# 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 the local minimum 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) where xa<xb<xc and func(xb) < func(xa), func(xc) or a pair (xa,xb) which are used as a starting interval for a downhill bracket search (see `bracket`). Providing the pair (xa,xb) does not always mean the obtained solution will satisfy xa<=x<=xb.

    tol float, optional

      Stop if between iteration change is less than tol.

    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

      Optimum value.

    iter int

      Number of iterations.

    funcalls int

      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 `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 need not necessarily lie in the range (xa,xb).

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

      >>> from scipy import optimize

      >>> minimum = optimize.brent(f,brack=(1,2))
      >>> minimum
      0.0
      >>> minimum = optimize.brent(f,brack=(-1,0.5,2))
      >>> minimum
      -2.7755575615628914e-17

scipy.optimize.fminbound scipy.optimize.golden