}
}
// Driver Code
public static void Main ()
{
int [,]A = {{1, 2},
{3, 4},
{1, 0}};
int [,]B = {{0, 5, 2},
{6, 7, 3}};
Kroneckerproduct(A, B);
}
}
// This code is contributed by nitin mittal.
PHP
<?php
// PHP code to find the
// Kronecker Product of two
// rowa and cola are no of
// rows and columns of matrix A
// rowb and colb are no of
// rows and columns of matrix B
$cola = 2;
$rowa = 3;
$colb = 3;
$rowb = 2;
// Function to computes the
// Kronecker Product of two matrices
function Kroneckerproduct($A, $B)
{
global $cola;
global $rowa;
global $colb;
global $rowb;
//$C[$rowa * $rowb][$cola * $colb];
$C;
// i loops till rowa
for ( $i = 0; $i < $rowa; $i++)
{
// k loops till rowb
for ($k = 0; $k < $rowb; $k++)
{
// j loops till cola
for ( $j = 0; $j < $cola; $j++)
{
// l loops till colb
for ($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][$l];
echo ($C[$i + $l + 1][$j + $k + 1]), "\t" ;
}
}
echo "\n";
}
}
}
// Driver Code
$A = array (array (1, 2),
array (3, 4),
array (1, 0));
$B = array (array (0, 5, 2),
array (6, 7, 3));
Kroneckerproduct($A, $B);
// This code is contributed by ajit
?>
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
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