#include <itkSymmetricSecondRankTensor.h>

Inheritance diagram for itk::SymmetricSecondRankTensor< TComponent, NDimension >:

Collaboration diagram for itk::SymmetricSecondRankTensor< TComponent, NDimension >:

Detailed Description

template<typename TComponent, unsigned int NDimension = 3>
class itk::SymmetricSecondRankTensor< TComponent, NDimension >

Represent a symmetric tensor of second rank.

This class implements a ND symmetric tensor of second rank.

Since SymmetricSecondRankTensor is a subclass of FixedArray, you can access its components as:

using TensorPixelType = itk::SymmetricSecondRankTensor< float >; TensorPixelType tensor;

tensor[0] = 1.233; tensor[1] = 1.456;

for convenience the indexed access is also available as

tensor(0,0) = 1.233; tensor(2,0) = 1.233;

The Tensor in principle represents a NxN matrix, but given that it is always symmetric the representation can be compacted into a N*(N+1)/2 elements array that derives from the itk::FixedArray<T>

Author: Jeffrey Duda from School of Engineering at University of Pennsylvania; Torsten Rohlfing from SRI International Neuroscience Program.

This class was mostly based on files that Jeffrey Duda, Torsten Rohlfing and Martin Styner contributed to the ITK users list during a discussion on support for DiffusionTensorImages. The funding for creating this class was largely provided by NAMIC (National Alliance for Medical Image Computing) (http://www.na-mic.org). A discussion on the design of this class can be found in the WIKI pages of NAMIC:

http://www.na-mic.org/Wiki/index.php/NAMIC_Wiki:DTI:ITK-DiffusionTensorPixelType

See Also: DiffusionTensor3D

Examples:: SphinxExamples/src/Nonunit/Review/SegmentBloodVesselsWithMultiScaleHessianBasedMeasure/Code.cxx.

Definition at line 75 of file itkSymmetricSecondRankTensor.h.

Public Types
using	AccumulateValueType = typename NumericTraits< ValueType >::RealType

using	BaseArray = FixedArray< TComponent, Self::InternalDimension >

typedef ComponentType	ComponentArrayType [Self::InternalDimension]

using	ComponentType = TComponent

using	EigenValuesArrayType = FixedArray< TComponent, NDimension >

using	EigenVectorsMatrixType = Matrix< TComponent, NDimension, NDimension >

using	MatrixType = Matrix< TComponent, NDimension, NDimension >

using	RealValueType = typename NumericTraits< ValueType >::RealType

using	Self = SymmetricSecondRankTensor

using	Superclass = FixedArray< TComponent, NDimension *(NDimension+1)/2 >

using	SymmetricEigenAnalysisType = SymmetricEigenAnalysisFixedDimension< Dimension, MatrixType, EigenValuesArrayType, EigenVectorsMatrixType >

using	ValueType = typename Superclass::ValueType

Public Types inherited from itk::FixedArray< TComponent, NDimension *(NDimension+1)/2 >
typedef ValueType	CArray [VLength]

using	const_pointer = const ValueType *

using	const_reference = const ValueType &

using	ConstIterator = const ValueType *

using	Iterator = ValueType *

using	pointer = ValueType *

using	reference = ValueType &

using	SizeType = unsigned int

using	ValueType = TComponent

Public Member Functions
void	ComputeEigenAnalysis (EigenValuesArrayType &eigenValues, EigenVectorsMatrixType &eigenVectors) const

void	ComputeEigenValues (EigenValuesArrayType &eigenValues) const

ComponentType	GetNthComponent (int c) const

AccumulateValueType	GetTrace () const

ValueType &	operator() (unsigned int row, unsigned int col)

const ValueType &	operator() (unsigned int row, unsigned int col) const

Self	operator* (const RealValueType &scalar) const

const Self &	operator*= (const RealValueType &scalar)

Self	operator+ (const Self &vec) const

const Self &	operator+= (const Self &vec)

Self	operator- (const Self &vec) const

const Self &	operator-= (const Self &vec)

Self	operator/ (const RealValueType &scalar) const

const Self &	operator/= (const RealValueType &scalar)

Self &	operator= (const ComponentType &r)

Self &	operator= (const ComponentArrayType r)

MatrixType	PostMultiply (const MatrixType &m) const

MatrixType	PreMultiply (const MatrixType &m) const

void	SetIdentity ()

void	SetNthComponent (int c, const ComponentType &v)

	SymmetricSecondRankTensor (const ComponentType &r)

template<typename TCoordRepB >
	SymmetricSecondRankTensor (const SymmetricSecondRankTensor< TCoordRepB, NDimension > &pa)

	SymmetricSecondRankTensor (const ComponentArrayType r)


	SymmetricSecondRankTensor ()

	SymmetricSecondRankTensor (const SymmetricSecondRankTensor &)=default

	SymmetricSecondRankTensor (SymmetricSecondRankTensor &&)=default

SymmetricSecondRankTensor &	operator= (const SymmetricSecondRankTensor &)=default

SymmetricSecondRankTensor &	operator= (SymmetricSecondRankTensor &&)=default

	~SymmetricSecondRankTensor ()=default


template<typename TCoordRepB >
Self &	operator= (const SymmetricSecondRankTensor< TCoordRepB, NDimension > &pa)


template<typename TMatrixValueType >
Self	Rotate (const Matrix< TMatrixValueType, NDimension, NDimension > &m) const

template<typename TMatrixValueType >
Self	Rotate (const vnl_matrix_fixed< TMatrixValueType, NDimension, NDimension > &m) const

template<typename TMatrixValueType >
Self	Rotate (const vnl_matrix< TMatrixValueType > &m) const

Public Member Functions inherited from itk::FixedArray< TComponent, NDimension *(NDimension+1)/2 >
Iterator	Begin ()

ConstIterator	Begin () const

Iterator	End ()

ConstIterator	End () const

void	Fill (const ValueType &)

	FixedArray (const TScalarValue *r)

ValueType *	GetDataPointer ()

const ValueType *	GetDataPointer () const

bool	operator!= (const FixedArray &r) const

FixedArray &	operator= (const ValueType r[VLength])

bool	operator== (const FixedArray &r) const

ReverseIterator	rBegin ()

ConstReverseIterator	rBegin () const

ReverseIterator	rEnd ()

ConstReverseIterator	rEnd () const

SizeType	Size () const

void	swap (FixedArray &other)

	FixedArray ()=default

	FixedArray (const FixedArray &)=default

	FixedArray (FixedArray &&)=default

FixedArray &	operator= (const FixedArray &)=default

FixedArray &	operator= (FixedArray &&)=default

	~FixedArray ()=default

	FixedArray (const ValueType r[VLength])

	FixedArray (const ValueType &)

	FixedArray (const FixedArray< TFixedArrayValueType, VLength > &r)

FixedArray &	operator= (const FixedArray< TFixedArrayValueType, VLength > &r)

reference	operator[] (short index)

const_reference	operator[] (short index) const

reference	operator[] (unsigned short index)

const_reference	operator[] (unsigned short index) const

reference	operator[] (int index)

const_reference	operator[] (int index) const

reference	operator[] (unsigned int index)

const_reference	operator[] (unsigned int index) const

reference	operator[] (long index)

const_reference	operator[] (long index) const

reference	operator[] (unsigned long index)

const_reference	operator[] (unsigned long index) const

reference	operator[] (long long index)

const_reference	operator[] (long long index) const

reference	operator[] (unsigned long long index)

const_reference	operator[] (unsigned long long index) const

void	SetElement (unsigned short index, const_reference value)

const_reference	GetElement (unsigned short index) const

Static Public Member Functions
static unsigned int	GetNumberOfComponents ()

Static Public Member Functions inherited from itk::FixedArray< TComponent, NDimension *(NDimension+1)/2 >
static FixedArray	Filled (const ValueType &)

Static Public Attributes
static constexpr unsigned int	Dimension = NDimension

static constexpr unsigned int	InternalDimension = NDimension * ( NDimension + 1 ) / 2

Static Public Attributes inherited from itk::FixedArray< TComponent, NDimension *(NDimension+1)/2 >
static constexpr unsigned int	Dimension

static constexpr unsigned int	Length