# QR.Auxiliaries {base}

### Description

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

### 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
- integer in the range
`1:nrow(qr$qr)`

. The number of columns to be in the reconstructed \bold{X}. The default when`complete`

is`FALSE`

is the first`min(ncol(X), nrow(X))`

columns of the original \bold{X} from which the qr object was constructed. The default when`complete`

is`TRUE`

is a square matrix with the original \bold{X} in the first`ncol(X)`

columns and an arbitrary orthogonal completion (unitary completion in the complex case) in the remaining columns. - 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
`1`

s. - ...
- potentially further arguments, passed potentially to non-default methods.

### Values

`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`

).

### See Also

`qr`

, `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: 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 R 3.0.2. License: GPL-2.