Here is a modified version of qraux.Rd, an edited version of R-2.14.0/src/library/base/man/qraux.Rd
This gives some details and an example for the case of pivoting. In this case, it is not true that X = QR; rather X[, pivot] = QR. It may save some other people bugs and time to have this information. Tim Hesterberg -------------------------------------------------- % File src/library/base/man/qraux.Rd % Part of the R package, http://www.R-project.org<http://www.r-project.org/> % Copyright 1995-2007 R Core Development Team % Distributed under GPL 2 or later \name{QR.Auxiliaries} \title{Reconstruct the Q, R, or X Matrices from a QR Object} \usage{ qr.X(qr, complete = FALSE, ncol =) qr.Q(qr, complete = FALSE, Dvec =) qr.R(qr, complete = FALSE) } \alias{qr.X} \alias{qr.Q} \alias{qr.R} \arguments{ \item{qr}{object representing a QR decomposition. This will typically have come from a previous call to \code{\link{qr}} or \code{\link{lsfit}}.} \item{complete}{logical expression of length 1. Indicates whether an arbitrary orthogonal completion of the \eqn{\bold{Q}} or \eqn{\bold{X}} matrices is to be made, or whether the \eqn{\bold{R}} matrix is to be completed by binding zero-value rows beneath the square upper triangle.} \item{ncol}{integer in the range \code{1:nrow(qr$qr)}. The number of columns to be in the reconstructed \eqn{\bold{X}}. The default when \code{complete} is \code{FALSE} is the first \code{min(ncol(X), nrow(X))} columns of the original \eqn{\bold{X}} from which the qr object was constructed. The default when \code{complete} is \code{TRUE} is a square matrix with the original \eqn{\bold{X}} in the first \code{ncol(X)} columns and an arbitrary orthogonal completion (unitary completion in the complex case) in the remaining columns.} \item{Dvec}{vector (not matrix) of diagonal values. Each column of the returned \eqn{\bold{Q}} will be multiplied by the corresponding diagonal value. Defaults to all \code{1}s.} } \description{ Returns the original matrix from which the object was constructed or the components of the decomposition. } \value{ \code{qr.X} returns \eqn{\bold{X}}, the original matrix from which the qr object was constructed, provided \code{ncol(X) <= nrow(X)}. If \code{complete} is \code{TRUE} or the argument \code{ncol} is greater than \code{ncol(X)}, additional columns from an arbitrary orthogonal (unitary) completion of \code{X} are returned. \code{qr.Q} returns part or all of \bold{Q}, the order-nrow(X) orthogonal (unitary) transformation represented by \code{qr}. If \code{complete} is \code{TRUE}, \bold{Q} has \code{nrow(X)} columns. If \code{complete} is \code{FALSE}, \bold{Q} has \code{ncol(X)} columns. When \code{Dvec} is specified, each column of \bold{Q} is multiplied by the corresponding value in \code{Dvec}. \code{qr.R} returns \bold{R}. This may be pivoted, e.g. if \code{a <- qr(x)} then \code{x[, a$pivot]} = \bold{QR}. The number of rows of \bold{R} is either \code{nrow(X)} or \code{ncol(X)} (and may depend on whether \code{complete} is \code{TRUE} or \code{FALSE}. } \seealso{ \code{\link{qr}}, \code{\link{qr.qy}}. } \examples{ p <- ncol(x <- LifeCycleSavings[,-1]) # not the 'sr' qrstr <- qr(x) # dim(x) == c(n,p) qrstr $ rank # = 4 = p Q <- qr.Q(qrstr) # dim(Q) == dim(x) R <- qr.R(qrstr) # dim(R) == ncol(x) X <- qr.X(qrstr) # X == x range(X - as.matrix(x))# ~ < 6e-12 ## X == Q \%*\% R if there has been no pivoting, as here. Q \%*\% R # example of pivoting x <- 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)) # singular, columns "b2" and "c3" are "extra" a <- qr(x) qr.R(a) # columns are int b1 c1 c2 b2 c3 a$pivot all.equal(x, qr.Q(a) \%*\% qr.R(a)) # no all.equal(x[, a$pivot], qr.Q(a) \%*\% qr.R(a)) # yes } \keyword{algebra} \keyword{array} [[alternative HTML version deleted]] ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
