Package org.apache.commons.math3.linear

Class BiDiagonalTransformer

  • class BiDiagonalTransformer
extends java.lang.Object
    Class transforming any matrix to bi-diagonal shape.

    Any m × n matrix A can be written as the product of three matrices: A = U × B × VT with U an m × m orthogonal matrix, B an m × n bi-diagonal matrix (lower diagonal if m < n, upper diagonal otherwise), and V an n × n orthogonal matrix.

    Transformation to bi-diagonal shape is often not a goal by itself, but it is an intermediate step in more general decomposition algorithms like Singular Value 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 Detail

      • householderVectors

        private final double[][] householderVectors
        Householder vectors.

      • main

        private final double[] main
        Main diagonal.

      • secondary

        private final double[] secondary
        Secondary diagonal.

      • cachedU

        private RealMatrix cachedU
        Cached value of U.

      • cachedB

        private RealMatrix cachedB
        Cached value of B.

      • cachedV

        private RealMatrix cachedV
        Cached value of V.

    • Constructor Detail

      • BiDiagonalTransformer

        BiDiagonalTransformer​(RealMatrix matrix)
        Build the transformation to bi-diagonal shape of a matrix.
        Parameters:
        matrix - the matrix to transform.

    • Method Detail

      • getU

        public RealMatrix getU()
        Returns the matrix U of the transform.

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

        Returns:
        the U matrix

      • getB

        public RealMatrix getB()
        Returns the bi-diagonal matrix B of the transform.
        Returns:
        the B matrix

      • getV

        public RealMatrix getV()
        Returns the matrix V of the transform.

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

        Returns:
        the V 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 B 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

      • getSecondaryDiagonalRef

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

      • isUpperBiDiagonal

        boolean isUpperBiDiagonal()
        Check if the matrix is transformed to upper bi-diagonal.
        Returns:
        true if the matrix is transformed to upper bi-diagonal

      • transformToUpperBiDiagonal

        private void transformToUpperBiDiagonal()
        Transform original matrix to upper bi-diagonal form.

        Transformation is done using alternate Householder transforms on columns and rows.

      • transformToLowerBiDiagonal

        private void transformToLowerBiDiagonal()
        Transform original matrix to lower bi-diagonal form.

        Transformation is done using alternate Householder transforms on rows and columns.