Collective Variables Module - Developer Documentation
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colvar_rotation_derivative.h
1#ifndef COLVAR_ROTATION_DERIVATIVE
2#define COLVAR_ROTATION_DERIVATIVE
3
4#include "colvartypes.h"
5#include <type_traits>
6#include <cstring>
7
8#ifndef _noalias
9#if defined(__INTEL_COMPILER) || (defined(__PGI) && !defined(__NVCOMPILER))
10#define _noalias restrict
11#elif defined(__GNUC__) || defined(__INTEL_LLVM_COMPILER) || defined(__NVCOMPILER)
12#define _noalias __restrict
13#else
14#define _noalias
15#endif
16#endif
17
19enum class rotation_derivative_dldq {
21 use_dl = 1 << 0,
23 use_dq = 1 << 1
24};
25
26inline constexpr rotation_derivative_dldq operator|(rotation_derivative_dldq Lhs, rotation_derivative_dldq Rhs) {
27 return static_cast<rotation_derivative_dldq>(
28 static_cast<std::underlying_type<rotation_derivative_dldq>::type>(Lhs) |
29 static_cast<std::underlying_type<rotation_derivative_dldq>::type>(Rhs));
30}
31
32inline constexpr bool operator&(rotation_derivative_dldq Lhs, rotation_derivative_dldq Rhs)
33{
34 return (static_cast<std::underlying_type<rotation_derivative_dldq>::type>(Lhs) &
35 static_cast<std::underlying_type<rotation_derivative_dldq>::type>(Rhs));
36}
37
39// template <typename T1, typename T2, bool soa = false>
40struct rotation_derivative {
42 const cvm::rotation &m_rot;
44 const std::vector<cvm::real> &m_pos1;
46 const std::vector<cvm::real> &m_pos2;
48 size_t m_num_atoms_pos1;
50 size_t m_num_atoms_pos2;
52 cvm::real tmp_Q0Q0[4][4];
53 cvm::real tmp_Q0Q0_L[4][4][4];
64 rotation_derivative(
65 const cvm::rotation &rot,
66 const std::vector<cvm::real> &pos1,
67 const std::vector<cvm::real> &pos2,
68 const size_t num_atoms_pos1,
69 const size_t num_atoms_pos2):
70 m_rot(rot), m_pos1(pos1), m_pos2(pos2),
71 m_num_atoms_pos1(num_atoms_pos1),
72 m_num_atoms_pos2(num_atoms_pos2) {}
79 void prepare_derivative(rotation_derivative_dldq require_dl_dq) {
80 if (require_dl_dq & rotation_derivative_dldq::use_dl) {
81 const auto &Q0 = m_rot.S_eigvec[0];
82 tmp_Q0Q0[0][0] = Q0[0] * Q0[0];
83 tmp_Q0Q0[0][1] = Q0[0] * Q0[1];
84 tmp_Q0Q0[0][2] = Q0[0] * Q0[2];
85 tmp_Q0Q0[0][3] = Q0[0] * Q0[3];
86 tmp_Q0Q0[1][0] = Q0[1] * Q0[0];
87 tmp_Q0Q0[1][1] = Q0[1] * Q0[1];
88 tmp_Q0Q0[1][2] = Q0[1] * Q0[2];
89 tmp_Q0Q0[1][3] = Q0[1] * Q0[3];
90 tmp_Q0Q0[2][0] = Q0[2] * Q0[0];
91 tmp_Q0Q0[2][1] = Q0[2] * Q0[1];
92 tmp_Q0Q0[2][2] = Q0[2] * Q0[2];
93 tmp_Q0Q0[2][3] = Q0[2] * Q0[3];
94 tmp_Q0Q0[3][0] = Q0[3] * Q0[0];
95 tmp_Q0Q0[3][1] = Q0[3] * Q0[1];
96 tmp_Q0Q0[3][2] = Q0[3] * Q0[2];
97 tmp_Q0Q0[3][3] = Q0[3] * Q0[3];
98 }
99 if (require_dl_dq & rotation_derivative_dldq::use_dq) {
100 const auto &Q0 = m_rot.S_eigvec[0];
101 const auto &Q1 = m_rot.S_eigvec[1];
102 const auto &Q2 = m_rot.S_eigvec[2];
103 const auto &Q3 = m_rot.S_eigvec[3];
104 cvm::real const L0 = m_rot.S_eigval[0];
105 cvm::real const L1 = m_rot.S_eigval[1];
106 cvm::real const L2 = m_rot.S_eigval[2];
107 cvm::real const L3 = m_rot.S_eigval[3];
108
109 tmp_Q0Q0_L[0][0][0] = (Q1[0] * Q0[0]) / (L0-L1) * Q1[0] +
110 (Q2[0] * Q0[0]) / (L0-L2) * Q2[0] +
111 (Q3[0] * Q0[0]) / (L0-L3) * Q3[0];
112 tmp_Q0Q0_L[1][0][0] = (Q1[0] * Q0[0]) / (L0-L1) * Q1[1] +
113 (Q2[0] * Q0[0]) / (L0-L2) * Q2[1] +
114 (Q3[0] * Q0[0]) / (L0-L3) * Q3[1];
115 tmp_Q0Q0_L[2][0][0] = (Q1[0] * Q0[0]) / (L0-L1) * Q1[2] +
116 (Q2[0] * Q0[0]) / (L0-L2) * Q2[2] +
117 (Q3[0] * Q0[0]) / (L0-L3) * Q3[2];
118 tmp_Q0Q0_L[3][0][0] = (Q1[0] * Q0[0]) / (L0-L1) * Q1[3] +
119 (Q2[0] * Q0[0]) / (L0-L2) * Q2[3] +
120 (Q3[0] * Q0[0]) / (L0-L3) * Q3[3];
121
122 tmp_Q0Q0_L[0][0][1] = (Q1[0] * Q0[1]) / (L0-L1) * Q1[0] +
123 (Q2[0] * Q0[1]) / (L0-L2) * Q2[0] +
124 (Q3[0] * Q0[1]) / (L0-L3) * Q3[0];
125 tmp_Q0Q0_L[1][0][1] = (Q1[0] * Q0[1]) / (L0-L1) * Q1[1] +
126 (Q2[0] * Q0[1]) / (L0-L2) * Q2[1] +
127 (Q3[0] * Q0[1]) / (L0-L3) * Q3[1];
128 tmp_Q0Q0_L[2][0][1] = (Q1[0] * Q0[1]) / (L0-L1) * Q1[2] +
129 (Q2[0] * Q0[1]) / (L0-L2) * Q2[2] +
130 (Q3[0] * Q0[1]) / (L0-L3) * Q3[2];
131 tmp_Q0Q0_L[3][0][1] = (Q1[0] * Q0[1]) / (L0-L1) * Q1[3] +
132 (Q2[0] * Q0[1]) / (L0-L2) * Q2[3] +
133 (Q3[0] * Q0[1]) / (L0-L3) * Q3[3];
134
135
136 tmp_Q0Q0_L[0][0][2] = (Q1[0] * Q0[2]) / (L0-L1) * Q1[0] +
137 (Q2[0] * Q0[2]) / (L0-L2) * Q2[0] +
138 (Q3[0] * Q0[2]) / (L0-L3) * Q3[0];
139 tmp_Q0Q0_L[1][0][2] = (Q1[0] * Q0[2]) / (L0-L1) * Q1[1] +
140 (Q2[0] * Q0[2]) / (L0-L2) * Q2[1] +
141 (Q3[0] * Q0[2]) / (L0-L3) * Q3[1];
142 tmp_Q0Q0_L[2][0][2] = (Q1[0] * Q0[2]) / (L0-L1) * Q1[2] +
143 (Q2[0] * Q0[2]) / (L0-L2) * Q2[2] +
144 (Q3[0] * Q0[2]) / (L0-L3) * Q3[2];
145 tmp_Q0Q0_L[3][0][2] = (Q1[0] * Q0[2]) / (L0-L1) * Q1[3] +
146 (Q2[0] * Q0[2]) / (L0-L2) * Q2[3] +
147 (Q3[0] * Q0[2]) / (L0-L3) * Q3[3];
148
149 tmp_Q0Q0_L[0][0][3] = (Q1[0] * Q0[3]) / (L0-L1) * Q1[0] +
150 (Q2[0] * Q0[3]) / (L0-L2) * Q2[0] +
151 (Q3[0] * Q0[3]) / (L0-L3) * Q3[0];
152 tmp_Q0Q0_L[1][0][3] = (Q1[0] * Q0[3]) / (L0-L1) * Q1[1] +
153 (Q2[0] * Q0[3]) / (L0-L2) * Q2[1] +
154 (Q3[0] * Q0[3]) / (L0-L3) * Q3[1];
155 tmp_Q0Q0_L[2][0][3] = (Q1[0] * Q0[3]) / (L0-L1) * Q1[2] +
156 (Q2[0] * Q0[3]) / (L0-L2) * Q2[2] +
157 (Q3[0] * Q0[3]) / (L0-L3) * Q3[2];
158 tmp_Q0Q0_L[3][0][3] = (Q1[0] * Q0[3]) / (L0-L1) * Q1[3] +
159 (Q2[0] * Q0[3]) / (L0-L2) * Q2[3] +
160 (Q3[0] * Q0[3]) / (L0-L3) * Q3[3];
161
162 tmp_Q0Q0_L[0][1][0] = (Q1[1] * Q0[0]) / (L0-L1) * Q1[0] +
163 (Q2[1] * Q0[0]) / (L0-L2) * Q2[0] +
164 (Q3[1] * Q0[0]) / (L0-L3) * Q3[0];
165 tmp_Q0Q0_L[1][1][0] = (Q1[1] * Q0[0]) / (L0-L1) * Q1[1] +
166 (Q2[1] * Q0[0]) / (L0-L2) * Q2[1] +
167 (Q3[1] * Q0[0]) / (L0-L3) * Q3[1];
168 tmp_Q0Q0_L[2][1][0] = (Q1[1] * Q0[0]) / (L0-L1) * Q1[2] +
169 (Q2[1] * Q0[0]) / (L0-L2) * Q2[2] +
170 (Q3[1] * Q0[0]) / (L0-L3) * Q3[2];
171 tmp_Q0Q0_L[3][1][0] = (Q1[1] * Q0[0]) / (L0-L1) * Q1[3] +
172 (Q2[1] * Q0[0]) / (L0-L2) * Q2[3] +
173 (Q3[1] * Q0[0]) / (L0-L3) * Q3[3];
174
175 tmp_Q0Q0_L[0][1][1] = (Q1[1] * Q0[1]) / (L0-L1) * Q1[0] +
176 (Q2[1] * Q0[1]) / (L0-L2) * Q2[0] +
177 (Q3[1] * Q0[1]) / (L0-L3) * Q3[0];
178 tmp_Q0Q0_L[1][1][1] = (Q1[1] * Q0[1]) / (L0-L1) * Q1[1] +
179 (Q2[1] * Q0[1]) / (L0-L2) * Q2[1] +
180 (Q3[1] * Q0[1]) / (L0-L3) * Q3[1];
181 tmp_Q0Q0_L[2][1][1] = (Q1[1] * Q0[1]) / (L0-L1) * Q1[2] +
182 (Q2[1] * Q0[1]) / (L0-L2) * Q2[2] +
183 (Q3[1] * Q0[1]) / (L0-L3) * Q3[2];
184 tmp_Q0Q0_L[3][1][1] = (Q1[1] * Q0[1]) / (L0-L1) * Q1[3] +
185 (Q2[1] * Q0[1]) / (L0-L2) * Q2[3] +
186 (Q3[1] * Q0[1]) / (L0-L3) * Q3[3];
187
188 tmp_Q0Q0_L[0][1][2] = (Q1[1] * Q0[2]) / (L0-L1) * Q1[0] +
189 (Q2[1] * Q0[2]) / (L0-L2) * Q2[0] +
190 (Q3[1] * Q0[2]) / (L0-L3) * Q3[0];
191 tmp_Q0Q0_L[1][1][2] = (Q1[1] * Q0[2]) / (L0-L1) * Q1[1] +
192 (Q2[1] * Q0[2]) / (L0-L2) * Q2[1] +
193 (Q3[1] * Q0[2]) / (L0-L3) * Q3[1];
194 tmp_Q0Q0_L[2][1][2] = (Q1[1] * Q0[2]) / (L0-L1) * Q1[2] +
195 (Q2[1] * Q0[2]) / (L0-L2) * Q2[2] +
196 (Q3[1] * Q0[2]) / (L0-L3) * Q3[2];
197 tmp_Q0Q0_L[3][1][2] = (Q1[1] * Q0[2]) / (L0-L1) * Q1[3] +
198 (Q2[1] * Q0[2]) / (L0-L2) * Q2[3] +
199 (Q3[1] * Q0[2]) / (L0-L3) * Q3[3];
200
201 tmp_Q0Q0_L[0][1][3] = (Q1[1] * Q0[3]) / (L0-L1) * Q1[0] +
202 (Q2[1] * Q0[3]) / (L0-L2) * Q2[0] +
203 (Q3[1] * Q0[3]) / (L0-L3) * Q3[0];
204 tmp_Q0Q0_L[1][1][3] = (Q1[1] * Q0[3]) / (L0-L1) * Q1[1] +
205 (Q2[1] * Q0[3]) / (L0-L2) * Q2[1] +
206 (Q3[1] * Q0[3]) / (L0-L3) * Q3[1];
207 tmp_Q0Q0_L[2][1][3] = (Q1[1] * Q0[3]) / (L0-L1) * Q1[2] +
208 (Q2[1] * Q0[3]) / (L0-L2) * Q2[2] +
209 (Q3[1] * Q0[3]) / (L0-L3) * Q3[2];
210 tmp_Q0Q0_L[3][1][3] = (Q1[1] * Q0[3]) / (L0-L1) * Q1[3] +
211 (Q2[1] * Q0[3]) / (L0-L2) * Q2[3] +
212 (Q3[1] * Q0[3]) / (L0-L3) * Q3[3];
213
214
215 tmp_Q0Q0_L[0][2][0] = (Q1[2] * Q0[0]) / (L0-L1) * Q1[0] +
216 (Q2[2] * Q0[0]) / (L0-L2) * Q2[0] +
217 (Q3[2] * Q0[0]) / (L0-L3) * Q3[0];
218 tmp_Q0Q0_L[1][2][0] = (Q1[2] * Q0[0]) / (L0-L1) * Q1[1] +
219 (Q2[2] * Q0[0]) / (L0-L2) * Q2[1] +
220 (Q3[2] * Q0[0]) / (L0-L3) * Q3[1];
221 tmp_Q0Q0_L[2][2][0] = (Q1[2] * Q0[0]) / (L0-L1) * Q1[2] +
222 (Q2[2] * Q0[0]) / (L0-L2) * Q2[2] +
223 (Q3[2] * Q0[0]) / (L0-L3) * Q3[2];
224 tmp_Q0Q0_L[3][2][0] = (Q1[2] * Q0[0]) / (L0-L1) * Q1[3] +
225 (Q2[2] * Q0[0]) / (L0-L2) * Q2[3] +
226 (Q3[2] * Q0[0]) / (L0-L3) * Q3[3];
227
228 tmp_Q0Q0_L[0][2][1] = (Q1[2] * Q0[1]) / (L0-L1) * Q1[0] +
229 (Q2[2] * Q0[1]) / (L0-L2) * Q2[0] +
230 (Q3[2] * Q0[1]) / (L0-L3) * Q3[0];
231 tmp_Q0Q0_L[1][2][1] = (Q1[2] * Q0[1]) / (L0-L1) * Q1[1] +
232 (Q2[2] * Q0[1]) / (L0-L2) * Q2[1] +
233 (Q3[2] * Q0[1]) / (L0-L3) * Q3[1];
234 tmp_Q0Q0_L[2][2][1] = (Q1[2] * Q0[1]) / (L0-L1) * Q1[2] +
235 (Q2[2] * Q0[1]) / (L0-L2) * Q2[2] +
236 (Q3[2] * Q0[1]) / (L0-L3) * Q3[2];
237 tmp_Q0Q0_L[3][2][1] = (Q1[2] * Q0[1]) / (L0-L1) * Q1[3] +
238 (Q2[2] * Q0[1]) / (L0-L2) * Q2[3] +
239 (Q3[2] * Q0[1]) / (L0-L3) * Q3[3];
240
241 tmp_Q0Q0_L[0][2][2] = (Q1[2] * Q0[2]) / (L0-L1) * Q1[0] +
242 (Q2[2] * Q0[2]) / (L0-L2) * Q2[0] +
243 (Q3[2] * Q0[2]) / (L0-L3) * Q3[0];
244 tmp_Q0Q0_L[1][2][2] = (Q1[2] * Q0[2]) / (L0-L1) * Q1[1] +
245 (Q2[2] * Q0[2]) / (L0-L2) * Q2[1] +
246 (Q3[2] * Q0[2]) / (L0-L3) * Q3[1];
247 tmp_Q0Q0_L[2][2][2] = (Q1[2] * Q0[2]) / (L0-L1) * Q1[2] +
248 (Q2[2] * Q0[2]) / (L0-L2) * Q2[2] +
249 (Q3[2] * Q0[2]) / (L0-L3) * Q3[2];
250 tmp_Q0Q0_L[3][2][2] = (Q1[2] * Q0[2]) / (L0-L1) * Q1[3] +
251 (Q2[2] * Q0[2]) / (L0-L2) * Q2[3] +
252 (Q3[2] * Q0[2]) / (L0-L3) * Q3[3];
253
254 tmp_Q0Q0_L[0][2][3] = (Q1[2] * Q0[3]) / (L0-L1) * Q1[0] +
255 (Q2[2] * Q0[3]) / (L0-L2) * Q2[0] +
256 (Q3[2] * Q0[3]) / (L0-L3) * Q3[0];
257 tmp_Q0Q0_L[1][2][3] = (Q1[2] * Q0[3]) / (L0-L1) * Q1[1] +
258 (Q2[2] * Q0[3]) / (L0-L2) * Q2[1] +
259 (Q3[2] * Q0[3]) / (L0-L3) * Q3[1];
260 tmp_Q0Q0_L[2][2][3] = (Q1[2] * Q0[3]) / (L0-L1) * Q1[2] +
261 (Q2[2] * Q0[3]) / (L0-L2) * Q2[2] +
262 (Q3[2] * Q0[3]) / (L0-L3) * Q3[2];
263 tmp_Q0Q0_L[3][2][3] = (Q1[2] * Q0[3]) / (L0-L1) * Q1[3] +
264 (Q2[2] * Q0[3]) / (L0-L2) * Q2[3] +
265 (Q3[2] * Q0[3]) / (L0-L3) * Q3[3];
266
267 tmp_Q0Q0_L[0][3][0] = (Q1[3] * Q0[0]) / (L0-L1) * Q1[0] +
268 (Q2[3] * Q0[0]) / (L0-L2) * Q2[0] +
269 (Q3[3] * Q0[0]) / (L0-L3) * Q3[0];
270 tmp_Q0Q0_L[1][3][0] = (Q1[3] * Q0[0]) / (L0-L1) * Q1[1] +
271 (Q2[3] * Q0[0]) / (L0-L2) * Q2[1] +
272 (Q3[3] * Q0[0]) / (L0-L3) * Q3[1];
273 tmp_Q0Q0_L[2][3][0] = (Q1[3] * Q0[0]) / (L0-L1) * Q1[2] +
274 (Q2[3] * Q0[0]) / (L0-L2) * Q2[2] +
275 (Q3[3] * Q0[0]) / (L0-L3) * Q3[2];
276 tmp_Q0Q0_L[3][3][0] = (Q1[3] * Q0[0]) / (L0-L1) * Q1[3] +
277 (Q2[3] * Q0[0]) / (L0-L2) * Q2[3] +
278 (Q3[3] * Q0[0]) / (L0-L3) * Q3[3];
279
280 tmp_Q0Q0_L[0][3][1] = (Q1[3] * Q0[1]) / (L0-L1) * Q1[0] +
281 (Q2[3] * Q0[1]) / (L0-L2) * Q2[0] +
282 (Q3[3] * Q0[1]) / (L0-L3) * Q3[0];
283 tmp_Q0Q0_L[1][3][1] = (Q1[3] * Q0[1]) / (L0-L1) * Q1[1] +
284 (Q2[3] * Q0[1]) / (L0-L2) * Q2[1] +
285 (Q3[3] * Q0[1]) / (L0-L3) * Q3[1];
286 tmp_Q0Q0_L[2][3][1] = (Q1[3] * Q0[1]) / (L0-L1) * Q1[2] +
287 (Q2[3] * Q0[1]) / (L0-L2) * Q2[2] +
288 (Q3[3] * Q0[1]) / (L0-L3) * Q3[2];
289 tmp_Q0Q0_L[3][3][1] = (Q1[3] * Q0[1]) / (L0-L1) * Q1[3] +
290 (Q2[3] * Q0[1]) / (L0-L2) * Q2[3] +
291 (Q3[3] * Q0[1]) / (L0-L3) * Q3[3];
292
293 tmp_Q0Q0_L[0][3][2] = (Q1[3] * Q0[2]) / (L0-L1) * Q1[0] +
294 (Q2[3] * Q0[2]) / (L0-L2) * Q2[0] +
295 (Q3[3] * Q0[2]) / (L0-L3) * Q3[0];
296 tmp_Q0Q0_L[1][3][2] = (Q1[3] * Q0[2]) / (L0-L1) * Q1[1] +
297 (Q2[3] * Q0[2]) / (L0-L2) * Q2[1] +
298 (Q3[3] * Q0[2]) / (L0-L3) * Q3[1];
299 tmp_Q0Q0_L[2][3][2] = (Q1[3] * Q0[2]) / (L0-L1) * Q1[2] +
300 (Q2[3] * Q0[2]) / (L0-L2) * Q2[2] +
301 (Q3[3] * Q0[2]) / (L0-L3) * Q3[2];
302 tmp_Q0Q0_L[3][3][2] = (Q1[3] * Q0[2]) / (L0-L1) * Q1[3] +
303 (Q2[3] * Q0[2]) / (L0-L2) * Q2[3] +
304 (Q3[3] * Q0[2]) / (L0-L3) * Q3[3];
305
306 tmp_Q0Q0_L[0][3][3] = (Q1[3] * Q0[3]) / (L0-L1) * Q1[0] +
307 (Q2[3] * Q0[3]) / (L0-L2) * Q2[0] +
308 (Q3[3] * Q0[3]) / (L0-L3) * Q3[0];
309 tmp_Q0Q0_L[1][3][3] = (Q1[3] * Q0[3]) / (L0-L1) * Q1[1] +
310 (Q2[3] * Q0[3]) / (L0-L2) * Q2[1] +
311 (Q3[3] * Q0[3]) / (L0-L3) * Q3[1];
312 tmp_Q0Q0_L[2][3][3] = (Q1[3] * Q0[3]) / (L0-L1) * Q1[2] +
313 (Q2[3] * Q0[3]) / (L0-L2) * Q2[2] +
314 (Q3[3] * Q0[3]) / (L0-L3) * Q3[2];
315 tmp_Q0Q0_L[3][3][3] = (Q1[3] * Q0[3]) / (L0-L1) * Q1[3] +
316 (Q2[3] * Q0[3]) / (L0-L2) * Q2[3] +
317 (Q3[3] * Q0[3]) / (L0-L3) * Q3[3];
318 }
319 }
327 template <bool use_dl, bool use_dq, bool use_ds>
328 void calc_derivative_impl(
329 const cvm::rvector (&ds)[4][4],
330 cvm::rvector* _noalias const dl0_out,
331 cvm::vector1d<cvm::rvector>* _noalias const dq0_out,
332 cvm::matrix2d<cvm::rvector>* _noalias const ds_out) const {
333 if (use_ds) {
334 // this code path is for debug_gradients, so not necessary to unroll the loop
335 *ds_out = cvm::matrix2d<cvm::rvector>(4, 4);
336 for (int i = 0; i < 4; ++i) {
337 for (int j = 0; j < 4; ++j) {
338 (*ds_out)[i][j] = ds[i][j];
339 }
340 }
341 }
342 if (use_dl) {
343 /* manually loop unrolling of the following loop:
344 dl0_1.reset();
345 for (size_t i = 0; i < 4; i++) {
346 for (size_t j = 0; j < 4; j++) {
347 dl0_1 += Q0[i] * ds_1[i][j] * Q0[j];
348 }
349 }
350 */
351 *dl0_out = tmp_Q0Q0[0][0] * ds[0][0] +
352 tmp_Q0Q0[0][1] * ds[0][1] +
353 tmp_Q0Q0[0][2] * ds[0][2] +
354 tmp_Q0Q0[0][3] * ds[0][3] +
355 tmp_Q0Q0[1][0] * ds[1][0] +
356 tmp_Q0Q0[1][1] * ds[1][1] +
357 tmp_Q0Q0[1][2] * ds[1][2] +
358 tmp_Q0Q0[1][3] * ds[1][3] +
359 tmp_Q0Q0[2][0] * ds[2][0] +
360 tmp_Q0Q0[2][1] * ds[2][1] +
361 tmp_Q0Q0[2][2] * ds[2][2] +
362 tmp_Q0Q0[2][3] * ds[2][3] +
363 tmp_Q0Q0[3][0] * ds[3][0] +
364 tmp_Q0Q0[3][1] * ds[3][1] +
365 tmp_Q0Q0[3][2] * ds[3][2] +
366 tmp_Q0Q0[3][3] * ds[3][3];
367 }
368 if (use_dq) {
369 // we can skip this check if a fixed-size array is used
370 if (dq0_out->size() != 4) dq0_out->resize(4);
371 /* manually loop unrolling of the following loop:
372 dq0_1.reset();
373 for (size_t p = 0; p < 4; p++) {
374 for (size_t i = 0; i < 4; i++) {
375 for (size_t j = 0; j < 4; j++) {
376 dq0_1[p] +=
377 (Q1[i] * ds_1[i][j] * Q0[j]) / (L0-L1) * Q1[p] +
378 (Q2[i] * ds_1[i][j] * Q0[j]) / (L0-L2) * Q2[p] +
379 (Q3[i] * ds_1[i][j] * Q0[j]) / (L0-L3) * Q3[p];
380 }
381 }
382 }
383 */
384 (*dq0_out)[0] = tmp_Q0Q0_L[0][0][0] * ds[0][0] +
385 tmp_Q0Q0_L[0][0][1] * ds[0][1] +
386 tmp_Q0Q0_L[0][0][2] * ds[0][2] +
387 tmp_Q0Q0_L[0][0][3] * ds[0][3] +
388 tmp_Q0Q0_L[0][1][0] * ds[1][0] +
389 tmp_Q0Q0_L[0][1][1] * ds[1][1] +
390 tmp_Q0Q0_L[0][1][2] * ds[1][2] +
391 tmp_Q0Q0_L[0][1][3] * ds[1][3] +
392 tmp_Q0Q0_L[0][2][0] * ds[2][0] +
393 tmp_Q0Q0_L[0][2][1] * ds[2][1] +
394 tmp_Q0Q0_L[0][2][2] * ds[2][2] +
395 tmp_Q0Q0_L[0][2][3] * ds[2][3] +
396 tmp_Q0Q0_L[0][3][0] * ds[3][0] +
397 tmp_Q0Q0_L[0][3][1] * ds[3][1] +
398 tmp_Q0Q0_L[0][3][2] * ds[3][2] +
399 tmp_Q0Q0_L[0][3][3] * ds[3][3];
400
401 (*dq0_out)[1] = tmp_Q0Q0_L[1][0][0] * ds[0][0] +
402 tmp_Q0Q0_L[1][0][1] * ds[0][1] +
403 tmp_Q0Q0_L[1][0][2] * ds[0][2] +
404 tmp_Q0Q0_L[1][0][3] * ds[0][3] +
405 tmp_Q0Q0_L[1][1][0] * ds[1][0] +
406 tmp_Q0Q0_L[1][1][1] * ds[1][1] +
407 tmp_Q0Q0_L[1][1][2] * ds[1][2] +
408 tmp_Q0Q0_L[1][1][3] * ds[1][3] +
409 tmp_Q0Q0_L[1][2][0] * ds[2][0] +
410 tmp_Q0Q0_L[1][2][1] * ds[2][1] +
411 tmp_Q0Q0_L[1][2][2] * ds[2][2] +
412 tmp_Q0Q0_L[1][2][3] * ds[2][3] +
413 tmp_Q0Q0_L[1][3][0] * ds[3][0] +
414 tmp_Q0Q0_L[1][3][1] * ds[3][1] +
415 tmp_Q0Q0_L[1][3][2] * ds[3][2] +
416 tmp_Q0Q0_L[1][3][3] * ds[3][3];
417
418 (*dq0_out)[2] = tmp_Q0Q0_L[2][0][0] * ds[0][0] +
419 tmp_Q0Q0_L[2][0][1] * ds[0][1] +
420 tmp_Q0Q0_L[2][0][2] * ds[0][2] +
421 tmp_Q0Q0_L[2][0][3] * ds[0][3] +
422 tmp_Q0Q0_L[2][1][0] * ds[1][0] +
423 tmp_Q0Q0_L[2][1][1] * ds[1][1] +
424 tmp_Q0Q0_L[2][1][2] * ds[1][2] +
425 tmp_Q0Q0_L[2][1][3] * ds[1][3] +
426 tmp_Q0Q0_L[2][2][0] * ds[2][0] +
427 tmp_Q0Q0_L[2][2][1] * ds[2][1] +
428 tmp_Q0Q0_L[2][2][2] * ds[2][2] +
429 tmp_Q0Q0_L[2][2][3] * ds[2][3] +
430 tmp_Q0Q0_L[2][3][0] * ds[3][0] +
431 tmp_Q0Q0_L[2][3][1] * ds[3][1] +
432 tmp_Q0Q0_L[2][3][2] * ds[3][2] +
433 tmp_Q0Q0_L[2][3][3] * ds[3][3];
434
435 (*dq0_out)[3] = tmp_Q0Q0_L[3][0][0] * ds[0][0] +
436 tmp_Q0Q0_L[3][0][1] * ds[0][1] +
437 tmp_Q0Q0_L[3][0][2] * ds[0][2] +
438 tmp_Q0Q0_L[3][0][3] * ds[0][3] +
439 tmp_Q0Q0_L[3][1][0] * ds[1][0] +
440 tmp_Q0Q0_L[3][1][1] * ds[1][1] +
441 tmp_Q0Q0_L[3][1][2] * ds[1][2] +
442 tmp_Q0Q0_L[3][1][3] * ds[1][3] +
443 tmp_Q0Q0_L[3][2][0] * ds[2][0] +
444 tmp_Q0Q0_L[3][2][1] * ds[2][1] +
445 tmp_Q0Q0_L[3][2][2] * ds[2][2] +
446 tmp_Q0Q0_L[3][2][3] * ds[2][3] +
447 tmp_Q0Q0_L[3][3][0] * ds[3][0] +
448 tmp_Q0Q0_L[3][3][1] * ds[3][1] +
449 tmp_Q0Q0_L[3][3][2] * ds[3][2] +
450 tmp_Q0Q0_L[3][3][3] * ds[3][3];
451 }
452 }
463 template <bool use_dl, bool use_dq, bool use_ds>
464 void calc_derivative_wrt_group1(
465 size_t ia, cvm::rvector* _noalias const dl0_1_out = nullptr,
466 cvm::vector1d<cvm::rvector>* _noalias const dq0_1_out = nullptr,
467 cvm::matrix2d<cvm::rvector>* _noalias const ds_1_out = nullptr) const {
468 // if (dl0_1_out == nullptr && dq0_1_out == nullptr) return;
469 const cvm::real a2x = m_pos2[ia];
470 const cvm::real a2y = m_pos2[ia + m_num_atoms_pos2];
471 const cvm::real a2z = m_pos2[ia + 2 * m_num_atoms_pos2];
472 const cvm::rvector ds_1[4][4] = {
473 {{ a2x, a2y, a2z}, { 0.0, a2z, -a2y}, {-a2z, 0.0, a2x}, { a2y, -a2x, 0.0}},
474 {{ 0.0, a2z, -a2y}, { a2x, -a2y, -a2z}, { a2y, a2x, 0.0}, { a2z, 0.0, a2x}},
475 {{-a2z, 0.0, a2x}, { a2y, a2x, 0.0}, {-a2x, a2y, -a2z}, { 0.0, a2z, a2y}},
476 {{ a2y, -a2x, 0.0}, { a2z, 0.0, a2x}, { 0.0, a2z, a2y}, {-a2x, -a2y, a2z}}};
477 calc_derivative_impl<use_dl, use_dq, use_ds>(ds_1, dl0_1_out, dq0_1_out, ds_1_out);
478 }
489 template <bool use_dl, bool use_dq, bool use_ds>
490 void calc_derivative_wrt_group2(
491 size_t ia, cvm::rvector* _noalias const dl0_2_out = nullptr,
492 cvm::vector1d<cvm::rvector>* _noalias const dq0_2_out = nullptr,
493 cvm::matrix2d<cvm::rvector>* _noalias const ds_2_out = nullptr) const {
494 // if (dl0_2_out == nullptr && dq0_2_out == nullptr) return;
495 const cvm::real a1x = m_pos1[ia];
496 const cvm::real a1y = m_pos1[ia + m_num_atoms_pos1];
497 const cvm::real a1z = m_pos1[ia + 2 * m_num_atoms_pos1];
498 const cvm::rvector ds_2[4][4] = {
499 {{ a1x, a1y, a1z}, { 0.0, -a1z, a1y}, { a1z, 0.0, -a1x}, {-a1y, a1x, 0.0}},
500 {{ 0.0, -a1z, a1y}, { a1x, -a1y, -a1z}, { a1y, a1x, 0.0}, { a1z, 0.0, a1x}},
501 {{ a1z, 0.0, -a1x}, { a1y, a1x, 0.0}, {-a1x, a1y, -a1z}, { 0.0, a1z, a1y}},
502 {{-a1y, a1x, 0.0}, { a1z, 0.0, a1x}, { 0.0, a1z, a1y}, {-a1x, -a1y, a1z}}};
503 calc_derivative_impl<use_dl, use_dq, use_ds>(ds_2, dl0_2_out, dq0_2_out, ds_2_out);
504 }
505};
506
507#endif // COLVAR_ROTATION_DERIVATIVE
colvarmodule::matrix2d
Arbitrary size array (two dimensions) suitable for linear algebra operations (i.e....
Definition: colvartypes.h:372
colvarmodule::rotation
A rotation between two sets of coordinates (for the moment a wrapper for colvarmodule::quaternion)
Definition: colvartypes.h:1359
colvarmodule::rotation::S_eigval
cvm::real S_eigval[4]
Eigenvalues of S.
Definition: colvartypes.h:1368
colvarmodule::rotation::S_eigvec
cvm::real S_eigvec[4][4]
Eigenvectors of S.
Definition: colvartypes.h:1371
colvarmodule::rvector
vector of real numbers with three components
Definition: colvartypes.h:723
colvarmodule::vector1d
Arbitrary size array (one dimensions) suitable for linear algebra operations (i.e....
Definition: colvartypes.h:33
colvarmodule::real
double real
Defining an abstract real number allows to switch precision.
Definition: colvarmodule.h:150
rotation_derivative
Helper class for calculating the derivative of rotation.
Definition: colvar_rotation_derivative.h:40
rotation_derivative::rotation_derivative
rotation_derivative(const cvm::rotation &rot, const std::vector< cvm::real > &pos1, const std::vector< cvm::real > &pos2, const size_t num_atoms_pos1, const size_t num_atoms_pos2)
Constructor of the cvm::rotation::derivative class for SOA.
Definition: colvar_rotation_derivative.h:64
rotation_derivative::prepare_derivative
void prepare_derivative(rotation_derivative_dldq require_dl_dq)
This function must be called before calc_derivative_wrt_group1 and calc_derivative_wrt_group2 in orde...
Definition: colvar_rotation_derivative.h:79
rotation_derivative::m_num_atoms_pos1
size_t m_num_atoms_pos1
Number of atoms in group1 (used in SOA)
Definition: colvar_rotation_derivative.h:48
rotation_derivative::calc_derivative_wrt_group1
void calc_derivative_wrt_group1(size_t ia, cvm::rvector *_noalias const dl0_1_out=nullptr, cvm::vector1d< cvm::rvector > *_noalias const dq0_1_out=nullptr, cvm::matrix2d< cvm::rvector > *_noalias const ds_1_out=nullptr) const
Calculate the derivatives of S, the leading eigenvalue L and the leading eigenvector Q with respect t...
Definition: colvar_rotation_derivative.h:464
rotation_derivative::tmp_Q0Q0
cvm::real tmp_Q0Q0[4][4]
Temporary variable that will be updated if prepare_derivative called.
Definition: colvar_rotation_derivative.h:52
rotation_derivative::m_pos1
const std::vector< cvm::real > & m_pos1
Reference to the atom positions of group 1.
Definition: colvar_rotation_derivative.h:44
rotation_derivative::calc_derivative_impl
void calc_derivative_impl(const cvm::rvector(&ds)[4][4], cvm::rvector *_noalias const dl0_out, cvm::vector1d< cvm::rvector > *_noalias const dq0_out, cvm::matrix2d< cvm::rvector > *_noalias const ds_out) const
Actual implementation of the derivative calculation.
Definition: colvar_rotation_derivative.h:328
rotation_derivative::calc_derivative_wrt_group2
void calc_derivative_wrt_group2(size_t ia, cvm::rvector *_noalias const dl0_2_out=nullptr, cvm::vector1d< cvm::rvector > *_noalias const dq0_2_out=nullptr, cvm::matrix2d< cvm::rvector > *_noalias const ds_2_out=nullptr) const
Calculate the derivatives of S, the leading eigenvalue L and the leading eigenvector Q with respect t...
Definition: colvar_rotation_derivative.h:490
rotation_derivative::m_rot
const cvm::rotation & m_rot
Reference to the rotation.
Definition: colvar_rotation_derivative.h:42
rotation_derivative::m_num_atoms_pos2
size_t m_num_atoms_pos2
Number of atoms in group1 (used in SOA)
Definition: colvar_rotation_derivative.h:50
rotation_derivative::m_pos2
const std::vector< cvm::real > & m_pos2
Reference to the atom positions of group 2.
Definition: colvar_rotation_derivative.h:46
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