function varargout = Emit_Parabola_Fit_kl_YProjection(varargin)
%global n  k sigx  sigy  gaux_sigma_sqrd   gaux_sigma_sqrd 
%sig_st = fopen('sig_st.txt', 'r');
%for n = 1:21,
%fprintf(sig_st, '%12d %12.8f %12.8f %12.8f %12.8f %12.8f \n', n, k(n), sigx(n), sigy(n), gaux_sigma_sqrd(n), gaux_sigma_sqrd(n));    
%end 
%fclose(sig_st);
   
%load -ascii HRRL_Emit_Parbola_Fit_Yaxis_as_BfieldStrength;
%Sig = HRRL_Emit_Parbola_Fit_Yaxis_as_BfieldStrength
load -ascii sigy.txt;
Sig = sigy
n = Sig(:,1);
B = Sig(:,2);
Er_B = Sig(:,3);
gauy_sigma_sqrd = Sig(:,4);
Er_sigmay_sqrd = Sig(:,5);

r_quad = 0.0254; %distance from center of dipole to the pole face is 1 inche
g = B/r_quad; %quadrupole gradiant
En = 10; % e- energy in Mev
me = 0.511; % electron rest mass in MeV
p = sqrt(En*En - me*me)/1000;% e- momentum in GeV/c
k1=0.2998*(g/p);%quadruople strength

% K1*L, L = 0.15 m
% K1*L, L = 0.165 m
% K1*L, L = 0.18 m
% K1*L, L = 0.20 m
% K1*L, L = 0.22 m

kl = 0.15*Sig(:,2);
%kl = 0.165*Sig(:,2);
%kl = 0.18*Sig(:,2);
%kl = 0.20*Sig(:,2);
%kl = 0.22*Sig(:,2);

%S12=2.07500;%m thin lense aproximation.
S12=2;%m (2.075 - 0.15/2)
%S12=1.9925;%m (2.075 - 0.165/2)
%S12=1.985;%m (2.075 - 0.18/2)
%S12=1.975;%m (2.075 - 0.20/2)
%S12=1.965;%m (2.075 - 0.22/2)

% kl, S^2 fitting
py = polyfit(kl,gauy_sigma_sqrd,2);
   
ay = py(1);
by = py(2);
cy = py(3);
   
fity = ay*(kl.*kl) + by*kl + cy;

pardaty = plot(kl,gauy_sigma_sqrd,'.');   
hold on

parfity = plot(kl,fity,'r');
set(parfity,'LineWidth',1);   
legend('Data Points','Y Projetion Fit');
hx = xlabel('QM Field: k_{1}*L (T)');
hy = ylabel('\sigma^2 (m^2)');
fit=title('k_{1}*L vs \sigma^2');
set(fit,'FontSize',12,'FontWeight','bold');
drawnow
   
gamma = En/me;
   
Ay=ay;
By=-by/(2*ay);
Cy=cy-(by)^2/(4*ay);
emit_y = sqrt(Ay*Cy)/((S12)^2);
emit_ny = emit_y*gamma
beta_y = sqrt(Ay/Cy)
alpha_y = sqrt(Ay/Cy)*(By + 1/S12)
    
fit_result = fopen('Parabole_fit_result.txt', 'w');
   %fprintf(fit_result, ' y-projection a=%12.9f, b=%12.9f, c=%12.9f,A=%12.9f, B=%12.9f, C=%12.9f, emit=%12.15f, emit_normy=%12.15f \n', ay, by, cy, Ay, By, Cy, emit_y, emit_ny );
   fprintf(fit_result, ' y-projection: emit=%12.15f, emit_normy=%12.15f \n', emit_y, emit_ny );  
   fclose(fit_result);
%return