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# scipy.sparse.linalg.lobpcg

`scipy.sparse.linalg.``lobpcg`(A, X, B=None, M=None, Y=None, tol=None, maxiter=20, largest=True, verbosityLevel=0, retLambdaHistory=False, retResidualNormsHistory=False)

  Solve symmetric partial eigenproblems with optional preconditioning

  This function implements the Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG).

  Parameters : | A : {sparse matrix, dense matrix, LinearOperator} The symmetric linear operator of the problem, usually a sparse matrix. Often called the “stiffness matrix”. X : array_like Initial approximation to the k eigenvectors. If A has shape=(n,n) then X should have shape shape=(n,k). B : {dense matrix, sparse matrix, LinearOperator}, optional the right hand side operator in a generalized eigenproblem. by default, B = Identity often called the “mass matrix” M : {dense matrix, sparse matrix, LinearOperator}, optional preconditioner to A; by default M = Identity M should approximate the inverse of A Y : array_like, optional n-by-sizeY matrix of constraints, sizeY < n The iterations will be performed in the B-orthogonal complement of the column-space of Y. Y must be full rank.
  Returns : | w : array Array of k eigenvalues v : array An array of k eigenvectors. V has the same shape as X.
  Other Parameters:
  | tol : scalar, optional Solver tolerance (stopping criterion) by default: tol=n*sqrt(eps) maxiter : integer, optional maximum number of iterations by default: maxiter=min(n,20) largest : boolean, optional when True, solve for the largest eigenvalues, otherwise the smallest verbosityLevel : integer, optional controls solver output. default: verbosityLevel = 0. retLambdaHistory : boolean, optional whether to return eigenvalue history retResidualNormsHistory : boolean, optional whether to return history of residual norms

  Notes

  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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