naginterfaces.library.lapackeig.dorgbr

naginterfaces.library.lapackeig.dorgbr(vect, k, a, tau)[source]

dorgbr generates one of the real orthogonal matrices or which were determined by dgebrd() when reducing a real matrix to bidiagonal form.

For full information please refer to the NAG Library document for f08kf

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/f08/f08kff.html

Parameters
vectstr, length 1

Indicates whether the orthogonal matrix or is generated.

is generated.

is generated.

kint

If , the number of columns in the original matrix .

If , the number of rows in the original matrix .

afloat, array-like, shape

Details of the vectors which define the elementary reflectors, as returned by dgebrd().

taufloat, array-like, shape

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

Further details of the elementary reflectors, as returned by dgebrd() in its argument if , or in its argument if .

Returns
afloat, ndarray, shape

The orthogonal matrix or , or the leading rows or columns thereof, as specified by , and .

Raises
NagValueError
(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: .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

dorgbr is intended to be used after a call to dgebrd(), which reduces a real rectangular matrix to bidiagonal form by an orthogonal transformation: . dgebrd() represents the matrices and as products of elementary reflectors.

This function may be used to generate or explicitly as square matrices, or in some cases just the leading columns of or the leading rows of .

The various possibilities are specified by the arguments , , and . The appropriate values to cover the most likely cases are as follows (assuming that was an matrix):

  1. To form the full matrix : set , and (note that the array must have at least columns).

  2. If , to form the leading columns of : set , and

  3. To form the full matrix : set , and (note that the array must have at least rows).

  4. If , to form the leading rows of : set and

References

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