Line data Source code
1 : // SPDX-FileCopyrightText: 2024 Pairinteraction Developers
2 : // SPDX-License-Identifier: LGPL-3.0-or-later
3 :
4 : #include "pairinteraction/basis/Basis.hpp"
5 :
6 : #include "pairinteraction/basis/BasisAtom.hpp"
7 : #include "pairinteraction/basis/BasisPair.hpp"
8 : #include "pairinteraction/enums/Parity.hpp"
9 : #include "pairinteraction/enums/TransformationType.hpp"
10 : #include "pairinteraction/ket/KetAtom.hpp"
11 : #include "pairinteraction/ket/KetPair.hpp"
12 : #include "pairinteraction/utils/eigen_assertion.hpp"
13 : #include "pairinteraction/utils/eigen_compat.hpp"
14 : #include "pairinteraction/utils/wigner.hpp"
15 :
16 : #include <cassert>
17 : #include <numeric>
18 : #include <set>
19 :
20 : namespace pairinteraction {
21 :
22 : template <typename Scalar>
23 : class BasisAtom;
24 :
25 : template <typename Derived>
26 134 : void Basis<Derived>::perform_sorter_checks(const std::vector<TransformationType> &labels) const {
27 : // Check if the labels are valid sorting labels
28 244 : for (const auto &label : labels) {
29 110 : if (!utils::is_sorting(label)) {
30 0 : throw std::invalid_argument("One of the labels is not a valid sorting label.");
31 : }
32 : }
33 134 : }
34 :
35 : template <typename Derived>
36 59 : void Basis<Derived>::perform_blocks_checks(
37 : const std::set<TransformationType> &unique_labels) const {
38 : // Check if the states are sorted by the requested labels
39 59 : std::set<TransformationType> unique_labels_present;
40 93 : for (const auto &label : get_transformation().transformation_type) {
41 60 : if (!utils::is_sorting(label) || unique_labels_present.size() >= unique_labels.size()) {
42 26 : break;
43 : }
44 34 : unique_labels_present.insert(label);
45 : }
46 59 : if (unique_labels != unique_labels_present) {
47 0 : throw std::invalid_argument("The states are not sorted by the requested labels.");
48 : }
49 :
50 : // Throw a meaningful error if getting the blocks by energy is requested as this might be a
51 : // common mistake
52 59 : if (unique_labels.count(TransformationType::SORT_BY_ENERGY) > 0) {
53 0 : throw std::invalid_argument("States do not store the energy and thus no energy blocks can "
54 : "be obtained. Use an energy operator instead.");
55 : }
56 59 : }
57 :
58 : template <typename Derived>
59 41 : Basis<Derived>::Basis(ketvec_t &&kets)
60 82 : : kets(std::move(kets)), coefficients{{static_cast<Eigen::Index>(this->kets.size()),
61 41 : static_cast<Eigen::Index>(this->kets.size())},
62 82 : {TransformationType::SORT_BY_KET}} {
63 41 : if (this->kets.empty()) {
64 0 : throw std::invalid_argument("The basis must contain at least one element.");
65 : }
66 41 : state_index_to_quantum_number_f.reserve(this->kets.size());
67 41 : state_index_to_quantum_number_m.reserve(this->kets.size());
68 41 : state_index_to_parity.reserve(this->kets.size());
69 41 : ket_to_ket_index.reserve(this->kets.size());
70 41 : size_t index = 0;
71 9757 : for (const auto &ket : this->kets) {
72 9716 : state_index_to_quantum_number_f.push_back(ket->get_quantum_number_f());
73 9716 : state_index_to_quantum_number_m.push_back(ket->get_quantum_number_m());
74 9716 : state_index_to_parity.push_back(ket->get_parity());
75 9716 : ket_to_ket_index[ket] = index++;
76 9716 : if (ket->get_quantum_number_f() == std::numeric_limits<real_t>::max()) {
77 8494 : _has_quantum_number_f = false;
78 : }
79 9716 : if (ket->get_quantum_number_m() == std::numeric_limits<real_t>::max()) {
80 0 : _has_quantum_number_m = false;
81 : }
82 9716 : if (ket->get_parity() == Parity::UNKNOWN) {
83 8494 : _has_parity = false;
84 : }
85 : }
86 41 : state_index_to_ket_index.resize(this->kets.size());
87 41 : std::iota(state_index_to_ket_index.begin(), state_index_to_ket_index.end(), 0);
88 41 : ket_index_to_state_index.resize(this->kets.size());
89 41 : std::iota(ket_index_to_state_index.begin(), ket_index_to_state_index.end(), 0);
90 41 : coefficients.matrix.setIdentity();
91 41 : }
92 :
93 : template <typename Derived>
94 9 : bool Basis<Derived>::has_quantum_number_f() const {
95 9 : return _has_quantum_number_f;
96 : }
97 :
98 : template <typename Derived>
99 18211 : bool Basis<Derived>::has_quantum_number_m() const {
100 18211 : return _has_quantum_number_m;
101 : }
102 :
103 : template <typename Derived>
104 9 : bool Basis<Derived>::has_parity() const {
105 9 : return _has_parity;
106 : }
107 :
108 : template <typename Derived>
109 157 : const Derived &Basis<Derived>::derived() const {
110 157 : return static_cast<const Derived &>(*this);
111 : }
112 :
113 : template <typename Derived>
114 73 : const typename Basis<Derived>::ketvec_t &Basis<Derived>::get_kets() const {
115 73 : return kets;
116 : }
117 :
118 : template <typename Derived>
119 : const Eigen::SparseMatrix<typename Basis<Derived>::scalar_t, Eigen::RowMajor> &
120 618 : Basis<Derived>::get_coefficients() const {
121 618 : return coefficients.matrix;
122 : }
123 :
124 : template <typename Derived>
125 : Eigen::SparseMatrix<typename Basis<Derived>::scalar_t, Eigen::RowMajor> &
126 0 : Basis<Derived>::get_coefficients() {
127 0 : return coefficients.matrix;
128 : }
129 :
130 : template <typename Derived>
131 0 : void Basis<Derived>::set_coefficients(
132 : const Eigen::SparseMatrix<scalar_t, Eigen::RowMajor> &values) {
133 0 : if (values.rows() != coefficients.matrix.rows()) {
134 0 : throw std::invalid_argument("Incompatible number of rows.");
135 : }
136 0 : if (values.cols() != coefficients.matrix.cols()) {
137 0 : throw std::invalid_argument("Incompatible number of columns.");
138 : }
139 :
140 0 : coefficients.matrix = values;
141 :
142 0 : std::fill(ket_index_to_state_index.begin(), ket_index_to_state_index.end(),
143 0 : std::numeric_limits<int>::max());
144 0 : std::fill(state_index_to_ket_index.begin(), state_index_to_ket_index.end(),
145 0 : std::numeric_limits<int>::max());
146 0 : std::fill(state_index_to_quantum_number_f.begin(), state_index_to_quantum_number_f.end(),
147 0 : std::numeric_limits<real_t>::max());
148 0 : std::fill(state_index_to_quantum_number_m.begin(), state_index_to_quantum_number_m.end(),
149 0 : std::numeric_limits<real_t>::max());
150 0 : std::fill(state_index_to_parity.begin(), state_index_to_parity.end(), Parity::UNKNOWN);
151 0 : _has_quantum_number_f = false;
152 0 : _has_quantum_number_m = false;
153 0 : _has_parity = false;
154 0 : }
155 :
156 : template <typename Derived>
157 34 : int Basis<Derived>::get_ket_index_from_ket(std::shared_ptr<const ket_t> ket) const {
158 34 : if (ket_to_ket_index.count(ket) == 0) {
159 0 : return -1;
160 : }
161 34 : return ket_to_ket_index.at(ket);
162 : }
163 :
164 : template <typename Derived>
165 : Eigen::VectorX<typename Basis<Derived>::scalar_t>
166 11 : Basis<Derived>::get_amplitudes(std::shared_ptr<const ket_t> ket) const {
167 11 : int ket_index = get_ket_index_from_ket(ket);
168 11 : if (ket_index < 0) {
169 0 : throw std::invalid_argument("The ket does not belong to the basis.");
170 : }
171 : // The following line is a more efficient alternative to
172 : // "get_amplitudes(get_canonical_state_from_ket(ket)).transpose()"
173 22 : return coefficients.matrix.row(ket_index);
174 : }
175 :
176 : template <typename Derived>
177 : Eigen::SparseMatrix<typename Basis<Derived>::scalar_t, Eigen::RowMajor>
178 0 : Basis<Derived>::get_amplitudes(std::shared_ptr<const Derived> other) const {
179 0 : return other->coefficients.matrix.adjoint() * coefficients.matrix;
180 : }
181 :
182 : template <typename Derived>
183 : Eigen::VectorX<typename Basis<Derived>::real_t>
184 11 : Basis<Derived>::get_overlaps(std::shared_ptr<const ket_t> ket) const {
185 11 : return get_amplitudes(ket).cwiseAbs2();
186 : }
187 :
188 : template <typename Derived>
189 : Eigen::SparseMatrix<typename Basis<Derived>::real_t, Eigen::RowMajor>
190 0 : Basis<Derived>::get_overlaps(std::shared_ptr<const Derived> other) const {
191 0 : return get_amplitudes(other).cwiseAbs2();
192 : }
193 :
194 : template <typename Derived>
195 0 : typename Basis<Derived>::real_t Basis<Derived>::get_quantum_number_f(size_t state_index) const {
196 0 : real_t quantum_number_f = state_index_to_quantum_number_f.at(state_index);
197 0 : if (quantum_number_f == std::numeric_limits<real_t>::max()) {
198 0 : throw std::invalid_argument("The state does not have a well-defined quantum number f.");
199 : }
200 0 : return quantum_number_f;
201 : }
202 :
203 : template <typename Derived>
204 18244 : typename Basis<Derived>::real_t Basis<Derived>::get_quantum_number_m(size_t state_index) const {
205 18244 : real_t quantum_number_m = state_index_to_quantum_number_m.at(state_index);
206 18244 : if (quantum_number_m == std::numeric_limits<real_t>::max()) {
207 0 : throw std::invalid_argument("The state does not have a well-defined quantum number m.");
208 : }
209 18244 : return quantum_number_m;
210 : }
211 :
212 : template <typename Derived>
213 43 : Parity Basis<Derived>::get_parity(size_t state_index) const {
214 43 : Parity parity = state_index_to_parity.at(state_index);
215 43 : if (parity == Parity::UNKNOWN) {
216 0 : throw std::invalid_argument("The state does not have a well-defined parity.");
217 : }
218 43 : return parity;
219 : }
220 :
221 : template <typename Derived>
222 : std::shared_ptr<const typename Basis<Derived>::ket_t>
223 38 : Basis<Derived>::get_corresponding_ket(size_t state_index) const {
224 38 : size_t ket_index = state_index_to_ket_index.at(state_index);
225 38 : if (ket_index == std::numeric_limits<int>::max()) {
226 0 : throw std::invalid_argument("The state does not belong to a ket in a well-defined way.");
227 : }
228 38 : return kets[ket_index];
229 : }
230 :
231 : template <typename Derived>
232 : std::shared_ptr<const typename Basis<Derived>::ket_t>
233 0 : Basis<Derived>::get_corresponding_ket(std::shared_ptr<const Derived> /*state*/) const {
234 0 : throw std::runtime_error("Not implemented yet.");
235 : }
236 :
237 : template <typename Derived>
238 4 : std::shared_ptr<const Derived> Basis<Derived>::get_state(size_t state_index) const {
239 : // Create a copy of the current object
240 4 : auto restricted = std::make_shared<Derived>(derived());
241 :
242 : // Restrict the copy to the state with the largest overlap
243 4 : restricted->coefficients.matrix = restricted->coefficients.matrix.col(state_index);
244 :
245 4 : std::fill(restricted->ket_index_to_state_index.begin(),
246 4 : restricted->ket_index_to_state_index.end(), std::numeric_limits<int>::max());
247 4 : restricted->ket_index_to_state_index[state_index_to_ket_index[state_index]] = 0;
248 :
249 4 : restricted->state_index_to_quantum_number_f = {state_index_to_quantum_number_f[state_index]};
250 4 : restricted->state_index_to_quantum_number_m = {state_index_to_quantum_number_m[state_index]};
251 4 : restricted->state_index_to_parity = {state_index_to_parity[state_index]};
252 4 : restricted->state_index_to_ket_index = {state_index_to_ket_index[state_index]};
253 :
254 8 : restricted->_has_quantum_number_f =
255 4 : restricted->state_index_to_quantum_number_f[0] != std::numeric_limits<real_t>::max();
256 8 : restricted->_has_quantum_number_m =
257 4 : restricted->state_index_to_quantum_number_m[0] != std::numeric_limits<real_t>::max();
258 4 : restricted->_has_parity = restricted->state_index_to_parity[0] != Parity::UNKNOWN;
259 :
260 8 : return restricted;
261 4 : }
262 :
263 : template <typename Derived>
264 : std::shared_ptr<const typename Basis<Derived>::ket_t>
265 0 : Basis<Derived>::get_ket(size_t ket_index) const {
266 0 : return kets[ket_index];
267 : }
268 :
269 : template <typename Derived>
270 2 : std::shared_ptr<const Derived> Basis<Derived>::get_corresponding_state(size_t ket_index) const {
271 2 : size_t state_index = ket_index_to_state_index.at(ket_index);
272 2 : if (state_index == std::numeric_limits<int>::max()) {
273 0 : throw std::runtime_error("The ket does not belong to a state in a well-defined way.");
274 : }
275 2 : return get_state(state_index);
276 : }
277 :
278 : template <typename Derived>
279 : std::shared_ptr<const Derived>
280 2 : Basis<Derived>::get_corresponding_state(std::shared_ptr<const ket_t> ket) const {
281 2 : int ket_index = get_ket_index_from_ket(ket);
282 2 : if (ket_index < 0) {
283 0 : throw std::invalid_argument("The ket does not belong to the basis.");
284 : }
285 2 : return get_corresponding_state(ket_index);
286 : }
287 :
288 : template <typename Derived>
289 2 : size_t Basis<Derived>::get_corresponding_state_index(size_t ket_index) const {
290 2 : int state_index = ket_index_to_state_index.at(ket_index);
291 2 : if (state_index == std::numeric_limits<int>::max()) {
292 0 : throw std::runtime_error("The ket does not belong to a state in a well-defined way.");
293 : }
294 2 : return state_index;
295 : }
296 :
297 : template <typename Derived>
298 2 : size_t Basis<Derived>::get_corresponding_state_index(std::shared_ptr<const ket_t> ket) const {
299 2 : int ket_index = get_ket_index_from_ket(ket);
300 2 : if (ket_index < 0) {
301 0 : throw std::invalid_argument("The ket does not belong to the basis.");
302 : }
303 2 : return get_corresponding_state_index(ket_index);
304 : }
305 :
306 : template <typename Derived>
307 0 : size_t Basis<Derived>::get_corresponding_ket_index(size_t state_index) const {
308 0 : int ket_index = state_index_to_ket_index.at(state_index);
309 0 : if (ket_index == std::numeric_limits<int>::max()) {
310 0 : throw std::runtime_error("The state does not belong to a ket in a well-defined way.");
311 : }
312 0 : return ket_index;
313 : }
314 :
315 : template <typename Derived>
316 0 : size_t Basis<Derived>::get_corresponding_ket_index(std::shared_ptr<const Derived> /*state*/) const {
317 0 : throw std::runtime_error("Not implemented yet.");
318 : }
319 :
320 : template <typename Derived>
321 : std::shared_ptr<const Derived>
322 19 : Basis<Derived>::get_canonical_state_from_ket(size_t ket_index) const {
323 : // Create a copy of the current object
324 19 : auto created = std::make_shared<Derived>(derived());
325 :
326 : // Fill the copy with the state corresponding to the ket index
327 19 : created->coefficients.matrix =
328 38 : Eigen::SparseMatrix<scalar_t, Eigen::RowMajor>(coefficients.matrix.rows(), 1);
329 19 : created->coefficients.matrix.coeffRef(ket_index, 0) = 1;
330 19 : created->coefficients.matrix.makeCompressed();
331 :
332 19 : std::fill(created->ket_index_to_state_index.begin(), created->ket_index_to_state_index.end(),
333 19 : std::numeric_limits<int>::max());
334 19 : created->ket_index_to_state_index[ket_index] = 0;
335 :
336 19 : created->state_index_to_quantum_number_f = {kets[ket_index]->get_quantum_number_f()};
337 19 : created->state_index_to_quantum_number_m = {kets[ket_index]->get_quantum_number_m()};
338 19 : created->state_index_to_parity = {kets[ket_index]->get_parity()};
339 19 : created->state_index_to_ket_index = {ket_index};
340 :
341 38 : created->_has_quantum_number_f =
342 19 : created->state_index_to_quantum_number_f[0] != std::numeric_limits<real_t>::max();
343 38 : created->_has_quantum_number_m =
344 19 : created->state_index_to_quantum_number_m[0] != std::numeric_limits<real_t>::max();
345 19 : created->_has_parity = created->state_index_to_parity[0] != Parity::UNKNOWN;
346 :
347 38 : return created;
348 19 : }
349 :
350 : template <typename Derived>
351 : std::shared_ptr<const Derived>
352 19 : Basis<Derived>::get_canonical_state_from_ket(std::shared_ptr<const ket_t> ket) const {
353 19 : int ket_index = get_ket_index_from_ket(ket);
354 19 : if (ket_index < 0) {
355 0 : throw std::invalid_argument("The ket does not belong to the basis.");
356 : }
357 19 : return get_canonical_state_from_ket(ket_index);
358 : }
359 :
360 : template <typename Derived>
361 6 : typename Basis<Derived>::Iterator Basis<Derived>::begin() const {
362 6 : return kets.begin();
363 : }
364 :
365 : template <typename Derived>
366 6 : typename Basis<Derived>::Iterator Basis<Derived>::end() const {
367 6 : return kets.end();
368 : }
369 :
370 : template <typename Derived>
371 12 : Basis<Derived>::Iterator::Iterator(typename ketvec_t::const_iterator it) : it{std::move(it)} {}
372 :
373 : template <typename Derived>
374 191 : bool Basis<Derived>::Iterator::operator!=(const Iterator &other) const {
375 191 : return other.it != it;
376 : }
377 :
378 : template <typename Derived>
379 185 : std::shared_ptr<const typename Basis<Derived>::ket_t> Basis<Derived>::Iterator::operator*() const {
380 185 : return *it;
381 : }
382 :
383 : template <typename Derived>
384 185 : typename Basis<Derived>::Iterator &Basis<Derived>::Iterator::operator++() {
385 185 : ++it;
386 185 : return *this;
387 : }
388 :
389 : template <typename Derived>
390 3291 : size_t Basis<Derived>::get_number_of_states() const {
391 3291 : return coefficients.matrix.cols();
392 : }
393 :
394 : template <typename Derived>
395 429 : size_t Basis<Derived>::get_number_of_kets() const {
396 429 : return coefficients.matrix.rows();
397 : }
398 :
399 : template <typename Derived>
400 : const Transformation<typename Basis<Derived>::scalar_t> &
401 60 : Basis<Derived>::get_transformation() const {
402 60 : return coefficients;
403 : }
404 :
405 : template <typename Derived>
406 : Transformation<typename Basis<Derived>::scalar_t>
407 0 : Basis<Derived>::get_rotator(real_t alpha, real_t beta, real_t gamma) const {
408 0 : Transformation<scalar_t> transformation{{static_cast<Eigen::Index>(coefficients.matrix.rows()),
409 : static_cast<Eigen::Index>(coefficients.matrix.rows())},
410 : {TransformationType::ROTATE}};
411 :
412 0 : std::vector<Eigen::Triplet<scalar_t>> entries;
413 :
414 0 : for (size_t idx_initial = 0; idx_initial < kets.size(); ++idx_initial) {
415 0 : real_t f = kets[idx_initial]->get_quantum_number_f();
416 0 : real_t m_initial = kets[idx_initial]->get_quantum_number_m();
417 :
418 0 : assert(2 * f == std::floor(2 * f) && f >= 0);
419 0 : assert(2 * m_initial == std::floor(2 * m_initial) && m_initial >= -f && m_initial <= f);
420 :
421 0 : for (real_t m_final = -f; m_final <= f; // NOSONAR m_final is precisely representable
422 : ++m_final) {
423 0 : auto val = wigner::wigner_uppercase_d_matrix<scalar_t>(f, m_initial, m_final, alpha,
424 : beta, gamma);
425 0 : size_t idx_final = get_ket_index_from_ket(
426 0 : kets[idx_initial]->get_ket_for_different_quantum_number_m(m_final));
427 0 : entries.emplace_back(idx_final, idx_initial, val);
428 : }
429 : }
430 :
431 0 : transformation.matrix.setFromTriplets(entries.begin(), entries.end());
432 0 : transformation.matrix.makeCompressed();
433 :
434 0 : return transformation;
435 0 : }
436 :
437 : template <typename Derived>
438 1 : Sorting Basis<Derived>::get_sorter(const std::vector<TransformationType> &labels) const {
439 1 : perform_sorter_checks(labels);
440 :
441 : // Throw a meaningful error if sorting by energy is requested as this might be a common mistake
442 1 : if (std::find(labels.begin(), labels.end(), TransformationType::SORT_BY_ENERGY) !=
443 2 : labels.end()) {
444 0 : throw std::invalid_argument("States do not store the energy and thus can not be sorted by "
445 : "the energy. Use an energy operator instead.");
446 : }
447 :
448 : // Initialize transformation
449 1 : Sorting transformation;
450 1 : transformation.matrix.resize(coefficients.matrix.cols());
451 1 : transformation.matrix.setIdentity();
452 :
453 : // Get the sorter
454 1 : get_sorter_without_checks(labels, transformation);
455 :
456 : // Check if all labels have been used for sorting
457 1 : if (labels != transformation.transformation_type) {
458 0 : throw std::invalid_argument("The states could not be sorted by all the requested labels.");
459 : }
460 :
461 1 : return transformation;
462 0 : }
463 :
464 : template <typename Derived>
465 : std::vector<IndicesOfBlock>
466 1 : Basis<Derived>::get_indices_of_blocks(const std::vector<TransformationType> &labels) const {
467 1 : perform_sorter_checks(labels);
468 :
469 1 : std::set<TransformationType> unique_labels(labels.begin(), labels.end());
470 1 : perform_blocks_checks(unique_labels);
471 :
472 : // Get the blocks
473 1 : IndicesOfBlocksCreator blocks_creator({0, static_cast<size_t>(coefficients.matrix.cols())});
474 1 : get_indices_of_blocks_without_checks(unique_labels, blocks_creator);
475 :
476 2 : return blocks_creator.create();
477 1 : }
478 :
479 : template <typename Derived>
480 33 : void Basis<Derived>::get_sorter_without_checks(const std::vector<TransformationType> &labels,
481 : Sorting &transformation) const {
482 33 : constexpr real_t numerical_precision = 100 * std::numeric_limits<real_t>::epsilon();
483 :
484 33 : int *perm_begin = transformation.matrix.indices().data();
485 33 : int *perm_end = perm_begin + coefficients.matrix.cols();
486 33 : const int *perm_back = perm_end - 1;
487 :
488 : // Sort the vector based on the requested labels
489 41634 : std::stable_sort(perm_begin, perm_end, [&](int a, int b) {
490 14881 : for (const auto &label : labels) {
491 10208 : switch (label) {
492 51 : case TransformationType::SORT_BY_PARITY:
493 51 : if (state_index_to_parity[a] != state_index_to_parity[b]) {
494 5504 : return state_index_to_parity[a] < state_index_to_parity[b];
495 : }
496 31 : break;
497 10157 : case TransformationType::SORT_BY_QUANTUM_NUMBER_M:
498 20314 : if (std::abs(state_index_to_quantum_number_m[a] -
499 20314 : state_index_to_quantum_number_m[b]) > numerical_precision) {
500 5484 : return state_index_to_quantum_number_m[a] < state_index_to_quantum_number_m[b];
501 : }
502 4673 : break;
503 0 : case TransformationType::SORT_BY_QUANTUM_NUMBER_F:
504 0 : if (std::abs(state_index_to_quantum_number_f[a] -
505 0 : state_index_to_quantum_number_f[b]) > numerical_precision) {
506 0 : return state_index_to_quantum_number_f[a] < state_index_to_quantum_number_f[b];
507 : }
508 0 : break;
509 0 : case TransformationType::SORT_BY_KET:
510 0 : if (state_index_to_ket_index[a] != state_index_to_ket_index[b]) {
511 0 : return state_index_to_ket_index[a] < state_index_to_ket_index[b];
512 : }
513 0 : break;
514 0 : default:
515 0 : std::abort(); // Can't happen because of previous checks
516 : }
517 : }
518 4673 : return false; // Elements are equal
519 : });
520 :
521 : // Check for invalid values and add transformation types
522 67 : for (const auto &label : labels) {
523 34 : switch (label) {
524 1 : case TransformationType::SORT_BY_PARITY:
525 1 : if (state_index_to_parity[*perm_back] == Parity::UNKNOWN) {
526 0 : throw std::invalid_argument(
527 : "States cannot be labeled and thus not sorted by the parity.");
528 : }
529 1 : transformation.transformation_type.push_back(TransformationType::SORT_BY_PARITY);
530 1 : break;
531 33 : case TransformationType::SORT_BY_QUANTUM_NUMBER_M:
532 33 : if (state_index_to_quantum_number_m[*perm_back] == std::numeric_limits<real_t>::max()) {
533 0 : throw std::invalid_argument(
534 : "States cannot be labeled and thus not sorted by the quantum number m.");
535 : }
536 33 : transformation.transformation_type.push_back(
537 33 : TransformationType::SORT_BY_QUANTUM_NUMBER_M);
538 33 : break;
539 0 : case TransformationType::SORT_BY_QUANTUM_NUMBER_F:
540 0 : if (state_index_to_quantum_number_f[*perm_back] == std::numeric_limits<real_t>::max()) {
541 0 : throw std::invalid_argument(
542 : "States cannot be labeled and thus not sorted by the quantum number f.");
543 : }
544 0 : transformation.transformation_type.push_back(
545 0 : TransformationType::SORT_BY_QUANTUM_NUMBER_F);
546 0 : break;
547 0 : case TransformationType::SORT_BY_KET:
548 0 : if (state_index_to_ket_index[*perm_back] == std::numeric_limits<int>::max()) {
549 0 : throw std::invalid_argument(
550 : "States cannot be labeled and thus not sorted by kets.");
551 : }
552 0 : transformation.transformation_type.push_back(TransformationType::SORT_BY_KET);
553 0 : break;
554 0 : default:
555 0 : std::abort(); // Can't happen because of previous checks
556 : }
557 : }
558 33 : }
559 :
560 : template <typename Derived>
561 33 : void Basis<Derived>::get_indices_of_blocks_without_checks(
562 : const std::set<TransformationType> &unique_labels,
563 : IndicesOfBlocksCreator &blocks_creator) const {
564 33 : constexpr real_t numerical_precision = 100 * std::numeric_limits<real_t>::epsilon();
565 :
566 33 : auto last_quantum_number_f = state_index_to_quantum_number_f[0];
567 33 : auto last_quantum_number_m = state_index_to_quantum_number_m[0];
568 33 : auto last_parity = state_index_to_parity[0];
569 33 : auto last_ket = state_index_to_ket_index[0];
570 :
571 1917 : for (int i = 0; i < coefficients.matrix.cols(); ++i) {
572 3685 : for (auto label : unique_labels) {
573 1895 : if (label == TransformationType::SORT_BY_QUANTUM_NUMBER_F) {
574 0 : if (std::abs(state_index_to_quantum_number_f[i] - last_quantum_number_f) >
575 : numerical_precision) {
576 0 : blocks_creator.add(i);
577 0 : break;
578 : }
579 1895 : } else if (label == TransformationType::SORT_BY_QUANTUM_NUMBER_M) {
580 1884 : if (std::abs(state_index_to_quantum_number_m[i] - last_quantum_number_m) >
581 : numerical_precision) {
582 94 : blocks_creator.add(i);
583 94 : break;
584 : }
585 11 : } else if (label == TransformationType::SORT_BY_PARITY) {
586 11 : if (state_index_to_parity[i] != last_parity) {
587 0 : blocks_creator.add(i);
588 0 : break;
589 : }
590 0 : } else if (label == TransformationType::SORT_BY_KET) {
591 0 : if (state_index_to_ket_index[i] != last_ket) {
592 0 : blocks_creator.add(i);
593 0 : break;
594 : }
595 : }
596 : }
597 1884 : last_quantum_number_f = state_index_to_quantum_number_f[i];
598 1884 : last_quantum_number_m = state_index_to_quantum_number_m[i];
599 1884 : last_parity = state_index_to_parity[i];
600 1884 : last_ket = state_index_to_ket_index[i];
601 : }
602 33 : }
603 :
604 : template <typename Derived>
605 75 : std::shared_ptr<const Derived> Basis<Derived>::transformed(const Sorting &transformation) const {
606 : // Create a copy of the current object
607 75 : auto transformed = std::make_shared<Derived>(derived());
608 :
609 75 : if (coefficients.matrix.cols() == 0) {
610 0 : return transformed;
611 : }
612 :
613 : // Apply the transformation
614 75 : transformed->coefficients.matrix = coefficients.matrix * transformation.matrix;
615 75 : transformed->coefficients.transformation_type = transformation.transformation_type;
616 :
617 75 : transformed->state_index_to_quantum_number_f.resize(transformation.matrix.size());
618 75 : transformed->state_index_to_quantum_number_m.resize(transformation.matrix.size());
619 75 : transformed->state_index_to_parity.resize(transformation.matrix.size());
620 75 : transformed->state_index_to_ket_index.resize(transformation.matrix.size());
621 :
622 4982 : for (int i = 0; i < transformation.matrix.size(); ++i) {
623 4907 : transformed->state_index_to_quantum_number_f[i] =
624 4907 : state_index_to_quantum_number_f[transformation.matrix.indices()[i]];
625 4907 : transformed->state_index_to_quantum_number_m[i] =
626 4907 : state_index_to_quantum_number_m[transformation.matrix.indices()[i]];
627 4907 : transformed->state_index_to_parity[i] =
628 4907 : state_index_to_parity[transformation.matrix.indices()[i]];
629 4907 : transformed->state_index_to_ket_index[i] =
630 4907 : state_index_to_ket_index[transformation.matrix.indices()[i]];
631 4907 : transformed->ket_index_to_state_index
632 4907 : [state_index_to_ket_index[transformation.matrix.indices()[i]]] = i;
633 : }
634 :
635 75 : return transformed;
636 75 : }
637 :
638 : template <typename Derived>
639 : std::shared_ptr<const Derived>
640 59 : Basis<Derived>::transformed(const Transformation<scalar_t> &transformation) const {
641 : // TODO why is "numerical_precision = 100 * std::sqrt(coefficients.matrix.rows()) *
642 : // std::numeric_limits<real_t>::epsilon()" too small for figuring out whether m is conserved?
643 59 : real_t numerical_precision = 0.001;
644 :
645 : // If the transformation is a rotation, it should be a rotation and nothing else
646 59 : bool is_rotation = false;
647 118 : for (auto t : transformation.transformation_type) {
648 59 : if (t == TransformationType::ROTATE) {
649 0 : is_rotation = true;
650 0 : break;
651 : }
652 : }
653 59 : if (is_rotation && transformation.transformation_type.size() != 1) {
654 0 : throw std::invalid_argument("A rotation can not be combined with other transformations.");
655 : }
656 :
657 : // To apply a rotation, the object must only be sorted but other transformations are not allowed
658 59 : if (is_rotation) {
659 0 : for (auto t : coefficients.transformation_type) {
660 0 : if (!utils::is_sorting(t)) {
661 0 : throw std::runtime_error(
662 : "If the object was transformed by a different transformation "
663 : "than sorting, it can not be rotated.");
664 : }
665 : }
666 : }
667 :
668 : // Create a copy of the current object
669 59 : auto transformed = std::make_shared<Derived>(derived());
670 :
671 59 : if (coefficients.matrix.cols() == 0) {
672 0 : return transformed;
673 : }
674 :
675 : // Apply the transformation
676 : // If a quantum number turns out to be conserved by the transformation, it will be
677 : // rounded to the nearest half integer to avoid loss of numerical_precision.
678 59 : transformed->coefficients.matrix = coefficients.matrix * transformation.matrix;
679 59 : transformed->coefficients.transformation_type = transformation.transformation_type;
680 :
681 59 : Eigen::SparseMatrix<real_t> probs = transformation.matrix.cwiseAbs2().transpose();
682 :
683 : {
684 118 : auto map = Eigen::Map<const Eigen::VectorX<real_t>>(state_index_to_quantum_number_f.data(),
685 59 : state_index_to_quantum_number_f.size());
686 59 : Eigen::VectorX<real_t> val = probs * map;
687 59 : Eigen::VectorX<real_t> sq = probs * map.cwiseAbs2();
688 59 : Eigen::VectorX<real_t> diff = (val.cwiseAbs2() - sq).cwiseAbs();
689 59 : transformed->state_index_to_quantum_number_f.resize(probs.rows());
690 :
691 2185 : for (size_t i = 0; i < transformed->state_index_to_quantum_number_f.size(); ++i) {
692 2126 : if (diff[i] < numerical_precision) {
693 380 : transformed->state_index_to_quantum_number_f[i] = std::round(val[i] * 2) / 2;
694 : } else {
695 1746 : transformed->state_index_to_quantum_number_f[i] =
696 1746 : std::numeric_limits<real_t>::max();
697 1746 : transformed->_has_quantum_number_f = false;
698 : }
699 : }
700 59 : }
701 :
702 : {
703 118 : auto map = Eigen::Map<const Eigen::VectorX<real_t>>(state_index_to_quantum_number_m.data(),
704 59 : state_index_to_quantum_number_m.size());
705 59 : Eigen::VectorX<real_t> val = probs * map;
706 59 : Eigen::VectorX<real_t> sq = probs * map.cwiseAbs2();
707 59 : Eigen::VectorX<real_t> diff = (val.cwiseAbs2() - sq).cwiseAbs();
708 59 : transformed->state_index_to_quantum_number_m.resize(probs.rows());
709 :
710 2185 : for (size_t i = 0; i < transformed->state_index_to_quantum_number_m.size(); ++i) {
711 2126 : if (diff[i] < numerical_precision) {
712 1774 : transformed->state_index_to_quantum_number_m[i] = std::round(val[i] * 2) / 2;
713 : } else {
714 352 : transformed->state_index_to_quantum_number_m[i] =
715 352 : std::numeric_limits<real_t>::max();
716 352 : transformed->_has_quantum_number_m = false;
717 : }
718 : }
719 59 : }
720 :
721 : {
722 : using utype = std::underlying_type<Parity>::type;
723 59 : Eigen::VectorX<real_t> map(state_index_to_parity.size());
724 2503 : for (size_t i = 0; i < state_index_to_parity.size(); ++i) {
725 2444 : map[i] = static_cast<utype>(state_index_to_parity[i]);
726 : }
727 59 : Eigen::VectorX<real_t> val = probs * map;
728 59 : Eigen::VectorX<real_t> sq = probs * map.cwiseAbs2();
729 59 : Eigen::VectorX<real_t> diff = (val.cwiseAbs2() - sq).cwiseAbs();
730 59 : transformed->state_index_to_parity.resize(probs.rows());
731 :
732 2185 : for (size_t i = 0; i < transformed->state_index_to_parity.size(); ++i) {
733 2126 : if (diff[i] < numerical_precision) {
734 801 : transformed->state_index_to_parity[i] = static_cast<Parity>(std::lround(val[i]));
735 : } else {
736 1325 : transformed->state_index_to_parity[i] = Parity::UNKNOWN;
737 1325 : transformed->_has_parity = false;
738 : }
739 : }
740 59 : }
741 :
742 : {
743 : // In the following, we obtain a bijective map between state index and ket index.
744 :
745 : // Find the maximum value in each row and column
746 59 : std::vector<real_t> max_in_row(transformed->coefficients.matrix.rows(), 0);
747 59 : std::vector<real_t> max_in_col(transformed->coefficients.matrix.cols(), 0);
748 2503 : for (int row = 0; row < transformed->coefficients.matrix.outerSize(); ++row) {
749 2444 : for (typename Eigen::SparseMatrix<scalar_t, Eigen::RowMajor>::InnerIterator it(
750 2444 : transformed->coefficients.matrix, row);
751 45070 : it; ++it) {
752 42626 : real_t val = std::pow(std::abs(it.value()), 2);
753 42626 : max_in_row[row] = std::max(max_in_row[row], val);
754 42626 : max_in_col[it.col()] = std::max(max_in_col[it.col()], val);
755 : }
756 : }
757 :
758 : // Use the maximum values to define a cost for a sub-optimal mapping
759 59 : std::vector<real_t> costs;
760 59 : std::vector<std::pair<int, int>> mappings;
761 59 : costs.reserve(transformed->coefficients.matrix.nonZeros());
762 59 : mappings.reserve(transformed->coefficients.matrix.nonZeros());
763 2503 : for (int row = 0; row < transformed->coefficients.matrix.outerSize(); ++row) {
764 2444 : for (typename Eigen::SparseMatrix<scalar_t, Eigen::RowMajor>::InnerIterator it(
765 2444 : transformed->coefficients.matrix, row);
766 45070 : it; ++it) {
767 42626 : real_t val = std::pow(std::abs(it.value()), 2);
768 42626 : real_t cost = max_in_row[row] + max_in_col[it.col()] - 2 * val;
769 42626 : costs.push_back(cost);
770 42626 : mappings.push_back({row, it.col()});
771 : }
772 : }
773 :
774 : // Obtain from the costs in which order the mappings should be considered
775 59 : std::vector<size_t> order(costs.size());
776 59 : std::iota(order.begin(), order.end(), 0);
777 59 : std::sort(order.begin(), order.end(),
778 529685 : [&](size_t a, size_t b) { return costs[a] < costs[b]; });
779 :
780 : // Fill ket_index_to_state_index with invalid values as there can be more kets than states
781 59 : std::fill(transformed->ket_index_to_state_index.begin(),
782 59 : transformed->ket_index_to_state_index.end(), std::numeric_limits<int>::max());
783 :
784 : // Generate the bijective map
785 59 : std::vector<bool> row_used(transformed->coefficients.matrix.rows(), false);
786 59 : std::vector<bool> col_used(transformed->coefficients.matrix.cols(), false);
787 59 : int num_used = 0;
788 5359 : for (size_t idx : order) {
789 5357 : int row = mappings[idx].first; // corresponds to the ket index
790 5357 : int col = mappings[idx].second; // corresponds to the state index
791 5357 : if (!row_used[row] && !col_used[col]) {
792 2126 : row_used[row] = true;
793 2126 : col_used[col] = true;
794 2126 : num_used++;
795 2126 : transformed->state_index_to_ket_index[col] = row;
796 2126 : transformed->ket_index_to_state_index[row] = col;
797 : }
798 5357 : if (num_used == transformed->coefficients.matrix.cols()) {
799 57 : break;
800 : }
801 : }
802 59 : assert(num_used == transformed->coefficients.matrix.cols());
803 59 : }
804 :
805 59 : return transformed;
806 59 : }
807 :
808 : template <typename Derived>
809 9784 : size_t Basis<Derived>::hash::operator()(const std::shared_ptr<const ket_t> &k) const {
810 9784 : return typename ket_t::hash()(*k);
811 : }
812 :
813 : template <typename Derived>
814 68 : bool Basis<Derived>::equal_to::operator()(const std::shared_ptr<const ket_t> &lhs,
815 : const std::shared_ptr<const ket_t> &rhs) const {
816 68 : return *lhs == *rhs;
817 : }
818 :
819 : // Explicit instantiations
820 : template class Basis<BasisAtom<double>>;
821 : template class Basis<BasisAtom<std::complex<double>>>;
822 : template class Basis<BasisPair<double>>;
823 : template class Basis<BasisPair<std::complex<double>>>;
824 : } // namespace pairinteraction
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