naginterfaces.library.matop.real_​gen_​rq_​formq

naginterfaces.library.matop.real_gen_rq_formq(wheret, m, nrowp, a, zeta)[source]

real_gen_rq_formq returns the first rows of the real orthogonal matrix , where is given as the product of Householder transformation matrices.

This function is intended for use following real_gen_rq().

For full information please refer to the NAG Library document for f01qk

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/f01/f01qkf.html

Parameters
wheretstr, length 1

Indicates where the elements of are to be found.

(In )

The elements of are in .

(Separate)

The elements of are separate from , in .

mint

, the number of rows of the matrix .

nrowpint

, the required number of rows of .

If , an immediate return is effected.

afloat, array-like, shape

The leading strictly lower triangular part of the array , and the rectangular part of with top left-hand corner at element must contain details of the matrix . In addition, if , the diagonal elements of must contain the elements of .

zetafloat, array-like, shape

Note: the required length for this argument is determined as follows: if : ; otherwise: .

With , the array must contain the elements of . If then is assumed to be , otherwise is assumed to contain .

When , the array is not referenced.

Returns
afloat, ndarray, shape

The first rows of the array are overwritten by the first rows of the orthogonal matrix .

Raises
NagValueError
(errno )

On entry, , and .

Constraint: .

(errno )

On entry, and .

Constraint: and .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: or .

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

is assumed to be given by

where

is a scalar, is a () element vector and is an () element vector. must be supplied in the th row of in elements . must be supplied in the th row of in elements and must be supplied either in or in , depending upon the argument .

References

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore

Wilkinson, J H, 1965, The Algebraic Eigenvalue Problem, Oxford University Press, Oxford