%%%Unpacking Explicit Type 2 MSRK%%%%%%
%&& We are taking our coeficient vector X which is being fed through
%%% the optimizer and unpacking the pieces back into the original form

%%% A is explicit and has (S^2-S)/2 unknowns, with 0s padding the first row
%%% Ahat is (S-1)x(k-1)  unknowns, with 0s padding the first row
%%% B is 1 x S
%%% Bhat is 1x(k-1)
%%% D is (S-1)x k  unknowns, with [00....1] for the first row
%%% Theta is  1 x k

function [A ,Ahat, B, Bhat, D, Theta] =  unpackexplicitT2(x, s, k)


count1= (s^2-s)/2;
count2= count1 + (s-1)*(k-1);
count3= count2+s;
count4= count3 + (k-1);
count5 = count4 +(s-1)*(k-1);
count6= count5+k-1;



A=zeros(s-1,s);
count=1;
for i = 1:s-1
A(i,1:i)=x(count:count+i-1);
count= count+i;
end
A=[zeros(1,s);A];


Ahat=zeros(1,k-1);
Ahat= [Ahat; reshape(x(count1+1:count2),s-1,k-1)];

B= x(count2+1:count3);

Bhat= x(count3+1:count4);


D=reshape(x(count4+1:count5),s-1,k-1);
D(:,end+1) = 1- sum(D,2);

Theta = x(count5+1:count6);
Theta(end+1)= 1-sum(Theta);


%%Aa= [zeros(k-1,s+k-1);Ahat,A];
%%Bb= [Bhat, B];
%%Dd= [eye(k);D];
end