scipy.sparse.linalg.cg¶

scipy.sparse.linalg.
cg
(A, b, x0=None, tol=1e05, maxiter=None, xtype=None, M=None, callback=None)[source]¶ Use Conjugate Gradient iteration to solve
Ax = b
.Parameters: A : {sparse matrix, dense matrix, LinearOperator}
The real or complex NbyN 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 : 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
Usersupplied function to call after each iteration. It is called as callback(xk), where xk is the current solution vector.
xtype : {‘f’,’d’,’F’,’D’}
This parameter is deprecated – avoid using it.
The type of the result. If None, then it will be determined from A.dtype.char and b. If A does not have a typecode method then it will compute A.matvec(x0) to get a typecode. To save the extra computation when A does not have a typecode attribute use xtype=0 for the same type as b or use xtype=’f’,’d’,’F’,or ‘D’. This parameter has been superseded by LinearOperator.