lsst::geom::polynomials::ScaledBasis2d< Nested > Class Template Reference

A 2-d basis that transforms all input points before evaluating nested basis. More...

#include <ScaledBasis2d.h>

Public Types
using	Function = Function2d< ScaledBasis2d >
	A Function2d object that uses this basis. More...
using	Scaled = ScaledBasis2d< Nested >
	The type returned by scale(). More...
using	Workspace = typename Nested::Workspace
	The type returned by makeWorkspace(). More...
using	IndexRange = typename Nested::IndexRange
	The type returned by getIndices(). More...

Public Member Functions
	ScaledBasis2d (Nested const &nested, Scaling2d const &scaling)
	Construct a scaled basis from a nested basis and a scaling transform. More...
	ScaledBasis2d (std::size_t order, Box2D const &box)
	Construct a basis that remaps the given box to [-1, 1]x[-1, 1] before evaluating the nested polynomials polynomials. More...
	ScaledBasis2d (ScaledBasis2d const &)=default
	Default copy constructor. More...
	ScaledBasis2d (ScaledBasis2d &&)=default
	Default move constructor. More...
ScaledBasis2d &	operator= (ScaledBasis2d const &)=default
	Default copy assignment. More...
ScaledBasis2d &	operator= (ScaledBasis2d &&)=default
	Default move assignment. More...
Nested const &	getNested () const noexcept
	Return the nested basis. More...
Scaling2d const &	getScaling () const noexcept
	Return the scaling transform. More...
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 (Scaling2d const &first) const
	Return a scaled basis that delegates to a copy of this. More...
int	index (int x, int y) const
	Return the flattened index of the basis function with the given x and y orders. More...
IndexRange	getIndices () const
	Return a range of iterators that dereference to Index2d. More...
Workspace	makeWorkspace () const
	Allocate a workspace that can be passed to sumWith() and fill() to avoid repeated memory allocations. More...
template<typename Vector >
double	sumWith (geom::Point2D const &point, Vector const &coefficients, SumMode mode=SumMode::FAST) const
	Evaluate a basis expansion with the given coefficients. More...
template<typename Vector >
double	sumWith (geom::Point2D const &point, Vector const &coefficients, Workspace &workspace, SumMode mode=SumMode::FAST) const
	Evaluate a basis expansion with the given coefficients (external workspace version). More...
template<typename Vector >
void	fill (geom::Point2D const &point, Vector &&basis) const
	Evaluate the basis at a given point. More...
template<typename Vector >
void	fill (geom::Point2D const &point, Vector &&basis, Workspace &workspace) const
	Evaluate the basis at a given point (external workspace version). More...

Detailed Description

template<typename Nested>
class lsst::geom::polynomials::ScaledBasis2d< Nested >

A 2-d basis that transforms all input points before evaluating nested basis.

If the nested basis is defined by basis functions \(B_m(x)B_n(y)\), the scaled basis functions are \(B_m(U(x))B_n(V(y))\), where \(U(x)\) and \(V(y)\) together represent the scaling transform.

Both the nested basis and ScaledBasis2d itself are models of the Basis2d concept.

Definition at line 43 of file ScaledBasis2d.h.

Member Typedef Documentation

Function

template<typename Nested >

using lsst::geom::polynomials::ScaledBasis2d< Nested >::Function = Function2d<ScaledBasis2d>

A Function2d object that uses this basis.

Definition at line 47 of file ScaledBasis2d.h.

IndexRange

template<typename Nested >

using lsst::geom::polynomials::ScaledBasis2d< Nested >::IndexRange = typename Nested::IndexRange

The type returned by getIndices().

Definition at line 56 of file ScaledBasis2d.h.

Scaled

template<typename Nested >

using lsst::geom::polynomials::ScaledBasis2d< Nested >::Scaled = ScaledBasis2d<Nested>

The type returned by scale().

Definition at line 50 of file ScaledBasis2d.h.

Workspace

template<typename Nested >

using lsst::geom::polynomials::ScaledBasis2d< Nested >::Workspace = typename Nested::Workspace

The type returned by makeWorkspace().

Definition at line 53 of file ScaledBasis2d.h.

Constructor & Destructor Documentation

ScaledBasis2d() [1/4]

template<typename Nested >

lsst::geom::polynomials::ScaledBasis2d< Nested >::ScaledBasis2d ( Nested const &  nested, Scaling2d const &  scaling  )

inlineexplicit

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

Definition at line 59 of file ScaledBasis2d.h.

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

ScaledBasis2d() [2/4]

template<typename Nested >

lsst::geom::polynomials::ScaledBasis2d< Nested >::ScaledBasis2d ( std::size_t  order, Box2D const &  box  )

inline

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

Parameters

[in]	order	Maximum order of the basis (inclusive).
[in]	box	Box to be mapped to [-1, 1]x[-1, 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 77 of file ScaledBasis2d.h.

                                                      :
        _nested(order),
        _scaling(makeUnitRangeScaling2d(box))
    {}

ScaledBasis2d() [3/4]

template<typename Nested >

lsst::geom::polynomials::ScaledBasis2d< Nested >::ScaledBasis2d ( ScaledBasis2d< Nested > const &  )

default

Default copy constructor.

ScaledBasis2d() [4/4]

template<typename Nested >

lsst::geom::polynomials::ScaledBasis2d< Nested >::ScaledBasis2d ( ScaledBasis2d< Nested > &&  )

default

Default move constructor.

Member Function Documentation

fill() [1/2]

template<typename Nested >

template<typename Vector >

void lsst::geom::polynomials::ScaledBasis2d< Nested >::fill ( geom::Point2D const &  point, Vector &&  basis  ) const

inline

Evaluate the basis at a given point.

Parameters

[in]	point	Point at which to evaluate the basis functions.
[out]	basis	Flattened 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 186 of file ScaledBasis2d.h.

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

fill() [2/2]

template<typename Nested >

template<typename Vector >

void lsst::geom::polynomials::ScaledBasis2d< Nested >::fill ( geom::Point2D const &  point, Vector &&  basis, Workspace &  workspace  ) const

inline

Evaluate the basis at a given point (external workspace version).

Definition at line 193 of file ScaledBasis2d.h.

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

getIndices()

template<typename Nested >

IndexRange lsst::geom::polynomials::ScaledBasis2d< Nested >::getIndices ( ) const

inline

Return a range of iterators that dereference to Index2d.

This is the recommended way to interpret the packed coefficients and basis functions utilized by PackedBasis2d; for example,

// Evaluate basis functions at a point.
geom::Point2D point(x, y);
PolynomialBasis2d basis(order);
std::vector<double> values(basis.size());
basis.fill(point, values);
// Iterate over tuples of flattened indices and x and y orders.
for (auto const & index : basis.getIndices()) {
    double a = values[index.flat];
    // standard polynomial basis functions are just powers
    double b = std::pow(point.getX(), index.nx)*std::pow(point.getY(), index.ny)];
    assert(std::abs(a - b) < std::numeric_limits<double>::epsilon());
}

Definition at line 139 of file ScaledBasis2d.h.

{ return getNested().getIndices(); }

getNested()

template<typename Nested >

Nested const& lsst::geom::polynomials::ScaledBasis2d< Nested >::getNested ( ) const

inlinenoexcept

Return the nested basis.

Definition at line 95 of file ScaledBasis2d.h.

{ return _nested; }

getOrder()

template<typename Nested >

std::size_t lsst::geom::polynomials::ScaledBasis2d< Nested >::getOrder ( ) const

inline

Return the order of the basis.

Definition at line 101 of file ScaledBasis2d.h.

{ return getNested().getOrder(); }

getScaling()

template<typename Nested >

Scaling2d const& lsst::geom::polynomials::ScaledBasis2d< Nested >::getScaling ( ) const

inlinenoexcept

Return the scaling transform.

Definition at line 98 of file ScaledBasis2d.h.

{ return _scaling; }

index()

template<typename Nested >

int lsst::geom::polynomials::ScaledBasis2d< Nested >::index ( int  x, int  y  ) const

inline

Return the flattened index of the basis function with the given x and y orders.

Definition at line 117 of file ScaledBasis2d.h.

{ return getNested().index(x, y); }

makeWorkspace()

template<typename Nested >

Workspace lsst::geom::polynomials::ScaledBasis2d< Nested >::makeWorkspace ( ) const

inline

Allocate a workspace that can be passed to sumWith() and fill() to avoid repeated memory allocations.

Definition at line 142 of file ScaledBasis2d.h.

{ return getNested().makeWorkspace();}

operator=() [1/2]

template<typename Nested >

ScaledBasis2d& lsst::geom::polynomials::ScaledBasis2d< Nested >::operator= ( ScaledBasis2d< Nested > &&  )

default

Default move assignment.

operator=() [2/2]

template<typename Nested >

ScaledBasis2d& lsst::geom::polynomials::ScaledBasis2d< Nested >::operator= ( ScaledBasis2d< Nested > const &  )

default

Default copy assignment.

scaled()

template<typename Nested >

Scaled lsst::geom::polynomials::ScaledBasis2d< Nested >::scaled ( Scaling2d const &  first ) const

inline

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.

Definition at line 112 of file ScaledBasis2d.h.

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

size()

template<typename Nested >

std::size_t lsst::geom::polynomials::ScaledBasis2d< Nested >::size ( ) const

inline

Return the number of elements in the basis.

Definition at line 104 of file ScaledBasis2d.h.

{ return getNested().size(); }

sumWith() [1/2]

template<typename Nested >

template<typename Vector >

double lsst::geom::polynomials::ScaledBasis2d< Nested >::sumWith ( geom::Point2D const &  point, Vector const &  coefficients, SumMode  mode = SumMode::FAST  ) const

inline

Evaluate a basis expansion with the given coefficients.

If the 1-d basis elements are \(B_n(x)\) and the given coefficients are a vector \(a_{p, q}\), this computes

\[ \sum_{p = 0, q = 0}^{p + q \le N} a_{p,q} B_{p}(x) B_{q}(y) \]

Parameters

[in]	point	Point at which to evaluate the expansion.
[in]	coefficients	Flattened 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 163 of file ScaledBasis2d.h.

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

sumWith() [2/2]

template<typename Nested >

template<typename Vector >

double lsst::geom::polynomials::ScaledBasis2d< Nested >::sumWith ( geom::Point2D const &  point, Vector const &  coefficients, Workspace &  workspace, SumMode  mode = SumMode::FAST  ) const

inline

Evaluate a basis expansion with the given coefficients (external workspace version).

Definition at line 170 of file ScaledBasis2d.h.

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

---

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

• /j/snowflake/release/lsstsw/stack/lsst-scipipe-0.7.0/Linux64/geom/22.0.1-6-g8d3140d+720564cf76/include/lsst/geom/polynomials/ScaledBasis2d.h