``100*(N+1)`` is the maximum where N is the number of elements
    in `x0`.
band : tuple
    If set to a two-sequence containing the number of sub- and
    super-diagonals within the band of the Jacobi matrix, the
    Jacobi matrix is considered banded (only for ``jac=None``).
eps : float
    A suitable step length for the forward-difference
    approximation of the Jacobian (for ``jac=None``). If
    `eps` is less than the machine precision, it is assumed
    that the relative errors in the functions are of the order of
    the machine precision.
factor : float
    A parameter determining the initial step bound
    (``factor * || diag * x||``). Should be in the interval
    ``(0.1, 100)``.
diag : sequence
    N positive entries that serve as a scale factors for the
    variables.

r!