code: def maskedmean_riemann(
      X=None,
      masks=None,
      tol=10e-9,
      maxiter=100,
      init=None,
      sample_weight=None,
      covmats=None,
  ):
      """Masked Riemannian mean of SPD/HPD matrices.
  
      Given masks defined as semi-orthogonal matrices, the masked Riemannian mean
      of SPD/HPD matrices is obtained with a gradient descent minimizing the sum
      of affine-invariant Riemannian distances between masked SPD/HPD matrices
      and the masked mean [1]_.
  
      Parameters
      ----------
      X : ndarray, shape (n_matrices, n, n)
          Set of SPD/HPD matrices.
      masks : list of n_matrices ndarray of shape (n, n_i), \
              with different n_i, such that n_i <= n
          Masks, defined as semi-orthogonal matrices. See [1]_.
      tol : float, default=10e-9
          The tolerance to stop the gradient descent.
      maxiter : int, default=100
          The maximum number of iteration.
      init : None | ndarray, shape (n, n), default=None
          A SPD/HPD matrix used to initialize the gradient descent.
          If None, the Identity is used.
      sample_weight : None | ndarray, shape (n_matrices,), default=None
          Weights for each matrix. If None, it uses equal weights.
  
      Returns
      -------
      M : ndarray, shape (n, n)
          Masked Riemannian mean.
  
      Notes
      -----
      .. versionadded:: 0.3
  
      See Also
      --------
      mean_riemann
      mean_covariance
  
      References
      ----------
      .. [1] `Geodesically-convex optimization for averaging partially observed
          covariance matrices
          <https://hal.archives-ouvertes.fr/hal-02984423>`_
          F. Yger, S. Chevallier, Q. Barthélemy, and S. Sra. Asian Conference on
          Machine Learning (ACML), Nov 2020, Bangkok, Thailand. pp.417 - 432.
      """
      if masks is None:
          raise ValueError("Input masks can not be None")
      X = _deprecate_covmats(covmats, X)
      n_matrices, n, _ = X.shape
      sample_weight = check_weights(sample_weight, n_matrices)
      maskedX = _apply_masks(X, masks)
      if init is None:
          M = np.eye(n)
      else:
          M = init
  
      nu = 1.0
      tau = np.finfo(np.float64).max
      crit = np.finfo(np.float64).max
      for _ in range(maxiter):
          maskedM = _apply_masks(np.tile(M, (n_matrices, 1, 1)), masks)
          J = np.zeros((n, n), dtype=X.dtype)
          for i in range(n_matrices):
              M12, Mm12 = sqrtm(maskedM[i]), invsqrtm(maskedM[i])
              tmp = M12 @ logm(Mm12 @ maskedX[i] @ Mm12) @ M12
              J += sample_weight[i] * masks[i] @ tmp @ masks[i].T
          M12, Mm12 = sqrtm(M), invsqrtm(M)
          M = M12 @ expm(Mm12 @ (nu * J) @ Mm12) @ M12
  
          crit = np.linalg.norm(J, ord="fro")
          h = nu * crit
          if h < tau:
              nu = 0.95 * nu
              tau = h
          else:
              nu = 0.5 * nu
          if crit <= tol or nu <= tol:
              break
      else:
          warnings.warn("Convergence not reached")
  
      return M
  
imports: from copy import deepcopy
  import numpy
  import warnings
  from .ajd import ajd_pham
  from .base import sqrtm, invsqrtm, logm, expm, powm
  from .distance import distance_riemann
  from .geodesic import geodesic_riemann
  from .utils import check_weights
label_desc: Use image node_id 18 for calling a global function with example usage: maskedmean_riemann(X, masks, tol, maxiter, init, sample_weight, covmats) and returns: M