Package org.ejml.dense.row.decompose.hessenberg

Class TridiagonalDecompositionHouseholder_ZDRM

  • All Implemented Interfaces:
    org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.ZMatrixRMaj>, org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition<org.ejml.data.ZMatrixRMaj>, org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition_F64<org.ejml.data.ZMatrixRMaj>
    public class TridiagonalDecompositionHouseholder_ZDRM
extends java.lang.Object
implements org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition_F64<org.ejml.data.ZMatrixRMaj>

    Performs a complex similar tridiagonal decomposition on a square Hermitian matrix. Householder vectors perform the similar operation and the symmetry is taken advantage of for good performance.

    Finds the decomposition of a matrix in the form of:

    A = O*T*OH

    where A is a Hermitian m by m matrix, O is an orthogonal matrix, and T is a tridiagonal matrix.

    This implementation is inspired by description of the real symmetric decomposition in:

    David S. Watkins, "Fundamentals of Matrix Computations," Second Edition. Page 349-355

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      boolean decompose​(org.ejml.data.ZMatrixRMaj A)
      Decomposes the provided symmetric matrix.
      void getDiagonal​(double[] diag, double[] off)  
      double[] getGammas()  
      org.ejml.data.ZMatrixRMaj getQ​(org.ejml.data.ZMatrixRMaj Q, boolean transposed)
      An orthogonal matrix that has the following property: T = QHAQ
      org.ejml.data.ZMatrixRMaj getQT()
      Returns the internal matrix where the decomposed results are stored.
      org.ejml.data.ZMatrixRMaj getT​(org.ejml.data.ZMatrixRMaj T)
      Extracts the tridiagonal matrix found in the decomposition.
      void householderSymmetric​(int row, double gamma)
      Performs the householder operations on left and right and side of the matrix.
      void init​(org.ejml.data.ZMatrixRMaj A)
      If needed declares and sets up internal data structures.
      boolean inputModified()  

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

      • TridiagonalDecompositionHouseholder_ZDRM

        public TridiagonalDecompositionHouseholder_ZDRM()

    • Method Detail

      • getQT

        public org.ejml.data.ZMatrixRMaj getQT()
        Returns the internal matrix where the decomposed results are stored.
        Returns:

      • getDiagonal

        public void getDiagonal​(double[] diag,
                        double[] off)
        Specified by:
        getDiagonal in interface org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition_F64<org.ejml.data.ZMatrixRMaj>

      • getT

        public org.ejml.data.ZMatrixRMaj getT​(org.ejml.data.ZMatrixRMaj T)
        Extracts the tridiagonal matrix found in the decomposition.
        Specified by:
        getT in interface org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition<org.ejml.data.ZMatrixRMaj>
        Parameters:
        T - If not null then the results will be stored here. Otherwise a new matrix will be created.
        Returns:
        The extracted T matrix.

      • getQ

        public org.ejml.data.ZMatrixRMaj getQ​(org.ejml.data.ZMatrixRMaj Q,
                                      boolean transposed)
        An orthogonal matrix that has the following property: T = QHAQ
        Specified by:
        getQ in interface org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition<org.ejml.data.ZMatrixRMaj>
        Parameters:
        Q - If not null then the results will be stored here. Otherwise a new matrix will be created.
        Returns:
        The extracted Q matrix.

      • decompose

        public boolean decompose​(org.ejml.data.ZMatrixRMaj A)
        Decomposes the provided symmetric matrix.
        Specified by:
        decompose in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.ZMatrixRMaj>
        Parameters:
        A - Symmetric matrix that is going to be decomposed. Not modified.

      • householderSymmetric

        public void householderSymmetric​(int row,
                                 double gamma)
        Performs the householder operations on left and right and side of the matrix. QTAQ
        Parameters:
        row - Specifies the submatrix.
        gamma - The gamma for the householder operation

      • init

        public void init​(org.ejml.data.ZMatrixRMaj A)
        If needed declares and sets up internal data structures.
        Parameters:
        A - Matrix being decomposed.

      • inputModified

        public boolean inputModified()
        Specified by:
        inputModified in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.ZMatrixRMaj>

      • getGammas

        public double[] getGammas()