Skip to main content
`Ctrl`+`K`

# scipy.sparse.linalg.expm

scipy.sparse.linalg.expm(A)

  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

  [1]

  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.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]])