Module imagingbook.common
Package imagingbook.common.math.eigen

Interface RealEigenDecomposition

All Known Implementing Classes:
EigenDecompositionApache, EigenDecompositionJama, Eigensolver2x2, GeneralizedEigenDecomposition, GeneralizedSymmetricEigenDecomposition
public interface RealEigenDecomposition
Common interface for eigendecompositions capable of delivering solutions when all eigenvalues are real.
Version:
2022/07/08

  • Method Summary

    Modifier and Type
    Method
    Description
    default RealMatrix
    getD()
    Gets the block diagonal matrix D of the decomposition.
    RealVector
    getEigenvector(int k)
    Returns the k-th eigenvector, i.e., the k-th column vector of the matrix returned by getV().
    double
    getRealEigenvalue(int k)
    Returns the real part of the k-th eigenvalue
    double[]
    getRealEigenvalues()
    Returns a vector holding the real parts of the eigenvalues
    RealMatrix
    getV()
    Return the matrix of eigenvectors, which are its column vectors.
    boolean
    hasComplexEigenvalues()
    Returns whether the calculated eigenvalues are complex or real.

  • Method Details

    • hasComplexEigenvalues

      boolean hasComplexEigenvalues()
      Returns whether the calculated eigenvalues are complex or real.
      Returns:
      true if any of the eigenvalues is complex, false otherwise

    • getRealEigenvalue

      double getRealEigenvalue(int k)
      Returns the real part of the k-th eigenvalue
      Parameters:
      k - index of the eigenvalue @param k index of the eigenvector (0-based)
      Returns:
      real part of the k-th eigenvalue

    • getRealEigenvalues

      double[] getRealEigenvalues()
      Returns a vector holding the real parts of the eigenvalues
      Returns:
      real(diag(D))

    • getEigenvector

      RealVector getEigenvector(int k)
      Returns the k-th eigenvector, i.e., the k-th column vector of the matrix returned by getV().
      Parameters:
      k - index of the eigenvector (0-based)
      Returns:
      the k-th eigenvector (instance of RealVector)

    • getV

      RealMatrix getV()
      Return the matrix of eigenvectors, which are its column vectors.
      Returns:
      the matrix of eigenvectors

    • getD

      default RealMatrix getD()
      Gets the block diagonal matrix D of the decomposition. Real eigenvalues are on the diagonal while complex values are on 2x2 blocks {{real_pos imaginary}, {neg_imaginary, real}}.
      Returns:
      matrix D