`bracket.prod`

Bracket product

Description

Bracket product of a matrix and a 3-dimensional array.

Usage

bracket.prod(a, x)

Arguments

Argument	Description
`a`	a numeric matrix.
`x`	a three-dimensional array.

Details

Let $\mathbf{X} = (x_{tij})$ be a 3-dimensional $n\times p\times q$ array and $\mathbf{A}$ an $m\times n$ matrix, then $\mathbf{Y} = [\mathbf{A}][\mathbf{X}]$ is called the bracket product of $\mathbf{A}$ and $\mathbf{X}$ , that is an $m$$ \times p\times q$ with elements

\[y_{tij} = \sum\limits_{k=1}^n a_{tk}x_{kij}\]

Value

bracket.prod returns a 3-dimensional array of dimension $m\times p\times q$ .

References

Wei, B.C. (1998). Exponential Family Nonlinear Models . Springer, New York.

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 = 3, ncol = 2)

y <- bracket.prod(a, x) # a 3 x 3 x 3 array
y

bracket.prod