scipy.optimize.golden#

scipy.optimize.golden(func, args=(), brack=None, tol=1.4901161193847656e-08, full_output=0, maxiter=5000)[source]#

Return the minimizer of a function of one variable using the golden section method.

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

Parameters:

funccallable func(x,*args): Objective function to minimize.
argstuple, optional: Additional arguments (if present), passed to func.
bracktuple, optional: Either a triple (xa, xb, xc) where 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: x tolerance stop criterion
full_outputbool, optional: If True, return optional outputs.
maxiterint: Maximum number of iterations to perform.

Returns:

xminndarray: Optimum point.
fvalfloat: (Optional output) Optimum function value.
funcallsint: (Optional output) Number of objective function evaluations made.

See also

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

Notes

Uses analog of bisection method to decrease the bracketed interval.

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-1)**2

>>> from scipy import optimize

>>> minimizer = optimize.golden(f, brack=(1, 2))
>>> minimizer
1
>>> res = optimize.golden(f, brack=(-1, 0.5, 2), full_output=True)
>>> xmin, fval, funcalls = res
>>> f(xmin), fval
(9.925165290385052e-18, 9.925165290385052e-18)