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

Class HessenbergSimilarDecomposition_DDRM

java.lang.Object
org.ejml.dense.row.decomposition.hessenberg.HessenbergSimilarDecomposition_DDRM
All Implemented Interfaces:
org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DMatrixRMaj>
Direct Known Subclasses:
HessenbergSimilarDecomposition_MT_DDRM
public class HessenbergSimilarDecomposition_DDRM
extends java.lang.Object
implements org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DMatrixRMaj>

Finds the decomposition of a matrix in the form of:

A = OHOT

where A is an m by m matrix, O is an orthogonal matrix, and H is an upper Hessenberg matrix.

A matrix is upper Hessenberg if aij = 0 for all i > j+1. For example, the following matrix is upper Hessenberg.

WRITE IT OUT USING A TABLE

This decomposition is primarily used as a step for computing the eigenvalue decomposition of a matrix. The basic algorithm comes from David S. Watkins, "Fundamentals of MatrixComputations" Second Edition.

  • Field Summary

    Fields 
    Modifier and Type Field Description
    protected double[] b  
    protected double[] u  

  • Constructor Summary

    Constructors 
    Constructor Description
    HessenbergSimilarDecomposition_DDRM()  
    HessenbergSimilarDecomposition_DDRM​(int initialSize)
    Creates a decomposition that won't need to allocate new memory if it is passed matrices up to the specified size.

  • Method Summary

    Modifier and Type Method Description
    boolean decompose​(org.ejml.data.DMatrixRMaj A)
    Computes the decomposition of the provided matrix.
    double[] getGammas()  
    org.ejml.data.DMatrixRMaj getH​(@Nullable org.ejml.data.DMatrixRMaj H)
    An upper Hessenberg matrix from the decomposition.
    org.ejml.data.DMatrixRMaj getQ​(@Nullable org.ejml.data.DMatrixRMaj Q)
    An orthogonal matrix that has the following property: H = QTAQ
    org.ejml.data.DMatrixRMaj getQH()
    The raw QH matrix that is stored internally.
    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

    • b

      protected double[] b

    • u

      protected double[] u

  • Constructor Details

    • HessenbergSimilarDecomposition_DDRM

      public HessenbergSimilarDecomposition_DDRM​(int initialSize)
      Creates a decomposition that won't need to allocate new memory if it is passed matrices up to the specified size.
      Parameters:
      initialSize - Expected size of the matrices it will decompose.

    • HessenbergSimilarDecomposition_DDRM

      public HessenbergSimilarDecomposition_DDRM()

  • Method Details

    • decompose

      public boolean decompose​(org.ejml.data.DMatrixRMaj A)
      Computes the decomposition of the provided matrix. If no errors are detected then true is returned, false otherwise.
      Specified by:
      decompose in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DMatrixRMaj>
      Parameters:
      A - The matrix that is being decomposed. Not modified.
      Returns:
      If it detects any errors or not.

    • inputModified

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

    • getQH

      public org.ejml.data.DMatrixRMaj getQH()
      The raw QH matrix that is stored internally.
      Returns:
      QH matrix.

    • getH

      public org.ejml.data.DMatrixRMaj getH​(@Nullable @Nullable org.ejml.data.DMatrixRMaj H)
      An upper Hessenberg matrix from the decomposition.
      Parameters:
      H - If not null then the results will be stored here. Otherwise a new matrix will be created.
      Returns:
      The extracted H matrix.

    • getQ

      public org.ejml.data.DMatrixRMaj getQ​(@Nullable @Nullable org.ejml.data.DMatrixRMaj Q)
      An orthogonal matrix that has the following property: H = QTAQ
      Parameters:
      Q - If not null then the results will be stored here. Otherwise a new matrix will be created.
      Returns:
      The extracted Q matrix.

    • 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)

    • getGammas

      public double[] getGammas()