Class EigenOps

  • public class EigenOpsextends Object
    Additional functions related to eigenvalues and eigenvectors of a matrix.
    • Constructor Detail

      • EigenOps

        public EigenOps()
    • Method Detail

      • computeEigenValue

        public static double computeEigenValue(DenseMatrix64F A,                       DenseMatrix64F eigenVector)

        Given matrix A and an eigen vector of A, compute the corresponding eigen value. This is the Rayleigh quotient.

        xTAx / xTx

        A - Matrix. Not modified.
        eigenVector - An eigen vector of A. Not modified.
        The corresponding eigen value.
      • computeEigenVector

        public static Eigenpair computeEigenVector(DenseMatrix64F A,                           double eigenvalue)

        Given an eigenvalue it computes an eigenvector using inverse iteration:
        for i=1:MAX {
        (A - μI)z(i) = q(i-1)
        q(i) = z(i) / ||z(i)||
        λ(i) = q(i)T A q(i)

        NOTE: If there is another eigenvalue that is very similar to the provided one then there is a chance of it converging towards that one instead. The larger a matrix is the more likely this is to happen.

        A - Matrix whose eigenvector is being computed. Not modified.
        eigenvalue - The eigenvalue in the eigen pair.
        The eigenvector or null if none could be found.
      • dominantEigenpair

        public static Eigenpair dominantEigenpair(DenseMatrix64F A)

        Computes the dominant eigen vector for a matrix. The dominant eigen vector is an eigen vector associated with the largest eigen value.

        WARNING: This function uses the power method. There are known cases where it will not converge. It also seems to converge to non-dominant eigen vectors some times. Use at your own risk.

        A - A matrix. Not modified.
      • boundLargestEigenValue

        public static double[] boundLargestEigenValue(DenseMatrix64F A,                              double[] bound)

        Generates a bound for the largest eigen value of the provided matrix using Perron-Frobenius theorem. This function only applies to non-negative real matrices.

        For "stochastic" matrices (Markov process) this should return one for the upper and lower bound.

        A - Square matrix with positive elements. Not modified.
        bound - Where the results are stored. If null then a matrix will be declared. Modified.
        Lower and upper bound in the first and second elements respectively.
      • createMatrixD

        public static DenseMatrix64F createMatrixD(EigenDecomposition eig)

        A diagonal matrix where real diagonal element contains a real eigenvalue. If an eigenvalue is imaginary then zero is stored in its place.

        eig - An eigenvalue decomposition which has already decomposed a matrix.
        A diagonal matrix containing the eigenvalues.
      • createMatrixV

        public static DenseMatrix64F createMatrixV(EigenDecomposition<DenseMatrix64F> eig)

        Puts all the real eigenvectors into the columns of a matrix. If an eigenvalue is imaginary then the corresponding eigenvector will have zeros in its column.

        eig - An eigenvalue decomposition which has already decomposed a matrix.
        An m by m matrix containing eigenvectors in its columns.

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