Multi_field_operators.h

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/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
 *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
 *    Author(s):       Hannah Schreiber, Clément Maria
 *
 *    Copyright (C) 2022 Inria
 *
 *    Modification(s):
 *      - YYYY/MM Author: Description of the modification
 */

 
#ifndef MATRIX_FIELD_MULTI_OPERATORS_H_
#define MATRIX_FIELD_MULTI_OPERATORS_H_
 
#include <utility>
#include <vector>
#include <gmpxx.h>
#include <stdexcept>
 
#include <gudhi/Debug_utils.h>
 
namespace Gudhi {
namespace persistence_fields {

class Multi_field_operators
{
 public:
  using Element = mpz_class;      
  using Characteristic = Element; 
 
  inline static const Characteristic nullCharacteristic = 0; 

  Multi_field_operators() : productOfAllCharacteristics_(nullCharacteristic) /* , multiplicativeID_(1) */ {}

  Multi_field_operators(int minCharacteristic, int maxCharacteristic)
      : productOfAllCharacteristics_(nullCharacteristic)  //, multiplicativeID_(1)
  {
    set_characteristic(minCharacteristic, maxCharacteristic);
  }

  void set_characteristic(int minimum, int maximum)
  {
    if (maximum < 2) throw std::invalid_argument("Characteristic must be strictly positive");
    if (minimum > maximum) throw std::invalid_argument("The given interval is not valid.");
    if (minimum == maximum && !_is_prime(minimum))
      throw std::invalid_argument("The given interval does not contain a prime number.");
 
    unsigned int curr_prime = minimum;
    mpz_t tmp_prime;
    mpz_init_set_ui(tmp_prime, minimum);
    // 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);
    }
 
    primes_.clear();
    while (curr_prime <= static_cast<unsigned int>(maximum)) {
      primes_.push_back(curr_prime);
      mpz_nextprime(tmp_prime, tmp_prime);
      curr_prime = mpz_get_ui(tmp_prime);
    }
    mpz_clear(tmp_prime);
 
    if (primes_.empty()) throw std::invalid_argument("The given interval does not contain a prime number.");
 
    productOfAllCharacteristics_ = 1;
    for (const unsigned int p : primes_) {
      productOfAllCharacteristics_ *= p;
    }
 
    partials_.resize(primes_.size());
    for (unsigned int i = 0; i < primes_.size(); ++i) {
      unsigned int p = primes_[i];
      partials_[i] = productOfAllCharacteristics_ / p;
      mpz_powm_ui(partials_[i].get_mpz_t(), partials_[i].get_mpz_t(), p - 1, productOfAllCharacteristics_.get_mpz_t());
    }
 
    // If I understood the paper well, multiplicativeID_ always equals to 1. But in Clement's code,
    // multiplicativeID_ is computed (see commented loop below). TODO: verify with Clement.
    // for (unsigned int i = 0; i < partials_.size(); ++i) {
    //   multiplicativeID_ = (multiplicativeID_ + partials_[i]) % productOfAllCharacteristics_;
    // }
  }

  [[nodiscard]] const Characteristic& get_characteristic() const { return productOfAllCharacteristics_; }

  [[nodiscard]] Element get_value(Element e) const
  {
    get_value_inplace(e);
    return e;
  }

  void get_value_inplace(Element& e) const
  {
    if (e >= productOfAllCharacteristics_ || e < -productOfAllCharacteristics_)
      mpz_mod(e.get_mpz_t(), e.get_mpz_t(), productOfAllCharacteristics_.get_mpz_t());
    if (e < 0) e += productOfAllCharacteristics_;
  }

  [[nodiscard]] Element add(Element e1, const Element& e2) const
  {
    add_inplace(e1, e2);
    return e1;
  }

  void add_inplace(Element& e1, const Element& e2) const
  {
    e1 += e2;
    get_value_inplace(e1);
  }

  [[nodiscard]] Element subtract(Element e1, const Element& e2) const
  {
    subtract_inplace_front(e1, e2);
    return e1;
  }

  void subtract_inplace_front(Element& e1, const Element& e2) const
  {
    e1 -= e2;
    get_value_inplace(e1);
  }

  void subtract_inplace_back(const Element& e1, Element& e2) const
  {
    mpz_sub(e2.get_mpz_t(), e1.get_mpz_t(), e2.get_mpz_t());
    get_value_inplace(e2);
  }

  [[nodiscard]] Element multiply(Element e1, const Element& e2) const
  {
    multiply_inplace(e1, e2);
    return e1;
  }

  void multiply_inplace(Element& e1, const Element& e2) const
  {
    e1 *= e2;
    get_value_inplace(e1);
  }

  [[nodiscard]] Element multiply_and_add(Element e, const Element& m, const Element& a) const
  {
    multiply_and_add_inplace_front(e, m, a);
    return e;
  }

  void multiply_and_add_inplace_front(Element& e, const Element& m, const Element& a) const
  {
    e *= m;
    e += a;
    get_value_inplace(e);
  }

  void multiply_and_add_inplace_back(const Element& e, const Element& m, Element& a) const
  {
    a += e * m;
    get_value_inplace(a);
  }

  [[nodiscard]] Element add_and_multiply(Element e, const Element& a, const Element& m) const
  {
    add_and_multiply_inplace_front(e, a, m);
    return e;
  }

  void add_and_multiply_inplace_front(Element& e, const Element& a, const Element& m) const
  {
    e += a;
    e *= m;
    get_value_inplace(e);
  }

  void add_and_multiply_inplace_back(const Element& e, const Element& a, Element& m) const
  {
    m *= e + a;
    get_value_inplace(m);
  }

  bool are_equal(const Element& e1, const Element& e2) const
  {
    if (e1 == e2) return true;
    return get_value(e1) == get_value(e2);
  }

  [[nodiscard]] Element get_inverse(const Element& e) const
  {
    return get_partial_inverse(e, productOfAllCharacteristics_).first;
  }

  [[nodiscard]] std::pair<Element, Characteristic> get_partial_inverse(
      const Element& e,
      const Characteristic& productOfCharacteristics) const
  {
    GUDHI_CHECK(productOfCharacteristics >= 0 && productOfCharacteristics <= productOfAllCharacteristics_,
                std::invalid_argument(
                    "The given product is not the product of a subset of the current Multi-field characteristics."));
 
    Characteristic QR;
    mpz_gcd(QR.get_mpz_t(), e.get_mpz_t(), productOfCharacteristics.get_mpz_t());  // QR <- gcd(x,QS)
 
    if (QR == productOfCharacteristics) return {0, get_multiplicative_identity()};  // partial inverse is 0
 
    Characteristic QT = productOfCharacteristics / QR;
 
    Characteristic inv_qt;
    mpz_invert(inv_qt.get_mpz_t(), e.get_mpz_t(), QT.get_mpz_t());
 
    std::pair<Element, Characteristic> res(get_partial_multiplicative_identity(QT), QT);
    res.first *= inv_qt;
    get_value_inplace(res.first);
 
    return res;
  }

  static const Element& get_additive_identity() { return additiveID_; }

  static const Element& get_multiplicative_identity() { return multiplicativeID_; }

  [[nodiscard]] Element get_partial_multiplicative_identity(const Characteristic& productOfCharacteristics) const
  {
    GUDHI_CHECK(productOfCharacteristics >= 0 && productOfCharacteristics <= productOfAllCharacteristics_,
                std::invalid_argument(
                    "The given product is not the product of a subset of the current Multi-field characteristics."));
 
    if (productOfCharacteristics == nullCharacteristic || productOfCharacteristics == productOfAllCharacteristics_) {
      return get_multiplicative_identity();
    }
    Element multIdentity(0);
    for (unsigned int idx = 0; idx < primes_.size(); ++idx) {
      if ((productOfCharacteristics % primes_[idx]) == 0) {
        multIdentity += partials_[idx];
      }
    }
    get_value_inplace(multIdentity);
    return multIdentity;
  }

  friend void swap(Multi_field_operators& f1, Multi_field_operators& f2) noexcept
  {
    f1.primes_.swap(f2.primes_);
    std::swap(f1.productOfAllCharacteristics_, f2.productOfAllCharacteristics_);
    f1.partials_.swap(f2.partials_);
  }
 
 private:
  std::vector<unsigned int> primes_;           
  Characteristic productOfAllCharacteristics_; 
  std::vector<Characteristic> partials_;       
  inline static const Element multiplicativeID_ = 1;
  inline static const Element additiveID_ = 0;
 
  static constexpr bool _is_prime(const int p)
  {
    if (p <= 1) return false;
    if (p <= 3) return true;
    if (p % 2 == 0 || p % 3 == 0) return false;
 
    for (long i = 5; i * i <= p; i = i + 6)
      if (p % i == 0 || p % (i + 2) == 0) return false;
 
    return true;
  }
};
 
}  // namespace persistence_fields
}  // namespace Gudhi
 
#endif  // MATRIX_FIELD_MULTI_OPERATORS_H_