lsst::shapelet::HermiteTransformMatrix Class Reference

A class that computes a matrix that applies a linear transform to a 2-d Hermite polynomial expansion. More...

#include <HermiteTransformMatrix.h>

Public Member Functions
Eigen::MatrixXd	compute (Eigen::Matrix2d const &transform) const
	Compute the matrix for a new linear transform. More...
Eigen::MatrixXd	compute (geom::LinearTransform const &transform) const
	Compute the matrix for a new linear transform. More...
Eigen::MatrixXd	compute (Eigen::Matrix2d const &transform, int order) const
	Compute the matrix for a new linear transform at the given order (must be <= getOrder()). More...
Eigen::MatrixXd	compute (geom::LinearTransform const &transform, int order) const
	Compute the matrix for a new linear transform at the given order (must be <= getOrder()). More...
Eigen::MatrixXd	getCoefficientMatrix () const
	Return the matrix that maps (1-d) regular polynomials to the alternate Hermite polynomials. More...
Eigen::MatrixXd	getInverseCoefficientMatrix () const
	Return the matrix that maps (1-d) alternate Hermite polynomials to regular polynomials. More...
int	getOrder () const
	Return the maximum order at which the matrix can be computed. More...
	HermiteTransformMatrix (int order)
	Construct an instance able to compute the transform matrix at up to the given order. More...

Detailed Description

A class that computes a matrix that applies a linear transform to a 2-d Hermite polynomial expansion.

Let

\[ Z_{\boldsymbol{n}}\!(\boldsymbol{x}) \equiv \mathcal{H}_{n_0}\!(x_0)\;\mathcal{H}_{n_1}\!(x_1) \]

where

\[ \mathcal{H}_n(x)=(2^n \pi^{1/2} n!)^{-1/2}H_n(x) \]

is the \(i\)th "alternate" Hermite polynomial. This function computes the matrix \(\boldsymbol{Q}(\boldsymbol{U})\) given a linear transform \(\boldsymbol{U}\) such that

\[ Z_{\boldsymbol{m}}\!(\boldsymbol{U}\boldsymbol{x}) = \sum_{\boldsymbol{n}} Q_{\boldsymbol{m},\boldsymbol{n}}\!(\boldsymbol{U})\,Z_{\boldsymbol{n}}\!(\boldsymbol{x}) \]

Definition at line 54 of file HermiteTransformMatrix.h.

Constructor & Destructor Documentation

HermiteTransformMatrix()

lsst::shapelet::HermiteTransformMatrix::HermiteTransformMatrix ( int  order )

explicit

Construct an instance able to compute the transform matrix at up to the given order.

Member Function Documentation

compute() [1/4]

Eigen::MatrixXd lsst::shapelet::HermiteTransformMatrix::compute ( Eigen::Matrix2d const &  transform ) const

inline

Compute the matrix for a new linear transform.

Definition at line 58 of file HermiteTransformMatrix.h.

                                                                 {
        return compute(transform, _order);
    }

compute() [2/4]

Eigen::MatrixXd lsst::shapelet::HermiteTransformMatrix::compute	(	Eigen::Matrix2d const &	transform,
		int	order
	)		const

Compute the matrix for a new linear transform at the given order (must be <= getOrder()).

compute() [3/4]

Eigen::MatrixXd lsst::shapelet::HermiteTransformMatrix::compute ( geom::LinearTransform const &  transform ) const

inline

Compute the matrix for a new linear transform.

Definition at line 63 of file HermiteTransformMatrix.h.

                                                                       {
        return compute(transform.getMatrix(), _order);
    }

compute() [4/4]

Eigen::MatrixXd lsst::shapelet::HermiteTransformMatrix::compute ( geom::LinearTransform const &  transform, int  order  ) const

inline

Compute the matrix for a new linear transform at the given order (must be <= getOrder()).

Definition at line 71 of file HermiteTransformMatrix.h.

                                                                                  {
        return compute(transform.getMatrix(), order);
    }

getCoefficientMatrix()

Eigen::MatrixXd lsst::shapelet::HermiteTransformMatrix::getCoefficientMatrix ( ) const

inline

Return the matrix that maps (1-d) regular polynomials to the alternate Hermite polynomials.

The matrix is always lower triangular, and has size equal to getOrder()+1.

Definition at line 80 of file HermiteTransformMatrix.h.

{ return _coeffFwd; }

getInverseCoefficientMatrix()

Eigen::MatrixXd lsst::shapelet::HermiteTransformMatrix::getInverseCoefficientMatrix ( ) const

inline

Return the matrix that maps (1-d) alternate Hermite polynomials to regular polynomials.

The matrix is always lower triangular, and has size equal to getOrder()+1.

Definition at line 87 of file HermiteTransformMatrix.h.

{ return _coeffInv; }

getOrder()

int lsst::shapelet::HermiteTransformMatrix::getOrder ( ) const

inline

Return the maximum order at which the matrix can be computed.

Definition at line 90 of file HermiteTransformMatrix.h.

{ return _order; }

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

• /j/snowflake/release/lsstsw/stack/lsst-scipipe-0.7.0/Linux64/shapelet/22.0.1-1-g8e32f31+297cba6710/include/lsst/shapelet/HermiteTransformMatrix.h