程序代写 TemplateJAMA::QR class Reference

TemplateJAMA::QR class Reference

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JAMA::QR Class Template Reference
#include

List of all members.
Public Methods

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

Detailed Description

template 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:

 
rectangular (m>=n) matrix.

Member Function Documentation

template

TNT::Array2D< Real > JAMA::QR::getHouseholder (

void ) const [inline]

 

Retreive the Householder vectors from QR factorization

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:

 
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

template

int JAMA::QR::isFullRank (

) const [inline]

 

Flag to denote the matrix is of full rank.

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:

 
m x k Array (must conform).

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:

 
m-length array (vector).

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: jama_qr.h

Generated at Mon Jan 20 07:47:18 2003 for JAMA/C++ by

1.2.5 written by Dimitri van Heesch,
© 1997-2001

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