Simple lsqcurvefit does not work properly

Hello. I would like to do a simple lsqcurvefit. But it seems to be that I cannot write the code properly. The data is attached. For some background.

My code is:

n = 400;                        % number of partitions           
l = 13;                         % length of Basilarmembran in cm
x = linspace(0.01, 13, n)';     % length of each partition 0.01 - 13 cm
b = 0.5;                        % width in cm at Helicotrema
t = 0.04;                       % height in cm

beff = b.*x/l;                  % length of each trapezium
dx = x(2:n) - x(1:n-1);         % length of each mass oszillator 
zs = dx.*(beff(1:n-1)+2.*beff(2:n))./(3*beff(1:n-1)+3.*beff(2:n));      % centroid of an trapezial-area
xeff = zs + x(1:n-1);           % effectiv distance of each centroid 

%      ________BASIS     The tip counts from x = 0.01 cm (basis) to x = 13 cm (apex)
%     |        .        
%     |       /|\       
%    h|      /_|_\
%     |     /__|__\  <-- This is one trapezium
%     |    /   |   \    
%     |___/____|____\   
%         |_________|   APEX

filename = 'stifness.xls';
A = xlsread(filename);
xdata=A(:,1)/10;         % x-values in cm
fdata=A(:,2);            % y-values in Hz

s0 = [90, 1.7, 0.88];        % inital values, processed by hand
ub = [2e2, 2e0, 1e1];        % upper bound
lb = [1e1, 1e0, 1e-1];       % lower bound
options = optimset('TolFun',1.0e-15,'TolX',1.0e-15); 

Gfun = @(s,x)  s0(1).*(10.^(s0(2).*(13-x)/13)-s0(3));
fitfun = lsqcurvefit(Gfun,s0,xdata,fdata,lb,ub,options);

Gfuntest1 = s0(1).*(10.^(s0(2).*(13-xeff)/13)-s0(3));               % plot with inital values
Gfuntest2 = fitfun(1).*(10.^(fitfun(2).*(13-xeff)/13)-fitfun(3));   % plot with fitted values

semilogy(xeff, Gfuntest1,'g',xeff,Gfuntest2,'--k',xdata,fdata,'ob'); % plot data

Any suggestion for my little problem? I don't know, why the lsqcurvefit does not change the inital values. They are staying the same. It cannot be that I guessed perfect initial values.

Best regards

Henrik

EDIT: Sorry for the missed data. Now it is attached.

[John D'Errico]

We cannot run your code, since we lack the data. That means we cannot even test it out. And since we are not given any information as to the model, it is difficult to read your code. Yes, you made a picture, but not a terribly useful one.

[Star Strider]

Context — Fitting procedure for cochlear mechanics (link)

[Henrik Schädlich]

I thought the lsqcurvefit should work this time. That is why I did not try the other fitting procedure.

The data is attached properly now. Hopefully it is operating sufficiently now.

[Henrik Schädlich]

Is it correct if I add:

Gfun = @(s,x)  s(1).*(10.^(s(2).*(13-x)/13)-s(3));
fitfun = @(s) norm(fdata- Gfun (s,xdata));
options = optimoptions('ga', 'InitialPopulationMatrix',s0, 'MaxGenerations', 1E+5, 'FunctionTolerance',1E-8);
[a, fval, exitflag] = ga(fitfun, 3, [], [], [], [], [], [], [], options);

Is it ok to have seven times []?

Answer 1

[Henrik Schädlich]

It's been a while but i found the problem.

Gfun = @(s,x)  s(1).*(10.^(s(2).*(13-x)/13)-s(3));

Is the correct line.