# QR.Auxiliaries

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##### Reconstruct the Q, R, or X Matrices from a QR Object

Returns the original matrix from which the object was constructed or the components of the decomposition.

Keywords
algebra, array
##### Usage
qr.X(qr, complete = FALSE, ncol =)
qr.Q(qr, complete = FALSE, Dvec =)
qr.R(qr, complete = FALSE)
##### Arguments
qr

object representing a QR decomposition. This will typically have come from a previous call to qr or lsfit.

complete

logical expression of length 1. Indicates whether an arbitrary orthogonal completion of the $$\bold{Q}$$ or $$\bold{X}$$ matrices is to be made, or whether the $$\bold{R}$$ matrix is to be completed by binding zero-value rows beneath the square upper triangle.

ncol

##### See Also

qr, qr.qy.

• qr.X
• qr.Q
• qr.R
##### Examples
library(base) # NOT RUN { p <- ncol(x <- LifeCycleSavings[, -1]) # not the 'sr' qrstr <- qr(x) # dim(x) == c(n,p) qrstr $rank # = 4 = p Q <- qr.Q(qrstr) # dim(Q) == dim(x) R <- qr.R(qrstr) # dim(R) == ncol(x) X <- qr.X(qrstr) # X == x range(X - as.matrix(x)) # ~ < 6e-12 ## X == Q %*% R if there has been no pivoting, as here: all.equal(unname(X), unname(Q %*% R)) # example of pivoting x <- cbind(int = 1, b1 = rep(1:0, each = 3), b2 = rep(0:1, each = 3), c1 = rep(c(1,0,0), 2), c2 = rep(c(0,1,0), 2), c3 = rep(c(0,0,1),2)) x # is singular, columns "b2" and "c3" are "extra" a <- qr(x) zapsmall(qr.R(a)) # columns are int b1 c1 c2 b2 c3 a$pivot pivI <- sort.list(a$pivot) # the inverse permutation all.equal (x, qr.Q(a) %*% qr.R(a)) # no, no stopifnot( all.equal(x[, a$pivot], qr.Q(a) %*% qr.R(a)), # TRUE all.equal(x , qr.Q(a) %*% qr.R(a)[, pivI])) # TRUE too! # } 
Documentation reproduced from package base, version 3.6.1, License: Part of R 3.6.1

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