scipy.sparse.linalg.cg

scipy.sparse.linalg.cg(A, b, x0=None, tol=1e-05, maxiter=None, M=None, callback=None, atol=None)

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.

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.