itk::QRDecomposition< T > Class Template Reference

#include <itkQRDecomposition.h>

Detailed Description

template<typename T>
class itk::QRDecomposition< T >

QR decomposition A = Q R of a real or complex matrix, backed by Eigen.

Eigen-backed replacement for vnl_qr. The factors Q (orthonormal/unitary) and R (upper triangular) are computed once in the constructor via Eigen's HouseholderQR and stored as vnl matrices, so no Eigen type appears in the public interface. Q/R follow Eigen's sign convention; rely on the QR identities Q R == A and Q^* Q == I rather than on specific factor signs.

Definition at line 42 of file itkQRDecomposition.h.

Public Types
using	MatrixType = vnl_matrix<T>
using	VectorType = vnl_vector<T>

Public Member Functions
T	GetDeterminant () const
const MatrixType &	GetQ () const
const MatrixType &	GetR () const
	QRDecomposition (const MatrixType &A)
VectorType	Solve (const VectorType &b) const

Private Attributes
T	m_Determinant {}
MatrixType	m_Q
MatrixType	m_R
bool	m_Square { false }

Member Typedef Documentation

MatrixType

template<typename T>

using itk::QRDecomposition< T >::MatrixType = vnl_matrix<T>

Definition at line 45 of file itkQRDecomposition.h.

VectorType

template<typename T>

using itk::QRDecomposition< T >::VectorType = vnl_vector<T>

Definition at line 46 of file itkQRDecomposition.h.

Constructor & Destructor Documentation

QRDecomposition()

template<typename T>

itk::QRDecomposition< T >::QRDecomposition ( const MatrixType & A )

inlineexplicit

Definition at line 48 of file itkQRDecomposition.h.

References m_Determinant, m_Q, m_R, and m_Square.

Member Function Documentation

GetDeterminant()

template<typename T>

T itk::QRDecomposition< T >::GetDeterminant ( ) const

inline

Determinant of a square A (zero-initialized value for non-square A).

Definition at line 114 of file itkQRDecomposition.h.

References m_Determinant.

GetQ()

template<typename T>

const MatrixType & itk::QRDecomposition< T >::GetQ ( ) const

inline

Orthonormal/unitary factor Q (rows x rows).

Definition at line 73 of file itkQRDecomposition.h.

References m_Q.

GetR()

template<typename T>

const MatrixType & itk::QRDecomposition< T >::GetR ( ) const

inline

Upper-triangular factor R (rows x cols).

Definition at line 80 of file itkQRDecomposition.h.

References m_R.

Solve()

template<typename T>

VectorType itk::QRDecomposition< T >::Solve ( const VectorType & b ) const

inline

Solve A x = b (least-squares for an overdetermined A) using x = R^-1 Q^* b. A must have full column rank; a rank-deficient R yields a non-finite x.

Definition at line 88 of file itkQRDecomposition.h.

References m_Q, and m_R.

Member Data Documentation

m_Determinant

template<typename T>

T itk::QRDecomposition< T >::m_Determinant {}

private

Definition at line 122 of file itkQRDecomposition.h.

Referenced by GetDeterminant(), and QRDecomposition().

m_Q

template<typename T>

MatrixType itk::QRDecomposition< T >::m_Q

private

Definition at line 120 of file itkQRDecomposition.h.

Referenced by GetQ(), QRDecomposition(), and Solve().

m_R

template<typename T>

MatrixType itk::QRDecomposition< T >::m_R

private

Definition at line 121 of file itkQRDecomposition.h.

Referenced by GetR(), QRDecomposition(), and Solve().

m_Square

template<typename T>

bool itk::QRDecomposition< T >::m_Square { false }

private

Definition at line 123 of file itkQRDecomposition.h.

Referenced by QRDecomposition().

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

• itkQRDecomposition.h