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Module « scipy.sparse.linalg »

Fonction spilu - module scipy.sparse.linalg

Signature de la fonction spilu

def 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) 

Description

help(scipy.sparse.linalg.spilu)

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 array 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_array
>>> from scipy.sparse.linalg import spilu
>>> A = csc_array([[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.])

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