Index exceeds the number of array elements(3)

For a matrix :

A=[4 1 3 1;1 4 1 3;3 1 4 1;1 3 1 4]
[L,P,D]=eigen(A);

I have a function:

function [L,P,D]=eigen(A)
format
[~,n]=size(A);
P=[];
D=[];
L=eig(A);
L=transpose(L);
L=real(L);
L=sort(L);

for i= 1:n-1
    Temp1 = L(i);
    Temp2 = L(i+1);
    if closetozeroroundoff(Temp1-Temp2, 7)== 0
        L(1,i+1) = L(1, i);
    end 
end
        
if rank(L) ~= n
    L = closetozeroroundoff(L,7);
end

fprintf('all eigenvalues of A are\n')
display(L)

M = unique(L);
M = transpose(M);
display(M)

m = groupcounts(transpose(L));
display(m)


for i = 1:n
    fprintf('eigenvalue %d has multiplicity %i\n',M(i),m(i))
end

output:

That is intended to find the eigenvalues (L) and then checks how many times each unique eigenvalue (M) is repeated in L. But when I it, the groupcounts gives me an error, even though the output is correct, that says Index exceeds the number of array elements(3).

How do I fix it?

Answer 1

[Clayton Gotberg]

The error

Index exceeds the number of array elements (3).

This means that you are asking for an element beyond the boundaries of one of your arrays, which has 3 elements.

The cause

If we zoom out to

for i = 1:n
    fprintf('eigenvalue %d has multiplicity %i\n',M(i),m(i))
end

We see that there is one indexing variable, i, which is being used in M(i) and m(i). The for loop gives i values from 1 to n, which (from earlier) is the number of columns in your input matrix. Your input matrix is 4x4, so n = 4. When the program tries to use i = 4, it calls for M(4) and m(4), which do not exist because they are beyond the boundaries of those arrays.

You can see the program works as intended for i = 1:3, so the issue is that listing the eigenvalues with their multiplicities has changed the representation from 4 eigenvalues (allowing the possibility of duplicates) to 3 eigenvalues (removing duplicates).

The solution

When you have determined the unique eigenvalues, measure the size of that array and use that size with the for loop instead.

eig_count = size(m,1) % Only returns the number of rows in m

for i = 1:eig_count
    fprintf('eigenvalue %d has multiplicity %i\n',M(i),m(i))
end