Class HessenbergSimilarDecomposition_DDRM

java.lang.Object
org.ejml.dense.row.decomposition.hessenberg.HessenbergSimilarDecomposition_DDRM
All Implemented Interfaces:
DecompositionInterface<DMatrixRMaj>
Direct Known Subclasses:
HessenbergSimilarDecomposition_MT_DDRM

public class HessenbergSimilarDecomposition_DDRM extends Object implements DecompositionInterface<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 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(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 DecompositionInterface<DMatrixRMaj>
      Parameters:
      A - The matrix that is being decomposed. Not modified.
      Returns:
      If it detects any errors or not.
    • inputModified

      public boolean inputModified()
      Description copied from interface: DecompositionInterface
      Checks if the input matrix to DecompositionInterface.decompose(org.ejml.data.Matrix) is modified during the decomposition process.
      Specified by:
      inputModified in interface DecompositionInterface<DMatrixRMaj>
      Returns:
      true if the input matrix to decompose() is modified.
    • getQH

      public DMatrixRMaj getQH()
      The raw QH matrix that is stored internally.
      Returns:
      QH matrix.
    • getH

      public DMatrixRMaj getH(@Nullable @Nullable 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 DMatrixRMaj getQ(@Nullable @Nullable 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(DMatrixRMaj A, double gamma, int colA0, int w0, int w1)
    • rank1UpdateMultR

      protected void rank1UpdateMultR(DMatrixRMaj A, double gamma, int colA0, int w0, int w1)
    • getGammas

      public double[] getGammas()