Boost C++ Libraries

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PCHIP interpolation

Synopsis

```#include <boost/math/interpolators/pchip.hpp>

namespace boost::math::interpolators {

template <class RandomAccessContainer>
class pchip
{
public:

using Real = RandomAccessContainer::value_type;

pchip(RandomAccessContainer&& abscissas, RandomAccessContainer&& ordinates,
Real left_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN(),
Real right_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN());

Real operator()(Real x) const;

Real prime(Real x) const;

void push_back(Real x, Real y);

friend std::ostream& operator<<(std::ostream & os, const pchip & m);
};

} // namespaces
```

PCHIP Interpolation

The PCHIP interpolant takes non-equispaced data and interpolates between them via cubic Hermite polynomials whose slopes are chosen so that the resulting interpolant is monotonic; see Fritsch and Carlson for details. The interpolant is C1 and evaluation has 𝑶(log(N)) complexity. An example usage is as follows:

```std::vector<double> x{1, 5, 9 , 12};
std::vector<double> y{8,17, 4, -3};
using boost::math::interpolators::pchip;
auto spline = pchip(std::move(x), std::move(y));
// evaluate at a point:
double z = spline(3.4);
// evaluate derivative at a point:
double zprime = spline.prime(3.4);
```

Periodically, it is helpful to see what data the interpolator has, and the slopes it has chosen. This can be achieved via

```std::cout << spline << "\n";
```

Note that the interpolator is pimpl'd, so that copying the class is cheap, and hence it can be shared between threads. (The call operator and `.prime()` are threadsafe; `push_back` is not.)

This interpolant can be updated in constant time. Hence we can use `boost::circular_buffer` to do real-time interpolation:

```#include <boost/circular_buffer.hpp>
...
boost::circular_buffer<double> initial_x{1,2,3,4};
boost::circular_buffer<double> initial_y{4,5,6,7};
auto circular_pchip = pchip(std::move(initial_x), std::move(initial_y));
// interpolate via call operation:
double y = circular_pchip(3.5);
This interpolator chooses the slopes and forwards data to the cubic Hermite interpolator, so the performance is stated in the documentation for `cubic_hermite.hpp`.