Document

scipy 1.8.0 Pypi GitHub Homepage

expm_frechet(A, E, method=None, compute_expm=True, check_finite=True)

Notes

This section describes the available implementations that can be selected by the method parameter. The default method is SPS.

Method blockEnlarge is a naive algorithm.

Method SPS is Scaling-Pade-Squaring . It is a sophisticated implementation which should take only about 3/8 as much time as the naive implementation. The asymptotics are the same.

versionadded

Parameters

A : (N, N) array_like

Matrix of which to take the matrix exponential.

E : (N, N) array_like

Matrix direction in which to take the Frechet derivative.

method : str, optional

Choice of algorithm. Should be one of

:None:None:`SPS` (default)
:None:None:`blockEnlarge`

compute_expm : bool, optional

Whether to compute also :None:None:`expm_A` in addition to :None:None:`expm_frechet_AE`. Default is True.

check_finite : bool, optional

Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

Returns

expm_A : ndarray: Matrix exponential of A.
expm_frechet_AE : ndarray: Frechet derivative of the matrix exponential of A in the direction E.
For ``compute_expm = False``, only `expm_frechet_AE` is returned.

Frechet derivative of the matrix exponential of A in the direction E.

Examples

>>> import scipy.linalg
... rng = np.random.default_rng()
... A = rng.standard_normal((3, 3))
... E = rng.standard_normal((3, 3))
... expm_A, expm_frechet_AE = scipy.linalg.expm_frechet(A, E)
... expm_A.shape, expm_frechet_AE.shape
((3, 3), (3, 3))

>>> import scipy.linalg
... rng = np.random.default_rng()
... A = rng.standard_normal((3, 3))
... E = rng.standard_normal((3, 3))
... expm_A, expm_frechet_AE = scipy.linalg.expm_frechet(A, E)
... M = np.zeros((6, 6))
... M[:3, :3] = A; M[:3, 3:] = E; M[3:, 3:] = A
... expm_M = scipy.linalg.expm(M)
... np.allclose(expm_A, expm_M[:3, :3])
True

>>> np.allclose(expm_frechet_AE, expm_M[:3, 3:])
True

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.linalg._expm_frechet.expm_cond scipy.linalg._expm_frechet.expm_frechet_kronform

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them