kronecker.prod | R Documentation |
Computes the kronecker product of two matrices, x
and y
.
kronecker.prod(x, y = x)
x |
a numeric matrix or vector. |
y |
a numeric matrix or vector. |
Let \bold{X}
be an m\times n
and \bold{Y}
a p\times q
matrix.
The mp\times nq
matrix defined by
\left[{\begin{array}{ccc}
x_{11}\bold{Y} & \dots & x_{1n}\bold{Y} \\
\vdots & & \vdots \\
x_{m1}\bold{Y} & \dots & x_{mn}\bold{Y}
\end{array}}\right],
is called the Kronecker product of \bold{X}
and \bold{Y}
.
An array with dimensions dim(x) * dim(y)
.
Magnus, J.R., Neudecker, H. (2007). Matrix Differential Calculus with Applications in Statistics and Econometrics, 3rd Edition. Wiley, New York.
kronecker
function from base
package is based on outer
.
Our C
version is slightly faster.
# block diagonal matrix:
a <- diag(1:3)
b <- matrix(1:4, ncol = 2)
kronecker.prod(a, b)
# examples with vectors
ones <- rep(1, 4)
y <- 1:3
kronecker.prod(ones, y) # 12-dimensional vector
kronecker.prod(ones, t(y)) # 3 x 3 matrix
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.