Matrix (version 1.2-0)

qr-methods: QR Decomposition -- S4 Methods and Generic

Description

The "Matrix" package provides methods for the QR decomposition of special classes of matrices. There is a generic function which uses qr as default, but methods defined in this package can take extra arguments. In particular there is an option for determining a fill-reducing permutation of the columns of a sparse, rectangular matrix.

Usage

qr(x, ...)
qrR(qr, complete=FALSE, backPermute=TRUE)

Arguments

x

a numeric or complex matrix whose QR decomposition is to be computed. Logical matrices are coerced to numeric.

qr

a QR decomposition of the type computed by qr.

complete

logical indicating whether the $\bold{R}$ matrix is to be completed by binding zero-value rows beneath the square upper triangle.

backPermute

logical indicating if the rows of the $\bold{R}$ matrix should be back permuted such that qrR()'s result can be used directly to reconstruct the original matrix $\bold{X}$.

...

further arguments passed to or from other methods

See Also

qr; then, the class documentations, mainly sparseQR, and also dgCMatrix.

Examples

##------------- example of pivoting -- from base'  qraux.Rd -------------
X <- Matrix(cbind(int = 1,
                  b1=rep(1:0, each=3), b2=rep(0:1, each=3),
                  c1=rep(c(1,0,0), 2), c2=rep(c(0,1,0), 2), c3=rep(c(0,0,1),2)),
            sparse=TRUE)
X # is singular, columns "b2" and "c3" are "extra"
(qx <- qr(X))
# both @p and @q are non-trivial permutations

drop0(R. <- qr.R(qx), tol=1e-15) # columns are int b1 c1 c2 b2 c3
Q. <- qr.Q(qx)
qI <- sort.list(qx@q) # the inverse 'q' permutation
(X. <- drop0(Q. %*% R.[, qI], tol=1e-15))## just = X
stopifnot(all(X - X.) < 8*.Machine$double.eps,
          ## qR(.) returns R already "back permuted" (as with qI):
          identical(R.[, qI], qrR(qx)) )