Package org.apache.commons.math3.linear

Class TriDiagonalTransformer

  • class TriDiagonalTransformer
extends java.lang.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

    • Constructor Summary

      Constructors 
      Constructor Description
      TriDiagonalTransformer​(RealMatrix matrix)
      Build the transformation to tridiagonal shape of a symmetrical matrix.

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      (package private) double[][] getHouseholderVectorsRef()
      Get the Householder vectors of the transform.
      (package private) double[] getMainDiagonalRef()
      Get the main diagonal elements of the matrix T of the transform.
      RealMatrix getQ()
      Returns the matrix Q of the transform.
      RealMatrix getQT()
      Returns the transpose of the matrix Q of the transform.
      (package private) double[] getSecondaryDiagonalRef()
      Get the secondary diagonal elements of the matrix T of the transform.
      RealMatrix getT()
      Returns the tridiagonal matrix T of the transform.
      private void transform()
      Transform original matrix to tridiagonal form.

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Field Detail

      • 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 Detail

      • 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 Detail

      • 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.