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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

Steven Lord
on 5 Sep 2020

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.

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## Direct link to this comment

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