SciPy

scipy.sparse.linalg.expm

scipy.sparse.linalg.expm(A)[source]

Compute the matrix exponential using Pade approximation.

Parameters:

A : (M,M) array_like or sparse matrix

2D Array or Matrix (sparse or dense) to be exponentiated

Returns:

expA : (M,M) ndarray

Matrix exponential of A

Notes

This is algorithm (6.1) which is a simplification of algorithm (5.1).

New in version 0.12.0.

References

[R363]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.sparse import csc_matrix
>>> from scipy.sparse.linalg import expm
>>> A = csc_matrix([[1, 0, 0], [0, 2, 0], [0, 0, 3]])
>>> A.todense()
matrix([[1, 0, 0],
        [0, 2, 0],
        [0, 0, 3]], dtype=int64)
>>> Aexp = expm(A)
>>> Aexp
<3x3 sparse matrix of type '<class 'numpy.float64'>'
    with 3 stored elements in Compressed Sparse Column format>
>>> Aexp.todense()
matrix([[  2.71828183,   0.        ,   0.        ],
        [  0.        ,   7.3890561 ,   0.        ],
        [  0.        ,   0.        ,  20.08553692]])