klus package

Contains the main routines for the KLUS library. There are algorithms, kernels and other tools for the performing EDMD for Koopman decomposition.

Submodules

• klus.algorithms module
  • dmd()
  • dmdc()
  • amuse()
  • tica()
  • ulam()
  • edmd()
  • gedmd()
  • kedmd()
  • sindy()
  • kpca()
  • kcca()
  • cmd()
  • seba()
  • kcovedmd()
  • sortEig()
  • FeatureMatrix()
  • kgedmd()
• klus.domain module
  • discretization
    • discretization.dimension()
    • discretization.numBoxes()
    • discretization.rand()
    • discretization.randPerBox()
    • discretization.index()
    • discretization.mindex()
    • discretization.midpointGrid()
    • discretization.plot()
  • randb()
• klus.kernels module
  • gaussianKernel
    • gaussianKernel.diff()
    • gaussianKernel.ddiff()
    • gaussianKernel.laplace()
  • gaussianKernelGeneralized
    • gaussianKernelGeneralized.diff()
    • gaussianKernelGeneralized.ddiff()
    • gaussianKernelGeneralized.laplace()
  • laplacianKernel
    • laplacianKernel.diff()
    • laplacianKernel.ddiff()
    • laplacianKernel.laplace()
  • polynomialKernel
    • polynomialKernel.diff()
    • polynomialKernel.ddiff()
    • polynomialKernel.laplace()
  • periodicKernel1D
    • periodicKernel1D.diff()
    • periodicKernel1D.ddiff()
  • stringKernel
    • stringKernel.evaluate()
  • productKernel
    • productKernel.diff()
    • productKernel.ddiff()
    • productKernel.laplace()
  • gramian()
  • gramian2()
  • densityEstimate
    • densityEstimate.rho()
    • densityEstimate.V()
    • densityEstimate.gradV()
• klus.observables module
  • identity()
  • monomials
    • monomials.diff()
    • monomials.ddiff()
    • monomials.display()
  • indicators
  • gaussians
    • gaussians.diff()
    • gaussians.ddiff()
  • nchoosek()
  • nextMonomialPowers()
  • allMonomialPowers()
• klus.tools module
  • indexS2M()
  • indexM2S()
  • printVector()
  • printMatrix2()
  • printMatrix()
  • Timer
  • matmux
    • matmux.exportVars()
    • matmux.importVars()
    • matmux.figure()
    • matmux.close()
    • matmux.plot()
    • matmux.surf()
    • matmux.scatter()
    • matmux.scatter3()
    • matmux.pcolor()
    • matmux.imagesc()
    • matmux.plotDomain()

Module contents

Algorithm and utility functions for nonlinear analyses For Koopman and Perron analysis

Based on software from Stefan Klus

algorithms :

Routines for averaging and various computations. The implementations of the methods

• DMD, TICA, AMUSE

• Ulam's method

• EDMD, kernel EDMD, generator EDMD

• SINDy

• kernel PCA, kernel CCA

• CMD

• SEBA

are based on the publications listed here:

https://github.com/sklus/d3s

observables :

various functions for observables

kernels :

Definition of various kernels

tools :

Utilties for the rest of the modules.