org.jutil.math.matrix
Interface QRDecomposition

All Known Implementing Classes:

HouseholderQRDecomposition

public interface QRDecomposition

This class represents a QR factorization of a matrix. The methods Qtimes and QtranposeTimes are provide because the matrix Q itself isn't interesting most of the times, and isn't required explicitly to calculate Q * x and transpose(Q) * x.

Version:

$Revision: 1.3 $

Author:

Marko van Dooren

Field Summary

static java.lang.String

CVS_REVISION

Method Summary

Matrix	Q() public invariant Q().getNbColumns() == R().getNbRows(); public behavior post \result != null; post \result.getNbRows() == R().getNbRows(); post \result.getNbColumns() == R().getNbRows(); post \result.isOrthoNormal(); Return the Q matrix of this QR factorization.
Matrix	Qreduced() public behavior post \result.equals(Q().subMatrix(1,1,Q().getNbRows(), R().getNbColumns())); Return the reduced Q matrix.
Column	QreducedTimes(Column column) public behavior pre column != null; pre column.size() = Qreduced().getNbColumns(); post \result.equals(Qreduced().times(column)); Return Qreduced().times(column)
Column	QreducedTransposeTimes(Column column) public behavior pre column != null; pre column.size() = Qreduced().getNbRows(); post \result.equals(Qreduced().returnTranspose().times(column)); Return Qreduced().returnTranspose().times(column)
Column	Qtimes(Column column) public behavior pre column != null; pre column.size() = Q().getNbColumns(); post \result.equals(Q().times(column)); Return Q().times(column)
Column	QtransposeTimes(Column column) public behavior pre column != null; pre column.size() = Q().getNbRows(); post \result.equals(Q().returnTranspose().times(column)); Return Q().returnTranspose().times(column)
Matrix	R() public behavior post \result != null; post \result.isUpperTriangular(); Return the R matrix of this QR factorization.
Matrix	Rreduced() public behavior post \result.equals(R().subMatrix(1,1,R().getNbColumns(), R().getNbColumns())); Return the reduced R matrix.

Field Detail

CVS_REVISION

public static final java.lang.String CVS_REVISION

Method Detail

Q

public Matrix Q()

public invariant Q().getNbColumns() == R().getNbRows();

public behavior

post \result != null;
post \result.getNbRows() == R().getNbRows();
post \result.getNbColumns() == R().getNbRows();
post \result.isOrthoNormal();
Return the Q matrix of this QR factorization.

R

public Matrix R()

public behavior

post \result != null;
post \result.isUpperTriangular();
Return the R matrix of this QR factorization.

Qreduced

public Matrix Qreduced()

public behavior

post \result.equals(Q().subMatrix(1,1,Q().getNbRows(), R().getNbColumns()));
Return the reduced Q matrix.

Rreduced

public Matrix Rreduced()

public behavior

post \result.equals(R().subMatrix(1,1,R().getNbColumns(), R().getNbColumns()));
Return the reduced R matrix.

Qtimes

public Column Qtimes(Column column)

public behavior

pre column != null;
pre column.size() = Q().getNbColumns();

post \result.equals(Q().times(column));
Return Q().times(column)

Parameters:

column - The vector with which Q() must be multiplied

QreducedTimes

public Column QreducedTimes(Column column)

public behavior

pre column != null;
pre column.size() = Qreduced().getNbColumns();

post \result.equals(Qreduced().times(column));
Return Qreduced().times(column)

Parameters:

column - The vector with which Qreduced must be multiplied

QtransposeTimes

public Column QtransposeTimes(Column column)

public behavior

pre column != null;
pre column.size() = Q().getNbRows();

post \result.equals(Q().returnTranspose().times(column));
Return Q().returnTranspose().times(column)

Parameters:

column - The vector with which Q must be multiplied

QreducedTransposeTimes

public Column QreducedTransposeTimes(Column column)

public behavior

pre column != null;
pre column.size() = Qreduced().getNbRows();

post \result.equals(Qreduced().returnTranspose().times(column));
Return Qreduced().returnTranspose().times(column)

Parameters:

column - The vector with which Q must be multiplied