Using Optimizing Nonlinear Functions to find mutiple variations

Hi everyone, I'm having some problems when using Optimization to find some variations.

I have the equation as following:

xdata=125:2:145;
ydata=[0.002 0.003 0.009 0.025 0.053 0.089 0.104 0.09 0.07 0.041 0.017];
y=@(x)(-1/(dev*sqrt(2*pi))*exp(-1/2*((xdata-mean)/dev).^2);

with dev a.k.a deviation and mean is two fixed parameters I have to find.

I have referenced the Optimizing Nonlinear Functions and Solve a Constrained Nonlinear Problem, Solver-Based in Matlab.

This is my code.

%%%Function code
function sse = sseval(n,xdata,ydata)
mean=n(1);
dev=n(2);
sse=ydata-1/(dev*sqrt(2*pi))*exp(-1/2*((xdata-mean)/dev).^2);
end
%%%Main code
clc;
clear all;
close all;
xdata=[125 127 129 131 133 135 137 139 141 143 145];
ydata=[0.002 0.003 0.009 0.025 0.053 0.089 0.104 0.09 0.07 0.041 0.017];
%%%%Find mean and deviation value
rng default %for reproducibility
type sseval
fun = @(n)sseval(n,xdata,ydata);
x0=rand(2,1);
bestn=fminsearch(fun,x0)

The result showed the error and cannot run. Can anyone show me what is the problem with this? Thank you so much in advanced.

Answer 1

[Torsten]

xdata=[125 127 129 131 133 135 137 139 141 143 145];
ydata=[0.002 0.003 0.009 0.025 0.053 0.089 0.104 0.09 0.07 0.041 0.017];
%%%%Find mean and deviation value
fun = @(n)sseval(n,xdata,ydata);
x0=[135,1];
bestn=fminsearch(fun,x0)

bestn = 1×2

137.4512 3.8956

xsim = xdata;
ysim = 1/(bestn(2)*sqrt(2*pi))*exp(-1/2*((xsim-bestn(1))/bestn(2)).^2);
hold on
plot(xsim,ysim)
plot(xdata,ydata,'o')
hold off

%%%Function code
function sse = sseval(n,xdata,ydata)
  mean=n(1);
  dev=n(2);
  sse=ydata-1/(dev*sqrt(2*pi))*exp(-1/2*((xdata-mean)/dev).^2);
  sse = sum(sse.^2);
end

[Lam Ha]

Thank you so much for your help.

Answer 2

[Matt J]

There are also FEX downloads that can do gauss fitting for you, e.g.,

https://www.mathworks.com/matlabcentral/fileexchange/69116-gaussfitn

xdata=[125 127 129 131 133 135 137 139 141 143 145];
ydata=[0.002 0.003 0.009 0.025 0.053 0.089 0.104 0.09 0.07 0.041 0.017];

p=gaussfitn(xdata',ydata',[],{0,[],[]},{0,[],[]});

Local minimum possible.

lsqcurvefit stopped because the final change in the sum of squares relative to 
its initial value is less than the value of the function tolerance.

[~,A,mu,sig2]=deal(p{:});
mu,

mu = 137.4548

dev=sqrt(sig2)

dev = 3.9507

x=linspace(min(xdata),max(xdata));
yfit=@(xx) A*exp(-1/2*((xx-mu)/dev).^2);


plot(xdata,ydata,'o',x,yfit(x))

[Lam Ha]

Thank you for suggesting me another method. ^^