lsst::meas::algorithms::Shapelet Class Reference

#include <Shapelet.h>

Public Types
typedef float	PixelT
	This class includes the basic functionality for shapelets. More...
typedef boost::shared_ptr < Shapelet >	Ptr
typedef boost::shared_ptr < const Shapelet >	ConstPtr
typedef Eigen::VectorXd	ShapeletVector
typedef Eigen::MatrixXd	ShapeletCovariance
typedef lsst::afw::table::SourceRecord	Source
typedef lsst::afw::image::Exposure < PixelT >	Exposure
typedef lsst::afw::geom::PointD	PointD
typedef lsst::afw::image::MaskPixel	MaskPixel

Public Member Functions
	Shapelet (int order, double sigma)
	Basic constructor requires order and sigma. More...
	Shapelet (int order, double sigma, const ShapeletVector &vector)
	A constructor from a vector of values. More...
	Shapelet (int order, double sigma, const ShapeletVector &vector, const ShapeletCovariance &cov)
	A constructor from a vector of values, with covariance. More...
	~Shapelet ()
	Destructor needs to delete pImpl. More...
	Shapelet (const Shapelet &rhs)
	Copy constructor does a deep copy. More...
Shapelet &	operator= (const Shapelet &rhs)
	op= does a deep copy More...
int	getOrder () const
	get the order of the shapelet More...
double	getSigma () const
	get the scale size of the shapelet More...
int	size () const
	the size of the shapelet vector More...
const ShapeletVector &	getValues () const
	get the values as a vector. More...
bool	hasCovariance () const
	does the shapelet have a covariance matrix stored? More...
boost::shared_ptr< const ShapeletCovariance >	getCovariance () const
	get the covariance matrix More...
void	setSigma (double sigma)
	set a new value of sigma More...
std::complex< double >	getPQ (int p, int q)
	Get a complex b_pq value. More...
double	evaluateAt (const PointD &pos)
	Evaluate f(x,y) More...
double	evaluateAt (double x, double y)
bool	measureFromImage (const Source &source, const PointD &pos, bool isCentroidFixed, bool isSigmaFixed, double aperture, const Exposure &exposure, const MaskPixel okmask=0)
	measure shapelet decomposition of an image More...
	Shapelet (const shapelet::BVec &bvec)
	A constructor that is only used by various Shapelet implementations. More...
const shapelet::BVec &	viewAsBVec () const
	View the shapelet as a BVec. More...
shapelet::BVec &	viewAsBVec ()

Private Attributes
ShapeletImpl *	pImpl

Detailed Description

Definition at line 50 of file Shapelet.h.

Member Typedef Documentation

typedef boost::shared_ptr<const Shapelet> lsst::meas::algorithms::Shapelet::ConstPtr

Definition at line 95 of file Shapelet.h.

typedef lsst::afw::image::Exposure<PixelT> lsst::meas::algorithms::Shapelet::Exposure

Definition at line 101 of file Shapelet.h.

typedef lsst::afw::image::MaskPixel lsst::meas::algorithms::Shapelet::MaskPixel

Definition at line 103 of file Shapelet.h.

typedef float lsst::meas::algorithms::Shapelet::PixelT

This class includes the basic functionality for shapelets.

There are a few definitions of shapelets out there. This class implements the shapelets defined in Bernstein & Jarvis (2002) (where they are called the Gauss-Laguerre basis functions). These are similar to the "polar shapelets" of Massey & Refregier.

Shapelets are a complete basis set that can be used to describe any image. However, they are most useful for describing things that are intrinsically similar to a 2-d Gaussian. Since the PSF (for ground-based telescopes) is dominated by a Gaussian component, this makes them a good choice for describing the PSF.

For specificity, the basis functions we use are:

For p >= q: psi_pq(x,y,sigma) = (pi p! q!)^-1/2 z^m exp(-r^2/2) K_pq(r^2) where z = (x + Iy)/sigma m = p-q r = |z|^2 K_pq(r^2) = (-)^q q! L_q^(m) (r^2) L_q^(m)(x) are Laguerre polynomials

For any particular value of sigma, these define a complete set of basis functions.

The image is thus decomposed as:

f(x,y) = Sum_pq b_pq psi_pq(x,y)

As with any basis set, the decomposition is only exact if an infinite number of basis functions are used. We truncate the expansion at p+q <= order for some (specified) order.

Definition at line 93 of file Shapelet.h.

typedef lsst::afw::geom::PointD lsst::meas::algorithms::Shapelet::PointD

Definition at line 102 of file Shapelet.h.

typedef boost::shared_ptr<Shapelet> lsst::meas::algorithms::Shapelet::Ptr

Definition at line 94 of file Shapelet.h.

typedef Eigen::MatrixXd lsst::meas::algorithms::Shapelet::ShapeletCovariance

Definition at line 98 of file Shapelet.h.

typedef Eigen::VectorXd lsst::meas::algorithms::Shapelet::ShapeletVector

Definition at line 97 of file Shapelet.h.

typedef lsst::afw::table::SourceRecord lsst::meas::algorithms::Shapelet::Source

Definition at line 100 of file Shapelet.h.

Constructor & Destructor Documentation

lsst::meas::algorithms::Shapelet::Shapelet	(	int	order,
		double	sigma
	)

Basic constructor requires order and sigma.

order defines how many shapelet coefficients to measure. e.g. order = 4 includes: b00, b10, b20, b11, b30, b21, b40, b31, b22 (bii are real, the others are complex.)

sigma is the scale size of Gaussian factor in the shapelet decomposition, measured in arcsec.

Parameters

order	the maximum value of p+q to measure.
sigma	the scale size of the shapelet decomposition (arcsec).

Definition at line 145 of file Shapelet.cc.

                                              :
        pImpl(new ShapeletImpl(order,sigma)) 
    {}

lsst::meas::algorithms::Shapelet::Shapelet	(	int	order,
		double	sigma,
		const ShapeletVector &	vector
	)

A constructor from a vector of values.

The input vector should have (order+1)*(order+2)/2 elements.

Caveat: The input vector is real, not complex. See the comment for getValues for the expected order of values.

Parameters

order	the maximum value of p+q to measure.
sigma	the scale size of the shapelet decomposition (arcsec).
vector	the shapelet vector

Definition at line 149 of file Shapelet.cc.

                                                                            :
        pImpl(new ShapeletImpl(order,sigma,vector)) 
    {}

lsst::meas::algorithms::Shapelet::Shapelet	(	int	order,
		double	sigma,
		const ShapeletVector &	vector,
		const ShapeletCovariance &	cov
	)

A constructor from a vector of values, with covariance.

The input vector should have (order+1)*(order+2)/2 elements. The covariance matrix is of the input vector of values. So it should be square, symmetric, and have the same size in each dimension as the input vector.

Caveat: The input vector is real, not complex. See the comment for getValues for the expected order of values.

Parameters

order	the maximum value of p+q to measure.
sigma	the scale size of the shapelet decomposition (arcsec).
vector	the shapelet vector
cov	the covariance matrix

Definition at line 153 of file Shapelet.cc.

                                                                                                           :
        pImpl(new ShapeletImpl(order,sigma,vector,cov)) 
    {}

lsst::meas::algorithms::Shapelet::~Shapelet

(

)

Destructor needs to delete pImpl.

Definition at line 161 of file Shapelet.cc.

    { delete pImpl; pImpl = 0; }

lsst::meas::algorithms::Shapelet::Shapelet

(

const Shapelet &

rhs

)

Copy constructor does a deep copy.

Definition at line 157 of file Shapelet.cc.

                                          :
        pImpl(new ShapeletImpl(*rhs.pImpl))
    {}

lsst::meas::algorithms::Shapelet::Shapelet

(

const shapelet::BVec &

bvec

)

A constructor that is only used by various Shapelet implementations.

This is used by ShapeletInterpolation for example. It is more convenient to leave this public, but you can't actually use it, since BVec isn't defined publicly.

Definition at line 408 of file Shapelet.cc.

: pImpl(new ShapeletImpl(bvec)) {}

Member Function Documentation

double lsst::meas::algorithms::Shapelet::evaluateAt

(

const PointD &

pos

)

Evaluate f(x,y)

Evaluate the intensity as a function of chip position (x,y)

This is the approximation to the true f(x,y) defined by the decomposition Sum_pq b_pq psi_pq(x,y,sigma).

Definition at line 194 of file Shapelet.cc.

    { return evaluateAt(pos.getX(),pos.getY()); }

double lsst::meas::algorithms::Shapelet::evaluateAt	(	double	x,
		double	y
	)

Definition at line 197 of file Shapelet.cc.

    {
        // TODO: MJ - I couldn't reproduce the crash with g++ 4.3.3.
        //       Need to try this on lsst computers I guess.
#if 0                                   // crashes g++ 4.3.5
        return pImpl->evaluateAt(x,y);
#else
        // MJ - This is definitely wrong!  It starts an infinite loop!
        return evaluateAt(lsst::afw::geom::PointD(x, y));
#endif
    }

boost::shared_ptr< const Shapelet::ShapeletCovariance > lsst::meas::algorithms::Shapelet::getCovariance

(

)

const

get the covariance matrix

Definition at line 185 of file Shapelet.cc.

    { return pImpl->getCovariance(); }

int lsst::meas::algorithms::Shapelet::getOrder

(

)

const

get the order of the shapelet

Definition at line 170 of file Shapelet.cc.

    { return pImpl->getOrder(); }

std::complex< double > lsst::meas::algorithms::Shapelet::getPQ	(	int	p,
		int	q
	)

Get a complex b_pq value.

Get the coefficient b_pq for the shapelet decomposition.

Definition at line 191 of file Shapelet.cc.

    { return pImpl->getPQ(p,q); }

double lsst::meas::algorithms::Shapelet::getSigma

(

)

const

get the scale size of the shapelet

Definition at line 173 of file Shapelet.cc.

    { return pImpl->getSigma(); }

const Shapelet::ShapeletVector & lsst::meas::algorithms::Shapelet::getValues

(

)

const

get the values as a vector.

The order of values are: b00 real(b10) imag(b10) real(b20) imag(b20) b11 real(b30) imag(b30) real(b21) imag(b21) real(b40) imag(b40) real(b31) imag(b31) b22 etc.

where bpq corresponds to the coefficients $b_{pq}$ as defined in Bernstein and Jarvis (2002).

Definition at line 179 of file Shapelet.cc.

    { return pImpl->getValues(); }

bool lsst::meas::algorithms::Shapelet::hasCovariance

(

)

const

does the shapelet have a covariance matrix stored?

Definition at line 182 of file Shapelet.cc.

    { return pImpl->getCovariance().get(); }

bool lsst::meas::algorithms::Shapelet::measureFromImage	(	const Source &	source,
		const PointD &	pos,
		bool	isCentroidFixed,
		bool	isSigmaFixed,
		double	aperture,
		const Exposure &	exposure,
		const MaskPixel	okmask = 0
	)

measure shapelet decomposition of an image

The initial estimate of the centroid is taken from the source. The initial estimate of sigma is the value given by this->getSigma().

The normal operation would be to allow both values to shift to find the best values for the image. However, there are reasons to keep each fixed.

First, if we have very accurate positions given in the source object, and we want the PSF to include the centroid shift that is present in the seeing, then this would be a good reason to keep it fixed.

Second, interpolation of the PSF is more straightforward if all the stars are measured with the saem sigma. So the normal practice is to let sigma float for each star, then find the mean of all the stars in an image, and finally remeasure each star with this constant value of sigma.

So, there are two boolean parameters that govern what should be kept fixed during the calculation.

isCentroidFixed says whether to keep the centoid fixed. If it is false, then the centoid is allowed to vary until b10 = 0 (our definition of being centroided).

isSigmaFixed says whether to keep the sigma fixed. If it is false, then sigma is allowed to vary until b11 = 0 (which corresponds to when the measured shapelet components have the maximum signal-to-noise).

The measurement is done using a circular aperture, whose radius is given by the paremeter aperture. This aperture (given in arcsec) defines a circle in sky coordinates, not chip coordinates.

The return value is true if the measurement is successful, and falso if not.

Parameters

source	The source of which to measure the decomposition.
pos	The position of the object
isCentroidFixed	Is sigma fixed? or should it be allowed to vary?
isSigmaFixed	Is sigma fixed? or should it be allowed to vary?
aperture	The aperture size in arcsec for the measurement.
exposure	The exposure on which to measure the decompoisition.
okmask	The mask values that are ok to use

Definition at line 358 of file Shapelet.cc.

    {
        using shapelet::Ellipse;
        using shapelet::PixelList;

        std::vector<PixelList> pix(1);
        // Fill PixelList with pixel data around position pos:
        getPixList(pix[0], source, pos, aperture, exposure, okmask);

        double sigma = pImpl->getSigma();
        Ellipse ell;
        ell.fixGam();
        if (isCentroidFixed) ell.fixCen();
        else {
            // Initial crude estimates to get close to the right value
            // in case we have a poor starting point.
            // TODO: These might not be necessary for LSST.  
            // Should compare speed with and without this step.
            ell.peakCentroid(pix[0],aperture/3.);
            ell.crudeMeasure(pix[0],sigma);
        }
        if (isSigmaFixed) ell.fixMu();
        long flag = 0;
        int order = getOrder();
        if (!isCentroidFixed || !isSigmaFixed) {
            if (!ell.measure(pix,order,order+4,order,sigma,flag,1.e-4)) {
                return false;
            }
            if (flag) return false;
            if (!isSigmaFixed) {
                double mu = ell.getMu();
                sigma *= exp(mu);
                dbg<<"sigma = "<<sigma<<std::endl;
                Assert(sigma > 0);
                pImpl->setSigma(sigma);
            }
        }

        ShapeletCovariance* cov = pImpl->getCovariance().get();
        if (ell.measureShapelet(pix,*pImpl,order,order+4,order,cov)) {
            return true;
        } else {
            return false;
        }
    }

Shapelet & lsst::meas::algorithms::Shapelet::operator=

(

const Shapelet &

rhs

)

op= does a deep copy

Definition at line 164 of file Shapelet.cc.

    {
        *pImpl = *rhs.pImpl;
        return *this;
    }

void lsst::meas::algorithms::Shapelet::setSigma

(

double

sigma

)

set a new value of sigma

Definition at line 188 of file Shapelet.cc.

    { return pImpl->setSigma(sigma); }

int lsst::meas::algorithms::Shapelet::size

(

)

const

the size of the shapelet vector

Definition at line 176 of file Shapelet.cc.

    { return pImpl->size(); }

const shapelet::BVec & lsst::meas::algorithms::Shapelet::viewAsBVec

(

)

const

View the shapelet as a BVec.

This is also only used by various Shapelet implementations, but it is convenient to leave it public rather than define a bunch of friend classes.

Definition at line 410 of file Shapelet.cc.

{ return *pImpl; }

shapelet::BVec & lsst::meas::algorithms::Shapelet::viewAsBVec

(

)

Definition at line 411 of file Shapelet.cc.

{ return *pImpl; }

Member Data Documentation

ShapeletImpl* lsst::meas::algorithms::Shapelet::pImpl

private

Definition at line 306 of file Shapelet.h.

---

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

• /home/lsstsw/stack/Linux64/meas_algorithms/11.0-2-gb8b8ce7/include/lsst/meas/algorithms/Shapelet.h
• /home/lsstsw/stack/Linux64/meas_algorithms/11.0-2-gb8b8ce7/src/Shapelet.cc