void magmaf_dgetrf_piv( magma_int_t *m, magma_int_t *n, magma_int_t *NB, double *a, magma_int_t *lda, magma_int_t *ipiv, magma_int_t *info ) { magma_dgetrf_piv( *m, *n, *NB, a, *lda, ipiv, info ); }
/** Purpose ------- DGETRF_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 DOUBLE_PRECISION 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_dgesv_comp ********************************************************************/ extern "C" magma_int_t magma_dgetrf_m(magma_int_t num_gpus, magma_int_t m, magma_int_t n, double *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; double c_one = MAGMA_D_ONE; double c_neg_one = MAGMA_D_NEG_ONE; double *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_dgetrf_nb(m); maxm = ((m + 31)/32)*32; /* figure out NB */ size_t freeMem, totalMem; cudaMemGetInfo( &freeMem, &totalMem ); freeMem /= sizeof(double); /* 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_DGETRF_OOC printf( " * still fit in GPU memory.\n" ); #endif NB = n; } else { #ifdef CHECK_DGETRF_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_DGETRF_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_dgetrf(&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_dmalloc( &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_dsetmatrix_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_dsetmatrix_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_dtranspose( 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_dpermute_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_dsetmatrix_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_dtranspose( 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_dtrsm( 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_dgemm( 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_dgetrf1_mgpu(num_gpus, M-I, N, nb, I, dAT, ldn_local, ipiv+I, dA, A(0,I), lda, // (magma_queue_t **)stream, &iinfo); magma_dgetrf2_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_dgetmatrix_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_DGETRF( 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_dgetrf_piv(m, n, NB, A, lda, ipiv, info); return *info; } /* magma_dgetrf_m */