how to take whole matrix using loop index

whilw solving alernate optimzation problem, i am having issue with takiing whole matrix using loop. i have two matrices for example W=6*6 and theta1=6*6,

maximize(real(trace( theta1(i)*Hs*W(i)*Hs' )))

now i have to take whole matrices not elements like W and theta1 should be 6*6.

kindly some one help i am stuck here.

Answer 1

[Vinicius Pereira Mateus Borges]

I am not sure if I understand the question. Please attach some of your data and code as an example if the following does not help:

1) Instead of using a for loop, can you not just do element-wise multiplication between the matrices?

maximize(real(trace( theta1 .* Hs .* W * Hs' ))) % assuming Hs is a constant

2) If Hs is a changing part of a for loop, then you two options:

% double indexing with i and j for rows and colums
for i = 1:6
    for j = 1:6
        maximize(real(trace( theta1(i,j)*Hs*W(i,j)*Hs' )))
    end
end

% using linear indexing (so counting between 1:36)
for i = 1:36 % works for a 6 by 6 matrix, but you may want to soft code this 
    maximize(real(trace( theta1(i)*Hs*W(i)*Hs' )))
end

You may want to look at how linear indexing works before using the second option. For instance, in a 6-by-6 matrix, theta1(7) would be the first element of the second row (same as theta1(1,2)).

[wasif]

i have complex matrices for all hs, theta1 and W, in ist itration i have taken W with all one matrix, using all one W in prob#1 i have to find optimizte theta1(i) and then this theta1(i) is used in next prb#2 to get optimize W(i+1). my question is that this is itrative process and what should do to get a theta1 and W as matrices not an elements.

for i=1:1:100

%%prob#1

cvx_begin sdp

variable theta1(L+1,L+1) complex semidefinite

maximize(real(trace( theta1(i)*Hs*W(i)*Hs' )))

subject to

real(trace(theta1(i)*Hpk*W(i)*Hpk'))<=gamma_k;

for t=1:L+1

real(theta1(t,t))<=1;

end

%theta1(i) == semidefinite(L+1);

cvx_end

%% prob#2

cvx_begin sdp

variable W(M,M) complex semidefinite

maximize(real(trace( theta1(i)*Hs*W(i+1)*Hs' )))

subject to

real(trace(theta1(i,j)*Hpk*W(i+1,j+1)*Hpk'))<=gamma_k;

real(trace(W(i+1))<=P;

%W(i+1) == semidefinite(M);

cvx_end

%%etta is a factor =0.

etta(i+1)=trace(theta1(i)*Hs*W(i+1)*Hs');

tol_factor is also a scalar value

if real(etta(i+1,))-real(etta(i)<=tol_factor

break;

else

i=i+1;

j=j+1;

end

end