spsolve — SciPy v1.15.3 Manual (original) (raw)
scipy.sparse.linalg.
scipy.sparse.linalg.spsolve(A, b, permc_spec=None, use_umfpack=True)[source]#
Solve the sparse linear system Ax=b, where b may be a vector or a matrix.
Parameters:
Andarray or sparse array or matrix
The square matrix A will be converted into CSC or CSR form
bndarray or sparse array or matrix
The matrix or vector representing the right hand side of the equation. If a vector, b.shape must be (n,) or (n, 1).
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 [1], [2].
use_umfpackbool, optional
if True (default) then use UMFPACK for the solution [3], [4], [5],[6] . This is only referenced if b is a vector andscikits.umfpack is installed.
Returns:
xndarray or sparse array or matrix
the solution of the sparse linear equation. If b is a vector, then x is a vector of size A.shape[1] If b is a matrix, then x is a matrix of size (A.shape[1], b.shape[1])
Notes
For solving the matrix expression AX = B, this solver assumes the resulting matrix X is sparse, as is often the case for very sparse inputs. If the resulting X is dense, the construction of this sparse result will be relatively expensive. In that case, consider converting A to a dense matrix and using scipy.linalg.solve or its variants.
References
[1]
T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836: COLAMD, an approximate column minimum degree ordering algorithm, ACM Trans. on Mathematical Software, 30(3), 2004, pp. 377–380.DOI:10.1145/1024074.1024080
[2]
T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, A column approximate minimum degree ordering algorithm, ACM Trans. on Mathematical Software, 30(3), 2004, pp. 353–376. DOI:10.1145/1024074.1024079
[5]
T. A. Davis and I. S. Duff, A combined unifrontal/multifrontal method for unsymmetric sparse matrices, ACM Trans. on Mathematical Software, 25(1), 1999, pp. 1–19.https://doi.org/10.1145/305658.287640
[6]
T. A. Davis and I. S. Duff, An unsymmetric-pattern multifrontal method for sparse LU factorization, SIAM J. Matrix Analysis and Computations, 18(1), 1997, pp. 140–158.https://doi.org/10.1137/S0895479894246905T.
Examples
import numpy as np from scipy.sparse import csc_array from scipy.sparse.linalg import spsolve A = csc_array([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float) B = csc_array([[2, 0], [-1, 0], [2, 0]], dtype=float) x = spsolve(A, B) np.allclose(A.dot(x).toarray(), B.toarray()) True