Hello world!
I have to obtain a matrix T starting from a matrix A and a vector w. Specifically:
- matrix A is a reciprocal (i.e. A(i,j) = 1/A(j,i)) square matrix of dimension N composed by all positive elements between 0 and 9;
- w is a column vector of dimension N whose entries are between 0 and 1.
T is defined element-wise as T(i,j) = A(i,j)*w(i)/w(j), so it is still a square matrix of dimension n. I used two ways: a double for cycle and element-wise moltiplications. Before going for the element-wise operations, I tested if the two methods provide the same result using logical operations (T==T2), and it happened to be incorrect. An example follows. It occurs that matrices T and T2 are not completely identical (some elements in the logical variables ans are zeros), eventhough if I open T and T2 from workspace or display the critical elements in command window the two seem identical.
I'd say that the problem depends on the well-known problems of matlab with decimal digits, and most probably the bias is negligible, but here's where my doubt emerges: which one of the two is more correct (assuming that both are correct)?
A = [1 2 3 1 3 8;
1/2 1 7 3 1/5 1;
1/3 1/7 1 1/5 1/5 1/2;
1 1/3 5 1 1 1/3;
1/3 5 5 1 1 3;
1/8 1 2 3 1/3 1];
n = size(A,1);
[w, lambda] = eig(A);
[Lmax, indL] = max(diag(lambda));
w = w(:,indL)/(sum(w(:,indL)));
T = A.*(w'./w);
T2 = zeros(size(A));
for i = 1:n
for j = 1:n
T2(i,j) = A(i,j)*w(j)/w(i);
end
end
T == T2
Thank you in advance,
Riccardo
