A basis interface for 1-d series expansions. More...

#include <Basis1d.h>

Public Types
using	Function = ...
	A Function1d object that uses this basis.

using	Scaled = ...
	The type returned by scale().

Public Member Functions
std::size_t	getOrder () const
	Return the order of the basis.

std::size_t	size () const
	Return the number of elements in the basis.

Scaled	scaled (Scaling1d const &scaling) const
	Return a scaled basis that delegates to a copy of `this`.

template<typename Vector >
double	sumWith (double x, Vector const &coefficients) const
	Evaluate a basis expansion with the given coefficients.

template<typename Vector >
void	fill (double x, Vector &&basis) const
	Evaluate the basis at a given point.

Detailed Description

A basis interface for 1-d series expansions.

Note: This class is only present in the documentation, as it represents an abstract interface for which C++ (prior to C++20, at least) has no language support. It may be formalized into a true Concept when that language feature is available.

Definition at line 36 of file Basis1d.h.

Member Typedef Documentation

◆ Function

using lsst::geom::polynomials::Basis1d::Function = ...

A Function1d object that uses this basis.

Definition at line 40 of file Basis1d.h.

◆ Scaled

using lsst::geom::polynomials::Basis1d::Scaled = ...

The type returned by scale().

Definition at line 43 of file Basis1d.h.

Member Function Documentation

◆ fill()

template<typename Vector >

void lsst::geom::polynomials::Basis1d::fill	(	double	x,
		Vector &&	basis ) const

Evaluate the basis at a given point.

Parameters

[in]	x	Point at which to evaluate the basis functions.
[out]	basis	Output vector. May be any type for which `coefficients[n]` returns a non-const reference to a floating-point value. This includes `std::vector<double>`, `ndarray::Array<double,1>`, `Eigen::VectorXd`, `Eigen` view expressions, and mutable random access iterators.

Exception Safety: Does not throw unless coefficients[n] does, and provides basic exception safety if it does.

◆ getOrder()

std::size_t lsst::geom::polynomials::Basis1d::getOrder ( ) const

Return the order of the basis.

◆ scaled()

Scaled lsst::geom::polynomials::Basis1d::scaled ( Scaling1d const & scaling ) const

Return a scaled basis that delegates to a copy of this.

The scaled basis will transform all points by the given scaling before evaluating the basis functions in the same way as this.

◆ size()

std::size_t lsst::geom::polynomials::Basis1d::size ( ) const

Return the number of elements in the basis.

◆ sumWith()

template<typename Vector >

double lsst::geom::polynomials::Basis1d::sumWith	(	double	x,
		Vector const &	coefficients ) const

Evaluate a basis expansion with the given coefficients.

If the basis elements are \(B_n(x)\) and the given coefficients are a vector \(a_n\), this computes

\[ \sum_{n = 0}^{n \le N} a_n B_n(x) \]