scipy.optimize.brent#
- scipy.optimize.brent(func, args=(), brack=None, tol=1.48e-08, full_output=0, maxiter=500)[source]#
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
- funccallable f(x,*args)
Objective function.
- argstuple, optional
Additional arguments (if present).
- bracktuple, 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.- 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
Optimum value.
- iterint
Number of iterations.
- funcallsint
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