def _root_hybr(func, x0, args=(), jac=None,
               col_deriv=0, xtol=1.49012e-08, maxfev=0, band=None, eps=None,
               factor=100, diag=None, **unknown_options):
    """
    Find the roots of a multivariate function using MINPACK's hybrd and
    hybrj routines (modified Powell method).

    Options
    -------
    col_deriv : bool
        Specify whether the Jacobian function computes derivatives down
        the columns (faster, because there is no transpose operation).
    xtol : float
        The calculation will terminate if the relative error between two
        consecutive iterates is at most `xtol`.
    maxfev : int
        The maximum number of calls to the function. If zero, then
        ``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 ``fprime=None``).
    eps : float
        A suitable step length for the forward-difference
        approximation of the Jacobian (for ``fprime=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.

    """
    _check_unknown_options(unknown_options)
    epsfcn = eps

    x0 = asarray(x0).flatten()
    n = len(x0)
    if not isinstance(args, tuple):
        args = (args,)
    shape, dtype = _check_func('fsolve', 'func', func, x0, args, n, (n,))
    if epsfcn is None:
        epsfcn = finfo(dtype).eps
    Dfun = jac
    if Dfun is None:
        if band is None:
            ml, mu = -10, -10
        else:
            ml, mu = band[:2]
        if maxfev == 0:
            maxfev = 200 * (n + 1)
        retval = _minpack._hybrd(func, x0, args, 1, xtol, maxfev,
                                 ml, mu, epsfcn, factor, diag)
    else:
        _check_func('fsolve', 'fprime', Dfun, x0, args, n, (n, n))
        if (maxfev == 0):
            maxfev = 100 * (n + 1)
        retval = _minpack._hybrj(func, Dfun, x0, args, 1,
                                 col_deriv, xtol, maxfev, factor, diag)

    x, status = retval[0], retval[-1]

    errors = {0: "Improper input parameters were entered.",
              1: "The solution converged.",
              2: "The number of calls to function has "
                  "reached maxfev = %d." % maxfev,
              3: "xtol=%f is too small, no further improvement "
                  "in the approximate\n  solution "
                  "is possible." % xtol,
              4: "The iteration is not making good progress, as measured "
                  "by the \n  improvement from the last five "
                  "Jacobian evaluations.",
              5: "The iteration is not making good progress, "
                  "as measured by the \n  improvement from the last "
                  "ten iterations.",
              'unknown': "An error occurred."}

    info = retval[1]
    info['fun'] = info.pop('fvec')
    sol = OptimizeResult(x=x, success=(status == 1), status=status)
    sol.update(info)
    try:
        sol['message'] = errors[status]
    except __HOLE__:
        info['message'] = errors['unknown']

    return sol
dataset/ETHPy150Open scipy/scipy/scipy/optimize/minpack.py/_root_hybr