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)[source]#

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

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

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_tolfloat, optional

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

fill_factorfloat, optional

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

drop_rulestr, 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


Object, which has a solve method.

See also


complete LU decomposition


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.


>>> 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])
array([ 1.,  2.,  3.])
>>> B.solve(
array([ 1.,  2.,  3.])