`scipy.linalg._matfuncs:expm`

source: /scipy/linalg/_matfuncs.py :234

Signature

def expm ( A )

Summary

Compute the matrix exponential of an array.

Extended Summary

Array argument(s) of this function may have additional "batch" dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see linalg_batch for details.

Parameters

A : ndarray: Input with last two dimensions are square (..., n, n).

Returns

eA : ndarray: The resulting matrix exponential with the same shape of A

Notes

Implements the algorithm given in ^[1], which is essentially a Pade approximation with a variable order that is decided based on the array data.

For input with size n, the memory usage is in the worst case in the order of 8*(n**2). If the input data is not of single and double precision of real and complex dtypes, it is copied to a new array.

For cases n >= 400, the exact 1-norm computation cost, breaks even with 1-norm estimation and from that point on the estimation scheme given in ^[2] is used to decide on the approximation order.

Examples

import numpy as np
from scipy.linalg import expm, sinm, cosm

✓

Matrix version of the formula exp(0) = 1:

expm(np.zeros((3, 2, 2)))

✓

Euler's identity (exp(i*theta) = cos(theta) + i*sin(theta)) applied to a matrix:

a = np.array([[1.0, 2.0], [-1.0, 3.0]])

✓

expm(1j*a)
cosm(a) + 1j*sinm(a)