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# scipy.sparse.linalg.spilu

scipy.sparse.linalg.spilu(A, drop_tol=None, fill_factor=None, drop_rule=None, permc_spec=None, diag_pivot_thresh=None, relax=None, panel_size=None, options=None)

  Compute an incomplete LU decomposition for a sparse, square matrix.

  The resulting object is an approximation to the inverse of A.

  Parameters:
    A(N, N) array_like

      Sparse matrix to factorize. Most efficient when provided in CSC format. Other formats will be converted to CSC before factorization.

    drop_tol float, optional

      Drop tolerance (0 <= tol <= 1) for an incomplete LU decomposition. (default: 1e-4)

    fill_factor float, optional

      Specifies the fill ratio upper bound (>= 1.0) for ILU. (default: 10)

    drop_rule str, optional

      Comma-separated string of drop rules to use. Available rules: `basic`, `prows`, `column`, `area`, `secondary`, `dynamic`, `interp`. (Default: `basic,area`)

      See SuperLU documentation for details.

    Remaining other options

      Same as for `splu`

  Returns:
    invA_approx scipy.sparse.linalg.SuperLU

      Object, which has a `solve` method.

  See also

  `splu`

    complete LU decomposition

  Notes

  To improve the better approximation to the inverse, you may need to increase fill_factor AND decrease drop_tol.

  This function uses the SuperLU library.

  Examples

      >>> import numpy as np
      >>> from scipy.sparse import csc_matrix
      >>> from scipy.sparse.linalg import spilu
      >>> A = csc_matrix([[1., 0., 0.], [5., 0., 2.], [0., -1., 0.]], dtype=float)
      >>> B = spilu(A)
      >>> x = np.array([1., 2., 3.], dtype=float)
      >>> B.solve(x)
      array([ 1. , -3. , -1.5])
      >>> A.dot(B.solve(x))
      array([ 1.,  2.,  3.])
      >>> B.solve(A.dot(x))
      array([ 1.,  2.,  3.])