naginterfaces.library.lapackeig.dgehrd

naginterfaces.library.lapackeig.dgehrd(ilo, ihi, a)[source]

dgehrd reduces a real general matrix to Hessenberg form.

For full information please refer to the NAG Library document for f08ne

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/f08/f08nef.html

Parameters
iloint

If has been output by dgebal(), and must contain the values returned by that function. Otherwise, must be set to and to .

ihiint

If has been output by dgebal(), and must contain the values returned by that function. Otherwise, must be set to and to .

afloat, array-like, shape

The general matrix .

Returns
afloat, ndarray, shape

is overwritten by the upper Hessenberg matrix and details of the orthogonal matrix .

taufloat, ndarray, shape

Further details of the orthogonal matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

(errno )

On entry, error in parameter .

Notes

dgehrd reduces a real general matrix to upper Hessenberg form by an orthogonal similarity transformation: .

The matrix is not formed explicitly, but is represented as a product of elementary reflectors (see the F08 Introduction for details). Functions are provided to work with in this representation (see Further Comments).

The function can take advantage of a previous call to dgebal(), which may produce a matrix with the structure:

where and are upper triangular. If so, only the central diagonal block , in rows and columns to , needs to be reduced to Hessenberg form (the blocks and will also be affected by the reduction). Therefore, the values of and determined by dgebal() can be supplied to the function directly. If dgebal() has not previously been called however, then must be set to and to .

References

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