# naginterfaces.library.lapackeig.zgehrd¶

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

zgehrd reduces a complex general matrix to Hessenberg form.

For full information please refer to the NAG Library document for f08ns

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f08/f08nsf.html

Parameters
iloint

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

ihiint

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

acomplex, array-like, shape

The general matrix .

Returns
acomplex, ndarray, shape

is overwritten by the upper Hessenberg matrix and details of the unitary matrix . The subdiagonal elements of are real.

taucomplex, ndarray, shape

Further details of the unitary matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

(errno )

On entry, error in parameter .

Notes

zgehrd reduces a complex general matrix to upper Hessenberg form by a unitary similarity transformation: . has real subdiagonal elements.

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 zgebal(), 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 zgebal() can be supplied to the function directly. If zgebal() 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