naginterfaces.library.matop.complex_​gen_​matrix_​actexp

naginterfaces.library.matop.complex_gen_matrix_actexp(a, b, t)[source]

complex_gen_matrix_actexp computes the action of the matrix exponential , on the matrix , where is a complex matrix, is a complex matrix and is a complex scalar.

For full information please refer to the NAG Library document for f01ha

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/f01/f01haf.html

Parameters
acomplex, array-like, shape

The matrix .

bcomplex, array-like, shape

The matrix .

tcomplex

The scalar .

Returns
acomplex, ndarray, shape

is overwritten during the computation.

bcomplex, ndarray, shape

The matrix .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

has been computed using an IEEE double precision Taylor series, although the arithmetic precision is higher than IEEE double precision.

Notes

is computed using the algorithm described in Al–Mohy and Higham (2011) which uses a truncated Taylor series to compute the product without explicitly forming .

References

Al–Mohy, A H and Higham, N J, 2011, Computing the action of the matrix exponential, with an application to exponential integrators, SIAM J. Sci. Statist. Comput. (33(2)), 488-511

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