splu(A, permc_spec=None, diag_pivot_thresh=None, relax=None, panel_size=None, options={})

Notes

This function uses the SuperLU library.

Parameters

A : sparse matrix

Sparse matrix to factorize. Should be in CSR or CSC format.

permc_spec : str, 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_thresh : float, optional

Threshold used for a diagonal entry to be an acceptable pivot. See SuperLU user's guide for details

relax : int, optional

Expert option for customizing the degree of relaxing supernodes. See SuperLU user's guide for details

panel_size : int, optional

Expert option for customizing the panel size. See SuperLU user's guide for details

options : dict, optional

Dictionary containing additional expert options to SuperLU. See SuperLU user guide (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

invA : scipy.sparse.linalg.SuperLU

Object, which has a solve method.

Compute the LU decomposition of a sparse, square matrix.

See Also

spilu

incomplete LU decomposition

Examples

>>> 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.])

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.sparse.linalg._dsolve.linsolve.splu scipy.sparse.linalg._dsolve.linsolve.spilu

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