QRSolver Class Reference

A class which solves the least squares problem by the QR decomposition method. More...

#include <ls_solver.h>

Inheritance diagram for QRSolver:

Public Member Functions
	QRSolver (std::size_t numRow, std::size_t numCol, double *A, double limitR=1e-3)
	Constructor. More...
virtual int	solve (double *result, double *b)
	returns 0 if success and result will be non-empty returns k<0 if the kth argument is illegal, result is empty returns k>0, k=rank in this case, result is empty More...
Public Member Functions inherited from LSSolver
virtual	~LSSolver ()
	Destructor. More...

Additional Inherited Members
Protected Attributes inherited from LSSolver
std::size_t	m_iNumRow
	The number of rows in matrix A.
std::size_t	m_iNumCol
	The number of columns in matrix A.
double *	m_vA
	The matrix A.
double *	m_vb
	The vector b (the right-hand-side)

Detailed Description

A class which solves the least squares problem by the QR decomposition method.

Author

Chen, Hsin-Chiang (morri.nosp@m.sche.nosp@m.n2008.nosp@m.@gma.nosp@m.il.co.nosp@m.m)

Co-author: Yu, Kwangmin (yukwa.nosp@m.ngmi.nosp@m.n@gma.nosp@m.il.c.nosp@m.om) on initial interface design

Version

1.0

Date

2014/10/09

Created on: 2014/09/20

Constructor & Destructor Documentation

QRSolver::QRSolver ( std::size_t  numRow, std::size_t  numCol, double *  A, double  limitR = 1e-3  )

inline

Constructor.

Set up the matrix A and other scalar parameters of this class

Parameters

[in]	numRow	The number of rows in matrix A
[in]	numCol	The number of columns in matrix A
[in]	A	The matrix A
[in]	limitR	A specified scalar multiplier (<1) for trimming diagonal entry of R in the QR decomposition

Member Function Documentation

int QRSolver::solve ( double *  result, double *  b  )

virtual

returns 0 if success and result will be non-empty returns k<0 if the kth argument is illegal, result is empty returns k>0, k=rank in this case, result is empty

Solves the least squares problem Ax = b by the QR decomposition method

A is a mxn matrix, b is a mx1 vector, and x is the solution which is a nx1 vector This method solves for by the following steps:

1. Call the function LAPACKE_dgeqp3() in LAPACK to perform QR decomposition with column pivoting to obtain

   

   where is a permutation matrix
   
2. Multiply both sides on the left by to get

   

   
   
3. Use back substitution to get
   
4. Solves for
   

Parameters

[out]	result	The x in Ax = b, which is a nx1 vector
[in]	b	The right-hand-size, which is a mx1 vector

Returns

0 if success; otherwise if failure

Warning

The input array b is modified in this method

Implements LSSolver.

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

• ls_solver.h
• ls_solver.cpp