A procedure for counting the number of eigenvalues of a matrix in a region
surrounded by a closed curve is presented. It is based on the application of
the residual theorem. The quadrature is performed by evaluating the principal
argument of the logarithm of a function. A strategy is proposed for selecting a
path length that insures that the same branch of the logarithm is followed
during the integration. Numerical tests are reported for matrices obtained from
conventional matrix test sets.Comment: 21 page
