scipy.sparse.linalg.cgs¶

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

Use Conjugate Gradient Squared iteration to solve Ax = b.

Parameters:

Parameters:	A : {sparse matrix, dense matrix, LinearOperator} The real-valued N-by-N matrix of the linear system. 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 : float Tolerance to achieve. The algorithm terminates when either the relative or the absolute residual is below tol. 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.

A : {sparse matrix, dense matrix, LinearOperator}

The real-valued N-by-N matrix of the linear system.

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 : float

Tolerance to achieve. The algorithm terminates when either the relative or the absolute residual is below tol.

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.