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Optimization of parameters of the sigmoid function


Updated 30 Mar 2016

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Optimization of parameters of the sigmoid function


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 = [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

%% 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"
y=fsigm(param,x) + 0.1*randn(size(x));

%% standard parameter estimation

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

%% parameter estimation without plotting

Cite As

R P (2020). sigm_fit (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (24)

Jie Wang

Oded Scharf

Swati Jain

Great function!

Bram Mast

GDMFSOB Bloody brilliant! Thank you.

Sam Garrard


RJ Ellis

Works right out of the box. Thanks!


Works as expected!

Simple and effective. Similarly to polyfit-polyval, it would be great to include the related sigm_val function, to evaluate the generated sigmoidal curve.

noam josef

tried using the function with my data and the givven example but in both recieved "Undefined function 'sigm_fit' for input arguments of type

any thughts about it?


This requires a minmax() function - which toolbox is that in?


title update

plot bug fixed

minmax function used in plotting substituted by min and max functions

STAT output variable, with confidence intervals for parameters and distribution

MATLAB Release Compatibility
Created with R13
Compatible with any release
Platform Compatibility
Windows macOS Linux