sigm_fit

Optimization of parameters of the sigmoid function

Syntax:
[param]=sigm_fit(x,y)

that is the same that
[param]=sigm_fit(x,y,[],[],[]) % no fixed_params, automatic initial_params

[param]=sigm_fit(x,y,fixed_params) % automatic initial_params
[param]=sigm_fit(x,y,[],initial_params) % use it when the estimation is poor
[param]=sigm_fit(x,y,fixed_params,initial_params,plot_flag)

param = [min, max, x50, slope]

if fixed_params=[NaN, NaN , NaN , NaN] % or fixed_params=[]
optimization of "min", "max", "x50" and "slope" (default)

if fixed_params=[0, 1 , NaN , NaN]
optimization of x50 and slope of a sigmoid of ranging from 0 to 1


Additional information in the second output, STAT
[param,stat]=sigm_fit(x,y,fixed_params,initial_params,plot_flag)


Example:
%% generate data vectors (x and y)
fsigm = @(param,xval) param(1)+(param(2)-param(1))./(1+10.^((param(3)-xval)*param(4)))
param=[0 1 5 1]; % "min", "max", "x50", "slope"
x=0:0.1:10;
y=fsigm(param,x) + 0.1*randn(size(x));

%% standard parameter estimation
[estimated_params]=sigm_fit(x,y)

%% parameter estimation with forced 0.5 fixed min
[estimated_params]=sigm_fit(x,y,[0.5 NaN NaN NaN])

%% parameter estimation without plotting
[estimated_params]=sigm_fit(x,y,[],[],0)