`scipy.optimize._optimize:golden`

source: /scipy/optimize/_optimize.py :2757

Signature

   def     golden (    func    ,    args    =  ()   ,    brack    =  None   ,    tol    =  1.4901161193847656e-08   ,    full_output    =  0   ,    maxiter    =  5000     )

Summary

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

Extended Summary

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

func : callable func(x,*args): Objective function to minimize.
args : tuple, optional: Additional arguments (if present), passed to func.
brack : tuple, 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.
tol : float, optional: x tolerance stop criterion
full_output : bool, optional: If True, return optional outputs.
maxiter : int: Maximum number of iterations to perform.

Returns

xmin : ndarray: Optimum point.
fval : float: (Optional output) Optimum function value.
funcalls : int: (Optional output) Number of objective function evaluations made.

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

✗

res = optimize.golden(f, brack=(-1, 0.5, 2), full_output=True)
xmin, fval, funcalls = res
f(xmin), fval

✓

Aliases

scipy.optimize.golden