RWQRDecomp<T,QRCalc>

Module:  Linear Algebra   Group:  Decomposition classes

Does not inherit

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Members

cols() factor() operator=() P() PTx()

Px() Q() QTx() Qx() R()

Rdiagonal() Rinvx() rows() RTinvx() RTx()

RWQRDecomp() Rx()

#include <rw/lapack/qr.h>
#include <rw/lapack/qrcalcp3.h>

RWQRDecomp<double, RWQRCalcP3<double> > qr(A);  // A is a RWGenMat<double>

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

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<T,QRCalc> 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<T,QRCalc>. A common use of QR decompositions is to solve linear least squares problems; this is most conveniently done using the RWLeastSqQR<T,QRCalc> 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<T,QRCalc>, to do the construction.

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

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#include <rw/iostream>
#include <rw/math/genmat.h>
#include <rw/lapack/qr.h>
#include <rw/lapack/qrcalcp3.h>

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;
}

RWQRDecomp();

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

RWQRDecomp(const RWQRDecomp<T,QRCalc>& A);

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

RWQRDecomp(const RWGenMat<T>& 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<T,QRCalc>.

unsigned
cols();

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

void
factor(const RWGenMat<T>& A);

Builds a QR decomposition of A.

RWGenMat<T>
P();

Computes an explicit representation of the permutation matrix.

RWMathVec<T>
Px(const RWMathVec<T>& x);
RWMathVec<T>
PTx(const RWMathVec<T>& x);

Computes the inner product of the permutation, or its transpose, and the vector x.

RWGenMat<T>
Q();

Computes an explicit representation of the orthogonal matrix Q.

RWMathVec<T>
Qx(const RWMathVec<T>& x);
RWMathVec<T>
QTx(const RWMathVec<T>& x);

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

RWGenMat<T>
R();

Returns an explicit representation of the upper trapezoidal matrix R.

RWMathVec<T>
Rdiagonal();

Returns the main diagonal of the upper trapezoidal matrix R.

RWMathVec<T> 
Rx(const RWMathVec<T>& x);
RWMathVec<T>
RTx(const RWMathVec<T>& x);
RWMathVec<T> 
Rinvx(const RWMathVec<T>& x);
RWMathVec<T> 
RTinvx(const RWMathVec<T>& x);

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

unsigned
rows();

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

void
operator=(const RWQRDecomp<T,QRCalc>&);

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

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