예제 #1
0
extern "C" magma_int_t
magma_zgetrf2_mgpu(magma_int_t num_gpus, 
         magma_int_t m, magma_int_t n, magma_int_t nb, magma_int_t offset,
         cuDoubleComplex **d_lAT, magma_int_t lddat, magma_int_t *ipiv,
         cuDoubleComplex **d_lAP, cuDoubleComplex *w, magma_int_t ldw,
         cudaStream_t streaml[][2], magma_int_t *info)
#endif
{
/*  -- MAGMA (version 1.3.0) --
       Univ. of Tennessee, Knoxville
       Univ. of California, Berkeley
       Univ. of Colorado, Denver
       November 2010

    Purpose
    =======

    ZGETRF computes an LU factorization of a general M-by-N matrix A
    using partial pivoting with row interchanges.

    The factorization has the form
       A = P * L * U
    where P is a permutation matrix, L is lower triangular with unit
    diagonal elements (lower trapezoidal if m > n), and U is upper
    triangular (upper trapezoidal if m < n).

    This is the right-looking Level 3 BLAS version of the algorithm.
    Use two buffer to send panels..

    Arguments
    =========

    NUM_GPUS 
            (input) INTEGER
            The number of GPUS to be used for the factorization.

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

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

    A       (input/output) COMPLEX_16 array on the GPU, dimension (LDDA,N).
            On entry, the M-by-N matrix to be factored.
            On exit, the factors L and U from the factorization
            A = P*L*U; the unit diagonal elements of L are not stored.

    LDDA     (input) INTEGER
            The leading dimension of the array A.  LDDA >= max(1,M).

    IPIV    (output) INTEGER array, dimension (min(M,N))
            The pivot indices; for 1 <= i <= min(M,N), row i of the
            matrix was interchanged with row IPIV(i).

    INFO    (output) INTEGER
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
                  if INFO = -7, internal GPU memory allocation failed.
            > 0:  if INFO = i, U(i,i) is exactly zero. The factorization
                  has been completed, but the factor U is exactly
                  singular, and division by zero will occur if it is used
                  to solve a system of equations.
    =====================================================================    */

#define inAT(id,i,j)  (d_lAT[(id)] + ((offset)+(i)*nb)*lddat + (j)*nb)
#define W(j) (w+((j)%num_gpus)*nb*ldw)

    cuDoubleComplex c_one     = MAGMA_Z_ONE;
    cuDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;

    magma_int_t block_size = 32;
    magma_int_t iinfo, n_local[4]; 
    magma_int_t maxm, mindim;
    magma_int_t i, ii, d, dd, rows, cols, s, ldpan[4];
    magma_int_t id, i_local, i_local2, nb0, nb1;
    cuDoubleComplex *d_panel[4], *panel_local[4];
    //cudaStream_t streaml[4][2];

    /* Check arguments */
    *info = 0;
    if (m < 0)
    *info = -2;
    else if (n < 0)
    *info = -3;
    else if (num_gpus*lddat < max(1,n))
    *info = -5;

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

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

    /* Function Body */
    mindim = min(m, n);
    //nb     = magma_get_zgetrf_nb(m);
    if( num_gpus > ceil((double)n/nb) ) {
      *info = -1;
      return *info;
    }

    {
      /* Use hybrid blocked code. */
      maxm  = ((m + block_size-1)/block_size)*block_size;

      /* some initializations */
      for(i=0; i<num_gpus; i++){
        magmaSetDevice(i);

        n_local[i] = ((n/nb)/num_gpus)*nb;
        if (i < (n/nb)%num_gpus)
           n_local[i] += nb;
        else if (i == (n/nb)%num_gpus)
           n_local[i] += n%nb;

        /* workspaces */
        d_panel[i] = &(d_lAP[i][nb*maxm]);   /* temporary panel storage */

        /* create local streams */
        //magma_queue_create(&streaml[i][0]);
        //magma_queue_create(&streaml[i][1]);
      }
      trace_init( 1, num_gpus, 2, (CUstream_st**)streaml );

      /* start sending the panel to cpu */
      nb0 = min(mindim, nb);
      magmaSetDevice(0);
      magmablasSetKernelStream(streaml[0][1]);
      trace_gpu_start( 0, 1, "comm", "get" );
      if( nb0 == nb )
        magmablas_ztranspose(  d_lAP[0], maxm, inAT(0,0,0), lddat, nb0, maxm );
      else
        magmablas_ztranspose2( d_lAP[0], maxm, inAT(0,0,0), lddat, nb0, maxm );
      magma_zgetmatrix_async( m, nb0,
                              d_lAP[0], maxm,
                              W(0),     ldw, streaml[0][1] );
      trace_gpu_end( 0, 1 );

      /* ------------------------------------------------------------------------------------- */
#ifdef  PROFILE
      magma_timestr_t start_timer, end_timer;
      start_timer = get_current_time();
#endif
      s = mindim / nb;
      for( i=0; i<s; i++ )
            {
                /* Set the GPU number that holds the current panel */
                id = i%num_gpus;
                magmaSetDevice(id);

                /* Set the local index where the current panel is */
                i_local = i/num_gpus;
                cols  = maxm - i*nb;
                rows  = m - i*nb;

                /* synchrnoize i-th panel from id-th gpu into work */
                magma_queue_sync( streaml[id][1] );

                /* i-th panel factorization */
                trace_cpu_start( 0, "getrf", "getrf" );
#ifdef PANEL_FACT_MC
                cntxt->nb = 12;
                magma_zgetrf_mc(cntxt, &rows, &nb, W(i), &ldw, ipiv+i*nb, &iinfo);
#else
                lapackf77_zgetrf( &rows, &nb, W(i), &ldw, ipiv+i*nb, &iinfo);
#endif
                if ( (*info == 0) && (iinfo > 0) ) {
                    *info = iinfo + i*nb;
                    //break;
                }
                trace_cpu_end( 0 );

                /* start sending the panel to all the gpus */
                d = (i+1)%num_gpus;
                for( dd=0; dd<num_gpus; dd++ ) {
                  magmaSetDevice(d);
                  trace_gpu_start( 0, 1, "comm", "set" );
                  magma_zsetmatrix_async( rows, nb,
                                          W(i),     ldw,
                                          d_lAP[d], cols, streaml[d][1] );
                  trace_gpu_end( 0, 1 );
                  d = (d+1)%num_gpus;
                }

                /* apply the pivoting */
                d = (i+1)%num_gpus;
                for( dd=0; dd<num_gpus; dd++ ) {
                  magmaSetDevice(d);
                  magmablasSetKernelStream(streaml[d][0]);

                  trace_gpu_start( d, 1, "pivot", "pivot" );
                  if( dd == 0 )
                    magmablas_zpermute_long2( lddat, inAT(d,0,0), lddat, ipiv, nb, i*nb );
                  else
                    magmablas_zpermute_long3(        inAT(d,0,0), lddat, ipiv, nb, i*nb );
                  trace_gpu_end( d, 1 );
                  d = (d+1)%num_gpus;
                }


                /* update the trailing-matrix/look-ahead */
                d = (i+1)%num_gpus;
                for( dd=0; dd<num_gpus; dd++ ) {
                  magmaSetDevice(d);

                  /* storage for panel */
                  if( d == id ) {
                    /* the panel belond to this gpu */
                    panel_local[d] = inAT(d,i,i_local);
                    ldpan[d] = lddat;
                    /* next column */
                    i_local2 = i_local+1;
                  } else {
                    /* the panel belong to another gpu */
                    panel_local[d] = &d_panel[d][(i%2)*nb*maxm];
                    //panel_local[d] = d_panel[d];
                    ldpan[d] = nb;
                    /* next column */
                    i_local2 = i_local;
                    if( d < id ) i_local2 ++;
                  }
                  /* the size of the next column */
                  if ( s > (i+1) ) {
                    nb0 = nb;
                  } else {
                    nb0 = n_local[d]-nb*(s/num_gpus);
                    if( d < s%num_gpus ) nb0 -= nb;
                  }
                  if( d == (i+1)%num_gpus) {
                    /* owns the next column, look-ahead the column */
                    nb1 = nb0;
                    magmablasSetKernelStream(streaml[d][1]);

                    /* make sure all the pivoting has been applied */
                    magma_queue_sync(streaml[d][0]);
                    trace_gpu_start( d, 1, "gemm", "gemm" );
                  } else {
                    /* update the entire trailing matrix */
                    nb1 = n_local[d] - i_local2*nb;
                    magmablasSetKernelStream(streaml[d][0]);

                    /* synchronization to make sure panel arrived on gpu */
                    magma_queue_sync(streaml[d][1]);
                    trace_gpu_start( d, 0, "gemm", "gemm" );
                  }
                  magmablas_ztranspose(panel_local[d], ldpan[d], d_lAP[d], cols, cols, nb);

                  /* gpu updating the trailing matrix */
                  //magmablas_ztrsm(
                  magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit, 
                               nb1, nb, c_one,
                               panel_local[d],       ldpan[d],
                               inAT(d, i, i_local2), lddat);
                  //cublasZgemm
                  magma_zgemm( MagmaNoTrans, MagmaNoTrans, 
                               nb1, m-(i+1)*nb, nb, 
                               c_neg_one, inAT(d, i,   i_local2),         lddat,
                                          &(panel_local[d][nb*ldpan[d]]), ldpan[d], 
                               c_one,     inAT(d, i+1, i_local2),         lddat );

                  if( d == (i+1)%num_gpus ) 
                  {
                    /* Set the local index where the current panel is */
                    int loff    = i+1;
                    int i_local = (i+1)/num_gpus;
                    int ldda    = maxm - (i+1)*nb;
                    int cols    = m - (i+1)*nb;
                    nb0 = min(nb, mindim - (i+1)*nb); /* size of the diagonal block */
                    trace_gpu_end( d, 1 );

                    if( nb0 > 0 ) {
                        /* transpose the panel for sending it to cpu */
                        trace_gpu_start( d, 1, "comm", "get" );
                        if( i+1 < s ) 
                          magmablas_ztranspose(  d_lAP[d], ldda, inAT(d,loff,i_local), lddat, nb0, ldda );
                        else
                          magmablas_ztranspose2(  d_lAP[d], ldda, inAT(d,loff,i_local), lddat, nb0, ldda );

                        /* send the panel to cpu */
                        magma_zgetmatrix_async( cols, nb0,
                                                d_lAP[d], ldda,
                                                W(i+1),   ldw, streaml[d][1] );
                        trace_gpu_end( d, 1 );
                    }
                  } else {
                    trace_gpu_end( d, 0 );
                  }

                  d = (d+1)%num_gpus;
                }

                /* update the remaining matrix by gpu owning the next panel */
                if( (i+1) < s ) {
                  int i_local = (i+1)/num_gpus;
                  int rows  = m - (i+1)*nb;

                  d = (i+1)%num_gpus;
                  magmaSetDevice(d);
                  magmablasSetKernelStream(streaml[d][0]);
                  trace_gpu_start( d, 0, "gemm", "gemm" );
                  //magmablas_ztrsm
                  magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit, 
                               n_local[d] - (i_local+1)*nb, nb, 
                               c_one, panel_local[d],       ldpan[d], 
                                      inAT(d,i,i_local+1),  lddat );
                  //cublasZgemm
                  magma_zgemm( MagmaNoTrans, MagmaNoTrans, 
                               n_local[d]-(i_local+1)*nb, rows, nb, 
                               c_neg_one, inAT(d,i,i_local+1),            lddat, 
                                          &(panel_local[d][nb*ldpan[d]]), ldpan[d], 
                               c_one,     inAT(d,i+1,  i_local+1),        lddat );
                  trace_gpu_end( d, 0 );
                }
             } /* end of for i=1..s */
             /* ------------------------------------------------------------------------------ */

            /* Set the GPU number that holds the last panel */
            id = s%num_gpus;

            /* Set the local index where the last panel is */
            i_local = s/num_gpus;

            /* size of the last diagonal-block */
            nb0 = min(m - s*nb, n - s*nb);
            rows = m    - s*nb;
            cols = maxm - s*nb;

            if( nb0 > 0 ) {
              magmaSetDevice(id);

              /* wait for the last panel on cpu */
              magma_queue_sync( streaml[id][1] );

              /* factor on cpu */
              lapackf77_zgetrf( &rows, &nb0, W(s), &ldw, ipiv+s*nb, &iinfo);
              if ( (*info == 0) && (iinfo > 0) )
              *info = iinfo + s*nb;

              /* send the factor to gpus */
              for( d=0; d<num_gpus; d++ ) {
                magmaSetDevice(d);
                i_local2 = i_local;
                if( d < id ) i_local2 ++;

                if( d == id || n_local[d] > i_local2*nb ) {
                  magma_zsetmatrix_async( rows, nb0,
                                          W(s),     ldw,
                                          d_lAP[d], cols, streaml[d][1] );
                }
              }

              for( d=0; d<num_gpus; d++ ) {
                magmaSetDevice(d);
                magmablasSetKernelStream(streaml[d][0]);
                if( d == 0 )
                  magmablas_zpermute_long2( lddat, inAT(d,0,0), lddat, ipiv, nb0, s*nb );
                else
                  magmablas_zpermute_long3(        inAT(d,0,0), lddat, ipiv, nb0, s*nb );
              }

              for( d=0; d<num_gpus; d++ ) {
                magmaSetDevice(d);
                magmablasSetKernelStream(streaml[d][1]);

                /* wait for the pivoting to be done */
                magma_queue_sync( streaml[d][0] );

                i_local2 = i_local;
                if( d < id ) i_local2++;
                if( d == id ) {
                  /* the panel belond to this gpu */
                  panel_local[d] = inAT(d,s,i_local);

                  /* next column */
                  nb1 = n_local[d] - i_local*nb-nb0;

                  magmablas_ztranspose2( panel_local[d], lddat, d_lAP[d], cols, rows, nb0);

                  if( nb1 > 0 )
                  //cublasZtrsm
                  magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit, 
                               nb1, nb0, c_one,
                               panel_local[d],        lddat, 
                               inAT(d,s,i_local)+nb0, lddat);
                } else if( n_local[d] > i_local2*nb ) {
                  /* the panel belong to another gpu */
                  panel_local[d] = &d_panel[d][(s%2)*nb*maxm];
                  //panel_local[d] = d_panel[d];

                  /* next column */
                  nb1 = n_local[d] - i_local2*nb;

                  magmablas_ztranspose2( panel_local[d], nb, d_lAP[d], cols, rows, nb0);
                  //cublasZtrsm
                  magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit, 
                               nb1, nb0, c_one,
                               panel_local[d],     nb, 
                               inAT(d,s,i_local2), lddat);
                }
              }
            } /* if( nb0 > 0 ) */

            /* clean up */
            trace_finalize( "zgetrf_mgpu.svg","trace.css" );
            for( d=0; d<num_gpus; d++ ) {
              magmaSetDevice(d);
              magma_queue_sync( streaml[d][0] );
              magma_queue_sync( streaml[d][1] );
              //magma_queue_destroy(streaml[d][0]);
              //magma_queue_destroy(streaml[d][1]);
              magmablasSetKernelStream(NULL);
            } 
            magmaSetDevice(0);
#ifdef  PROFILE
            end_timer = get_current_time();
            printf("\n Performance %f GFlop/s\n", (2./3.*n*n*n /1000000.) / GetTimerValue(start_timer, end_timer));
#endif
    }

    return *info;
    /* End of MAGMA_ZGETRF2_MGPU */
}
예제 #2
0
/**
    Purpose
    -------
    ZGETRF_m computes an LU factorization of a general M-by-N matrix A
    using partial pivoting with row interchanges.  This version does not
    require work space on the GPU passed as input. GPU memory is allocated
    in the routine. The matrix may not fit entirely in the GPU memory.

    The factorization has the form
       A = P * L * U
    where P is a permutation matrix, L is lower triangular with unit
    diagonal elements (lower trapezoidal if m > n), and U is upper
    triangular (upper trapezoidal if m < n).

    This is the right-looking Level 3 BLAS version of the algorithm.

    Note: The factorization of big panel is done calling multiple-gpu-interface.
    Pivots are applied on GPU within the big panel.

    Arguments
    ---------
    @param[in]
    num_gpus INTEGER
             The number of GPUs.  num_gpus > 0.

    @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]
    A       COMPLEX_16 array, dimension (LDA,N)
            On entry, the M-by-N matrix to be factored.
            On exit, the factors L and U from the factorization
            A = P*L*U; the unit diagonal elements of L are not stored.
    \n
            Higher performance is achieved if A is in pinned memory, e.g.
            allocated using magma_malloc_pinned.

    @param[in]
    lda     INTEGER
            The leading dimension of the array A.  LDA >= max(1,M).

    @param[out]
    ipiv    INTEGER array, dimension (min(M,N))
            The pivot indices; for 1 <= i <= min(M,N), row i of the
            matrix was interchanged with row IPIV(i).

    @param[out]
    info    INTEGER
      -     = 0:  successful exit
      -     < 0:  if INFO = -i, the i-th argument had an illegal value
                  or another error occured, such as memory allocation failed.
      -     > 0:  if INFO = i, U(i,i) is exactly zero. The factorization
                  has been completed, but the factor U is exactly
                  singular, and division by zero will occur if it is used
                  to solve a system of equations.

    @ingroup magma_zgesv_comp
    ********************************************************************/
extern "C" magma_int_t
magma_zgetrf_m(magma_int_t num_gpus, magma_int_t m, magma_int_t n,
               magmaDoubleComplex *A, magma_int_t lda,
               magma_int_t *ipiv, magma_int_t *info)
{
#define     A(i,j) (A      + (j)*lda + (i))
#define dAT(d,i,j) (dAT[d] + (i)*nb*ldn_local + (j)*nb)
#define dPT(d,i,j) (dPT[d] + (i)*nb*nb + (j)*nb*maxm)

    magma_timer_t time=0, time_total=0, time_alloc=0, time_set=0, time_get=0, time_comp=0;
    timer_start( time_total );
    real_Double_t flops;

    magmaDoubleComplex c_one     = MAGMA_Z_ONE;
    magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
    magmaDoubleComplex *dAT[MagmaMaxGPUs], *dA[MagmaMaxGPUs], *dPT[MagmaMaxGPUs];
    magma_int_t        iinfo = 0, nb, nbi, maxm, n_local[MagmaMaxGPUs], ldn_local;
    magma_int_t        N, M, NB, NBk, I, d, num_gpus0 = num_gpus;
    magma_int_t        ii, jj, h, offset, ib, rows, s;
    
    magma_queue_t stream[MagmaMaxGPUs][2];
    magma_event_t  event[MagmaMaxGPUs][2];

    *info = 0;

    if (m < 0)
        *info = -1;
    else if (n < 0)
        *info = -2;
    else if (lda < max(1,m))
        *info = -4;

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

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

    /* initialize nb */
    nb = magma_get_zgetrf_nb(m);
    maxm = ((m  + 31)/32)*32;

    /* figure out NB */
    size_t freeMem, totalMem;
    cudaMemGetInfo( &freeMem, &totalMem );
    freeMem /= sizeof(magmaDoubleComplex);
    
    /* number of columns in the big panel */
    h = 1+(2+num_gpus0);
    NB = (magma_int_t)(0.8*freeMem/maxm-h*nb);
    const char* ngr_nb_char = getenv("MAGMA_NGR_NB");
    if ( ngr_nb_char != NULL ) NB = max( nb, min( NB, atoi(ngr_nb_char) ) );
    //NB = 5*max(nb,32);

    if ( num_gpus0 > ceil((double)NB/nb) ) {
        num_gpus = (int)ceil((double)NB/nb);
        h = 1+(2+num_gpus);
        NB = (magma_int_t)(0.8*freeMem/maxm-h*nb);
    } else {
        num_gpus = num_gpus0;
    }
    if ( num_gpus*NB >= n ) {
        #ifdef CHECK_ZGETRF_OOC
        printf( "      * still fit in GPU memory.\n" );
        #endif
        NB = n;
    } else {
        #ifdef CHECK_ZGETRF_OOC
        printf( "      * don't fit in GPU memory.\n" );
        #endif
        NB = num_gpus*NB;
        NB = max( nb, (NB / nb) * nb); /* making sure it's devisable by nb (x64) */
    }

    #ifdef CHECK_ZGETRF_OOC
    if ( NB != n ) printf( "      * running in out-core mode (n=%d, NB=%d, nb=%d, freeMem=%.2e).\n", n, NB, nb, (double)freeMem );
    else          printf( "      * running in in-core mode  (n=%d, NB=%d, nb=%d, freeMem=%.2e).\n", n, NB, nb, (double)freeMem );
    #endif

    if ( (nb <= 1) || (nb >= min(m,n)) ) {
        /* Use CPU code for scalar of one tile. */
        lapackf77_zgetrf(&m, &n, A, &lda, ipiv, info);
    } else {
        /* Use hybrid blocked code. */

    /* allocate memory on GPU to store the big panel */
    timer_start( time_alloc );
    n_local[0] = (NB/nb)/num_gpus;
    if ( NB%(nb*num_gpus) != 0 ) n_local[0] ++;
    n_local[0] *= nb;
    ldn_local = ((n_local[0]+31)/32)*32;

    for( d=0; d < num_gpus; d++ ) {
        magma_setdevice(d);
        if (MAGMA_SUCCESS != magma_zmalloc( &dA[d], (ldn_local+h*nb)*maxm )) {
            *info = MAGMA_ERR_DEVICE_ALLOC;
            return *info;
        }
        dPT[d] = dA[d] + nb*maxm;      /* for storing the previous panel from CPU */
        dAT[d] = dA[d] + h*nb*maxm;    /* for storing the big panel               */
        magma_queue_create( &stream[d][0] );
        magma_queue_create( &stream[d][1] );
        magma_event_create( &event[d][0] );
        magma_event_create( &event[d][1] );
    }
    //magma_setdevice(0);
    timer_stop( time_alloc );
    
    for( I=0; I < n; I += NB ) {
        M = m;
        N = min( NB, n-I );       /* number of columns in this big panel             */
        s = min( max(m-I,0), N )/nb; /* number of small block-columns in this big panel */

        maxm = ((M + 31)/32)*32;
        if ( num_gpus0 > ceil((double)N/nb) ) {
            num_gpus = (int)ceil((double)N/nb);
        } else {
            num_gpus = num_gpus0;
        }

        for( d=0; d < num_gpus; d++ ) {
            n_local[d] = ((N/nb)/num_gpus)*nb;
            if (d < (N/nb)%num_gpus)
                n_local[d] += nb;
            else if (d == (N/nb)%num_gpus)
                n_local[d] += N%nb;
        }
        ldn_local = ((n_local[0]+31)/32)*32;
        
        /* upload the next big panel into GPU, transpose (A->A'), and pivot it */
        timer_start( time );
        magmablas_zsetmatrix_transpose_mgpu(num_gpus, stream, A(0,I), lda,
                                            dAT, ldn_local, dA, maxm, M, N, nb);
        for( d=0; d < num_gpus; d++ ) {
            magma_setdevice(d);
            magma_queue_sync( stream[d][0] );
            magma_queue_sync( stream[d][1] );
            magmablasSetKernelStream(NULL);
        }
        time_set += timer_stop( time );

        timer_start( time );
        /* == --------------------------------------------------------------- == */
        /* == loop around the previous big-panels to update the new big-panel == */
        for( offset = 0; offset < min(m,I); offset += NB ) {
            NBk = min( m-offset, NB );
            /* start sending the first tile from the previous big-panels to gpus */
            for( d=0; d < num_gpus; d++ ) {
                magma_setdevice(d);
                nbi  = min( nb, NBk );
                magma_zsetmatrix_async( (M-offset), nbi,
                                        A(offset,offset), lda,
                                        dA[d],            (maxm-offset), stream[d][0] );
                
                /* make sure the previous update finished */
                magmablasSetKernelStream(stream[d][0]);
                //magma_queue_sync( stream[d][1] );
                magma_queue_wait_event( stream[d][0], event[d][0] );
                
                /* transpose */
                magmablas_ztranspose( M-offset, nbi, dA[d], maxm-offset, dPT(d,0,0), nb );
            }
            
            /* applying the pivot from the previous big-panel */
            for( d=0; d < num_gpus; d++ ) {
                magma_setdevice(d);
                magmablasSetKernelStream(stream[d][1]);
                magmablas_zpermute_long3( dAT(d,0,0), ldn_local, ipiv, NBk, offset );
            }
            
            /* == going through each block-column of previous big-panels == */
            for( jj=0, ib=offset/nb; jj < NBk; jj += nb, ib++ ) {
                ii   = offset+jj;
                rows = maxm - ii;
                nbi  = min( nb, NBk-jj );
                for( d=0; d < num_gpus; d++ ) {
                    magma_setdevice(d);
                    
                    /* wait for a block-column on GPU */
                    magma_queue_sync( stream[d][0] );
                    
                    /* start sending next column */
                    if ( jj+nb < NBk ) {
                        magma_zsetmatrix_async( (M-ii-nb), min(nb,NBk-jj-nb),
                                                A(ii+nb,ii+nb), lda,
                                                dA[d],          (rows-nb), stream[d][0] );
                        
                        /* make sure the previous update finished */
                        magmablasSetKernelStream(stream[d][0]);
                        //magma_queue_sync( stream[d][1] );
                        magma_queue_wait_event( stream[d][0], event[d][(1+jj/nb)%2] );
                        
                        /* transpose next column */
                        magmablas_ztranspose( M-ii-nb, nb, dA[d], rows-nb, dPT(d,0,(1+jj/nb)%2), nb );
                    }
                    
                    /* update with the block column */
                    magmablasSetKernelStream(stream[d][1]);
                    magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
                                 n_local[d], nbi, c_one, dPT(d,0,(jj/nb)%2), nb, dAT(d,ib,0), ldn_local );
                    if ( M > ii+nb ) {
                        magma_zgemm( MagmaNoTrans, MagmaNoTrans,
                            n_local[d], M-(ii+nb), nbi, c_neg_one, dAT(d,ib,0), ldn_local,
                            dPT(d,1,(jj/nb)%2), nb, c_one, dAT(d,ib+1,0), ldn_local );
                    }
                    magma_event_record( event[d][(jj/nb)%2], stream[d][1] );
                
                } /* end of for each block-columns in a big-panel */
            }
        } /* end of for each previous big-panels */
        for( d=0; d < num_gpus; d++ ) {
            magma_setdevice(d);
            magma_queue_sync( stream[d][0] );
            magma_queue_sync( stream[d][1] );
            magmablasSetKernelStream(NULL);
        }

        /* calling magma-gpu interface to panel-factorize the big panel */
        if ( M > I ) {
            //magma_zgetrf1_mgpu(num_gpus, M-I, N, nb, I, dAT, ldn_local, ipiv+I, dA, A(0,I), lda,
            //                   (magma_queue_t **)stream, &iinfo);
            magma_zgetrf2_mgpu(num_gpus, M-I, N, nb, I, dAT, ldn_local, ipiv+I, dA, A(0,I), lda,
                               stream, &iinfo);
            if ( iinfo < 0 ) {
                *info = iinfo;
                break;
            } else if ( iinfo != 0 ) {
                *info = iinfo + I * NB;
                //break;
            }
            /* adjust pivots */
            for( ii=I; ii < min(I+N,m); ii++ )
                ipiv[ii] += I;
        }
        time_comp += timer_stop( time );

        /* download the current big panel to CPU */
        timer_start( time );
        magmablas_zgetmatrix_transpose_mgpu(num_gpus, stream, dAT, ldn_local, A(0,I), lda, dA, maxm, M, N, nb);
        for( d=0; d < num_gpus; d++ ) {
            magma_setdevice(d);
            magma_queue_sync( stream[d][0] );
            magma_queue_sync( stream[d][1] );
            magmablasSetKernelStream(NULL);
        }
        time_get += timer_stop( time );
    } /* end of for */

    timer_stop( time_total );
    flops = FLOPS_ZGETRF( m, n ) / 1e9;
    timer_printf(" memory-allocation time: %e\n", time_alloc );
    timer_printf(" NB=%d nb=%d\n", (int) NB, (int) nb );
    timer_printf(" memcopy and transpose %e seconds\n", time_set );
    timer_printf(" total time %e seconds\n", time_total );
    timer_printf(" Performance %f GFlop/s, %f seconds without htod and dtoh\n",     flops / (time_comp),               time_comp               );
    timer_printf(" Performance %f GFlop/s, %f seconds with    htod\n",              flops / (time_comp + time_set),    time_comp + time_set    );
    timer_printf(" Performance %f GFlop/s, %f seconds with    dtoh\n",              flops / (time_comp + time_get),    time_comp + time_get    );
    timer_printf(" Performance %f GFlop/s, %f seconds without memory-allocation\n", flops / (time_total - time_alloc), time_total - time_alloc );

    for( d=0; d < num_gpus0; d++ ) {
        magma_setdevice(d);
        magma_free( dA[d] );
        magma_event_destroy( event[d][0] );
        magma_event_destroy( event[d][1] );
        magma_queue_destroy( stream[d][0] );
        magma_queue_destroy( stream[d][1] );
        magmablasSetKernelStream(NULL);
    }
    magma_setdevice(0);
    
    }
    if ( *info >= 0 ) magma_zgetrf_piv(m, n, NB, A, lda, ipiv, info);
    return *info;
} /* magma_zgetrf_m */