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. 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.

infointeger

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, atolfloat, 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.

maxiterinteger

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.

callbackfunction

User-supplied function to call after each iteration. It is called as callback(xk), where xk is the current solution vector.