Write matlab code for the following algorithm

I have this algorithm

I write this code for my example

A = [10 -10; 1 0; -1 0; 0 -1 ; 0 1; 11 -10; -1 -1];
C = cov(A).^(-1/2).*A;
M = size(A,1);
omega = C*C';
x0=[];x1=[];x2=[];PS=[];
for i0=1:M
    for i1=1:M
        for i2=1:M
            j = 0;
            if isequal(i2,i1)
                x2(j) = abs(omega(i1,i0)+omega(i2,i0));
                j = j+1;
            end
        end
        x1(j) = min(median(x2,'all')); % lower median
    end
    x0(j) = 1.1 .* min(median(x1,'all')); % lower median
end

for i3=1:M
    PS(i3) = max(omega(i3)/x0);
end

but the above-mentioned code has many problems. I do not know how to fix it.

the result should be

PS = [16.77;0.839;0.839;0.839;0.839;17.609;1.677];

Answer 1

[Karim]

I'm not familiar with the algoritm, so it could still have some mistakes left...

However, i was able to identify a couple of mistakes:

• x1 should be indexed with i1 and x0 with i0
• you first need to update j before you can use it as an index into x2
• the condition states that you should enter if i2 is not equal to i1
• i'm guessing that the matrix A you provided does not have the correct dimensions, i assume it should be a 7x7 matrix?
• also min( median( ) ) is not the same as the low median, since x2 is a vector the median will return a scalar

Below i used an random A matrix, hence the 'PS' result is not the same as the one you expect. Where did you obtain the matrix A and the expected result?

A = [10 -10; 1 0; -1 0; 0 -1 ; 0 1; 11 -10; -1 -1];

% use a random A matrix...
A = rand(7) * 100;

C = cov(A)^(-1/2) * A;
M = size(A,1);
omega = C*C';

x0 = zeros(M  ,1);
x1 = zeros(M  ,1);
x2 = zeros(M-1,1); % 1 element less since we neglect the case where i2 == i1
PS = zeros(M  ,1);

for i0 = 1:M
    for i1 = 1:M
        j = 0;
        for i2 = 1:M
            if i2 ~= i1
                j = j + 1;
                x2( j ) = abs( omega(i1,i0) + omega(i2,i0) );
            end
        end
        x1( i1 ) = median(x2,'all');
    end
    x0( i0 ) = 1.1 * median(x1,'all');
end

for i3 = 1:M
    PS(i3) = max( omega(i3)/x0 );
end

PS

PS = 7×1

0.2077 0 0.3258 0.2614 0.4130 0 0

[NA]

Thank you for your time.

C = cov(A)^(-1/2) * A

the above line means that we normalize the A matrix by its covariance

covariance here is R = eye( M )