Calculation in inter dependency matrix

Can someone help me to solve the below-mentioned calculation? i have vectors

A1(221X1), D1(221X1) and P(221X1) and my formula to calculate utility is Utility= (((1-P(1,1))*(D(1,1)/(D(1,1)+A1(1,1)))* V)-C + (((1-P(2,1))*(D(2,1)/(D(2,1)+A1(2,1)))* V)-C +.........till (((1-P(221,1))*(D(221,1)/(D(221,1)+A1(221,1)))* V)-C

My requirement is:

For iteration 1:

% A1= (221X1) random values

% X1= (221X1) calculated values

% D1= (221X1) random values

% utility1= (((1-P(1,1))*(D(1,1)/(D(1,1)+A1(1,1)))* V)-C + (((1-P(2,1))*(D(2,1)/(D(2,1)+A1(2,1)))* V)-C +.........till (((1-P(221,1))*(D(221,1)/(D(221,1)+A1(221,1)))* V)-C%

% store the calculated utilty1 value %

% store the generated A1 vector used in the iteration1 utility calculation %

% store the generated D1 vector used in the iteration1 utility calculation %

% store the calculated P vector used in the iteration1 utility calculation %

start the iteration 2

% Do the same as iteration1 and save all newly generated D1, A1, and P %

%Repeat for 1000 iteration and store the newly generated A1, D1, P vector of size (221X1) and utility of size (1) for 1000 iterations %

%Find the maximum utility of 1000 iteration and show the corresponding D1, P and A1 vectors used in the calculation of that maximum utility%

 V= 0.2;
C=0.2;
I= eye(221);
s = string({'CR';'E';'R';'S';'SR'})
s1 = s([2,5])' + (1:20)'
s1 = [s([2,3,2,4]) + [101;1;106;1];s1(:)] + (0:4)
d = {tril(ones(44,4),-1),diag(ones(20,1),-24)}
d{2} = d{2}(:,1:end-4)
dd = repmat({[d{:}]},1,5)
str = cellstr([s(1);s1(:)])
out = [{nan},str(:)';str, num2cell([zeros(1,221);[ones(220,1),blkdiag(dd{:})]]) ];
A= out(2:end,2:end);
for i=1:1000
A1= ( randn(221,1) * 0.1 ) + 0.45;
X11= cell2mat(A)*A1;
P= zeros(221,1);
P(:)= X11(:)/sum(X11)
D1= ( randn(221,1) * 0.1 ) + 0.45;
% Utility= (((1-P(1,1))*(D(1,1)/(D(1,1)+A1(1,1)))* V)-C + (((1-P(2,1))*(D(2,1)/(D(2,1)+A1(2,1)))* V)-C +.........till (((1-P(221,1))*(D(221,1)/(D(221,1)+A1(221,1)))* V)-C 
    end %

Answer 1

[Basil C.]

You could use a 3D matrix to store the new values of A1, D1, P and Utility

 result=zeros(221,4,1000);
for (i=1:1000)
    A1= ( randn(221,1) * 0.1 ) + 0.45;
    X11= cell2mat(A)*A1;
    P= zeros(221,1);
    P(:)= X11(:)/sum(X11)
    D1= ( randn(221,1) * 0.1 ) + 0.45;
    Utility=0;
     for(j=1:221)
         Utility= (((1-P(j))*(D(j)/(D(j)+A1(j)))* V)-C +Utility;
     end
    result(:,1,i)=A1;
    result(:,2,i)=D1;
    result(:,3,i)=P;
    result(1,4,i)=Utility;
 end

• To find the maximum Utility use:

 [Utility_max,index_max]=max(result(1,4,:));
 A1_max=result(:,1,index_max);
 D1_max=result(:,2,index_max);
 P_max=result(:,3,index_max);

where A1_max, D1_max, P_max are the values of A1, D1, P at maximum Utility

[Santhosh Chandrasekar]

Thank you very much, sir! This is what I required.