qr.X
Reconstruct the Q, R, or X Matrices from a QR Object
Description
Returns the original matrix from which the object was constructed.
Usage
qr.X(qr, complete = FALSE,
ncol = if (complete) nrow(R) else min(dim(R))
qr.Q(qr, complete = FALSE, Dvec = <<see below>>)
qr.R(qr, complete = FALSE)
Arguments
| qr |
an object representing a QR decomposition. Typically, this argument results from a
previous call to qr or lsfit.
|
| complete |
a logical expression. If TRUE:
- For Q or X matrices, specifies an arbitrary orthogonal completion with the matrix columns.
- For an R matrix, binds zero-value rows beneath the square upper triangle.
The default is FALSE.
|
| ncol |
an integer in the range 1:max(dim(qr\$qr)). Specifies the number of columns to be in the
reconstructed matrix.
- If complete == FALSE, the default is the minimum of the dimension of the matrix from which the qr object was constructed.
- If complete == TRUE, the default is a
square matrix with its size equal to the number of rows in the original matrix.
If ncol is larger than the original number of columns, but less than or equal to the
original number of rows, the first ncol(qr$qr) columns are the original columns.
The additional columns are an arbitrary orthogonal completion
(a unitary completion in the complex case) of the original matrix.
|
| Dvec |
a vector (not a matrix) of diagonal values. Each column of the returned Q is
multiplied by the corresponding diagonal value. The default value is a vector that replicates
1 or 1+0i(for complex) n times, where n is
the minimum of the dimension (if complete == FALSE)
or the number of rows (if complete == TRUE) of the matrix
from which the qr object was constructed.
|
Value
| qr.X | returns:
- X, the original matrix from which the qr object was constructed.
- a column subset of X.
- an orthogonal column completion of X.
If complete == TRUE and/or the argument ncol is greater than ncol(X)
and less than or equal to nrow(X), additional columns from an arbitrary orthogonal (unitary) completion
of X are returned. If X has more columns than rows, ncol has to be given to get the complete matrix. |
| qr.Q | returns Q, the order-nrow(X) orthogonal (unitary) transformation
represented by qr.
- If complete == TRUE, Q has nrow(X) columns.
- If complete == FALSE, Q has min(dim(X)) columns.
When Dvec is specified, each column of Q is multiplied by the corresponding value in Dvec.
|
| qr.R | returns R, the c(ncol(X),ncol(X)) upper triangular matrix
such that X == Q %*% R.
- If complete == TRUE, R has nrow(X) rows.
- If complete == FALSE, R has min(dim(X)) rows.
|
See Also
Examples
n <- 4
p <- 3
x <- matrix(rnorm(n * p), n, p)
qrstr <- qr(x) # dim(x) == c(n,p), n >= p
Q <- qr.Q(qrstr) # dim(Q) == c(n, p)
R <- qr.R(qrstr) # dim(R) == c(p, p)
X <- qr.X(qrstr) # X == x
# X == Q %*% R
Qc <- qr.Q(qrstr, complete = TRUE) # dim(Qc) == c(n, n)
QD <- qr.Q(qrstr, Dvec = seq(p)) # QD == Q %*% diag(D)
Rc <- qr.R(qrstr, complete = TRUE) # dim(Rc) == c(n, p)
Xc <- qr.X(qrstr, complete = TRUE) # Xc[, seq(p)] == x ;
dim(Xc) == c(n, n)
# x == Qc %*% Rc