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Module « scipy.sparse.linalg »

Fonction spsolve - module scipy.sparse.linalg

Signature de la fonction spsolve

def spsolve(A, b, permc_spec=None, use_umfpack=True) 

Description

help(scipy.sparse.linalg.spsolve)

Solve the sparse linear system Ax=b, where b may be a vector or a matrix.

Parameters
----------
A : ndarray or sparse array or matrix
    The square matrix A will be converted into CSC or CSR form
b : ndarray 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_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 [1]_, [2]_.

use_umfpack : bool, optional
    if True (default) then use UMFPACK for the solution [3]_, [4]_, [5]_,
    [6]_ . This is only referenced if b is a vector and
    ``scikits.umfpack`` is installed.

Returns
-------
x : ndarray 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`

.. [3] T. A. Davis, Algorithm 832:  UMFPACK - an unsymmetric-pattern
       multifrontal method with a column pre-ordering strategy, ACM
       Trans. on Mathematical Software, 30(2), 2004, pp. 196--199.
       https://dl.acm.org/doi/abs/10.1145/992200.992206

.. [4] T. A. Davis, A column pre-ordering strategy for the
       unsymmetric-pattern multifrontal method, ACM Trans.
       on Mathematical Software, 30(2), 2004, pp. 165--195.
       https://dl.acm.org/doi/abs/10.1145/992200.992205

.. [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

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