#include <itkSymmetricSecondRankTensor.h>

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

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

Public Types
typedef NumericTraits < ValueType >::RealType	AccumulateValueType
typedef FixedArray< TComponent, itkGetStaticConstMacro(InternalDimension) >	BaseArray
typedef ComponentType	ComponentArrayType [itkGetStaticConstMacro(InternalDimension)]
typedef TComponent	ComponentType
typedef FixedArray< TComponent, NDimension >	EigenValuesArrayType
typedef Matrix< TComponent, NDimension, NDimension >	EigenVectorsMatrixType
typedef Matrix< TComponent, NDimension, NDimension >	MatrixType
typedef NumericTraits < ValueType >::RealType	RealValueType
typedef SymmetricSecondRankTensor	Self
typedef FixedArray< TComponent, NDimension *(NDimension+1)/2 >	Superclass
typedef SymmetricEigenAnalysis < MatrixType, EigenValuesArrayType, EigenVectorsMatrixType >	SymmetricEigenAnalysisType
typedef Superclass::ValueType	ValueType
Public Types inherited from itk::FixedArray< TComponent, NDimension *(NDimension+1)/2 >
typedef ValueType	CArray [VLength]
typedef const ValueType *	const_pointer
typedef const ValueType &	const_reference
typedef const ValueType *	ConstIterator
typedef ValueType *	Iterator
typedef ValueType *	pointer
typedef ValueType &	reference
typedef unsigned int	SizeType

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

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 &)
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
	FixedArray ()
	FixedArray (const ValueType r[VLength])
	FixedArray (const ValueType &r)
	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 const unsigned int	Dimension = NDimension
static const unsigned int	InternalDimension = ( NDimension * ( NDimension + 1 ) / 2 )
Static Public Attributes inherited from itk::FixedArray< TComponent, NDimension *(NDimension+1)/2 >
static const unsigned int	Length

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:

typedef itk::SymmetricSecondRankTensor< float > TensorPixelType; 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

Definition at line 75 of file itkSymmetricSecondRankTensor.h.

Member Typedef Documentation

template<typename TComponent, unsigned int NDimension = 3>

typedef NumericTraits< ValueType >::RealType itk::SymmetricSecondRankTensor< TComponent, NDimension >::AccumulateValueType

Reimplemented in itk::DiffusionTensor3D< TComponent >.

Definition at line 102 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef FixedArray< TComponent, itkGetStaticConstMacro(InternalDimension) > itk::SymmetricSecondRankTensor< TComponent, NDimension >::BaseArray

Convenience typedefs.

Definition at line 90 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef ComponentType itk::SymmetricSecondRankTensor< TComponent, NDimension >::ComponentArrayType[itkGetStaticConstMacro(InternalDimension)]

Reimplemented in itk::DiffusionTensor3D< TComponent >.

Definition at line 118 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef TComponent itk::SymmetricSecondRankTensor< TComponent, NDimension >::ComponentType

Define the component type.

Reimplemented in itk::DiffusionTensor3D< TComponent >.

Definition at line 100 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef FixedArray< TComponent, NDimension > itk::SymmetricSecondRankTensor< TComponent, NDimension >::EigenValuesArrayType

Array of eigen-values.

Reimplemented in itk::DiffusionTensor3D< TComponent >.

Definition at line 93 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef Matrix< TComponent, NDimension, NDimension > itk::SymmetricSecondRankTensor< TComponent, NDimension >::EigenVectorsMatrixType

Reimplemented in itk::DiffusionTensor3D< TComponent >.

Definition at line 97 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef Matrix< TComponent, NDimension, NDimension > itk::SymmetricSecondRankTensor< TComponent, NDimension >::MatrixType

Matrix of eigen-vectors.

Definition at line 96 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef NumericTraits< ValueType >::RealType itk::SymmetricSecondRankTensor< TComponent, NDimension >::RealValueType

Reimplemented in itk::DiffusionTensor3D< TComponent >.

Definition at line 103 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef SymmetricSecondRankTensor itk::SymmetricSecondRankTensor< TComponent, NDimension >::Self

Standard class typedefs.

Reimplemented in itk::DiffusionTensor3D< TComponent >.

Definition at line 80 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef FixedArray< TComponent, NDimension *( NDimension + 1 ) / 2 > itk::SymmetricSecondRankTensor< TComponent, NDimension >::Superclass

Reimplemented in itk::DiffusionTensor3D< TComponent >.

Definition at line 81 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef SymmetricEigenAnalysis< MatrixType, EigenValuesArrayType, EigenVectorsMatrixType > itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricEigenAnalysisType

Definition at line 106 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

typedef Superclass::ValueType itk::SymmetricSecondRankTensor< TComponent, NDimension >::ValueType

The element type stored at each location in the FixedArray.

Reimplemented from itk::FixedArray< TComponent, NDimension *(NDimension+1)/2 >.

Reimplemented in itk::DiffusionTensor3D< TComponent >.

Definition at line 101 of file itkSymmetricSecondRankTensor.h.

Constructor & Destructor Documentation

template<typename TComponent, unsigned int NDimension = 3>

itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricSecondRankTensor ( )

inline

Default constructor has nothing to do.

Definition at line 109 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricSecondRankTensor ( const ComponentType & r )

inline

Definition at line 111 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

template<typename TCoordRepB >

itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricSecondRankTensor ( const SymmetricSecondRankTensor< TCoordRepB, NDimension > & pa )

inline

Constructor to enable casting...

Definition at line 115 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricSecondRankTensor ( const ComponentArrayType r )

inline

Pass-through constructor for the Array base class.

Definition at line 121 of file itkSymmetricSecondRankTensor.h.

Member Function Documentation

template<typename TComponent, unsigned int NDimension = 3>

void itk::SymmetricSecondRankTensor< TComponent, NDimension >::ComputeEigenAnalysis	(	EigenValuesArrayType &	eigenValues,
		EigenVectorsMatrixType &	eigenVectors
	)		const

Return an array containing EigenValues, and a matrix containing Eigen vectors.

template<typename TComponent, unsigned int NDimension = 3>

void itk::SymmetricSecondRankTensor< TComponent, NDimension >::ComputeEigenValues ( EigenValuesArrayType & eigenValues ) const

Return an array containing EigenValues.

template<typename TComponent, unsigned int NDimension = 3>

ComponentType itk::SymmetricSecondRankTensor< TComponent, NDimension >::GetNthComponent ( int c ) const

inline

Return the value for the Nth component.

Definition at line 163 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

static unsigned int itk::SymmetricSecondRankTensor< TComponent, NDimension >::GetNumberOfComponents ( )

inlinestatic

Return the number of components.

Definition at line 157 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

AccumulateValueType itk::SymmetricSecondRankTensor< TComponent, NDimension >::GetTrace ( ) const

Get Trace value

Reimplemented in itk::DiffusionTensor3D< TComponent >.

template<typename TComponent, unsigned int NDimension = 3>

ValueType& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator()	(	unsigned int	row,
		unsigned int	col
	)

Matrix notation, in const and non-const forms.

template<typename TComponent, unsigned int NDimension = 3>

const ValueType& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator()	(	unsigned int	row,
		unsigned int	col
	)		const

template<typename TComponent, unsigned int NDimension = 3>

Self itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator* ( const RealValueType & scalar ) const

Arithmetic operations between tensors and scalars

template<typename TComponent, unsigned int NDimension = 3>

const Self& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator*= ( const RealValueType & scalar )

template<typename TComponent, unsigned int NDimension = 3>

Self itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator+ ( const Self & vec ) const

Aritmetic operations between pixels. Return a new SymmetricSecondRankTensor.

template<typename TComponent, unsigned int NDimension = 3>

const Self& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator+= ( const Self & vec )

template<typename TComponent, unsigned int NDimension = 3>

Self itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator- ( const Self & vec ) const

template<typename TComponent, unsigned int NDimension = 3>

const Self& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator-= ( const Self & vec )

template<typename TComponent, unsigned int NDimension = 3>

Self itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator/ ( const RealValueType & scalar ) const

template<typename TComponent, unsigned int NDimension = 3>

const Self& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator/= ( const RealValueType & scalar )

template<typename TComponent, unsigned int NDimension = 3>

template<typename TCoordRepB >

Self& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator= ( const SymmetricSecondRankTensor< TCoordRepB, NDimension > & pa )

inline

Templated Pass-through assignment for the Array base class.

Definition at line 125 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

Self& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator= ( const ComponentType & r )

Pass-through assignment operator for the Array base class.

Reimplemented in itk::DiffusionTensor3D< TComponent >.

template<typename TComponent, unsigned int NDimension = 3>

Self& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator= ( const ComponentArrayType r )

template<typename TComponent, unsigned int NDimension = 3>

MatrixType itk::SymmetricSecondRankTensor< TComponent, NDimension >::PostMultiply ( const MatrixType & m ) const

Post-Multiply by a Matrix as ResultingMatrix = ThisTensor * Matrix.

template<typename TComponent, unsigned int NDimension = 3>

MatrixType itk::SymmetricSecondRankTensor< TComponent, NDimension >::PreMultiply ( const MatrixType & m ) const

Pre-Multiply by a Matrix as ResultingMatrix = Matrix * ThisTensor.

template<typename TComponent, unsigned int NDimension = 3>

template<typename TMatrixValueType >

Self itk::SymmetricSecondRankTensor< TComponent, NDimension >::Rotate ( const Matrix< TMatrixValueType, NDimension, NDimension > & m ) const

Returns the tensor rotated by the provided matrix. ResultingTensor = Matrix * ThisTensor * Matrix.GetTranspose()

Referenced by itk::SymmetricSecondRankTensor< TComponent, 3 >::Rotate().

template<typename TComponent, unsigned int NDimension = 3>

template<typename TMatrixValueType >

Self itk::SymmetricSecondRankTensor< TComponent, NDimension >::Rotate ( const vnl_matrix_fixed< TMatrixValueType, NDimension, NDimension > & m ) const

inline

Returns the tensor rotated by the provided matrix. ResultingTensor = Matrix * ThisTensor * Matrix.GetTranspose()

Definition at line 194 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

template<typename TMatrixValueType >

Self itk::SymmetricSecondRankTensor< TComponent, NDimension >::Rotate ( const vnl_matrix< TMatrixValueType > & m ) const

inline

Returns the tensor rotated by the provided matrix. ResultingTensor = Matrix * ThisTensor * Matrix.GetTranspose()

Definition at line 199 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

void itk::SymmetricSecondRankTensor< TComponent, NDimension >::SetIdentity ( )

Set the tensor to an identity tensor. This has 1 in its diagonal elements and zero elsewhere.

template<typename TComponent, unsigned int NDimension = 3>

void itk::SymmetricSecondRankTensor< TComponent, NDimension >::SetNthComponent	(	int	c,
		const ComponentType &	v
	)

inline

Set the Nth component to v.

Definition at line 166 of file itkSymmetricSecondRankTensor.h.

Member Data Documentation

template<typename TComponent, unsigned int NDimension = 3>

const unsigned int itk::SymmetricSecondRankTensor< TComponent, NDimension >::Dimension = NDimension

static

Dimension of the vector space.

Reimplemented from itk::FixedArray< TComponent, NDimension *(NDimension+1)/2 >.

Definition at line 84 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>

const unsigned int itk::SymmetricSecondRankTensor< TComponent, NDimension >::InternalDimension = ( NDimension * ( NDimension + 1 ) / 2 )

static

Dimension of the vector space.

Definition at line 85 of file itkSymmetricSecondRankTensor.h.

Referenced by itk::SymmetricSecondRankTensor< TComponent, 3 >::GetNumberOfComponents().

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

itkSymmetricSecondRankTensor.h

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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