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#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; }; }}
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.