Trying to find a minimum value

In this code, I am trying to find the minimum value of rho_Tw, and find the associated w value with it (so basically trying to find the x value associated with the minimum y value). However, whenever I run the following code, I get 0. Any corrections would be greatly appreciated.

AA = [2 0 -2 0 0 0 0 0 0 0;

0 2 0 -2 0 0 0 0 0 0;

0 -1 7 -2 -3 0 0 0 0 0;

0 0 0 1 -1 0 0 0 0 0;

0 0 0 0 4 0 0 -2 0 0;

0 0 0 0 0 1 0 0 0 -1;

-2 0 0 0 0 0 2 0 0 0;

0 0 -4 0 0 -1 0 8 -3 0;

0 0 0 0 0 -2 0 0 7 -4;

0 0 0 0 0 0 -3 0 0 4];

L = -tril(AA, -1);

U = -triu(AA, 1);

D = diag(AA);

DD = diag(D);

Tj=inv(DD)*(L+U);

rho_Tj=max(abs(eig(Tj)));

for w = 0:0.0005:2

wb=0;

rho_min=0;

Tw=inv(DD-w*L)*(((1-w)*DD)+(w*U));

rho_Tw=max(abs(eig(Tw)))

scatter(w, rho_Tw)

hold on

if w == 0

rho_min = rho_Tw;

wb = w;

end

if rho_Tw < rho_min

rho_min = rho_Tw;

wb=w;

end

end

disp(wb)

Answer 1

[Jon]

You may have some additional problems but one is that you reset wb to zero with every loop iteration, first line in your loop is

wb=0

So although wb get set to the minimum value in your if statement, it immediately gets wiped out in the next loop iteration

I would suggest that rather than finding the minimum yourself with the if statements you just caculate a vector of rho_Tw values and then use MATLAB's min function like this

AA = [2 0 -2 0 0 0 0 0 0 0;
    0 2 0 -2 0 0 0 0 0 0;
    0 -1 7 -2 -3 0 0 0 0 0;
    0 0 0 1 -1 0 0 0 0 0;
    0 0 0 0 4 0 0 -2 0 0;
    0 0 0 0 0 1 0 0 0 -1;
    -2 0 0 0 0 0 2 0 0 0;
    0 0 -4 0 0 -1 0 8 -3 0;
    0 0 0 0 0 -2 0 0 7 -4;
    0 0 0 0 0 0 -3 0 0 4];
L = -tril(AA, -1);
U = -triu(AA, 1);
D = diag(AA);
DD = diag(D);
Tj=inv(DD)*(L+U);
rho_Tj=max(abs(eig(Tj)));

% assign w vector
w = 0:0.0005:2;
% preallocate array to hold rho_Tw values
rho_Tw = zeros(length(w),1);

% loop to evaluate rho_Tw as a function of w
for k = 1:length(w)
    Tw=inv(DD-w(k)*L)*(((1-w(k))*DD)+(w(k)*U));
    rho_Tw(k) =max(abs(eig(Tw)));
end

% find minimum
[rho_min,idxMin] = min(rho_Tw);
wb = w(idxMin);

% plot results
scatter(w,rho_Tw)

% display results
disp(rho_min)
disp(wb)