RWQRDecomp< TypeT, QRCalc > Class Template Reference

Used to construct and work with QR decompositions. More...

#include <rw/lapack/qr.h>

Inherits QRCalc.

Public Member Functions
	RWQRDecomp ()
	RWQRDecomp (const RWGenMat< TypeT > &A)
	RWQRDecomp (const RWQRDecomp< TypeT, QRCalc > &)
unsigned	cols () const
void	factor (const RWGenMat< TypeT > &A)
RWQRDecomp< TypeT, QRCalc > &	operator= (const RWQRDecomp< TypeT, QRCalc > &)
RWGenMat< TypeT >	P () const
RWMathVec< TypeT >	PTx (const RWMathVec< TypeT > &x) const
RWMathVec< TypeT >	Px (const RWMathVec< TypeT > &x) const
RWGenMat< TypeT >	Q () const
RWMathVec< TypeT >	QTx (const RWMathVec< TypeT > &x) const
RWMathVec< TypeT >	Qx (const RWMathVec< TypeT > &x) const
RWGenMat< TypeT >	R () const
RWMathVec< TypeT >	Rdiagonal () const
RWMathVec< TypeT >	Rinvx (const RWMathVec< TypeT > &x) const
unsigned	rows () const
RWMathVec< TypeT >	RTinvx (const RWMathVec< TypeT > &x) const
RWMathVec< TypeT >	RTx (const RWMathVec< TypeT > &x) const
RWMathVec< TypeT >	Rx (const RWMathVec< TypeT > &x) const

Friends
class	RWCODecomp< TypeT, QRCalc >
class	RWQRDecompServer< TypeT, QRCalc >

Detailed Description

template<class TypeT, class QRCalc>
class RWQRDecomp< TypeT, QRCalc >

A QR decomposition is a representation of a matrix A of the form:

\[ AP = QR \]

where P is a permutation matrix, Q is orthogonal, and R is upper trapezoidal, or upper triangular if A is full rank, with no more columns than rows.

The class RWQRDecomp is used to construct and work with QR decompositions. Sometimes it is desirable to zero out the rectangular part of the trapezoidal matrix R; this can be done using the orthogonal decomposition class,RWQRDecomp. A common use of QR decompositions is to solve linear least squares problems; this is most conveniently done using the RWLeastSqQR class.

You may need more control over the computation of the decomposition than is provided by this class. For example, if you don't want to use pivoting, you can use the QR decomposition server class, RWQRDecompServer, to do the construction.

Note

For greater flexibility, the user can implement this method, or the Linear Algebra Module provides two classes to perform this function — RWQRCalc and RWQRCalcP3. Please see their descriptions in this reference guide for more information.

Synopsis

#include <rw/lapack/qr.h>
#include <rw/lapack/qrcalcp3.h>
 
// A is a RWGenMat<double>
RWQRDecomp<double, RWQRCalcP3<double> > qr(A);

Example

#include <rw/lapack/qr.h>
#include <rw/lapack/qrcalcp3.h>
#include <rw/math/genmat.h>
#include <rw/iostream>
 
int main() {
  RWGenMat<double> A;
  std::cin >> A;
  RWQRDecomp<double, RWQRCalc3P<double> > qr(A);
  std::cout << "Input matrix: " << A << std::endl;
  std::cout << "Permutation: " << qr.P() << std::endl;
  std::cout << "Q: " << qr.Q() << std::endl;
  std::cout << "R: " << qr.R() << std::endl;
  return 0;
}

Constructor & Destructor Documentation

RWQRDecomp() [1/3]

template<class TypeT , class QRCalc >

RWQRDecomp< TypeT, QRCalc >::RWQRDecomp

(

)

Default constructor. Builds a decomposition of size 0 x 0.

RWQRDecomp() [2/3]

template<class TypeT , class QRCalc >

RWQRDecomp< TypeT, QRCalc >::RWQRDecomp

(

const RWQRDecomp< TypeT, QRCalc > &

)

Copy constructor. References the data in the original decomposition for efficiency.

RWQRDecomp() [3/3]

template<class TypeT , class QRCalc >

RWQRDecomp< TypeT, QRCalc >::RWQRDecomp

(

const RWGenMat< TypeT > &

A

)

Builds a QR decomposition of A. By default, pivoting is done so that the entries along the diagonal of R are non-increasing. To construct a QR decomposition with non-default options, use the QR decomposition server class RWQRDecompServer.

Member Function Documentation

cols()

template<class TypeT , class QRCalc >

unsigned RWQRDecomp< TypeT, QRCalc >::cols ( ) const

inline

Returns the number of columns in the matrix that the decomposition represents.

factor()

template<class TypeT , class QRCalc >

void RWQRDecomp< TypeT, QRCalc >::factor

(

const RWGenMat< TypeT > &

A

)

Builds a QR decomposition of A.

operator=()

template<class TypeT , class QRCalc >

RWQRDecomp< TypeT, QRCalc > & RWQRDecomp< TypeT, QRCalc >::operator=

(

const RWQRDecomp< TypeT, QRCalc > &

)

Assigns the passed value to this decomposition. The current contents of the decomposition are lost.

P()

template<class TypeT , class QRCalc >

RWGenMat< TypeT > RWQRDecomp< TypeT, QRCalc >::P

(

)

const

Computes an explicit representation of the permutation matrix.

PTx()

template<class TypeT , class QRCalc >

RWMathVec< TypeT > RWQRDecomp< TypeT, QRCalc >::PTx

(

const RWMathVec< TypeT > &

x

)

const

Computes the inner product of the transpose of the permutation matrix P and the vector x.

Px()

template<class TypeT , class QRCalc >

RWMathVec< TypeT > RWQRDecomp< TypeT, QRCalc >::Px

(

const RWMathVec< TypeT > &

x

)

const

Computes the inner product of the permutation matrix P and the vector x.

Q()

template<class TypeT , class QRCalc >

RWGenMat< TypeT > RWQRDecomp< TypeT, QRCalc >::Q

(

)

const

Computes an explicit representation of the orthogonal matrix Q.

QTx()

template<class TypeT , class QRCalc >

RWMathVec< TypeT > RWQRDecomp< TypeT, QRCalc >::QTx

(

const RWMathVec< TypeT > &

x

)

const

Computes the inner product of the (conjugate) transpose of orthogonal matrix Q and the vector x.

Qx()

template<class TypeT , class QRCalc >

RWMathVec< TypeT > RWQRDecomp< TypeT, QRCalc >::Qx

(

const RWMathVec< TypeT > &

x

)

const

Computes the inner product of the orthogonal matrix Q and the vector x.

R()

template<class TypeT , class QRCalc >

RWGenMat< TypeT > RWQRDecomp< TypeT, QRCalc >::R

(

)

const

Returns an explicit representation of the upper trapezoidal matrix R.

Rdiagonal()

template<class TypeT , class QRCalc >

RWMathVec< TypeT > RWQRDecomp< TypeT, QRCalc >::Rdiagonal

(

)

const

Returns the main diagonal of the upper trapezoidal matrix R.

Rinvx()

template<class TypeT , class QRCalc >

RWMathVec< TypeT > RWQRDecomp< TypeT, QRCalc >::Rinvx

(

const RWMathVec< TypeT > &

x

)

const

Computes the inner product of the inverse of matrix R and the vector x. An exception is raised if you call this for a singular decomposition.

rows()

template<class TypeT , class QRCalc >

unsigned RWQRDecomp< TypeT, QRCalc >::rows ( ) const

inline

Returns the number of rows in the matrix that the decomposition represents.

RTinvx()

template<class TypeT , class QRCalc >

RWMathVec< TypeT > RWQRDecomp< TypeT, QRCalc >::RTinvx

(

const RWMathVec< TypeT > &

x

)

const

Computes the inner product of the (conjugate) transpose inverse of matrix R and the vector x. An exception is raised if you call this for a singular decomposition.

RTx()

template<class TypeT , class QRCalc >

RWMathVec< TypeT > RWQRDecomp< TypeT, QRCalc >::RTx

(

const RWMathVec< TypeT > &

x

)

const

Computes the inner product of the (conjugate) transpose of the matrix R and the vector x.

Rx()

template<class TypeT , class QRCalc >

RWMathVec< TypeT > RWQRDecomp< TypeT, QRCalc >::Rx

(

const RWMathVec< TypeT > &

x

)

const

Computes the inner product of the matrix R and the vector x.