splu#
- 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 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.
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.])