intrp::UniformCardinalBSpline Class Reference

A cubic B-spline interpolant of uniformly spaced samples. More...

#include <UniformCardinalBSpline.hpp>

Public Member Functions
	UniformCardinalBSpline (std::vector< double > values, double start_time, double time_step)
	Construct from uniformly spaced samples.
double	operator() (double time) const
	Evaluate the interpolant at time, clamped to the bounds()
const std::vector< double > &	values () const
	The sampled function values.
double	start_time () const
	The time of the first sample.
double	time_step () const
	The spacing between samples.
std::array< double, 2 >	bounds () const
	The first and last sample time.
void	pup (PUP::er &p)

Detailed Description

A cubic B-spline interpolant of uniformly spaced samples.

Interpolates samples \(f_i = f(t_0 + i \Delta t)\), \(i = 0, \ldots, N-1\), with a cubic B-spline. The interpolation error decreases as \(\mathcal{O}(\Delta t^4)\) for smooth data. This class wraps boost::math::interpolators::cardinal_cubic_b_spline and adds:

• Serialization: the samples, start time, and time step fully determine the interpolant, so it can be sent in a pup and rebuilt on the receiving side.
• Clamped evaluation: evaluation is clamped to the bounds of the sampled interval, so times that fall outside the interval by roundoff evaluate to the boundary values instead of extrapolating the spline. Times outside the bounds beyond roundoff trigger an ASSERT in debug builds.

Here is an example how to use this class:

    const intrp::UniformCardinalBSpline interpolant{
        sample_function(function, start_time, time_step, num_samples),
        start_time, time_step};
    const double interpolated_value =
        interpolant(0.5 * (start_time + end_time));

Note

Requires Boost 1.81 or newer at runtime because of an accuracy fix for the estimate of the derivative at the right endpoint in the Boost implementation, see https://github.com/boostorg/math/commit/4809e714d4806c07da3a3def0c4550daa0529b8d. The constructor raises an error for older Boost versions.

Constructor & Destructor Documentation

UniformCardinalBSpline()

intrp::UniformCardinalBSpline::UniformCardinalBSpline	(	std::vector< double >	values,
		double	start_time,
		double	time_step )

Construct from uniformly spaced samples.

Parameters

values	The sampled function values \(f(t_0 + i \Delta t)\). At least 5 samples are required.
start_time	The time \(t_0\) of the first sample.
time_step	The (positive) spacing \(\Delta t\) between samples.

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The documentation for this class was generated from the following file:

• src/NumericalAlgorithms/Interpolation/UniformCardinalBSpline.hpp