naginterfaces.library.eigen.complex_​gen_​eigsys

naginterfaces.library.eigen.complex_gen_eigsys(crit, n, a, wl, wu, mest)[source]

complex_gen_eigsys computes selected eigenvalues and eigenvectors of a complex general matrix.

For full information please refer to the NAG Library document for f02gc

https://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/f02/f02gcf.html

Parameters
critstr, length 1

Indicates the criterion for selecting eigenvalues.

Eigenvalues are selected according to their moduli: .

Eigenvalues are selected according to their real parts: .

nint

, the order of the matrix .

acomplex, array-like, shape

The general matrix .

wlfloat

and , the lower and upper bounds on the criterion for the selected eigenvalues (see ).

wufloat

and , the lower and upper bounds on the criterion for the selected eigenvalues (see ).

mestint

must be an upper bound on , the number of eigenvalues and eigenvectors selected. No eigenvectors are computed if .

Returns
acomplex, ndarray, shape

Contains the Hessenberg form of the balanced input matrix (see Further Comments).

mint

, the number of eigenvalues actually selected.

wcomplex, ndarray, shape

The first elements of hold the selected eigenvalues; elements to contain the other eigenvalues.

vcomplex, ndarray, shape

Contains the selected eigenvectors, with the th column holding the eigenvector associated with the eigenvalue (stored in ).

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: or .

(errno )

The algorithm failed to converge: only eigenvalues have been computed; no eigenvectors have been computed.

(errno )

There are more than eigenvalues in the specified range. (number of eigenvalues in range) and . No eigenvectors have been computed. Rerun with second dimension of .

Warns
NagAlgorithmicWarning
(errno )

Inverse iteration failed to compute all the specified eigenvectors. The number of eigenvectors which failed to converge is . The corresponding columns of are set to zero.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

complex_gen_eigsys computes selected eigenvalues and the corresponding right eigenvectors of a complex general matrix :

Eigenvalues may be selected either by modulus, satisfying

or by real part, satisfying

References

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