lsst::afw::math::Chebyshev1Function2< ReturnT > Class Template Reference

2-dimensional weighted sum of Chebyshev polynomials of the first kind. More...

#include <FunctionLibrary.h>

Inheritance diagram for lsst::afw::math::Chebyshev1Function2< ReturnT >:

Public Types
typedef Function2< ReturnT >::Ptr	Function2Ptr
Public Types inherited from lsst::afw::math::BasePolynomialFunction2< ReturnT >
typedef Function2< ReturnT >::Ptr	Function2Ptr
Public Types inherited from lsst::afw::math::Function2< ReturnT >
typedef boost::shared_ptr < Function2< ReturnT > >	Ptr
Public Types inherited from lsst::daf::base::Citizen
enum	{ magicSentinel = 0xdeadbeef }
typedef unsigned long	memId
	Type of the block's ID. More...
typedef memId(*	memNewCallback )(const memId cid)
	A function used to register a callback. More...
typedef memId(*	memCallback )(const Citizen *ptr)

Public Member Functions
	Chebyshev1Function2 (unsigned int order, lsst::afw::geom::Box2D const &xyRange=lsst::afw::geom::Box2D(lsst::afw::geom::Point2D(-1.0,-1.0), lsst::afw::geom::Point2D(1.0, 1.0)))
	Construct a Chebyshev polynomial of specified order and range. More...
	Chebyshev1Function2 (std::vector< double > params, lsst::afw::geom::Box2D const &xyRange=lsst::afw::geom::Box2D(lsst::afw::geom::Point2D(-1.0,-1.0), lsst::afw::geom::Point2D(1.0, 1.0)))
	Construct a Chebyshev polynomial with specified parameters and range. More...
virtual	~Chebyshev1Function2 ()
virtual Function2Ptr	clone () const
	Return a pointer to a deep copy of this function. More...
lsst::afw::geom::Box2D	getXYRange () const
	Get x,y range. More...
virtual Chebyshev1Function2	truncate (int truncOrder) const
	Return a truncated copy of lower (or equal) order. More...
virtual ReturnT	operator() (double x, double y) const
virtual std::string	toString (std::string const &prefix) const
	Return a string representation of the function. More...
virtual bool	isPersistable () const
	Return true if this particular object can be persisted using afw::table::io. More...
Public Member Functions inherited from lsst::afw::math::BasePolynomialFunction2< ReturnT >
	BasePolynomialFunction2 (unsigned int order)
	Construct a polynomial function of specified order. More...
	BasePolynomialFunction2 (std::vector< double > params)
	Construct a polynomial function with specified parameters. More...
virtual	~BasePolynomialFunction2 ()
int	getOrder () const
	Get the polynomial order. More...
virtual bool	isLinearCombination () const
	Is the function a linear combination of its parameters? More...
virtual std::vector< double >	getDFuncDParameters (double x, double y) const
Public Member Functions inherited from lsst::afw::math::Function2< ReturnT >
	Function2 (unsigned int nParams)
	Construct a Function2 given the number of function parameters. More...
	Function2 (std::vector< double > const &params)
	Construct a Function2 given the function parameters. More...
virtual	~Function2 ()
Public Member Functions inherited from lsst::afw::math::Function< ReturnT >
	Function (unsigned int nParams)
	Construct a Function given the number of function parameters. More...
	Function (std::vector< double > const &params)
	Construct a Function given the function parameters. More...
virtual	~Function ()
unsigned int	getNParameters () const
	Return the number of function parameters. More...
virtual double	getParameter (unsigned int ind) const
	Get one function parameter without range checking. More...
std::vector< double > const &	getParameters () const
	Return all function parameters. More...
void	setParameter (unsigned int ind, double newValue)
	Set one function parameter without range checking. More...
void	setParameters (std::vector< double > const &params)
	Set all function parameters. More...
Public Member Functions inherited from lsst::daf::base::Citizen
	Citizen (const std::type_info &)
	Citizen (Citizen const &)
	~Citizen ()
Citizen &	operator= (Citizen const &)
std::string	repr () const
	Return a string representation of a Citizen. More...
void	markPersistent (void)
	Mark a Citizen as persistent and not destroyed until process end. More...
memId	getId () const
	Return the Citizen's ID. More...
Public Member Functions inherited from lsst::afw::table::io::Persistable
void	writeFits (std::string const &fileName, std::string const &mode="w") const
	Write the object to a regular FITS file. More...
void	writeFits (fits::MemFileManager &manager, std::string const &mode="w") const
	Write the object to a FITS image in memory. More...
void	writeFits (fits::Fits &fitsfile) const
	Write the object to an already-open FITS object. More...
virtual	~Persistable ()

Protected Member Functions
virtual std::string	getPersistenceName () const
	Return the unique name used to persist this object and look up its factory. More...
virtual void	write (afw::table::io::OutputArchiveHandle &handle) const
	Write the object to one or more catalogs. More...
	Chebyshev1Function2 ()
Protected Member Functions inherited from lsst::afw::math::BasePolynomialFunction2< ReturnT >
	BasePolynomialFunction2 ()
Protected Member Functions inherited from lsst::afw::math::Function2< ReturnT >
	Function2 ()
Protected Member Functions inherited from lsst::afw::math::Function< ReturnT >
virtual std::string	getPythonModule () const
	Return the fully-qualified Python module that should be imported to guarantee that its factory is registered. More...
	Function ()
Protected Member Functions inherited from lsst::afw::table::io::Persistable
	Persistable ()
	Persistable (Persistable const &other)
void	operator= (Persistable const &other)

Private Member Functions
void	_initialize (lsst::afw::geom::Box2D const &xyRange)
	initialize private constants More...
template<class Archive >
void	serialize (Archive &ar, unsigned int const version)

Private Attributes
double	_oldYPrime
std::vector< double >	_yCheby
	working vector: value of Tn(y') More...
std::vector< double >	_xCoeffs
	working vector: transformed coeffs of x polynomial More...
double	_minX
	minimum allowed x More...
double	_minY
	minimum allowed y More...
double	_maxX
	maximum allowed x More...
double	_maxY
	maximum allowed y More...
double	_scaleX
	x' = (x + _offsetX) * _scaleX More...
double	_scaleY
	y' = (y + _offsetY) * _scaleY More...
double	_offsetX
	x' = (x + _offsetX) * _scaleX More...
double	_offsetY
	y' = (y + _offsetY) * _scaleY More...

Friends
class	boost::serialization::access

Additional Inherited Members
Static Public Member Functions inherited from lsst::afw::math::BasePolynomialFunction2< ReturnT >
static int	nParametersFromOrder (int order)
	Compute number of parameters from polynomial order. More...
static int	orderFromNParameters (int nParameters)
	Compute polynomial order from the number of parameters. More...
Static Public Member Functions inherited from lsst::afw::table::io::PersistableFacade< Function2< ReturnT > >
static boost::shared_ptr < Function2< ReturnT > >	readFits (fits::Fits &fitsfile)
	Read an object from an already open FITS object. More...
static boost::shared_ptr < Function2< ReturnT > >	readFits (std::string const &fileName, int hdu=0)
	Read an object from a regular FITS file. More...
static boost::shared_ptr < Function2< ReturnT > >	readFits (fits::MemFileManager &manager, int hdu=0)
	Read an object from a FITS file in memory. More...
Static Public Member Functions inherited from lsst::daf::base::Citizen
static bool	hasBeenCorrupted ()
	Check all allocated blocks for corruption. More...
static memId	getNextMemId ()
	Return the memId of the next object to be allocated. More...
static int	init ()
	Called once when the memory system is being initialised. More...
static int	census (int, memId startingMemId=0)
	How many active Citizens are there? More...
static void	census (std::ostream &stream, memId startingMemId=0)
	Print a list of all active Citizens to stream, sorted by ID. More...
static const std::vector < const Citizen * > *	census ()
	Return a (newly allocated) std::vector of active Citizens sorted by ID. More...
static memId	setNewCallbackId (memId id)
	Call the NewCallback when block is allocated. More...
static memId	setDeleteCallbackId (memId id)
	Call the current DeleteCallback when block is deleted. More...
static memNewCallback	setNewCallback (memNewCallback func)
	Set the NewCallback function. More...
static memCallback	setDeleteCallback (memCallback func)
	Set the DeleteCallback function. More...
static memCallback	setCorruptionCallback (memCallback func)
	Set the CorruptionCallback function. More...
Static Public Member Functions inherited from lsst::afw::table::io::PersistableFacade< Function< ReturnT > >
static boost::shared_ptr < Function< ReturnT > >	readFits (fits::Fits &fitsfile)
	Read an object from an already open FITS object. More...
static boost::shared_ptr < Function< ReturnT > >	readFits (std::string const &fileName, int hdu=0)
	Read an object from a regular FITS file. More...
static boost::shared_ptr < Function< ReturnT > >	readFits (fits::MemFileManager &manager, int hdu=0)
	Read an object from a FITS file in memory. More...
Protected Types inherited from lsst::afw::table::io::Persistable
typedef io::OutputArchiveHandle	OutputArchiveHandle
Protected Attributes inherited from lsst::afw::math::BasePolynomialFunction2< ReturnT >
int	_order
	order of polynomial More...
Protected Attributes inherited from lsst::afw::math::Function< ReturnT >
std::vector< double >	_params
bool	_isCacheValid

Detailed Description

template<typename ReturnT>
class lsst::afw::math::Chebyshev1Function2< ReturnT >

2-dimensional weighted sum of Chebyshev polynomials of the first kind.

f(x,y) = c0 T0(x') T0(y') # order 0

• c1 T1(x') T0(y') + c2 T0(x') T1(y') # order 1
• c3 T2(x') T0(y') + c4 T1(x') T1(y') + c5 T0(x') T2(y') # order 2
• ...

= c0 # order 0

• c1 T1(x') + c2 T1(y') # order 1
• c3 T2(x') + c4 T1(x') T1(y') + c5 T2(y') # order 2
• ...

where:

• Tn(x) is the nth Chebyshev function of the first kind: T0(x) = 1 T1(x) = x Tn+1(x) = 2xTn(x) + Tn-1(x)
• x' is x offset and scaled to range [-1, 1] as x ranges over [minX, maxX]
• y' is y offset and scaled to range [-1, 1] as y ranges over [minY, maxY]

Return value is incorrect if function arguments are not in the range [minX, maxX], [minY, maxY].

Definition at line 823 of file FunctionLibrary.h.

Member Typedef Documentation

template<typename ReturnT>

typedef Function2<ReturnT>::Ptr lsst::afw::math::Chebyshev1Function2< ReturnT >::Function2Ptr

Definition at line 825 of file FunctionLibrary.h.

Constructor & Destructor Documentation

template<typename ReturnT>

lsst::afw::math::Chebyshev1Function2< ReturnT >::Chebyshev1Function2 ( unsigned int  order, lsst::afw::geom::Box2D const &  xyRange = lsst::afw::geom::Box2D(lsst::afw::geom::Point2D(-1.0, -1.0),                                       lsst::afw::geom::Point2D( 1.0,  1.0))  )

inlineexplicit

Construct a Chebyshev polynomial of specified order and range.

The parameters are initialized to zero.

Parameters

order	order of polynomial (0 for constant)
xyRange	allowed x,y range

Definition at line 832 of file FunctionLibrary.h.

        :
            BasePolynomialFunction2<ReturnT>(order),
            _oldYPrime(0),
            _yCheby(this->_order + 1),
            _xCoeffs(this->_order + 1)
        {
            _initialize(xyRange);
        }

template<typename ReturnT>

lsst::afw::math::Chebyshev1Function2< ReturnT >::Chebyshev1Function2 ( std::vector< double >  params, lsst::afw::geom::Box2D const &  xyRange = lsst::afw::geom::Box2D(lsst::afw::geom::Point2D(-1.0, -1.0),                                       lsst::afw::geom::Point2D( 1.0,  1.0))  )

inlineexplicit

Construct a Chebyshev polynomial with specified parameters and range.

The order of the polynomial is set to the length of the params vector.

Exceptions

lsst::pex::exceptions::InvalidParameterError

if params is empty

Parameters

params	polynomial coefficients length must be one of 1, 3, 6, 10, 15...
xyRange	allowed x,y range

Definition at line 853 of file FunctionLibrary.h.

        :
            BasePolynomialFunction2<ReturnT>(params),
            _oldYPrime(0),
            _yCheby(this->_order + 1),
            _xCoeffs(this->_order + 1)
        {
            _initialize(xyRange);
        }

template<typename ReturnT>

virtual lsst::afw::math::Chebyshev1Function2< ReturnT >::~Chebyshev1Function2 ( )

inlinevirtual

Definition at line 868 of file FunctionLibrary.h.

{}

template<typename ReturnT>

lsst::afw::math::Chebyshev1Function2< ReturnT >::Chebyshev1Function2 ( )

inlineexplicitprotected

Definition at line 1009 of file FunctionLibrary.h.

                                       : BasePolynomialFunction2<ReturnT>(),
            _oldYPrime(0),
            _yCheby(0),
            _xCoeffs(0),
            _minX(0.0), _minY(0.0),
            _maxX(0.0), _maxY(0.0),
            _scaleX(1.0), _scaleY(1.0),
            _offsetX(0.0), _offsetY(0.0) {}

Member Function Documentation

template<typename ReturnT>

void lsst::afw::math::Chebyshev1Function2< ReturnT >::_initialize ( lsst::afw::geom::Box2D const &  xyRange )

inlineprivate

initialize private constants

Definition at line 996 of file FunctionLibrary.h.

                                                          {
            _minX = xyRange.getMinX();
            _minY = xyRange.getMinY();
            _maxX = xyRange.getMaxX();
            _maxY = xyRange.getMaxY();
            _scaleX = 2.0 / (_maxX - _minX);
            _scaleY = 2.0 / (_maxY - _minY);
            _offsetX = -(_minX + _maxX) * 0.5;
            _offsetY = -(_minY + _maxY) * 0.5;
        }

template<typename ReturnT>

virtual Function2Ptr lsst::afw::math::Chebyshev1Function2< ReturnT >::clone ( ) const

inlinevirtual

Return a pointer to a deep copy of this function.

This function exists instead of a copy constructor so one can obtain a copy of an actual function instead of a useless copy of the base class.

Every non-virtual function must override this method.

Returns

a pointer to a deep copy of the function

Implements lsst::afw::math::Function2< ReturnT >.

Definition at line 870 of file FunctionLibrary.h.

                                           {
            return Function2Ptr(new Chebyshev1Function2(this->_params, this->getXYRange()));
        }

template<typename ReturnT>

virtual std::string lsst::afw::math::Chebyshev1Function2< ReturnT >::getPersistenceName ( ) const

protectedvirtual

Return the unique name used to persist this object and look up its factory.

Must be less than ArchiveIndexSchema::MAX_NAME_LENGTH characters.

Reimplemented from lsst::afw::table::io::Persistable.

template<typename ReturnT>

lsst::afw::geom::Box2D lsst::afw::math::Chebyshev1Function2< ReturnT >::getXYRange ( ) const

inline

Get x,y range.

Definition at line 877 of file FunctionLibrary.h.

                                            {
            return lsst::afw::geom::Box2D(lsst::afw::geom::Point2D(_minX, _minY),
                                          lsst::afw::geom::Point2D(_maxX, _maxY));
        };

template<typename ReturnT>

virtual bool lsst::afw::math::Chebyshev1Function2< ReturnT >::isPersistable ( ) const

inlinevirtual

Return true if this particular object can be persisted using afw::table::io.

Reimplemented from lsst::afw::table::io::Persistable.

Definition at line 972 of file FunctionLibrary.h.

{ return true; }

template<typename ReturnT>

virtual ReturnT lsst::afw::math::Chebyshev1Function2< ReturnT >::operator() ( double  x, double  y  ) const

inlinevirtual

Implements lsst::afw::math::Function2< ReturnT >.

Definition at line 900 of file FunctionLibrary.h.

                                                              {
            /* Solve as follows:
            - f(x,y) = Cy0 T0(y') + Cy1 T1(y') + Cy2 T2(y') + Cy3 T3(y') + ...
            where:
              Cy0 = P0 T0(x') + P1 T1(x') + P3 T2(x') + P6 T3(x') + ...
              Cy1 = P2 T0(x') + P4 T1(x') + P7 T2(x') + ...
              Cy2 = P5 T0(x') + P8 T1(x') + ...
              Cy3 = P9 T0(x') + ...
              ...

            First compute Tn(x') for each n
            Then use that to compute Cy0, Cy1, ...Cyn
            Then solve the y Chebyshev polynomial using the Clenshaw algorithm
            */
            double const xPrime = (x + _offsetX) * _scaleX;
            double const yPrime = (y + _offsetY) * _scaleY;

            const int nParams = static_cast<int>(this->_params.size());
            const int order = this->_order;

            if (order == 0) {
                return this->_params[0];  // No caching required
            }

            if ((yPrime != _oldYPrime) || !this->_isCacheValid) {
                // update cached _yCheby and _xCoeffs
                _yCheby[0] = 1.0;
                _yCheby[1] = yPrime;
                for (int chebyInd = 2; chebyInd <= order; chebyInd++) {
                    _yCheby[chebyInd] = (2 * yPrime * _yCheby[chebyInd-1]) - _yCheby[chebyInd-2];
                }

                for (int coeffInd=0; coeffInd <= order; coeffInd++) {
                    _xCoeffs[coeffInd] = 0;
                }
                for (int coeffInd = 0, endCoeffInd = 0, paramInd = 0; paramInd < nParams; paramInd++) {
                    _xCoeffs[coeffInd] += this->_params[paramInd] * _yCheby[endCoeffInd];
                    --coeffInd;
                    ++endCoeffInd;
                    if (coeffInd < 0) {
                        coeffInd = endCoeffInd;
                        endCoeffInd = 0;
                    }
                }

                _oldYPrime = yPrime;
                this->_isCacheValid = true;
            }

            // Clenshaw function for solving the Chebyshev polynomial
            // Non-recursive version from Kresimir Cosic
            if (order == 1) {
                return _xCoeffs[0] + (_xCoeffs[1] * xPrime);
            }
            double cshPrev = _xCoeffs[order];
            double csh = (2 * xPrime * _xCoeffs[order]) + _xCoeffs[order-1];
            for (int i = order - 2; i > 0; --i) {
                double cshNext = (2 * xPrime * csh) + _xCoeffs[i] - cshPrev;
                cshPrev = csh;
                csh = cshNext;
            }
            return (xPrime * csh) + _xCoeffs[0] - cshPrev;
        }

template<typename ReturnT>

template<class Archive >

void lsst::afw::math::Chebyshev1Function2< ReturnT >::serialize ( Archive &  ar, unsigned int const  version  )

inlineprivate

Definition at line 1021 of file FunctionLibrary.h.

                                                                {
            ar & make_nvp("fn2", boost::serialization::base_object<BasePolynomialFunction2<ReturnT> >(*this));
            ar & make_nvp("minX", this->_minX);
            ar & make_nvp("minY", this->_minY);
            ar & make_nvp("maxX", this->_maxX);
            ar & make_nvp("maxY", this->_maxY);
            ar & make_nvp("scaleX", this->_scaleX);
            ar & make_nvp("scaleY", this->_scaleY);
            ar & make_nvp("offsetX", this->_offsetX);
            ar & make_nvp("offsetY", this->_offsetY);
            ar & make_nvp("xCheby", this->_yCheby); // sets size of _yCheby; name is historical
            _xCoeffs.resize(_yCheby.size());
        }

template<typename ReturnT>

virtual std::string lsst::afw::math::Chebyshev1Function2< ReturnT >::toString ( std::string const &  ) const

inlinevirtual

Return a string representation of the function.

Returns

a string representation of the function

Reimplemented from lsst::afw::math::Function2< ReturnT >.

Definition at line 964 of file FunctionLibrary.h.

                                                                  {
            std::ostringstream os;
            os << "Chebyshev1Function2 [";
            os << this->_order << ", " << this->getXYRange() << "]";
            os << Function2<ReturnT>::toString(prefix);
            return os.str();
        }

template<typename ReturnT>

virtual Chebyshev1Function2 lsst::afw::math::Chebyshev1Function2< ReturnT >::truncate ( int  truncOrder ) const

inlinevirtual

Return a truncated copy of lower (or equal) order.

Exceptions

lsst::pex::exceptions::InvalidParameter

if truncated order > original order

Parameters

truncOrder

order of truncated polynomial

Definition at line 887 of file FunctionLibrary.h.

                {
            if (truncOrder > this->_order) {
                std::ostringstream os;
                os << "truncated order=" << truncOrder << " must be <= original order=" << this->_order;
                throw LSST_EXCEPT(lsst::pex::exceptions::InvalidParameterError, os.str());
            }
            int truncNParams = this->nParametersFromOrder(truncOrder);
            std::vector<double> truncParams(this->_params.begin(), this->_params.begin() + truncNParams);
            return Chebyshev1Function2(truncParams, this->getXYRange());
        }

template<typename ReturnT>

virtual void lsst::afw::math::Chebyshev1Function2< ReturnT >::write ( afw::table::io::OutputArchiveHandle &  handle ) const

protectedvirtual

Write the object to one or more catalogs.

The handle object passed to this function provides an interface for adding new catalogs and adding nested objects to the same archive (while checking for duplicates). See OutputArchiveHandle for more information.

Reimplemented from lsst::afw::table::io::Persistable.

Friends And Related Function Documentation

template<typename ReturnT>

friend class boost::serialization::access

friend

Definition at line 1019 of file FunctionLibrary.h.

Member Data Documentation

template<typename ReturnT>

double lsst::afw::math::Chebyshev1Function2< ReturnT >::_maxX

private

maximum allowed x

Definition at line 986 of file FunctionLibrary.h.

template<typename ReturnT>

double lsst::afw::math::Chebyshev1Function2< ReturnT >::_maxY

private

maximum allowed y

Definition at line 987 of file FunctionLibrary.h.

template<typename ReturnT>

double lsst::afw::math::Chebyshev1Function2< ReturnT >::_minX

private

minimum allowed x

Definition at line 984 of file FunctionLibrary.h.

template<typename ReturnT>

double lsst::afw::math::Chebyshev1Function2< ReturnT >::_minY

private

minimum allowed y

Definition at line 985 of file FunctionLibrary.h.

template<typename ReturnT>

double lsst::afw::math::Chebyshev1Function2< ReturnT >::_offsetX

private

x' = (x + _offsetX) * _scaleX

Definition at line 990 of file FunctionLibrary.h.

template<typename ReturnT>

double lsst::afw::math::Chebyshev1Function2< ReturnT >::_offsetY

private

y' = (y + _offsetY) * _scaleY

Definition at line 991 of file FunctionLibrary.h.

template<typename ReturnT>

double lsst::afw::math::Chebyshev1Function2< ReturnT >::_oldYPrime

mutableprivate

Definition at line 981 of file FunctionLibrary.h.

template<typename ReturnT>

double lsst::afw::math::Chebyshev1Function2< ReturnT >::_scaleX

private

x' = (x + _offsetX) * _scaleX

Definition at line 988 of file FunctionLibrary.h.

template<typename ReturnT>

double lsst::afw::math::Chebyshev1Function2< ReturnT >::_scaleY

private

y' = (y + _offsetY) * _scaleY

Definition at line 989 of file FunctionLibrary.h.

template<typename ReturnT>

std::vector<double> lsst::afw::math::Chebyshev1Function2< ReturnT >::_xCoeffs

mutableprivate

working vector: transformed coeffs of x polynomial

Definition at line 983 of file FunctionLibrary.h.

template<typename ReturnT>

std::vector<double> lsst::afw::math::Chebyshev1Function2< ReturnT >::_yCheby

mutableprivate

working vector: value of Tn(y')

Definition at line 982 of file FunctionLibrary.h.

---

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

• /home/lsstsw/stack/Linux64/afw/11.0-2-g04d2804/include/lsst/afw/math/FunctionLibrary.h