maths_fns.kronecker

1 ############################################################################### 2 # # 3 # Copyright (C) 2009 Edward d'Auvergne # 4 # # 5 # This file is part of the program relax. # 6 # # 7 # relax is free software; you can redistribute it and/or modify # 8 # it under the terms of the GNU General Public License as published by # 9 # the Free Software Foundation; either version 2 of the License, or # 10 # (at your option) any later version. # 11 # # 12 # relax is distributed in the hope that it will be useful, # 13 # but WITHOUT ANY WARRANTY; without even the implied warranty of # 14 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # 15 # GNU General Public License for more details. # 16 # # 17 # You should have received a copy of the GNU General Public License # 18 # along with relax; if not, write to the Free Software # 19 # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA # 20 # # 21 ############################################################################### 22 23 # Module docstring. 24 """Module for the calculation of the Kronecker product.""" 25 26 # Python imports. 27 from numpy import concatenate, outer 28 29 30

31 -def kron_prod(A, B):

32 """Calculate the Kronecker product of the matrices A and B. 33 34 @param A: ixj matrix. 35 @type A: rank-2 numpy array 36 @param B: kxl matrix. 37 @type B: rank-2 numpy array 38 @return: The Kronecker product. 39 @rtype: ikxjl rank-2 numpy array 40 """ 41 42 # The outer product. 43 C = outer(A, B) 44 45 # Redefine the shape. 46 orig_shape = C.shape 47 C.shape = A.shape + B.shape 48 49 # Generate and return the Kronecker product matrix. 50 transpose_23(C) 51 C.shape = orig_shape 52 return C

53 54

55 -def transpose_12(matrix):

56 """Perform the 1,2 transpose of a rank-4, 3D tensor. 57 58 @param matrix: The rank-4 tensor either in (9, 9) shape for a matrix or the (3, 3, 3, 3) shape 59 for the tensor form. 60 @type matrix: numpy array 61 """ 62 63 # Reshape if necessary. 64 reshape = False 65 if matrix.shape == (9, 9): 66 reshape = True 67 matrix.shape = (3, 3, 3, 3) 68 69 # Perform the transpose. 70 for i in range(3): 71 for j in range(i, 3): 72 for k in range(3): 73 for l in range(3): 74 # Store the element. 75 element = matrix[i, j, k, l] 76 77 # Overwrite. 78 matrix[i, j, k, l] = matrix[j, i, k, l] 79 matrix[j, i, k, l] = element 80 81 # Undo the reshape. 82 if reshape: 83 matrix.shape = (9, 9)

84 85

86 -def transpose_13(matrix):

87 """Perform the 1,3 transpose of a rank-4, 3D tensor. 88 89 @param matrix: The rank-4 tensor either in (9, 9) shape for a matrix or the (3, 3, 3, 3) shape 90 for the tensor form. 91 @type matrix: numpy array 92 """ 93 94 # Reshape if necessary. 95 reshape = False 96 if matrix.shape == (9, 9): 97 reshape = True 98 matrix.shape = (3, 3, 3, 3) 99 100 # Perform the transpose. 101 for i in range(3): 102 for j in range(3): 103 for k in range(i, 3): 104 for l in range(3): 105 # Store the element. 106 element = matrix[i, j, k, l] 107 108 # Overwrite. 109 matrix[i, j, k, l] = matrix[k, j, i, l] 110 matrix[k, j, i, l] = element 111 112 # Undo the reshape. 113 if reshape: 114 matrix.shape = (9, 9)

115 116

117 -def transpose_14(matrix):

118 """Perform the 1,4 transpose of a rank-4, 3D tensor. 119 120 @param matrix: The rank-4 tensor either in (9, 9) shape for a matrix or the (3, 3, 3, 3) shape 121 for the tensor form. 122 @type matrix: numpy array 123 """ 124 125 # Reshape if necessary. 126 reshape = False 127 if matrix.shape == (9, 9): 128 reshape = True 129 matrix.shape = (3, 3, 3, 3) 130 131 # Perform the transpose. 132 for i in range(3): 133 for j in range(3): 134 for k in range(3): 135 for l in range(i, 3): 136 # Store the element. 137 element = matrix[i, j, k, l] 138 139 # Overwrite. 140 matrix[i, j, k, l] = matrix[l, j, k, i] 141 matrix[l, j, k, i] = element 142 143 # Undo the reshape. 144 if reshape: 145 matrix.shape = (9, 9)

146 147

148 -def transpose_23(matrix):

149 """Perform the 2,3 transpose of a rank-4, 3D tensor. 150 151 @param matrix: The rank-4 tensor either in (9, 9) shape for a matrix or the (3, 3, 3, 3) shape 152 for the tensor form. 153 @type matrix: numpy array 154 """ 155 156 # Reshape if necessary. 157 reshape = False 158 if matrix.shape == (9, 9): 159 reshape = True 160 matrix.shape = (3, 3, 3, 3) 161 162 # Perform the transpose. 163 for i in range(3): 164 for j in range(3): 165 for k in range(j, 3): 166 for l in range(3): 167 # Store the element. 168 element = matrix[i, j, k, l] 169 170 # Overwrite. 171 matrix[i, j, k, l] = matrix[i, k, j, l] 172 matrix[i, k, j, l] = element 173 174 # Undo the reshape. 175 if reshape: 176 matrix.shape = (9, 9)

177 178

179 -def transpose_24(matrix):

180 """Perform the 2,4 transpose of a rank-4, 3D tensor. 181 182 @param matrix: The rank-4 tensor either in (9, 9) shape for a matrix or the (3, 3, 3, 3) shape 183 for the tensor form. 184 @type matrix: numpy array 185 """ 186 187 # Reshape if necessary. 188 reshape = False 189 if matrix.shape == (9, 9): 190 reshape = True 191 matrix.shape = (3, 3, 3, 3) 192 193 # Perform the transpose. 194 for i in range(3): 195 for j in range(3): 196 for k in range(3): 197 for l in range(j, 3): 198 # Store the element. 199 element = matrix[i, j, k, l] 200 201 # Overwrite. 202 matrix[i, j, k, l] = matrix[i, l, k, j] 203 matrix[i, l, k, j] = element 204 205 # Undo the reshape. 206 if reshape: 207 matrix.shape = (9, 9)

208 209

210 -def transpose_34(matrix):

211 """Perform the 3,4 transpose of a rank-4, 3D tensor. 212 213 @param matrix: The rank-4 tensor either in (9, 9) shape for a matrix or the (3, 3, 3, 3) shape 214 for the tensor form. 215 @type matrix: numpy array 216 """ 217 218 # Reshape if necessary. 219 reshape = False 220 if matrix.shape == (9, 9): 221 reshape = True 222 matrix.shape = (3, 3, 3, 3) 223 224 # Perform the transpose. 225 for i in range(3): 226 for j in range(3): 227 for k in range(3): 228 for l in range(k, 3): 229 # Store the element. 230 element = matrix[i, j, k, l] 231 232 # Overwrite. 233 matrix[i, j, k, l] = matrix[i, j, l, k] 234 matrix[i, j, l, k] = element 235 236 # Undo the reshape. 237 if reshape: 238 matrix.shape = (9, 9)

239

Source Code for Module maths_fns.kronecker_product