# facmul: Multiplication by Decomposition Factors In Matrix: Sparse and Dense Matrix Classes and Methods

## Description

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

## Usage

 `1` ```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

 ```1 2 3 4 5 6 7 8``` ```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) ```

Matrix documentation built on June 11, 2021, 3 p.m.