naginterfaces.library.lapackeig.dormql

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

dormql multiplies a general real matrix by the real orthogonal matrix from a factorization computed by dgeqlf().

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

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/f08/f08cgf.html

Parameters
sidestr, length 1

Indicates how or is to be applied to .

or is applied to from the left.

or is applied to from the right.

transstr, length 1

Indicates whether or is to be applied to .

is applied to .

is applied to .

afloat, array-like, shape

Note: the required extent for this argument in dimension 1 is determined as follows: if : ; if : ; otherwise: .

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

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

cfloat, array-like, shape

The matrix .

Returns
cfloat, ndarray, shape

is overwritten by or or or as specified by and .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

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

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

overwriting the result on , which may be any real rectangular 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