Apply the projection and store inner product.

        :param v: the vector resulting from an application of :math:`M_lAM_r`
          to the current Arnoldi vector. (CG needs special treatment, here).

def _apply_projection(self, Av):
        '''Apply the projection and store inner product.

        :param v: the vector resulting from an application of :math:`M_lAM_r`
          to the current Arnoldi vector. (CG needs special treatment, here).
        '''
        PAv, UAv = self.projection.apply_complement(Av, return_Ya=True)
        self.C = numpy.c_[self.C, UAv]
        return PAv