%% E3_9
%% Carol Lucas
%% This program computes the Eadie-Hofstress plot using direct solutions 
%%    that are possible since this is a linear system as well as going through
%%    simulations - more like the experimental approach would be.
format compact

Gin=0.0;

Gray=[2:2:20];

N=length(Gray);

mess=' Model tested over even Gout values between two and twenty.'
mess=' Each simulation is proceeded by a PAUSE.  Hit return to continue.'

for k=1:N;

Gout=Gray(k)

k12=2.4;k43=2.4;k21=42;k34=42;k14=1000;k41=1000;k23=1000;k32=1000;

%% METHOD 1:  Solve directly for ss values

A=[-k12*Gout-k41-k14   k21-k41            -k41;
    k12*Gout          -k21-k23           k32;
	- k43*Gin          k23-k43*Gin       -k32-k34-k43*Gin];
	
b=[k41;
   0;
   k43*Gin];
   
Xss=-inv(A)*b;
x1ss=Xss(1);x2ss=Xss(2);x3ss=Xss(3);x4ss=1-x1ss-x2ss-x3ss;
R(k)=2*(k34*x3ss-k43*x4ss*Gin);

%% Method 2 - like an experimenter would do it

[t,x]=ode45('glutfun',[0:.01:.3],[1;0;0],[],Gin,Gout);
figure(1);clf;plot(t,x);pause;

last=length(t);
x1ss=x(last,1);x2ss=x(last,2);x3ss=x(last,3);x4ss=1-x1ss-x2ss-x3ss;
Rexp(k)=2*(k34*x3ss-k43*x4ss*Gin);


end

mess = 'END RESULTS EXACT METHOD, Hit return to continue'

plot(R./Gray,R,'ro');xlabel('R/Gout');ylabel('R');
title(' Direct Solution of SS with fit');hold on;

x1=R(2)/Gray(2);
y1=R(2);
x2=R(N)/Gray(N);
y2=R(N);

slope=(y2-y1)/(x2-x1)

Rmax=y1-slope*x1

ytest=Rmax+slope*R./Gray;
plot(R./Gray,ytest);pause;

Mess= 'END RESULTS EXPERIMENTAL METHOD'

R=Rexp;

figure(2);clf;plot(R./Gray,R,'ro');xlabel('R/Gout');ylabel('R');
title('Simulated Steady State with fit');hold on;

x1=R(2)/Gray(2);
y1=R(2);
x2=R(N)/Gray(N);
y2=R(N);

slope=(y2-y1)/(x2-x1)

Rmax=y1-slope*x1

ytest=Rmax+slope*R./Gray;
plot(R./Gray,ytest);