EigenvalueDecomposition
cern.colt.matrix.linalg

Class EigenvalueDecomposition

  • All Implemented Interfaces:
    Serializable


    public class EigenvalueDecompositionextends Objectimplements Serializable
    Eigenvalues and eigenvectors of a real matrix A.

    If A is symmetric, then A = V*D*V' where the eigenvalue matrix D isdiagonal and the eigenvector matrix V is orthogonal.I.e. A = V.mult(D.mult(transpose(V))) and V.mult(transpose(V)) equals the identity matrix.

    If A is not symmetric, then the eigenvalue matrix D is block diagonalwith the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D,i.e. A.mult(V) equals V.mult(D). The matrix V may be badlyconditioned, or even singular, so the validity of the equationA = V*D*inverse(V) depends upon Algebra.cond(V).

    See Also:
    Serialized Form
    • Constructor Detail

      • EigenvalueDecomposition

        public EigenvalueDecomposition(DoubleMatrix2D A)
        Constructs and returns a new eigenvalue decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.Checks for symmetry, then constructs the eigenvalue decomposition.
        Parameters:
        A - A square matrix.
        Throws:
        IllegalArgumentException - if A is not square.
    • Method Detail

      • getD

        public DoubleMatrix2D getD()
        Returns the block diagonal eigenvalue matrix, D.
        Returns:
        D
      • getImagEigenvalues

        public DoubleMatrix1D getImagEigenvalues()
        Returns the imaginary parts of the eigenvalues.
        Returns:
        imag(diag(D))
      • getRealEigenvalues

        public DoubleMatrix1D getRealEigenvalues()
        Returns the real parts of the eigenvalues.
        Returns:
        real(diag(D))
      • getV

        public DoubleMatrix2D getV()
        Returns the eigenvector matrix, V
        Returns:
        V
      • toString

        public String toString()
        Returns a String with (propertyName, propertyValue) pairs.Useful for debugging or to quickly get the rough picture.For example,
        rank          : 3trace         : 0
        Overrides:
        toString in class Object

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