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

Class TridiagonalDecompositionHouseholder_ZDRM

java.lang.Object
org.ejml.dense.row.decompose.hessenberg.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 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

  • Constructor Summary

    Constructors
    Constructor
    Description
    TridiagonalDecompositionHouseholder_ZDRM()
     

  • Method Summary

    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(@Nullable 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(@Nullable 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 Details

    • TridiagonalDecompositionHouseholder_ZDRM

      public TridiagonalDecompositionHouseholder_ZDRM()

  • Method Details

    • getQT

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

    • 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(@Nullable @Nullable 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(@Nullable @Nullable 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()