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ITK
4.13.0
Insight Segmentation and Registration Toolkit
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ITK
4.13.0
Insight Segmentation and Registration Toolkit
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#include <itkSymmetricEigenAnalysis.h>
Inheritance diagram for 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 (double *d, double *e, double *z) const |
| unsigned int | ComputeEigenValuesUsingQL (double *d, double *e) const |
| void | ReduceToTridiagonalMatrix (double *inputMatrix, double *d, double *e, double *e2) const |
| void | ReduceToTridiagonalMatrixAndGetTransformation (double *inputMatrix, double *diagonalElements, double *subDiagonalElements, double *transformMatrix) const |
Private Attributes | |
| unsigned int | m_Dimension |
| unsigned int | m_Order |
| EigenValueOrderType | m_OrderEigenValues |
| typedef TEigenMatrix itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::EigenMatrixType |
Definition at line 85 of file itkSymmetricEigenAnalysis.h.
| typedef TMatrix itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::MatrixType |
Definition at line 84 of file itkSymmetricEigenAnalysis.h.
| typedef TVector itk::SymmetricEigenAnalysis< TMatrix, TVector, TEigenMatrix >::VectorType |
Definition at line 86 of file itkSymmetricEigenAnalysis.h.
| enum itk::SymmetricEigenAnalysis::EigenValueOrderType |
| Enumerator | |
|---|---|
| OrderByValue | |
| OrderByMagnitude | |
| DoNotOrder | |
Definition at line 64 of file itkSymmetricEigenAnalysis.h.
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Definition at line 72 of file itkSymmetricEigenAnalysis.h.
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Definition at line 77 of file itkSymmetricEigenAnalysis.h.
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Definition at line 82 of file itkSymmetricEigenAnalysis.h.
| 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()().
| 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).
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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]
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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]
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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<<().
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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<<().
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Definition at line 163 of file itkSymmetricEigenAnalysis.h.
Referenced by itk::operator<<().
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Definition at line 151 of file itkSymmetricEigenAnalysis.h.
Referenced by itk::operator<<().
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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).
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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).
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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().
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Matrix order. Defaults to matrix dimension if not set
Definition at line 131 of file itkSymmetricEigenAnalysis.h.
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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().
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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().
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Definition at line 182 of file itkSymmetricEigenAnalysis.h.
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Definition at line 183 of file itkSymmetricEigenAnalysis.h.
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Definition at line 184 of file itkSymmetricEigenAnalysis.h.
1.8.5
