% Gyration1.m just calculates the radius of gyration of a small-angle
% x-ray scattering curve.
% The input should be a two column matrix of q's and scattering strengths.
% For a gyration calculation, early data will be unreasonable because of the 
% beamstop while data with a high-q will no longer fit the expansion.
% The fit assumes that I(q) = I(0) * ( 1 - q^2 Rg^2 / 3) - bad, bad, bad! 

function [Io,Rg] = Gyration1(data)

%  Find the beginning and the end of the region for a Guiner fit!
X = [data(:,1)];
Y = [data(:,2)];
plot(X,Y);
hold ;
min_q = input('What is the lowest value of Q to start fit at?');
max_q = input('What is the maximum value of Q to terminate fit at?');
min_i = 1;
while(X(min_i)<min_q) min_i=min_i+1; end
max_i = min_i + 1;
while(X(max_i)<max_q) max_i= max_i+1; end

%  Do the fit
A(max_i-min_i+1,2) = 0.0;
B(max_i-min_i+1) = 0.0;
for i=min_i: max_i,
    A(i-min_i+1,1) = 1;
    A(i-min_i+1,2) = X(i)*X(i);
    B(i-min_i+1) = Y(i);
end
C = A'*A;
D = A'*B';
E = inv(C)* D;
Io = E(1);
Rg = E(2);

% And plot it
Z(size(X)) = 0.0;
for i=1:size(X),
    Z(i) = Io + Rg*X(i)*X(i);
    if (Z(i)<0) Z(i) = 0.0 ;end
end
plot(X,Z,'c');
hold off ;

Rg = (-3.0*E(2)/Io)^0.5;