Fix an infinite while loop by properly counting the number of elements added to an array

I am trying to calculate the condition numbers of multiple square 2x2 matrices. I generate a matrix A with random value of l, m and n and of the form A = [l,m;m,n];. Then I calculate A's eigenvalues with the built in MATLAB function. If the eigenvalues are real I store matrix A and the matlab condition number in their appropriate arrays, and then calculate the theoretical condition number for A an store that value in an array. The total amount of stored matrices should be 100, but my code currently runs forever b/c my acceptance counter which is supposed to track how many matrices Ive stored does not activate. Any help with solving this problem would be appreciated. My code is posted below.

clear
close
clc
% Create matrix A and calculate Eigenvalues

acceptance_count = 0;
itr = 0;
A_storage = {};

while acceptance_count < 100
itr = itr+1;
A = zeros(2);

l = rand(1);
m = rand(1);
n = rand(1);

A(1,1) = l;
A(1,2) = m;
A(2,1) = m;
A(2,2) = n;

[K_mat, A, tf] = K_matlab(A);
Kmat(itr) = K_mat;
A_storage(itr) = {A};


if tf == 1
A_storage(itr) = {A};
acceptance_count = acceptance_count+1;
[lambda, K_th]  = K_quadtheory(1,(l+n),(l*n-m^2));
Kth(itr) = K_th;
end

end
%%
function [K_mat, A, tf] = K_matlab(A)
eigen_values = eig(A);
tf = isreal(eigen_values);
if tf == 1
eigen_max = max(eigen_values);
eigen_min = min(eigen_values);
K_mat = abs(eigen_max/eigen_min);
end
end

function [lambda, K_th]  = K_quadtheory(a,b,c)
 lambda = zeros(2,1);
 d = sqrt(b*b-4*a*c); 
 lambda(1) = (-b-d)/(2*a);
 if b*b/(4*a*c) > 1.e5 
 lambda(2) = -2*c/(b+d);
 else
 lambda(2) = (-b+d)/(2*a);
 end
 K_th = abs(max(lambda)/min(lambda));
end

[Star Strider]

To do the Updates:

In the MATLAB window, either:

Add-Ons —> Check for Updates

or:

Help —> Check for Updates

(I don’t remember when that changed.)

I deleted my Answer since it was not Acecepted.

[James Peach]

thank you! I will try both out and see what works

Answer 1

[James Peach]

EDIT: I solved my problem by moving the acceptance counter into my if statement within the while loop instead of relying on changing the size of the storage matrix.

Answer 2

[Steven Lord]

There's at least one bug and a bit of an unusual pattern in your code. Let's skip down to your call to K_matlab.

[K_mat, A, tf] = K_matlab(A);

If K_matlab modified its input argument A internally, returning it would make sense. But looking at that function:

function [K_mat, A, tf] = K_matlab(A)
eigen_values = eig(A);
tf = isreal(eigen_values);
if tf == 1
eigen_max = max(eigen_values);
eigen_min = min(eigen_values);
K_mat = abs(eigen_max/eigen_min);
end
end

A is not modified in K_matlab. So why return the (unmodified) A from K_matlab?

This is also where a bug is located. What happens if your eigenvalues are not real? tf will be false and the body of the if statement will not execute. So what does K_matlab return as its first output argument in that scenario? K_mat was never assigned a value (that only occurs in the body of the if statement that was skipped.) So MATLAB will error.

I'm assuming this is part of a homework assignment, since otherwise you should just use the built-in cond function.

[James Peach]

I removed the A cause intially I was modifiying it in the function, but abandon that tack once I came up with the current code. Also the eigenvalues can never be not real numbers, since each of the values of l m and n are always positive and 0 isn't a positve number so the calculations for lambda can be a bit less robust.