Module « scipy.sparse.linalg »

Fonction cg - module scipy.sparse.linalg

Signature de la fonction cg

def cg(A, b, x0=None, tol=1e-05, maxiter=None, M=None, callback=None, atol=None) 

Description

cg.__doc__

Use Conjugate Gradient iteration to solve ``Ax = b``.

Parameters
----------
A : {sparse matrix, dense matrix, LinearOperator}
    The real or complex N-by-N matrix of the linear system.
    ``A`` must represent a hermitian, positive definite matrix.
    Alternatively, ``A`` can be a linear operator which can
    produce ``Ax`` using, e.g.,
    ``scipy.sparse.linalg.LinearOperator``.
b : {array, matrix}
    Right hand side of the linear system. Has shape (N,) or (N,1).

Returns
-------
x : {array, matrix}
    The converged solution.
info : integer
    Provides convergence information:
        0  : successful exit
        >0 : convergence to tolerance not achieved, number of iterations
        <0 : illegal input or breakdown

Other Parameters
----------------
x0  : {array, matrix}
    Starting guess for the solution.
tol, atol : float, optional
    Tolerances for convergence, ``norm(residual) <= max(tol*norm(b), atol)``.
    The default for ``atol`` is ``'legacy'``, which emulates
    a different legacy behavior.

    .. warning::

       The default value for `atol` will be changed in a future release.
       For future compatibility, specify `atol` explicitly.
maxiter : integer
    Maximum number of iterations.  Iteration will stop after maxiter
    steps even if the specified tolerance has not been achieved.
M : {sparse matrix, dense matrix, LinearOperator}
    Preconditioner for A.  The preconditioner should approximate the
    inverse of A.  Effective preconditioning dramatically improves the
    rate of convergence, which implies that fewer iterations are needed
    to reach a given error tolerance.
callback : function
    User-supplied function to call after each iteration.  It is called
    as callback(xk), where xk is the current solution vector.