pair<const vec_t *, const vec_t *> model::regress(const mat_t &training_input, const mat_t &testing_input)
{
    for (int i = 0; i < testing_input.n_cols; ++i)
    {
        COV_FUNC->comp_ker(mixture_cov.get(), training_input, testing_input.col(i));
        COV_FUNC->comp_ker(testing_cov.get(), testing_input.col(i), testing_input.col(i));
        (*testing_cov)(0, 0) += VAR_NOISE;
        *v = arma::solve(arma::trimatl(chol_cov->t()), *mixture_cov);
    
        (*testing_target)(i) = arma::sum(mixture_cov->t() * *alpha);
        (*testing_var)(i) = arma::sum(*testing_cov - v->t() * *v);
    }

    return make_pair(testing_target.get(), testing_var.get());
}
    void dTv1(mat_t& drt3_dt1, mat_t& dt3_dt1)
    {                
        drt3_dt1.create(3, 3);     dt3_dt1.create(3, 3);
                    
        for(int i = 0; i < 3; ++i) 
        {
            ev.setTo(Scalar(0));    ev(i, 0) = eps;                        
                        
            composeRT( rv1, tv1 + ev, rv2, tv2, rv3_p, tv3_p);            
            composeRT( rv1, tv1 - ev, rv2, tv2, rv3_m, tv3_m);

            drt3_dt1.col(i) = rv3_p - rv3_m;            
            dt3_dt1.col(i) = tv3_p - tv3_m;                         
        }
        drt3_dt1 /= 2 * eps;       dt3_dt1 /= 2 * eps;
    }
    void dRv2(mat_t& dr3_dr2, mat_t& dt3_dr2)
    {                
        dr3_dr2.create(3, 3);     dt3_dr2.create(3, 3);
                    
        for(int i = 0; i < 3; ++i) 
        {
            ev.setTo(Scalar(0));    ev(i, 0) = eps;                        
                        
            composeRT( rv1, tv1, rv2 + ev, tv2, rv3_p, tv3_p);            
            composeRT( rv1, tv1, rv2 - ev, tv2, rv3_m, tv3_m);

            dr3_dr2.col(i) = rv3_p - rv3_m;            
            dt3_dr2.col(i) = tv3_p - tv3_m;                         
        }
        dr3_dr2 /= 2 * eps;       dt3_dr2 /= 2 * eps;
    }