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)[source]#
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_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
- Returns:
- invA_approxscipy.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.])