ITK  4.4.0
Insight Segmentation and Registration Toolkit
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itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix > Class Template Reference

#include <itkSymmetricEigenAnalysis.h>

+ Inheritance diagram for itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >:

Detailed Description

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
class itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >

Find Eigen values of a real 2D symmetric matrix. It serves as a thread-safe alternative to the class: vnl_symmetric_eigensystem, which uses netlib routines.

The class is templated over the input matrix (which is expected to provide access to its elements with the [][] operator), matrix to store eigen values (must provide write operations on its elements with the [] operator), and EigenMatrix to store eigen vectors (must provide write access to its elements with the [][] operator).

The SetOrderEigenValues() method can be used to order eigen values (and their corresponding eigen vectors if computed) in ascending order. This is the default ordering scheme. Eigen vectors and values can be obtained without ordering by calling SetOrderEigenValues(false).

The SetOrderEigenMagnitudes() method can be used to order eigen values (and their corresponding eigen vectors if computed) by magnitude in ascending order.

The user of this class is explicitly supposed to set the dimension of the 2D matrix using the SetDimension() method.

The class contains routines taken from netlib sources (www.netlib.org). netlib/tql1.c netlib/tql2.c netlib/tred1.c netlib/tred2.c

Reference: num. math. 11, 293-306(1968) by bowdler, martin, reinsch, and wilkinson. handbook for auto. comp., vol.ii-linear algebra, 227-240(1971).

Definition at line 61 of file itkSymmetricEigenAnalysis.h.

Public Types

typedef TEigenMatrix EigenMatrixType
 
enum  EigenValueOrderType {
  OrderByValue = 1,
  OrderByMagnitude,
  DoNotOrder
}
 
typedef TMatrix MatrixType
 
typedef TVector VectorType
 

Public Member Functions

unsigned int ComputeEigenValues (const TMatrix &A, TVector &EigenValues) const
 
unsigned int ComputeEigenValuesAndVectors (const TMatrix &A, TVector &EigenValues, TEigenMatrix &EigenVectors) const
 
unsigned int GetDimension () const
 
unsigned int GetOrder () const
 
bool GetOrderEigenMagnitudes () const
 
bool GetOrderEigenValues () const
 
void SetOrder (const unsigned int n)
 
 SymmetricEigenAnalysis ()
 
 SymmetricEigenAnalysis (const unsigned int dimension)
 
 ~SymmetricEigenAnalysis ()
 
void SetOrderEigenValues (const bool b)
 
void SetOrderEigenMagnitudes (const bool b)
 
void SetDimension (const unsigned int n)
 

Private Member Functions

unsigned int ComputeEigenValuesAndVectorsUsingQL (VectorType &d, double *e, double *z) const
 
unsigned int ComputeEigenValuesUsingQL (VectorType &d, double *e) const
 
void ReduceToTridiagonalMatrix (double *inputMatrix, VectorType &d, double *e, double *e2) const
 
void ReduceToTridiagonalMatrixAndGetTransformation (double *inputMatrix, VectorType &diagonalElements, double *subDiagonalElements, double *transformMatrix) const
 

Private Attributes

unsigned int m_Dimension
 
unsigned int m_Order
 
EigenValueOrderType m_OrderEigenValues
 

Member Typedef Documentation

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
typedef TEigenMatrix itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::EigenMatrixType

Definition at line 85 of file itkSymmetricEigenAnalysis.h.

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
typedef TMatrix itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::MatrixType

Definition at line 84 of file itkSymmetricEigenAnalysis.h.

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
typedef TVector itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::VectorType

Definition at line 86 of file itkSymmetricEigenAnalysis.h.

Member Enumeration Documentation

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
enum itk::SymmetricEigenAnalysis::EigenValueOrderType
Enumerator
OrderByValue 
OrderByMagnitude 
DoNotOrder 

Definition at line 64 of file itkSymmetricEigenAnalysis.h.

Constructor & Destructor Documentation

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::SymmetricEigenAnalysis ( )
inline

Definition at line 72 of file itkSymmetricEigenAnalysis.h.

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::SymmetricEigenAnalysis ( const unsigned int  dimension)
inline

Definition at line 77 of file itkSymmetricEigenAnalysis.h.

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::~SymmetricEigenAnalysis ( )
inline

Definition at line 82 of file itkSymmetricEigenAnalysis.h.

Member Function Documentation

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
unsigned int itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::ComputeEigenValues ( const TMatrix &  A,
TVector &  EigenValues 
) const

Compute Eigen values of A A is any type that overloads the [][] operator and contains the symmetric matrix. In practice only the upper triangle of the matrix will be accessed. (Both itk::Matrix and vnl_matrix overload [][] operator.)

'EigenValues' is any type that overloads the [][] operator and will contain the eigen values.

No size checking is performed. A is expected to be a square matrix of size m_Dimension. 'EigenValues' is expected to be of length m_Dimension. The matrix is not checked to see if it is symmetric.

Referenced by itk::Functor::SymmetricEigenAnalysisFunction< TInputImage::PixelType, TOutputImage::PixelType >::operator()().

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
unsigned int itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::ComputeEigenValuesAndVectors ( const TMatrix &  A,
TVector &  EigenValues,
TEigenMatrix &  EigenVectors 
) const

Compute Eigen values and vectors of A A is any type that overloads the [][] operator and contains the symmetric matrix. In practice only the upper triangle of the matrix will be accessed. (Both itk::Matrix and vnl_matrix overload [][] operator.)

'EigenValues' is any type that overloads the [][] operator and will contain the eigen values.

'EigenVectors' is any type that provides access to its elements with the [][] operator. It is expected be of size m_Dimension * m_Dimension.

No size checking is performed. A is expected to be a square matrix of size m_Dimension. 'EigenValues' is expected to be of length m_Dimension. The matrix is not checked to see if it is symmetric.

Each row of the matrix 'EigenVectors' represents an eigen vector. (unlike MATLAB where the columns of the [EigenVectors, EigenValues] = eig(A) contains the eigenvectors).

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
unsigned int itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::ComputeEigenValuesAndVectorsUsingQL ( VectorType d,
double *  e,
double *  z 
) const
private

Finds the eigenvalues and eigenvectors of a symmetric tridiagonal matrix by the ql method.

On input: 'd' contains the diagonal elements of the input matrix. 'e' contains the subdiagonal elements of the input matrix in its last n-1 positions. e(1) is arbitrary. 'z' contains the transformation matrix produced in the reduction by ReduceToTridiagonalMatrixAndGetTransformation(), if performed. If the eigenvectors of the tridiagonal matrix are desired, z must contain the identity matrix.

On Output: 'd' contains the eigenvalues. 'e' has been destroyed. 'z' contains orthonormal eigenvectors of the symmetric tridiagonal (or full) matrix.

Returns: zero for normal return, j if the j-th eigenvalue has not been determined after 1000 iterations.

Reference This subroutine is a translation of the algol procedure tql1, num. math. 11, 293-306(1968) by bowdler, martin, reinsch, and wilkinson. handbook for auto. comp., vol.ii-linear algebra, 227-240(1971).

Questions and comments should be directed to Burton s. Garbow, Mathematics and Computer Science Div., Argonne National Laboratory. This version dated august 1983.

Function Adapted from netlib/tql2.c. [Changed: remove static vars, enforce const correctness. Use vnl routines as necessary]

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
unsigned int itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::ComputeEigenValuesUsingQL ( VectorType d,
double *  e 
) const
private

Finds the eigenvalues of a symmetric tridiagonal matrix by the ql method.

On input: 'd' contains the diagonal elements of the input matrix. 'e' contains the subdiagonal elements of the input matrix in its last n-1 positions. e(1) is arbitrary. On Output: 'd' contains the eigenvalues. 'e' has been destroyed.

Returns: zero for normal return, j if the j-th eigenvalue has not been determined after 30 iterations.

Reference This subroutine is a translation of the algol procedure tql1, num. math. 11, 293-306(1968) by bowdler, martin, reinsch, and wilkinson. handbook for auto. comp., vol.ii-linear algebra, 227-240(1971).

Questions and comments should be directed to Burton s. Garbow, Mathematics and Computer Science Div., Argonne National Laboratory. This version dated august 1983.

Function Adapted from netlib/tql1.c. [Changed: remove static vars, enforce const correctness. Use vnl routines as necessary]

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
unsigned int itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::GetDimension ( void  ) const
inline

Get Matrix dimension, Will be 0 unless explicitly set by a call to SetDimension.

Definition at line 179 of file itkSymmetricEigenAnalysis.h.

Referenced by itk::Functor::SymmetricEigenAnalysisFunction< TInputImage::PixelType, TOutputImage::PixelType >::GetDimension(), and itk::operator<<().

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
unsigned int itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::GetOrder ( ) const
inline

Get the Matrix order. Will be 0 unless explicitly set, or unless a call to SetDimension has been made in which case it will be the matrix dimension.

Definition at line 139 of file itkSymmetricEigenAnalysis.h.

Referenced by itk::operator<<().

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
bool itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::GetOrderEigenMagnitudes ( ) const
inline

Definition at line 163 of file itkSymmetricEigenAnalysis.h.

Referenced by itk::operator<<().

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
bool itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::GetOrderEigenValues ( ) const
inline

Definition at line 151 of file itkSymmetricEigenAnalysis.h.

Referenced by itk::operator<<().

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
void itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::ReduceToTridiagonalMatrix ( double *  inputMatrix,
VectorType d,
double *  e,
double *  e2 
) const
private

Reduces a real symmetric matrix to a symmetric tridiagonal matrix using orthogonal similarity transformations. 'inputMatrix' contains the real symmetric input matrix. Only the lower triangle of the matrix need be supplied. The upper triangle is unaltered. 'd' contains the diagonal elements of the tridiagonal matrix. 'e' contains the subdiagonal elements of the tridiagonal matrix in its last n-1 positions. e(1) is set to zero. 'e2' contains the squares of the corresponding elements of e. 'e2' may coincide with e if the squares are not needed. questions and comments should be directed to burton s. garbow. mathematics and computer science div, argonne national laboratory this version dated august 1983.

Function adapted from netlib/tred1.c. [Changed: remove static vars, enforce const correctness. Use vnl routines as necessary]. Reference: num. math. 11, 181-195(1968) by martin, reinsch, and wilkinson. handbook for auto. comp., vol.ii-linear algebra, 212-226(1971).

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
void itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::ReduceToTridiagonalMatrixAndGetTransformation ( double *  inputMatrix,
VectorType diagonalElements,
double *  subDiagonalElements,
double *  transformMatrix 
) const
private

Reduces a real symmetric matrix to a symmetric tridiagonal matrix using and accumulating orthogonal similarity transformations. 'inputMatrix' contains the real symmetric input matrix. Only the lower triangle of the matrix need be supplied. The upper triangle is unaltered. 'diagonalElements' will contains the diagonal elements of the tridiagonal matrix. 'subDiagonalElements' will contain the subdiagonal elements of the tridiagonal matrix in its last n-1 positions. subDiagonalElements(1) is set to zero. 'transformMatrix' contains the orthogonal transformation matrix produced in the reduction.

Questions and comments should be directed to Burton s. Garbow, Mathematics and Computer Science Div., Argonne National Laboratory. This version dated august 1983.

Function adapted from netlib/tred2.c. [Changed: remove static vars, enforce const correctness. Use vnl routines as necessary]. Reference: num. math. 11, 181-195(1968) by martin, reinsch, and wilkinson. handbook for auto. comp., vol.ii-linear algebra, 212-226(1971).

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
void itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::SetDimension ( const unsigned int  n)
inline

Set the dimension of the input matrix A. A is a square matrix of size m_Dimension.

Definition at line 167 of file itkSymmetricEigenAnalysis.h.

Referenced by itk::Functor::SymmetricEigenAnalysisFunction< TInputImage::PixelType, TOutputImage::PixelType >::SetDimension().

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
void itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::SetOrder ( const unsigned int  n)
inline

Matrix order. Defaults to matrix dimension if not set

Definition at line 131 of file itkSymmetricEigenAnalysis.h.

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
void itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::SetOrderEigenMagnitudes ( const bool  b)
inline

Set/Get methods to order the eigen value magnitudes in ascending order. In other words, |lambda_1| < |lambda_2| < .....

Definition at line 156 of file itkSymmetricEigenAnalysis.h.

Referenced by itk::Functor::SymmetricEigenAnalysisFunction< TInputImage::PixelType, TOutputImage::PixelType >::OrderEigenValuesBy().

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
void itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::SetOrderEigenValues ( const bool  b)
inline

Set/Get methods to order the eigen values in ascending order. This is the default. ie lambda_1 < lambda_2 < ....

Definition at line 144 of file itkSymmetricEigenAnalysis.h.

Referenced by itk::Functor::SymmetricEigenAnalysisFunction< TInputImage::PixelType, TOutputImage::PixelType >::OrderEigenValuesBy().

Member Data Documentation

template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
unsigned int itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::m_Dimension
private
template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
unsigned int itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::m_Order
private
template<typename TMatrix, typename TVector, typename TEigenMatrix = TMatrix>
EigenValueOrderType itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::m_OrderEigenValues
private

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