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

Other Parameters

x0 : ndarray

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 :None:None:`atol` will be changed in a future release. For future compatibility, specify :None:None:`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, ndarray, 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.

Parameters

A : {sparse matrix, ndarray, LinearOperator}

The real-valued N-by-N matrix of the linear system. Alternatively, A can be a linear operator which can produce Ax using, e.g., scipy.sparse.linalg.LinearOperator .

b : ndarray

Right hand side of the linear system. Has shape (N,) or (N,1).

Returns

x : ndarray

The converged solution.

info : integer

Use Conjugate Gradient Squared iteration to solve Ax = b .

Examples

See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /scipy/sparse/linalg/_isolve/iterative.py#354
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