naginterfaces.library.lapackeig.dormql

naginterfaces.library.lapackeig.dormql(side, trans, a, tau, c)

dormql multiplies a general real $m\times n$ matrix $C$ by the real orthogonal matrix $Q$ from a $QL$ factorization computed by dgeqlf().

For full information please refer to the NAG Library document for f08cg

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f08/f08cgf.html

Parameters

sidestr, length 1

Indicates how $Q$ or $Q^T$ is to be applied to $C$.

$side=\text{'L'}$

$Q$ or $Q^T$ is applied to $C$ from the left.

$side=\text{'R'}$

$Q$ or $Q^T$ is applied to $C$ from the right.

transstr, length 1

Indicates whether $Q$ or $Q^T$ is to be applied to $C$.

$trans=\text{'N'}$

$Q$ is applied to $C$.

$trans=\text{'T'}$

$Q^T$ is applied to $C$.

afloat, array-like, shape $(:,k)$

Note: the required extent for this argument in dimension 1 is determined as follows: if $side=\text{'L'}$: $m$; if $side=\text{'R'}$: $n$; otherwise: $0$.

On entry: details of the vectors which define the elementary reflectors, as returned by dgeqlf().

On exit: is modified by dormql but restored on exit.

taufloat, array-like, shape $\left(k\right)$

Further details of the elementary reflectors, as returned by dgeqlf().

cfloat, array-like, shape $(m,n)$

The $m\times n$ matrix $C$.

Returns

cfloat, ndarray, shape $(m,n)$

$c$ is overwritten by $QC$ or $Q^{T}C$ or $CQ$ or $C{Q}^T$ as specified by $side$ and $trans$.

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $side$.

Constraint: $side=\text{'L'}$ or $\text{'R'}$.

(errno $-2$)

On entry, error in parameter $trans$.

Constraint: $trans=\text{'N'}$ or $\text{'T'}$.

(errno $-3$)

On entry, error in parameter $\text{m}$.

Constraint: $m\ge 0$.

(errno $-4$)

On entry, error in parameter $\text{n}$.

Constraint: $n\ge 0$.

(errno $-5$)

On entry, error in parameter $\text{k}$.

Constraint: $m\ge k\ge 0$.

(errno $-5$)

On entry, error in parameter $\text{k}$.

Constraint: $n\ge k\ge 0$.

Notes

dormql is intended to be used following a call to dgeqlf(), which performs a $QL$ factorization of a real matrix $A$ and represents the orthogonal matrix $Q$ as a product of elementary reflectors.

This function may be used to form one of the matrix products

$$QC\text{,}{Q}^{T}C\text{,}CQ\text{,}C{Q}^T\text{,}$$

overwriting the result on $C$, which may be any real rectangular $m\times n$ matrix.

A common application of this function is in solving linear least squares problems, as described in the F08 Introduction.

References

Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia, https://www.netlib.org/lapack/lug