`scipy.sparse.linalg._expm_multiply:expm_multiply`

source: build-install/usr/lib/python3.14/site-packages/scipy/sparse/linalg/_expm_multiply.py:109

Signature

def expm_multiply(A, B, start = None, stop = None, num = None, endpoint = None, traceA = None)

Summary

Compute the action of the matrix exponential of A on B.

Parameters

A : transposable linear operator: The operator whose exponential is of interest.
B : ndarray, sparse array: The matrix or vector to be multiplied by the matrix exponential of A.
start : scalar, optional: The starting time point of the sequence.
stop : scalar, optional: The end time point of the sequence, unless endpoint is set to False. In that case, the sequence consists of all but the last of num + 1 evenly spaced time points, so that stop is excluded. Note that the step size changes when endpoint is False.
num : int, optional: Number of time points to use.
endpoint : bool, optional: If True, stop is the last time point. Otherwise, it is not included.
traceA : scalar, optional: Trace of A. If not given the trace is estimated for linear operators, or calculated exactly for sparse matrices. It is used to precondition A, thus an approximate trace is acceptable. For linear operators, traceA should be provided to ensure performance as the estimation is not guaranteed to be reliable for all cases.
versionadded 1.9.0

Returns

expm_A_B : ndarray: The result of the action $e^{t_{k} A} B$ .

Warns

: UserWarning: If A is a linear operator and traceA=None (default).

Notes

The optional arguments defining the sequence of evenly spaced time points are compatible with the arguments of numpy.linspace.

The output ndarray shape is somewhat complicated so I explain it here. The ndim of the output could be either 1, 2, or 3. It would be 1 if you are computing the expm action on a single vector at a single time point. It would be 2 if you are computing the expm action on a vector at multiple time points, or if you are computing the expm action on a matrix at a single time point. It would be 3 if you want the action on a matrix with multiple columns at multiple time points. If multiple time points are requested, expm_A_B[0] will always be the action of the expm at the first time point, regardless of whether the action is on a vector or a matrix.

Examples

import numpy as np
from scipy.sparse import csc_array
from scipy.sparse.linalg import expm, expm_multiply
A = csc_array([[1, 0], [0, 1]])

✓

A.toarray()

✗

array([[1, 0],
       [0, 1]])

B = np.array([np.exp(-1.), np.exp(-2.)])

✓

B
expm_multiply(A, B, start=1, stop=2, num=3, endpoint=True)
expm(A).dot(B)                  # Verify 1st timestep
expm(1.5*A).dot(B)              # Verify 2nd timestep
expm(2*A).dot(B)                # Verify 3rd timestep

✗

array([2.71828, 1.     ])

Aliases

scipy.sparse.linalg.expm_multiply