code: def get_OPinv_matvec(A, M, sigma, symmetric=False, tol=0):
      if sigma == 0:
          return get_inv_matvec(A, symmetric=symmetric, tol=tol)
  
      if M is None:
          # M is the identity matrix
          if isdense(A):
              if (
                  np.issubdtype(A.dtype, np.complexfloating)
                  or np.imag(sigma) == 0
              ):
                  A = np.copy(A)
              else:
                  A = A + 0j
              A.flat[:: A.shape[1] + 1] -= sigma
              return LuInv(A).matvec
          elif isspmatrix(A):
              A = A - sigma * identity(A.shape[0])
              if symmetric and isspmatrix_csr(A):
                  A = A.T
              return SpLuInv(A.tocsc()).matvec
          else:
              return IterOpInv(
                  _aslinearoperator_with_dtype(A), M, sigma, tol=tol
              ).matvec
      else:
          if (not isdense(A) and not isspmatrix(A)) or (
              not isdense(M) and not isspmatrix(M)
          ):
              return IterOpInv(
                  _aslinearoperator_with_dtype(A),
                  _aslinearoperator_with_dtype(M),
                  sigma,
                  tol=tol,
              ).matvec
          elif isdense(A) or isdense(M):
              return LuInv(A - sigma * M).matvec
          else:
              OP = A - sigma * M
              if symmetric and isspmatrix_csr(OP):
                  OP = OP.T
              return SpLuInv(OP.tocsc()).matvec
  
imports: from scipy.sparse.linalg.eigen.arpack import _arpack
  import numpy
  from scipy.sparse.linalg.interface import aslinearoperator, LinearOperator
  from scipy.sparse import identity, isspmatrix, isspmatrix_csr
  from scipy.linalg import lu_factor, lu_solve
  from scipy.sparse.sputils import isdense
  from scipy.sparse.linalg import gmres, splu
  import scipy
  import functools
  import operator
  from distutils.version import LooseVersion
label_desc: Use image node_id 4 for calling a global function with example usage: get_OPinv_matvec(A, M, sigma, symmetric, tol) and returns: get_inv_matvec, LuInv, IterOpInv, SpLuInv, IterOpInv, LuInv, SpLuInv