Example #1
0
//===================================================================================================================
//===================================================================================================================
//===================================================================================================================
extern "C" void
magma_dlarft_sm32x32_batched(magma_int_t n, magma_int_t k, 
                    double **v_array, magma_int_t ldv,
                    double **tau_array, 
                    double **T_array, magma_int_t ldt, 
                    magma_int_t batchCount, magma_queue_t queue)
{
    if ( k <= 0) return;

     //==================================
     //          GEMV
     //==================================
#define USE_GEMV2
#define use_gemm_larft_sm32

    #if defined(use_gemm_larft_sm32)
    magma_dgemm_batched( MagmaConjTrans, MagmaNoTrans, 
                         k, k, n, 
                         MAGMA_D_ONE, v_array, ldv, 
                         v_array, ldv, 
                         MAGMA_D_ZERO, T_array, ldt, 
                         batchCount, queue );
    magmablas_dlaset_batched( MagmaLower, k, k, 
            MAGMA_D_ZERO, MAGMA_D_ZERO, 
            T_array, ldt, batchCount, queue );
    #else
    #if 1
    for (magma_int_t i=0; i < k; i++)
    {
        //W(1:i-1) := - tau(i) * V(i:n,1:i-1)' * V(i:n,i)
        //T( i, i ) = tau( i ) 
        //custom implementation.
        #ifdef USE_GEMV2
        magmablas_dlarft_gemvrowwise_batched( n-i, i, 
                            tau_array,
                            v_array, ldv, 
                            T_array, ldt,
                            batchCount, queue);
                            
        #else       
        magmablas_dlarft_gemvcolwise_batched( n-i, i, v_array, ldv, T_array, ldt, tau_array, batchCount, queue);
        #endif
    }
    #else
        //seems to be very slow when k=32 while the one by one loop above is faster
        dlarft_gemv_loop_inside_kernel_batched(n, k, tau_array, v_array, ldv, T_array, ldt, batchCount, queue); 
    #endif
    #endif
     //==================================
     //          TRMV
     //==================================
     //T(1:i-1,i) := T(1:i-1,1:i-1) * W(1:i-1) i=[1:k]
     magmablas_dlarft_dtrmv_sm32x32_batched(k, k, tau_array, T_array, ldt, T_array, ldt, batchCount, queue);
}
Example #2
0
/***************************************************************************//**
    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;
}
Example #3
0
//===================================================================================================================
//===================================================================================================================
//===================================================================================================================
extern "C" magma_int_t
magma_dlarft_batched(magma_int_t n, magma_int_t k, magma_int_t stair_T, 
                double **v_array, magma_int_t ldv,
                double **tau_array, double **T_array, magma_int_t ldt, 
                double **work_array, magma_int_t lwork, 
                magma_int_t batchCount, magma_queue_t queue)
{
    double c_one  = MAGMA_D_ONE;
    double c_zero = MAGMA_D_ZERO;

    if ( k <= 0) return 0;
    if ( stair_T > 0 && k <= stair_T) return 0;

    magma_int_t maxnb = max_shared_bsiz;

    if ( lwork < k*ldt) 
    {
        magma_xerbla( __func__, -(10) );
        return -10;
    }

    if ( stair_T > 0 && stair_T > maxnb)
    { 
        magma_xerbla( __func__, -(3) );
        return -3;
    }
    magma_int_t DEBUG=0;
    magma_int_t nb = stair_T == 0 ? min(k,maxnb) : stair_T;

    magma_int_t i, j, prev_n, mycol, rows;

    double **dW1_displ  = NULL;
    double **dW2_displ  = NULL;
    double **dW3_displ  = NULL;
    double **dTstep_array  = NULL;

    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**)&dTstep_array,  batchCount * sizeof(*dTstep_array));

    //double *Tstep =  k > nb ? work : T;
    if (k > nb)
    {
        magma_ddisplace_pointers(dTstep_array, work_array, lwork, 0, 0, batchCount, queue);
    }
    else
    {
        magma_ddisplace_pointers(dTstep_array, T_array, ldt, 0, 0, batchCount, queue);
    }

    //magma_int_t ldtstep = k > nb ? k : ldt;
    magma_int_t ldtstep = ldt; //a enlever
    // stair_T = 0 meaning all T
    // stair_T > 0 meaning the triangular portion of T has been computed. 
    //                    the value of stair_T is the nb of these triangulars
   

    //GEMV compute the whole triangular upper portion of T (phase 1)
    // TODO addcublas to check perf

    magma_dgemm_batched( MagmaConjTrans, MagmaNoTrans, 
                         k, k, n, 
                         c_one,  v_array, ldv, 
                                 v_array, ldv, 
                         c_zero, dTstep_array, ldtstep, 
                         batchCount, queue );

    magmablas_dlaset_batched( MagmaLower, k, k, MAGMA_D_ZERO, MAGMA_D_ZERO, dTstep_array, ldtstep, batchCount, queue );
    // no need for it as T is expected to be lower zero
    //if (k > nb) magmablas_dlaset_batched( MagmaLower, k, k, MAGMA_D_ZERO, MAGMA_D_ZERO, dTstep_array, ldtstep, batchCount, queue );
    

    //TRMV
    //T(1:i-1,i) := T(1:i-1,1:i-1) * W(1:i-1) i=[1:k]
    // TRMV is split over block of column of size nb 
    // the update should be done from top to bottom so:
    // 1- a gemm using the previous computed columns
    //    of T to update rectangular upper protion above 
    //    the triangle of my columns 
    // 2- the columns need to be updated by a serial 
    //    loop over of gemv over itself. since we limit the
    //    shared memory to nb, this nb column 
    //    are split vertically by chunk of nb rows

    dim3 grid(1, 1, batchCount);

    for (j=0; j < k; j += nb)
    {
        prev_n =  j;
        mycol  =  min(nb, k-j);
        // note that myrow = prev_n + mycol;
        if (prev_n > 0 && mycol > 0) {
            if (DEBUG == 3) {
                printf("doing gemm on the rectangular portion of size %d %d of T(%d,%d)\n",
                        (int) prev_n, (int) mycol, 0, (int) j );
            }

            magma_ddisplace_pointers(dW1_displ, dTstep_array, ldtstep, 0, j, batchCount, queue);
            magma_ddisplace_pointers(dW2_displ, T_array,     ldt, 0, j, batchCount, queue);
            magma_dgemm_batched( MagmaNoTrans, MagmaNoTrans, 
                                 prev_n, mycol, prev_n, 
                                 c_one,  T_array, ldt, 
                                         dW1_displ, ldtstep, 
                                 c_zero, dW2_displ, ldt, 
                                 batchCount, queue );

            // update my rectangular portion (prev_n,mycol) using sequence of gemv 
            magma_ddisplace_pointers(dW1_displ, dTstep_array, ldtstep, j, j, batchCount, queue);
            magma_ddisplace_pointers(dW3_displ, tau_array,  1, j, 0, batchCount, queue);

            for (i=0; i < prev_n; i += nb)
            {
                rows = min(nb,prev_n-i);
                if (DEBUG == 3) {
                    printf("        doing recdtrmv on the rectangular portion of size %d %d of T(%d,%d)\n",
                            (int) rows, (int) mycol, (int) i, (int) j );
                }

                if (rows > 0 && mycol > 0)
                {
                    magma_ddisplace_pointers(dW2_displ, T_array,     ldt, i, j, batchCount, queue);
                    magmablas_dlarft_recdtrmv_sm32x32_batched(rows, mycol, dW3_displ, dW2_displ, ldt, dW1_displ, ldtstep, batchCount, queue);
                }
            }
        }

        // the upper rectangular protion is updated, now if needed update the triangular portion
        if (stair_T == 0) {
            if (DEBUG == 3) {
                printf("doing dtrmv on the triangular portion of size %d %d of T(%d,%d)\n",
                        (int) mycol, (int) mycol, (int) j, (int) j );
            }

            if (mycol > 0)
            {
                magma_ddisplace_pointers(dW1_displ, dTstep_array, ldtstep, j, j, batchCount, queue);
                magma_ddisplace_pointers(dW3_displ, tau_array,  1, j, 0, batchCount, queue);
                magma_ddisplace_pointers(dW2_displ, T_array,     ldt, j, j, batchCount, queue);
                magmablas_dlarft_dtrmv_sm32x32_batched(mycol, mycol, dW3_displ, dW1_displ, ldtstep, dW2_displ, ldt, batchCount, queue);
            }
        }
    }// end of j

    magma_free(dW1_displ);
    magma_free(dW2_displ);
    magma_free(dW3_displ);
    magma_free(dTstep_array);

    return 0;
}
Example #4
0
extern "C" magma_int_t
magma_dgeqrf_panel_batched(
        magma_int_t m, magma_int_t n, magma_int_t nb,    
        double** dA_array,    magma_int_t ldda,
        double** tau_array, 
        double** dT_array, magma_int_t ldt, 
        double** dR_array, magma_int_t ldr,
        double** dW0_displ, 
        double** dW1_displ,
        double   *dwork,  
        double** dW2_displ, 
        double** dW3_displ,
        magma_int_t *info_array,
        magma_int_t batchCount, magma_queue_t queue)
{
    magma_int_t j, jb;
    magma_int_t ldw = nb; 
    magma_int_t minmn = min(m,n); 

    for( j=0; j < minmn; j += nb)
    {
        jb = min(nb, minmn-j);

        magma_ddisplace_pointers(dW0_displ, dA_array, ldda, j, j, batchCount, queue); 
        magma_ddisplace_pointers(dW2_displ, tau_array, 1, j, 0, batchCount, queue);
        magma_ddisplace_pointers(dW3_displ, dR_array, ldr, j, j, batchCount, queue); // 

        //sub-panel factorization 
        magma_dgeqr2_batched(
                m-j, jb,
                dW0_displ, ldda,      
                dW2_displ, 
                info_array, 
                batchCount,
                queue);

        //copy th whole rectangular n,jb from of dA to dR (it's lower portion (which is V's) will be set to zero if needed at the end)
        magma_ddisplace_pointers(dW0_displ, dA_array, ldda, 0, j, batchCount, queue); 
        magma_ddisplace_pointers(dW3_displ, dR_array, ldr, 0, j, batchCount, queue); 
        magmablas_dlacpy_batched( MagmaFull, minmn, jb, dW0_displ, ldda, dW3_displ, ldr, batchCount, queue );

        //set the upper jbxjb portion of V dA(j,j) to 1/0s (note that the rectangular on the top of this triangular of V still non zero but has been copied to dR).
        magma_ddisplace_pointers(dW0_displ, dA_array, ldda, j, j, batchCount, queue); 
        magmablas_dlaset_batched( MagmaUpper, jb, jb, MAGMA_D_ZERO, MAGMA_D_ONE, dW0_displ, ldda, batchCount, queue ); 

        if ( (n-j-jb) > 0) //update the trailing matrix inside the panel
        {
            magma_dlarft_sm32x32_batched(m-j, jb,
                    dW0_displ, ldda,
                    dW2_displ,
                    dT_array, ldt, 
                    batchCount, queue);

            magma_ddisplace_pointers( dW1_displ, dA_array, ldda, j, j + jb, batchCount, queue );
            magma_dset_pointer( dW2_displ,  dwork, 1, 0, 0,  ldw*n, batchCount, queue );
            magma_dset_pointer( dW3_displ, dwork + ldw*n*batchCount, 1, 0, 0,  ldw*n, batchCount, queue );

            magma_dlarfb_gemm_batched( 
                    MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
                    m-j, n-j-jb, jb,
                    (const double**)dW0_displ, ldda,
                    (const double**)dT_array, ldt,
                    dW1_displ,  ldda,
                    dW2_displ,  ldw, 
                    dW3_displ, ldw,
                    batchCount, queue );
        }
    }

    // copy the remaining portion of dR from dA in case m < n
    if ( m < n )
    {
        magma_ddisplace_pointers(dW0_displ, dA_array, ldda, 0, minmn, batchCount, queue); 
        magma_ddisplace_pointers(dW3_displ, dR_array, ldr, 0, minmn, batchCount, queue); 
        magmablas_dlacpy_batched( MagmaFull, minmn, n-minmn, dW0_displ, ldda, dW3_displ, ldr, batchCount, queue );
    }
    // to be consistent set the whole upper nbxnb of V to 0/1s, in this case no need to set it inside dgeqrf_batched
    magma_ddisplace_pointers(dW0_displ, dA_array, ldda, 0, 0, batchCount, queue); 
    magmablas_dlaset_batched( MagmaUpper, minmn, n, MAGMA_D_ZERO, MAGMA_D_ONE, dW0_displ, ldda, batchCount, queue ); 

    return MAGMA_SUCCESS;
}