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Args: A (array-like): The symmetric linear operator of the problem, usually a sparse matrix. Can be of the following types - cupy.ndarray - cupyx.scipy.sparse.csr_matrix - cupy.scipy.sparse.linalg.LinearOperator X (cupy.ndarray): Initial approximation to the ``k`` eigenvectors (non-sparse). If `A` has ``shape=(n,n)`` then `X` should have shape ``shape=(n,k)``. B (array-like): The right hand side operator in a generalized eigenproblem. By default, ``B = Identity``. Can be of following types: - cupy.ndarray - cupyx.scipy.sparse.csr_matrix - cupy.scipy.sparse.linalg.LinearOperator M (array-like): Preconditioner to `A`; by default ``M = Identity``. `M` should approximate the inverse of `A`. Can be of the following types: - cupy.ndarray - cupyx.scipy.sparse.csr_matrix - cupy.scipy.sparse.linalg.LinearOperator Y (cupy.ndarray): `n-by-sizeY` matrix of constraints (non-sparse), `sizeY < n` The iterations will be performed in the B-orthogonal complement of the column-space of Y. Y must be full rank. tol (float): Solver tolerance (stopping criterion). The default is ``tol=n*sqrt(eps)``. maxiter (int): Maximum number of iterations. The default is ``maxiter = 20``. largest (bool): When True, solve for the largest eigenvalues, otherwise the smallest. verbosityLevel (int): Controls solver output. The default is ``verbosityLevel=0``. retLambdaHistory (bool): Whether to return eigenvalue history. Default is False. retResidualNormsHistory (bool): Whether to return history of residual norms. Default is False. Returns: tuple: - `w` (cupy.ndarray): Array of ``k`` eigenvalues - `v` (cupy.ndarray) An array of ``k`` eigenvectors. `v` has the same shape as `X`. - `lambdas` (list of cupy.ndarray): The eigenvalue history, if `retLambdaHistory` is True. - `rnorms` (list of cupy.ndarray): The history of residual norms, if `retResidualNormsHistory` is True. .. seealso:: :func:`scipy.sparse.linalg.lobpcg` .. note:: If both ``retLambdaHistory`` and ``retResidualNormsHistory`` are `True` the return tuple has the following format ``(lambda, V, lambda history, residual norms history)``. 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