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

QR.Auxiliaries {base}

R Documentation

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

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 = 1)
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 Q or X matrices is to be made, or whether the 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 X. The default when `complete` is `FALSE` is the first `min(ncol(X), nrow(X))` columns of the original X from which the qr object was constructed. The default when `complete` is `TRUE` is a square matrix with the original 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 Q will be multiplied by the corresponding diagonal value.

Value

qr.X returns 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 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, the upper triangular matrix such that X == Q %*% R. The number of rows of R is nrow(X) or ncol(X), depending on whether complete is TRUE or FALSE.

Examples

data(LifeCycleSavings)
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 :
all((1 - X /( Q %*% R))< 100*.Machine$double.eps)#TRUE

dim(Qc <- qr.Q(qrstr, complete=TRUE)) # Square: dim(Qc) == rep(nrow(x),2)
all((crossprod(Qc) - diag(nrow(x))) < 10*.Machine $double.eps)

QD <- qr.Q(qrstr, D=1:p)      # QD == Q %*% diag(1:p)
all(QD - Q %*% diag(1:p)  < 8* .Machine$double.eps)

dim(Rc <- qr.R(qrstr, complete=TRUE)) # == dim(x)
dim(Xc <- qr.X(qrstr, complete=TRUE)) # square: nrow(x) ^ 2
all(Xc[,1:p] == X)