bernstein.h

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#ifndef _CLASS_BERNSTEIN
#define _CLASS_BERNSTEIN
 
#include <math.h>
 
#include <stdexcept>
#include <vector>
 
#include "MathDefs.h"
#include "curve_abc.h"
 
namespace ndcurves {
inline unsigned int bin(const unsigned int n, const unsigned int k) {
  if (k > n)
    throw std::runtime_error("binomial coefficient higher than degree");
  if (k == 0) return 1;
  if (k > n / 2) return bin(n, n - k);
  return n * bin(n - 1, k - 1) / k;
}

template <typename Numeric = double>
struct Bern {
  Bern() {}
  Bern(const unsigned int m, const unsigned int i)
      : m_minus_i(m - i), i_(i), bin_m_i_(bin(m, i)) {}
 
  virtual ~Bern() {}

  Numeric operator()(const Numeric u) const {
    if (!(u >= 0. && u <= 1.)) {
      throw std::invalid_argument("u needs to be betwen 0 and 1.");
    }
    return bin_m_i_ * (pow(u, i_)) * pow((1 - u), m_minus_i);
  }

  virtual bool operator==(const Bern& other) const {
    return ndcurves::isApprox<Numeric>(m_minus_i, other.m_minus_i) &&
           ndcurves::isApprox<Numeric>(i_, other.i_) &&
           ndcurves::isApprox<Numeric>(bin_m_i_, other.bin_m_i_);
  }

  virtual bool operator!=(const Bern& other) const { return !(*this == other); }
 
  /* Attributes */
  Numeric m_minus_i;
  Numeric i_;
  Numeric bin_m_i_;
  /* Attributes */
 
  // Serialization of the class
  friend class boost::serialization::access;
  template <class Archive>
  void serialize(Archive& ar, const unsigned int version) {
    if (version) {
      // Do something depending on version ?
    }
    ar& boost::serialization::make_nvp("m_minus_i", m_minus_i);
    ar& boost::serialization::make_nvp("i", i_);
    ar& boost::serialization::make_nvp("bin_m_i", bin_m_i_);
  }
};  // End struct Bern

template <typename Numeric>
std::vector<Bern<Numeric> > makeBernstein(const unsigned int n) {
  std::vector<Bern<Numeric> > res;
  for (unsigned int i = 0; i <= n; ++i) {
    res.push_back(Bern<Numeric>(n, i));
  }
  return res;
}
}  // namespace ndcurves
 
DEFINE_CLASS_TEMPLATE_VERSION(typename Numeric, ndcurves::Bern<Numeric>)
 
#endif  //_CLASS_BERNSTEIN