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

Class HessenbergSimilarDecomposition_ZDRM

java.lang.Object
org.ejml.dense.row.decompose.hessenberg.HessenbergSimilarDecomposition_ZDRM
All Implemented Interfaces:
org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.ZMatrixRMaj>
public class HessenbergSimilarDecomposition_ZDRM extends Object implements org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.ZMatrixRMaj>

Complex Hessenberg decomposition. It find matrices O and P such that:

A = OPOH

where A is an m by m matrix, O is an orthogonal matrix, and P 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.

  • Constructor Summary

    Constructors
    Constructor
    Description
    HessenbergSimilarDecomposition_ZDRM()
     
    HessenbergSimilarDecomposition_ZDRM(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.ZMatrixRMaj A)
    Computes the decomposition of the provided matrix.
    double[]
    getGammas()
     
    org.ejml.data.ZMatrixRMaj
    getH(@Nullable org.ejml.data.ZMatrixRMaj H)
    An upper Hessenberg matrix from the decomposition.
    org.ejml.data.ZMatrixRMaj
    getQ(@Nullable org.ejml.data.ZMatrixRMaj Q)
    An orthogonal matrix that has the following property: H = QTAQ
    org.ejml.data.ZMatrixRMaj
    getQH()
    The raw QH matrix that is stored internally.
    boolean
    inputModified()
     

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • HessenbergSimilarDecomposition_ZDRM

      public HessenbergSimilarDecomposition_ZDRM(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_ZDRM

      public HessenbergSimilarDecomposition_ZDRM()

  • Method Details

    • decompose

      public boolean decompose(org.ejml.data.ZMatrixRMaj 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.ZMatrixRMaj>
      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.ZMatrixRMaj>

    • getQH

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

    • getH

      public org.ejml.data.ZMatrixRMaj getH(@Nullable @Nullable org.ejml.data.ZMatrixRMaj 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.ZMatrixRMaj getQ(@Nullable @Nullable org.ejml.data.ZMatrixRMaj 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.

    • getGammas

      public double[] getGammas()