Exemple #1
0
void magmaf_dlarfb_gpu_gemm(
    magma_side_t *side, magma_trans_t *trans, magma_direct_t *direct, magma_storev_t *storev, magma_int_t *m, magma_int_t *n, magma_int_t *k,
    const double *dv, magma_int_t *ldv,
    const double *dt, magma_int_t *ldt,
    double *dc, magma_int_t *ldc,
    double *dwork, magma_int_t *ldwork,
    double *dworkvt, magma_int_t *ldworkvt )
{
    magma_dlarfb_gpu_gemm(
        *side, *trans, *direct, *storev, *m, *n, *k,
        dv, *ldv,
        dt, *ldt,
        dc, *ldc,
        dwork, *ldwork,
        dworkvt, *ldworkvt );
}
/***************************************************************************//**
    Purpose
    -------
    DGEQRF computes a QR factorization of a real M-by-N matrix A:
    A = Q * R.
    
    Arguments
    ---------
    @param[in]
    m       INTEGER
            The number of rows of the matrix A.  M >= 0.

    @param[in]
    n       INTEGER
            The number of columns of the matrix A.  N >= 0.

    @param[in,out]
    dA_array Array of pointers, dimension (batchCount).
             Each is a DOUBLE PRECISION array on the GPU, dimension (LDDA,N)
             On entry, the M-by-N matrix A.
             On exit, the elements on and above the diagonal of the array
             contain the min(M,N)-by-N upper trapezoidal matrix R (R is
             upper triangular if m >= n); the elements below the diagonal,
             with the array TAU, represent the orthogonal matrix Q as a
             product of min(m,n) elementary reflectors (see Further
             Details).

    @param[in]
    ldda     INTEGER
             The leading dimension of the array dA.  LDDA >= max(1,M).
             To benefit from coalescent memory accesses LDDA must be
             divisible by 16.

    @param[in,out]
    dR_array Array of pointers, dimension (batchCount).
             Each is a DOUBLE PRECISION array on the GPU, dimension (LDDR, N/NB)
             dR should be of size (LDDR, N) when provide_RT > 0 and 
             of size (LDDT, NB) otherwise. NB is the local blocking size.
             On exit, the elements of R are stored in dR only when provide_RT > 0.

    @param[in]
    lddr     INTEGER
             The leading dimension of the array dR.  
             LDDR >= min(M,N) when provide_RT == 1
             otherwise LDDR >= min(NB, min(M,N)). 
             NB is the local blocking size.
             To benefit from coalescent memory accesses LDDR must be
             divisible by 16.

    @param[in,out]
    dT_array Array of pointers, dimension (batchCount).
             Each is a DOUBLE PRECISION array on the GPU, dimension (LDDT, N/NB)
             dT should be of size (LDDT, N) when provide_RT > 0 and 
             of size (LDDT, NB) otherwise. NB is the local blocking size.
             On exit, the elements of T are stored in dT only when provide_RT > 0.

    @param[in]
    lddt     INTEGER
             The leading dimension of the array dT.  
             LDDT >= min(NB,min(M,N)). NB is the local blocking size.
             To benefit from coalescent memory accesses LDDR must be
             divisible by 16.

    @param[out]
    dtau_array Array of pointers, dimension (batchCount).
             Each is a DOUBLE PRECISION array, dimension (min(M,N))
             The scalar factors of the elementary reflectors (see Further
             Details).

    @param[in]
    provide_RT INTEGER
               provide_RT = 0 no R and no T in output. 
               dR and dT are used as local workspace to store the R and T of each step.
               provide_RT = 1 the whole R of size (min(M,N), N) and the nbxnb  block of T are provided in output. 
               provide_RT = 2 the nbxnb diag block of R and of T are provided in output. 

    @param[out]
    info_array  Array of INTEGERs, dimension (batchCount), for corresponding matrices.
      -     = 0:  successful exit
      -     < 0:  if INFO = -i, the i-th argument had an illegal value
                  or another error occured, such as memory allocation failed.

    @param[in]
    batchCount  INTEGER
                The number of matrices to operate on.

    @param[in]
    queue   magma_queue_t
            Queue to execute in.

    Further Details
    ---------------
    The matrix Q is represented as a product of elementary reflectors

        Q = H(1) H(2) . . . H(k), where k = min(m,n).

    Each H(i) has the form

        H(i) = I - tau * v * v'

    where tau is a real scalar, and v is a real vector with
    v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
    and tau in TAU(i).

    @ingroup magma_geqrf_batched
*******************************************************************************/
extern "C" magma_int_t
magma_dgeqrf_expert_batched(
    magma_int_t m, magma_int_t n, 
    double **dA_array, magma_int_t ldda, 
    double **dR_array, magma_int_t lddr,
    double **dT_array, magma_int_t lddt,
    double **dtau_array, magma_int_t provide_RT,
    magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
{
    #define dA(i, j)  (dA + (i) + (j)*ldda)
    
    /* Local Parameter */
    magma_int_t nb = magma_get_dgeqrf_batched_nb(m);
    
    magma_int_t nnb = 8;
    magma_int_t min_mn = min(m, n);

    /* Check arguments */
    cudaMemset(info_array, 0, batchCount*sizeof(magma_int_t));
    magma_int_t arginfo = 0;
    if (m < 0)
        arginfo = -1;
    else if (n < 0)
        arginfo = -2;
    else if (ldda < max(1,m))
        arginfo = -4;
    else if (lddr < min_mn && provide_RT == 1)
        arginfo = -6;
    else if (lddr < min(min_mn, nb))
        arginfo = -6;
    else if (lddt < min(min_mn, nb))
        arginfo = -8;

    if (arginfo != 0) {
        magma_xerbla( __func__, -(arginfo) );
        return arginfo;
    }

    /* Quick return if possible */
    if (m == 0 || n == 0)
        if (min_mn == 0 ) return arginfo;

    if ( m >  2048 || n > 2048 ) {
        printf("=========================================================================================\n");
        printf("   WARNING batched routines are designed for small sizes it might be better to use the\n   Native/Hybrid classical routines if you want performance\n");
        printf("=========================================================================================\n");
    }


    magma_int_t i, k, ib=nb, jb=nnb, offset_RT=0, use_stream;
    magma_int_t ldw, offset; 

    double **dW0_displ = NULL;
    double **dW1_displ = NULL;
    double **dW2_displ = NULL;
    double **dW3_displ = NULL;
    double **dW4_displ = NULL;
    double **dW5_displ = NULL;
    double **dR_displ  = NULL;
    double **dT_displ  = NULL;

    double *dwork = NULL;
    double **cpuAarray = NULL;
    double **cpuTarray = NULL;

    magma_malloc((void**)&dW0_displ, batchCount * sizeof(*dW0_displ));
    magma_malloc((void**)&dW1_displ, batchCount * sizeof(*dW1_displ));
    magma_malloc((void**)&dW2_displ, batchCount * sizeof(*dW2_displ));
    magma_malloc((void**)&dW3_displ, batchCount * sizeof(*dW3_displ));
    magma_malloc((void**)&dW4_displ, batchCount * sizeof(*dW4_displ));
    magma_malloc((void**)&dW5_displ, batchCount * sizeof(*dW5_displ));
    magma_malloc((void**)&dR_displ,  batchCount * sizeof(*dR_displ));
    magma_malloc((void**)&dT_displ,  batchCount * sizeof(*dT_displ));

    magma_dmalloc(&dwork,  (2 * nb * n) * batchCount);
    magma_malloc_cpu((void**) &cpuAarray, batchCount*sizeof(double*));
    magma_malloc_cpu((void**) &cpuTarray, batchCount*sizeof(double*));

    /* check allocation */
    if ( dW0_displ == NULL || dW1_displ == NULL || dW2_displ == NULL || 
         dW3_displ == NULL || dW4_displ == NULL || dW5_displ == NULL || 
         dR_displ  == NULL || dT_displ  == NULL || dwork     == NULL ||
         cpuAarray == NULL || cpuTarray == NULL ) {
        magma_free(dW0_displ);
        magma_free(dW1_displ);
        magma_free(dW2_displ);
        magma_free(dW3_displ);
        magma_free(dW4_displ);
        magma_free(dW5_displ);
        magma_free(dR_displ);
        magma_free(dT_displ);
        magma_free(dwork);
        magma_free_cpu(cpuAarray);
        magma_free_cpu(cpuTarray);
        magma_int_t info = MAGMA_ERR_DEVICE_ALLOC;
        magma_xerbla( __func__, -(info) );
        return info;
    }

    magma_ddisplace_pointers(dR_displ, dR_array, lddr, 0, 0, batchCount, queue); 
    magma_ddisplace_pointers(dT_displ, dT_array, lddt, 0, 0, batchCount, queue); 
    // set dwork to zero because our GEMM routine does propagate NAN when C=betaC+alphaA*B and beta=0
    magmablas_dlaset_q( MagmaFull, 2*nb, n*batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dwork, 2*nb, queue );

    // set dR and dT to zero. if provide_RT == 0 only a tile of size nbxnb is used and overwritten at each step
    magmablas_dlaset_batched( MagmaFull, lddr, (provide_RT > 0 ? n:min(min_mn,nb)), MAGMA_D_ZERO, MAGMA_D_ZERO, dR_displ, lddr, batchCount, queue ); 
    magmablas_dlaset_batched( MagmaFull, lddt, (provide_RT > 0 ? n:min(min_mn,nb)), MAGMA_D_ZERO, MAGMA_D_ZERO, dT_displ, lddt, batchCount, queue );
    /*
    if ( provide_RT > 0 )
    {
        magmablas_dlaset_q( MagmaFull, lddr, n*batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dR, lddr, queue );
        magmablas_dlaset_q( MagmaFull, lddt, n*batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dT, lddt, queue );
    }
    else
    {
        magmablas_dlaset_q( MagmaFull, lddr, nb*batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dR, lddr, queue );
        magmablas_dlaset_q( MagmaFull, lddt, nb*batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dT, lddt, queue );
    }
    */
    magma_int_t streamid;
    const magma_int_t nbstreams=10;
    magma_queue_t queues[nbstreams];
    for (i=0; i < nbstreams; i++) {
        magma_device_t cdev;
        magma_getdevice( &cdev );
        magma_queue_create( cdev, &queues[i] );
    }
    magma_getvector( batchCount, sizeof(double*), dA_array, 1, cpuAarray, 1, queue);
    magma_getvector( batchCount, sizeof(double*), dT_array, 1, cpuTarray, 1, queue);


    for (i=0; i < min_mn; i += nb)
    {
        ib = min(nb, min_mn-i);  
        //===============================================
        // panel factorization
        //===============================================

        magma_ddisplace_pointers(dW0_displ, dA_array, ldda, i, i, batchCount, queue); 
        magma_ddisplace_pointers(dW2_displ, dtau_array, 1, i, 0, batchCount, queue);
        if ( provide_RT > 0 )
        {
            offset_RT = i;
            magma_ddisplace_pointers(dR_displ, dR_array, lddr, (provide_RT == 1 ? offset_RT:0), offset_RT, batchCount, queue); 
            magma_ddisplace_pointers(dT_displ, dT_array, lddt, 0, offset_RT, batchCount, queue); 
        }

        //dwork is used in panel factorization and trailing matrix update
        //dW4_displ, dW5_displ are used as workspace and configured inside
        magma_dgeqrf_panel_batched(m-i, ib, jb, 
                                   dW0_displ, ldda, 
                                   dW2_displ, 
                                   dT_displ, lddt, 
                                   dR_displ, lddr,
                                   dW1_displ,
                                   dW3_displ,
                                   dwork, 
                                   dW4_displ, dW5_displ,
                                   info_array,
                                   batchCount, queue);
           
        //===============================================
        // end of panel
        //===============================================

        //===============================================
        // update trailing matrix
        //===============================================
        if ( (n-ib-i) > 0)
        {
            //dwork is used in panel factorization and trailing matrix update
            //reset dW4_displ
            ldw = nb;
            magma_dset_pointer( dW4_displ, dwork, 1, 0, 0,  ldw*n, batchCount, queue );
            offset = ldw*n*batchCount;
            magma_dset_pointer( dW5_displ, dwork + offset, 1, 0, 0,  ldw*n, batchCount, queue );    

            // set the diagonal of v as one and the upper triangular part as zero already set inside geqrf_panel
            //magmablas_dlaset_batched( MagmaUpper, ib, ib, MAGMA_D_ZERO, MAGMA_D_ONE, dW0_displ, ldda, batchCount, queue ); 
            //magma_ddisplace_pointers(dW2_displ, dtau_array, 1, i, 0, batchCount, queue); 

            // it is faster since it is using BLAS-3 GEMM routines, different from lapack implementation 
            magma_dlarft_batched(m-i, ib, 0,
                             dW0_displ, ldda,
                             dW2_displ,
                             dT_displ, lddt, 
                             dW4_displ, nb*lddt,
                             batchCount, queue);

            
            // perform C = (I-V T^H V^H) * C, C is the trailing matrix
            //-------------------------------------------
            //          USE STREAM  GEMM
            //-------------------------------------------
            use_stream = magma_drecommend_cublas_gemm_stream(MagmaNoTrans, MagmaNoTrans, m-i-ib, n-i-ib, ib);
            if ( use_stream )   
            { 
                magma_queue_sync(queue); 
                for (k=0; k < batchCount; k++)
                {
                    streamid = k%nbstreams;                                       
                    // the queue gemm must take cpu pointer 
                    magma_dlarfb_gpu_gemm( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
                                m-i, n-i-ib, ib,
                                cpuAarray[k] + i + i * ldda, ldda, 
                                cpuTarray[k] + offset_RT*lddt, lddt,
                                cpuAarray[k] + i + (i+ib) * ldda, ldda,
                                dwork + nb * n * k, -1,
                                dwork + nb * n * batchCount + nb * n * k, -1, queues[streamid] );
                }

                // need to synchronise to be sure that panel does not start before
                // finishing the update at least of the next panel
                // if queue is NULL, no need to sync
                if ( queue != NULL ) {
                    for (magma_int_t s=0; s < nbstreams; s++)
                        magma_queue_sync(queues[s]);
                }
            }
            //-------------------------------------------
            //          USE BATCHED GEMM
            //-------------------------------------------
            else
            {
                //direct trailing matrix in dW1_displ
                magma_ddisplace_pointers(dW1_displ, dA_array, ldda, i, i+ib, batchCount, queue); 

                magma_dlarfb_gemm_batched( 
                            MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise, 
                            m-i, n-i-ib, ib,
                            (const double**)dW0_displ, ldda,
                            (const double**)dT_displ, lddt,
                            dW1_displ,  ldda,
                            dW4_displ,  ldw,
                            dW5_displ, ldw,
                            batchCount, queue );
            }
        }// update the trailing matrix 
        //===============================================

        // copy dR back to V after the trailing matrix update, 
        // only when provide_RT=0 otherwise the nbxnb block of V is set to diag=1/0
        // The upper portion of V could be set totaly to 0 here
        if ( provide_RT == 0 )
        {
            magmablas_dlacpy_batched( MagmaUpper, ib, ib, dR_displ, lddr, dW0_displ, ldda, batchCount, queue );
        }
    }

    magma_queue_sync(queue);
    for (k=0; k < nbstreams; k++) {
        magma_queue_destroy( queues[k] );
    }
    
    magma_free(dW0_displ);
    magma_free(dW1_displ);
    magma_free(dW2_displ);
    magma_free(dW3_displ);
    magma_free(dW4_displ);
    magma_free(dW5_displ);
    magma_free(dR_displ);
    magma_free(dT_displ);
    magma_free(dwork);
    magma_free_cpu(cpuAarray);
    magma_free_cpu(cpuTarray);

    return arginfo;
}
Exemple #3
0
extern "C" magma_int_t
magma_dbulge_applyQ_v2_m(
    magma_int_t ngpu,
    magma_side_t side,
    magma_int_t NE, magma_int_t N,
    magma_int_t NB, magma_int_t Vblksiz,
    double *E, magma_int_t lde,
    double *V, magma_int_t ldv,
    double *T, magma_int_t ldt,
    magma_int_t *info)
{
    //%===========================
    //%   local variables
    //%===========================
    magma_int_t Vm, Vn, mt, nt;
    magma_int_t myrow, mycol, blkj, blki;
    magma_int_t blkid,vpos,tpos;
    magma_int_t firstrow, nbcolinvolvd;
    magma_int_t versionL  = 113;
    magma_int_t versionR  = 92;
    magma_int_t Vchunksiz = 10;
    *info=0;

    /* Quick return */
    if ( NE == 0 ) {
        return *info;
    }
    if ( N == 0 ) {
        return *info;
    }
    if ( NB == 0 ) {
        return *info;
    }
    /* ==========================================
     * some infos for developer
     * Initialisation and checking nb of cores
     * ==========================================*/
    /* we have 2 algo for left (113 114) and 2 algo for right (91 92)
     * which correspond to versionL versionR.
     * They are very similar (detail explained in tech report and matlab code)
     * however version 114 and 92 improve locality.
     * while version 113 is used in case WNATZ=1 (construct Q2) which allow
     * the construction to be done in an optimized way taking into
     * consideration that the matrix is Identity so making less flops.
     *
    */

    // Initialize streaming and events
    //magma_device_sync();
    magma_device_t orig_dev;
    magma_getdevice( &orig_dev );

    magma_int_t  nevents =2, nstream=2;
    magma_queue_t queues[MagmaMaxGPUs][20];
    magma_event_t  myevent[MagmaMaxGPUs][20];
    for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
        magma_setdevice( dev );
        for( magma_int_t i = 0; i < nstream; ++i ) {
            magma_queue_create( dev, &queues[dev][i] );
        }
        for( magma_int_t i = 0; i < nevents; ++i ) {
            cudaEventCreateWithFlags(&myevent[dev][i],cudaEventDisableTiming);
            //magma_event_create(&myevent[dev][i]);
        }
    }



    // Azzam 21/11/2012
    // NOTE THAT dwork was of size 2*NE*Vblksiz+...
    // but I am thinking why not modifing it to NE*Vblksiz+...
    // BUT NO because the 2* is used because of making 2 queues working and so
    // they might be using dwork in parallel
    double *dE[MagmaMaxGPUs];
    double *dwork[MagmaMaxGPUs], *dwork0[MagmaMaxGPUs], *dwork1[MagmaMaxGPUs];
    //double *dwvt[MagmaMaxGPUs];
    double *dwvt0[MagmaMaxGPUs], *dwvt1[MagmaMaxGPUs];
    double *dT0[MagmaMaxGPUs], *dV0[MagmaMaxGPUs], *dT1[MagmaMaxGPUs], *dV1[MagmaMaxGPUs];
    magma_int_t dev;
    magma_int_t ldde = N;
    magma_int_t lddv = ldv;
    magma_int_t lddt = ldt;
    magma_int_t ne_loc = magma_ceildiv(NE, ngpu);
    if (ne_loc < 256)
       ne_loc=256;
    magma_int_t dwVTsiz  = lddv*Vblksiz;  // lddv*lddv + lddv*NE; // lddv*Vblksiz;
    magma_int_t dworksiz = ne_loc*Vblksiz;  // lddv*Vblksiz;      // NE*Vblksiz;

    ngpu = min(ngpu, magma_ceildiv(NE,ne_loc)); // Don't use GPU that will not have data.
    // copy dE to GPUs
    for (dev=0; dev < ngpu; ++dev) {
        magma_setdevice( dev );
        if (MAGMA_SUCCESS != magma_dmalloc( &dE[dev], ldde * ne_loc)) {
            printf ("!!!!  magma_dbulge_applyQ magma_alloc failed for: dE\n" );
            exit(-1);
        }
        if (MAGMA_SUCCESS != magma_dmalloc( &dwork[dev], 2*dworksiz + 2*dwVTsiz + 2*Vchunksiz* (Vblksiz* (lddv+lddt)) )) {
            printf ("!!!!  magma_dbulge_applyQ magma_alloc failed for: dwork\n" );
            exit(-1);
        }

        dwork0[dev] = dwork[dev];               // size = dworksiz;
        dwork1[dev] = dwork0[dev] + dworksiz;   // size = dworksiz;
        dwvt0[dev]  = dwork[dev] + 2*dworksiz;  // size = dwVTsiz;
        dwvt1[dev]  = dwvt0[dev] + dwVTsiz;     // size = dwVTsiz;
        dV0[dev]    = dwork[dev] + 2*dworksiz + 2*dwVTsiz;
        dT0[dev]    = dV0[dev]   + Vchunksiz*Vblksiz*lddv;
        dV1[dev]    = dT0[dev]   + Vchunksiz*Vblksiz*lddt;
        dT1[dev]    = dV1[dev]   + Vchunksiz*Vblksiz*lddv;

        magma_int_t ie_loc = min(ne_loc, NE - ne_loc*dev);
        magma_dsetmatrix_async( N, ie_loc, E+lde*ne_loc*dev, lde, dE(dev, 0, 0), ldde, queues[dev][1] );
    }


    // make overlapped copy
    magma_int_t ncpy = 0;
    magma_int_t copyed=0, copyst=0;
    magma_int_t blkcnt,nothing, mysiz, flip, vld,tld, locpos;
    findVTsiz(N, NB, Vblksiz, &blkcnt, &nothing);
    
    flip = 0;


    /* SIDE LEFT  meaning apply E = Q*E = (q_1*q_2*.....*q_n) * E ==> so traverse Vs in reverse order (forward) from q_n to q_1
     *            Also E is splitten by row meaning each apply consist in a block of row (horizontal block) */
    /* SIDE RIGHT meaning apply E = E*Q = E * (q_1*q_2*.....*q_n) ==> so tarverse Vs in normal  order (forward) from q_1 to q_n
     *            Also E is splitten by col meaning each apply consist in a block of col (vertical block) */

    #ifdef ENABLE_DEBUG
    printf("  APPLY Q_v22_m GPU with NGPU %d  N %d, NE %d,  NB %d, Vblksiz %d, versionL %d versionR %d  SIDE %c \n",
          ngpu, N, NE, NB, Vblksiz, versionL, versionR, side);
    #endif


    /*
     * MagmamaLeft
     */
    if (side == MagmaLeft) {
        /*
         * Version 113:
         * loop over the block_col (nt) and for each find the
         * number of tiles (mt) in this block_col. then loop over mt, find
         * the size of the V's(Vm,Vn) and apply it to the corresponding
         * portion of E.
         */
        if ( versionL == 113 ) {
            nt  = magma_ceildiv((N-1),Vblksiz);
            for (blkj=nt-1; blkj >= 0; blkj--) {
                /* the index of the first row on the top of block (blkj) */
                firstrow = blkj * Vblksiz + 1;
                /*find the number of tile for this block */
                if ( blkj == nt-1 )
                    mt = magma_ceildiv( N -  firstrow,    NB);
                else
                    mt = magma_ceildiv( N - (firstrow+1), NB);
                /*loop over the tiles find the size of the Vs and apply it */
                for (blki=mt; blki > 0; blki--) {
                    /*calculate the size of each losange of Vs= (Vm,Vn)*/
                    myrow     = firstrow + (mt-blki)*NB;
                    mycol     = blkj*Vblksiz;
                    Vm = min( NB+Vblksiz-1, N-myrow);
                    if ( ( blkj == nt-1 ) && ( blki == mt ) ) {
                        Vn = min (Vblksiz, Vm);
                    } else {
                        Vn = min (Vblksiz, Vm-1);
                    }
                    /*calculate the pointer to the Vs and the Ts.
                     * Note that Vs and Ts have special storage done
                     * by the bulgechasing function*/
                    //printf("voici blkj %d blki %d  Vm %d  Vn %d mycol %d vpos %d \n",blkj,blki,Vm, Vn,mycol,vpos);
                    magma_bulge_findpos113(N, NB, Vblksiz, mycol, myrow, &blkid);
               
                    // COPY Vchunksiz Vs and Vchunksiz Ts to GPU and store it in dV0/dV1 and dT0/dT1
                    if (ncpy == 0) {
                        // flip = 1 for this.
                        copyst = 0;                             // meaning that copy will start copying from blkid =copyst
                        copyed = min(copyst+Vchunksiz, blkcnt); // meaning that copy will end copying at blkid =copyed-1==> next copy had to start at copyed
                        mysiz  = copyed-copyst;                 // the size of the chunk to be copied
                        if (mysiz > 0) {
                            ncpy = 1;
                            flip = 1;
                            vpos = copyst*Vblksiz*ldv;
                            tpos = copyst*Vblksiz*ldt;
                            vld  = mysiz * ldv;
                            tld  = mysiz * ldt;
                            for( dev = 0; dev < ngpu; ++dev ) {
                                magma_setdevice( dev );
                                magma_dsetmatrix_async(vld, Vblksiz, V(vpos), vld, dV1[dev], vld, queues[dev][1]);
                                magma_dsetmatrix_async(tld, Vblksiz, T(tpos), tld, dT1[dev], tld, queues[dev][1]);
                            }
                            //printf("doing the first copy   of mysiz %2d copyst %2d copyed %2d vpos %8d tpos %8d into dV1 dT1\n",mysiz,copyst,copyed,vpos,tpos);
                        }
                    }
                   
                    if (blkid == copyst) {
                        flip   = ncpy % 2;
                        copyst = copyed;                             // meaning that copy will start copying from blkid =copyst
                        copyed = min(copyst+Vchunksiz, blkcnt); // meaning that copy will end copying at blkid =copyed-1==> next copy had to start at copyed
                        mysiz  = copyed-copyst;                 // the size of the chunk to be copied
                        //printf(" get to copy blkid %d blkid+(2*Vchunksiz) %d copyst %d copyed %d\n",blkid,blkid+(Vchunksiz),copyst,copyed);
                        if (mysiz > 0) {
                            ncpy = ncpy + 1;
                            vpos = copyst*Vblksiz*ldv;
                            tpos = copyst*Vblksiz*ldt;
                            vld  = mysiz * ldv;
                            tld  = mysiz * ldt;
                            if (flip == 0) { // now I am working on dV0 so copy the next and put it on dV1
                                //printf("doing overlapping copy of mysiz %2d copyst %2d copyed %2d vpos %8d tpos %8d into dV1 dT1\n",mysiz,copyst,copyed,vpos,tpos);
                                for( dev = 0; dev < ngpu; ++dev ) {
                                    magma_setdevice( dev );
                                    magma_dsetmatrix_async(vld, Vblksiz, V(vpos), vld, dV1[dev], vld, queues[dev][1]);
                                    magma_dsetmatrix_async(tld, Vblksiz, T(tpos), tld, dT1[dev], tld, queues[dev][1]);
                                }
                            } else { // now I am working on dV1 so copy the next and put it on dV0
                                //printf("doing overlapping copy of mysiz %2d copyst %2d copyed %2d vpos %8d tpos %8d into dV0 dT0\n",mysiz,copyst,copyed,vpos,tpos);
                                for( dev = 0; dev < ngpu; ++dev ) {
                                    magma_setdevice( dev );
                                    magma_dsetmatrix_async(vld, Vblksiz, V(vpos), vld, dV0[dev], vld, queues[dev][0]);
                                    magma_dsetmatrix_async(tld, Vblksiz, T(tpos), tld, dT0[dev], tld, queues[dev][0]);
                                }
                            }
                        }
                    }

                    if ((Vm > 0) && (Vn > 0)) {
                        locpos = blkid%Vchunksiz;
                        magma_int_t lcvpos   = locpos*Vblksiz*lddv;
                        magma_int_t lctpos   = locpos*Vblksiz*lddt;
                        //printf("voici blkj %d blki %d  Vm %d  Vn %d mycol %d locvpos %5d loctpos %5d  blkid %2d  using data in dV%1d dT%1d \n",blkj,blki,Vm, Vn,mycol,lcvpos,lctpos, blkid,flip,flip);
                        if (flip == 0) {
                            for( dev = 0; dev < ngpu; ++dev ) {
                                magma_int_t ie_loc   = min(ne_loc, NE - ne_loc*dev);
                                magma_int_t nr_bl = magma_ceildiv(ie_loc,10000);       //nr of blocks
                                magma_int_t sz_bl = magma_ceildiv(ie_loc,nr_bl*64)*64; //maximum size of blocks (to have blocks of around the same size and multiple of 64)
                                magma_int_t ib;                                        //size of current block
                                magma_setdevice( dev );
                                magma_queue_wait_event( queues[dev][0], myevent[dev][1] );
                                for (magma_int_t i=0; i < ie_loc; i += sz_bl) {
                                    ib = min(sz_bl, ie_loc-i);
                                    //magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, Vm, ib, Vn, dV0[dev]+lcvpos, lddv, dT0[dev]+lctpos, lddt, dE(dev,myrow,i), ldde, dwork0[dev], ib, queues[dev][0] );
                                    magma_dlarfb_gpu_gemm( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, Vm, ib, Vn, dV0[dev]+lcvpos, lddv, dT0[dev]+lctpos, lddt, dE(dev,myrow,i), ldde, dwork0[dev], ib, dwvt0[dev], Vm, queues[dev][0] );
                                }
                                magma_event_record( myevent[dev][0], queues[dev][0] );
                            }
                        } else {
                            for( dev = 0; dev < ngpu; ++dev ) {
                                magma_int_t ie_loc   = min(ne_loc, NE - ne_loc*dev);
                                magma_int_t nr_bl = magma_ceildiv(ie_loc,10000);       //nr of blocks
                                magma_int_t sz_bl = magma_ceildiv(ie_loc,nr_bl*64)*64; //maximum size of blocks (to have blocks of around the same size and multiple of 64)
                                magma_int_t ib;                                        //size of current block
                                magma_setdevice( dev );
                                magma_queue_wait_event( queues[dev][1], myevent[dev][0] );
                                for (magma_int_t i=0; i < ie_loc; i += sz_bl) {
                                    ib = min(sz_bl, ie_loc-i);
                                    //magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, Vm, ib, Vn, dV1[dev]+lcvpos, lddv, dT1[dev]+lctpos, lddt, dE(dev,myrow,i), ldde, dwork1[dev], ib, queues[dev][1] );
                                    magma_dlarfb_gpu_gemm( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, Vm, ib, Vn, dV1[dev]+lcvpos, lddv, dT1[dev]+lctpos, lddt, dE(dev,myrow,i), ldde, dwork1[dev], ib, dwvt1[dev], Vm, queues[dev][1] );
                                }
                                magma_event_record( myevent[dev][1], queues[dev][1] );
                            }
                        }
                    }  // end for (Vm &Vn) > 0
                } // end for blki
            } // end for blkj
        } // end if version=113
        /*
         * Version 114:
         * loop over the block_row (mt) and for each find diagonally the
         * number of tiles (nt) in this block_row. then loop over nt, find
         * the size of the V's(Vm,Vn) and apply it to the corresponding
         * portion of E.
         */
        else {
            printf("versionL 114 not implemented in dbulge_applyQ_v2_m\n");
            exit(-1);
            mt    = magma_ceildiv((N-1),NB);
            for (blki = mt; blki > 0; blki--) {
                /* nbcolinvolvd = number of column corresponding to this block_row (blki) */
                nbcolinvolvd = min(N-1, blki*NB);
                /*find the number of tile for this block (diagonal row of tiles) */
                nt = magma_ceildiv(nbcolinvolvd,Vblksiz);
                /*loop over the tiles find the size of the Vs and apply it */
                for (blkj = nt-1; blkj >= 0; blkj--) {
                    /* the index of the first row of the first col meaning
                     * the block on the top left (blki) */
                    firstrow = (mt-blki)*NB+1;
                    /*calculate the size of each losange of Vs= (Vm,Vn)*/
                    myrow    = firstrow + blkj*Vblksiz;
                    mycol    = blkj*Vblksiz;
                    Vm = min( NB+Vblksiz-1, N-myrow);
                    if ( ( blkj == nt-1 ) && ( blki == mt ) ) {
                        Vn = min (Vblksiz, Vm);
                    } else {
                        Vn = min (Vblksiz, Vm-1);
                    }

                    if ((Vm > 0) && (Vn > 0)) {
                        /*calculate the pointer to the Vs and the Ts.
                         * Note that Vs and Ts have special storage done
                         * by the bulgechasing function*/
                        /*
                        magma_bulge_findVTpos(N, NB, Vblksiz, mycol, myrow, ldv, ldt, &vpos, &tpos);
                        magma_dsetmatrix_async(Vm, Vn, V(vpos), ldv, dV0, lddv, queues[dev][0]);
                        magma_dsetmatrix_async(Vn,  Vn, T(tpos), ldt, dT0, lddt, queues[dev][0]);
                        //printf("voici blki %d  rownbm %d mycol %d  coled %d  blkid %d vpos %d  tpos %d\n", blki, rownbm, mycol, coled, blkid, vpos, tpos);
                        for (magma_int_t i=0; i < NE; i += sz_bl) {
                            ib = min(sz_bl, NE-i);
                            magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, Vm, ib, Vn, dV0, lddv, dT0, lddt, dE(myrow,i), ldde, dwork, NE, queues[dev][0] );
                        }
                        */
                    } // end for (Vm &Vn) > 0
                } // end for blkj
            } // end for blki
        } // end version 114
    } // end LEFT
    /*
     * MagmaRight
     */
    else {
        printf("Side 'R' not implemented in dbulge_applyQ_v2_m\n");
        exit(-1);
        /*
         * Version 91:
         */
        if ( versionR == 91 ) {
            nt  = magma_ceildiv((N-1),Vblksiz);
            for (blkj=0; blkj < nt; blkj++) {
                /* the index of the first myrow on the top of block (blkj) */
                firstrow = blkj * Vblksiz + 1;
                /*find the number of tile for this block */
                if ( blkj == nt-1 )
                    mt = magma_ceildiv( N -  firstrow,    NB);
                else
                    mt = magma_ceildiv( N - (firstrow+1), NB);
                /*loop over the tiles find the size of the Vs and apply it */
                for (blki=1; blki <= mt; blki++) {
                    /*calculate the size of each losange of Vs= (Vm,Vn)*/
                    myrow  = firstrow + (mt-blki)*NB;
                    Vm = min( NB+Vblksiz-1, N-myrow);
                    if ( (blkj == nt-1) && (blki == mt) ) {
                        Vn = min (Vblksiz, Vm);
                    } else {
                        Vn = min (Vblksiz, Vm-1);
                    }
                    mycol     = blkj*Vblksiz;
                    if ((Vm > 0) && (Vn > 0)) {
                        /*calculate the pointer to the Vs and the Ts.
                         * Note that Vs and Ts have special storage done
                         * by the bulgechasing function*/
                        /*
                        magma_bulge_findVTpos(N, NB, Vblksiz, mycol, myrow, ldv, ldt, &vpos, &tpos);
                        magma_dsetmatrix_async(Vm, Vn, V(vpos), ldv, dV0, lddv, queues[dev][0]);
                        magma_dsetmatrix_async(Vn,  Vn, T(tpos), ldt, dT0, lddt, queues[dev][0]);
                        magma_dlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, NE, Vm, Vn, dV0, lddv, dT0, lddt, dE(0, myrow), ldde, dwork, NE, queues[dev][0] );
                        */
                    } // end for (Vm &Vn) > 0
                } // end for blki
            } // end fo blkj
        } // end of version 91
        /*
         * Version 92:
         */
        else {
            mt    = magma_ceildiv((N-1),NB);
            for (blki = 1; blki <= mt; blki++) {
                /* nbcolinvolvd = number of column corresponding to this block_row (blki) */
                nbcolinvolvd = min(N-1, blki*NB);
                /*find the number of tile for this block (diagonal row of tiles) */
                nt = magma_ceildiv(nbcolinvolvd,Vblksiz);
                /*loop over the tiles find the size of the Vs and apply it */
                for (blkj = 0; blkj < nt; blkj++) {
                    /* the index of the first row of the first col meaning
                     * the block on the top left (blki) */
                    firstrow = (mt-blki)*NB+1;
                    /*calculate the size of each losange of Vs= (Vm,Vn)*/
                    myrow    = firstrow + blkj*Vblksiz;
                    mycol    = blkj*Vblksiz;
                    Vm = min( NB+Vblksiz-1, N-myrow);
                    if ( ( blkj == nt-1 ) && ( blki == mt ) ) {
                        Vn = min (Vblksiz, Vm);
                    } else {
                        Vn = min (Vblksiz, Vm-1);
                    }
                    if ((Vm > 0) && (Vn > 0)) {
                        /*calculate the pointer to the Vs and the Ts.
                         * Note that Vs and Ts have special storage done
                         * by the bulgechasing function*/
                        /*
                        magma_bulge_findVTpos(N, NB, Vblksiz, mycol, myrow, ldv, ldt, &vpos, &tpos);
                        magma_dsetmatrix_async(Vm, Vn, V(vpos), ldv, dV0, lddv, queues[dev][0]);
                        magma_dsetmatrix_async(Vn,  Vn, T(tpos), ldt, dT0, lddt, queues[dev][0]);
                        magma_dlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, NE, Vm, Vn, dV0, lddv, dT0, lddt, dE(0, myrow), ldde, dwork, NE, queues[dev][0] );
                        */
                    } // end for (Vm &Vn) > 0
                } //end for blkj
            } // end for blki
        } //end of version 92
    } // end RIGHT

    // copy back the dE form each GPU
    for( dev = 0; dev < ngpu; ++dev ) {
        magma_setdevice( dev );
        magma_queue_wait_event( queues[dev][0], myevent[dev][1] );
        magma_queue_wait_event( queues[dev][0], myevent[dev][0] );
        magma_int_t ie_loc   = min(ne_loc, NE - ne_loc*dev);
        magma_dgetmatrix_async( N, ie_loc, dE(dev, 0, 0), ldde, E+lde*ne_loc*dev, lde, queues[dev][0] );
        magma_event_record( myevent[dev][0], queues[dev][0] );
    }


    for( dev = 0; dev < ngpu; ++dev ) {
        magma_setdevice( dev );
        magma_queue_wait_event( queues[dev][0], myevent[dev][0] );
        magma_queue_sync(queues[dev][0]);
        magma_queue_sync(queues[dev][1]);
        magma_free(dwork[dev]);
        magma_free(dE[dev]);
        for( magma_int_t i = 0; i < nevents; ++i ) {
            magma_event_destroy( myevent[dev][i] );
        }
        for( magma_int_t i = 0; i < nstream; ++i ) {
            magma_queue_destroy( queues[dev][i] );
        }
    }

    magma_setdevice( orig_dev );
    return *info;
}