Example #1
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing dsygvd
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    real_Double_t   gpu_time, cpu_time;
    double *h_A, *h_R, *h_B, *h_S, *h_work;
    double *w1, *w2;
    magma_int_t *iwork;
    magma_int_t N, n2, info, nb, lwork, liwork, lda;
    double result[4] = {0};

    double c_one     = MAGMA_D_ONE;
    double c_neg_one = MAGMA_D_NEG_ONE;

    double d_zero        =  0.;
    double d_one         =  1.;
    double d_neg_one     = -1.;
    //magma_int_t izero    = 0;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    magma_int_t status = 0;

    magma_opts opts;
    parse_opts( argc, argv, &opts );
    
    double tol    = opts.tolerance * lapackf77_dlamch("E");
    double tolulp = opts.tolerance * lapackf77_dlamch("P");
    
    if ( opts.check && opts.jobz == MagmaNoVec ) {
        fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
        opts.jobz = MagmaVec;
    }
    
    printf("using: itype = %d, jobz = %s, uplo = %s\n",
           (int) opts.itype, lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo));

    printf("    N   CPU Time (sec)   GPU Time(sec)\n");
    printf("======================================\n");
    for( int itest = 0; itest < opts.ntest; ++itest ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            N = opts.nsize[itest];
            lda    = N;
            n2     = N*lda;
            nb     = magma_get_dsytrd_nb(N);
            lwork  = 1 + 6*N*nb + 2* N*N;
            liwork = 3 + 5*N;

            TESTING_MALLOC_CPU( h_A,    double,      n2     );
            TESTING_MALLOC_CPU( h_B,    double,      n2     );
            TESTING_MALLOC_CPU( w1,     double,      N      );
            TESTING_MALLOC_CPU( w2,     double,      N      );
            TESTING_MALLOC_CPU( iwork,  magma_int_t, liwork );
            
            TESTING_MALLOC_PIN( h_R,    double,      n2     );
            TESTING_MALLOC_PIN( h_S,    double,      n2     );
            TESTING_MALLOC_PIN( h_work, double,      lwork  );
            
            /* Initialize the matrix */
            lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
            lapackf77_dlarnv( &ione, ISEED, &n2, h_B );
            magma_dmake_hpd( N, h_B, lda );
            lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
            lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &lda, h_S, &lda );
            
            /* warmup */
            if ( opts.warmup ) {
                magma_dsygvd( opts.itype, opts.jobz, opts.uplo,
                              N, h_R, lda, h_S, lda, w1,
                              h_work, lwork,
                              iwork, liwork,
                              &info );
                if (info != 0)
                    printf("magma_dsygvd returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
                
                lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
                lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &lda, h_S, &lda );
            }
            
            /* ====================================================================
               Performs operation using MAGMA
               =================================================================== */
            gpu_time = magma_wtime();
            magma_dsygvd( opts.itype, opts.jobz, opts.uplo,
                          N, h_R, lda, h_S, lda, w1,
                          h_work, lwork,
                          iwork, liwork,
                          &info );
            gpu_time = magma_wtime() - gpu_time;
            if (info != 0)
                printf("magma_dsygvd returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            
            if ( opts.check ) {
                /* =====================================================================
                   Check the results following the LAPACK's [zc]hegvd routine.
                   A x = lambda B x is solved
                   and the following 3 tests computed:
                   (1)    | A Z - B Z D | / ( |A||Z| N )   (itype = 1)
                          | A B Z - Z D | / ( |A||Z| N )   (itype = 2)
                          | B A Z - Z D | / ( |A||Z| N )   (itype = 3)
                   (2)    | I - V V' B | / ( N )           (itype = 1,2)
                          | B - V V' | / ( |B| N )         (itype = 3)
                   (3)    | S(with V) - S(w/o V) | / | S |
                   =================================================================== */
                double temp1, temp2;
                //double *tau;
                
                if ( opts.itype == 1 || opts.itype == 2 ) {
                    lapackf77_dlaset( "A", &N, &N, &d_zero, &c_one, h_S, &lda);
                    blasf77_dgemm("N", "C", &N, &N, &N, &c_one, h_R, &lda, h_R, &lda, &d_zero, h_work, &N);
                    blasf77_dsymm("R", lapack_uplo_const(opts.uplo), &N, &N, &c_neg_one, h_B, &lda, h_work, &N, &c_one, h_S, &lda);
                    result[1] = lapackf77_dlange("1", &N, &N, h_S, &lda, h_work) / N;
                }
                else if ( opts.itype == 3 ) {
                    lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &lda, h_S, &lda);
                    blasf77_dsyrk(lapack_uplo_const(opts.uplo), "N", &N, &N, &d_neg_one, h_R, &lda, &d_one, h_S, &lda);
                    result[1] = lapackf77_dlansy("1", lapack_uplo_const(opts.uplo), &N, h_S, &lda, h_work) / N
                              / lapackf77_dlansy("1", lapack_uplo_const(opts.uplo), &N, h_B, &lda, h_work);
                }
                
                result[0] = 1.;
                result[0] /= lapackf77_dlansy("1", lapack_uplo_const(opts.uplo), &N, h_A, &lda, h_work);
                result[0] /= lapackf77_dlange("1", &N, &N, h_R, &lda, h_work);
                
                if ( opts.itype == 1 ) {
                    blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_A, &lda, h_R, &lda, &d_zero, h_work, &N);
                    for(int i=0; i<N; ++i)
                        blasf77_dscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_neg_one, h_B, &lda, h_R, &lda, &c_one, h_work, &N);
                    result[0] *= lapackf77_dlange("1", &N, &N, h_work, &N, &temp1)/N;
                }
                else if ( opts.itype == 2 ) {
                    blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_B, &lda, h_R, &lda, &d_zero, h_work, &N);
                    for(int i=0; i<N; ++i)
                        blasf77_dscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_A, &lda, h_work, &N, &c_neg_one, h_R, &lda);
                    result[0] *= lapackf77_dlange("1", &N, &N, h_R, &lda, &temp1)/N;
                }
                else if ( opts.itype == 3 ) {
                    blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_A, &lda, h_R, &lda, &d_zero, h_work, &N);
                    for(int i=0; i<N; ++i)
                        blasf77_dscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_B, &lda, h_work, &N, &c_neg_one, h_R, &lda);
                    result[0] *= lapackf77_dlange("1", &N, &N, h_R, &lda, &temp1)/N;
                }
                
                /*
                lapackf77_dsyt21(&ione, lapack_uplo_const(opts.uplo), &N, &izero,
                                 h_A, &lda,
                                 w1, w1,
                                 h_R, &lda,
                                 h_R, &lda,
                                 tau, h_work, rwork, &result[0]);
                */
                
                lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
                lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &lda, h_S, &lda );
                
                magma_dsygvd( opts.itype, MagmaNoVec, opts.uplo,
                              N, h_R, lda, h_S, lda, w2,
                              h_work, lwork,
                              iwork, liwork,
                              &info );
                if (info != 0)
                    printf("magma_dsygvd returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
                
                temp1 = temp2 = 0;
                for(int j=0; j<N; j++) {
                    temp1 = max(temp1, absv(w1[j]));
                    temp1 = max(temp1, absv(w2[j]));
                    temp2 = max(temp2, absv(w1[j]-w2[j]));
                }
                result[2] = temp2 / temp1;
            }
            
            /* =====================================================================
               Performs operation using LAPACK
               =================================================================== */
            if ( opts.lapack ) {
                cpu_time = magma_wtime();
                lapackf77_dsygvd( &opts.itype, lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
                                  &N, h_A, &lda, h_B, &lda, w2,
                                  h_work, &lwork,
                                  iwork, &liwork,
                                  &info );
                cpu_time = magma_wtime() - cpu_time;
                if (info != 0)
                    printf("lapackf77_dsygvd returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
                
                printf("%5d     %7.2f         %7.2f\n",
                       (int) N, cpu_time, gpu_time);
            }
            else {
                printf("%5d       ---           %7.2f\n",
                       (int) N, gpu_time);
            }
            
            /* =====================================================================
               Print execution time
               =================================================================== */
            if ( opts.check ) {
                printf("Testing the eigenvalues and eigenvectors for correctness:\n");
                if ( opts.itype==1 ) {
                    printf("(1)    | A Z - B Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed") );
                }
                else if ( opts.itype==2 ) {
                    printf("(1)    | A B Z - Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed") );
                }
                else if ( opts.itype==3 ) {
                    printf("(1)    | B A Z - Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed") );
                }
                if ( opts.itype==1 || opts.itype==2 ) {
                    printf("(2)    | I -   Z Z' B | /  N         = %8.2e   %s\n",   result[1], (result[1] < tol    ? "ok" : "failed") );
                }
                else {
                    printf("(2)    | B -  Z Z' | / (|B| N)       = %8.2e   %s\n",   result[1], (result[1] < tol    ? "ok" : "failed") );
                }
                printf(    "(3)    | D(w/ Z) - D(w/o Z) | / |D|  = %8.2e   %s\n\n", result[2], (result[2] < tolulp ? "ok" : "failed") );
                status += ! (result[0] < tol && result[1] < tol && result[2] < tolulp);
            }
            
            TESTING_FREE_CPU( h_A   );
            TESTING_FREE_CPU( h_B   );
            TESTING_FREE_CPU( w1    );
            TESTING_FREE_CPU( w2    );
            TESTING_FREE_CPU( iwork );
            
            TESTING_FREE_PIN( h_R    );
            TESTING_FREE_PIN( h_S    );
            TESTING_FREE_PIN( h_work );
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }
    
    TESTING_FINALIZE();
    return status;
}
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing dsygvdx
*/
int main( int argc, char** argv)
{

    TESTING_INIT();

    real_Double_t gpu_time;

    double *h_A, *h_R, *h_B, *h_S, *h_work;

    #if defined(PRECISION_z) || defined(PRECISION_c)
    double *rwork;
    magma_int_t lrwork;
    #endif

    /* Matrix size */
    double *w1, *w2, result[2]={0,0};
    magma_int_t *iwork;
    magma_int_t N, n2, info, lwork, liwork;
    double c_zero    = MAGMA_D_ZERO;
    double c_one     = MAGMA_D_ONE;
    double c_neg_one = MAGMA_D_NEG_ONE;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    magma_int_t status = 0;

    magma_opts opts;
    parse_opts( argc, argv, &opts );
    
    double tol    = opts.tolerance * lapackf77_dlamch("E");
    double tolulp = opts.tolerance * lapackf77_dlamch("P");

    magma_range_t range = MagmaRangeAll;
    if (opts.fraction != 1)
        range = MagmaRangeI;

    if ( opts.check && opts.jobz == MagmaNoVec ) {
        fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
        opts.jobz = MagmaVec;
    }

    printf("using: itype = %d, jobz = %s, range = %s, uplo = %s, opts.check = %d, fraction = %6.4f\n",
           (int) opts.itype, lapack_vec_const(opts.jobz), lapack_range_const(range), lapack_uplo_const(opts.uplo),
           (int) opts.check, opts.fraction);

    printf("    N     M   GPU Time (sec)\n");
    printf("============================\n");
    magma_int_t threads = magma_get_parallel_numthreads();
    for( int itest = 0; itest < opts.ntest; ++itest ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            N = opts.nsize[itest];
            n2     = N*N;
            #if defined(PRECISION_z) || defined(PRECISION_c)
            lwork  = magma_dbulge_get_lq2(N, threads) + 2*N + N*N;
            lrwork = 1 + 5*N +2*N*N;
            #else
            lwork  = magma_dbulge_get_lq2(N, threads) + 1 + 6*N + 2*N*N;
            #endif
            liwork = 3 + 5*N;

            /* Allocate host memory for the matrix */
            TESTING_MALLOC_CPU( h_A,    double, n2 );
            TESTING_MALLOC_CPU( h_B,    double, n2 );
            TESTING_MALLOC_CPU( w1,     double, N );
            TESTING_MALLOC_CPU( w2,     double, N );
            TESTING_MALLOC_CPU( iwork,  magma_int_t, liwork );
            
            TESTING_MALLOC_PIN( h_R,    double, n2 );
            TESTING_MALLOC_PIN( h_S,    double, n2 );
            TESTING_MALLOC_PIN( h_work, double, lwork );
            #if defined(PRECISION_z) || defined(PRECISION_c)
            TESTING_MALLOC_PIN( rwork,  double, lrwork);
            #endif

            /* Initialize the matrix */
            lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
            lapackf77_dlarnv( &ione, ISEED, &n2, h_B );
            magma_dmake_hpd( N, h_B, N );
            magma_dmake_symmetric( N, h_A, N );

            magma_int_t m1 = 0;
            double vl = 0;
            double vu = 0;
            magma_int_t il = 0;
            magma_int_t iu = 0;

            if (range == MagmaRangeI) {
                il = 1;
                iu = (int) (opts.fraction*N);
            }

            // ==================================================================
            // Warmup using MAGMA
            // ==================================================================
            if (opts.warmup) {
                lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
                lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );

                magma_dsygvdx_2stage(opts.itype, opts.jobz, range, opts.uplo,
                                     N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
                                     h_work, lwork,
                                     #if defined(PRECISION_z) || defined(PRECISION_c)
                                     rwork, lrwork,
                                     #endif
                                     iwork, liwork,
                                     &info);
            }
            // ===================================================================
            // Performs operation using MAGMA
            // ===================================================================
            lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
            lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );

            gpu_time = magma_wtime();
            magma_dsygvdx_2stage(opts.itype, opts.jobz, range, opts.uplo,
                                 N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
                                 h_work, lwork,
                                 #if defined(PRECISION_z) || defined(PRECISION_c)
                                 rwork, lrwork,
                                 #endif
                                 iwork, liwork,
                                 &info);
            gpu_time = magma_wtime() - gpu_time;


            if ( opts.check ) {
                /* =====================================================================
                   Check the results following the LAPACK's [zc]hegvdx routine.
                   A x = lambda B x is solved
                   and the following 3 tests computed:
                   (1)    | A Z - B Z D | / ( |A||Z| N )  (itype = 1)
                   | A B Z - Z D | / ( |A||Z| N )  (itype = 2)
                   | B A Z - Z D | / ( |A||Z| N )  (itype = 3)
                   (2)    | S(with V) - S(w/o V) | / | S |
                   =================================================================== */
                #if defined(PRECISION_d) || defined(PRECISION_s)
                double *rwork = h_work + N*N;
                #endif
                double temp1, temp2;

                result[0] = 1.;
                result[0] /= lapackf77_dlansy("1", lapack_uplo_const(opts.uplo), &N, h_A, &N, rwork);
                result[0] /= lapackf77_dlange("1", &N, &m1, h_R, &N, rwork);

                if (opts.itype == 1) {
                    blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
                    for(int i=0; i<m1; ++i)
                        blasf77_dscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_neg_one, h_B, &N, h_R, &N, &c_one, h_work, &N);
                    result[0] *= lapackf77_dlange("1", &N, &m1, h_work, &N, rwork)/N;
                }
                else if (opts.itype == 2) {
                    blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_B, &N, h_R, &N, &c_zero, h_work, &N);
                    for(int i=0; i<m1; ++i)
                        blasf77_dscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_work, &N, &c_neg_one, h_R, &N);
                    result[0] *= lapackf77_dlange("1", &N, &m1, h_R, &N, rwork)/N;
                }
                else if (opts.itype == 3) {
                    blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
                    for(int i=0; i<m1; ++i)
                        blasf77_dscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_B, &N, h_work, &N, &c_neg_one, h_R, &N);
                    result[0] *= lapackf77_dlange("1", &N, &m1, h_R, &N, rwork)/N;
                }

                lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
                lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );

                magma_int_t m2 = m1;
                lapackf77_dsygvd(&opts.itype, "N", lapack_uplo_const(opts.uplo), &N,
                              h_R, &N, h_S, &N, w2,
                              h_work, &lwork,
                              #if defined(PRECISION_z) || defined(PRECISION_c)
                              rwork, &lrwork,
                              #endif
                              iwork, &liwork,
                              &info);

                temp1 = temp2 = 0;
                for(int j=0; j<m2; j++) {
                    temp1 = max(temp1, fabs(w1[j]));
                    temp1 = max(temp1, fabs(w2[j]));
                    temp2 = max(temp2, fabs(w1[j]-w2[j]));
                }
                result[1] = temp2 / (((double)m2)*temp1);
            }


            /* =====================================================================
               Print execution time
               =================================================================== */
            printf("%5d %5d   %7.2f\n",
                   (int) N, (int) m1, gpu_time);
            if ( opts.check ) {
                printf("Testing the eigenvalues and eigenvectors for correctness:\n");
                if (opts.itype==1) {
                    printf("(1)    | A Z - B Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed"));
                }
                else if (opts.itype==2) {
                    printf("(1)    | A B Z - Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed"));
                }
                else if (opts.itype==3) {
                    printf("(1)    | B A Z - Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed"));
                }
                printf(    "(2)    | D(w/ Z) - D(w/o Z) | / |D|  = %8.2e   %s\n\n", result[1], (result[1] < tolulp ? "ok" : "failed"));
                status += ! (result[0] < tol && result[1] < tolulp);
            }

            TESTING_FREE_CPU( h_A   );
            TESTING_FREE_CPU( h_B   );
            TESTING_FREE_CPU( w1    );
            TESTING_FREE_CPU( w2    );
            TESTING_FREE_CPU( iwork );
            
            TESTING_FREE_PIN( h_R );
            TESTING_FREE_PIN( h_S );
            TESTING_FREE_PIN( h_work );
            #if defined(PRECISION_z) || defined(PRECISION_c)
            TESTING_FREE_PIN( rwork );
            #endif
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }

    /* Shutdown */
    TESTING_FINALIZE();
    return status;
}
Example #3
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing magma_dsymm_mgpu
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    double c_neg_one = MAGMA_D_NEG_ONE;
    double alpha     = MAGMA_D_MAKE( 3.456, 5.678 );
    double beta      = MAGMA_D_MAKE( 1.234, 2.456 );
    
    real_Double_t    gflops, gpu_perf=0., cpu_perf=0., gpu_time=0., cpu_time=0.;
    real_Double_t    gpu_perf2=0., gpu_time2=0.;
    double           Anorm, error, work[1];
    double *hA, *hB, *hC, *hR;
    magmaDouble_ptr dA[MagmaMaxGPUs], dB[MagmaMaxGPUs], dC[MagmaMaxGPUs], dwork[MagmaMaxGPUs];
    magmaDouble_ptr dA2;
    magma_int_t i, j, dev, M, N, size, lda, ldb, ldc, ldda, lddb, lddc, msize, nb;
    magma_int_t ione     = 1;
    magma_int_t iseed[4] = {0,0,0,1};
    magma_int_t status = 0;
    
    magma_opts opts;
    opts.parse_opts( argc, argv );
    opts.ngpu = abs( opts.ngpu );  // always uses multi-GPU code
    
    double tol = opts.tolerance * lapackf77_dlamch("E");
    
    // default values
    nb = (opts.nb > 0 ? opts.nb : 64);
    
    magma_int_t gnode[MagmaMaxGPUs][MagmaMaxGPUs+2];
    magma_int_t ncmplx = 0;
    magma_buildconnection_mgpu( gnode, &ncmplx, opts.ngpu );
    
    printf("%% Initializing communication pattern... GPU-ncmplx %d\n", (int) ncmplx);
    for (i=0; i < ncmplx; ++i) {
        magma_int_t myngpu = gnode[i][MagmaMaxGPUs];
        printf("%% cmplx %d has %d GPUs:", i, myngpu);
        for (j=0; j < myngpu; ++j) {
            printf(" %d", (int) gnode[i][j]);
            if (j < myngpu-1) {
                printf(",");
            }
        }
        printf("\n");
    }

    // number of queues per GPU. Requires ngpu.
    magma_int_t nqueue  = opts.ngpu;
    // number of events per GPU. Require ngpu*ngpu.
    magma_int_t nevents = opts.ngpu*opts.ngpu;
    magma_queue_t queues[MagmaMaxGPUs][20], queues0[MagmaMaxGPUs];
    magma_event_t events[MagmaMaxGPUs][MagmaMaxGPUs*MagmaMaxGPUs + 10];
    for( dev = 0; dev < opts.ngpu; ++dev ) {
        magma_setdevice( dev );
        for( i = 0; i < nqueue; ++i ) {
            magma_queue_create( dev, &queues[dev][i] );
        }
        queues0[dev] = queues[dev][0];
        for( i = 0; i < nevents; ++i ) {
            cudaEventCreateWithFlags( &events[dev][i], cudaEventDisableTiming );
        }
    }

    printf("%% nb %d, ngpu %d, version %d\n", (int) nb, (int) opts.ngpu, (int) opts.version );
    printf("%%   M     N    nb offset  CPU Gflop/s (sec)   GPU Gflop/s (sec)   CUBLAS hemm (sec)   ||R|| / ||A||*||B||\n");
    printf("%%========================================================================================================\n");
    for( int itest = 0; itest < opts.ntest; ++itest ) {
      M = opts.msize[itest];
      N = opts.nsize[itest];
      for( int offset = 0; offset < N; offset += min(N,nb) ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            msize = M - offset;
            lda   = M;  // TODO depends on side
            ldb   = M;
            ldc   = M;
            ldda  = magma_roundup( lda, opts.align );  // multiple of 32 by default
            lddb  = magma_roundup( ldb, opts.align );  // multiple of 32 by default
            lddc  = magma_roundup( ldc, opts.align );  // multiple of 32 by default
            gflops = FLOPS_DSYMM( MagmaLeft, (double)msize, (double)N ) / 1e9;
            
            magma_int_t dworksiz = lddc*N + (M*N)*opts.ngpu;
            
            TESTING_MALLOC_CPU( hA, double, lda*M );
            TESTING_MALLOC_CPU( hB, double, ldb*N );
            TESTING_MALLOC_CPU( hC, double, ldc*N );
            
            TESTING_MALLOC_PIN( hR, double, ldc*N );

            for( dev = 0; dev < opts.ngpu; ++dev ) {
                magma_int_t mlocal = ((M / nb) / opts.ngpu + 1) * nb;
                magma_setdevice( dev );
                TESTING_MALLOC_DEV( dA[dev],    double, ldda*mlocal );
                TESTING_MALLOC_DEV( dB[dev],    double, lddb*N      );
                TESTING_MALLOC_DEV( dC[dev],    double, lddc*N      );
                TESTING_MALLOC_DEV( dwork[dev], double, dworksiz    );
            }
            
            if ( opts.check ) {
                magma_setdevice( 0 );
                TESTING_MALLOC_DEV( dA2, double, ldda*M );
            }

            size = lda*M;
            lapackf77_dlarnv( &ione, iseed, &size, hA );
            magma_dmake_symmetric( M, hA, lda );
            
            size = ldb*N;
            lapackf77_dlarnv( &ione, iseed, &size, hB );
            size = ldc*N;
            lapackf77_dlarnv( &ione, iseed, &size, hC );
            lapackf77_dlacpy( "Full", &M, &N, hC, &ldc, hR, &lda );
            
            /* ====================================================================
               Performs operation using MAGMA
               =================================================================== */
            magma_dsetmatrix_1D_col_bcyclic( M, M, hA, lda, dA, ldda, opts.ngpu, nb, queues0 );
            for( dev = 0; dev < opts.ngpu; ++dev ) {
                magma_setdevice( dev );
                magma_dsetmatrix( M, N, hB, lda, dB[dev], ldda, opts.queue );
                // since when offset != 0, the GPU that does beta*C may not be 0,
                // send initial hC to all GPUs.
                magma_dsetmatrix( M, N, hC, lda, dC[dev], ldda, opts.queue );
            }
            
            trace_init( 1, opts.ngpu, nqueue, (magma_queue_t*) queues );
            
            gpu_time = magma_sync_wtime(0);
            
            magmablas_dsymm_mgpu(
                MagmaLeft, MagmaLower, msize, N,
                alpha, dA, ldda, offset,
                       dB, ldda,
                beta,  dC, ldda, dwork, dworksiz,
                opts.ngpu, nb, queues, nqueue, events, nevents, gnode, ncmplx);
            
            gpu_time = magma_sync_wtime(0) - gpu_time;
            gpu_perf = gflops / gpu_time;
            
            #ifdef TRACING
            char buf[80];
            snprintf( buf, sizeof(buf), "dsymm-m%d-n%d-nb%d-ngpu%d-run%d.svg",
                      (int) M, (int) N, (int) nb, (int) opts.ngpu, (int) iter );
            trace_finalize( buf, "trace.css" );
            #endif
            
            /* ====================================================================
               Performs operation using CUBLAS
               =================================================================== */
            if ( opts.check && iter == 0 ) {
                magma_setdevice( 0 );
                magma_dsetmatrix( M, M, hA, lda, dA2, ldda, opts.queue );
                magma_dsetmatrix( M, N, hB, lda, dB[0], ldda, opts.queue );
                magma_dsetmatrix( M, N, hC, lda, dwork[0], ldda, opts.queue );
                
                gpu_time2 = magma_sync_wtime(0);
                magma_dsymm(
                    MagmaLeft, MagmaLower, msize, N,
                    alpha, dA2 + offset + offset*ldda, ldda,
                           dB[0],    ldda,
                    beta,  dwork[0], ldda, opts.queue );
                gpu_time2 = magma_sync_wtime(0) - gpu_time2;
                gpu_perf2 = gflops / gpu_time2;
            }
            
            /* =====================================================================
               Performs operation using LAPACK
               =================================================================== */
            if ( opts.check ) {
                // store ||A||*||B||
                Anorm  = lapackf77_dlange("fro", &msize, &msize, hA + offset + offset*lda, &lda, work );
                Anorm *= lapackf77_dlange("fro", &msize, &N, hB, &lda, work );
                
                //printf( "A =" ); magma_dprint( M, M, hA, lda );
                //printf( "B =" ); magma_dprint( M, N, hB, lda );
                //printf( "C =" ); magma_dprint( M, N, hC, lda );
                
                cpu_time = magma_wtime();
                blasf77_dsymm( "Left", "Lower", &msize, &N,
                                &alpha, hA + offset + offset*lda, &lda,
                                        hB, &lda,
                                &beta,  hC, &lda );
                cpu_time = magma_wtime() - cpu_time;
                cpu_perf = gflops / cpu_time;
                
                for (dev=0; dev < opts.ngpu; ++dev) {
                    magma_setdevice( dev );
                    magma_dgetmatrix( M, N, dC[dev], ldda, hR, lda, opts.queue );
                    
                    // compute relative error ||R||/||A||*||B||, where R := C_magma - C_lapack = R - C
                    size = ldc*N;
                    blasf77_daxpy( &size, &c_neg_one, hC, &ione, hR, &ione );
                    error = lapackf77_dlange("fro", &msize, &N, hR, &lda, work) / Anorm;
                    
                    //printf( "R ="  ); magma_dprint( M, N, hR, lda );
                    bool okay = (error < tol);
                    status += ! okay;
                    if (dev == 0) {
                        printf( "%5d %5d %5d %5d   %7.1f (%7.4f)   %7.1f (%7.4f)   %7.1f (%7.4f)   %8.2e   %s\n",
                                (int) M, (int) N, (int) nb, (int) offset,
                                cpu_perf, cpu_time,
                                gpu_perf, gpu_time,
                                gpu_perf2, gpu_time2,
                                error, (okay ? "ok" : "failed") );
                    }
                    else {
                        printf( "    dev %d %74s  %8.2e   %s\n", dev, "",
                                error, (okay ? "ok" : "failed") );
                    }
                }
            } else {
                printf( "%5d %5d %5d %5d     ---   (  ---  )   %7.1f (%7.4f)     ---   (  ---  )   ---\n",
                        (int) M, (int) N, (int) nb, (int) offset,
                        gpu_perf, gpu_time );
            }
            
            TESTING_FREE_CPU( hA );
            TESTING_FREE_CPU( hB );
            TESTING_FREE_CPU( hC );
            
            TESTING_FREE_PIN( hR );
            
            for( dev = 0; dev < opts.ngpu; ++dev ) {
                magma_setdevice( dev );
                TESTING_FREE_DEV( dA[dev]    );
                TESTING_FREE_DEV( dB[dev]    );
                TESTING_FREE_DEV( dC[dev]    );
                TESTING_FREE_DEV( dwork[dev] );
            }
            
            if ( opts.check ) {
                magma_setdevice( 0 );
                TESTING_FREE_DEV( dA2 );
            }
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
      }  // offset
      printf( "\n" );
    }

    for( dev = 0; dev < opts.ngpu; ++dev ) {
        magma_setdevice( dev );
        for( i = 0; i < nqueue; ++i ) {
            magma_queue_destroy( queues[dev][i] );
        }
        for( i = 0; i < nevents; ++i ) {
            magma_event_destroy( events[dev][i] );
        }
    }
    
    opts.cleanup();
    TESTING_FINALIZE();
    return status;
}