%In physics, a three-parameter Lorentzian function is often used, as follows:
%  f(x;x0,?,I) = I/(1 + ( (x-x0)/? )^2)
% I: is the height of the peak.
% x0: is the location paremeter, specifying the location of the peak.
% ?: is the scale parameter which specifies the half-width at half-maximum (HWHM).
% ? is also equal to half the interquartile range and is sometimes called the probable error.

%If you would want,e. g., to ?t a Lorentzian y = a1/((x ? a2)^2 + a3) to a data set Xi, Yi, 
%you should define in MATLAB a function resulting in the sum of the squared residuals

% a(1)= I
% a(2)= x0
% a(3)= ?

function chisq = Assym_Gau_devsum(a,X,Y)
%a
% a(1) = sigma_0
% a(2) = x0
% a(3) = off-set
%Gau = a(3)+1/(sqrt(2*pi)*a(1))*exp( -(X-a(2)).^2 / (2*a(1).^2) );% Gaussian
%Gau = 1/(sqrt(2*pi)*a(1))*exp( -(X-a(2)).^2 / (2*a(1).^2) );% Gaussian
%Gau = a(3)*exp( -(X-a(2)).^2 / (2*a(1).^2) );% Gaussian
%Gau = 1/(sqrt(2*pi)*(a(3)+a(4)))*exp( -(X-a(2)).^2 / (2*a(1).^2) );% Assymetric Gaussian
sigma = (a(3)+a(4))/2;
Es = ( a(4)-a(3) )/( a(3)+a(4) );
signe = sign(X-a(2));
sigma2 = (a(7)+a(8))/2;
Es2 = ( a(8)-a(7) )/( a(7)+a(8) );
signe2 = sign(X-a(6));
[col,row] = size(X);
%fprintf('1.a');
%signe = sign(X-a(2));

%signe'
%size(signe')

%X'
%size(X')
%signe = 1;
%Gau = a(1)*exp( -(X-a(2)).^2 / ( 2*(sigma*(1+Es ).^2) ));% Assymetric Gaussian
for i=1:col
         %if signe(i)<=0
         Gau(i) = a(5)*exp( -0.5*((X(i)-a(6))/(sigma2*(1+signe2(i)*Es2))).^2 ) + a(1)*exp( -0.5*((X(i)-a(2))/(sigma*(1+signe(i)*Es))).^2 );
         
         %Gau(i) = a(5)*exp( -0.5*((X(i)-a(6))/a(7)).^2 ) + a(1)*exp( -0.5*((X(i)-a(2))/(sigma*(1+signe(i)*Es))).^2 );
         %Gau(i) = a(8)*X(i) + a(5)*exp( -0.5*((X(i)-a(6))/a(7)).^2 ) + a(1)*exp( -0.5*((X(i)-a(2))/(sigma*(1+signe(i)*Es))).^2 );
         %Gau(i) = a(5)*X(i) + a(1)*exp( -0.5*((X(i)-a(2))/(sigma*(1+signe(i)*Es))).^2 );
         %Gau_fit(i) = par(1)*exp( -0.5*((Ene(i)-par(2))/(sigma*(1+signe(i)*Es))).^2 );
         %end
end
         
csq = (Y - Gau').^2;
chisq = sum(csq); 
%csq
%chisq
%a
return