clear all

tau0 = 1.0e-8;

%%% Part I: to generate the matrix G
n = 500;
% Here G is a nxn random symmetric matrix with entries in [-1,1]
G = 2.0*rand(n,n)-ones(n,n);
G = triu(G) + triu(G,1)';   
for i=1:n
    G(i,i) =1;    
end

  
lh = 5;  % the number of fixed off-diagonal elements at each row
ll = 8;  % the number of low bound elements at each row
lu = 10;  % the number of upper bound elements at each row


%%% Part II: to generate the index sets: I_e&J_e
% I_d and J_d correspond to the fixed diagonal elements
I_d = [1:1:n]';
J_d = I_d;
% I_h and J_h correspond to the fixed off-diagonal elements
lh = min(lh,n-1);
I_h = [];
J_h = [];
for i = 1:n-lh
    r = rand(n-i,1);
    [r,ind] = sort(r);
    I_h = [I_h; i*ones(lh,1)];
    J_h = [J_h; i+ind(n-i-lh+1:n-i)];
end
for i = ((n-lh)+1):(n-1)
    I_h = [I_h; i*ones(n-i,1)];
    J_h = [J_h;[(i+1):n]'];
end
k_h = length(I_h);
I_e = [I_d;I_h];
J_e = [J_d;J_h];



%%% Part III: to generate the index sets: I_l & J_l    
ll = min(ll,n-1);
I_l = [];
J_l = [];
for i = 1:n-ll
    r = rand(n-i,1);
    [r,ind] = sort(r);
    I_l = [I_l; i*ones(ll,1)];
    J_l = [J_l; i+ind(n-i-ll+1:n-i)];
end
for i = ((n-ll)+1):(n-1)
    I_l = [I_l; i*ones(n-i,1)];
    J_l = [J_l;[(i+1):n]'];
end
k_l = length(I_l);


%%% Part IV: to generate the index sets: I_u & J_u     
lu = min(lu,n-1);
I_u = [];
J_u = [];
for i = 1:n-lu
    r = rand(n-i,1);
    [r,ind] = sort(r);
    I_u = [I_u; i*ones(lu,1)];
    J_u = [J_u; i+ind(n-i-lu+1:n-i)];

end
for i = ((n-lu)+1):(n-1)
    I_u = [I_u; i*ones(n-i,1)];
    J_u = [J_u;[(i+1):n]'];
end
k_u = length(I_u);



%%% Part V: to generate: e,l,and u
rhs = ones(n,1);     
alpha = 0;
rhs = alpha *rhs + (1-alpha)*rand(n,1);
h = zeros(k_h,1);

e = [rhs;h];
l = -0.1*ones(k_l,1);
u = 0.1*ones(k_u,1);   






%%% test CaliMat.m
[X,z_e,z_l,z_u] = CaliMat(G,e,I_e,J_e,l,I_l,J_l,u,I_u,J_u,tau0);