code: def largest_lyauponov_exponent(epochs, param=lyaup_param):
      def LLE_1d(x, tau, n, T, fs):
          Em = _embed_seq(x, tau, n)
          M = len(Em)
          A = np.tile(Em, (len(Em), 1, 1))
          B = np.transpose(A, [1, 0, 2])
          square_dists = (
              A - B
          ) ** 2  # square_dists[i,j,k] = (Em[i][k]-Em[j][k])^2
          D = np.sqrt(
              square_dists[:, :, :].sum(axis=2)
          )  # D[i,j] = ||Em[i]-Em[j]||_2
  
          # Exclude elements within T of the diagonal
          band = np.tri(D.shape[0], k=T) - np.tri(D.shape[0], k=-T - 1)
          band[band == 1] = np.inf
          neighbors = (D + band).argmin(
              axis=0
          )  # nearest neighbors more than T steps away
  
          # in_bounds[i,j] = (i+j <= M-1 and i+neighbors[j] <= M-1)
          inc = np.tile(np.arange(M), (M, 1))
          row_inds = np.tile(np.arange(M), (M, 1)).T + inc
          col_inds = np.tile(neighbors, (M, 1)) + inc.T
          in_bounds = np.logical_and(
              row_inds <= M - 1, col_inds <= M - 1
          )
          # Uncomment for old (miscounted) version
          # in_bounds = numpy.logical_and(row_inds < M - 1, col_inds < M - 1)
          row_inds[~in_bounds] = 0
          col_inds[~in_bounds] = 0
  
          # neighbor_dists[i,j] = ||Em[i+j]-Em[i+neighbors[j]]||_2
          neighbor_dists = np.ma.MaskedArray(
              D[row_inds, col_inds], ~in_bounds
          )
          J = (~neighbor_dists.mask).sum(
              axis=1
          )  # number of in-bounds indices by row
          # Set invalid (zero) values to 1; log(1) = 0 so sum is unchanged
  
          neighbor_dists[neighbor_dists == 0] = 1
  
          # !!! this fixes the divide by zero in log error !!!
          neighbor_dists.data[neighbor_dists.data == 0] = 1
  
          d_ij = np.sum(np.log(neighbor_dists.data), axis=1)
          mean_d = d_ij[J > 0] / J[J > 0]
  
          x = np.arange(len(mean_d))
          X = np.vstack((x, np.ones(len(mean_d)))).T
          [m, c] = np.linalg.lstsq(X, mean_d, rcond=None)[0]
          Lexp = fs * m
          return Lexp
  
      return [
          (
              "Tau_{}__n_{}__T_{}__fs_{}".format(
                  par["Tau"], par["n"], par["T"], par["fs"]
              ),
              np.apply_along_axis(
                  LLE_1d,
                  0,
                  epochs,
                  par["Tau"],
                  par["n"],
                  par["T"],
                  par["fs"],
              ).ravel()[0],
          )
          for par in param
      ]
  
imports: import pandas
  import numpy
  from statsmodels.tsa.stattools import acf, adfuller, pacf
  import itertools
  from statsmodels.tsa.ar_model import AR
  from scipy.signal import cwt, find_peaks_cwt, ricker, welch
  from scipy.stats import linregress
  import scipy.stats
  from scipy.stats import kurtosis
  from scipy.stats import skew
  import numpy
  from scipy import signal, integrate
  from scipy.interpolate import interp1d
  import math
  from statsmodels.tools.sm_exceptions import MissingDataError
  from numpy.linalg import LinAlgError
label_desc: Use image node_id 46 for calling a global function with example usage: largest_lyauponov_exponent(epochs, param) and returns: unknown, Lexp