lsst::jointcal::PhotometryTransformChebyshev Class Reference

nth-order 2d Chebyshev photometry transform. More...

#include <PhotometryTransform.h>

Inheritance diagram for lsst::jointcal::PhotometryTransformChebyshev:

Public Member Functions
	PhotometryTransformChebyshev (size_t order, geom::Box2D const &bbox, bool identity)
	Create a Chebyshev transform with terms up to order in (x*y).
	PhotometryTransformChebyshev (ndarray::Array< double, 2, 2 > const &coefficients, geom::Box2D const &bbox)
	Create a Chebyshev transform with the specified coefficients.
double	transformError (double x, double y, double value, double valueErr) const override
	Return the transformed valueErr at Point(x,y).
void	print (std::ostream &out) const override
	Print the transform coefficients to stream.
std::size_t	getNpar () const override
	Return the number of parameters (used to compute chisq)
void	offsetParams (Eigen::VectorXd const &delta) override
	Offset the parameters by some (negative) amount during fitting.
ndarray::Array< double, 2, 2 >	getCoefficients () const
	Get a copy of the coefficients of the polynomials, as a 2d array (NOTE: layout is [y][x])
Eigen::VectorXd	getParameters () const override
	Get a copy of the parameters of this model, in the same order as offsetParams.
ndarray::Size	getOrder () const
geom::Box2D	getBBox () const
double	mean (geom::Box2D const &bbox) const
	Compute the mean of this tranform on the bbox (default to our bbox).
double	mean () const
double	integrate (geom::Box2D const &bbox) const
double	integrate () const
virtual double	transform (double x, double y, double value) const =0
	Return the transform of value at (x,y).
double	transform (Point const &in, double value) const
	Return the transformed value at Point(x,y).
double	transformError (Point const &in, double value, double valueErr) const
	Return the transformed valueErr at Point(x,y).
virtual std::shared_ptr< PhotometryTransform >	clone () const =0
	return a copy (allocated by new) of the transformation.
virtual void	computeParameterDerivatives (double x, double y, double value, Eigen::Ref< Eigen::VectorXd > derivatives) const =0
	Compute the derivatives with respect to the parameters (i.e.

Protected Member Functions
double	computeChebyshev (double x, double y) const
	Return the value of this polynomial at x,y.
void	computeChebyshevDerivatives (double x, double y, Eigen::Ref< Eigen::VectorXd > derivatives) const
	Set the derivatives of this polynomial at x,y.

Detailed Description

nth-order 2d Chebyshev photometry transform.

The 2-d Chebyshev polynomial used here is defined as:

\[ f(x,y) = \sum_i \sum_j a_{i,j} T_i(x) T_j(y) \]

where \(T_n(x)\) is the n-th order Chebyshev polynomial of \(x\) and \(a_{i,j}\) is the corresponding coefficient of the (i,j) polynomial term.

Note that the polynomial order=n means that the highest terms will be of the form:

\[ a_{0,n}*x^n*y^0, a_{n-1,1}*x^(n-1)*y^1, ..., a_{1,n-1}*x^1*y^(n-1), a_{n,0}*x^0*y^n \]

Definition at line 222 of file PhotometryTransform.h.

Constructor & Destructor Documentation

PhotometryTransformChebyshev() [1/2]

lsst::jointcal::PhotometryTransformChebyshev::PhotometryTransformChebyshev	(	size_t	order,
		geom::Box2D const &	bbox,
		bool	identity )

Create a Chebyshev transform with terms up to order in (x*y).

Parameters

[in]	order	The maximum order in (x*y).
[in]	bbox	The bounding box it is valid within, to rescale it to [-1,1].
[in]	identity	If true, set a_0,0==1, otherwise all coefficients are 0.

Definition at line 91 of file PhotometryTransform.cc.

        : _bbox(bbox),
          _toChebyshevRange(makeChebyshevRangeTransform(bbox)),
          _coefficients(_initializeChebyshev(order, identity)),
          _order(order),
          _nParameters((order + 1) * (order + 2) / 2) {}

PhotometryTransformChebyshev() [2/2]

lsst::jointcal::PhotometryTransformChebyshev::PhotometryTransformChebyshev	(	ndarray::Array< double, 2, 2 > const &	coefficients,
		geom::Box2D const &	bbox )

Create a Chebyshev transform with the specified coefficients.

The polynomial order is determined from the number of coefficients, taking only the anti-diagonal upper triangle portion of the passed-in coefficients

Parameters

	coefficients	The polynomial coefficients.
[in]	bbox	The bounding box it is valid within, to rescale it to [-1,1].

Definition at line 99 of file PhotometryTransform.cc.

        : _bbox(bbox),
          _toChebyshevRange(makeChebyshevRangeTransform(bbox)),
          _coefficients(coefficients),
          _order(coefficients.size() - 1),
          _nParameters((_order + 1) * (_order + 2) / 2) {}

Member Function Documentation

clone()

virtual std::shared_ptr< PhotometryTransform > lsst::jointcal::PhotometryTransform::clone ( ) const

pure virtualinherited

return a copy (allocated by new) of the transformation.

Implemented in lsst::jointcal::FluxTransformSpatiallyInvariant, lsst::jointcal::MagnitudeTransformSpatiallyInvariant, lsst::jointcal::FluxTransformChebyshev, and lsst::jointcal::MagnitudeTransformChebyshev.

computeChebyshev()

double lsst::jointcal::PhotometryTransformChebyshev::computeChebyshev ( double x, double y ) const

protected

Return the value of this polynomial at x,y.

For use in the sublcass transform() methods.

Definition at line 224 of file PhotometryTransform.cc.

                                                                              {
    geom::Point2D p = _toChebyshevRange(geom::Point2D(x, y));
    return evaluateFunction1d(RecursionArrayImitator(_coefficients, p.getX()), p.getY(),
                              _coefficients.getSize<0>());
}

computeChebyshevDerivatives()

void lsst::jointcal::PhotometryTransformChebyshev::computeChebyshevDerivatives ( double x, double y, Eigen::Ref< Eigen::VectorXd > derivatives ) const

protected

Set the derivatives of this polynomial at x,y.

For use in the sublcass computeParameterDerivatives() methods.

Definition at line 230 of file PhotometryTransform.cc.

                                                                       {
    geom::Point2D p = _toChebyshevRange(geom::Point2D(x, y));
    // Algorithm: compute all the individual components recursively (since we'll need them anyway),
    // then combine them into the final answer vectors.
    Eigen::VectorXd Tnx(_order + 1);
    Eigen::VectorXd Tmy(_order + 1);
    Tnx[0] = 1;
    Tmy[0] = 1;
    if (_order >= 1) {
        Tnx[1] = p.getX();
        Tmy[1] = p.getY();
    }
    for (ndarray::Size i = 2; i <= _order; ++i) {
        Tnx[i] = 2 * p.getX() * Tnx[i - 1] - Tnx[i - 2];
        Tmy[i] = 2 * p.getY() * Tmy[i - 1] - Tmy[i - 2];
    }
 
    // NOTE: the indexing in this method and offsetParams must be kept consistent!
    Eigen::VectorXd::Index k = 0;
    for (ndarray::Size j = 0; j <= _order; ++j) {
        ndarray::Size const iMax = _order - j;  // to save re-computing `i+j <= order` every inner step.
        for (ndarray::Size i = 0; i <= iMax; ++i, ++k) {
            derivatives[k] = Tmy[j] * Tnx[i];
        }
    }
}

computeParameterDerivatives()

virtual void lsst::jointcal::PhotometryTransform::computeParameterDerivatives ( double x, double y, double value, Eigen::Ref< Eigen::VectorXd > derivatives ) const

pure virtualinherited

Compute the derivatives with respect to the parameters (i.e.

the coefficients).

Parameters

[in]	x	The x coordinate to compute at (in the appropriate units for this transform).
[in]	y	The y coordinate to compute at (in the appropriate units for this transform).
[in]	value	The instrument flux or magnitude to compute the derivative at.
[out]	derivatives	The computed derivatives, in the same order as the deltas in offsetParams.

Implemented in lsst::jointcal::FluxTransformSpatiallyInvariant, lsst::jointcal::MagnitudeTransformSpatiallyInvariant, lsst::jointcal::FluxTransformChebyshev, and lsst::jointcal::MagnitudeTransformChebyshev.

getBBox()

geom::Box2D lsst::jointcal::PhotometryTransformChebyshev::getBBox ( ) const

inline

Definition at line 264 of file PhotometryTransform.h.

{ return _bbox; }

getCoefficients()

ndarray::Array< double, 2, 2 > lsst::jointcal::PhotometryTransformChebyshev::getCoefficients ( ) const

inline

Get a copy of the coefficients of the polynomials, as a 2d array (NOTE: layout is [y][x])

Definition at line 257 of file PhotometryTransform.h.

{ return ndarray::copy(_coefficients); }

getNpar()

std::size_t lsst::jointcal::PhotometryTransformChebyshev::getNpar ( ) const

inlineoverridevirtual

Return the number of parameters (used to compute chisq)

Implements lsst::jointcal::PhotometryTransform.

Definition at line 251 of file PhotometryTransform.h.

{ return _nParameters; }

getOrder()

ndarray::Size lsst::jointcal::PhotometryTransformChebyshev::getOrder ( ) const

inline

Definition at line 262 of file PhotometryTransform.h.

{ return _order; }

getParameters()

Eigen::VectorXd lsst::jointcal::PhotometryTransformChebyshev::getParameters ( ) const

overridevirtual

Get a copy of the parameters of this model, in the same order as offsetParams.

Implements lsst::jointcal::PhotometryTransform.

Definition at line 210 of file PhotometryTransform.cc.

                                                                {
    Eigen::VectorXd parameters(_nParameters);
    // NOTE: the indexing in this method and offsetParams must be kept consistent!
    Eigen::VectorXd::Index k = 0;
    for (ndarray::Size j = 0; j <= _order; ++j) {
        ndarray::Size const iMax = _order - j;  // to save re-computing `i+j <= order` every inner step.
        for (ndarray::Size i = 0; i <= iMax; ++i, ++k) {
            parameters[k] = _coefficients[j][i];
        }
    }
 
    return parameters;
}

integrate() [1/2]

double lsst::jointcal::PhotometryTransformChebyshev::integrate

(

)

const

Definition at line 193 of file PhotometryTransform.cc.

                                                     {
    double result = 0;
    double determinant = _bbox.getArea() / 4.0;
    for (ndarray::Size j = 0; j < _coefficients.getSize<0>(); j++) {
        for (ndarray::Size i = 0; i < _coefficients.getSize<1>(); i++) {
            result += _coefficients[j][i] * integrateTn(i) * integrateTn(j);
        }
    }
    return result * determinant;
}

integrate() [2/2]

double lsst::jointcal::PhotometryTransformChebyshev::integrate

(

geom::Box2D const &

bbox

)

const

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 181 of file PhotometryTransform.cc.

                                                                          {
    double result = 0;
 
    result += oneIntegral(bbox.getMaxX(), bbox.getMaxY());
    result += oneIntegral(bbox.getMinX(), bbox.getMinY());
    result -= oneIntegral(bbox.getMaxX(), bbox.getMinY());
    result -= oneIntegral(bbox.getMinX(), bbox.getMaxY());
 
    // scale factor due to the change of limits in the integral
    return result / _toChebyshevRange.getLinear().computeDeterminant();
}

mean() [1/2]

double lsst::jointcal::PhotometryTransformChebyshev::mean

(

)

const

Definition at line 208 of file PhotometryTransform.cc.

{ return integrate() / _bbox.getArea(); }

mean() [2/2]

double lsst::jointcal::PhotometryTransformChebyshev::mean

(

geom::Box2D const &

bbox

)

const

Compute the mean of this tranform on the bbox (default to our bbox).

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 204 of file PhotometryTransform.cc.

                                                                     {
    return integrate(bbox) / bbox.getArea();
}

offsetParams()

void lsst::jointcal::PhotometryTransformChebyshev::offsetParams ( Eigen::VectorXd const & delta )

overridevirtual

Offset the parameters by some (negative) amount during fitting.

Equivalent to flatten(parameters) -= delta

Ordering of delta is the same as the ordering of the derivatives returned from computeParameterDerivatives.

Implements lsst::jointcal::PhotometryTransform.

Definition at line 107 of file PhotometryTransform.cc.

                                                                          {
    // NOTE: the indexing in this method and computeParameterDerivatives must be kept consistent!
    Eigen::VectorXd::Index k = 0;
    for (ndarray::Size j = 0; j <= _order; ++j) {
        ndarray::Size const iMax = _order - j;  // to save re-computing `i+j <= order` every inner step.
        for (ndarray::Size i = 0; i <= iMax; ++i, ++k) {
            _coefficients[j][i] -= delta[k];
        }
    }
}

print()

void lsst::jointcal::PhotometryTransformChebyshev::print ( std::ostream & out ) const

inlineoverridevirtual

Print the transform coefficients to stream.

Implements lsst::jointcal::PhotometryTransform.

Definition at line 248 of file PhotometryTransform.h.

{ out << "PhotometryTransformChebyshev: " << _coefficients; }

transform() [1/2]

virtual double lsst::jointcal::PhotometryTransform::transform ( double x, double y, double value ) const

pure virtualinherited

Return the transform of value at (x,y).

Implemented in lsst::jointcal::MagnitudeTransformSpatiallyInvariant, lsst::jointcal::FluxTransformSpatiallyInvariant, lsst::jointcal::FluxTransformChebyshev, and lsst::jointcal::MagnitudeTransformChebyshev.

transform() [2/2]

double lsst::jointcal::PhotometryTransform::transform ( Point const & in, double value ) const

inlineinherited

Return the transformed value at Point(x,y).

Definition at line 58 of file PhotometryTransform.h.

{ return transform(in.x, in.y, value); }

transformError() [1/2]

double lsst::jointcal::PhotometryTransformChebyshev::transformError ( double x, double y, double value, double valueErr ) const

inlineoverridevirtual

Return the transformed valueErr at Point(x,y).

Implements lsst::jointcal::PhotometryTransform.

Definition at line 245 of file PhotometryTransform.h.

{ return 0; }

transformError() [2/2]

double lsst::jointcal::PhotometryTransform::transformError ( Point const & in, double value, double valueErr ) const

inlineinherited

Return the transformed valueErr at Point(x,y).

Definition at line 64 of file PhotometryTransform.h.

                                                                                {
        return transformError(in.x, in.y, value, valueErr);
    }

---

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

• /j/snowflake/release/lsstsw/stack/lsst-scipipe-9.0.0/Linux64/jointcal/g82479be7b0+ed77629bff/include/lsst/jointcal/PhotometryTransform.h
• /j/snowflake/release/lsstsw/stack/lsst-scipipe-9.0.0/Linux64/jointcal/g82479be7b0+ed77629bff/src/PhotometryTransform.cc