Calculation of matrix rank?

[maikl]

It seems that IT++ does not provide the calculation of the rank of a given mat/cmat? I would appreciate if anyone can offer some help in this matter. Many thanks.

[Martin Senst]

You can perform an SVD and count the number of nonzero singular values. I took Matlab's rank function and translated it to IT++:

template <class Num_T>
int rank(const itpp::Mat<Num_T>& m, double tol = -1.0)
{
if (m.cols() == 0 || m.rows() == 0) return 0;

itpp::vec singular_values = itpp::svd(m);

if (tol <= 0) // Calculate default tolerance
{
    tol = itpp::eps * singular_values(0) * (m.rows() > m.cols() ? m.rows() : m.cols());
}

// Count number of nonzero singular values
int r;
for (r = 0 ; r < length(singular_values); r++)
{
    if (singular_values(r) < tol) break;
}
return r;

}

Cheers
Martin

[maikl]

Many thanks Martin for your help - this is very much appreciated.

Just one queston: what is the rationale for the calculation of the default tol? Why it is calculated as stated?

tol = itpp::eps * singular_values(0) * (m.rows() > m.cols() ? m.rows() : m.cols());

Thanks again.

[Martin Senst]

Well, I have to admit that I can't really explain this choice of tol. I simply took it from the Matlab-version of rank(). The only difference is that they use eps(max(singular_values)), which is close to eps(1)*max(singular_values), but not equal. I can't tell if this difference is important.

Sorry for not being able to help you here...

[maikl]

thank you very much for your reply. it's already very helpful. thx