The “dominant_eigenvalue” package

The package is designed by procedural programming and contains various functions to optimize the method’s parameters, perform the dominant eigenvalue analysis and visualize the optimization and the analysis results. The package provides useful tools to estimate the eigenvalues and absolute dominant eigenvalues of a system that is described by a single time series. The package contains three modules with the following functions:

  1. dominant_eigenvalue.param_opt

    1. embedding_attractor_reconstruction(data, E, index_shift)

    2. false_NN(data, time, index_shift, start_order = 1, end_order = 15, NN_threshold = 30)

    3. various_R_threshold_fnn(data, index_shift= 1, start_threshold = 15, end_threshold = 50, start_order = 1, end_order = 15, save = False, save_name = ‘fnn_R_threshold_series_default00.npy’)

    4. avg_distance_from_diagonal(data, E, start_lag = 1, end_lag = 10, image = False)

  2. dominant_eigenvalue.analysis

    1. interaction_coeff_calc(data, order)

    2. jacobian(AR_params)

    3. max_eigenvalue_calc(matrix)

    4. AR_EV_calc(gendata, rolling_window_size, order)

    5. detrend_fct(…)

  3. dominant_eigenvalue.graphics

    1. abs_max_eigval_plot(…)

    2. prep_plot_imaginary_plane(eigvals)

    3. max_eigval_gauss_plot(…)

    4. plot_fnn(…)

    5. plot_avg_DD(…)

The first dominant_eigenvalue.param_opt module contains basic tools to optimize the parameters for the eigenvalue estimation. The eigenvalue estimation tools can be found in the dominant_eigenvalue.analysis module. The third dominant_eigenvalue.graphics module provides some functions to plot the results of the analysis.