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, returna local minimizer of the function isolated to a fractional precisionof tol.

Parameters:

funccallable f(x,*args)

Objective function.

argstuple, optional

Additional arguments (if present).

bracktuple, optional

Either a triple(xa,xb,xc) satisfyingxa<xb<xc andfunc(xb)<func(xa)and func(xb)<func(xc), or a pair(xa,xb) to be used as initial points for a downhill bracket search(seescipy.optimize.bracket).The minimizerx will not necessarily satisfyxa<=x<=xb.

tolfloat, optional

Relative error in solutionxopt 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 upconvergence of golden section method.

Does not ensure that the minimum lies in the range specified bybrack. Seescipy.optimize.fminbound.

Examples

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We illustrate the behaviour of the function whenbrack is ofsize 2 and 3 respectively. In the case wherebrack is of theform(xa,xb), we can see for the given values, the output doesnot necessarily lie in the range(xa,xb).

>>>deff(x):...return(x-1)**2

>>>fromscipyimportoptimize

>>>minimizer=optimize.brent(f,brack=(1,2))>>>minimizer1>>>res=optimize.brent(f,brack=(-1,0.5,2),full_output=True)>>>xmin,fval,iter,funcalls=res>>>f(xmin),fval(0.0, 0.0)

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