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scipy.sparse.linalg.bicgstab

# scipy.sparse.linalg.bicg

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

  Use BIConjugate 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. It is required that the linear operator can produce `Ax` and `A^T x`.

  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.

  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 This parameter has been superseded by LinearOperator.