scipy.linalg.expm¶
-
scipy.linalg.
expm
(A)[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
- 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.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]])