%Estimate parameters under consideration by solving the proposed
%optimization model 

%Read in patient data

A0 = xlsread('patient data.xlsx', 'Sheet1', 'A2:D340');

P=zeros(49, 7); % set the output matrix

tau_0 = 4.5; % set estimation tolerance 4.5 pmol/L of FT4 

global B;
global NumOfvisit;

NumOfvisit = 5;  %Number of patient visits to be used in the dataset  

for i=1:49

temp = find(A0(:, 1) ==i);   %define the row indices wrt patient i
B =A0(temp,2:4);    %define patient data (d, t, y) wrt patient i
m = size(B, 1);  % row number of B
 
x0= 0.35*ones(4,1);   

  A=[];
  b=[];
  Aeq=[];
  beq=[];

 ub=zeros(4,1);
 lb=zeros(4,1);
 
for k=1:4
    ub(k)=10^(6);
    lb(k)=10^(-4);
end

ub(2)=150; 

[x, fval, exitflag]=fmincon('objfun', x0, A, b, Aeq, beq, lb, ub, 'constraint');

P(i, 1) = i;      % deine patient SN
P(i, 2) = x(1);   % define A: rate of synthesis of FT4 concentration  
P(i, 3) = x(2);   % define IC_50: dose of ATD that reduces y by half  
P(i, 4) = x(3);   % define C: constant decay rate
P(i, 5) = - x(4);  % define C1: constrant of general solution of ODE  
P(i, 6) = exitflag;  % convergence indicator
P(i, 7) = m;      % number of patient visits 
    
filename = 'Parameter estimation results.xlsx';
cname_input=[{'Patient S/N'},{'A'},{'IC_50'}, {'C'}, {'C1'}, {'Exitflag'}, {'Number of visits'}];
xlswrite(filename, cname_input,'Sheet1','A1')
xlswrite(filename, P, 'Sheet1', 'A2');

end

return