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.

Field Summary
static java.lang.String	CVS_REVISION

 

Method Summary
abstract  Matrix	H()           Return the Hessenberg matrix of this HessenbergReduction.
abstract  Matrix	Q()           Return the unitary Q matrix of this HessenbergReduction.
abstract  Column	Qtimes(Column column)           Return Q().times(column)
abstract  Column	QtransposeTimes(Column column)           Return Q().returnTranspose().times(column)

 

Field Detail

CVS_REVISION

public static final java.lang.String CVS_REVISION

H

public abstract Matrix H()

Return the Hessenberg matrix of this HessenbergReduction.

Specifications:

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

Q

public abstract Matrix Q()

Return the unitary Q matrix of this HessenbergReduction.

Specifications:

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

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));

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));