| QR.Auxiliaries {base} | R Documentation |
Returns the original matrix from which the object was constructed or the components of the decomposition.
qr.X(qr, complete = FALSE, ncol =) qr.Q(qr, complete = FALSE, Dvec =) qr.R(qr, complete = FALSE)
qr |
object representing a QR decomposition. This will
typically have come from a previous call to |
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 |
integer in the range |
Dvec |
vector (not matrix) of diagonal values. Each column of
the returned \bold{Q} will be multiplied by the corresponding
diagonal value. Defaults to all |
qr.X returns \bold{X}, the original matrix from
which the qr object was constructed, provided ncol(X) <= nrow(X).
If complete is TRUE or the argument ncol is greater than
ncol(X), additional columns from an arbitrary orthogonal
(unitary) completion of X are returned.
qr.Q returns part or all of Q, the order-nrow(X)
orthogonal (unitary) transformation represented by qr. If
complete is TRUE, Q has nrow(X) columns.
If complete is FALSE, Q has ncol(X)
columns. When Dvec is specified, each column of Q is
multiplied by the corresponding value in Dvec.
qr.R returns R. This may be pivoted, e.g., if
a <- qr(x) then x[, a$pivot] = QR. The number of
rows of R is either nrow(X) or ncol(X) (and may
depend on whether complete is TRUE or FALSE).
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))
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!