and Nicholas J. Higham (2011) "Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators." SIAM Journal on Scientific Computing, 33 (2). pp. 488-511. ISSN 1064-8275 http://eprints.ma.man.ac.uk/1591/ .. [2] Nicholas J. Higham and Awad H. Al-Mohy (2010) "Computing Matrix Functions." Acta Numerica, 19. 159-208. ISSN 0962-4929 http://eprints.ma.man.ac.uk/1451/ Examples -------- >>> import numpy as np >>> from scipy.sparse import csc_array >>> from scipy.sparse.linalg import expm, expm_multiply >>> A = csc_array([[1, 0], [0, 1]]) >>> A.toarray() array([[1, 0], [0, 1]], dtype=int64) >>> B = np.array([np.exp(-1.), np.exp(-2.)]) >>> B array([ 0.36787944, 0.13533528]) >>> expm_multiply(A, B, start=1, stop=2, num=3, endpoint=True) array([[ 1. , 0.36787944], [ 1.64872127, 0.60653066], [ 2.71828183, 1. ]]) >>> expm(A).dot(B) # Verify 1st timestep array([ 1. , 0.36787944]) >>> expm(1.5*A).dot(B) # Verify 2nd timestep array([ 1.64872127, 0.60653066]) >>> expm(2*A).dot(B) # Verify 3rd timestep array([ 2.71828183, 1. ]) c