2-dimensional polynomial function with cross terms More...

#include <FunctionLibrary.h>

Inheritance diagram for lsst.afw.math::PolynomialFunction2< 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
	PolynomialFunction2 (unsigned int order)
	Construct a polynomial function of specified order. More...

	PolynomialFunction2 (std::vector< double > params)
	Construct a polynomial function with specified parameters. More...

virtual	~PolynomialFunction2 ()

virtual Function2Ptr	clone () const
	Return a pointer to a deep copy of this function. More...

virtual ReturnT	operator() (double x, double y) const

virtual std::vector< double >	getDFuncDParameters (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...

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...

	PolynomialFunction2 ()

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
template<class Archive >
void	serialize (Archive &ar, unsigned int const version)

Private Attributes
double	_oldY
	value of y for which _xCoeffs is valid More...

std::vector< double >	_xCoeffs
	working vector 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::PolynomialFunction2< ReturnT >

2-dimensional polynomial function with cross terms

f(x,y) = c0 (0th order)

c1 x + c2 y (1st order)
c3 x^2 + c4 x y + c5 y^2 (2nd order)
c6 x^3 + c7 x^2 y + c8 x y^2 + c9 y^3 (3rd order)
...

Intermediate products for the most recent y are cached, so when computing for a set of x, y it is more efficient to change x before you change y.

Definition at line 524 of file FunctionLibrary.h.

Member Typedef Documentation

template<typename ReturnT>

typedef Function2<ReturnT>::Ptr lsst.afw.math::PolynomialFunction2< ReturnT >::Function2Ptr

Definition at line 526 of file FunctionLibrary.h.

Constructor & Destructor Documentation

template<typename ReturnT>

lsst.afw.math::PolynomialFunction2< ReturnT >::PolynomialFunction2 ( unsigned int order )

inlineexplicit

Construct a polynomial function of specified order.

The polynomial will have (order + 1) * (order + 2) / 2 coefficients

The parameters are initialized to zero.

Parameters

order order of polynomial (0 for constant)

Definition at line 535 of file FunctionLibrary.h.

         :
             BasePolynomialFunction2<ReturnT>(order),
             _oldY(0),
             _xCoeffs(this->_order + 1)
         {}

template<typename ReturnT>

lsst.afw.math::PolynomialFunction2< ReturnT >::PolynomialFunction2 ( std::vector< double > params )

inlineexplicit

Construct a polynomial function with specified parameters.

The order of the polynomial is determined from the length of the params vector: order = (sqrt(1 + 8 * length) - 3) / 2 and if this is not an integer then the length is unsuitable

Exceptions

lsst::pex::exceptions::InvalidParameterError	if params length is unsuitable
lsst::pex::exceptions::Exception	if an internal sanity check fails

Parameters

params polynomial coefficients (const, x, y, x^2, xy, y^2...); length must be one of 1, 3, 6, 10, 15...

Definition at line 553 of file FunctionLibrary.h.

         :
             BasePolynomialFunction2<ReturnT>(params),
             _oldY(0),
             _xCoeffs(this->_order + 1)
         {}

template<typename ReturnT>

virtual lsst.afw.math::PolynomialFunction2< ReturnT >::~PolynomialFunction2 ( )

inlinevirtual

Definition at line 562 of file FunctionLibrary.h.

562 {}

template<typename ReturnT>

lsst.afw.math::PolynomialFunction2< ReturnT >::PolynomialFunction2 ( )

inlineexplicitprotected

Definition at line 641 of file FunctionLibrary.h.

641 : BasePolynomialFunction2<ReturnT>(), _oldY(0), _xCoeffs(0) {}

lsst.afw.math::PolynomialFunction2::_oldY

double _oldY

value of y for which _xCoeffs is valid

Definition: FunctionLibrary.h:636

lsst.afw.math::PolynomialFunction2::_xCoeffs

std::vector< double > _xCoeffs

working vector

Definition: FunctionLibrary.h:637

Member Function Documentation

template<typename ReturnT>

virtual Function2Ptr lsst.afw.math::PolynomialFunction2< 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 564 of file FunctionLibrary.h.

                                            {
             return Function2Ptr(new PolynomialFunction2(this->_params));
         }

template<typename ReturnT >

std::vector< double > lsst.afw.math::PolynomialFunction2< ReturnT >::getDFuncDParameters	(	double	x,
		double	y
	)		const

virtual

Return the coefficients of the Function's parameters, evaluated at (x, y) I.e. given c0, c1, c2, c3 ... return 1, x, y, x^2 ...

Reimplemented from lsst.afw.math::BasePolynomialFunction2< ReturnT >.

Definition at line 36 of file Function.cc.

                                                                                                    {
     std::vector<double> coeffs(this->getNParameters());
 
     //
     // Go through params order by order, evaluating x^r y^s;  we do this by first evaluating
     // y^s for a complete order, then going through again multiplying by x^r
     //
     int i0 = 0;                         // starting index for this order's coefficients
     for (int order = 0; order <= this->_order; ++order) {
         coeffs[i0] = 1;
         double zn = y;                  // y^s
         for (int i = 1; i <= order; ++i) {
             coeffs[i0 + i] = zn;
             zn *= y;
         }
 
         zn = x;                         // x^r
         for (int i = order - 1; i >= 0; --i) {
             coeffs[i0 + i] *= zn;
             zn *= x;
         }
 
 
         i0 += order + 1;
     }
 
     assert (i0 == static_cast<int>(coeffs.size()));
 
     return coeffs;
 }

template<typename ReturnT>

virtual std::string lsst.afw.math::PolynomialFunction2< 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>

virtual bool lsst.afw.math::PolynomialFunction2< 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 627 of file FunctionLibrary.h.

627 { return true; }

template<typename ReturnT>

virtual ReturnT lsst.afw.math::PolynomialFunction2< ReturnT >::operator()	(	double	x,
		double	y
	)		const

inlinevirtual

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

Definition at line 568 of file FunctionLibrary.h.

                                                               {
             /* Solve as follows:
             - f(x,y) = Cx0 + Cx1 x + Cx2 x^2 + Cx3 x^3 + ...
             where:
               Cx0 = P0 + P2 y + P5 y^2 + P9 y^3 + ...
               Cx1 = P1 + P4 y + P8 y2 + ...
               Cx2 = P3 + P7 y + ...
               Cx3 = P6 + ...
               ...
 
             Compute Cx0, Cx1...Cxn by solving 1-d polynomials in y in the usual way.
             These values are cached and only recomputed for new values of Y or if the parameters change.
 
             Then compute f(x,y) by solving the 1-d polynomial in x in the usual way.
             */
             const int maxXCoeffInd = this->_order;
 
             if ((y != _oldY) || !this->_isCacheValid) {
                 // update _xCoeffs cache
                 // note: paramInd is decremented in both of the following loops
                 int paramInd = static_cast<int>(this->_params.size()) - 1;
 
                 // initialize _xCoeffs to coeffs for pure y^n; e.g. for 3rd order:
                 // _xCoeffs[0] = _params[9], _xCoeffs[1] = _params[8], ... _xCoeffs[3] = _params[6]
                 for (int xCoeffInd = 0; xCoeffInd <= maxXCoeffInd; ++xCoeffInd, --paramInd) {
                     _xCoeffs[xCoeffInd] = this->_params[paramInd];
                 }
 
                 // finish computing _xCoeffs
                 for (int xCoeffInd = 0, endXCoeffInd = maxXCoeffInd; paramInd >= 0; --paramInd) {
                     _xCoeffs[xCoeffInd] = (_xCoeffs[xCoeffInd] * y) + this->_params[paramInd];
                     ++xCoeffInd;
                     if (xCoeffInd >= endXCoeffInd) {
                         xCoeffInd = 0;
                         --endXCoeffInd;
                     }
                 }
 
                 _oldY = y;
                 this->_isCacheValid = true;
             }
 
             // use _xCoeffs to compute result
             double retVal = _xCoeffs[maxXCoeffInd];
             for (int xCoeffInd = maxXCoeffInd - 1; xCoeffInd >= 0; --xCoeffInd) {
                 retVal = (retVal * x) + _xCoeffs[xCoeffInd];
             }
             return static_cast<ReturnT>(retVal);
         }

template<typename ReturnT>

template<class Archive >

void lsst.afw.math::PolynomialFunction2< ReturnT >::serialize	(	Archive &	ar,
		unsigned int const	version
	)

inlineprivate

Definition at line 646 of file FunctionLibrary.h.

                                                                 {
             ar & make_nvp("fn2", boost::serialization::base_object<BasePolynomialFunction2<ReturnT> >(*this));
             ar & make_nvp("yCoeffs", this->_xCoeffs); // sets size of _xCoeffs; name is historical
         }

template<typename ReturnT>

virtual std::string lsst.afw.math::PolynomialFunction2< 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 620 of file FunctionLibrary.h.

                                                                   {
             std::ostringstream os;
             os << "PolynomialFunction2 [" << this->_order << "]: ";
             os << Function2<ReturnT>::toString(prefix);
             return os.str();
         }

template<typename ReturnT>

virtual void lsst.afw.math::PolynomialFunction2< 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 644 of file FunctionLibrary.h.

Member Data Documentation

template<typename ReturnT>

double lsst.afw.math::PolynomialFunction2< ReturnT >::_oldY

mutableprivate

value of y for which _xCoeffs is valid

Definition at line 636 of file FunctionLibrary.h.

template<typename ReturnT>

std::vector<double> lsst.afw.math::PolynomialFunction2< ReturnT >::_xCoeffs

mutableprivate

working vector

Definition at line 637 of file FunctionLibrary.h.

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

/home/lsstsw/stack/Linux64/afw/11.0.rc2+4/include/lsst/afw/math/FunctionLibrary.h
/home/lsstsw/stack/Linux64/afw/11.0.rc2+4/src/math/Function.cc

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Friends

Additional Inherited Members

Detailed Description

template<typename ReturnT> class lsst.afw.math::PolynomialFunction2< ReturnT >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<typename ReturnT>
class lsst.afw.math::PolynomialFunction2< ReturnT >