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 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)