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/*
* Copyright Nick Thompson, 2019
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
*/
#ifndef BOOST_MATH_INTERPOLATORS_VECTOR_BARYCENTRIC_RATIONAL_DETAIL_HPP
#define BOOST_MATH_INTERPOLATORS_VECTOR_BARYCENTRIC_RATIONAL_DETAIL_HPP
#include <vector>
#include <utility> // for std::move
#include <limits>
#include <boost/assert.hpp>
namespace boost{ namespace math{ namespace detail{
template <class TimeContainer, class SpaceContainer>
class vector_barycentric_rational_imp
{
public:
using Real = typename TimeContainer::value_type;
using Point = typename SpaceContainer::value_type;
vector_barycentric_rational_imp(TimeContainer&& t, SpaceContainer&& y, size_t approximation_order);
void operator()(Point& p, Real t) const;
void eval_with_prime(Point& x, Point& dxdt, Real t) const;
// The barycentric weights are only interesting to the unit tests:
Real weight(size_t i) const { return w_[i]; }
private:
void calculate_weights(size_t approximation_order);
TimeContainer t_;
SpaceContainer y_;
TimeContainer w_;
};
template <class TimeContainer, class SpaceContainer>
vector_barycentric_rational_imp<TimeContainer, SpaceContainer>::vector_barycentric_rational_imp(TimeContainer&& t, SpaceContainer&& y, size_t approximation_order)
{
using std::numeric_limits;
t_ = std::move(t);
y_ = std::move(y);
BOOST_ASSERT_MSG(t_.size() == y_.size(), "There must be the same number of time points as space points.");
BOOST_ASSERT_MSG(approximation_order < y_.size(), "Approximation order must be < data length.");
for (size_t i = 1; i < t_.size(); ++i)
{
BOOST_ASSERT_MSG(t_[i] - t_[i-1] > (numeric_limits<typename TimeContainer::value_type>::min)(), "The abscissas must be listed in strictly increasing order t[0] < t[1] < ... < t[n-1].");
}
calculate_weights(approximation_order);
}
template<class TimeContainer, class SpaceContainer>
void vector_barycentric_rational_imp<TimeContainer, SpaceContainer>::calculate_weights(size_t approximation_order)
{
using Real = typename TimeContainer::value_type;
using std::abs;
int64_t n = t_.size();
w_.resize(n, Real(0));
for(int64_t k = 0; k < n; ++k)
{
int64_t i_min = (std::max)(k - (int64_t) approximation_order, (int64_t) 0);
int64_t i_max = k;
if (k >= n - (std::ptrdiff_t)approximation_order)
{
i_max = n - approximation_order - 1;
}
for(int64_t i = i_min; i <= i_max; ++i)
{
Real inv_product = 1;
int64_t j_max = (std::min)(static_cast<int64_t>(i + approximation_order), static_cast<int64_t>(n - 1));
for(int64_t j = i; j <= j_max; ++j)
{
if (j == k)
{
continue;
}
Real diff = t_[k] - t_[j];
inv_product *= diff;
}
if (i % 2 == 0)
{
w_[k] += 1/inv_product;
}
else
{
w_[k] -= 1/inv_product;
}
}
}
}
template<class TimeContainer, class SpaceContainer>
void vector_barycentric_rational_imp<TimeContainer, SpaceContainer>::operator()(typename SpaceContainer::value_type& p, typename TimeContainer::value_type t) const
{
using Real = typename TimeContainer::value_type;
for (auto & x : p)
{
x = Real(0);
}
Real denominator = 0;
for(size_t i = 0; i < t_.size(); ++i)
{
// See associated commentary in the scalar version of this function.
if (t == t_[i])
{
p = y_[i];
return;
}
Real x = w_[i]/(t - t_[i]);
for (decltype(p.size()) j = 0; j < p.size(); ++j)
{
p[j] += x*y_[i][j];
}
denominator += x;
}
for (decltype(p.size()) j = 0; j < p.size(); ++j)
{
p[j] /= denominator;
}
return;
}
template<class TimeContainer, class SpaceContainer>
void vector_barycentric_rational_imp<TimeContainer, SpaceContainer>::eval_with_prime(typename SpaceContainer::value_type& x, typename SpaceContainer::value_type& dxdt, typename TimeContainer::value_type t) const
{
using Point = typename SpaceContainer::value_type;
using Real = typename TimeContainer::value_type;
this->operator()(x, t);
Point numerator;
for (decltype(x.size()) i = 0; i < x.size(); ++i)
{
numerator[i] = 0;
}
Real denominator = 0;
for(decltype(t_.size()) i = 0; i < t_.size(); ++i)
{
if (t == t_[i])
{
Point sum;
for (decltype(x.size()) i = 0; i < x.size(); ++i)
{
sum[i] = 0;
}
for (decltype(t_.size()) j = 0; j < t_.size(); ++j)
{
if (j == i)
{
continue;
}
for (decltype(sum.size()) k = 0; k < sum.size(); ++k)
{
sum[k] += w_[j]*(y_[i][k] - y_[j][k])/(t_[i] - t_[j]);
}
}
for (decltype(sum.size()) k = 0; k < sum.size(); ++k)
{
dxdt[k] = -sum[k]/w_[i];
}
return;
}
Real tw = w_[i]/(t - t_[i]);
Point diff;
for (decltype(diff.size()) j = 0; j < diff.size(); ++j)
{
diff[j] = (x[j] - y_[i][j])/(t-t_[i]);
}
for (decltype(diff.size()) j = 0; j < diff.size(); ++j)
{
numerator[j] += tw*diff[j];
}
denominator += tw;
}
for (decltype(dxdt.size()) j = 0; j < dxdt.size(); ++j)
{
dxdt[j] = numerator[j]/denominator;
}
return;
}
}}}
#endif
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