Multiplication by Decomposition Factors --- Generic Function

DESCRIPTION:

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

This function is an S Version 3 generic (see Methods); method functions can be written to handle specific S Version 3 classes of data. Classes which already have methods for this function include:
, , .

USAGE:

facmul(x, factor, y, transpose = F, left = T, ...) 

REQUIRED 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.

OPTIONAL ARGUMENTS:

transpose
a logical value indicating whether or not the transpose of the factor should be applied. The default is to use the untransposed factor.
left
a logical value indicating whether the multiplication should occur on the left or on the right of y . The default is multiplication on the left.
...
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. Golub, G., and Van Loan, C. F. (1989). Matrix Computations, 2nd edition, Johns Hopkins, Baltimore.

SEE ALSO:

, , , .

EXAMPLES:

library(Matrix) 
x <- Matrix(rnorm(9), 3, 3) 
qrx <- qr(x)                      # QR factorization of x 
y <- rnorm(3) 
facmul( qr(x), factor = "Q", y)   # form Q y