Measure the coherence (or incoherence) of two/one matrix/ces

Dear all I would like to ask you if there is in matlab a fuction that based on two/one input matrices to calculate the coherence or incoherence between those two or the mutual coherence of itself.

http://en.wikipedia.org/wiki/Mutual_coherence_(linear_algebra)

I would like to thank you in advance for your help

Regards Alex

Answer 1

[Wayne King]

For a single matrix, X, compute

X'*X

and then find the largest absolute value not on the main diagonal.

    X = randn(4,4);
    X = X/(diag(sqrt(diag(X'*X))));
    mcoh = abs(X'*X);
    V = diag(mcoh);
    V = -diag(V,0);
    mcoh = mcoh+V;
    max(max(mcoh))

You want to normalize the column vectors in X to have unit norm first.

[SUMIT]

how can i calculate coherence between two matrices??

Answer 2

[Pushkar Khatri]

For the mutual coherence of a single matrix, you can make your own function and implement it later in command line. Here is my function(I had used the convention X*X' for my purpose, you can use change it to X'*X) :-

function z = mutual_coherence(X)

 [m,n] = size(X);    
for i =1:m
        d1 = norm(X(i,:));
        for j =1:m
            d2 =  norm(X(j,:));
            if i ==j
                continue;
            else
                z = max((sqrt((X(i,:)*X(j,:)')^2 ))/(d1*d2));
            end
        end
    end

end

[Kobi]

about your function

what if the number of rows is different then the number of columns?

n is unused.

[Pushkar Khatri]

As per the function, it finds out the mutual coherence of a single matrix X. So for that you need to find the matrix multiplication of X with its transpose. In my function number of rows and columns are different. if you do X * X' , you'll get m by m matrix and if you do X' * X you'll get n by n matrix. The point is not to loose the importanat information. So if m>n, find coherence using rows(i.e m) { in this way, you get coherence for m*n elements and rest of the elements out of total m*m elements will be zero },

else if n>m , use n instead of m in the function.

Does that clear your doubt?