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

1 2 3 |

`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 |

`ncol` |
integer in the range |

`Dvec` |
vector (not matrix) of diagonal values. Each column of
the returned |

`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`

).

`qr`

,
`qr.qy`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ```
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!
``` |

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