Esempio n. 1
0
void magmaf_dgeqrs3_gpu(
    magma_int_t *m, magma_int_t *n, magma_int_t *nrhs,
    devptr_t *dA, magma_int_t *ldda,
    double *tau,
    devptr_t *dT,
    devptr_t *dB, magma_int_t *lddb,
    double *hwork, magma_int_t *lhwork,
    magma_int_t *info )
{
    magma_dgeqrs3_gpu(
        *m, *n, *nrhs,
        magma_ddevptr(dA), *ldda,
        tau,
        magma_ddevptr(dT),
        magma_ddevptr(dB), *lddb,
        hwork, *lhwork,
        info );
}
Esempio n. 2
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing dgeqrf
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    real_Double_t    gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
    double           error, work[1];
    double  c_neg_one = MAGMA_D_NEG_ONE;
    double *h_A, *d_A, *h_R, *tau, *dT, *h_work, tmp[1];
    magma_int_t M, N, n2, lda, ldda, lwork, info, min_mn, nb, size;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1}, ISEED2[4];
    
    magma_opts opts;
    parse_opts( argc, argv, &opts );
 
    magma_int_t status = 0;
    double tol;
    opts.lapack |= (opts.version == 2 && opts.check == 2);  // check (-c2) implies lapack (-l)

    if ( opts.version != 2 && opts.check == 1 ) {
        printf( "  ===================================================================\n"
                "  NOTE: -c check for this version will be wrong\n"
                "  because tester ignores the special structure of MAGMA dgeqrf resuls.\n"
                "  We reset it to -c2.\n" 
                "  ===================================================================\n\n");
        opts.check = 2;
    }
    if ( opts.version == 2 ) {
        if ( opts.check == 1 ) {
            printf("  M     N     CPU GFlop/s (sec)   GPU GFlop/s (sec)   ||R-Q'A||_1 / (M*||A||_1*eps) ||I-Q'Q||_1 / (M*eps)\n");
            printf("=========================================================================================================\n");
        } else {
            printf("  M     N     CPU GFlop/s (sec)   GPU GFlop/s (sec)   ||R||_F / ||A||_F\n");
            printf("=======================================================================\n");
        }
        tol = 1.0;
    } else {
        printf("  M     N     CPU GFlop/s (sec)   GPU GFlop/s (sec)   ||Ax-b||_F/(N*||A||_F*||x||_F)\n");
        printf("====================================================================================\n");
        tol = opts.tolerance * lapackf77_dlamch("E");
    }
    for( int itest = 0; itest < opts.ntest; ++itest ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            M = opts.msize[itest];
            N = opts.nsize[itest];
            min_mn = min(M, N);
            lda    = M;
            n2     = lda*N;
            ldda   = ((M+31)/32)*32;
            gflops = FLOPS_DGEQRF( M, N ) / 1e9;
            
            // query for workspace size
            lwork = -1;
            lapackf77_dgeqrf(&M, &N, NULL, &M, NULL, tmp, &lwork, &info);
            lwork = (magma_int_t)MAGMA_D_REAL( tmp[0] );
            
            TESTING_MALLOC_CPU( tau,    double, min_mn );
            TESTING_MALLOC_CPU( h_A,    double, n2     );
            TESTING_MALLOC_CPU( h_work, double, lwork  );
            
            TESTING_MALLOC_PIN( h_R,    double, n2     );
            
            TESTING_MALLOC_DEV( d_A,    double, ldda*N );
            
            /* Initialize the matrix */
            for ( int j=0; j<4; j++ ) ISEED2[j] = ISEED[j]; // saving seeds
            lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
            lapackf77_dlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
            magma_dsetmatrix( M, N, h_R, lda, d_A, ldda );
            
            /* ====================================================================
               Performs operation using MAGMA
               =================================================================== */
            gpu_time = magma_wtime();
            if ( opts.version == 2 ) {
                magma_dgeqrf2_gpu( M, N, d_A, ldda, tau, &info);
            }
            else {
                nb = magma_get_dgeqrf_nb( M );
                size = (2*min(M, N) + (N+31)/32*32 )*nb;
                TESTING_MALLOC_DEV( dT, double, size );
                if ( opts.version == 3 ) {
                    magma_dgeqrf3_gpu( M, N, d_A, ldda, tau, dT, &info);
                }
                else {
                    magma_dgeqrf_gpu( M, N, d_A, ldda, tau, dT, &info);
                }
            }
            gpu_time = magma_wtime() - gpu_time;
            gpu_perf = gflops / gpu_time;
            if (info != 0)
                printf("magma_dgeqrf returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            
            if ( opts.lapack ) {
                /* =====================================================================
                   Performs operation using LAPACK
                   =================================================================== */
                double *tau2;
                TESTING_MALLOC_CPU( tau2, double, min_mn );
                cpu_time = magma_wtime();
                lapackf77_dgeqrf(&M, &N, h_A, &lda, tau2, h_work, &lwork, &info);
                cpu_time = magma_wtime() - cpu_time;
                cpu_perf = gflops / cpu_time;
                if (info != 0)
                    printf("lapackf77_dgeqrf returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
                TESTING_FREE_CPU( tau2 );
            }

            if ( opts.check == 1 ) {
                /* =====================================================================
                   Check the result 
                   =================================================================== */
                magma_int_t lwork = n2+N;
                double *h_W1, *h_W2, *h_W3;
                double *h_RW, results[2];
                magma_dgetmatrix( M, N, d_A, ldda, h_R, M );

                TESTING_MALLOC_CPU( h_W1, double, n2    ); // Q
                TESTING_MALLOC_CPU( h_W2, double, n2    ); // R
                TESTING_MALLOC_CPU( h_W3, double, lwork ); // WORK
                TESTING_MALLOC_CPU( h_RW, double, M );  // RWORK
                lapackf77_dlarnv( &ione, ISEED2, &n2, h_A );
                lapackf77_dqrt02( &M, &N, &min_mn, h_A, h_R, h_W1, h_W2, &lda, tau, h_W3, &lwork,
                                  h_RW, results );

                if ( opts.lapack ) {
                    printf("%5d %5d   %7.2f (%7.2f)   %7.2f (%7.2f)   %8.2e                      %8.2e",
                           (int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time, results[0], results[1] );
                } else {
                    printf("%5d %5d     ---   (  ---  )   %7.2f (%7.2f)    %8.2e                      %8.2e",
                           (int) M, (int) N, gpu_perf, gpu_time, results[0], results[1] );
                } 
                // todo also check results[1] < tol?
                printf("   %s\n", (results[0] < tol ? "ok" : "failed"));
                status += ! (results[0] < tol);
            
                TESTING_FREE_CPU( h_W1 );
                TESTING_FREE_CPU( h_W2 );
                TESTING_FREE_CPU( h_W3 );
                TESTING_FREE_CPU( h_RW );
            }
            else if ( opts.check == 2 ) {
                if ( opts.version == 2 ) {
                    /* =====================================================================
                       Check the result compared to LAPACK
                       =================================================================== */
                    magma_dgetmatrix( M, N, d_A, ldda, h_R, M );
                    error = lapackf77_dlange("f", &M, &N, h_A, &lda, work);
                    blasf77_daxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
                    error = lapackf77_dlange("f", &M, &N, h_R, &lda, work) / error;

                    if ( opts.lapack ) {
                        printf("%5d %5d   %7.2f (%7.2f)   %7.2f (%7.2f)   %8.2e",
                               (int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time, error );
                    } else {
                        printf("%5d %5d     ---   (  ---  )   %7.2f (%7.2f)   %8.2e",
                               (int) M, (int) N, gpu_perf, gpu_time, error );
                    }
                    printf("   %s\n", (error < tol ? "ok" : "failed"));
                    status += ! (error < tol);
                }
                else if ( M >= N ) {
                    magma_int_t lwork;
                    double *x, *b, *d_B, *hwork;
                    const double c_zero    = MAGMA_D_ZERO;
                    const double c_one     = MAGMA_D_ONE;
                    const double c_neg_one = MAGMA_D_NEG_ONE;
                    const magma_int_t ione = 1;

                    // initialize RHS, b = A*random
                    TESTING_MALLOC_CPU( x, double, N );
                    TESTING_MALLOC_CPU( b, double, M );
                    lapackf77_dlarnv( &ione, ISEED, &N, x );
                    blasf77_dgemv( "Notrans", &M, &N, &c_one, h_A, &lda, x, &ione, &c_zero, b, &ione );
                    // copy to GPU
                    TESTING_MALLOC_DEV( d_B, double, M );
                    magma_dsetvector( M, b, 1, d_B, 1 );

                    if ( opts.version == 1 ) {
                        // allocate hwork
                        magma_dgeqrs_gpu( M, N, 1,
                                          d_A, ldda, tau, dT,
                                          d_B, M, tmp, -1, &info );
                        lwork = (magma_int_t)MAGMA_D_REAL( tmp[0] );
                        TESTING_MALLOC_CPU( hwork, double, lwork );

                        // solve linear system
                        magma_dgeqrs_gpu( M, N, 1,
                                          d_A, ldda, tau, dT,
                                          d_B, M, hwork, lwork, &info );
                       if (info != 0)
                           printf("magma_dgeqrs returned error %d: %s.\n",
                                  (int) info, magma_strerror( info ));
                        TESTING_FREE_CPU( hwork );
                    }
                    else {
                        // allocate hwork
                        magma_dgeqrs3_gpu( M, N, 1,
                                           d_A, ldda, tau, dT,
                                           d_B, M, tmp, -1, &info );
                        lwork = (magma_int_t)MAGMA_D_REAL( tmp[0] );
                        TESTING_MALLOC_CPU( hwork, double, lwork );

                        // solve linear system
                        magma_dgeqrs3_gpu( M, N, 1,
                                           d_A, ldda, tau, dT,
                                           d_B, M, hwork, lwork, &info );
                       if (info != 0)
                           printf("magma_dgeqrs3 returned error %d: %s.\n",
                                  (int) info, magma_strerror( info ));
                        TESTING_FREE_CPU( hwork );
                    }
                    magma_dgetvector( N, d_B, 1, x, 1 );

                    // compute r = Ax - b, saved in b
                    lapackf77_dlarnv( &ione, ISEED2, &n2, h_A );
                    blasf77_dgemv( "Notrans", &M, &N, &c_one, h_A, &lda, x, &ione, &c_neg_one, b, &ione );

                    // compute residual |Ax - b| / (n*|A|*|x|)
                    double norm_x, norm_A, norm_r, work[1];
                    norm_A = lapackf77_dlange( "F", &M, &N, h_A, &lda, work );
                    norm_r = lapackf77_dlange( "F", &M, &ione, b, &M, work );
                    norm_x = lapackf77_dlange( "F", &N, &ione, x, &N, work );

                    TESTING_FREE_CPU( x );
                    TESTING_FREE_CPU( b );
                    TESTING_FREE_DEV( d_B );

                    error = norm_r / (N * norm_A * norm_x);
                    if ( opts.lapack ) {
                        printf("%5d %5d   %7.2f (%7.2f)   %7.2f (%7.2f)   %8.2e",
                               (int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time, error );
                    } else {
                        printf("%5d %5d     ---   (  ---  )   %7.2f (%7.2f)   %8.2e",
                               (int) M, (int) N, gpu_perf, gpu_time, error );
                    }
                    printf("   %s\n", (error < tol ? "ok" : "failed"));
                    status += ! (error < tol);
                }
                else {
                    if ( opts.lapack ) {
                        printf("%5d %5d   %7.2f (%7.2f)   %7.2f (%7.2f)   --- ",
                               (int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
                    } else {
                        printf("%5d %5d     ---   (  ---  )   %7.2f (%7.2f)     --- ",
                               (int) M, (int) N, gpu_perf, gpu_time);
                    }
                    printf("%s\n", (opts.check != 0 ? "  (error check only for M >= N)" : ""));
                }
            }
            else {
                if ( opts.lapack ) {
                    printf("%5d %5d   %7.2f (%7.2f)   %7.2f (%7.2f)   ---\n",
                           (int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
                } else {
                    printf("%5d %5d     ---   (  ---  )   %7.2f (%7.2f)     ---  \n",
                           (int) M, (int) N, gpu_perf, gpu_time);
                }

            }
            
            TESTING_FREE_CPU( tau    );
            TESTING_FREE_CPU( h_A    );
            TESTING_FREE_CPU( h_work );
            
            TESTING_FREE_PIN( h_R );
            
            TESTING_FREE_DEV( d_A );
            
            if ( opts.version != 2 )
                TESTING_FREE_DEV( dT );
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }
    
    TESTING_FINALIZE();
    return status;
}
Esempio n. 3
0
extern "C" magma_int_t
magma_dgels3_gpu( char trans, magma_int_t m, magma_int_t n, magma_int_t nrhs,
                  double *dA,    magma_int_t ldda,
                  double *dB,    magma_int_t lddb,
                  double *hwork, magma_int_t lwork,
                  magma_int_t *info)
{
/*  -- MAGMA (version 1.4.0) --
       Univ. of Tennessee, Knoxville
       Univ. of California, Berkeley
       Univ. of Colorado, Denver
       August 2013

    Purpose
    =======
    Solves the overdetermined, least squares problem
           min || A*X - C ||
    using the QR factorization A.
    The underdetermined problem (m < n) is not currently handled.


    Arguments
    =========
    TRANS   (input) CHARACTER*1
            = 'N': the linear system involves A.
            Only trans='N' is currently handled.

    M       (input) INTEGER
            The number of rows of the matrix A. M >= 0.

    N       (input) INTEGER
            The number of columns of the matrix A. M >= N >= 0.

    NRHS    (input) INTEGER
            The number of columns of the matrix C. NRHS >= 0.

    A       (input/output) DOUBLE_PRECISION array, dimension (LDA,N)
            On entry, the M-by-N matrix A.
            On exit, A is overwritten by details of its QR
            factorization as returned by DGEQRF3.

    LDDA    (input) INTEGER
            The leading dimension of the array A, LDDA >= M.

    DB      (input/output) DOUBLE_PRECISION array on the GPU, dimension (LDDB,NRHS)
            On entry, the M-by-NRHS matrix C.
            On exit, the N-by-NRHS solution matrix X.

    LDDB    (input) INTEGER
            The leading dimension of the array DB. LDDB >= M.

    HWORK   (workspace/output) DOUBLE_PRECISION array, dimension MAX(1,LWORK).
            On exit, if INFO = 0, HWORK(1) returns the optimal LWORK.

    LWORK   (input) INTEGER
            The dimension of the array HWORK,
            LWORK >= (M - N + NB)*(NRHS + NB) + NRHS*NB,
            where NB is the blocksize given by magma_get_dgeqrf_nb( M ).

            If LWORK = -1, then a workspace query is assumed; the routine
            only calculates the optimal size of the HWORK array, returns
            this value as the first entry of the HWORK array.

    INFO    (output) INTEGER
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
    =====================================================================    */

    #define a_ref(a_1,a_2) (dA + (a_2)*(ldda) + (a_1))

    double *dT, *tau;
    magma_int_t k;

    magma_int_t nb     = magma_get_dgeqrf_nb(m);
    magma_int_t lwkopt = (m - n + nb)*(nrhs + nb) + nrhs*nb;
    int lquery = (lwork == -1);

    hwork[0] = MAGMA_D_MAKE( (double)lwkopt, 0. );

    *info = 0;
    /* For now, N is the only case working */
    if ( (trans != 'N') && (trans != 'n' ) )
        *info = -1;
    else if (m < 0)
        *info = -2;
    else if (n < 0 || m < n) /* LQ is not handle for now*/
        *info = -3;
    else if (nrhs < 0)
        *info = -4;
    else if (ldda < max(1,m))
        *info = -6;
    else if (lddb < max(1,m))
        *info = -8;
    else if (lwork < lwkopt && ! lquery)
        *info = -10;

    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }
    else if (lquery)
        return *info;

    k = min(m,n);
    if (k == 0) {
        hwork[0] = MAGMA_D_ONE;
        return *info;
    }

    /*
     * Allocate temporary buffers
     */
    int ldtwork = ( 2*k + ((n+31)/32)*32 )*nb;
    if (nb < nrhs)
        ldtwork = ( 2*k + ((n+31)/32)*32 )*nrhs;
    if (MAGMA_SUCCESS != magma_dmalloc( &dT, ldtwork )) {
        *info = MAGMA_ERR_DEVICE_ALLOC;
        return *info;
    }
    
    magma_dmalloc_cpu( &tau, k );
    if ( tau == NULL ) {
        magma_free( dT );
        *info = MAGMA_ERR_HOST_ALLOC;
        return *info;
    }

    magma_dgeqrf3_gpu( m, n, dA, ldda, tau, dT, info );
    if ( *info == 0 ) {
        magma_dgeqrs3_gpu( m, n, nrhs,
                           dA, ldda, tau, dT,
                           dB, lddb, hwork, lwork, info );
    }

    magma_free( dT );
    magma_free_cpu(tau);
    return *info;
}
Esempio n. 4
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing dgeqrf
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    const double             d_neg_one = MAGMA_D_NEG_ONE;
    const double             d_one     = MAGMA_D_ONE;
    const double c_neg_one = MAGMA_D_NEG_ONE;
    const double c_one     = MAGMA_D_ONE;
    const double c_zero    = MAGMA_D_ZERO;
    const magma_int_t        ione      = 1;
    
    real_Double_t    gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
    double           Anorm, error=0, error2=0;
    double *h_A, *h_R, *tau, *h_work, tmp[1];
    magmaDouble_ptr d_A, dT;
    magma_int_t M, N, n2, lda, ldda, lwork, info, min_mn, nb, size;
    magma_int_t ISEED[4] = {0,0,0,1};
    
    magma_opts opts;
    parse_opts( argc, argv, &opts );
    
    magma_int_t status = 0;
    double tol = opts.tolerance * lapackf77_dlamch("E");
    
    printf( "version %d\n", (int) opts.version );
    if ( opts.version == 2 ) {
        printf("    M     N   CPU GFlop/s (sec)   GPU GFlop/s (sec)   |R - Q^H*A|   |I - Q^H*Q|\n");
        printf("===============================================================================\n");
    }
    else {
        printf("    M     N   CPU GFlop/s (sec)   GPU GFlop/s (sec)    |b - A*x|\n");
        printf("================================================================\n");
    }
    for( int itest = 0; itest < opts.ntest; ++itest ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            M = opts.msize[itest];
            N = opts.nsize[itest];
            min_mn = min(M, N);
            lda    = M;
            n2     = lda*N;
            ldda   = ((M+31)/32)*32;
            gflops = FLOPS_DGEQRF( M, N ) / 1e9;
            
            // query for workspace size
            lwork = -1;
            lapackf77_dgeqrf(&M, &N, NULL, &M, NULL, tmp, &lwork, &info);
            lwork = (magma_int_t)MAGMA_D_REAL( tmp[0] );
            
            TESTING_MALLOC_CPU( tau,    double, min_mn );
            TESTING_MALLOC_CPU( h_A,    double, n2     );
            TESTING_MALLOC_CPU( h_work, double, lwork  );
            
            TESTING_MALLOC_PIN( h_R,    double, n2     );
            
            TESTING_MALLOC_DEV( d_A,    double, ldda*N );
            
            /* Initialize the matrix */
            lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
            lapackf77_dlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
            magma_dsetmatrix( M, N, h_R, lda, d_A, ldda );
            
            /* ====================================================================
               Performs operation using MAGMA
               =================================================================== */
            gpu_time = magma_wtime();
            if ( opts.version == 2 ) {
                // LAPACK complaint arguments
                magma_dgeqrf2_gpu( M, N, d_A, ldda, tau, &info );
            }
            else {
                nb = magma_get_dgeqrf_nb( M );
                size = (2*min(M, N) + (N+31)/32*32 )*nb;
                TESTING_MALLOC_DEV( dT, double, size );
                if ( opts.version == 1 ) {
                    // stores dT, V blocks have zeros, R blocks inverted & stored in dT
                    magma_dgeqrf_gpu( M, N, d_A, ldda, tau, dT, &info );
                }
                #ifdef HAVE_CUBLAS
                else if ( opts.version == 3 ) {
                    // stores dT, V blocks have zeros, R blocks stored in dT
                    magma_dgeqrf3_gpu( M, N, d_A, ldda, tau, dT, &info );
                }
                #endif
                else {
                    printf( "Unknown version %d\n", (int) opts.version );
                    exit(1);
                }
            }
            gpu_time = magma_wtime() - gpu_time;
            gpu_perf = gflops / gpu_time;
            if (info != 0)
                printf("magma_dgeqrf returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            
            if ( opts.check && opts.version == 2 ) {
                /* =====================================================================
                   Check the result, following zqrt01 except using the reduced Q.
                   This works for any M,N (square, tall, wide).
                   Only for version 2, which has LAPACK complaint output.
                   =================================================================== */
                magma_dgetmatrix( M, N, d_A, ldda, h_R, lda );
                
                magma_int_t ldq = M;
                magma_int_t ldr = min_mn;
                double *Q, *R;
                double *work;
                TESTING_MALLOC_CPU( Q,    double, ldq*min_mn );  // M by K
                TESTING_MALLOC_CPU( R,    double, ldr*N );       // K by N
                TESTING_MALLOC_CPU( work, double,             min_mn );
                
                // generate M by K matrix Q, where K = min(M,N)
                lapackf77_dlacpy( "Lower", &M, &min_mn, h_R, &lda, Q, &ldq );
                lapackf77_dorgqr( &M, &min_mn, &min_mn, Q, &ldq, tau, h_work, &lwork, &info );
                assert( info == 0 );
                
                // copy K by N matrix R
                lapackf77_dlaset( "Lower", &min_mn, &N, &c_zero, &c_zero, R, &ldr );
                lapackf77_dlacpy( "Upper", &min_mn, &N, h_R, &lda,        R, &ldr );
                
                // error = || R - Q^H*A || / (N * ||A||)
                blasf77_dgemm( "Conj", "NoTrans", &min_mn, &N, &M,
                               &c_neg_one, Q, &ldq, h_A, &lda, &c_one, R, &ldr );
                Anorm = lapackf77_dlange( "1", &M,      &N, h_A, &lda, work );
                error = lapackf77_dlange( "1", &min_mn, &N, R,   &ldr, work );
                if ( N > 0 && Anorm > 0 )
                    error /= (N*Anorm);
                
                // set R = I (K by K identity), then R = I - Q^H*Q
                // error = || I - Q^H*Q || / N
                lapackf77_dlaset( "Upper", &min_mn, &min_mn, &c_zero, &c_one, R, &ldr );
                blasf77_dsyrk( "Upper", "Conj", &min_mn, &M, &d_neg_one, Q, &ldq, &d_one, R, &ldr );
                error2 = lapackf77_dlansy( "1", "Upper", &min_mn, R, &ldr, work );
                if ( N > 0 )
                    error2 /= N;
                
                TESTING_FREE_CPU( Q    );  Q    = NULL;
                TESTING_FREE_CPU( R    );  R    = NULL;
                TESTING_FREE_CPU( work );  work = NULL;
            }
            else if ( opts.check && M >= N ) {
                /* =====================================================================
                   Check the result by solving consistent linear system, A*x = b.
                   Only for versions 1 & 3 with M >= N.
                   =================================================================== */
                magma_int_t lwork;
                double *x, *b, *hwork;
                magmaDouble_ptr d_B;
                const double c_zero    = MAGMA_D_ZERO;
                const double c_one     = MAGMA_D_ONE;
                const double c_neg_one = MAGMA_D_NEG_ONE;
                const magma_int_t ione = 1;

                // initialize RHS, b = A*random
                TESTING_MALLOC_CPU( x, double, N );
                TESTING_MALLOC_CPU( b, double, M );
                lapackf77_dlarnv( &ione, ISEED, &N, x );
                blasf77_dgemv( "Notrans", &M, &N, &c_one, h_A, &lda, x, &ione, &c_zero, b, &ione );
                // copy to GPU
                TESTING_MALLOC_DEV( d_B, double, M );
                magma_dsetvector( M, b, 1, d_B, 1 );

                if ( opts.version == 1 ) {
                    // allocate hwork
                    magma_dgeqrs_gpu( M, N, 1,
                                      d_A, ldda, tau, dT,
                                      d_B, M, tmp, -1, &info );
                    lwork = (magma_int_t)MAGMA_D_REAL( tmp[0] );
                    TESTING_MALLOC_CPU( hwork, double, lwork );

                    // solve linear system
                    magma_dgeqrs_gpu( M, N, 1,
                                      d_A, ldda, tau, dT,
                                      d_B, M, hwork, lwork, &info );
                    if (info != 0)
                        printf("magma_dgeqrs returned error %d: %s.\n",
                               (int) info, magma_strerror( info ));
                    TESTING_FREE_CPU( hwork );
                }
                #ifdef HAVE_CUBLAS
                else if ( opts.version == 3 ) {
                    // allocate hwork
                    magma_dgeqrs3_gpu( M, N, 1,
                                       d_A, ldda, tau, dT,
                                       d_B, M, tmp, -1, &info );
                    lwork = (magma_int_t)MAGMA_D_REAL( tmp[0] );
                    TESTING_MALLOC_CPU( hwork, double, lwork );

                    // solve linear system
                    magma_dgeqrs3_gpu( M, N, 1,
                                       d_A, ldda, tau, dT,
                                       d_B, M, hwork, lwork, &info );
                    if (info != 0)
                        printf("magma_dgeqrs3 returned error %d: %s.\n",
                               (int) info, magma_strerror( info ));
                    TESTING_FREE_CPU( hwork );
                }
                #endif
                else {
                    printf( "Unknown version %d\n", (int) opts.version );
                    exit(1);
                }
                magma_dgetvector( N, d_B, 1, x, 1 );

                // compute r = Ax - b, saved in b
                blasf77_dgemv( "Notrans", &M, &N, &c_one, h_A, &lda, x, &ione, &c_neg_one, b, &ione );

                // compute residual |Ax - b| / (n*|A|*|x|)
                double norm_x, norm_A, norm_r, work[1];
                norm_A = lapackf77_dlange( "F", &M, &N, h_A, &lda, work );
                norm_r = lapackf77_dlange( "F", &M, &ione, b, &M, work );
                norm_x = lapackf77_dlange( "F", &N, &ione, x, &N, work );

                TESTING_FREE_CPU( x );
                TESTING_FREE_CPU( b );
                TESTING_FREE_DEV( d_B );

                error = norm_r / (N * norm_A * norm_x);
            }
            
            /* =====================================================================
               Performs operation using LAPACK
               =================================================================== */
            if ( opts.lapack ) {
                cpu_time = magma_wtime();
                lapackf77_dgeqrf(&M, &N, h_A, &lda, tau, h_work, &lwork, &info);
                cpu_time = magma_wtime() - cpu_time;
                cpu_perf = gflops / cpu_time;
                if (info != 0)
                    printf("lapackf77_dgeqrf returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
            }
            
            /* =====================================================================
               Print performance and error.
               =================================================================== */
            printf("%5d %5d   ", (int) M, (int) N );
            if ( opts.lapack ) {
                printf( "%7.2f (%7.2f)", cpu_perf, cpu_time );
            }
            else {
                printf("  ---   (  ---  )" );
            }
            printf( "   %7.2f (%7.2f)   ", gpu_perf, gpu_time );
            if ( opts.check ) {
                if ( opts.version == 2 ) {
                    bool okay = (error < tol && error2 < tol);
                    status += ! okay;
                    printf( "%11.2e   %11.2e   %s\n", error, error2, (okay ? "ok" : "failed") );
                }
                else if ( M >= N ) {
                    bool okay = (error < tol);
                    status += ! okay;
                    printf( "%10.2e   %s\n", error, (okay ? "ok" : "failed") );
                }
                else {
                    printf( "(error check only for M >= N)\n" );
                }
            }
            else {
                printf( "    ---\n" );
            }
            
            TESTING_FREE_CPU( tau    );
            TESTING_FREE_CPU( h_A    );
            TESTING_FREE_CPU( h_work );
            
            TESTING_FREE_PIN( h_R );
            
            TESTING_FREE_DEV( d_A );
            
            if ( opts.version != 2 )
                TESTING_FREE_DEV( dT );
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }
    
    TESTING_FINALIZE();
    return status;
}