simplex - Nelder-Mead simplex optimizer (amoeba)

simplex

Minimize a function using Nelder-Mead downhill simplex algorithm.

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>)

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:

fcallable f(x,*args)

The objective function to be minimized.

x0ndarray

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)

xndarray

Parameter that minimizes function.

fxfloat

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

itersint

Number of iterations performed.

callsint

Number of function calls made.

successboolean

True if fit completed successfully.

Other Parameters:

xtolfloat

Relative error in xopt acceptable for convergence.

ftolnumber

Relative error in func(xopt) acceptable for convergence.

maxiterint=200*N

Maximum number of iterations to perform. Defaults

update_handlercallable

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_testcallable

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.