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kron

Kronecker tensor product

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Syntax

K = kron(A,B)

Description

example

K = kron(A,B)returns theKronecker tensor product矩阵的A和B. IfAis anm-by-nmatrix andBis ap-by-q然后kron(A,B)is anm*p-by-n*qmatrix formed by taking all possible products between the elements ofA和the matrixB.

Examples

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Open Live Script

Create a block diagonal matrix.

创建一个4 x-4的身份矩阵和一个2 by-2矩阵，您希望沿对角线重复。

一个=眼(4);B = (1 -1;-1 1];

Usekronto find the Kronecker tensor product.

K = kron(A,B)
K =8×81 -1 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 -1 1

The result is an 8-by-8 block diagonal matrix.

Open Live Script

Expand the size of a matrix by repeating elements.

Create a 2-by-2 matrix of ones and a 2-by-3 matrix whose elements you want to repeat.

A = [1 2 3; 4 5 6]; B = ones(2);

Calculate the Kronecker tensor product usingkron.

K = kron(A,B)
K =4×61 1 2 2 3 3 1 1 2 2 3 3 4 4 5 5 6 6 4 4 5 5 6 6

The result is a 4-by-6 block matrix.

Open Live Script

This example visualizes a sparse Laplacian operator matrix.

The matrix representation of the discrete Laplacian operator on a two-dimensional,n-by-ngrid is an*n-by-n*nsparse matrix. There are at most five nonzero elements in each row or column. You can generate the matrix as the Kronecker product of one-dimensional difference operators. In this examplen = 5.

n = 5;i = speye（n，n）;e =稀疏（2：n，1：n-1,1，n，n）;d = e+e'-2*i;a = kron（d，i）+kron（i，d）;

Visualize the sparsity pattern with间谍.

间谍(A,'k')

Figure contains an axes object. The axes object contains an object of type line.

Input Arguments

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Input matrices, specified as scalars, vectors, or matrices. If eitherA或者B稀疏，然后kronmultiplies only nonzero elements and the result is also sparse.

Data Types:single|double|int8|int16|int32|int64|uint8|uint16|uint32|uint64|logical
Complex Number Support:Yes

More About

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Kronecker Tensor Product

IfAis anm-by-nmatrix andBis ap-by-q然后the Kronecker tensor product ofA和Bis a large matrix formed by multiplyingBby each element ofA

A ⊗ B = [ a 11 B a 12 B ⋯ a 1 n B a 21 B ⋮ a 22 B ⋮ ⋯ ⋱ a 2 n B ⋮ a m 1 B a m 2 B ⋯ a m n B ] .

For example, two simple 2-by-2 matrices produce

A = [ 1 − 2 − 1 0 ] , B = [ 4 − 3 2 3 ] A ⊗ B = [ 1 · 4 1 · − 3 − 2 · 4 − 2 · − 3 1 · 2 1 · 3 − 2 · 2 − 2 · 3 − 1 · 4 − 1 · − 3 0 · 4 0 · − 3 − 1 · 2 − 1 · 3 0 · 2 0 · 3 ] = [ 4 − 3 − 8 6 2 3 − 4 − 6 − 4 3 0 0 − 2 − 3 0 0 ] .

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced before R2006a

See Also

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