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itk::SymmetricSecondRankTensor

itk::SymmetricSecondRankTensor< TComponent, NDimension > Class Template Reference
[Image Representation Objects, Objects Related to Tensor Images, Geometry Representation Objects]

#include <itkSymmetricSecondRankTensor.h>

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List of all members.

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 74 of file itkSymmetricSecondRankTensor.h.


Public Types

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

Public Member Functions

void ComputeEigenAnalysis (EigenValuesArrayType &eigenValues, EigenVectorsMatrixType &eigenVectors) const
void ComputeEigenValues (EigenValuesArrayType &eigenValues) const
ComponentType GetNthComponent (int c) const
AccumulateValueType GetTrace () const
 itkStaticConstMacro (Dimension, unsigned int, VLength)
 itkStaticConstMacro (Length, unsigned int, VLength)
Self PostMultiply (const MatrixType &m) const
Self PreMultiply (const MatrixType &m) const
void SetIdentity ()
void SetNthComponent (int c, const ComponentType &v)
 SymmetricSecondRankTensor (const ComponentType &r)
 SymmetricSecondRankTensor ()
ConstIterator Begin () const
Iterator Begin ()
ConstIterator End () const
Iterator End ()
void Fill (const ValueType &)
ConstReverseIterator rBegin () const
ReverseIterator rBegin ()
ConstReverseIterator rEnd () const
ReverseIterator rEnd ()
SizeType Size () const
const ValueType * GetDataPointer () const
ValueType * GetDataPointer ()
const_reference GetElement (unsigned short index) const
void SetElement (unsigned short index, const_reference value)
 itkStaticConstMacro (InternalDimension, unsigned int, NDimension *(NDimension+1)/2)
 itkStaticConstMacro (Dimension, unsigned int, NDimension)
bool operator!= (const FixedArray &r) const
bool operator== (const FixedArray &r) const
const ValueType & operator() (unsigned int row, unsigned int col) const
ValueType & operator() (unsigned int row, unsigned int col)
Self operator* (const RealValueType &scalar) const
const Self & operator*= (const RealValueType &scalar)
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 ComponentArrayType r)
Self & operator= (const ComponentType &r)
Self & operator= (const Self &r)
const_reference operator[] (unsigned long index) const
reference operator[] (unsigned long index)
const_reference operator[] (long index) const
reference operator[] (long index)
const_reference operator[] (unsigned int index) const
reference operator[] (unsigned int index)
const_reference operator[] (int index) const
reference operator[] (int index)
const_reference operator[] (unsigned short index) const
reference operator[] (unsigned short index)
const_reference operator[] (short index) const
reference operator[] (short index)
 SymmetricSecondRankTensor (const ComponentArrayType r)
 SymmetricSecondRankTensor (const Self &r)

Static Public Member Functions

static FixedArray Filled (const ValueType &)
static unsigned int GetNumberOfComponents ()

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 101 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 89 of file itkSymmetricSecondRankTensor.h.

typedef ValueType itk::FixedArray< TComponent , VLength >::CArray[VLength] [inherited]

A type representing the C-array version of this FixedArray.

Definition at line 77 of file itkFixedArray.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 112 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 99 of file itkSymmetricSecondRankTensor.h.

typedef const ValueType* itk::FixedArray< TComponent , VLength >::const_pointer [inherited]

A const pointer to the ValueType.

Definition at line 125 of file itkFixedArray.h.

typedef const ValueType& itk::FixedArray< TComponent , VLength >::const_reference [inherited]

A const reference to the ValueType.

Definition at line 131 of file itkFixedArray.h.

typedef const ValueType* itk::FixedArray< TComponent , VLength >::ConstIterator [inherited]

A const iterator through the array.

Definition at line 83 of file itkFixedArray.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 92 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 96 of file itkSymmetricSecondRankTensor.h.

typedef ValueType* itk::FixedArray< TComponent , VLength >::Iterator [inherited]

An iterator through the array.

Definition at line 80 of file itkFixedArray.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 95 of file itkSymmetricSecondRankTensor.h.

typedef ValueType* itk::FixedArray< TComponent , VLength >::pointer [inherited]

A pointer to the ValueType.

Definition at line 122 of file itkFixedArray.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 102 of file itkSymmetricSecondRankTensor.h.

typedef ValueType& itk::FixedArray< TComponent , VLength >::reference [inherited]

A reference to the ValueType.

Definition at line 128 of file itkFixedArray.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 79 of file itkSymmetricSecondRankTensor.h.

typedef unsigned int itk::FixedArray< TComponent , VLength >::SizeType [inherited]

Definition at line 133 of file itkFixedArray.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 80 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>
typedef SymmetricEigenAnalysis< MatrixType, EigenValuesArrayType, EigenVectorsMatrixType > itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricEigenAnalysisType

Definition at line 105 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 100 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 108 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>
itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricSecondRankTensor ( const ComponentType &  r  )  [inline]

Definition at line 110 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>
itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricSecondRankTensor ( const Self &  r  )  [inline]

Pass-through constructor for the Array base class.

Definition at line 115 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>
itk::SymmetricSecondRankTensor< TComponent, NDimension >::SymmetricSecondRankTensor ( const ComponentArrayType  r  )  [inline]

Definition at line 116 of file itkSymmetricSecondRankTensor.h.

Member Function Documentation

ConstIterator itk::FixedArray< TComponent , VLength >::Begin ( void   )  const [inherited]

Iterator itk::FixedArray< TComponent , VLength >::Begin ( void   )  [inherited]

Get various iterators to the array.

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.

ConstIterator itk::FixedArray< TComponent , VLength >::End ( void   )  const [inherited]

Iterator itk::FixedArray< TComponent , VLength >::End ( void   )  [inherited]

void itk::FixedArray< TComponent , VLength >::Fill ( const ValueType &   )  [inherited]

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

static FixedArray itk::FixedArray< TComponent , VLength >::Filled ( const ValueType &   )  [static, inherited]

const ValueType* itk::FixedArray< TComponent , VLength >::GetDataPointer (  )  const [inline, inherited]

Definition at line 218 of file itkFixedArray.h.

ValueType* itk::FixedArray< TComponent , VLength >::GetDataPointer (  )  [inline, inherited]

Return a pointer to the data.

Definition at line 217 of file itkFixedArray.h.

const_reference itk::FixedArray< TComponent , VLength >::GetElement ( unsigned short  index  )  const [inline, inherited]

Definition at line 213 of file itkFixedArray.h.

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 146 of file itkSymmetricSecondRankTensor.h.

template<typename TComponent, unsigned int NDimension = 3>
static unsigned int itk::SymmetricSecondRankTensor< TComponent, NDimension >::GetNumberOfComponents (  )  [inline, static]

Return the number of components.

Definition at line 140 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 >.

itk::FixedArray< TComponent , VLength >::itkStaticConstMacro ( Dimension  ,
unsigned  int,
VLength   
) [inherited]

Dimension constant

itk::FixedArray< TComponent , VLength >::itkStaticConstMacro ( Length  ,
unsigned  int,
VLength   
) [inherited]

Length constant

template<typename TComponent, unsigned int NDimension = 3>
itk::SymmetricSecondRankTensor< TComponent, NDimension >::itkStaticConstMacro ( InternalDimension  ,
unsigned  int,
NDimension *(NDimension+1)/  2 
)

template<typename TComponent, unsigned int NDimension = 3>
itk::SymmetricSecondRankTensor< TComponent, NDimension >::itkStaticConstMacro ( Dimension  ,
unsigned  int,
NDimension   
)

Dimension of the vector space.

bool itk::FixedArray< TComponent , VLength >::operator!= ( const FixedArray< TComponent, NDimension *(NDimension+1)/2 > &  r  )  const [inline, inherited]

Definition at line 189 of file itkFixedArray.h.

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>
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>
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  ) 

Arithmetic operations between tensors and scalars

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  ) 

Aritmetic operations between pixels. Return a new SymmetricSecondRankTensor.

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  ) 

Aritmetic operations between pixels. Return a new SymmetricSecondRankTensor.

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  ) 

Arithmetic operations between tensors and scalars

template<typename TComponent, unsigned int NDimension = 3>
Self& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator= ( const ComponentArrayType  r  ) 

template<typename TComponent, unsigned int NDimension = 3>
Self& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator= ( const ComponentType &  r  ) 

template<typename TComponent, unsigned int NDimension = 3>
Self& itk::SymmetricSecondRankTensor< TComponent, NDimension >::operator= ( const Self &  r  ) 

Pass-through assignment operator for the Array base class.

bool itk::FixedArray< TComponent , VLength >::operator== ( const FixedArray< TComponent, NDimension *(NDimension+1)/2 > &  r  )  const [inherited]

Operators == and != are used to compare whether two arrays are equal. Note that arrays are equal when the number of components (size) is the same, and each component value is equal.

const_reference itk::FixedArray< TComponent , VLength >::operator[] ( unsigned long  index  )  const [inline, inherited]

Definition at line 207 of file itkFixedArray.h.

reference itk::FixedArray< TComponent , VLength >::operator[] ( unsigned long  index  )  [inline, inherited]

Definition at line 206 of file itkFixedArray.h.

const_reference itk::FixedArray< TComponent , VLength >::operator[] ( long  index  )  const [inline, inherited]

Definition at line 205 of file itkFixedArray.h.

reference itk::FixedArray< TComponent , VLength >::operator[] ( long  index  )  [inline, inherited]

Definition at line 204 of file itkFixedArray.h.

const_reference itk::FixedArray< TComponent , VLength >::operator[] ( unsigned int  index  )  const [inline, inherited]

Definition at line 203 of file itkFixedArray.h.

reference itk::FixedArray< TComponent , VLength >::operator[] ( unsigned int  index  )  [inline, inherited]

Definition at line 202 of file itkFixedArray.h.

const_reference itk::FixedArray< TComponent , VLength >::operator[] ( int  index  )  const [inline, inherited]

Definition at line 201 of file itkFixedArray.h.

reference itk::FixedArray< TComponent , VLength >::operator[] ( int  index  )  [inline, inherited]

Definition at line 200 of file itkFixedArray.h.

const_reference itk::FixedArray< TComponent , VLength >::operator[] ( unsigned short  index  )  const [inline, inherited]

Definition at line 199 of file itkFixedArray.h.

reference itk::FixedArray< TComponent , VLength >::operator[] ( unsigned short  index  )  [inline, inherited]

Definition at line 198 of file itkFixedArray.h.

const_reference itk::FixedArray< TComponent , VLength >::operator[] ( short  index  )  const [inline, inherited]

Definition at line 197 of file itkFixedArray.h.

reference itk::FixedArray< TComponent , VLength >::operator[] ( short  index  )  [inline, inherited]

Allow the FixedArray to be indexed normally. No bounds checking is done. The separate versions are a work-around for an integer conversion bug in Visual C++.

Definition at line 196 of file itkFixedArray.h.

Referenced by itk::SymmetricSecondRankTensor< TComponent, 3 >::GetNthComponent(), and itk::SymmetricSecondRankTensor< TComponent, 3 >::SetNthComponent().

template<typename TComponent, unsigned int NDimension = 3>
Self itk::SymmetricSecondRankTensor< TComponent, NDimension >::PostMultiply ( const MatrixType &  m  )  const

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

template<typename TComponent, unsigned int NDimension = 3>
Self itk::SymmetricSecondRankTensor< TComponent, NDimension >::PreMultiply ( const MatrixType &  m  )  const

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

ConstReverseIterator itk::FixedArray< TComponent , VLength >::rBegin (  )  const [inherited]

ReverseIterator itk::FixedArray< TComponent , VLength >::rBegin (  )  [inherited]

ConstReverseIterator itk::FixedArray< TComponent , VLength >::rEnd (  )  const [inherited]

ReverseIterator itk::FixedArray< TComponent , VLength >::rEnd (  )  [inherited]

void itk::FixedArray< TComponent , VLength >::SetElement ( unsigned short  index,
const_reference  value 
) [inline, inherited]

Set/Get element methods are more convenient in wrapping languages

Definition at line 211 of file itkFixedArray.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 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 150 of file itkSymmetricSecondRankTensor.h.

SizeType itk::FixedArray< TComponent , VLength >::Size ( void   )  const [inherited]

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