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.

Class Specifications

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

Field Summary
static java.lang.String	CVS_REVISION

 

Method Summary
abstract  Matrix	Q()           Return the Q matrix of this QR factorization.
abstract  Matrix	Qreduced()           Return the reduced Q matrix.
abstract  Column	QreducedTimes(Column column)           Return Qreduced().times(column)
abstract  Column	QreducedTransposeTimes(Column column)           Return Qreduced().returnTranspose().times(column)
abstract  Column	Qtimes(Column column)           Return Q().times(column)
abstract  Column	QtransposeTimes(Column column)           Return Q().returnTranspose().times(column)
abstract  Matrix	R()           Return the R matrix of this QR factorization.
abstract  Matrix	Rreduced()           Return the reduced R matrix.

 

Field Detail

CVS_REVISION

public static final java.lang.String CVS_REVISION

Q

public abstract Matrix Q()

Return the Q matrix of this QR factorization.

Specifications:

public behavior
ensures \result != null;
ensures \result .getNbRows() == R().getNbRows();
ensures \result .getNbColumns() == R().getNbRows();

R

public abstract Matrix R()

Return the R matrix of this QR factorization.

Specifications:

public behavior
ensures \result != null;
ensures \result .isUpperTriangular();

Qreduced

public abstract Matrix Qreduced()

Return the reduced Q matrix.

Specifications:

public behavior
ensures \result .equals(Q().subMatrix(1,1,Q().getNbRows(),R().getNbColumns()));

Rreduced

public abstract Matrix Rreduced()

Return the reduced R matrix.

Specifications:

public behavior
ensures \result .equals(R().subMatrix(1,1,R().getNbColumns(),R().getNbColumns()));

Qtimes

public abstract Column Qtimes(Column column)

Return Q().times(column)

Parameters:

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

Specifications:

public behavior
requires column != null;
requires column.size() == Q().getNbColumns();
ensures \result .equals(Q().times(column));

QreducedTimes

public abstract Column QreducedTimes(Column column)

Return Qreduced().times(column)

Parameters:

column - The vector with which Qreduced must be multiplied

Specifications:

public behavior
requires column != null;
requires column.size() == Qreduced().getNbColumns();
ensures \result .equals(Qreduced().times(column));

QtransposeTimes

public abstract Column QtransposeTimes(Column column)

Return Q().returnTranspose().times(column)

Parameters:

column - The vector with which Q must be multiplied

Specifications:

public behavior
requires column != null;
requires column.size() == Q().getNbRows();
ensures \result .equals(Q().returnTranspose().times(column));

QreducedTransposeTimes

public abstract Column QreducedTransposeTimes(Column column)

Return Qreduced().returnTranspose().times(column)

Parameters:

column - The vector with which Q must be multiplied

Specifications:

public behavior
requires column != null;
requires column.size() == Qreduced().getNbRows();
ensures \result .equals(Qreduced().returnTranspose().times(column));