MATLAB: Lsqcurvefit initial values stays the same

Question

Hi all, I am working on this non-linear square curvefit function, however, despite many attempts, the initial guessess were always chosen despite of given boundaries. Unbounded worked. But that isn't within the bounds. I really at my end of working on possible ideas. The data given as a total of 101 for each array.

EDIT: I have made some changes which is now bounded and using the default trust-region-reflective algorithm

T = readtable('skin3.csv','ReadVariableNames',true); %skin3 Measured data
x = T{:,1}; %freq
y = T{:,2}; %real
%Transpose
freq = x.';
e_real = y.';
%optimoptions(@lsqnonlin,'StepTolerance',1e-6);
options = optimset('MaxFunEvals',10000);
options=optimset(options,'MaxIter',10000);
guess = 40;
UB = guess + 10;
LB = guess - 10;
lb = [-20,LB,1,0,-0.1];
ub = [20,UB,40,1,0.1];
x0 = [0.9,guess,8.2,0.236,0.05];
x  = lsqcurvefit(@flsq,x0,freq,e_real,lb,ub,options)
e_f = x(1);
e_del = x(2)*1e2;
tau1 = x(3)*1e-12;
alf1 = x(4);
sig = x(5);
yfit = real(flsq(x,freq));
%plot e_real against freq
plot(freq,e_real,'k.',freq,yfit,'b-')
legend('Data','Fitted exponential')
title('Data and Fitted Curve')

Function:

function y = flsq(x,freq)
    x(3)=x(3)*1e-12;
    y = x(1) + (x(2)-x(1))./(1 + ((1j*2*pi.*freq*x(3)).^(1-x(4))))+x(5)./(1j*2*pi*freq*8.854e-12);
    
end

As you can see the result remained the same while the curve is not even close:

Answer 1

Have a look the results below, it is curve fitting of complex function:

Root of Mean Square Error (RMSE): 0.41174673299835

Sum of Squared Residual: 34.2461451712325

Correlation Coef. (R): 0.993473244156721

R-Square: 0.986989086855279

Adjusted R-Square: 0.98661284187563

Determination Coef. (DC): 0.984776903952251

F-Statistic: 6477.07873557149

Parameter Best Estimate

-------------------- -------------

x1 -11.6554338755058

x2 42.431711066831

x3 -4.55460615654172E-12

x4 0.295425568159937

x5 -0.527862954468673