# 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: Returns: 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). 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 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.

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