simplex - Nelder-Mead simplex optimizer (amoeba)¶

Downhill simplex optimizer.

bumps.simplex.simplex(f, x0=None, bounds=None, radius=0.05, xtol=0.0001, ftol=0.0001, maxiter=None, update_handler=None, abort_test=<function dont_abort>)[source]¶

Minimize a function using Nelder-Mead downhill simplex algorithm.

This optimizer is also known as Amoeba (from Numerical Recipes) and the Nealder-Mead simplex algorithm. This is not the simplex algorithm for solving constrained linear systems.

Downhill simplex is a robust derivative free algorithm for finding minima. It proceeds by choosing a set of points (the simplex) forming an n-dimensional triangle, and transforming that triangle so that the worst vertex is improved, either by stretching, shrinking or reflecting it about the center of the triangle. This algorithm is not known for its speed, but for its simplicity and robustness, and is a good algorithm to start your problem with.

Parameters:

f : callable f(x,*args)

The objective function to be minimized.

x0 : ndarray

Initial guess.

bounds : (ndarray,ndarray) or None

Bounds on the parameter values for the function.

radius: float

Size of the initial simplex. For bounded parameters (those which have finite lower and upper bounds), radius is clipped to a value in (0,0.5] representing the portion of the range to use as the size of the initial simplex.

Returns: Result (park.simplex.Result)

x : ndarray

Parameter that minimizes function.

fx : float

Value of function at minimum: fopt = func(xopt).

iters : int

Number of iterations performed.

calls : int

Number of function calls made.

success : boolean

True if fit completed successfully.

Other Parameters:

xtol : float

Relative error in xopt acceptable for convergence.

ftol : number

Relative error in func(xopt) acceptable for convergence.

maxiter : int=200*N

Maximum number of iterations to perform. Defaults

update_handler : callable

Called after each iteration, as callback(k,n,xk,fxk), where k is the current iteration, n is the maximum iteration, xk is the simplex and fxk is the value of the simplex vertices. xk[0],fxk[0] is the current best.

abort_test : callable

Called after each iteration, as callback(), to see if an external process has requested stop.

Notes

Uses a Nelder-Mead simplex algorithm to find the minimum of function of one or more variables.