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