Source Code for Module maths_fns.alignment_tensor

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