qr(x, tol=1e-07) qr.coef(qr, y) qr.qy(qr, y) qr.qty(qr, y) qr.resid(qr, y) qr.fitted(qr, y, k=qr$rank) is.qr(x) as.qr(x)
x
| a matrix whose QR decomposition is to be computed. | ||||
tol
|
the tolerance for detecting linear dependencies in
the columns of x.
|
qr provides an interface to the techniques used in the LINPACK
routine DQRDC.
The QR decompostion plays an important role in many statistical
techniques.
In particular it can be used to solve the equation
\bold{Ax} = \bold{b} for given matrix \bold{A},
and vector \bold{b}.
It is useful for computing regression coefficients and in applying the
Newton-Raphson algorithm.
The functions qr.coef, qr.qy, qr.qty,
qr.resid, and qr.fitted use a computed
QR decomposition to compute various quantities of interest.
is.qr returns true if x is a list with a
component named qr and false otherwise.
It is not possible to coerce objects to mode qr.
Objects either are qr decompositions or they are not.
Coercion is not possible.
Values
The QR decomposition of the matrix as computed by LINPACK.
The components in the returned value correspond directly
to the values returned by DQRDC.
qr
a matrix with the same dimensions as x.
The upper triangle contains the R of the decomposition
and the lower triangle contains information on the Q
of the decomposition (stored in compact form).
qraux
a vector of length ncol(x) which contains
additional information on Q.
rank
the rank of x as computed by the decomposition.
pivot
information on the pivoting strategy used during
the decomposition.
References
Dongarra, J. J., J. R. Bunch, C. B. Moler and G. W. Stewart (1978).
LINPACK Users Guide, SIAM Publications, Philadelphia.
See Also
solve.qr, qr.coef, lsfit.
Examples
v <- qr(x)