Compute the mixing probability for each filter.

def _compute_mixing_probabilities(self):
        """
        Compute the mixing probability for each filter.
        """

        self.cbar = dot(self.mu, self.M)
        for i in range(self.N):
            for j in range(self.N):
                self.omega[i, j] = (self.M[i, j]*self.mu[i]) / self.cbar[j]