code: def train_gmm(X, max_iter, tol, means, covariances):
      xp = cupy.get_array_module(X)
      lower_bound = -np.inf
      converged = False
      weights = xp.array([0.5, 0.5], dtype=np.float32)
      inv_cov = 1 / xp.sqrt(covariances)
  
      for n_iter in range(max_iter):
          prev_lower_bound = lower_bound
          log_prob_norm, log_resp = e_step(X, inv_cov, means, weights)
          weights, means, covariances = m_step(X, xp.exp(log_resp))
          inv_cov = 1 / xp.sqrt(covariances)
          lower_bound = log_prob_norm
          change = lower_bound - prev_lower_bound
          if abs(change) < tol:
              converged = True
              break
  
      if not converged:
          print("Failed to converge. Increase max-iter or tol.")
  
      return inv_cov, means, weights, covariances
  
file_path: cupy/examples/gmm/gmm.py
imports: import argparse
  import contextlib
  import time
  import matplotlib.pyplot
  import numpy
  from scipy import stats
  import cupy
label_desc: Use image node_id 5 for calling a global function with example usage: train_gmm(X, max_iter, tol, means, covariances) and returns: inv_cov,  means,  weights,  covariances