expm(A)

Notes

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

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

Compute the matrix exponential using Pade approximation.

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.toarray()
array([[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.toarray()
array([[  2.71828183,   0.        ,   0.        ],
       [  0.        ,   7.3890561 ,   0.        ],
       [  0.        ,   0.        ,  20.08553692]])

See :

Back References

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

scipy.sparse.linalg._matfuncs.expm scipy.sparse.linalg._expm_multiply.expm_multiply

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