org.hipparchus.linear

## Class HessenbergTransformer

• public class HessenbergTransformer
extends Object
Class transforming a general real matrix to Hessenberg form.

A m × m matrix A can be written as the product of three matrices: A = P × H × PT with P an orthogonal matrix and H a Hessenberg matrix. Both P and H are m × m matrices.

Transformation to Hessenberg form is often not a goal by itself, but it is an intermediate step in more general decomposition algorithms like eigen decomposition. This class is therefore intended for internal use by the library and is not public. As a consequence of this explicitly limited scope, many methods directly returns references to internal arrays, not copies.

This class is based on the method orthes in class EigenvalueDecomposition from the JAMA library.

MathWorld, Householder Transformations
• ### Constructor Summary

Constructors
Constructor and Description
HessenbergTransformer(RealMatrix matrix)
Build the transformation to Hessenberg form of a general matrix.
• ### Method Summary

All Methods
Modifier and Type Method and Description
RealMatrix getH()
Returns the Hessenberg matrix H of the transform.
RealMatrix getP()
Returns the matrix P of the transform.
RealMatrix getPT()
Returns the transpose of the matrix P of the transform.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### HessenbergTransformer

public HessenbergTransformer(RealMatrix matrix)
Build the transformation to Hessenberg form of a general matrix.
Parameters:
matrix - matrix to transform
Throws:
MathIllegalArgumentException - if the matrix is not square
• ### Method Detail

• #### getP

public RealMatrix getP()
Returns the matrix P of the transform.

P is an orthogonal matrix, i.e. its inverse is also its transpose.

Returns:
the P matrix
• #### getPT

public RealMatrix getPT()
Returns the transpose of the matrix P of the transform.

P is an orthogonal matrix, i.e. its inverse is also its transpose.

Returns:
the transpose of the P matrix
• #### getH

public RealMatrix getH()
Returns the Hessenberg matrix H of the transform.
Returns:
the H matrix