void magmaf_dpotrf_m( magma_int_t *num_gpus, magma_uplo_t *uplo, magma_int_t *n, double *A, magma_int_t *lda, magma_int_t *info ) { magma_dpotrf_m( *num_gpus, *uplo, *n, A, *lda, info ); }
int main() { //Magma initialization magma_init(); //Declaration of local variables double *a, *b, *dev_a, results=0; const int N=16384; int i,j; magma_int_t info=0, lda=N, ngpu=6; //Memory Allocation Segment magma_malloc_pinned((void**) &a,(N*N)*sizeof(double)); magma_malloc_pinned((void**) &b,(N*N)*sizeof(double)); //Generate two copies of Symmetric Positive Definite Matrix for(i=0;i<N;i++) { for(j=0;j<i;j++) { a[i*N+j] = 1e-9* (double)rand(); a[j*N+i] = a[i*N+j]; b[i*N+j] = a[i*N+j]; b[j*N+i] = b[i*N+j]; } a[i*N+i] = 1e-9*(double)rand() + 1000.0; b[i*N+i] = a[i*N+i]; } /* for(i=0;i<20;i++) { printf("%g\t%g\n",a[i],a[i*N]); } printf("*******************\n"); for(i=0;i<20;i++) { printf("%g\t%g\n",b[i],b[i*N]); }*/ //Call custom Magma Cholesky for obtaining results rr_dpotrf_m(ngpu,MagmaUpper,N,a,N,&info); sleep(1); //Call Standard Magma Cholesky for result validation magma_dpotrf_m(ngpu,MagmaUpper,N,b,N,&info); if(info != 0) { printf("magma_dpotrf original returned error %d: %s. \n",(int) info, magma_strerror(info)); } //print some values /*for(i=0;i<20;i++) { printf("%g\t%g\n",a[i],a[i*N]); } printf("*******************\n"); for(i=0;i<20;i++) { printf("%g\t%g\n",b[i],b[i*N]); }*/ //Validate the results; Compute the RMS error value. for(i=0;i<N;i++) for(j=i;j<N;j++) results = results + (a[i*N+j] - b[i*N+j]) * (a[i*N+j] - b[i*N+j]); //Display the results of the test if(results < 1e-5) printf("The two functions have identical results\n"); else printf("The custom function had significant errors. The RMS value was %g\n",results); magma_free_pinned(a); magma_free_pinned(b); magma_finalize(); return 0; }
SEXP magmaCholeskyFinal_m(SEXP A, SEXP n, SEXP NB, SEXP zeroTri, SEXP ngpu, SEXP lowerTri) { magma_init(); int ndevices; double *h_R; ndevices = INTEGER_VALUE(ngpu); int idevice; for(idevice=0; idevice < ndevices; idevice++) { magma_setdevice(idevice); if(CUBLAS_STATUS_SUCCESS != cublasInit()) { printf("Error: gpu %d: cublasInit failed\n", idevice); magma_finalize(); exit(-1); } } // magma_print_devices(); int In, INB; In = INTEGER_VALUE(n); INB = INTEGER_VALUE(NB); double *PA = NUMERIC_POINTER(A); int i,j; //magma_timestr_t start, end; double gpu_time; printf("Inside magma_dpotrf_m"); /*for(i = 0; i < 5; i++) { for(j = 0; j < 5; j++) { printf("%.8f ", PA[i+j*In]); } printf("\n"); } */ magma_int_t N, status, info, nGPU, n2, lda; clock_t t1, t2; N = In; status = 0; int nGPUs = ndevices; lda = N; n2 = lda*N; if ( MAGMA_SUCCESS != magma_malloc_pinned( (void**) &h_R, (n2)*sizeof(double) )) { fprintf( stderr, "!!!! magma_malloc_pinned failed for: %s\n", h_R ); magma_finalize(); exit(-1); } lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, PA, &lda, h_R, &lda ); //printf("Modified by Vinay in 2 GPU\n"); //INB = magma_get_dpotrf_nb(N); // INB = 224; // printf("INB = %d\n", INB); //ngpu = ndevices; // printf("ngpu = %d\n", ngpu); //max_size = INB*(1+N/(INB*ndevices))*INB*((N+INB-1)/INB); // printf("max_size = %d\n", max_size); //int imax_size = max_size; //double *dA; //magma_dmalloc_pinned((void**)&dA, In*In*sizeof(double)); //ldda = (1+N/(INB*ndevices))*INB; // printf("ldda = %d\n", ldda); //magma_dsetmatrix_1D_row_bcyclic(N, N, PA, N, dA, ldda, ngpu, INB); //magma_dpotrf_mgpu(ngpu, MagmaLower, N, dA, ldda, &info); int lTri; lTri = INTEGER_VALUE(lowerTri); if(lTri){ t1 = clock(); magma_dpotrf_m(nGPUs, MagmaLower, N, h_R, N, &info); t2 = clock (); } else{ t1 = clock(); magma_dpotrf_m(nGPUs, MagmaUpper, N, h_R, N, &info); t2 = clock (); } gpu_time = (double) (t2-t1)/(CLOCKS_PER_SEC) ; // Magma time printf (" magma_dpotrf_m time : %f sec. \n", gpu_time ); if(info != 0) { printf("magma_dpotrf returned error %d: %s.\n", (int) info, magma_strerror(info)); } //magma_dgetmatrix_1D_row_bcyclic(N, N, dA, ldda, PA, N, ngpu, INB); //for(dev = 0; dev < ndevices; dev++) //{ //magma_setdevice(dev); //cudaFree(dA[dev]); //} lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_R, &lda, PA, &lda ); magma_free_pinned(h_R); magma_finalize(); cublasShutdown(); int IZeroTri; IZeroTri = INTEGER_VALUE(zeroTri); if(IZeroTri & lTri) { for(i = 1; i < In; i++) { for(j=0; j< i; j++) { PA[i*In+j] = 0.0; } } } else if(IZeroTri){ for(i = 0; i < In; i++) { for(j=i+1; j < In; j++) { PA[i*In+j] = 0.0; } } } return(R_NilValue); }
/** Purpose ------- DSYGVDX_2STAGE computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be Hermitian and B is also positive definite. It uses a two-stage algorithm for the tridiagonalization. If eigenvectors are desired, it uses a divide and conquer algorithm. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. Arguments --------- @param[in] nrgpu INTEGER Number of GPUs to use. @param[in] itype INTEGER Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x @param[in] range magma_range_t - = MagmaRangeAll: all eigenvalues will be found. - = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU] will be found. - = MagmaRangeI: the IL-th through IU-th eigenvalues will be found. @param[in] jobz magma_vec_t - = MagmaNoVec: Compute eigenvalues only; - = MagmaVec: Compute eigenvalues and eigenvectors. @param[in] uplo magma_uplo_t - = MagmaUpper: Upper triangles of A and B are stored; - = MagmaLower: Lower triangles of A and B are stored. @param[in] n INTEGER The order of the matrices A and B. N >= 0. @param[in,out] A DOUBLE PRECISION array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. \n On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I. If JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper) or the lower triangle (if UPLO=MagmaLower) of A, including the diagonal, is destroyed. @param[in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). @param[in,out] B DOUBLE PRECISION array, dimension (LDB, N) On entry, the Hermitian matrix B. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = MagmaLower, the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B. \n On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H. @param[in] ldb INTEGER The leading dimension of the array B. LDB >= max(1,N). @param[in] vl DOUBLE PRECISION @param[in] vu DOUBLE PRECISION If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI. @param[in] il INTEGER @param[in] iu INTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV. @param[out] m INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1. @param[out] w DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. @param[out] work (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. @param[in] lwork INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LWORK >= LQ2 + 2*N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= LQ2 + 1 + 6*N + 2*N**2. where LQ2 is the size needed to store the Q2 matrix and is returned by magma_bulge_get_lq2. \n If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. @param[out] iwork (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. @param[in] liwork INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1. If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N. \n If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. @param[out] info INTEGER - = 0: successful exit - < 0: if INFO = -i, the i-th argument had an illegal value - > 0: ZPOTRF or ZHEEVD returned an error code: <= N: if INFO = i and JOBZ = MagmaNoVec, then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = MagmaVec, then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1); > N: if INFO = N + i, for 1 <= i <= N, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. Further Details --------------- Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA Modified so that no backsubstitution is performed if ZHEEVD fails to converge (NEIG in old code could be greater than N causing out of bounds reference to A - reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05. @ingroup magma_dsygv_driver ********************************************************************/ extern "C" magma_int_t magma_dsygvdx_2stage_m(magma_int_t nrgpu, magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, double *A, magma_int_t lda, double *B, magma_int_t ldb, double vl, double vu, magma_int_t il, magma_int_t iu, magma_int_t *m, double *w, double *work, magma_int_t lwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) { const char* uplo_ = lapack_uplo_const( uplo ); const char* jobz_ = lapack_vec_const( jobz ); double d_one = MAGMA_D_ONE; magma_int_t lower; magma_trans_t trans; magma_int_t wantz; magma_int_t lquery; magma_int_t alleig, valeig, indeig; magma_int_t lwmin; magma_int_t liwmin; /* determine the number of threads */ magma_int_t parallel_threads = magma_get_parallel_numthreads(); wantz = (jobz == MagmaVec); lower = (uplo == MagmaLower); alleig = (range == MagmaRangeAll); valeig = (range == MagmaRangeV); indeig = (range == MagmaRangeI); lquery = (lwork == -1 || liwork == -1); *info = 0; if (itype < 1 || itype > 3) { *info = -1; } else if (! (alleig || valeig || indeig)) { *info = -2; } else if (! (wantz || (jobz == MagmaNoVec))) { *info = -3; } else if (! (lower || (uplo == MagmaUpper))) { *info = -4; } else if (n < 0) { *info = -5; } else if (lda < max(1,n)) { *info = -7; } else if (ldb < max(1,n)) { *info = -9; } else { if (valeig) { if (n > 0 && vu <= vl) { *info = -11; } } else if (indeig) { if (il < 1 || il > max(1,n)) { *info = -12; } else if (iu < min(n,il) || iu > n) { *info = -13; } } } magma_int_t nb = magma_get_dbulge_nb(n, parallel_threads); magma_int_t lq2 = magma_dbulge_get_lq2(n, parallel_threads); if (wantz) { lwmin = lq2 + 1 + 6*n + 2*n*n; liwmin = 3 + 5*n; } else { lwmin = 2*n + n*nb; liwmin = 1; } // multiply by 1+eps (in Double!) to ensure length gets rounded up, // if it cannot be exactly represented in floating point. real_Double_t one_eps = 1. + lapackf77_dlamch("Epsilon"); work[0] = lwmin * one_eps; iwork[0] = liwmin; if (lwork < lwmin && ! lquery) { *info = -17; } else if (liwork < liwmin && ! lquery) { *info = -19; } if (*info != 0) { magma_xerbla( __func__, -(*info)); return *info; } else if (lquery) { return *info; } /* Quick return if possible */ if (n == 0) { return *info; } /* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */ if (n <= 128) { #ifdef ENABLE_DEBUG printf("--------------------------------------------------------------\n"); printf(" warning matrix too small N=%d NB=%d, calling lapack on CPU \n", (int) n, (int) nb); printf("--------------------------------------------------------------\n"); #endif lapackf77_dsygvd(&itype, jobz_, uplo_, &n, A, &lda, B, &ldb, w, work, &lwork, iwork, &liwork, info); *m = n; return *info; } /* Form A Cholesky factorization of B. */ magma_timer_t time=0; timer_start( time ); magma_dpotrf_m(nrgpu, uplo, n, B, ldb, info); if (*info != 0) { *info = n + *info; return *info; } timer_stop( time ); timer_printf( "time dpotrf_m = %6.2f\n", time ); timer_start( time ); /* Transform problem to standard eigenvalue problem and solve. */ magma_dsygst_m(nrgpu, itype, uplo, n, A, lda, B, ldb, info); timer_stop( time ); timer_printf( "time dsygst_m = %6.2f\n", time ); timer_start( time ); magma_dsyevdx_2stage_m(nrgpu, jobz, range, uplo, n, A, lda, vl, vu, il, iu, m, w, work, lwork, iwork, liwork, info); timer_stop( time ); timer_printf( "time dsyevdx_2stage_m = %6.2f\n", time ); if (wantz && *info == 0) { timer_start( time ); /* Backtransform eigenvectors to the original problem. */ if (itype == 1 || itype == 2) { /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ if (lower) { trans = MagmaTrans; } else { trans = MagmaNoTrans; } magma_dtrsm_m(nrgpu, MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, d_one, B, ldb, A, lda); } else if (itype == 3) { /* For B*A*x=(lambda)*x; backtransform eigenvectors: x = L*y or U'*y */ if (lower) { trans = MagmaNoTrans; } else { trans = MagmaTrans; } //magma_dtrmm_m(nrgpu, MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, d_one, B, ldb, A, lda); printf("--- the multi GPU version is falling back to 1 GPU to perform the last TRMM since there is no TRMM_mgpu --- \n"); double *dA=NULL, *dB=NULL; magma_int_t ldda = n; magma_int_t lddb = n; if (MAGMA_SUCCESS != magma_dmalloc( &dB, n*lddb ) ) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } if (MAGMA_SUCCESS != magma_dmalloc( &dA, n*ldda ) ) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magma_dsetmatrix( n, n, B, ldb, dB, lddb ); magma_dsetmatrix( n, n, A, lda, dA, ldda ); magma_dtrmm(MagmaLeft, uplo, trans, MagmaNonUnit, n, n, d_one, dB, lddb, dA, ldda); magma_dgetmatrix( n, n, dA, ldda, A, lda ); } timer_stop( time ); timer_printf( "time dtrsm/mm + getmatrix = %6.2f\n", time ); } work[0] = lwmin * one_eps; iwork[0] = liwmin; return *info; } /* magma_dsygvdx_2stage_m */
/** Purpose ------- DPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix A. This version does not require work space on the GPU passed as input. GPU memory is allocated in the routine. The factorization has the form A = U**H * U, if uplo = MagmaUpper, or A = L * L**H, if uplo = MagmaLower, where U is an upper triangular matrix and L is lower triangular. This is the block version of the algorithm, calling Level 3 BLAS. This uses multiple queues to overlap communication and computation. Arguments --------- @param[in] uplo magma_uplo_t - = MagmaUpper: Upper triangle of A is stored; - = MagmaLower: Lower triangle of A is stored. @param[in] n INTEGER The order of the matrix A. N >= 0. @param[in,out] A DOUBLE PRECISION array, dimension (LDA,N) On entry, the symmetric matrix A. If uplo = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. \n On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**H * U or A = L * L**H. \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,N). @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, the leading minor of order i is not positive definite, and the factorization could not be completed. @ingroup magma_dposv_comp ********************************************************************/ extern "C" magma_int_t magma_dpotrf( magma_uplo_t uplo, magma_int_t n, double *A, magma_int_t lda, magma_int_t *info ) { #define A(i_, j_) (A + (i_) + (j_)*lda) #ifdef HAVE_clBLAS #define dA(i_, j_) dA, ((i_) + (j_)*ldda) #else #define dA(i_, j_) (dA + (i_) + (j_)*ldda) #endif /* Constants */ const double c_one = MAGMA_D_ONE; const double c_neg_one = MAGMA_D_NEG_ONE; const double d_one = 1.0; const double d_neg_one = -1.0; /* Local variables */ const char* uplo_ = lapack_uplo_const( uplo ); bool upper = (uplo == MagmaUpper); magma_int_t j, jb, ldda, nb; magmaDouble_ptr dA = NULL; /* Check arguments */ *info = 0; if (! upper && uplo != MagmaLower) { *info = -1; } else if (n < 0) { *info = -2; } else if (lda < max(1,n)) { *info = -4; } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } /* Quick return */ if ( n == 0 ) return *info; nb = magma_get_dpotrf_nb( n ); if (nb <= 1 || nb >= n) { lapackf77_dpotrf( uplo_, &n, A, &lda, info ); } else { /* Use hybrid blocked code. */ ldda = magma_roundup( n, 32 ); magma_int_t ngpu = magma_num_gpus(); if ( ngpu > 1 ) { /* call multi-GPU non-GPU-resident interface */ return magma_dpotrf_m( ngpu, uplo, n, A, lda, info ); } if (MAGMA_SUCCESS != magma_dmalloc( &dA, n*ldda )) { /* alloc failed so call the non-GPU-resident version */ return magma_dpotrf_m( ngpu, uplo, n, A, lda, info ); } magma_queue_t queues[2] = { NULL, NULL }; magma_device_t cdev; magma_getdevice( &cdev ); magma_queue_create( cdev, &queues[0] ); magma_queue_create( cdev, &queues[1] ); if (upper) { /* Compute the Cholesky factorization A = U'*U. */ for (j=0; j < n; j += nb) { /* Update and factorize the current diagonal block and test for non-positive-definiteness. */ jb = min( nb, n-j ); magma_dsetmatrix_async( jb, n-j, A(j, j), lda, dA(j, j), ldda, queues[1] ); magma_dsyrk( MagmaUpper, MagmaConjTrans, jb, j, d_neg_one, dA(0, j), ldda, d_one, dA(j, j), ldda, queues[1] ); magma_queue_sync( queues[1] ); magma_dgetmatrix_async( jb, jb, dA(j, j), ldda, A(j, j), lda, queues[0] ); if (j+jb < n) { magma_dgemm( MagmaConjTrans, MagmaNoTrans, jb, n-j-jb, j, c_neg_one, dA(0, j ), ldda, dA(0, j+jb), ldda, c_one, dA(j, j+jb), ldda, queues[1] ); } magma_queue_sync( queues[0] ); // this could be on any queue; it isn't needed until exit. magma_dgetmatrix_async( j, jb, dA(0, j), ldda, A(0, j), lda, queues[0] ); lapackf77_dpotrf( MagmaUpperStr, &jb, A(j, j), &lda, info ); if (*info != 0) { *info = *info + j; break; } magma_dsetmatrix_async( jb, jb, A(j, j), lda, dA(j, j), ldda, queues[0] ); magma_queue_sync( queues[0] ); if (j+jb < n) { magma_dtrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit, jb, n-j-jb, c_one, dA(j, j ), ldda, dA(j, j+jb), ldda, queues[1] ); } } } else { //used for timing CPU and GPU int iter = 0; float cpu_time = 0.0; float gpu_time = 0.0; double gpu_iter1_low = 2103.143311; double gpu_iter1_high = 754.506104; double cpu_iter1_low = 794.636108; double cpu_iter1_high = 600.295227; double gpu_pred_high = gpu_iter1_high; double gpu_pred_low = gpu_iter1_low; double cpu_pred_high = cpu_iter1_high; double cpu_pred_low = cpu_iter1_low; double ratio_split_freq = 0; double time_until_interrupt = 0; cudaEvent_t start_cpu, stop_cpu; cudaEvent_t start_gpu, stop_gpu; // switches for different modes bool timing = false; //for initial setting only, greatly impact performance bool dvfs = false; //turn on dvfs energy saving bool relax = false; //turn on relax scheme bool r2h = false; // turn on race to halt //these parameters need to be tuned in future works. double dvfs_converage = 0.5; double prediction_offset_gpu = 0.65; double prediction_offset_cpu = 0.65; //========================================================= // Compute the Cholesky factorization A = L*L'. for (j=0; j < n; j += nb) { // Update and factorize the current diagonal block and test // for non-positive-definiteness. jb = min( nb, n-j ); magma_dsetmatrix_async( n-j, jb, A(j, j), lda, dA(j, j), ldda, queues[1] ); magma_dsyrk( MagmaLower, MagmaNoTrans, jb, j, d_neg_one, dA(j, 0), ldda, d_one, dA(j, j), ldda, queues[1] ); magma_queue_sync( queues[1] ); magma_dgetmatrix_async( jb, jb, dA(j,j), ldda, A(j,j), lda, queues[0] ); if (timing) { //start gpu timing cudaEventCreate(&start_gpu); cudaEventCreate(&stop_gpu); cudaEventRecord(start_gpu, 0); } if (j+jb < n) { magma_dgemm( MagmaNoTrans, MagmaConjTrans, n-j-jb, jb, j, c_neg_one, dA(j+jb, 0), ldda, dA(j, 0), ldda, c_one, dA(j+jb, j), ldda, queues[1] ); } double ratio_slack_pred = 1.0 - (double)nb/(n-iter*nb); cpu_pred_high = cpu_pred_high * ratio_slack_pred; cpu_pred_low = cpu_pred_low * ratio_slack_pred; gpu_pred_high = gpu_pred_high * ratio_slack_pred * ratio_slack_pred; gpu_pred_low = gpu_pred_low * ratio_slack_pred * ratio_slack_pred; if (timing) { printf("iter:%d GPU time pred:%f\n", iter, gpu_pred_high); printf("iter:%d CPU time pred:%f\n", iter, cpu_pred_high); } if (iter < dvfs_converage*(n/nb)) { if (cpu_pred_high > gpu_pred_high) { //slack on GPU ratio_split_freq = (cpu_pred_high - gpu_pred_high) / (gpu_pred_high * ((gpu_iter1_low / gpu_iter1_high) - 1)); time_until_interrupt = gpu_pred_low * ratio_split_freq; //printf("iter:%d time_until_interrupt:%f\n", iter, time_until_interrupt); // printf("iter:%d ratio_split_freq:%f\n", iter, ratio_split_freq); if (dvfs) { if ((!relax) || (relax && ratio_split_freq > 0.05)) { if (ratio_split_freq < 1) dvfs_adjust(time_until_interrupt*prediction_offset_gpu, 'g'); else dvfs_adjust(cpu_pred_high, 'g'); } } else if (r2h) { r2h_adjust(gpu_pred_high, cpu_pred_high - gpu_pred_high, 'g'); } } else { //slack on CPU ratio_split_freq = (gpu_pred_high - cpu_pred_high) / (cpu_pred_high * ((cpu_iter1_low / cpu_iter1_high) - 1)); time_until_interrupt = cpu_pred_low * ratio_split_freq; if (dvfs) { if ((!relax) || (relax && ratio_split_freq > 0.05)) { if (ratio_split_freq < 1) dvfs_adjust(time_until_interrupt*prediction_offset_cpu, 'c'); else dvfs_adjust(gpu_pred_high, 'c'); } } else if (r2h) { r2h_adjust(cpu_pred_high, gpu_pred_high - cpu_pred_high, 'c'); } } } if (timing) { //end gpu timing cudaEventRecord(stop_gpu, 0); cudaEventSynchronize(stop_gpu); cudaEventElapsedTime(&gpu_time, start_gpu, stop_gpu); cudaEventDestroy(start_gpu); cudaEventDestroy(stop_gpu); //printf("iter:%d GPU time:%f\n", iter, gpu_time); } magma_queue_sync( queues[0] ); // this could be on any queue; it isn't needed until exit. magma_dgetmatrix_async( jb, j, dA(j, 0), ldda, A(j, 0), lda, queues[0] ); if (timing) { //start cpu timing cudaEventCreate(&start_cpu); cudaEventCreate(&stop_cpu); cudaEventRecord(start_cpu, 0); } lapackf77_dpotrf( MagmaLowerStr, &jb, A(j, j), &lda, info ); if (timing) { //end cpu timing cudaEventRecord(stop_cpu, 0); cudaEventSynchronize(stop_cpu); cudaEventElapsedTime(&cpu_time, start_cpu, stop_cpu); cudaEventDestroy(start_cpu); cudaEventDestroy(stop_cpu); // printf("iter:%d CPU time:%f\n", iter, cpu_time); // if (gpu_time < cpu_time) { // printf("slack: +\n"); // } else { // printf("slack: -\n"); // } } if (*info != 0) { *info = *info + j; break; } magma_dsetmatrix_async( jb, jb, A(j, j), lda, dA(j, j), ldda, queues[0] ); magma_queue_sync( queues[0] ); if (j+jb < n) { magma_dtrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit, n-j-jb, jb, c_one, dA(j, j), ldda, dA(j+jb, j), ldda, queues[1] ); } } } magma_queue_destroy( queues[0] ); magma_queue_destroy( queues[1] ); magma_free( dA ); } return *info; } /* magma_dpotrf */
/** Purpose ------- DPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix A. This version does not require work space on the GPU passed as input. GPU memory is allocated in the routine. The factorization has the form A = U**H * U, if uplo = MagmaUpper, or A = L * L**H, if uplo = MagmaLower, where U is an upper triangular matrix and L is lower triangular. This is the block version of the algorithm, calling Level 3 BLAS. If the current stream is NULL, this version replaces it with a new stream to overlap computation with communication. Arguments --------- @param[in] uplo magma_uplo_t - = MagmaUpper: Upper triangle of A is stored; - = MagmaLower: Lower triangle of A is stored. @param[in] n INTEGER The order of the matrix A. N >= 0. @param[in,out] A DOUBLE_PRECISION array, dimension (LDA,N) On entry, the symmetric matrix A. If uplo = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. \n On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**H * U or A = L * L**H. \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,N). @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, the leading minor of order i is not positive definite, and the factorization could not be completed. @ingroup magma_dposv_comp ********************************************************************/ extern "C" magma_int_t magma_dpotrf( magma_uplo_t uplo, magma_int_t n, double *A, magma_int_t lda, magma_int_t *info) { #define A(i_, j_) (A + (j_)*lda + (i_)) #define dA(i_, j_) (dA + (j_)*ldda + (i_)) /* Local variables */ const char* uplo_ = lapack_uplo_const( uplo ); magma_int_t ldda, nb; magma_int_t j, jb; double c_one = MAGMA_D_ONE; double c_neg_one = MAGMA_D_NEG_ONE; magmaDouble_ptr dA; double d_one = 1.0; double d_neg_one = -1.0; int upper = (uplo == MagmaUpper); *info = 0; if (! upper && uplo != MagmaLower) { *info = -1; } else if (n < 0) { *info = -2; } else if (lda < max(1,n)) { *info = -4; } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } /* Quick return */ if ( n == 0 ) return *info; magma_int_t ngpu = magma_num_gpus(); if ( ngpu > 1 ) { /* call multiple-GPU interface */ return magma_dpotrf_m(ngpu, uplo, n, A, lda, info); } ldda = ((n+31)/32)*32; if (MAGMA_SUCCESS != magma_dmalloc( &dA, (n)*ldda )) { /* alloc failed so call the non-GPU-resident version */ return magma_dpotrf_m(ngpu, uplo, n, A, lda, info); } /* Define user stream if current stream is NULL */ magma_queue_t stream[3]; magma_queue_t orig_stream; magmablasGetKernelStream( &orig_stream ); magma_queue_create( &stream[0] ); magma_queue_create( &stream[2] ); if (orig_stream == NULL) { magma_queue_create( &stream[1] ); magmablasSetKernelStream(stream[1]); } else { stream[1] = orig_stream; } nb = magma_get_dpotrf_nb(n); if (nb <= 1 || nb >= n) { lapackf77_dpotrf(uplo_, &n, A, &lda, info); } else { /* Use hybrid blocked code. */ if (upper) { /* Compute the Cholesky factorization A = U'*U. */ for (j=0; j < n; j += nb) { /* Update and factorize the current diagonal block and test for non-positive-definiteness. Computing MIN */ jb = min(nb, (n-j)); magma_dsetmatrix_async( jb, (n-j), A(j, j), lda, dA(j, j), ldda, stream[1]); magma_dsyrk(MagmaUpper, MagmaConjTrans, jb, j, d_neg_one, dA(0, j), ldda, d_one, dA(j, j), ldda); magma_queue_sync( stream[1] ); magma_dgetmatrix_async( jb, jb, dA(j, j), ldda, A(j, j), lda, stream[0] ); if ( (j+jb) < n) { magma_dgemm(MagmaConjTrans, MagmaNoTrans, jb, (n-j-jb), j, c_neg_one, dA(0, j ), ldda, dA(0, j+jb), ldda, c_one, dA(j, j+jb), ldda); } magma_dgetmatrix_async( j, jb, dA(0, j), ldda, A (0, j), lda, stream[2] ); magma_queue_sync( stream[0] ); lapackf77_dpotrf(MagmaUpperStr, &jb, A(j, j), &lda, info); if (*info != 0) { *info = *info + j; break; } magma_dsetmatrix_async( jb, jb, A(j, j), lda, dA(j, j), ldda, stream[0] ); magma_queue_sync( stream[0] ); if ( (j+jb) < n ) { magma_dtrsm(MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit, jb, (n-j-jb), c_one, dA(j, j ), ldda, dA(j, j+jb), ldda); } } } else { //========================================================= // Compute the Cholesky factorization A = L*L'. for (j=0; j < n; j += nb) { // Update and factorize the current diagonal block and test // for non-positive-definiteness. Computing MIN jb = min(nb, (n-j)); magma_dsetmatrix_async( (n-j), jb, A(j, j), lda, dA(j, j), ldda, stream[1]); magma_dsyrk(MagmaLower, MagmaNoTrans, jb, j, d_neg_one, dA(j, 0), ldda, d_one, dA(j, j), ldda); magma_queue_sync( stream[1] ); magma_dgetmatrix_async( jb, jb, dA(j,j), ldda, A(j,j), lda, stream[0] ); if ( (j+jb) < n) { magma_dgemm( MagmaNoTrans, MagmaConjTrans, (n-j-jb), jb, j, c_neg_one, dA(j+jb, 0), ldda, dA(j, 0), ldda, c_one, dA(j+jb, j), ldda); } magma_dgetmatrix_async( jb, j, dA(j, 0), ldda, A(j, 0), lda, stream[2] ); magma_queue_sync( stream[0] ); lapackf77_dpotrf(MagmaLowerStr, &jb, A(j, j), &lda, info); if (*info != 0) { *info = *info + j; break; } magma_dsetmatrix_async( jb, jb, A(j, j), lda, dA(j, j), ldda, stream[0] ); magma_queue_sync( stream[0] ); if ( (j+jb) < n) { magma_dtrsm(MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit, (n-j-jb), jb, c_one, dA(j, j), ldda, dA(j+jb, j), ldda); } } } } magma_queue_destroy( stream[0] ); magma_queue_destroy( stream[2] ); if (orig_stream == NULL) { magma_queue_destroy( stream[1] ); } magmablasSetKernelStream( orig_stream ); magma_free( dA ); return *info; } /* magma_dpotrf */