# scipy.sparse.linalg.splu#

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

Compute the LU decomposition of a sparse, square matrix.

Parameters:
Asparse matrix

Sparse matrix 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 specify options=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.

spilu

incomplete LU decomposition

Notes

This function uses the SuperLU library.

References

[1] (1,2,3,4)

Examples

>>> import numpy as np
>>> from scipy.sparse import csc_matrix
>>> from scipy.sparse.linalg import splu
>>> A = csc_matrix([[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.])