| array.mult {fastmatrix} | R Documentation |
Array multiplication
Description
Multiplication of 3-dimensional arrays was first introduced by Bates and Watts (1980). More extensions and technical details can be found in Wei (1998).
Usage
array.mult(a, b, x)
Arguments
a |
a numeric matrix. |
b |
a numeric matrix. |
x |
a three-dimensional array. |
Details
Let \bold{X} = (x_{tij}) be a 3-dimensional n\times p\times q where
indices t, i and j indicate face, row and column, respectively. The
product \bold{Y} = \bold{AXB} is an n\times r\times s array, with
\bold{A} and \bold{B} are r\times p and q\times s matrices
respectively. The elements of \bold{Y} are defined as:
y_{tkl} = \sum\limits_{i=1}^p\sum\limits_{j=1}^q a_{ki}x_{tij}b_{jl}
Value
array.mult returns a 3-dimensional array of dimension n\times r\times s.
References
Bates, D.M., Watts, D.G. (1980). Relative curvature measures of nonlinearity. Journal of the Royal Statistical Society, Series B 42, 1-25.
Wei, B.C. (1998). Exponential Family Nonlinear Models. Springer, New York.
See Also
Examples
x <- array(0, dim = c(2,3,3)) # 2 x 3 x 3 array
x[,,1] <- c(1,2,2,4,3,6)
x[,,2] <- c(2,4,4,8,6,12)
x[,,3] <- c(3,6,6,12,9,18)
a <- matrix(1, nrow = 2, ncol = 3)
b <- matrix(1, nrow = 3, ncol = 2)
y <- array.mult(a, b, x) # a 2 x 2 x 2 array
y