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
.
Note that qr.Q(qr, *)
is a special case of
qr.qy(qr, y)
(with a “diagonal” y
), and
qr.X(qr, *)
is basically qr.qy(qr, R)
(apart from
pivoting and dimnames
setting).
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: 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!