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

naginterfaces.library.matop.complex_gen_matrix_actexp(a, b, t)

complex_gen_matrix_actexp computes the action of the matrix exponential $e^{tA}$, on the matrix $B$, where $A$ is a complex $n\times n$ matrix, $B$ is a complex $n\times m$ matrix and $t$ is a complex scalar.

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

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/f01/f01haf.html

Parameters

acomplex, array-like, shape $(n,n)$

The $n\times n$ matrix $A$.

bcomplex, array-like, shape $(n,m)$

The $n\times m$ matrix $B$.

tcomplex

The scalar $t$.

Returns

acomplex, ndarray, shape $(n,n)$

$A$ is overwritten during the computation.

bcomplex, ndarray, shape $(n,m)$

The $n\times m$ matrix $e^{tA}B$.

Raises

NagValueError

(errno $-2$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 0$.

(errno $-1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

Warns

NagAlgorithmicWarning

(errno $2$)

$e^{tA}B$ has been computed using an IEEE double precision Taylor series, although the arithmetic precision is higher than IEEE double precision.

Notes

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

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