org.jutil.math.matrix
Class HouseholderQRDecomposition

java.lang.Object
  |
  +--org.jutil.math.matrix.HouseholderQRDecomposition

All Implemented Interfaces:

QRDecomposition

public class HouseholderQRDecomposition

extends java.lang.Object

implements QRDecomposition

This class represents a HouseHolder QR factorization of a matrix.

Specifications inherited from interface QRDecomposition

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

Field Summary
static java.lang.String	CVS_REVISION

 

Constructor Summary

HouseholderQRDecomposition(Matrix R, Column[] vs)           Initialize a new HouseholderQRDecomposition combination with the given R matrix and v vectors.

 

Method Summary
Column	getV(int i)           Return the i-th v vector as computed by the Householder algorithm that computed this QR decomposition.
Matrix	Q()           See superclass
Matrix	Qreduced()           See superclass
Column	QreducedTimes(Column column)           See superclass
Column	QreducedTransposeTimes(Column column)           See superclass
Column	Qtimes(Column column)           See superclass
Column	QtransposeTimes(Column column)           See superclass
Matrix	R()           See superclass
Matrix	Rreduced()           See superclass

 

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

 

Field Detail

CVS_REVISION

public static final java.lang.String CVS_REVISION

HouseholderQRDecomposition

public HouseholderQRDecomposition(Matrix R,
                                  Column[] vs)

Initialize a new HouseholderQRDecomposition combination with the given R matrix and v vectors.

Parameters:

R - The R matrix of the QR factorization

vs - An array of v vectors produce by the HouseHolder factorization The first vector of the algorithm is at position -, the last vector is at position vs.length - 1

Specifications:

public behavior
requires R != null;
requires R.isUpperTriangular();
requires vs != null;
requires vs.length == R.getNbRows();
requires ( \forall int i; i >= 0&&i < vs.length; (vs[i] != null)&&(vs[i].size() == R.getNbRows()-i));
ensures R().equals(R);
ensures ( \forall int i; i >= 1&&i <= vs.length; getV(i).equals(vs[i-1]));

R

public Matrix R()

See superclass

Specifications inherited from overridden method in interface QRDecomposition:

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

getV

public Column getV(int i)

Return the i-th v vector as computed by the Householder algorithm that computed this QR decomposition.

Parameters:

i -

The index of the requested v vector. Indices start from 1.

Q

public Matrix Q()

See superclass

Specifications inherited from overridden method in interface QRDecomposition:

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

Qreduced

public Matrix Qreduced()

See superclass

Specifications inherited from overridden method in interface QRDecomposition:

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

Rreduced

public Matrix Rreduced()

See superclass

Specifications inherited from overridden method in interface QRDecomposition:

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

Qtimes

public Column Qtimes(Column column)

See superclass

Specifications inherited from overridden method in interface QRDecomposition:

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

QreducedTimes

public Column QreducedTimes(Column column)

See superclass

Specifications inherited from overridden method in interface QRDecomposition:

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

QtransposeTimes

public Column QtransposeTimes(Column column)

See superclass

Specifications inherited from overridden method in interface QRDecomposition:

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

QreducedTransposeTimes

public Column QreducedTransposeTimes(Column column)

See superclass

Specifications inherited from overridden method in interface QRDecomposition:

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