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# JAMA::QR Class Template Reference

#include <jama_qr.h>

List of all members.

## Public Methods

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

## Detailed Description

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

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

 template JAMA::QR::QR ( const TNT::Array2D< Real > & A ) [inline]

Create a QR factorization object for A.

Parameters:
 A rectangular (m>=n) matrix.

## Member Function Documentation

 template TNT::Array2D< Real > JAMA::QR::getHouseholder ( void ) const [inline]
 Retreive the Householder vectors from QR factorization Returns: lower trapezoidal matrix whose columns define the reflections

 template TNT::Array2D< Real > JAMA::QR::getQ ( ) const [inline]

Generate and return the (economy-sized) orthogonal factor

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

 template TNT::Array2D< Real > JAMA::QR::getR ( ) const [inline]
 Return the upper triangular factor, R, of the QR factorization Returns: R

 template int JAMA::QR::isFullRank ( ) const [inline]
 Flag to denote the matrix is of full rank. Returns: 1 if matrix is full rank, 0 otherwise.

 template TNT::Array2D< Real > JAMA::QR::solve ( const TNT::Array2D< Real > & B ) const [inline]

Least squares solution of A*X = B

Parameters:
 B m 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.

 template TNT::Array1D< Real > JAMA::QR::solve ( const TNT::Array1D< Real > & b ) const [inline]

Least squares solution of A*x = b

Parameters:
 B m-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.

The documentation for this class was generated from the following file:
Generated at Mon Jan 20 07:47:18 2003 for JAMA/C++ by 1.2.5 written by Dimitri van Heesch, © 1997-2001