# naginterfaces.library.lapackeig.dgeev¶

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

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

For full information please refer to the NAG Library document for f08na

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f08/f08naf.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.

afloat, array-like, shape

The matrix .

Returns
afloat, ndarray, shape

has been overwritten.

wrfloat, ndarray, shape

and contain the real and imaginary parts, respectively, of the computed eigenvalues. Complex conjugate pairs of eigenvalues appear consecutively with the eigenvalue having the positive imaginary part first.

wifloat, ndarray, shape

and contain the real and imaginary parts, respectively, of the computed eigenvalues. Complex conjugate pairs of eigenvalues appear consecutively with the eigenvalue having the positive imaginary part first.

vlfloat, ndarray, shape

If , the left eigenvectors are stored one after another in the columns of , in the same order as their corresponding eigenvalues. If the th eigenvalue is real, then , for . If the th and st eigenvalues form a complex conjugate pair, then and , for .

If , is not referenced.

vrfloat, ndarray, shape

If , the right eigenvectors are stored one after another in the columns of , in the same order as their corresponding eigenvalues. If the th eigenvalue is real, then , for . If the th and st eigenvalues form a complex conjugate pair, then and , 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 and 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 orthogonal similarity transformations, and the algorithm is then used to further reduce the matrix to upper quasi-triangular Schur form, , with and blocks on the main diagonal. The eigenvalues are computed from , the blocks corresponding to complex conjugate pairs and, optionally, the eigenvectors of are computed and backtransformed to the eigenvectors 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