Seekpeaks

find maxima of an arbitrary function

[xm,ym,xx,yy]=Seekpeaks(fun,x,y,y_tol,Nsteps,varargin)
Searches the maxima of the function 'fun', which is an object such as produced by inline or by a m-function. y=fun(x,P1,P2,...), where P1, P2,...are additional parameters used in the function 'fun' and are given in 'varargin' in Seekpeaks as p1,p2,... (see example below)
Note: use 'fun' for m-function and (just) fun for inline function

The INPUT x and y (=fun(x)) are the samples used to locate the maxima and the program will refine iterativeley around the local maxima to find the exact maxima. y_tol gives the relative stop criteria for stopping the maxima search and Nsteps is a number to terminate the session in case it takes long time to find the maxima. Default are 1e-6 and 50 and will be used in case [],[] are used as arguments in the function.

The OUTPUT xm gives the positions of the maxima and ym the corresponding values (vectors). xx and yy gives the union of all values that are found during the refinement including the input sample x and y (it is useful for plot-purposes).

%%% Example:

define a function fun(x) with an additional parameter s
fun1=inline('s^2*(1./(s^2+(x-1).^2)+1./(s^2+(x-2).^2))','x','s')
% calculate a rough sample (x,y) of the function
x=linspace(0,3,20);
s=0.001; %parameter
y=fun1(x,s);
% Seek the peaks of the function fun1
[xm,ym,xx,yy]=Seekpeaks(fun1,x,y,[],[],s);
xm
plot(xx,yy,x,y,'.');