This function takes a matrix that is Kronecker product \(A \otimes B\) (Definition 3.5), where \(A\) is \(P x Q\) and \(B\) is \(N x M\), and outputs the matrix \(B \otimes A\).
reverse.kronecker(ab, p, qq)The \((NP) \times (QM)\) matrix \(A \otimes B\).
The number of rows of \(A\).
The number of columns of \(A\).
The \((NP) \times (QM)\) matrix \(B \otimes A\).
# Create matrices
(A <- diag(1, 3))
#> [,1] [,2] [,3]
#> [1,] 1 0 0
#> [2,] 0 1 0
#> [3,] 0 0 1
(B <- matrix(1:6, ncol = 2))
#> [,1] [,2]
#> [1,] 1 4
#> [2,] 2 5
#> [3,] 3 6
# Perform kronecker
(kron <- kronecker(A, B))
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 1 4 0 0 0 0
#> [2,] 2 5 0 0 0 0
#> [3,] 3 6 0 0 0 0
#> [4,] 0 0 1 4 0 0
#> [5,] 0 0 2 5 0 0
#> [6,] 0 0 3 6 0 0
#> [7,] 0 0 0 0 1 4
#> [8,] 0 0 0 0 2 5
#> [9,] 0 0 0 0 3 6
# Perform reverse kronecker product
(reverse.kronecker(kron, 3, 3))
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 1 0 0 4 0 0
#> [2,] 0 1 0 0 4 0
#> [3,] 0 0 1 0 0 4
#> [4,] 2 0 0 5 0 0
#> [5,] 0 2 0 0 5 0
#> [6,] 0 0 2 0 0 5
#> [7,] 3 0 0 6 0 0
#> [8,] 0 3 0 0 6 0
#> [9,] 0 0 3 0 0 6
# Perform kronecker again
(kron2 <- kronecker(B, A))
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 1 0 0 4 0 0
#> [2,] 0 1 0 0 4 0
#> [3,] 0 0 1 0 0 4
#> [4,] 2 0 0 5 0 0
#> [5,] 0 2 0 0 5 0
#> [6,] 0 0 2 0 0 5
#> [7,] 3 0 0 6 0 0
#> [8,] 0 3 0 0 6 0
#> [9,] 0 0 3 0 0 6