lsst::geom::polynomials::Basis1d Class Reference

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

#include <Basis1d.h>

Public Types
using	Function = ...
	A Function1d object that uses this basis. More...
using	Scaled = ...
	The type returned by scale(). More...

Public Member Functions
std::size_t	getOrder () const
	Return the order of the basis. More...
std::size_t	size () const
	Return the number of elements in the basis. More...
Scaled	scaled (Scaling1d const &scaling) const
	Return a scaled basis that delegates to a copy of this. More...
template<typename Vector >
double	sumWith (double x, Vector const &coefficients) const
	Evaluate a basis expansion with the given coefficients. More...
template<typename Vector >
void	fill (double x, Vector &&basis) const
	Evaluate the basis at a given point. More...

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

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

Parameters

[in]	x	Point at which to evaluate the expansion.
[in]	coefficients	Coefficients vector. May be any type for which coefficients[n] returns an object convertible to double for all n <= getOrder(). This includes std::vector<double>, ndarray::Array<double,1>, Eigen::VectorXd, and random access iterators. If a lazy expression template object is passed, the elements of the expression will be evaluated only once.

Exception Safety

Does not throw unless coefficients[n] does, and provides the same exception safety as it if it does.

---

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

• /j/snowflake/release/lsstsw/stack/Linux64/geom/19.0.0-1-ge3aa853/include/lsst/geom/polynomials/Basis1d.h