% Vector components: [ sm, ah, cs, ps, rv, nl ]
% NOTE: sm = Steel Meridian, ah = Arbiters of Hexis, etc...

% Syndicate mixing matrix
W = [ 1 0 0 -1 0.5 -0.5; 0 1 0.5 -0.5 -1 0; 0 0.5 1 0 -0.5 -1; -1 -0.5 0 1 0 0.5; 0.5 -1 -0.5 0 1 0; -0.5 0 -1 0.5 0 1 ];

% Starting syndicate standing (accumulate over rank)
s0 = [ 372000, 372000, 372000, -71000, 372000, -71000 ]';

% Target syndicate standing (all but Perrin Sequence)
s = [ 372000, 372000, 372000, -71000, 372000, 372000 ]';

% All 6 syndicates at max rank example
% If you have 5 syndicates initially maxed
%s0 = [ 372000, 372000, 372000, -71000, 372000, 372000 ]';
%s = [ 283400, 283400, 283400, -71000, 283400, 283400 ]';

% Mask out Perrin Sequence
M = eye(6);
M(4,4) = 0;

Z = eye(6) - 1.0/6;
Wh = M*W;

% Shorthand for \hat{W}^T*\hat{W}
Q = Wh'*Wh;

% Pseudo inverse
Qi = Z*inv(Q + 1)*Z;

uh = Qi*Wh'*(s-s0);

c = -6.0*min(uh);
p = uh/c + 1/6;

format longG

disp("Starting syndicate standing: ")
s0
disp("Target syndicate standing: ")
s
disp("Total standing needed (not including the +50%): ")
round(c) % The W will distribute the +50%

disp("Total cumulative standing earned across: ")
round(c*1.5)

format shortG
disp("Proportion of standing to accumulate per syndicate: ")
p

format longG
disp("Ending standing: ")
round(s0 + c*W*p)