code: def updateTBATSFMatrix(
      F, phi, alpha, beta, gamma_bold, ar_coeffs, ma_coeffs, p, q, tau
  ):
      if beta is not None:
          F[0, 1] = phi
          F[1, 1] = phi
          betaAdjust = 1
      else:
          betaAdjust = 0
      if ar_coeffs is not None:
          F[0, (betaAdjust + tau + 1) : (betaAdjust + tau + p + 1)] = (
              alpha * ar_coeffs
          )
          if betaAdjust == 1:
              F[
                  1, (betaAdjust + tau + 1) : (betaAdjust + tau + p + 1)
              ] = (beta * ar_coeffs)
          if tau > 0:
              B = np.dot(
                  gamma_bold.reshape(-1, 1), ar_coeffs.reshape(1, -1)
              )
              F[
                  (1 + betaAdjust) : (betaAdjust + tau + 1),
                  (betaAdjust + tau + 1) : (betaAdjust + tau + p + 1),
              ] = B
          F[
              betaAdjust + tau + 1,
              (betaAdjust + tau + 1) : (betaAdjust + tau + p + 1),
          ] = ar_coeffs
      if ma_coeffs is not None:
          F[
              0,
              (betaAdjust + tau + p + 1) : (
                  betaAdjust + tau + p + q + 1
              ),
          ] = (
              alpha * ma_coeffs
          )
          if betaAdjust == 1:
              F[
                  1,
                  (betaAdjust + tau + p + 1) : (
                      betaAdjust + tau + p + q + 1
                  ),
              ] = (
                  beta * ma_coeffs
              )
          if tau > 0:
              C = np.dot(
                  gamma_bold.reshape(-1, 1), ma_coeffs.reshape(1, -1)
              )
              F[
                  (1 + betaAdjust) : (betaAdjust + tau + 1),
                  (betaAdjust + tau + p + 1) : (
                      betaAdjust + tau + p + q + 1
                  ),
              ] = C
          if ar_coeffs is not None:
              F[
                  betaAdjust + tau + 1,
                  (betaAdjust + tau + p + 1) : (
                      betaAdjust + tau + p + q + 1
                  ),
              ] = ma_coeffs
  
      return F
  
imports: import warnings
  from functools import partial
  import numpy
  import pandas
  import scipy.linalg
  import statsmodels.api
  from numba import njit
  from numpy.polynomial.polynomial import Polynomial
  from scipy.special import inv_boxcox
  from scipy.stats import boxcox
  from scipy.optimize import minimize
  from statsmodels.tsa.stattools import adfuller
  from .arima import auto_arima_f
  from .utils import NOGIL, CACHE
label_desc: Use image node_id 12 for calling a global function with example usage: updateTBATSFMatrix(F, phi, alpha, beta, gamma_bold, ar_coeffs, ma_coeffs, p, q, tau) and returns: F