R: Bracket product

bracket.prod {fastmatrix} | R Documentation

## 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} = ∑\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

[Package fastmatrix version 0.4-1 Index]