R: Multiplication by Decomposition Factors

facmul {Matrix} | R Documentation

## Multiplication by Decomposition Factors

### Description

Performs multiplication by factors for certain decompositions (and allows explicit formation of those factors).

### Usage

    facmul(x, factor, y, transpose, left, ...)

### Arguments

`x` | a matrix decomposition. No missing values or IEEE special values are allowed.
`factor` | an indicator for selecting a particular factor for multiplication.
`y` | a matrix or vector to be multiplied by the factor or its transpose. No missing values or IEEE special values are allowed.
`transpose` | a logical value. When `FALSE` (the default) the factor is applied. When `TRUE` the transpose of the factor is applied.
`left` | a logical value. When `TRUE` (the default) the factor is applied from the left. When `FALSE` the factor is applied from the right.
`...` | the method for `"qr.Matrix"` has additional arguments.

### Value

the product of the selected factor (or its transpose) and `y`

### NOTE

Factors for decompositions such as `lu` and `qr` can be stored in a compact form. The function `facmul` allows multiplication without explicit formation of the factors, saving both storage and operations.

### References

Golub, G., and Van Loan, C. F. (1989). Matrix Computations, 2nd edition, Johns Hopkins, Baltimore.

### Examples

    library(Matrix)
    x <- Matrix(rnorm(9), 3, 3)
    ## Not run:
    qrx <- qr(x)                      # QR factorization of x
    y <- rnorm(3)
    facmul( qr(x), factor = "Q", y)   # form Q y

    ## End(Not run)

[Package Matrix version 1.4-1 Index]