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