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-/* This file is part of the Gudhi Library. The Gudhi library
- * (Geometric Understanding in Higher Dimensions) is a generic C++
- * library for computational topology.
- *
- * Author(s): Clément Maria
- *
- * Copyright (C) 2014 Inria
- *
- * This program is free software: you can redistribute it and/or modify
- * it under the terms of the GNU General Public License as published by
- * the Free Software Foundation, either version 3 of the License, or
- * (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program. If not, see <http://www.gnu.org/licenses/>.
- */
-
-#ifndef PERSISTENT_COHOMOLOGY_MULTI_FIELD_H_
-#define PERSISTENT_COHOMOLOGY_MULTI_FIELD_H_
-
-#include <gmpxx.h>
-
-#include <vector>
-#include <utility>
-
-namespace Gudhi {
-
-namespace persistent_cohomology {
-
-/** \brief Structure representing coefficients in a set of finite fields simultaneously
- * using the chinese remainder theorem.
- *
- * \implements CoefficientField
- * \ingroup persistent_cohomology
-
- * Details on the algorithms may be found in \cite boissonnat:hal-00922572
- */
-class Multi_field {
- public:
- typedef mpz_class Element;
-
- Multi_field()
- : prod_characteristics_(0),
- mult_id_all(0),
- add_id_all(0) {
- }
-
- /* Initialize the multi-field. The generation of prime numbers might fail with
- * a very small probability.*/
- void init(int min_prime, int max_prime) {
- if (max_prime < 2) {
- std::cerr << "There is no prime less than " << max_prime << std::endl;
- }
- if (min_prime > max_prime) {
- std::cerr << "No prime in [" << min_prime << ":" << max_prime << "]"
- << std::endl;
- }
- // fill the list of prime numbers
- int curr_prime = min_prime;
- mpz_t tmp_prime;
- mpz_init_set_ui(tmp_prime, min_prime);
- // test if min_prime is prime
- int is_prime = mpz_probab_prime_p(tmp_prime, 25); // probabilistic primality test
-
- if (is_prime == 0) { // min_prime is composite
- mpz_nextprime(tmp_prime, tmp_prime);
- curr_prime = mpz_get_ui(tmp_prime);
- }
-
- while (curr_prime <= max_prime) {
- primes_.push_back(curr_prime);
- mpz_nextprime(tmp_prime, tmp_prime);
- curr_prime = mpz_get_ui(tmp_prime);
- }
- mpz_clear(tmp_prime);
- // set m to primorial(bound_prime)
- prod_characteristics_ = 1;
- for (auto p : primes_) {
- prod_characteristics_ *= p;
- }
-
- // Uvect_
- Element Ui;
- Element tmp_elem;
- for (auto p : primes_) {
- assert(p > 0); // division by zero + non negative values
- tmp_elem = prod_characteristics_ / p;
- // Element tmp_elem_bis = 10;
- mpz_powm_ui(tmp_elem.get_mpz_t(), tmp_elem.get_mpz_t(), p - 1,
- prod_characteristics_.get_mpz_t());
- Uvect_.push_back(tmp_elem);
- }
- mult_id_all = 0;
- for (auto uvect : Uvect_) {
- assert(prod_characteristics_ > 0); // division by zero + non negative values
- mult_id_all = (mult_id_all + uvect) % prod_characteristics_;
- }
- }
-
- /** \brief Returns the additive idendity \f$0_{\Bbbk}\f$ of the field.*/
- const Element& additive_identity() const {
- return add_id_all;
- }
- /** \brief Returns the multiplicative identity \f$1_{\Bbbk}\f$ of the field.*/
- const Element& multiplicative_identity() const {
- return mult_id_all;
- } // 1 everywhere
-
- Element multiplicative_identity(Element Q) {
- if (Q == prod_characteristics_) {
- return multiplicative_identity();
- }
-
- assert(prod_characteristics_ > 0); // division by zero + non negative values
- Element mult_id = 0;
- for (unsigned int idx = 0; idx < primes_.size(); ++idx) {
- assert(primes_[idx] > 0); // division by zero + non negative values
- if ((Q % primes_[idx]) == 0) {
- mult_id = (mult_id + Uvect_[idx]) % prod_characteristics_;
- }
- }
- return mult_id;
- }
-
- /** Returns y * w */
- Element times(const Element& y, const Element& w) {
- return plus_times_equal(0, y, w);
- }
-
- Element plus_equal(const Element& x, const Element& y) {
- return plus_times_equal(x, y, (Element)1);
- }
-
- /** \brief Returns the characteristic \f$p\f$ of the field.*/
- const Element& characteristic() const {
- return prod_characteristics_;
- }
-
- /** Returns the inverse in the field. Modifies P. ??? */
- std::pair<Element, Element> inverse(Element x, Element QS) {
- Element QR;
- mpz_gcd(QR.get_mpz_t(), x.get_mpz_t(), QS.get_mpz_t()); // QR <- gcd(x,QS)
- if (QR == QS)
- return std::pair<Element, Element>(additive_identity(), multiplicative_identity()); // partial inverse is 0
- Element QT = QS / QR;
- Element inv_qt;
- mpz_invert(inv_qt.get_mpz_t(), x.get_mpz_t(), QT.get_mpz_t());
-
- assert(prod_characteristics_ > 0); // division by zero + non negative values
- return { (inv_qt * multiplicative_identity(QT)) % prod_characteristics_, QT };
- }
- /** Returns -x * y.*/
- Element times_minus(const Element& x, const Element& y) {
- assert(prod_characteristics_ > 0); // division by zero + non negative values
- /* This assumes that (x*y)%pc cannot be zero, but Field_Zp has specific code for the 0 case ??? */
- return prod_characteristics_ - ((x * y) % prod_characteristics_);
- }
-
- /** Set x <- x + w * y*/
- Element plus_times_equal(const Element& x, const Element& y, const Element& w) {
- assert(prod_characteristics_ > 0); // division by zero + non negative values
- Element result = (x + w * y) % prod_characteristics_;
- if (result < 0)
- result += prod_characteristics_;
- return result;
- }
-
- Element prod_characteristics_; // product of characteristics of the fields
- // represented by the multi-field class
- std::vector<int> primes_; // all the characteristics of the fields
- std::vector<Element> Uvect_;
- Element mult_id_all;
- const Element add_id_all;
-};
-
-} // namespace persistent_cohomology
-
-} // namespace Gudhi
-
-#endif // PERSISTENT_COHOMOLOGY_MULTI_FIELD_H_
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