naginterfaces.library.lapackeig.zgeev¶

naginterfaces.library.lapackeig.zgeev(jobvl, jobvr, a)[source]

zgeev computes the eigenvalues and, optionally, the left and/or right eigenvectors for an complex nonsymmetric matrix .

For full information please refer to the NAG Library document for f08nn

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/f08/f08nnf.html

Parameters
jobvlstr, length 1

If , the left eigenvectors of are not computed.

If , the left eigenvectors of are computed.

jobvrstr, length 1

If , the right eigenvectors of are not computed.

If , the right eigenvectors of are computed.

acomplex, array-like, shape

The matrix .

Returns
acomplex, ndarray, shape

has been overwritten.

wcomplex, ndarray, shape

Contains the computed eigenvalues.

vlcomplex, ndarray, shape

If , the left eigenvectors are stored one after another in the columns of , in the same order as their corresponding eigenvalues; that is , for .

If , is not referenced.

vrcomplex, ndarray, shape

If , the right eigenvectors are stored one after another in the columns of , in the same order as their corresponding eigenvalues; that is , for .

If , is not referenced.

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

The algorithm failed to compute all the eigenvalues, and no eigenvectors have been computed; elements to of contain eigenvalues which have converged.

Notes

The right eigenvector of satisfies

where is the th eigenvalue of . The left eigenvector of satisfies

where denotes the conjugate transpose of .

The matrix is first reduced to upper Hessenberg form by means of unitary similarity transformations, and the algorithm is then used to further reduce the matrix to upper triangular Schur form, , from which the eigenvalues are computed. Optionally, the eigenvectors of are also computed and backtransformed to those of .

References

Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia, https://www.netlib.org/lapack/lug

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