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.

Field Summary
static java.lang.String	CVS_REVISION

 

Constructor Summary

HouseholderHessenbergReduction(Matrix H, Column[] vs)           Initialize a new HouseholderHessenbergReduction combination with the given H 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 Hessenberg decomposition.
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

HouseholderHessenbergReduction

public HouseholderHessenbergReduction(Matrix H,
                                      Column[] vs)

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

Specifications:

public behavior
requires H != null;
requires H.isSquare();
requires vs != null;
requires vs.length == H.getNbColumns()-2;
requires ( \forall int i; i >= 0&&i < vs.length; (vs[i] != null)&&(vs[i].size() == H.getNbRows()-i-1));
ensures H().equals(H);
ensures ( \forall int i; i >= 1&&i <= vs.length; getV(i).equals(vs[i-1]));

H

public Matrix H()

See superclass

Specifications inherited from overridden method in interface HessenbergReduction:

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

getV

public Column getV(int i)

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.

Specifications:

public behavior
requires i >= 1;
requires i <= H().getNbColumns()-2;
ensures \result != null;

Q

public Matrix Q()

See superclass

Specifications inherited from overridden method in interface HessenbergReduction:

public behavior
ensures \result != null;
ensures \result .isSquare();
ensures (* \result.isUnitary() *);

Qtimes

public Column Qtimes(Column column)

See superclass

Specifications inherited from overridden method in interface HessenbergReduction:

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

QtransposeTimes

public Column QtransposeTimes(Column column)

See superclass

Specifications inherited from overridden method in interface HessenbergReduction:

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