| qr-methods {Matrix} | R Documentation |
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.
qr(x, ...) qrR(qr, complete=FALSE, backPermute=TRUE)
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 |
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 |
... |
further arguments passed to or from other methods |
QR decomposition of a general sparse
double-precision matrix with nrow(x) >= ncol(x). Returns
an object of class "sparseQR".
works via "dgCMatrix".
qr; then, the class documentations,
mainly sparseQR, and also
dgCMatrix.
##------------- 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)) )