# naginterfaces.library.lapackeig.dgebrd¶

naginterfaces.library.lapackeig.dgebrd(a)[source]

dgebrd reduces a real matrix to bidiagonal form.

For full information please refer to the NAG Library document for f08ke

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f08/f08kef.html

Parameters
afloat, array-like, shape

The matrix .

Returns
afloat, ndarray, shape

If , the diagonal and first superdiagonal are overwritten by the upper bidiagonal matrix , elements below the diagonal are overwritten by details of the orthogonal matrix and elements above the first superdiagonal are overwritten by details of the orthogonal matrix .

If , the diagonal and first subdiagonal are overwritten by the lower bidiagonal matrix , elements below the first subdiagonal are overwritten by details of the orthogonal matrix and elements above the diagonal are overwritten by details of the orthogonal matrix .

dfloat, ndarray, shape

The diagonal elements of the bidiagonal matrix .

efloat, ndarray, shape

The off-diagonal elements of the bidiagonal matrix .

tauqfloat, ndarray, shape

Further details of the orthogonal matrix .

taupfloat, ndarray, shape

Further details of the orthogonal matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

dgebrd reduces a real matrix to bidiagonal form by an orthogonal transformation: , where and are orthogonal matrices of order and respectively.

If , the reduction is given by:

where is an upper bidiagonal matrix and consists of the first columns of .

If , the reduction is given by

where is an lower bidiagonal matrix and consists of the first rows of .

The orthogonal matrices and are not formed explicitly but are represented as products of elementary reflectors (see the F08 Introduction for details). Functions are provided to work with and in this representation (see Further Comments).

References

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