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LSST Data Management Base Package
Public Types | Public Member Functions | List of all members
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

A Function1d object that uses this basis.

Definition at line 40 of file Basis1d.h.

◆ 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]xPoint at which to evaluate the basis functions.
[out]basisOutput 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]xPoint at which to evaluate the expansion.
[in]coefficientsCoefficients 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: