naginterfaces.library.matop.real_​symm_​matrix_​exp¶

naginterfaces.library.matop.real_symm_matrix_exp(uplo, a)[source]

real_symm_matrix_exp computes the matrix exponential, , of a real symmetric matrix .

For full information please refer to the NAG Library document for f01ed

https://www.nag.com/numeric/nl/nagdoc_29/flhtml/f01/f01edf.html

Parameters
uplostr, length 1

Indicates whether the upper or lower triangular part of is stored.

The upper triangular part of is stored.

The lower triangular part of is stored.

afloat, array-like, shape

The symmetric matrix .

Returns
afloat, ndarray, shape

If no exception or warning is raised, the upper or lower triangular part of the matrix exponential, .

Raises
NagValueError
(errno )

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: or .

(errno )

The computation of the spectral factorization failed to converge.

Notes

is computed using a spectral factorization of

where is the diagonal matrix whose diagonal elements, , are the eigenvalues of , and is an orthogonal matrix whose columns are the eigenvectors of . is then given by

where is the diagonal matrix whose th diagonal element is . See for example Section 4.5 of Higham (2008).

References

Higham, N J, 2008, Functions of Matrices: Theory and Computation, SIAM, Philadelphia, PA, USA

Moler, C B and Van Loan, C F, 2003, Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev. (45), 3–49