Class TriDiagonalTransformer

java.lang.Object
org.apache.commons.math3.linear.TriDiagonalTransformer
class TriDiagonalTransformer extends Object
Class transforming a symmetrical matrix to tridiagonal shape.

A symmetrical m × m matrix A can be written as the product of three matrices: A = Q × T × QT with Q an orthogonal matrix and T a symmetrical tridiagonal matrix. Both Q and T are m × m matrices.

This implementation only uses the upper part of the matrix, the part below the diagonal is not accessed at all.

Transformation to tridiagonal shape 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.

Since:
2.0

  • Field Details

    • householderVectors

      private final double[][] householderVectors
      Householder vectors.

    • main

      private final double[] main
      Main diagonal.

    • secondary

      private final double[] secondary
      Secondary diagonal.

    • cachedQ

      private RealMatrix cachedQ
      Cached value of Q.

    • cachedQt

      private RealMatrix cachedQt
      Cached value of Qt.

    • cachedT

      private RealMatrix cachedT
      Cached value of T.

  • Constructor Details

    • TriDiagonalTransformer

      TriDiagonalTransformer(RealMatrix matrix)
      Build the transformation to tridiagonal shape of a symmetrical matrix.

      The specified matrix is assumed to be symmetrical without any check. Only the upper triangular part of the matrix is used.

      Parameters:
      matrix - Symmetrical matrix to transform.
      Throws:
      NonSquareMatrixException - if the matrix is not square.

  • Method Details

    • getQ

      public RealMatrix getQ()
      Returns the matrix Q of the transform.

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

      Returns:
      the Q matrix

    • getQT

      public RealMatrix getQT()
      Returns the transpose of the matrix Q of the transform.

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

      Returns:
      the Q matrix

    • getT

      public RealMatrix getT()
      Returns the tridiagonal matrix T of the transform.
      Returns:
      the T 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

    • getMainDiagonalRef

      double[] getMainDiagonalRef()
      Get the main diagonal elements of the matrix T 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 T matrix

    • getSecondaryDiagonalRef

      double[] getSecondaryDiagonalRef()
      Get the secondary diagonal elements of the matrix T 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 secondary diagonal elements of the T matrix

    • transform

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

      Transformation is done using Householder transforms.