Package org.ejml.dense.row

Class EigenOps_FDRM

  • public class EigenOps_FDRM
extends java.lang.Object
    Additional functions related to eigenvalues and eigenvectors of a matrix.

    • Constructor Summary

      Constructors 
      Constructor Description
      EigenOps_FDRM()  

    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static float[] boundLargestEigenValue​(org.ejml.data.FMatrixRMaj A, float[] bound)
      Generates a bound for the largest eigen value of the provided matrix using Perron-Frobenius theorem.
      static float computeEigenValue​(org.ejml.data.FMatrixRMaj A, org.ejml.data.FMatrixRMaj eigenVector)
      Given matrix A and an eigen vector of A, compute the corresponding eigen value.
      static org.ejml.data.FEigenpair computeEigenVector​(org.ejml.data.FMatrixRMaj A, float 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)
      }
      static org.ejml.data.FMatrixRMaj createMatrixD​(org.ejml.interfaces.decomposition.EigenDecomposition_F32 eig)
      A diagonal matrix where real diagonal element contains a real eigenvalue.
      static org.ejml.data.FMatrixRMaj createMatrixV​(org.ejml.interfaces.decomposition.EigenDecomposition_F32<org.ejml.data.FMatrixRMaj> eig)
      Puts all the real eigenvectors into the columns of a matrix.
      static org.ejml.data.FEigenpair dominantEigenpair​(org.ejml.data.FMatrixRMaj A)
      Computes the dominant eigen vector for a matrix.

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Constructor Detail

      • EigenOps_FDRM

        public EigenOps_FDRM()

    • Method Detail

      • computeEigenValue

        public static float computeEigenValue​(org.ejml.data.FMatrixRMaj A,
                                      org.ejml.data.FMatrixRMaj eigenVector)

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

        xTAx / xTx

        Parameters:
        A - Matrix. Not modified.
        eigenVector - An eigen vector of A. Not modified.
        Returns:
        The corresponding eigen value.

      • computeEigenVector

        public static org.ejml.data.FEigenpair computeEigenVector​(org.ejml.data.FMatrixRMaj A,
                                                          float 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.

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

      • dominantEigenpair

        public static org.ejml.data.FEigenpair dominantEigenpair​(org.ejml.data.FMatrixRMaj 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.

        Parameters:
        A - A matrix. Not modified.

      • boundLargestEigenValue

        public static float[] boundLargestEigenValue​(org.ejml.data.FMatrixRMaj A,
                                             float[] 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.

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

      • createMatrixD

        public static org.ejml.data.FMatrixRMaj createMatrixD​(org.ejml.interfaces.decomposition.EigenDecomposition_F32 eig)

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

        Parameters:
        eig - An eigenvalue decomposition which has already decomposed a matrix.
        Returns:
        A diagonal matrix containing the eigenvalues.

      • createMatrixV

        public static org.ejml.data.FMatrixRMaj createMatrixV​(org.ejml.interfaces.decomposition.EigenDecomposition_F32<org.ejml.data.FMatrixRMaj> 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.

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