# Boost C++ Libraries

...one of the most highly regarded and expertly designed C++ library projects in the world.

## Vector-valued Barycentric Rational Interpolation

#### 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;
};

}}
```

#### 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.