Source Code for Module lib.linear_algebra.matrix_exponential

 1  ############################################################################### 
 2  #                                                                             # 
 3  # Copyright (C) 2013-2014 Edward d'Auvergne                                   # 
 4  #                                                                             # 
 5  # This file is part of the program relax (http://www.nmr-relax.com).          # 
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20  ############################################################################### 
21   
22  # Module docstring. 
23  """Module for the calculation of the matrix exponential.""" 
24   
25  # Python module imports. 
26  from numpy import array, diag, dot, exp 
27  from numpy.linalg import eig, inv 
28   
29  # relax module imports. 
30  from lib.check_types import is_complex 
31   
32   
33 -def matrix_exponential(A): 
34      """Calculate the exact matrix exponential using the eigenvalue decomposition approach. 
35   
36      @param A:   The square matrix to calculate the matrix exponential of. 
37      @type A:    numpy rank-2 array 
38      @return:    The matrix exponential.  This will have the same dimensionality as the A matrix. 
39      @rtype:     numpy rank-2 array 
40      """ 
41   
42      # Is the original matrix real? 
43      complex_flag = is_complex(A[0, 0]) 
44   
45      # The eigenvalue decomposition. 
46      W, V = eig(A) 
47   
48      # Calculate the exact exponential. 
49      eA = dot(dot(V, diag(exp(W))), inv(V)) 
50   
51      # Return the complex matrix. 
52      if complex_flag: 
53          return array(eA) 
54   
55      # Return only the real part. 
56      else: 
57          return array(eA.real) 
58