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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:
    funccallable f(x,*args)

      Objective function.

    argstuple, optional

      Additional arguments (if present).

    bracktuple, 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`.

    tolfloat, optional

      Relative error in solution xopt acceptable for convergence.

    full_outputbool, optional

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

    maxiterint, optional

      Maximum number of iterations in solution.

  Returns:
    xminndarray

      Optimum point.

    fvalfloat

      (Optional output) Optimum function value.

    iterint

      (Optional output) Number of iterations.

    funcallsint

      (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)