Source Code for Module lib.linear_algebra.matrix_exponential

 1  ############################################################################### 
 2  #                                                                             # 
 3  # Copyright (C) 2013 Edward d'Auvergne                                        # 
 4  # Copyright (C) 2014 Troels E. Linnet                                         # 
 5  #                                                                             # 
 6  # This file is part of the program relax (http://www.nmr-relax.com).          # 
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 8  # This program is free software: you can redistribute it and/or modify        # 
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13  # This program is distributed in the hope that it will be useful,             # 
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16  # GNU General Public License for more details.                                # 
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19  # along with this program.  If not, see <http://www.gnu.org/licenses/>.       # 
20  #                                                                             # 
21  ############################################################################### 
22   
23  # Module docstring. 
24  """Module for the calculation of the matrix exponential.""" 
25   
26  # Python module imports. 
27  from numpy import array, diag, dot, exp 
28  from numpy.linalg import eig, inv 
29   
30  # relax module imports. 
31  from lib.check_types import is_complex 
32   
33   
34 -def matrix_exponential(A): 
35      """Calculate the exact matrix exponential using the eigenvalue decomposition approach. 
36   
37      @param A:   The square matrix to calculate the matrix exponential of. 
38      @type A:    numpy rank-2 array 
39      @return:    The matrix exponential.  This will have the same dimensionality as the A matrix. 
40      @rtype:     numpy rank-2 array 
41      """ 
42   
43      # Is the original matrix real? 
44      complex_flag = is_complex(A[0, 0]) 
45   
46      # The eigenvalue decomposition. 
47      W, V = eig(A) 
48   
49      # Calculate the exact exponential. 
50      eA = dot(dot(V, diag(exp(W))), inv(V)) 
51   
52      # Return the complex matrix. 
53      if complex_flag: 
54          return array(eA) 
55   
56      # Return only the real part. 
57      else: 
58          return array(eA.real) 
59