scipy.sparse.linalg.spsolve¶
-
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 matrix
The square matrix A will be converted into CSC or CSR form
- bndarray or sparse 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
- use_umfpackbool, optional
if True (default) then use umfpack for the solution. This is only referenced if b is a vector and
scikit-umfpack
is installed.
- Returns
- xndarray or sparse 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.
Examples
>>> from scipy.sparse import csc_matrix >>> from scipy.sparse.linalg import spsolve >>> A = csc_matrix([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float) >>> B = csc_matrix([[2, 0], [-1, 0], [2, 0]], dtype=float) >>> x = spsolve(A, B) >>> np.allclose(A.dot(x).todense(), B.todense()) True