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

Class TridiagonalDecompositionHouseholder_CDRM

java.lang.Object
org.ejml.dense.row.decompose.hessenberg.TridiagonalDecompositionHouseholder_CDRM
All Implemented Interfaces:
DecompositionInterface<CMatrixRMaj>, TridiagonalSimilarDecomposition<CMatrixRMaj>, TridiagonalSimilarDecomposition_F32<CMatrixRMaj>
@Generated("org.ejml.dense.row.decompose.hessenberg.TridiagonalDecompositionHouseholder_ZDRM") public class TridiagonalDecompositionHouseholder_CDRM extends Object implements TridiagonalSimilarDecomposition_F32<CMatrixRMaj>

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 Details

    • TridiagonalDecompositionHouseholder_CDRM

      public TridiagonalDecompositionHouseholder_CDRM()

  • Method Details

    • getQT

      public CMatrixRMaj getQT()
      Returns the internal matrix where the decomposed results are stored.

    • getDiagonal

      public void getDiagonal(float[] diag, float[] off)
      Description copied from interface: TridiagonalSimilarDecomposition_F32
      Extracts the diagonal and off diagonal elements of the decomposed tridiagonal matrix. Since it is symmetric only one off diagonal array is returned.
      Specified by:
      getDiagonal in interface TridiagonalSimilarDecomposition_F32<CMatrixRMaj>
      Parameters:
      diag - Diagonal elements. Modified.
      off - off diagonal elements. Modified.

    • getT

      public CMatrixRMaj getT(@Nullable @Nullable CMatrixRMaj T)
      Extracts the tridiagonal matrix found in the decomposition.
      Specified by:
      getT in interface TridiagonalSimilarDecomposition<CMatrixRMaj>
      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 CMatrixRMaj getQ(@Nullable @Nullable CMatrixRMaj Q, boolean transposed)
      An orthogonal matrix that has the following property: T = QHAQ
      Specified by:
      getQ in interface TridiagonalSimilarDecomposition<CMatrixRMaj>
      Parameters:
      Q - If not null then the results will be stored here. Otherwise a new matrix will be created.
      transposed - If true then the transpose (real) or conjugate transpose (complex) of Q is returned.
      Returns:
      The extracted Q matrix.

    • decompose

      public boolean decompose(CMatrixRMaj A)
      Decomposes the provided symmetric matrix.
      Specified by:
      decompose in interface DecompositionInterface<CMatrixRMaj>
      Parameters:
      A - Symmetric matrix that is going to be decomposed. Not modified.
      Returns:
      Returns if it was able to decompose the matrix.

    • householderSymmetric

      public void householderSymmetric(int row, float 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(CMatrixRMaj A)
      If needed declares and sets up internal data structures.
      Parameters:
      A - Matrix being decomposed.

    • 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<CMatrixRMaj>
      Returns:
      true if the input matrix to decompose() is modified.

    • getGammas

      public float[] getGammas()