bracket.prod {fastmatrix}

Bracket product

Description

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

Usage

bracket.prod(a, x)

Arguments

a

a numeric matrix.

x

a three-dimensional array.

Details

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

See Also

array, matrix, array.mult.

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