SciPy

scipy.linalg.expm

scipy.linalg.expm(A, q=None)[source]

Compute the matrix exponential using Pade approximation.

Parameters:

A : (N, N) array_like or sparse matrix

Matrix to be exponentiated.

Returns:

expm : (N, N) ndarray

Matrix exponential of A.

References

[R80]Awad H. Al-Mohy and Nicholas J. Higham (2009) “A New Scaling and Squaring Algorithm for the Matrix Exponential.” SIAM Journal on Matrix Analysis and Applications. 31 (3). pp. 970-989. ISSN 1095-7162

Examples

>>> from scipy.linalg import expm, sinm, cosm

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

>>> expm(np.zeros((2,2)))
array([[ 1.,  0.],
       [ 0.,  1.]])

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)
array([[ 0.42645930+1.89217551j, -2.13721484-0.97811252j],
       [ 1.06860742+0.48905626j, -1.71075555+0.91406299j]])
>>> cosm(a) + 1j*sinm(a)
array([[ 0.42645930+1.89217551j, -2.13721484-0.97811252j],
       [ 1.06860742+0.48905626j, -1.71075555+0.91406299j]])

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