#include <AbstractProperty.h>

Inheritance diagram for TBTK::Property::AbstractProperty< DataType >:

Public Member Functions
unsigned int	getBlockSize () const

unsigned int	getSize () const

const std::vector< DataType > &	getData () const

std::vector< DataType > &	getDataRW ()

unsigned int	getDimensions () const

std::vector< int >	getRanges () const

int	getOffset (const Index &index) const

const IndexDescriptor &	getIndexDescriptor () const

bool	contains (const Index &index) const

void	reduce (const std::vector< Index > &targetPatterns, const std::vector< Index > &newPatterns)

void	hermitianConjugate ()

std::vector< SparseMatrix< DataType > >	toSparseMatrices (const Model &model) const

virtual const DataType &	operator() (const Index &index, unsigned int offset=0) const

virtual DataType &	operator() (const Index &index, unsigned int offset=0)

DataType &	operator() (const std::initializer_list< Subindex > &index)

const DataType &	operator() (const std::initializer_list< Subindex > &index) const

virtual const DataType &	operator() (unsigned int offset) const

virtual DataType &	operator() (unsigned int offset)

void	setAllowIndexOutOfBoundsAccess (bool allowIndexOutOfBoundsAccess)

void	setDefaultValue (const DataType &defaultValue)

void	replaceValues (const DataType &targetValue, const DataType &replacementValue)

virtual std::string	toString () const

virtual std::string	serialize (Mode mode) const

Public Member Functions inherited from TBTK::Serializable
template<>
std::string	serialize (const bool &data, Mode mode)

template<>
std::string	serialize (const double &data, Mode mode)

template<>
std::string	serialize (const std::complex< double > &data, Mode mode)

template<>
std::string	serialize (const int &data, Mode mode)

template<>
std::string	serialize (const unsigned int &data, Mode mode)

template<>
std::string	serialize (const SpinMatrix &data, Mode mode)

template<>
std::string	serialize (const Statistics &data, Mode mode)

template<>
std::string	serialize (const std::vector< std::complex< double >> &data, Mode mode)

template<>
int	deserialize (const std::string &serialization, Mode mode)

Protected Member Functions
	AbstractProperty ()

	AbstractProperty (unsigned int blockSize)

	AbstractProperty (unsigned int blockSize, const DataType *data)

	AbstractProperty (const std::vector< int > &ranges, unsigned int blockSize)

	AbstractProperty (const std::vector< int > &ranges, unsigned int blockSize, const DataType *data)

	AbstractProperty (const IndexTree &indexTree, unsigned int blockSize)

	AbstractProperty (const IndexTree &indexTree, unsigned int blockSize, const DataType *data)

	AbstractProperty (const AbstractProperty &abstractProperty)

	AbstractProperty (AbstractProperty &&abstractProperty)

	AbstractProperty (const std::string &serialization, Mode mode)

virtual	~AbstractProperty ()

AbstractProperty &	operator= (const AbstractProperty &abstractProperty)

AbstractProperty &	operator= (AbstractProperty &&abstractProperty)

AbstractProperty &	operator+= (const AbstractProperty &rhs)

AbstractProperty &	operator-= (const AbstractProperty &rhs)

AbstractProperty &	operator*= (const DataType &rhs)

AbstractProperty &	operator/= (const DataType &rhs)

Protected Member Functions inherited from TBTK::Property::Property
	Property ()

virtual	~Property ()

Additional Inherited Members
Public Types inherited from TBTK::Serializable
enum	Mode { Debug, Binary, XML, JSON }

Static Public Member Functions inherited from TBTK::Serializable
static bool	hasID (const std::string &serialization, Mode mode)

static std::string	getID (const std::string &serialization, Mode mode)

static std::string	extractComponent (const std::string &serialization, const std::string &containerID, const std::string &componentID, const std::string &componentName, Mode mode)

Static Protected Member Functions inherited from TBTK::Serializable
static bool	validate (const std::string &serialization, const std::string &id, Mode mode)

static std::string	getContent (const std::string &serialization, Mode mode)

static std::vector< std::string >	split (const std::string &content, Mode mode)

template<typename DataType >
static std::enable_if<!std::is_pointer< DataType >::value, std::string >::type	serialize (const DataType &data, Mode mode)

template<typename DataType >
static std::enable_if< std::is_pointer< DataType >::value, std::string >::type	serialize (const DataType &data, Mode mode)

template<typename DataType >
static DataType	deserialize (const std::string &serialization, Mode mode)

static std::string	extract (const std::string &serialization, Mode mode, std::string component)

Detailed Description

template<typename DataType>
class TBTK::Property::AbstractProperty< DataType >

Abstract Property class.

The AbstractProperty provides a generic storage structure for the property classes that inherit from it. For more information about specific Properties, see:

Custom storage structure

There are three different layers at which the storage structure can be customized to suit the needs for the specific property: the DataType, the block size, and the Index structure.

DataType

The DataType determines the data type of the individual data elements.

Block size

The data is group into blocks of equal size. It is up to the individual properties to determine the internal structure of these blocks. For example, EnergyResolvedProperties stores the data points for a range of energies in a block, while the Density has a single element per block.

Index structure

The Index structure determines how blocks are organized and accessed as a function of Indices.

IndexDescriptor::Format::None

Used for properties that has no Index structure. For example, the DOS.

IndexDescriptor::Format::Ranges

Used to store properties on a regular grid. It imposes an array like structure on the data that is easy to export to other softwares using, for example, the FileWriter.

IndexDescriptor::Format::Custom

Used to store properties for arbitrary combinations of Indices. When the Custom format is used, the data can be accessed using the function notation property(index) or property(index, n). Here index is an Index that selects a block, while n is a number that indexes into the given block.

Out-of-bounds access

By default, it is an error to access property(index, n) if the Index index is not included in the property. However, it is possible to configure the property such that out-of-bounds access is allowed. To allow for this we call

property.setAllowIndexOutOfBoundsAccess(true);

property.setDefaultValue(defaultValue);

The last call specifies the value to return when out-of-bounds access occurs.

It is recommended to not use out-of-bounds access frivolously since out-of-bounds access typically is a sign of an error in the code. Enabling out-of-bounds access can therefore mask faulty behavior.

Constructor & Destructor Documentation

◆ AbstractProperty() [1/10]

template<typename DataType >

TBTK::Property::AbstractProperty< DataType >::AbstractProperty

protected

Constructs an uninitialized AbstractProperty.

◆ AbstractProperty() [2/10]

template<typename DataType >

TBTK::Property::AbstractProperty< DataType >::AbstractProperty ( unsigned int blockSize )

protected

Constructs an AbstractProperty with a single data block (i.e. no Index structure).

Parameters

blockSize The number of data elements in the block.

◆ AbstractProperty() [3/10]

template<typename DataType >

TBTK::Property::AbstractProperty< DataType >::AbstractProperty	(	unsigned int	blockSize,
		const DataType *	data
	)

protected

Constructs an AbstractProperty with a single data block (i.e. no Index structure) and fills the internal memory with the data provided as input.

Parameters

blockSize	The number of data elements in the block.
data	The data stored on the raw format described in the detailed description of the class.

◆ AbstractProperty() [4/10]

template<typename DataType >

TBTK::Property::AbstractProperty< DataType >::AbstractProperty	(	const std::vector< int > &	ranges,
		unsigned int	blockSize
	)

protected

Constructs an AbstractProperty with the Ranges format.

Parameters

ranges	A list of upper limits for the ranges of the different dimensions. The nth dimension will have the range [0, ranges[n]).
blockSize	The number of data elements per block.

◆ AbstractProperty() [5/10]

template<typename DataType >

TBTK::Property::AbstractProperty< DataType >::AbstractProperty	(	const std::vector< int > &	ranges,
		unsigned int	blockSize,
		const DataType *	data
	)

protected

Constructs an AbstractProperty with the Ranges format and fills the internal memory with the data provided as input.

Parameters

ranges	A list of upper limits for the ranges of the different dimensions. The nth dimension will have the range [0, ranges[n]).
blockSize	The number of data elements per block.
data	The data stored on the raw format described in the detailed description of the class.

◆ AbstractProperty() [6/10]

template<typename DataType >

TBTK::Property::AbstractProperty< DataType >::AbstractProperty	(	const IndexTree &	indexTree,
		unsigned int	blockSize
	)

protected

Constructs and AbstractProperty with the Custom format.

Parameters

indexTree	IndexTree containing the Indices that the AbstractProperty should contain data for.
blockSize	The number of data elements per block.

◆ AbstractProperty() [7/10]

template<typename DataType >

TBTK::Property::AbstractProperty< DataType >::AbstractProperty	(	const IndexTree &	indexTree,
		unsigned int	blockSize,
		const DataType *	data
	)

protected

Constructs and AbstractProperty with the Custom format.

Parameters

indexTree	IndexTree containing the Indices that the AbstractProperty should contain data for.
blockSize	The number of data elements per block.
data	The data stored on the raw format described in the detailed description of the class.

◆ AbstractProperty() [8/10]

template<typename DataType >

TBTK::Property::AbstractProperty< DataType >::AbstractProperty ( const AbstractProperty< DataType > & abstractProperty )

protected

Copy constructor.

Parameters

abstractProperty AbstractProperty to copy.

◆ AbstractProperty() [9/10]

template<typename DataType >

TBTK::Property::AbstractProperty< DataType >::AbstractProperty ( AbstractProperty< DataType > && abstractProperty )

protected

Move constructor.

Parameters

abstractProperty AbstractProperty to move.

◆ AbstractProperty() [10/10]

template<typename DataType >

TBTK::Property::AbstractProperty< DataType >::AbstractProperty	(	const std::string &	serialization,
		Mode	mode
	)

inlineprotected

Constructor. Constructs the AbstractProperty from a serialization string.

Parameters

serialization	Serialization string from which to construct the AbstractProperty.
mode	Mode with which the string has been serialized.

◆ ~AbstractProperty()

template<typename DataType >

TBTK::Property::AbstractProperty< DataType >::~AbstractProperty

inlineprotectedvirtual

Destructor.

Member Function Documentation

◆ contains()

template<typename DataType >

bool TBTK::Property::AbstractProperty< DataType >::contains ( const Index & index ) const

inline

Returns true if the property contains data for the given index. [Only works for the Custom format.]

Parameters

index Index to check.

@raturn True if the Property contains data for the given Index.

◆ getBlockSize()

template<typename DataType >

unsigned int TBTK::Property::AbstractProperty< DataType >::getBlockSize

inline

Get block size.

Returns: The size per block.

◆ getData()

template<typename DataType >

const std::vector< DataType > & TBTK::Property::AbstractProperty< DataType >::getData

inline

Get data.

Returns: The data on the raw format described in the detailed description.

◆ getDataRW()

template<typename DataType >

std::vector< DataType > & TBTK::Property::AbstractProperty< DataType >::getDataRW

inline

Get data. Same as AbstractProperty::getData(), but with write access.

Returns: The data on the raw format described in the detailed description.

◆ getDimensions()

template<typename DataType >

unsigned int TBTK::Property::AbstractProperty< DataType >::getDimensions

inline

Get the dimension of the data. [Only works for the Ranges format.]

Returns: The dimension of the grid that the data is calculated on.

◆ getIndexDescriptor()

template<typename DataType >

const IndexDescriptor & TBTK::Property::AbstractProperty< DataType >::getIndexDescriptor

inline

Get IndexDescriptor.

Returns: The IndexDescriptor that is used internally to handle the different formats.

◆ getOffset()

template<typename DataType >

int TBTK::Property::AbstractProperty< DataType >::getOffset ( const Index & index ) const

inline

Get the memory offset that should be used to access the raw data for the given Index. [Only works for the Custom format.]

Parameters

index Index for which to get the offset.

Returns: The memory offset for the given Index.

◆ getRanges()

template<typename DataType >

std::vector< int > TBTK::Property::AbstractProperty< DataType >::getRanges

inline

Get the ranges for the dimensions of the density. [Only works for the Ranges format.]

Returns: A list of ranges for the different dimensions of the grid the data is calculated on.

◆ getSize()

template<typename DataType >

unsigned int TBTK::Property::AbstractProperty< DataType >::getSize

inline

Get size.

Returns: The total number of data elements in the Property. I.e. the number of blocks times the block size.

◆ hermitianConjugate()

template<typename DataType >

void TBTK::Property::AbstractProperty< DataType >::hermitianConjugate

inline

Turns the property into its Hermitian conjugate. Only works for the format Format::Custom. The Index structure also need to be such that every Index is a composit Index with two component Indices.

◆ operator()() [1/6]

template<typename DataType >

DataType & TBTK::Property::AbstractProperty< DataType >::operator()	(	const Index &	index,
		unsigned int	offset = `0`
	)

inlinevirtual

Function call operator. Returns the data element for the given Index and offset. By default the Property does not accept Indices that are not contained in the Property. However, AbstractProperty::setAllowIndexOutOfBounds(true) is called the Property will return the value set by a call to AbstractProperty::setDefaultVlue(). Note that although it is safe to write to out of bounds elements, doing so does not result in the value being stored in the Property. [Only works for Format::Custom].

Parameters

index	The Index to get the data for.
offset	The offset to apply inside the block for the given Index. If not specified, the first element is returned. The function can therefore be used without specifying the offset when Properties with only a single element per block. [Only works for the Custom format.]

Returns: The data element for the given Index and offset.

Reimplemented in TBTK::Property::WaveFunctions.

◆ operator()() [2/6]

template<typename DataType >

const DataType & TBTK::Property::AbstractProperty< DataType >::operator()	(	const Index &	index,
		unsigned int	offset = `0`
	)		const

inlinevirtual

Function call operator. Returns the data element for the given Index and offset. By default the Property does not accept Indices that are not contained in the Property. However, AbstractProperty::setAllowIndexOutOfBounds(true) is called the Property will return the value set by a call to AbstractProperty::setDefaultVlue(). [Only works for the Custom format.]

Parameters

index	The Index to get the data for.
offset	The offset to apply inside the block for the given Index. If not specified, the first element is returned. The function can therefore be used without specifying the offset when Properties with only a single element per block. [Only works for the Custom format.]

Returns: The data element for the given Index and offset.

Reimplemented in TBTK::Property::WaveFunctions.

◆ operator()() [3/6]

template<typename DataType >

DataType & TBTK::Property::AbstractProperty< DataType >::operator() ( const std::initializer_list< Subindex > & index )

inline

Alias for operator()(const Index &index, unsigned int offset = 0). Ensures that operator()(unsigned int offset) is not called when calling the function operator default offset and a single subindex index operator()({1}). Without this {1} would be cast to 1 instead of Index({1}).

Parameters

index The Index to get the data for.

Returns: The data element for the given Index.

◆ operator()() [4/6]

template<typename DataType >

const DataType & TBTK::Property::AbstractProperty< DataType >::operator() ( const std::initializer_list< Subindex > & index ) const

inline

Alias for operator()(const Index &index, unsigned int offset = 0). Ensures that operator()(unsigned int offset) is not called when calling the function operator default offset and a single subindex index operator()({1}). Without this {1} would be cast to 1 instead of Index({1}).

Parameters

index The Index to get the data for.

Returns: The data element for the given Index.

◆ operator()() [5/6]

template<typename DataType >

DataType & TBTK::Property::AbstractProperty< DataType >::operator() ( unsigned int offset )

inlinevirtual

Function call operator. Returns the data element for the given offset.

Parameters

offset The offset to apply. The offset is an index into the raw data.

Returns: The data element for the given offset.

◆ operator()() [6/6]

template<typename DataType >

const DataType & TBTK::Property::AbstractProperty< DataType >::operator() ( unsigned int offset ) const

inlinevirtual

Alias for operator()(const Index &index, unsigned int offset = 0). Ensures that operator()(unsigned int offset) is not called when calling the function operator default offset and a single subindex index operator()({1}). Without this {1} would be cast to 1 instead of Index({1}).

Parameters

index The Index to get the data for.

Returns: The data element for the given Index. Alias for operator()(const Index &index, unsigned int offset = 0). Ensures that operator()(unsigned int offset) is not called when calling the function operator default offset and a single subindex index operator()({1}). Without this {1} would be cast to 1 instead of Index({1}).

Parameters

index The Index to get the data for.

Returns: The data element for the given Index. Function call operator. Returns the data element for the given offset.

Parameters

offset The offset to apply. The offset is an index into the raw data.

Returns: The data element for the given offset.

◆ operator*=()

template<typename DataType >

AbstractProperty< DataType > & TBTK::Property::AbstractProperty< DataType >::operator*= ( const DataType & rhs )

inlineprotected

Multiplication assignment operator. Child classes that want to use this function must override this function and call the parents multiplication assignment operator after having performed checks whether the multiplication is possible, and before performing the multiplication of the child class parameters.

Parameters

The	value to multiply the left hand side by.

Returns: The left hand side after having been multiplied by the right hand side.

◆ operator+=()

template<typename DataType >

AbstractProperty< DataType > & TBTK::Property::AbstractProperty< DataType >::operator+= ( const AbstractProperty< DataType > & rhs )

inlineprotected

Addition assignment operator. Child classes that want to use this function must override this function and call the parents addition assignment operator after having performed checks whether the addition is possible, and before performing the addition of the child class parameters.

Parameters

The	AbstractProperty to be added to the left hand side.

Returns: The left hand side after the right hand side has been added.

◆ operator-=()

template<typename DataType >

AbstractProperty< DataType > & TBTK::Property::AbstractProperty< DataType >::operator-= ( const AbstractProperty< DataType > & rhs )

inlineprotected

Subtraction assignment operator. Child classes that want to use this function must override this function and call the parents subtraction assignment operator after having performed checks whether the subtraction is possible, and before performing the subtraction of the child class parameters.

Parameters

The	AbstractProperty to be subtracted from the left hand side.

Returns: The left hand side after the right hand side has been subtracted.

◆ operator/=()

template<typename DataType >

AbstractProperty< DataType > & TBTK::Property::AbstractProperty< DataType >::operator/= ( const DataType & rhs )

inlineprotected

Division assignment operator. Child classes that want to use this function must override this function and call the parents division assignment operator after having performed checks whether the division is possible, and before performing the division of the child class parameters.

Parameters

The	value to divide the left hand side by.

Returns: The left hand side after having been divided by the right hand side.

◆ operator=() [1/2]

template<typename DataType >

AbstractProperty< DataType > & TBTK::Property::AbstractProperty< DataType >::operator= ( AbstractProperty< DataType > && abstractProperty )

protected

Move assignment operator.

Parameters

rhs	AbstractProperty to assign to the left hand side.

Returns: Reference to the assigned AbstractProperty.

◆ operator=() [2/2]

template<typename DataType >

AbstractProperty< DataType > & TBTK::Property::AbstractProperty< DataType >::operator= ( const AbstractProperty< DataType > & abstractProperty )

protected

Assignment operator.

Parameters

rhs	AbstractProperty to assign to the left hand side.

Returns: Reference to the assigned AbstractProperty.

◆ reduce()

template<typename DataType >

void TBTK::Property::AbstractProperty< DataType >::reduce	(	const std::vector< Index > &	targetPatterns,
		const std::vector< Index > &	newPatterns
	)

inline

Reduces the size of the Property by only keeping values for indices that match the given target patterns. If a matching target pattern exists for a given value, the value will be stored with an Index that matches a corresponding new pattern. E.g., assume the target patterns are { {0, IDX_ALL_0, IDX_ALL_1, IDX_ALL_1}, {1, IDX_ALL_0, IDX_ALL_0} } and the new patterns are { {0, IDX_ALL_0, IDX_ALL_1}, {1, IDX_ALL_0} }. Then the data for indices such as {0, 1, 2, 3} and {1, 2, 3} will be droped since the two last subindices are not the same, which is required by both of the target patterns. However, the data for the indices {0, 1, 2, 2} and {1, 2, 2} will be kept and available through the new indices {0, 1, 2} and {1, 2}, respectively. More specifically, {0, 1, 2, 2} match the first pattern and {1, 2, 2} matches the second pattern. {0, 1, 2, 3} is therefore kept and transformed to the form {0, IDX_ALL_0, IDX_ALL_1}, while {1, 2, 2} is kept and transformed to the form {1, IDX_ALL_0}.

Parameters

targetPatterns	List of patterns for indices to keep.
newPatterns	List of new patterns to convert the preserved indices to.

◆ replaceValues()

template<typename DataType >

void TBTK::Property::AbstractProperty< DataType >::replaceValues	(	const DataType &	targetValue,
		const DataType &	replacementValue
	)

inline

Replace all values with a given target value by a given replacement value. Can be used to for example replace NaN and inf by finite numbers.

Parameters

targetValue	The value to replace.
replacementValue.	The value to replace with.

◆ serialize()

template<typename DataType >

std::string TBTK::Property::AbstractProperty< DataType >::serialize ( Mode mode ) const

inlinevirtual

Implements Serializable::serialize().

Implements TBTK::Serializable.

Reimplemented in TBTK::Property::EnergyResolvedProperty< DataType >, TBTK::Property::EnergyResolvedProperty< SpinMatrix >, TBTK::Property::EnergyResolvedProperty< double >, TBTK::Property::EnergyResolvedProperty< std::complex< double > >, TBTK::Property::LDOS, TBTK::Property::Density, TBTK::Property::DOS, TBTK::Property::SpinPolarizedLDOS, TBTK::Property::EigenValues, TBTK::Property::WaveFunctions, and TBTK::Property::Magnetization.

◆ setAllowIndexOutOfBoundsAccess()

template<typename DataType >

void TBTK::Property::AbstractProperty< DataType >::setAllowIndexOutOfBoundsAccess ( bool allowIndexOutOfBoundsAccess )

inline

Set whether the access of data elements for Indices that are not contained in the Property is allowed or not when using the function operator AbstractProperty::operator(). If enabled, remember to also initialize the value that is used for out of bounds access using AbstractProperty::setDefaultValue(). [Only meaningful for the Custom format.]

Parameters

allowIndexOutOfBoundsAccess True to enable out of bounds access.

◆ setDefaultValue()

template<typename DataType >

void TBTK::Property::AbstractProperty< DataType >::setDefaultValue ( const DataType & defaultValue )

inline

Set the value that is returned when accessing indices not contained in the Property using the function operator AbstractProperty::operator(). Only used if AbstractProperty::setAllowIndexOutOfBoundsAccess(true) is called. [Only meaningful for the Custom format.]

Parameters

defaultValue The value that will be returned for out of bounds access.

◆ toSparseMatrices()

template<typename DataType >

std::vector< SparseMatrix< DataType > > TBTK::Property::AbstractProperty< DataType >::toSparseMatrices ( const Model & model ) const

inline

Converts the matrix to a set of SparseMatrices . This only works for Properties on the Format::Custom. In addition, the Index structure has to be such that every Index is a composit Index with exactly two component Indices.

Parameters

model A model that determines the maping from the physical indices in the Property and the linear indices in the matrix representation.

Returns: A vector of SparseMatrices . One SparseMatrix for every block index.

◆ toString()

template<typename DataType >

std::string TBTK::Property::AbstractProperty< DataType >::toString

inlinevirtual

Implements Serializable::toString().

Implements TBTK::Streamable.

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

/TBTK/Lib/include/TBTK/Property/AbstractProperty.h

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

template<typename DataType> class TBTK::Property::AbstractProperty< DataType >

Custom storage structure

DataType

Block size

Index structure

IndexDescriptor::Format::None

IndexDescriptor::Format::Ranges

IndexDescriptor::Format::Custom

Out-of-bounds access

Constructor & Destructor Documentation

◆ AbstractProperty() [1/10]

◆ AbstractProperty() [2/10]

◆ AbstractProperty() [3/10]

◆ AbstractProperty() [4/10]

◆ AbstractProperty() [5/10]

◆ AbstractProperty() [6/10]

◆ AbstractProperty() [7/10]

◆ AbstractProperty() [8/10]

◆ AbstractProperty() [9/10]

◆ AbstractProperty() [10/10]

◆ ~AbstractProperty()

Member Function Documentation

◆ contains()

◆ getBlockSize()

◆ getData()

◆ getDataRW()

◆ getDimensions()

◆ getIndexDescriptor()

◆ getOffset()

◆ getRanges()

◆ getSize()

◆ hermitianConjugate()

◆ operator()() [1/6]

◆ operator()() [2/6]

◆ operator()() [3/6]

◆ operator()() [4/6]

◆ operator()() [5/6]

◆ operator()() [6/6]

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ reduce()

◆ replaceValues()

◆ serialize()

◆ setAllowIndexOutOfBoundsAccess()

◆ setDefaultValue()

◆ toSparseMatrices()

◆ toString()

template<typename DataType>
class TBTK::Property::AbstractProperty< DataType >