splu — SciPy v1.15.3 Manual (original) (raw)

scipy.sparse.linalg.

scipy.sparse.linalg.splu(A, permc_spec=None, diag_pivot_thresh=None, relax=None, panel_size=None, options=None)[source]#

Compute the LU decomposition of a sparse, square matrix.

Parameters:

Asparse array or matrix

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

permc_specstr, optional

How to permute the columns of the matrix for sparsity preservation. (default: ‘COLAMD’)

• NATURAL: natural ordering.
• MMD_ATA: minimum degree ordering on the structure of A^T A.
• MMD_AT_PLUS_A: minimum degree ordering on the structure of A^T+A.
• COLAMD: approximate minimum degree column ordering

diag_pivot_threshfloat, optional

Threshold used for a diagonal entry to be an acceptable pivot. See SuperLU user’s guide for details [1]

relaxint, optional

Expert option for customizing the degree of relaxing supernodes. See SuperLU user’s guide for details [1]

panel_sizeint, optional

Expert option for customizing the panel size. See SuperLU user’s guide for details [1]

optionsdict, optional

Dictionary containing additional expert options to SuperLU. See SuperLU user guide [1] (section 2.4 on the ‘Options’ argument) for more details. For example, you can specifyoptions=dict(Equil=False, IterRefine='SINGLE'))to turn equilibration off and perform a single iterative refinement.

Returns:

invAscipy.sparse.linalg.SuperLU

Object, which has a solve method.

See also

spilu

incomplete LU decomposition

Notes

This function uses the SuperLU library.

References

Examples

import numpy as np from scipy.sparse import csc_array from scipy.sparse.linalg import splu A = csc_array([[1., 0., 0.], [5., 0., 2.], [0., -1., 0.]], dtype=float) B = splu(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.])