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- [/
- Copyright 2019 Nick Thompson
- Distributed under 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).
- ]
- [section:vector_barycentric Vector-valued Barycentric Rational Interpolation]
- [heading Synopsis]
- ``
- #include <boost/math/interpolators/vector_barycentric_rational.hpp>
- namespace boost{ namespace math{
- template<class TimeContainer, class SpaceContainer>
- class vector_barycentric_rational
- {
- public:
- using Real = typename TimeContainer::value_type;
- using Point = typename SpaceContainer::value_type;
- vector_barycentric_rational(TimeContainer&& times, SpaceContainer&& points, size_t approximation_order = 3);
- void operator()(Point& x, Real t) const;
- Point operator()(Real t) const;
- void prime(Point& dxdt, Real t) const;
- Point prime(Real t);
- void eval_with_prime(Point& x, Point& dxdt, Real t) const;
- std::pair<Point, Point> eval_with_prime(Real t) const;
- };
- }}
- ``
- [heading Description]
- The /n/ dimensional vector-valued barycentric rational interpolator is exactly the same as /n/ scalar-valued barycentric rational interpolators.
- This is provided primarily for convenience and a slight improvement in efficiency over using /n/ different rational interpolators and combining their results.
- Use of the class requires a `Point`-type which has size known at compile-time.
- These requirements are satisfied by (for example) `Eigen::Vector2d`s and `std::array<Real, N>` classes.
- The call to the constructor computes the weights:
- using boost::math::vector_barycentric_rational;
- std::vector<double> t(100);
- std::vector<Eigen::Vector2d> y(100);
- // initialize t and y . . .
- vector_barycentric_rational<decltype(t), decltype(y)> interpolant(std::move(t), std::move(y));
- To evaluate the interpolant, use
- double t = 2.3;
- Eigen::Vector2d y = interpolant(t);
- If you want to populate a vector passed into the interpolant, rather than get it returned, that syntax is supported:
- Eigen::Vector2d y;
- interpolant(y, t);
- We tested this with `Eigen::Vector`s and found no performance benefit, but other `Point`-types might not be the same.
- To evaluate the derivative of the interpolant use
- auto [y, y_prime] = interpolant.eval_with_prime(x);
- Computation of the derivative requires evaluation, so if you can try to use both values at once.
- [endsect] [/section:vector_barycentric Vector Barycentric Rational Interpolation]
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