Class EigenOps_DDRM

java.lang.Object
org.ejml.dense.row.EigenOps_DDRM

public class EigenOps_DDRM
extends Object
Additional functions related to eigenvalues and eigenvectors of a matrix.
  • Constructor Details

    • EigenOps_DDRM

      public EigenOps_DDRM()
  • Method Details

    • computeEigenValue

      public static double computeEigenValue​(DMatrixRMaj A, DMatrixRMaj 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

      @Nullable public static @Nullable DEigenpair computeEigenVector​(DMatrixRMaj 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.

      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

      @Nullable public static @Nullable DEigenpair dominantEigenpair​(DMatrixRMaj 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 double[] boundLargestEigenValue​(DMatrixRMaj A, @Nullable @org.jetbrains.annotations.Nullable 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.

      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 DMatrixRMaj createMatrixD​(EigenDecomposition_F64<?> 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 DMatrixRMaj createMatrixV​(EigenDecomposition_F64<DMatrixRMaj> 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.