Package org.ejml.dense.row.decomposition.hessenberg

Class TridiagonalDecompositionHouseholder_DDRM

java.lang.Object
org.ejml.dense.row.decomposition.hessenberg.TridiagonalDecompositionHouseholder_DDRM
All Implemented Interfaces:
org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DMatrixRMaj>, org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition<org.ejml.data.DMatrixRMaj>, org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition_F64<org.ejml.data.DMatrixRMaj>
Direct Known Subclasses:
TridiagonalDecompositionHouseholder_MT_DDRM
public class TridiagonalDecompositionHouseholder_DDRM extends Object implements org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition_F64<org.ejml.data.DMatrixRMaj>

Performs a similar tridiagonal decomposition on a square symmetric input 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*OT

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

This implementation is based off of the algorithm described in:

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

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    protected double[]
    b
     
    protected double[]
    gammas
     
    protected int
    N
     
    protected org.ejml.data.DMatrixRMaj
    QT
    Only the upper right triangle is used.
    protected double[]
    w
     

  • Constructor Summary

    Constructors
    Constructor
    Description
    TridiagonalDecompositionHouseholder_DDRM()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    boolean
    decompose(org.ejml.data.DMatrixRMaj A)
    Decomposes the provided symmetric matrix.
    void
    getDiagonal(double[] diag, double[] off)
     
    org.ejml.data.DMatrixRMaj
    getQ(@Nullable org.ejml.data.DMatrixRMaj Q, boolean transposed)
    An orthogonal matrix that has the following property: T = QTAQ
    org.ejml.data.DMatrixRMaj
    getQT()
    Returns the internal matrix where the decomposed results are stored.
    org.ejml.data.DMatrixRMaj
    getT(@Nullable org.ejml.data.DMatrixRMaj 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.DMatrixRMaj A)
    If needed declares and sets up internal data structures.
    boolean
    inputModified()
     
    protected void
    rank1UpdateMultL(org.ejml.data.DMatrixRMaj A, double gamma, int colA0, int w0, int w1)
     
    protected void
    rank1UpdateMultR(org.ejml.data.DMatrixRMaj A, double gamma, int colA0, int w0, int w1)
     

    Methods inherited from class java.lang.Object

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

  • Field Details

    • QT

      protected org.ejml.data.DMatrixRMaj QT
      Only the upper right triangle is used. The Tridiagonal portion stores the tridiagonal matrix. The rows store householder vectors.

    • N

      protected int N

    • w

      protected double[] w

    • gammas

      protected double[] gammas

    • b

      protected double[] b

  • Constructor Details

    • TridiagonalDecompositionHouseholder_DDRM

      public TridiagonalDecompositionHouseholder_DDRM()

  • Method Details

    • getQT

      public org.ejml.data.DMatrixRMaj 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.DMatrixRMaj>

    • getT

      public org.ejml.data.DMatrixRMaj getT(@Nullable @Nullable org.ejml.data.DMatrixRMaj T)
      Extracts the tridiagonal matrix found in the decomposition.
      Specified by:
      getT in interface org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition<org.ejml.data.DMatrixRMaj>
      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.DMatrixRMaj getQ(@Nullable @Nullable org.ejml.data.DMatrixRMaj Q, boolean transposed)
      An orthogonal matrix that has the following property: T = QTAQ
      Specified by:
      getQ in interface org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition<org.ejml.data.DMatrixRMaj>
      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.DMatrixRMaj A)
      Decomposes the provided symmetric matrix.
      Specified by:
      decompose in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DMatrixRMaj>
      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.DMatrixRMaj A)
      If needed declares and sets up internal data structures.
      Parameters:
      A - Matrix being decomposed.

    • rank1UpdateMultL

      protected void rank1UpdateMultL(org.ejml.data.DMatrixRMaj A, double gamma, int colA0, int w0, int w1)

    • rank1UpdateMultR

      protected void rank1UpdateMultR(org.ejml.data.DMatrixRMaj A, double gamma, int colA0, int w0, int w1)

    • inputModified

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