Class ShapeletFunction

Class Documentation

class ShapeletFunction

A 2-d function defined by an expansion onto a Gauss-Laguerre or Gauss-Hermite basis.

The coefficients are in units of flux, not surface brightness; increasing the area of the basis ellipse while leaving the coefficients unchanged will decrease the surface brightness by the ratio of the areas of the new and old ellipses. This convention is necessary to ensure that convolution with a delta function is sane. Because the BasisEvaluator class does not deal with ellipses, it is necessary to divide its output by R^2 to get the same result as a ShapeletFunctionEvaluator whose ellipse has determinant radius of R.

The coefficient normalization is not identical to that of a Gaussian, however; a zeroth-order ShapeletFunction with its only coefficient value set to 1 has a flux of 2.0 * pi^(1/2). This value is defined as ShapeletFunction::FLUX_FACTOR. Of course, to get the flux of a more complex shapelet expansion you have to use ShapeletFunctionEvaluator::integrate().

Note that the units of the coefficients would have to be radius for basis functions with the same ellipse to be orthonormal, but this orthonormality isn’t very useful, because the basis functions aren’t even orthogonal in the more common case that the ellipses differ. However, basis functions defined on the unit circle are still orthonormal.

Public Types

typedef std::shared_ptr<ShapeletFunction> Ptr
typedef std::shared_ptr<ShapeletFunction const> ConstPtr
typedef ShapeletFunctionEvaluator Evaluator

Public Functions

int getOrder() const

Return the maximum order (inclusive), either \(n_x + n_y\) or \(p + q\).

afw::geom::ellipses::Ellipse const &getEllipse() const

Get the ellipse (const).

afw::geom::ellipses::Ellipse &getEllipse()

Get the ellipse (non-const).

void setEllipse(afw::geom::ellipses::Ellipse const &ellipse)

Set the ellipse.

BasisTypeEnum getBasisType() const

Return the basis type (HERMITE or LAGUERRE).

void changeBasisType(BasisTypeEnum basisType)

Change the basis type and convert coefficients in-place correspondingly.

void normalize(double value = 1.0)

Normalize the integral of the shapelet function to the given value.

ndarray::Array<double, 1, 1> const getCoefficients()

Return the coefficient vector.

ndarray::Array<double const, 1, 1> const getCoefficients() const

Return the coefficient vector (const).

ShapeletFunction convolve(ShapeletFunction const &other) const

Convolve the shapelet function.

ShapeletFunctionEvaluator evaluate() const

Construct a helper object that can efficiently evaluate the function.

void shiftInPlace(geom::Extent2D const &offset)

Shift the shapelet function by shifting the basis ellipse.

void transformInPlace(geom::AffineTransform const &transform)

Transform the shapelet function by transforming the basis ellipse.

ShapeletFunction(int order, BasisTypeEnum basisType)

Construct a function with a unit-circle ellipse and set all coefficients to zero.

ShapeletFunction(int order, BasisTypeEnum basisType, ndarray::Array<double, 1, 1> const &coefficients)

Construct a function with a unit-circle ellipse and a deep-copied coefficient vector.

ShapeletFunction(int order, BasisTypeEnum basisType, double radius, geom::Point2D const &center = geom::Point2D())

Construct a function with a circular ellipse and set all coefficients to zero.

ShapeletFunction(int order, BasisTypeEnum basisType, double radius, geom::Point2D const &center, ndarray::Array<double, 1, 1> const &coefficients)

Construct a function with a circular ellipse and a deep-copied coefficient vector.

ShapeletFunction(int order, BasisTypeEnum basisType, afw::geom::ellipses::Ellipse const &ellipse)

Construct a function and set all coefficients to zero.

ShapeletFunction(int order, BasisTypeEnum basisType, afw::geom::ellipses::Ellipse const &ellipse, ndarray::Array<double const, 1, 1> const &coefficients)

Construct a function with a deep-copied coefficient vector.

ShapeletFunction(ShapeletFunction const &other)

Copy constructor (deep).

ShapeletFunction &operator=(ShapeletFunction const &other)

Assignment (deep).

ShapeletFunction()

Default constructor to appease SWIG (used by std::list). Not for use by users.

Public Static Attributes

double const FLUX_FACTOR