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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 Sophia Antipolis-Méditerranée (France)
*
* 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 GUDHI_MULTI_FIELD_H
#define GUDHI_MULTI_FIELD_H
#include <iostream>
#include <vector>
#include <gmpxx.h>
namespace Gudhi{
/** \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 () {}
/* 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
unsigned 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);
}
//set m to primorial(bound_prime)
prod_characteristics_ = 1;
for(auto p : primes_)
{ mpz_mul_ui(prod_characteristics_.get_mpz_t(),
prod_characteristics_.get_mpz_t(),
p);
}
num_primes_ = primes_.size();
//Uvect_
Element Ui; Element tmp_elem;
for(auto p : primes_)
{
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(int idx = 0; idx < num_primes_; ++idx)
{ mult_id_all = (mult_id_all + Uvect_[idx]) % prod_characteristics_; }
}
void clear_coefficient(Element & x) { mpz_clear(x.get_mpz_t()); }
/** \brief Returns the additive idendity \f$0_{\Bbbk}\f$ of the field.*/
Element additive_identity () { return 0; }
/** \brief Returns the multiplicative identity \f$1_{\Bbbk}\f$ of the field.*/
Element multiplicative_identity () { return mult_id_all; }// 1 everywhere
Element multiplicative_identity (Element Q)
{
if(Q == prod_characteristics_) { return multiplicative_identity(); }
Element mult_id = 0;
for(int idx = 0; idx < num_primes_; ++idx) {
if( (Q % primes_[idx]) == 0 )
{ mult_id = (mult_id + Uvect_[idx]) % prod_characteristics_; }
}
return mult_id;
}
/** Returns y * w */
Element times ( Element y, int w ) {
Element tmp = (y*w) % prod_characteristics_;
if(tmp < 0) return prod_characteristics_ + tmp;
return tmp;
}
void plus_equal(Element & x, Element y)
{ x += y; x %= prod_characteristics_; }
/** \brief Returns the characteristic \f$p\f$ of the field.*/
Element characteristic() { 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());
return std::pair<Element,Element>(
(inv_qt * multiplicative_identity(QT)) % prod_characteristics_
, QT );
}
/** Returns -x * y.*/
Element times_minus ( Element x, Element y )
{ return prod_characteristics_ - ((x*y)%prod_characteristics_); }
/** Set x <- x + w * y*/
void plus_times_equal ( Element & x, Element y, Element w )
{ x = (x + w * y) % prod_characteristics_; }
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_;
size_t num_primes_; //number of fields
Element mult_id_all;
};
} // namespace GUDHI
#endif // GUDHI_MULTI_FIELD_H
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