org.jutil.math.matrix
Class HouseholderHessenbergReduction

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

All Implemented Interfaces:

HessenbergReduction

public class HouseholderHessenbergReduction

extends java.lang.Object

implements HessenbergReduction

This class represents a HouseHolder Hessenberg factorization of a matrix.

Version:

$Revision: 1.4 $

Author:

Marko van Dooren

Field Summary

static java.lang.String

CVS_REVISION

Constructor Summary

HouseholderHessenbergReduction(Matrix H, Column[] vs)
public behavior

pre H != null;
pre H.isSquare();
pre H.isHessenberg();
pre vs != null;
pre vs.length == H.getNbColumns() - 2;
pre (\forall int i; i>=0 && i vs[i] != null
vs[i].size() == H.getNbRows() - i - 1);

post H().equals(H);
post (\forall int i; i>=1 && i<= vs.length;
getV(i).equals(vs[i-1]));
Initialize a new HouseholderHessenbergReduction combination with the given H matrix and v vectors.

Method Summary

Column	getV(int i) public behavior pre i>=1; pre i<=H().getNbColumns() - 2; post \result != null;
Matrix	H() See superclass
Matrix	Q() See superclass
Column	Qtimes(Column column) See superclass
Column	QtransposeTimes(Column column) 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

Constructor Detail

HouseholderHessenbergReduction

public HouseholderHessenbergReduction(Matrix H,
                                      Column[] vs)

public behavior

pre H != null;
pre H.isSquare();
pre H.isHessenberg();
pre vs != null;
pre vs.length == H.getNbColumns() - 2;
pre (\forall int i; i>=0 && i vs[i] != null
vs[i].size() == H.getNbRows() - i - 1);

post H().equals(H);
post (\forall int i; i>=1 && i<= vs.length;
getV(i).equals(vs[i-1]));
Initialize a new HouseholderHessenbergReduction combination with the given H matrix and v vectors.

Parameters:

H - The H matrix of the Hessenberg reduction.

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

Method Detail

H

public Matrix H()

See superclass

Specified by:

H in interface HessenbergReduction

getV

public Column getV(int i)

public behavior

pre i>=1;
pre i<=H().getNbColumns() - 2;

post \result != null;

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

Parameters:

i -

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

Q

public Matrix Q()

See superclass

Specified by:

Q in interface HessenbergReduction

Qtimes

public Column Qtimes(Column column)

See superclass

Specified by:

Qtimes in interface HessenbergReduction

Following copied from interface: org.jutil.math.matrix.HessenbergReduction

Parameters:

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

QtransposeTimes

public Column QtransposeTimes(Column column)

See superclass

Specified by:

QtransposeTimes in interface HessenbergReduction

Following copied from interface: org.jutil.math.matrix.HessenbergReduction

Parameters:

column - The vector with which Q must be multiplied