Line data Source code
1 1 : // Distributed under the MIT License.
2 : // See LICENSE.txt for details.
3 :
4 : /// \file
5 : /// Defines a list of useful type aliases for tensors
6 :
7 : #pragma once
8 :
9 : #include "DataStructures/Tensor/IndexType.hpp"
10 : #include "DataStructures/Tensor/Symmetry.hpp"
11 :
12 : /// \cond
13 : class DataVector;
14 : template <typename X, typename Symm, typename IndexList>
15 : class Tensor;
16 : /// \endcond
17 :
18 : /// \ingroup TensorGroup
19 : /// Scalar type
20 : template <typename T>
21 1 : using Scalar = Tensor<T, Symmetry<>, index_list<>>;
22 :
23 : /*!
24 : * \ingroup TensorGroup
25 : * \brief Type aliases to construct common Tensors
26 : *
27 : * Lower case letters represent covariant indices and upper case letters
28 : * represent contravariant indices. Letters a, b, c, d represent spacetime
29 : * indices and i, j, k, l represent spatial indices.
30 : */
31 1 : namespace tnsr {
32 : // Rank 1
33 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
34 : IndexType Index = IndexType::Spacetime>
35 0 : using a = Tensor<DataType, tmpl::integral_list<std::int32_t, 1>,
36 : index_list<Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo,
37 : Fr, Index>>>;
38 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
39 : IndexType Index = IndexType::Spacetime>
40 0 : using A = Tensor<DataType, tmpl::integral_list<std::int32_t, 1>,
41 : index_list<Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up,
42 : Fr, Index>>>;
43 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
44 0 : using i = Tensor<DataType, tmpl::integral_list<std::int32_t, 1>,
45 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
46 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
47 0 : using I = Tensor<DataType, tmpl::integral_list<std::int32_t, 1>,
48 : index_list<SpatialIndex<SpatialDim, UpLo::Up, Fr>>>;
49 :
50 : // Rank 2
51 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
52 : IndexType Index = IndexType::Spacetime>
53 0 : using ab = Tensor<
54 : DataType, tmpl::integral_list<std::int32_t, 2, 1>,
55 : index_list<
56 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
57 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>>>;
58 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
59 : IndexType Index = IndexType::Spacetime>
60 0 : using Ab = Tensor<
61 : DataType, tmpl::integral_list<std::int32_t, 2, 1>,
62 : index_list<
63 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
64 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>>>;
65 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
66 : IndexType Index = IndexType::Spacetime>
67 0 : using aB = Tensor<
68 : DataType, tmpl::integral_list<std::int32_t, 2, 1>,
69 : index_list<
70 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
71 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>>>;
72 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
73 : IndexType Index = IndexType::Spacetime>
74 0 : using AB = Tensor<
75 : DataType, tmpl::integral_list<std::int32_t, 2, 1>,
76 : index_list<
77 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
78 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>>>;
79 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
80 0 : using aI =
81 : Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1>,
82 : index_list<Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr,
83 : IndexType::Spacetime>,
84 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr,
85 : IndexType::Spatial>>>;
86 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
87 0 : using ij = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1>,
88 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
89 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
90 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
91 0 : using iJ = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1>,
92 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
93 : SpatialIndex<SpatialDim, UpLo::Up, Fr>>>;
94 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
95 0 : using Ij = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1>,
96 : index_list<SpatialIndex<SpatialDim, UpLo::Up, Fr>,
97 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
98 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
99 0 : using IJ = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1>,
100 : index_list<SpatialIndex<SpatialDim, UpLo::Up, Fr>,
101 : SpatialIndex<SpatialDim, UpLo::Up, Fr>>>;
102 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
103 0 : using iA = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1>,
104 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
105 : SpacetimeIndex<SpatialDim, UpLo::Up, Fr>>>;
106 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
107 0 : using ia = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1>,
108 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
109 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>>>;
110 :
111 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
112 : IndexType Index = IndexType::Spacetime>
113 0 : using aa = Tensor<
114 : DataType, tmpl::integral_list<std::int32_t, 1, 1>,
115 : index_list<
116 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
117 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>>>;
118 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
119 : IndexType Index = IndexType::Spacetime>
120 0 : using AA = Tensor<
121 : DataType, tmpl::integral_list<std::int32_t, 1, 1>,
122 : index_list<
123 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
124 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>>>;
125 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
126 0 : using ii = Tensor<DataType, tmpl::integral_list<std::int32_t, 1, 1>,
127 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
128 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
129 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
130 0 : using II = Tensor<DataType, tmpl::integral_list<std::int32_t, 1, 1>,
131 : index_list<SpatialIndex<SpatialDim, UpLo::Up, Fr>,
132 : SpatialIndex<SpatialDim, UpLo::Up, Fr>>>;
133 :
134 : // Rank 3 - spacetime
135 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
136 : IndexType Index = IndexType::Spacetime>
137 0 : using abc = Tensor<
138 : DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
139 : index_list<
140 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
141 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
142 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>>>;
143 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
144 : IndexType Index = IndexType::Spacetime>
145 0 : using abC = Tensor<
146 : DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
147 : index_list<
148 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
149 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
150 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>>>;
151 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
152 : IndexType Index = IndexType::Spacetime>
153 0 : using aaB = Tensor<
154 : DataType, tmpl::integral_list<std::int32_t, 2, 2, 1>,
155 : index_list<
156 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
157 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
158 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>>>;
159 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
160 : IndexType Index = IndexType::Spacetime>
161 0 : using aBc = Tensor<
162 : DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
163 : index_list<
164 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
165 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
166 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>>>;
167 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
168 : IndexType Index = IndexType::Spacetime>
169 0 : using Abc = Tensor<
170 : DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
171 : index_list<
172 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
173 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
174 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>>>;
175 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
176 : IndexType Index = IndexType::Spacetime>
177 0 : using aBC = Tensor<
178 : DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
179 : index_list<
180 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
181 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
182 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>>>;
183 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
184 : IndexType Index = IndexType::Spacetime>
185 0 : using AbC = Tensor<
186 : DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
187 : index_list<
188 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
189 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
190 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>>>;
191 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
192 : IndexType Index = IndexType::Spacetime>
193 0 : using ABc = Tensor<
194 : DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
195 : index_list<
196 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
197 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
198 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>>>;
199 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
200 : IndexType Index = IndexType::Spacetime>
201 0 : using ABC = Tensor<
202 : DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
203 : index_list<
204 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
205 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
206 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>>>;
207 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
208 : IndexType Index = IndexType::Spacetime>
209 0 : using abb = Tensor<
210 : DataType, tmpl::integral_list<std::int32_t, 2, 1, 1>,
211 : index_list<
212 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
213 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
214 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>>>;
215 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
216 : IndexType Index = IndexType::Spacetime>
217 0 : using Abb = Tensor<
218 : DataType, tmpl::integral_list<std::int32_t, 2, 1, 1>,
219 : index_list<
220 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
221 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
222 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>>>;
223 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
224 : IndexType Index = IndexType::Spacetime>
225 0 : using aBB = Tensor<
226 : DataType, tmpl::integral_list<std::int32_t, 2, 1, 1>,
227 : index_list<
228 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
229 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
230 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>>>;
231 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
232 : IndexType Index = IndexType::Spacetime>
233 0 : using ABB = Tensor<
234 : DataType, tmpl::integral_list<std::int32_t, 2, 1, 1>,
235 : index_list<
236 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
237 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
238 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>>>;
239 :
240 : // Rank 3 - spatial
241 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
242 0 : using iii = Tensor<DataType, tmpl::integral_list<std::int32_t, 1, 1, 1>,
243 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
244 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
245 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
246 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
247 0 : using ijk = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
248 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
249 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
250 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
251 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
252 0 : using ijK = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
253 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
254 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
255 : SpatialIndex<SpatialDim, UpLo::Up, Fr>>>;
256 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
257 0 : using iiJ = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 2, 1>,
258 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
259 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
260 : SpatialIndex<SpatialDim, UpLo::Up, Fr>>>;
261 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
262 0 : using iJk = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
263 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
264 : SpatialIndex<SpatialDim, UpLo::Up, Fr>,
265 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
266 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
267 0 : using Ijk = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
268 : index_list<SpatialIndex<SpatialDim, UpLo::Up, Fr>,
269 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
270 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
271 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
272 0 : using iJK = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
273 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
274 : SpatialIndex<SpatialDim, UpLo::Up, Fr>,
275 : SpatialIndex<SpatialDim, UpLo::Up, Fr>>>;
276 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
277 0 : using IjK = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
278 : index_list<SpatialIndex<SpatialDim, UpLo::Up, Fr>,
279 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
280 : SpatialIndex<SpatialDim, UpLo::Up, Fr>>>;
281 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
282 0 : using IJk = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
283 : index_list<SpatialIndex<SpatialDim, UpLo::Up, Fr>,
284 : SpatialIndex<SpatialDim, UpLo::Up, Fr>,
285 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
286 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
287 0 : using IJK = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
288 : index_list<SpatialIndex<SpatialDim, UpLo::Up, Fr>,
289 : SpatialIndex<SpatialDim, UpLo::Up, Fr>,
290 : SpatialIndex<SpatialDim, UpLo::Up, Fr>>>;
291 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
292 0 : using ijj = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1, 1>,
293 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
294 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
295 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
296 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
297 0 : using Ijj = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1, 1>,
298 : index_list<SpatialIndex<SpatialDim, UpLo::Up, Fr>,
299 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
300 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
301 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
302 0 : using iJJ = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1, 1>,
303 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
304 : SpatialIndex<SpatialDim, UpLo::Up, Fr>,
305 : SpatialIndex<SpatialDim, UpLo::Up, Fr>>>;
306 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
307 0 : using IJJ = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1, 1>,
308 : index_list<SpatialIndex<SpatialDim, UpLo::Up, Fr>,
309 : SpatialIndex<SpatialDim, UpLo::Up, Fr>,
310 : SpatialIndex<SpatialDim, UpLo::Up, Fr>>>;
311 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
312 0 : using III = Tensor<DataType, tmpl::integral_list<std::int32_t, 1, 1, 1>,
313 : index_list<SpatialIndex<SpatialDim, UpLo::Up, Fr>,
314 : SpatialIndex<SpatialDim, UpLo::Up, Fr>,
315 : SpatialIndex<SpatialDim, UpLo::Up, Fr>>>;
316 :
317 : // Rank 3 - mixed spacetime spatial
318 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
319 0 : using iab = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
320 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
321 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>,
322 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>>>;
323 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
324 0 : using iaB = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
325 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
326 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>,
327 : SpacetimeIndex<SpatialDim, UpLo::Up, Fr>>>;
328 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
329 0 : using iAb = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
330 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
331 : SpacetimeIndex<SpatialDim, UpLo::Up, Fr>,
332 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>>>;
333 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
334 0 : using iAB = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1>,
335 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
336 : SpacetimeIndex<SpatialDim, UpLo::Up, Fr>,
337 : SpacetimeIndex<SpatialDim, UpLo::Up, Fr>>>;
338 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
339 0 : using iaa = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1, 1>,
340 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
341 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>,
342 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>>>;
343 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
344 0 : using aia = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1, 2>,
345 : index_list<SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>,
346 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
347 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>>>;
348 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
349 0 : using iAA = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1, 1>,
350 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
351 : SpacetimeIndex<SpatialDim, UpLo::Up, Fr>,
352 : SpacetimeIndex<SpatialDim, UpLo::Up, Fr>>>;
353 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
354 0 : using Iaa = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1, 1>,
355 : index_list<SpatialIndex<SpatialDim, UpLo::Up, Fr>,
356 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>,
357 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>>>;
358 :
359 : // Rank 4 - Mixed
360 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
361 0 : using ijaa = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1, 1>,
362 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
363 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
364 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>,
365 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>>>;
366 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
367 0 : using iiaa = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 2, 1, 1>,
368 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
369 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
370 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>,
371 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>>>;
372 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
373 0 : using iiAA = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 2, 1, 1>,
374 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
375 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
376 : SpacetimeIndex<SpatialDim, UpLo::Up, Fr>,
377 : SpacetimeIndex<SpatialDim, UpLo::Up, Fr>>>;
378 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
379 0 : using iAbb = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1, 1>,
380 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
381 : SpacetimeIndex<SpatialDim, UpLo::Up, Fr>,
382 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>,
383 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>>>;
384 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
385 0 : using iabb = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1, 1>,
386 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
387 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>,
388 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>,
389 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>>>;
390 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
391 0 : using Ijaa = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1, 1>,
392 : index_list<SpatialIndex<SpatialDim, UpLo::Up, Fr>,
393 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
394 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>,
395 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>>>;
396 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
397 0 : using aaBB = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 2, 1, 1>,
398 : index_list<SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>,
399 : SpacetimeIndex<SpatialDim, UpLo::Lo, Fr>,
400 : SpacetimeIndex<SpatialDim, UpLo::Up, Fr>,
401 : SpacetimeIndex<SpatialDim, UpLo::Up, Fr>>>;
402 :
403 : // Rank 4 - generic (default spacetime)
404 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
405 : IndexType Index = IndexType::Spacetime>
406 0 : using abcc = Tensor<
407 : DataType, tmpl::integral_list<std::int32_t, 3, 2, 1, 1>,
408 : index_list<
409 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
410 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
411 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
412 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>>>;
413 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial,
414 : IndexType Index = IndexType::Spacetime>
415 0 : using aBcc = Tensor<
416 : DataType, tmpl::integral_list<std::int32_t, 3, 2, 1, 1>,
417 : index_list<
418 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
419 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Up, Fr, Index>,
420 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>,
421 : Tensor_detail::TensorIndexType<SpatialDim, UpLo::Lo, Fr, Index>>>;
422 :
423 : // Rank 4 - spatial
424 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
425 0 : using ijkk = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1, 1>,
426 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
427 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
428 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
429 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
430 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
431 0 : using iJkk = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1, 1>,
432 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
433 : SpatialIndex<SpatialDim, UpLo::Up, Fr>,
434 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
435 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
436 :
437 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
438 0 : using iijj = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 2, 1, 1>,
439 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
440 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
441 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
442 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;
443 :
444 : template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
445 0 : using iiJJ = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 2, 1, 1>,
446 : index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
447 : SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
448 : SpatialIndex<SpatialDim, UpLo::Up, Fr>,
449 : SpatialIndex<SpatialDim, UpLo::Up, Fr>>>;
450 : } // namespace tnsr
451 :
452 : /*!
453 : * \brief Inverse Jacobian $(J^{-1})^\hat{i}_j =
454 : * \frac{\partial \xi^\hat{i}}{\partial x^j}$
455 : *
456 : * The first (upper) index is in the \p SourceFrame with coordinates
457 : * $\xi^\hat{i}$ (often "logical"), and the second (lower) index is in the
458 : * \p TargetFrame with coordinates $x^j$ (often "inertial").
459 : */
460 : template <typename DataType, size_t Dim, typename SourceFrame,
461 : typename TargetFrame>
462 1 : using InverseJacobian =
463 : Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1>,
464 : index_list<SpatialIndex<Dim, UpLo::Up, SourceFrame>,
465 : SpatialIndex<Dim, UpLo::Lo, TargetFrame>>>;
466 :
467 : /*!
468 : * \brief Jacobian $J^i_\hat{j} = \frac{\partial x^i}{\partial \xi^\hat{j}}$
469 : *
470 : * The first (upper) index is in the \p TargetFrame with coordinates $x^i$
471 : * (often "inertial"), and the second (lower) index is in the \p SourceFrame
472 : * with coordinates $\xi^\hat{j}$ (often "logical").
473 : *
474 : * \note The indices produced by the `logical_partial_derivative` function
475 : * are in the opposite order.
476 : */
477 : template <typename DataType, size_t Dim, typename SourceFrame,
478 : typename TargetFrame>
479 1 : using Jacobian = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1>,
480 : index_list<SpatialIndex<Dim, UpLo::Up, TargetFrame>,
481 : SpatialIndex<Dim, UpLo::Lo, SourceFrame>>>;
482 :
483 : /*!
484 : * \brief Inverse Hessian $(H^{-1})^\hat{i}_{jk} =
485 : * \frac{\partial \xi^\hat{i}}{\partial x^j \partial x^k}$
486 : *
487 : * The first (upper) index is in the \p SourceFrame with coordinates
488 : * $\xi^\hat{i}$ (often "logical"), and the second and third (lower) indices are
489 : * in the \p TargetFrame with coordinates $x^j$ (often "inertial").
490 : */
491 : template <typename DataType, size_t Dim, typename SourceFrame,
492 : typename TargetFrame>
493 1 : using InverseHessian =
494 : Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1, 1>,
495 : index_list<SpatialIndex<Dim, UpLo::Up, SourceFrame>,
496 : SpatialIndex<Dim, UpLo::Lo, TargetFrame>,
497 : SpatialIndex<Dim, UpLo::Lo, TargetFrame>>>;
498 :
499 : /*!
500 : * \brief Hessian $H^i_{\hat{j}\hat{k}} =
501 : * \frac{\partial x^i}{\partial \xi^\hat{j} \partial \xi^\hat{k}}$
502 : *
503 : * The first (upper) index is in the \p TargetFrame with coordinates $x^i$
504 : * (often "inertial"), and the second and third (lower) indices are in the
505 : * \p SourceFrame with coordinates $\xi^\hat{j}$ (often "logical").
506 : */
507 : template <typename DataType, size_t Dim, typename SourceFrame,
508 : typename TargetFrame>
509 1 : using Hessian = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 1, 1>,
510 : index_list<SpatialIndex<Dim, UpLo::Up, TargetFrame>,
511 : SpatialIndex<Dim, UpLo::Lo, SourceFrame>,
512 : SpatialIndex<Dim, UpLo::Lo, SourceFrame>>>;
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