Source Code for Module maths_fns.alignment_tensor

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  2  #                                                                             # 
  3  # Copyright (C) 2008 Edward d'Auvergne                                        # 
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  5  # This file is part of the program relax.                                     # 
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 21  ############################################################################### 
 22   
 23  # Module docstring. 
 24  """Module for the manipulation of alignment tensors.""" 
 25   
 26  # Python imports. 
 27  from numpy.linalg import eigvals 
 28   
 29   
 30 -def dAi_dAxx(A): 
 31      """The dAi/dAxx gradient. 
 32   
 33      This function will modify the A matrix to be equal to:: 
 34   
 35        dAi   | 1  0  0 | 
 36       ---- = | 0  0  0 | 
 37       dAxx   | 0  0 -1 | 
 38   
 39   
 40      @param A:   The alignment tensor object. 
 41      @type A:    numpy rank-2 3D tensor 
 42      """ 
 43   
 44      # Set all elements. 
 45      A[0, 0] = 1.0;  A[0, 1] = 0.0;  A[0, 2] = 0.0 
 46      A[1, 0] = 0.0;  A[1, 1] = 0.0;  A[1, 2] = 0.0 
 47      A[2, 0] = 0.0;  A[2, 1] = 0.0;  A[2, 2] = -1.0 
 48   
 49   
 50 -def dAi_dAyy(A): 
 51      """The dAi/dAyy gradient. 
 52   
 53      This function will modify the A matrix to be equal to:: 
 54   
 55        dAi   | 0  0  0 | 
 56       ---- = | 0  1  0 | 
 57       dAyy   | 0  0 -1 | 
 58   
 59   
 60      @param A:   The alignment tensor object. 
 61      @type A:    numpy rank-2 3D tensor 
 62      """ 
 63   
 64      # Set all elements. 
 65      A[0, 0] = 0.0;  A[0, 1] = 0.0;  A[0, 2] = 0.0 
 66      A[1, 0] = 0.0;  A[1, 1] = 1.0;  A[1, 2] = 0.0 
 67      A[2, 0] = 0.0;  A[2, 1] = 0.0;  A[2, 2] = -1.0 
 68   
 69   
 70 -def dAi_dAxy(A): 
 71      """The dAi/dAxy gradient. 
 72   
 73      This function will modify the A matrix to be equal to:: 
 74   
 75        dAi   | 0  1  0 | 
 76       ---- = | 1  0  0 | 
 77       dAxy   | 0  0  0 | 
 78   
 79   
 80      @param A:   The alignment tensor object. 
 81      @type A:    numpy rank-2 3D tensor 
 82      """ 
 83   
 84      # Set all elements. 
 85      A[0, 0] = 0.0;  A[0, 1] = 1.0;  A[0, 2] = 0.0 
 86      A[1, 0] = 1.0;  A[1, 1] = 0.0;  A[1, 2] = 0.0 
 87      A[2, 0] = 0.0;  A[2, 1] = 0.0;  A[2, 2] = 0.0 
 88   
 89   
 90 -def dAi_dAxz(A): 
 91      """The dAi/dAxz gradient. 
 92   
 93      This function will modify the A matrix to be equal to:: 
 94   
 95        dAi   | 0  0  1 | 
 96       ---- = | 0  0  0 | 
 97       dAxz   | 1  0  0 | 
 98   
 99   
100      @param A:   The alignment tensor object. 
101      @type A:    numpy rank-2 3D tensor 
102      """ 
103   
104      # Set all elements. 
105      A[0, 0] = 0.0;  A[0, 1] = 0.0;  A[0, 2] = 1.0 
106      A[1, 0] = 0.0;  A[1, 1] = 0.0;  A[1, 2] = 0.0 
107      A[2, 0] = 1.0;  A[2, 1] = 0.0;  A[2, 2] = 0.0 
108   
109   
110 -def dAi_dAyz(A): 
111      """The dAi/dAyz gradient. 
112   
113      This function will modify the A matrix to be equal to:: 
114   
115        dAi   | 0  0  0 | 
116       ---- = | 0  0  1 | 
117       dAyz   | 0  1  0 | 
118   
119   
120      @param A:   The alignment tensor object. 
121      @type A:    numpy rank-2 3D tensor 
122      """ 
123   
124      # Set all elements. 
125      A[0, 0] = 0.0;  A[0, 1] = 0.0;  A[0, 2] = 0.0 
126      A[1, 0] = 0.0;  A[1, 1] = 0.0;  A[1, 2] = 1.0 
127      A[2, 0] = 0.0;  A[2, 1] = 1.0;  A[2, 2] = 0.0 
128   
129   
130 -def maxA(tensor): 
131      """Find the maximal alignment - the Azz component in the alignment frame. 
132   
133      @param tensor:      The alignment tensor object. 
134      @type tensor:       numpy rank-2 3D tensor 
135      @return:            The Azz component in the alignment frame. 
136      """ 
137   
138      # Return the value. 
139      return max(abs(eigvals(tensor))) 
140   
141   
142 -def to_5D(vector_5D, tensor): 
143      """Convert the rank-2 3D alignment tensor matrix to the 5D vector format. 
144   
145      @param vector_5D:   The 5D vector object to populate.  The vector format is {Axx, Ayy, Axy, Axz, 
146                          Ayz}. 
147      @type vector_5D:    numpy 5D vector 
148      @param tensor:      The alignment tensor object. 
149      @type tensor:       numpy rank-2 3D tensor 
150      """ 
151   
152      # Convert the matrix form to the vector form. 
153      vector_5D[0] = tensor[0, 0] 
154      vector_5D[1] = tensor[1, 1] 
155      vector_5D[2] = tensor[0, 1] 
156      vector_5D[3] = tensor[0, 2] 
157      vector_5D[4] = tensor[1, 2] 
158   
159   
160 -def to_tensor(tensor, vector_5D): 
161      """Convert the 5D vector alignment tensor form to the rank-2 3D matrix from. 
162   
163      @param tensor:      The alignment tensor object, in matrix format, to populate. 
164      @type tensor:       numpy rank-2 3D tensor 
165      @param vector_5D:   The 5D vector object.  The vector format is {Axx, Ayy, Axy, Axz, Ayz}. 
166      @type vector_5D:    numpy 5D vector 
167      """ 
168   
169      # Convert the vector form to the matrix form. 
170      tensor[0, 0] = vector_5D[0] 
171      tensor[0, 1] = vector_5D[2] 
172      tensor[0, 2] = vector_5D[3] 
173      tensor[1, 0] = vector_5D[2] 
174      tensor[1, 1] = vector_5D[1] 
175      tensor[1, 2] = vector_5D[4] 
176      tensor[2, 0] = vector_5D[3] 
177      tensor[2, 1] = vector_5D[4] 
178      tensor[2, 2] = -vector_5D[0] -vector_5D[1] 
179