lsst::geom::polynomials::ScaledBasis1d< Nested > Class Template Reference

A 1-d basis that transforms all input points before evaluating nested basis. More...

#include <ScaledBasis1d.h>

Public Types
using	Function = Function1d<ScaledBasis1d>
	A Function1d object that uses this basis.
using	Scaled = ScaledBasis1d<Nested>
	The type returned by scale().

Public Member Functions
	ScaledBasis1d (Nested const &nested, Scaling1d const &scaling)
	Construct a scaled basis from a nested basis and a scaling transform.
	ScaledBasis1d (std::size_t order, double min, double max)
	Construct a basis that remaps the given interval to [-1, 1] before evaluating the nested basis.
	ScaledBasis1d (ScaledBasis1d const &)=default
	Default copy constructor.
	ScaledBasis1d (ScaledBasis1d &&)=default
	Default move constructor.
ScaledBasis1d &	operator= (ScaledBasis1d const &)=default
	Default copy assignment.
ScaledBasis1d &	operator= (ScaledBasis1d &&)=default
	Default move assignment.
Nested const &	getNested () const noexcept
	Return the nested basis.
Scaling1d const &	getScaling () const noexcept
	Return the scaling transform.
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 &first) const
	Return a further-scaled basis with the same order.
template<typename Vector>
double	sumWith (double x, Vector const &coefficients, SumMode mode=SumMode::FAST) 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

template<typename Nested>
class lsst::geom::polynomials::ScaledBasis1d< Nested >

A 1-d basis that transforms all input points before evaluating nested basis.

If the nested basis is defined by basis functions \(B_n(x)\), the scaled basis functions are \(B_n(S(x))\), where \(S(x)\) is the scaling transform.

Both the nested basis and ScaledBasis1d itself are models of the Basis1d concept.

Definition at line 44 of file ScaledBasis1d.h.

Member Typedef Documentation

Function

template<typename Nested>

using lsst::geom::polynomials::ScaledBasis1d< Nested >::Function = Function1d<ScaledBasis1d>

A Function1d object that uses this basis.

Definition at line 48 of file ScaledBasis1d.h.

Scaled

template<typename Nested>

using lsst::geom::polynomials::ScaledBasis1d< Nested >::Scaled = ScaledBasis1d<Nested>

The type returned by scale().

Definition at line 51 of file ScaledBasis1d.h.

Constructor & Destructor Documentation

ScaledBasis1d() [1/4]

template<typename Nested>

lsst::geom::polynomials::ScaledBasis1d< Nested >::ScaledBasis1d ( Nested const & nested, Scaling1d const & scaling )

inlineexplicit

Construct a scaled basis from a nested basis and a scaling transform.

Definition at line 54 of file ScaledBasis1d.h.

                                                                             :
        _nested(nested),
        _scaling(scaling)
    {}

ScaledBasis1d() [2/4]

template<typename Nested>

lsst::geom::polynomials::ScaledBasis1d< Nested >::ScaledBasis1d ( std::size_t order, double min, double max )

inline

Construct a basis that remaps the given interval to [-1, 1] before evaluating the nested basis.

Parameters

[in]	order	Maximum order of the basis (inclusive).
[in]	min	Minimum point of the interval, mapped to -1.
[in]	max	Maximum point of the interval, mapped to 1.

This constructor is particularly useful for Chebyshev polynomials, for which most of the special functions of the basis are only active when the domain is limited to [-1, 1].

This signature requires that Nested(order) be a valid constructor.

Definition at line 73 of file ScaledBasis1d.h.

                                                           :
        _nested(order),
        _scaling(makeUnitRangeScaling1d(min, max))
    {}

ScaledBasis1d() [3/4]

template<typename Nested>

lsst::geom::polynomials::ScaledBasis1d< Nested >::ScaledBasis1d ( ScaledBasis1d< Nested > const & )

default

Default copy constructor.

ScaledBasis1d() [4/4]

template<typename Nested>

lsst::geom::polynomials::ScaledBasis1d< Nested >::ScaledBasis1d ( ScaledBasis1d< Nested > && )

default

Default move constructor.

Member Function Documentation

fill()

template<typename Nested>

template<typename Vector>

void lsst::geom::polynomials::ScaledBasis1d< Nested >::fill ( double x, Vector && basis ) const

inline

Evaluate the basis at a given point.

Parameters

[in]	x	Point at which to evaluate the basis functions.
[out]	basis	Output vector. See Basis1d::fill more information.

Exception Safety

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

Definition at line 146 of file ScaledBasis1d.h.

                                               {
        return getNested().fill(getScaling().applyForward(x), std::forward<Vector>(basis));
    }

getNested()

template<typename Nested>

Nested const & lsst::geom::polynomials::ScaledBasis1d< Nested >::getNested ( ) const

inlinenoexcept

Return the nested basis.

Definition at line 91 of file ScaledBasis1d.h.

{ return _nested; }

getOrder()

template<typename Nested>

std::size_t lsst::geom::polynomials::ScaledBasis1d< Nested >::getOrder ( ) const

inline

Return the order of the basis.

Definition at line 97 of file ScaledBasis1d.h.

{ return getNested().getOrder(); }

getScaling()

template<typename Nested>

Scaling1d const & lsst::geom::polynomials::ScaledBasis1d< Nested >::getScaling ( ) const

inlinenoexcept

Return the scaling transform.

Definition at line 94 of file ScaledBasis1d.h.

{ return _scaling; }

operator=() [1/2]

template<typename Nested>

ScaledBasis1d & lsst::geom::polynomials::ScaledBasis1d< Nested >::operator= ( ScaledBasis1d< Nested > && )

default

Default move assignment.

operator=() [2/2]

template<typename Nested>

ScaledBasis1d & lsst::geom::polynomials::ScaledBasis1d< Nested >::operator= ( ScaledBasis1d< Nested > const & )

default

Default copy assignment.

scaled()

template<typename Nested>

Scaled lsst::geom::polynomials::ScaledBasis1d< Nested >::scaled ( Scaling1d const & first ) const

inline

Return a further-scaled basis with the same order.

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

Definition at line 108 of file ScaledBasis1d.h.

                                                 {
        return getNested().scaled(first.then(getScaling()));
    }

size()

template<typename Nested>

std::size_t lsst::geom::polynomials::ScaledBasis1d< Nested >::size ( ) const

inline

Return the number of elements in the basis.

Definition at line 100 of file ScaledBasis1d.h.

{ return getNested().size(); }

sumWith()

template<typename Nested>

template<typename Vector>

double lsst::geom::polynomials::ScaledBasis1d< Nested >::sumWith ( double x, Vector const & coefficients, SumMode mode = SumMode::FAST ) const

inline

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. See Basis1d::sumWith for more information.
[in]	mode	Enum indicating the tradeoff to make between speed and numerical precision.

Exception Safety

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

Definition at line 131 of file ScaledBasis1d.h.

                                                                                          {
        return getNested().sumWith(getScaling().applyForward(x), coefficients, mode);
    }

---

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

• /j/snowflake/release/lsstsw/stack/lsst-scipipe-10.1.0/Linux/geom/g90f42f885a+6054cc57f1/include/lsst/geom/polynomials/ScaledBasis1d.h