Class HessenbergTransformer

java.lang.Object
org.apache.commons.math3.linear.HessenbergTransformer

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.

Since:
3.1
See Also:
  • Field Details

    • householderVectors

      private final double[][] householderVectors
      Householder vectors.
    • ort

      private final double[] ort
      Temporary storage vector.
    • cachedP

      private RealMatrix cachedP
      Cached value of P.
    • cachedPt

      private RealMatrix cachedPt
      Cached value of Pt.
    • cachedH

      private RealMatrix cachedH
      Cached value of H.
  • Constructor Details

    • HessenbergTransformer

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

    • 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
    • getHouseholderVectorsRef

      double[][] getHouseholderVectorsRef()
      Get the Householder vectors of the transform.

      Note that since this class is only intended for internal use, it returns directly a reference to its internal arrays, not a copy.

      Returns:
      the main diagonal elements of the B matrix
    • transform

      private void transform()
      Transform original matrix to Hessenberg form.

      Transformation is done using Householder transforms.