org.jutil.math.matrix
Interface HessenbergReduction

All Known Implementing Classes:

HouseholderHessenbergReduction

public interface HessenbergReduction

A HessenbergReduction represents a Hessenberg reduction of a matrix.

The Hessenberg reduction of a matrix A contains a Hessenberg matrix H and a unitary matrix Q such that H=(Q*)*A*Q. (Q*) is the adjoint of Q.

Version:

$Revision: 1.3 $

Author:

Marko van Dooren

Field Summary

static java.lang.String

CVS_REVISION

Method Summary

Matrix	H() public behavior post \result != null; post \result.isSquare(); post \result.isHessenberg(); Return the Hessenberg matrix of this HessenbergReduction.
Matrix	Q() public behavior post \result != null; post \result.isSquare(); post (* \result.isUnitary() *); Return the unitary Q matrix of this HessenbergReduction.
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)

Field Detail

CVS_REVISION

public static final java.lang.String CVS_REVISION

Method Detail

H

public Matrix H()

public behavior

post \result != null;
post \result.isSquare();
post \result.isHessenberg();
Return the Hessenberg matrix of this HessenbergReduction.

Q

public Matrix Q()

public behavior

post \result != null;
post \result.isSquare();
post (* \result.isUnitary() *);
Return the unitary Q matrix of this HessenbergReduction.

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

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