Essentia  2.1-beta5-dev
QR< Real > Class Template Reference

#include <jama_qr.h>

Public Member Functions

 QR (const TNT::Array2D< Real > &A)
 
int isFullRank () const
 
TNT::Array2D< Real > getHouseholder (void) const
 
TNT::Array2D< Real > getR () const
 
TNT::Array2D< Real > getQ () const
 
TNT::Array1D< Real > solve (const TNT::Array1D< Real > &b) const
 
TNT::Array2D< Real > solve (const TNT::Array2D< Real > &B) const
 

Private Attributes

TNT::Array2D< Real > QR_
 
int m
 
int n
 
TNT::Array1D< Real > Rdiag
 

Detailed Description

template<class Real>
class JAMA::QR< Real >

Classical QR Decompisition: for an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q*R.

The QR decompostion always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if isFullRank() returns 0 (false).

The Q and R factors can be retrived via the getQ() and getR() methods. Furthermore, a solve() method is provided to find the least squares solution of Ax=b using the QR factors.

(Adapted from JAMA, a Java Matrix Library, developed by jointly by the Mathworks and NIST; see http://math.nist.gov/javanumerics/jama).

Constructor & Destructor Documentation

◆ QR()

QR ( const TNT::Array2D< Real > &  A)
inline

Create a QR factorization object for A.

Parameters
Arectangular (m>=n) matrix.

References Array2D< T >::copy(), Array2D< T >::dim1(), Array2D< T >::dim2(), TNT::hypot(), QR< Real >::m, and QR< Real >::n.

Member Function Documentation

◆ getHouseholder()

TNT::Array2D<Real> getHouseholder ( void  ) const
inline

Retreive the Householder vectors from QR factorization

Returns
lower trapezoidal matrix whose columns define the reflections

References QR< Real >::m, and QR< Real >::n.

◆ getQ()

TNT::Array2D<Real> getQ ( ) const
inline

Generate and return the (economy-sized) orthogonal factor

Parameters
Qthe (ecnomy-sized) orthogonal factor (Q*R=A).

References QR< Real >::m, and QR< Real >::n.

◆ getR()

TNT::Array2D<Real> getR ( ) const
inline

Return the upper triangular factor, R, of the QR factorization

Returns
R

References QR< Real >::n.

◆ isFullRank()

int isFullRank ( ) const
inline

Flag to denote the matrix is of full rank.

Returns
1 if matrix is full rank, 0 otherwise.

References QR< Real >::n.

Referenced by QR< Real >::solve().

◆ solve() [1/2]

TNT::Array1D<Real> solve ( const TNT::Array1D< Real > &  b) const
inline

Least squares solution of A*x = b

Parameters
Bm-length array (vector).
Returns
x n-length array (vector) that minimizes the two norm of Q*R*X-B. If B is non-conformant, or if QR.isFullRank() is false, the routine returns a null (0-length) vector.

References Array1D< T >::copy(), Array1D< T >::dim1(), QR< Real >::isFullRank(), QR< Real >::m, and QR< Real >::n.

◆ solve() [2/2]

TNT::Array2D<Real> solve ( const TNT::Array2D< Real > &  B) const
inline

Least squares solution of A*X = B

Parameters
Bm x k Array (must conform).
Returns
X n x k Array that minimizes the two norm of Q*R*X-B. If B is non-conformant, or if QR.isFullRank() is false, the routine returns a null (0x0) array.

References Array2D< T >::copy(), Array2D< T >::dim1(), Array2D< T >::dim2(), QR< Real >::isFullRank(), QR< Real >::m, and QR< Real >::n.

Member Data Documentation

◆ m

int m
private

Row and column dimensions. column dimension. row dimension.

Referenced by QR< Real >::getHouseholder(), QR< Real >::getQ(), QR< Real >::QR(), and QR< Real >::solve().

◆ n

◆ QR_

TNT::Array2D<Real> QR_
private

Array for internal storage of decomposition. internal array storage.

◆ Rdiag

TNT::Array1D<Real> Rdiag
private

Array for internal storage of diagonal of R. diagonal of R.


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