I need to make a Gaussian fit, problem is i dont know how to type the parameters using lsqcurvefit

Equation of Gaussian distribution

if it's not gonna work with lsqcurvefit then please suggest another Function

[name,path]=uigetfile({'*.xlsx'});

Error using matlab.internal.lang.capability.Capability.require
Support for Java user interfaces is required, which is not available on this platform.

Error in uigetfile (line 117)
Capability.require(Capability.Swing);

filename = [path name];
opts = detectImportOptions(filename);
preview(filename,opts);
newtable = readtable(filename,'Range','A1:D15');
newtable(:,1)=[]; % Discard A Column
newtable(:,2)=[]; % Discard C Column
figure;
x = newtable{:,1};
y = newtable{:,2};
plot(x,y)

title('Energy in Relation of Beam Insulation');
xlabel('Movement on y Axis [mm]');
ylabel('Energy [mW]');
dydx = gradient(y(:))./gradient(x(:));
mitt=mean(dydx); % Average
sig = std(dydx); % Standard Deviation
fun = @(z,x)z(1)*exp(; % Here is the Problem !!!!
x0 = [1 1];
z = lsqcurvefit(fun,x0,x,dydx)
times = linspace(x(1),x(end));
plot(x,dydx,'ko',times,fun(z,times),'b-')
set(gca, 'YDir','reverse')
legend('Data','Fitted exponential')
title('Data and Fitted Curve')

Answer 1

[Torsten]

M = [				
    24.6			1.518572825			
    24.7			1.5083088954			
    24.8			1.5210166178			
    24.9			1.4203323558			
    24.95			1.1490713587				
    24.97			0.9853372434		
    24.99			0.811827957		
    25.01			0.6217008798		
    25.03			0.4384164223		
    25.05			0.2776148583			
    25.07			0.1495601173		
    25.09			0.0654936461			
    25.11			0.0151515152				
    25.16			0		
    25.26			0	];
x = M(:,1);
y = M(:,2);
dydx = -gradient(y(:))./gradient(x(:));
mitt=mean(dydx); % Average
sig = std(dydx); % Standard Deviation
fun1 = @(z)1/(z(2)*sqrt(2*pi))*exp(-(x-z(1)).^2/(2*z(2)^2));   
fun= @(z)fun1(z)-dydx;
z0 = [mitt sig];
z = lsqnonlin(fun,z0)	

Local minimum possible.

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

z = 1×2

25.0069 0.0457

plot(x,dydx)
hold on
plot(x,fun1(z))

[Hussam Saddour]

thank you very much! although i didnt quite understand whats the idea of substracting dydx from fun1, and is there a method to make the curve smoother?

[Torsten]

lsqnonlin tries to determine parameters such that res_i(p1,p2,...,pn) = 0.

So in contrast to lsqcurvefit where you define

f_i = 1/(z(2)*sqrt(2*pi))*exp(-(x_i-z(1)).^2/(2*z(2)^2))

and the solver subtracts dydx(i) internally from f_i, you must provide the residual

res_i = f_i - dydx(i)

for lsqnonlin directly.