Parameters :  F : function(x) > f
Function whose root to find; should take and return an arraylike
object.
x0 : array_like
Initial guess for the solution
alpha : float, optional
Initial guess for the Jacobian is (1/alpha).
reduction_method : str or tuple, optional
Method used in ensuring that the rank of the Broyden matrix
stays low. Can either be a string giving the name of the method,
or a tuple of the form (method, param1, param2, ...)
that gives the name of the method and values for additional parameters.
Methods available:
 restart: drop all matrix columns. Has no extra parameters.
 simple: drop oldest matrix column. Has no extra parameters.
 svd: keep only the most significant SVD components.
Takes an extra parameter, to_retain`, which determines the
number of SVD components to retain when rank reduction is done.
Default is ``max_rank  2.
max_rank : int, optional
Maximum rank for the Broyden matrix.
Default is infinity (ie., no rank reduction).
iter : int, optional
Number of iterations to make. If omitted (default), make as many
as required to meet tolerances.
verbose : bool, optional
Print status to stdout on every iteration.
maxiter : int, optional
Maximum number of iterations to make. If more are needed to
meet convergence, NoConvergence is raised.
f_tol : float, optional
Absolute tolerance (in maxnorm) for the residual.
If omitted, default is 6e6.
f_rtol : float, optional
Relative tolerance for the residual. If omitted, not used.
x_tol : float, optional
Absolute minimum step size, as determined from the Jacobian
approximation. If the step size is smaller than this, optimization
is terminated as successful. If omitted, not used.
x_rtol : float, optional
Relative minimum step size. If omitted, not used.
tol_norm : function(vector) > scalar, optional
Norm to use in convergence check. Default is the maximum norm.
line_search : {None, ‘armijo’ (default), ‘wolfe’}, optional
Which type of a line search to use to determine the step size in the
direction given by the Jacobian approximation. Defaults to ‘armijo’.
callback : function, optional
Optional callback function. It is called on every iteration as
callback(x, f) where x is the current solution and f
the corresponding residual.
