a class used in function calls to indicate that no Function1 is being provided More...

#include <Function.h>

Inheritance diagram for lsst::afw::math::NullFunction1< ReturnT >:

Public Member Functions
	NullFunction1 ()

std::shared_ptr< Function1< ReturnT > >	clone () const override
	Return a pointer to a deep copy of this function. More...

std::string	toString (std::string const &prefix="") const override
	Return a string representation of the function. More...

virtual void	computeCache (int const n)

unsigned int	getNParameters () const noexcept
	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 noexcept
	Return all function parameters. More...

virtual bool	isLinearCombination () const noexcept
	Is the function a linear combination of its 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...

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 bool	isPersistable () const noexcept
	Return true if this particular object can be persisted using afw::table::io. More...

Static Public Member Functions
static std::shared_ptr< Function1< ReturnT > >	readFits (fits::Fits &fitsfile)
	Read an object from an already open FITS object. More...

static std::shared_ptr< Function1< ReturnT > >	readFits (std::string const &fileName, int hdu=fits::DEFAULT_HDU)
	Read an object from a regular FITS file. More...

static std::shared_ptr< Function1< ReturnT > >	readFits (fits::MemFileManager &manager, int hdu=fits::DEFAULT_HDU)
	Read an object from a FITS file in memory. More...

static std::shared_ptr< Function< ReturnT > >	readFits (fits::Fits &fitsfile)
	Read an object from an already open FITS object. More...

static std::shared_ptr< Function< ReturnT > >	readFits (std::string const &fileName, int hdu=fits::DEFAULT_HDU)
	Read an object from a regular FITS file. More...

static std::shared_ptr< Function< ReturnT > >	readFits (fits::MemFileManager &manager, int hdu=fits::DEFAULT_HDU)
	Read an object from a FITS file in memory. More...

static std::shared_ptr< Function1< ReturnT > >	dynamicCast (std::shared_ptr< Persistable > const &ptr)
	Dynamically cast a shared_ptr. More...

static std::shared_ptr< Function< ReturnT > >	dynamicCast (std::shared_ptr< Persistable > const &ptr)
	Dynamically cast a shared_ptr. More...

Protected Types
using	OutputArchiveHandle = io::OutputArchiveHandle

Protected Member Functions
std::string	getPythonModule () const override
	Return the fully-qualified Python module that should be imported to guarantee that its factory is registered. More...

virtual std::string	getPersistenceName () const
	Return the unique name used to persist this object and look up its factory. More...

virtual void	write (OutputArchiveHandle &handle) const
	Write the object to one or more catalogs. More...

Protected Attributes
std::vector< double >	_params

bool	_isCacheValid

Detailed Description

template<typename ReturnT>
class lsst::afw::math::NullFunction1< ReturnT >

a class used in function calls to indicate that no Function1 is being provided

Definition at line 441 of file Function.h.

Member Typedef Documentation

◆ OutputArchiveHandle

using lsst::afw::table::io::Persistable::OutputArchiveHandle = io::OutputArchiveHandle

protectedinherited

Definition at line 108 of file Persistable.h.

Constructor & Destructor Documentation

◆ NullFunction1()

template<typename ReturnT >

lsst::afw::math::NullFunction1< ReturnT >::NullFunction1 ( )

inlineexplicit

Definition at line 443 of file Function.h.

443 : Function1<ReturnT>(0) {}

Member Function Documentation

◆ clone()

template<typename ReturnT >

std::shared_ptr<Function1<ReturnT> > lsst::afw::math::NullFunction1< ReturnT >::clone ( ) const

inlineoverridevirtual

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 concrete subclass must override this method.

Returns: a pointer to a deep copy of the function

Implements lsst::afw::math::Function1< ReturnT >.

Definition at line 444 of file Function.h.

                                                              {
         return std::shared_ptr<Function1<ReturnT>>(new NullFunction1());
     }

◆ computeCache()

template<typename ReturnT >

virtual void lsst::afw::math::Function1< ReturnT >::computeCache ( int const n )

inlinevirtualinherited

Definition at line 244 of file Function.h.

244 {}

◆ dynamicCast() [1/2]

template std::shared_ptr< meas::extensions::psfex::PsfexPsf > lsst::afw::table::io::PersistableFacade< Function1< ReturnT > >::dynamicCast ( std::shared_ptr< Persistable > const & ptr )

staticinherited

Dynamically cast a shared_ptr.

Dynamically cast a shared pointer and raise on failure.

You must provide an explicit template instantiation in the .cc file for each class that inherits from PersistableFacade. Designed to work around RTTI issues on macOS with hidden symbols;

Exceptions

lsst::pex::exceptions::LogicError if the cast fails

param[in] ptr The pointer to be cast.

Returns: The cast pointer.

Exceptions

lsst::pex::exceptions::TypeError If the dynamic cast fails.

Definition at line 218 of file Persistable.cc.

                                                                                         {
     auto result = std::dynamic_pointer_cast<T>(ptr);
     if (!result) {
         throw LSST_EXCEPT(pex::exceptions::TypeError, "Dynamic pointer cast failed");
     }
     return result;
 }

◆ dynamicCast() [2/2]

template std::shared_ptr< meas::extensions::psfex::PsfexPsf > lsst::afw::table::io::PersistableFacade< Function< ReturnT > >::dynamicCast ( std::shared_ptr< Persistable > const & ptr )

staticinherited

Dynamically cast a shared_ptr.

Dynamically cast a shared pointer and raise on failure.

You must provide an explicit template instantiation in the .cc file for each class that inherits from PersistableFacade. Designed to work around RTTI issues on macOS with hidden symbols;

Exceptions

lsst::pex::exceptions::LogicError if the cast fails

param[in] ptr The pointer to be cast.

Returns: The cast pointer.

Exceptions

lsst::pex::exceptions::TypeError If the dynamic cast fails.

Definition at line 218 of file Persistable.cc.

                                                                                         {
     auto result = std::dynamic_pointer_cast<T>(ptr);
     if (!result) {
         throw LSST_EXCEPT(pex::exceptions::TypeError, "Dynamic pointer cast failed");
     }
     return result;
 }

◆ getNParameters()

template<typename ReturnT >

unsigned int lsst::afw::math::Function< ReturnT >::getNParameters ( ) const

inlinenoexceptinherited

Return the number of function parameters.

Returns: the number of function parameters

Definition at line 112 of file Function.h.

112 { return _params.size(); }

lsst::afw::math::Function::_params

std::vector< double > _params

Definition: Function.h:185

std::vector::size

T size(T... args)

◆ getParameter()

template<typename ReturnT >

virtual double lsst::afw::math::Function< ReturnT >::getParameter ( unsigned int ind ) const

inlinevirtualinherited

Get one function parameter without range checking.

Returns: the specified function parameter

Parameters

ind	index of parameter

Definition at line 119 of file Function.h.

                   {
         return _params[ind];
     }

◆ getParameters()

template<typename ReturnT >

std::vector<double> const& lsst::afw::math::Function< ReturnT >::getParameters ( ) const

inlinenoexceptinherited

Return all function parameters.

Returns: the function parameters as a vector

Definition at line 129 of file Function.h.

129 { return _params; }

◆ getPersistenceName()

std::string lsst::afw::table::io::Persistable::getPersistenceName ( ) const

protectedvirtualinherited

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

Must be less than ArchiveIndexSchema::MAX_NAME_LENGTH characters.

Reimplemented in lsst::meas::modelfit::Mixture, lsst::meas::algorithms::WarpedPsf, lsst::meas::algorithms::SingleGaussianPsf, lsst::meas::algorithms::KernelPsf, lsst::meas::algorithms::DoubleGaussianPsf, lsst::meas::algorithms::CoaddPsf, lsst::meas::algorithms::CoaddBoundedField, lsst::afw::typehandling::StorableHelper< Base >, lsst::afw::math::WarpingControl, lsst::afw::math::NearestWarpingKernel, lsst::afw::math::BilinearWarpingKernel, lsst::afw::math::LanczosWarpingKernel, lsst::afw::math::TransformBoundedField, lsst::afw::math::ProductBoundedField, lsst::afw::math::PixelAreaBoundedField, lsst::afw::math::LinearCombinationKernel, lsst::afw::math::DeltaFunctionKernel, lsst::afw::math::AnalyticKernel, lsst::afw::math::FixedKernel, lsst::afw::math::Chebyshev1Function2< ReturnT >, lsst::afw::math::PolynomialFunction2< ReturnT >, lsst::afw::math::DoubleGaussianFunction2< ReturnT >, lsst::afw::math::GaussianFunction2< ReturnT >, lsst::afw::math::ChebyshevBoundedField, lsst::afw::image::VisitInfo, lsst::afw::image::PhotoCalib, lsst::afw::image::CoaddInputs, lsst::afw::geom::Transform< FromEndpoint, ToEndpoint >, lsst::afw::geom::Transform< afw::geom::Point2Endpoint, afw::geom::GenericEndpoint >, lsst::afw::geom::SkyWcs, lsst::afw::geom::polygon::Polygon, lsst::afw::detection::HeavyFootprint< ImagePixelT, MaskPixelT, VariancePixelT >, lsst::afw::detection::GaussianPsf, lsst::afw::detection::Footprint, lsst::afw::cameraGeom::DetectorCollection, and lsst::afw::image::FilterLabel.

Definition at line 34 of file Persistable.cc.

34 { return std::string(); }

std::string

◆ getPythonModule()

template<typename ReturnT >

std::string lsst::afw::math::Function< ReturnT >::getPythonModule ( ) const

inlineoverrideprotectedvirtualinherited

Return the fully-qualified Python module that should be imported to guarantee that its factory is registered.

Must be less than ArchiveIndexSchema::MAX_MODULE_LENGTH characters.

Will be ignored if empty.

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

Definition at line 188 of file Function.h.

188 { return "lsst.afw.math"; }

◆ isLinearCombination()

template<typename ReturnT >

virtual bool lsst::afw::math::Function< ReturnT >::isLinearCombination ( ) const

inlinevirtualnoexceptinherited

Is the function a linear combination of its parameters?

Returns: true if the function can be expressed as: sum over i of parameter_i * function_i(args)

Warning: : subclasses must override if true.

Reimplemented in lsst::afw::math::Chebyshev1Function1< ReturnT >, lsst::afw::math::PolynomialFunction1< ReturnT >, and lsst::afw::math::BasePolynomialFunction2< ReturnT >.

Definition at line 138 of file Function.h.

138 { return false; }

◆ isPersistable()

virtual bool lsst::afw::table::io::Persistable::isPersistable ( ) const

inlinevirtualnoexceptinherited

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

Reimplemented in lsst::meas::modelfit::Mixture, lsst::meas::extensions::psfex::PsfexPsf, lsst::meas::algorithms::WarpedPsf, lsst::meas::algorithms::SingleGaussianPsf, lsst::meas::algorithms::KernelPsf, lsst::meas::algorithms::DoubleGaussianPsf, lsst::meas::algorithms::CoaddPsf, lsst::meas::algorithms::CoaddBoundedField, lsst::afw::typehandling::StorableHelper< Base >, lsst::afw::math::WarpingControl, lsst::afw::math::NearestWarpingKernel, lsst::afw::math::BilinearWarpingKernel, lsst::afw::math::LanczosWarpingKernel, lsst::afw::math::TransformBoundedField, lsst::afw::math::ProductBoundedField, lsst::afw::math::PixelAreaBoundedField, lsst::afw::math::LinearCombinationKernel, lsst::afw::math::DeltaFunctionKernel, lsst::afw::math::AnalyticKernel, lsst::afw::math::FixedKernel, lsst::afw::math::Chebyshev1Function2< ReturnT >, lsst::afw::math::PolynomialFunction2< ReturnT >, lsst::afw::math::DoubleGaussianFunction2< ReturnT >, lsst::afw::math::GaussianFunction2< ReturnT >, lsst::afw::math::ChebyshevBoundedField, lsst::afw::image::VisitInfo, lsst::afw::image::PhotoCalib, lsst::afw::image::FilterLabel, lsst::afw::image::CoaddInputs, lsst::afw::image::ApCorrMap, lsst::afw::geom::Transform< FromEndpoint, ToEndpoint >, lsst::afw::geom::Transform< afw::geom::Point2Endpoint, afw::geom::GenericEndpoint >, lsst::afw::geom::SpanSet, lsst::afw::geom::SkyWcs, lsst::afw::geom::polygon::Polygon, lsst::afw::detection::GaussianPsf, lsst::afw::detection::Footprint, lsst::afw::cameraGeom::TransformMap, lsst::afw::cameraGeom::DetectorCollection, lsst::afw::cameraGeom::Detector, and lsst::afw::cameraGeom::Camera.

Definition at line 102 of file Persistable.h.

102 { return false; }

◆ readFits() [1/6]

static std::shared_ptr<Function1< ReturnT > > lsst::afw::table::io::PersistableFacade< Function1< ReturnT > >::readFits ( fits::Fits & fitsfile )

inlinestaticinherited

Read an object from an already open FITS object.

Parameters

[in] fitsfile FITS object to read from, already positioned at the desired HDU.

Definition at line 183 of file Persistable.h.

                                                          {
         return dynamicCast(Persistable::_readFits(fitsfile));
     }

◆ readFits() [2/6]

static std::shared_ptr<Function< ReturnT > > lsst::afw::table::io::PersistableFacade< Function< ReturnT > >::readFits ( fits::Fits & fitsfile )

inlinestaticinherited

Read an object from an already open FITS object.

Parameters

[in] fitsfile FITS object to read from, already positioned at the desired HDU.

Definition at line 183 of file Persistable.h.

                                                          {
         return dynamicCast(Persistable::_readFits(fitsfile));
     }

◆ readFits() [3/6]

static std::shared_ptr<Function< ReturnT > > lsst::afw::table::io::PersistableFacade< Function< ReturnT > >::readFits	(	fits::MemFileManager &	manager,
		int	hdu = `fits::DEFAULT_HDU`
	)

inlinestaticinherited

Read an object from a FITS file in memory.

Parameters

[in]	manager	Manager for the memory to read from.
[in]	hdu	HDU to read, where 0 is the primary. The special value of afw::fits::DEFAULT_HDU skips the primary HDU if it is empty.

Definition at line 205 of file Persistable.h.

                                                                                              {
         return dynamicCast(Persistable::_readFits(manager, hdu));
     }

◆ readFits() [4/6]

static std::shared_ptr<Function1< ReturnT > > lsst::afw::table::io::PersistableFacade< Function1< ReturnT > >::readFits	(	fits::MemFileManager &	manager,
		int	hdu = `fits::DEFAULT_HDU`
	)

inlinestaticinherited

Read an object from a FITS file in memory.

Parameters

[in]	manager	Manager for the memory to read from.
[in]	hdu	HDU to read, where 0 is the primary. The special value of afw::fits::DEFAULT_HDU skips the primary HDU if it is empty.

Definition at line 205 of file Persistable.h.

                                                                                              {
         return dynamicCast(Persistable::_readFits(manager, hdu));
     }

◆ readFits() [5/6]

static std::shared_ptr<Function< ReturnT > > lsst::afw::table::io::PersistableFacade< Function< ReturnT > >::readFits	(	std::string const &	fileName,
		int	hdu = `fits::DEFAULT_HDU`
	)

inlinestaticinherited

Read an object from a regular FITS file.

Parameters

[in]	fileName	Name of the file to read.
[in]	hdu	HDU to read, where 0 is the primary. The special value of afw::fits::DEFAULT_HDU skips the primary HDU if it is empty.

Definition at line 194 of file Persistable.h.

                                                                                            {
         return dynamicCast(Persistable::_readFits(fileName, hdu));
     }

◆ readFits() [6/6]

static std::shared_ptr<Function1< ReturnT > > lsst::afw::table::io::PersistableFacade< Function1< ReturnT > >::readFits	(	std::string const &	fileName,
		int	hdu = `fits::DEFAULT_HDU`
	)

inlinestaticinherited

Read an object from a regular FITS file.

Parameters

[in]	fileName	Name of the file to read.
[in]	hdu	HDU to read, where 0 is the primary. The special value of afw::fits::DEFAULT_HDU skips the primary HDU if it is empty.

Definition at line 194 of file Persistable.h.

                                                                                            {
         return dynamicCast(Persistable::_readFits(fileName, hdu));
     }

◆ setParameter()

template<typename ReturnT >

void lsst::afw::math::Function< ReturnT >::setParameter	(	unsigned int	ind,
		double	newValue
	)

inlineinherited

Set one function parameter without range checking.

Parameters

ind	index of parameter
newValue	new value for parameter

Definition at line 143 of file Function.h.

     {
         _isCacheValid = false;
         _params[ind] = newValue;
     }

◆ setParameters()

template<typename ReturnT >

void lsst::afw::math::Function< ReturnT >::setParameters ( std::vector< double > const & params )

inlineinherited

Set all function parameters.

Exceptions

lsst::pex::exceptions::InvalidParameterError if the wrong number of parameters is supplied.

Parameters

params vector of function parameters

Definition at line 156 of file Function.h.

     {
         if (_params.size() != params.size()) {
             throw LSST_EXCEPT(
                     pexExcept::InvalidParameterError,
                     (boost::format("params has %d entries instead of %d") % params.size() % _params.size())
                             .str());
         }
         _isCacheValid = false;
         _params = params;
     }

◆ toString()

template<typename ReturnT >

std::string lsst::afw::math::Function1< ReturnT >::toString ( std::string const & = "" ) const

inlineoverridevirtualinherited

Return a string representation of the function.

Returns: a string representation of the function

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

Reimplemented in lsst::afw::math::IntegerDeltaFunction1< ReturnT >, lsst::afw::math::LanczosFunction1< ReturnT >, lsst::afw::math::Chebyshev1Function1< ReturnT >, lsst::afw::math::PolynomialFunction1< ReturnT >, and lsst::afw::math::GaussianFunction1< ReturnT >.

Definition at line 240 of file Function.h.

                                                                     {
         return std::string("Function1: ") + Function<ReturnT>::toString(prefix);
     }

◆ write()

void lsst::afw::table::io::Persistable::write ( OutputArchiveHandle & handle ) const

protectedvirtualinherited

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 in lsst::afw::typehandling::StorableHelper< Base >, lsst::afw::image::FilterLabel, lsst::meas::modelfit::Mixture, lsst::meas::algorithms::WarpedPsf, lsst::meas::algorithms::SingleGaussianPsf, lsst::meas::algorithms::KernelPsf, lsst::meas::algorithms::DoubleGaussianPsf, lsst::meas::algorithms::CoaddPsf, lsst::meas::algorithms::CoaddBoundedField, lsst::afw::math::WarpingControl, lsst::afw::math::NearestWarpingKernel, lsst::afw::math::BilinearWarpingKernel, lsst::afw::math::LanczosWarpingKernel, lsst::afw::math::TransformBoundedField, lsst::afw::math::ProductBoundedField, lsst::afw::math::PixelAreaBoundedField, lsst::afw::math::LinearCombinationKernel, lsst::afw::math::DeltaFunctionKernel, lsst::afw::math::AnalyticKernel, lsst::afw::math::FixedKernel, lsst::afw::math::ChebyshevBoundedField, lsst::afw::image::VisitInfo, lsst::afw::image::PhotoCalib, lsst::afw::image::CoaddInputs, lsst::afw::geom::Transform< FromEndpoint, ToEndpoint >, lsst::afw::geom::Transform< afw::geom::Point2Endpoint, afw::geom::GenericEndpoint >, lsst::afw::geom::SkyWcs, lsst::afw::geom::polygon::Polygon, lsst::afw::detection::HeavyFootprint< ImagePixelT, MaskPixelT, VariancePixelT >, lsst::afw::detection::GaussianPsf, lsst::afw::detection::Footprint, lsst::afw::cameraGeom::DetectorCollection, lsst::afw::cameraGeom::Camera, lsst::meas::extensions::psfex::PsfexPsf, lsst::afw::math::Chebyshev1Function2< ReturnT >, lsst::afw::math::PolynomialFunction2< ReturnT >, lsst::afw::math::DoubleGaussianFunction2< ReturnT >, and lsst::afw::math::GaussianFunction2< ReturnT >.

Definition at line 38 of file Persistable.cc.

                                                    {
     assert(!isPersistable());
     throw LSST_EXCEPT(pex::exceptions::LogicError,
                       "afw::table-based persistence is not supported for this object.");
 }

◆ writeFits() [1/3]

void lsst::afw::table::io::Persistable::writeFits ( fits::Fits & fitsfile ) const

inherited

Write the object to an already-open FITS object.

Parameters

[in] fitsfile Open FITS object to write to.

Definition at line 18 of file Persistable.cc.

                                                     {
     OutputArchive archive;
     archive.put(this);
     archive.writeFits(fitsfile);
 }

◆ writeFits() [2/3]

void lsst::afw::table::io::Persistable::writeFits	(	fits::MemFileManager &	manager,
		std::string const &	mode = `"w"`
	)		const

inherited

Write the object to a FITS image in memory.

Parameters

[in]	manager	Name of the file to write to.
[in]	mode	If "w", any existing file with the given name will be overwritten. If "a", new HDUs will be appended to an existing file.

Definition at line 29 of file Persistable.cc.

                                                                                     {
     fits::Fits fitsfile(manager, mode, fits::Fits::AUTO_CLOSE | fits::Fits::AUTO_CHECK);
     writeFits(fitsfile);
 }

◆ writeFits() [3/3]

void lsst::afw::table::io::Persistable::writeFits	(	std::string const &	fileName,
		std::string const &	mode = `"w"`
	)		const

inherited

Write the object to a regular FITS file.

Parameters

[in]	fileName	Name of the file to write to.
[in]	mode	If "w", any existing file with the given name will be overwritten. If "a", new HDUs will be appended to an existing file.

Definition at line 24 of file Persistable.cc.

                                                                                   {
     fits::Fits fitsfile(fileName, mode, fits::Fits::AUTO_CLOSE | fits::Fits::AUTO_CHECK);
     writeFits(fitsfile);
 }

Member Data Documentation

◆ _isCacheValid

template<typename ReturnT >

bool lsst::afw::math::Function< ReturnT >::_isCacheValid

mutableprotectedinherited

Definition at line 186 of file Function.h.

◆ _params

template<typename ReturnT >

std::vector<double> lsst::afw::math::Function< ReturnT >::_params

protectedinherited

Definition at line 185 of file Function.h.

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

/j/snowflake/release/lsstsw/stack/lsst-scipipe-0.7.0/Linux64/afw/22.0.1-42-gca6935d93+ba5e5ca3eb/include/lsst/afw/math/Function.h

Public Member Functions

Static Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Detailed Description

template<typename ReturnT> class lsst::afw::math::NullFunction1< ReturnT >

Member Typedef Documentation

◆ OutputArchiveHandle

Constructor & Destructor Documentation

◆ NullFunction1()

Member Function Documentation

◆ clone()

◆ computeCache()

◆ dynamicCast() [1/2]

◆ dynamicCast() [2/2]

◆ getNParameters()

◆ getParameter()

◆ getParameters()

◆ getPersistenceName()

◆ getPythonModule()

◆ isLinearCombination()

◆ isPersistable()

◆ readFits() [1/6]

◆ readFits() [2/6]

◆ readFits() [3/6]

◆ readFits() [4/6]

◆ readFits() [5/6]

◆ readFits() [6/6]

◆ setParameter()

◆ setParameters()

◆ toString()

◆ write()

◆ writeFits() [1/3]

◆ writeFits() [2/3]

◆ writeFits() [3/3]

Member Data Documentation

◆ _isCacheValid

◆ _params

template<typename ReturnT>
class lsst::afw::math::NullFunction1< ReturnT >