EQ2EMu/EQ2/source/depends/boost_1_72_0/libs/math/doc/interpolators/vector_barycentric_rational.qbk

[/
  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]