# scipy.optimize.brent

scipy.optimize.brent(func, args=(), brack=None, tol=1.48e-08, full_output=0, maxiter=500)

  Given a function of one variable and a possible bracket, return a local minimizer of the function isolated to a fractional precision of tol.

  Parameters:
    func callable f(x,*args)

      Objective function.

    args tuple, optional

      Additional arguments (if present).

    brack tuple, optional

      Either a triple `(xa, xb, xc)` satisfying `xa < xb < xc` and `func(xb) < func(xa) and func(xb) < func(xc)`, or a pair `(xa, xb)` to be used as initial points for a downhill bracket search (see `scipy.optimize.bracket`). The minimizer `x` will not necessarily satisfy `xa <= x <= xb`.

    tol float, optional

      Relative error in solution xopt acceptable for convergence.

    full_output bool, optional

      If True, return all output args (xmin, fval, iter, funcalls).

    maxiter int, optional

      Maximum number of iterations in solution.

  Returns:
    xmin ndarray

      Optimum point.

    fval float

      (Optional output) Optimum function value.

    iter int

      (Optional output) Number of iterations.

    funcalls int

      (Optional output) Number of objective function evaluations made.

  See also

  `minimize_scalar`

    Interface to minimization algorithms for scalar univariate functions. See the ‘Brent’ method in particular.

  Notes

  Uses inverse parabolic interpolation when possible to speed up convergence of golden section method.

  Does not ensure that the minimum lies in the range specified by brack. See `scipy.optimize.fminbound`.

  Examples

  We illustrate the behaviour of the function when brack is of size 2 and 3 respectively. In the case where brack is of the form `(xa, xb)`, we can see for the given values, the output does not necessarily lie in the range `(xa, xb)`.

      >>> def f(x):
      ...     return (x-1)**2

      >>> from scipy import optimize

      >>> minimizer = optimize.brent(f, brack=(1, 2))
      >>> minimizer
      1
      >>> res = optimize.brent(f, brack=(-1, 0.5, 2), full_output=True)
      >>> xmin, fval, iter, funcalls = res
      >>> f(xmin), fval
      (0.0, 0.0)