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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
*
* Modification(s):
* - YYYY/MM Author: Description of the modification
*/
#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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