extern "C" magma_int_t magma_ssygvd(magma_int_t itype, char jobz, char uplo, magma_int_t n, float *a, magma_int_t lda, float *b, magma_int_t ldb, float *w, float *work, magma_int_t lwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) { /* -- MAGMA (version 1.3.0) -- Univ. of Tennessee, Knoxville Univ. of California, Berkeley Univ. of Colorado, Denver November 2012 Purpose ======= SSYGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-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 symmetric and B is also positive definite. 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 ========= ITYPE (input) 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 JOBZ (input) CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO (input) CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored. N (input) INTEGER The order of the matrices A and B. N >= 0. A (input/output) COMPLEX*16 array, dimension (LDA, N) On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**T * B * Z = I; if ITYPE = 3, Z**T * inv(B) * Z = I. If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). B (input/output) COMPLEX*16 array, dimension (LDB, N) On entry, the symmetric matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B. 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**T * U or B = L * L**T. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). W (output) DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= 2*N*nb + 1. If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N*nb + 2*N**2. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. LIWORK (input) INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = 'N' and N > 1, LIWORK >= 1. If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: SPOTRF or SSYEVD returned an error code: <= N: if INFO = i and JOBZ = 'N', 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 = 'V', 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 SSYEVD 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. ===================================================================== */ char uplo_[2] = {uplo, 0}; char jobz_[2] = {jobz, 0}; float d_one = MAGMA_S_ONE; float *da; float *db; magma_int_t ldda = n; magma_int_t lddb = n; magma_int_t lower; char trans[1]; magma_int_t wantz, lquery; magma_int_t lopt, lwmin, liopt, liwmin; cudaStream_t stream; magma_queue_create( &stream ); wantz = lapackf77_lsame(jobz_, MagmaVectorsStr); lower = lapackf77_lsame(uplo_, MagmaLowerStr); lquery = lwork == -1 || liwork == -1; *info = 0; if (itype < 1 || itype > 3) { *info = -1; } else if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVectorsStr))) { *info = -2; } else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) { *info = -3; } else if (n < 0) { *info = -4; } else if (lda < max(1,n)) { *info = -6; } else if (ldb < max(1,n)) { *info = -8; } magma_int_t nb = magma_get_ssytrd_nb(n); if (n < 1) { liwmin = 1; lwmin = 1; } else if (wantz) { lwmin = 1 + 6 * n * nb + 2* n * n; liwmin = 5 * n + 3; } else { lwmin = 2 * n * nb + 1; liwmin = 1; } lopt = lwmin; liopt = liwmin; work[ 0] = lopt; iwork[0] = liopt; if (lwork < lwmin && ! lquery) { *info = -11; } else if (liwork < liwmin && ! lquery) { *info = -13; } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return MAGMA_ERR_ILLEGAL_VALUE; } else if (lquery) { return MAGMA_SUCCESS; } /* Quick return if possible */ if (n == 0) { return 0; } if (MAGMA_SUCCESS != magma_smalloc( &da, n*ldda ) || MAGMA_SUCCESS != magma_smalloc( &db, n*lddb )) { *info = -17; return MAGMA_ERR_DEVICE_ALLOC; } /* Form a Cholesky factorization of B. */ magma_ssetmatrix( n, n, b, ldb, db, lddb ); magma_ssetmatrix_async( n, n, a, lda, da, ldda, stream ); magma_spotrf_gpu(uplo_[0], n, db, lddb, info); if (*info != 0) { *info = n + *info; return 0; } magma_queue_sync( stream ); magma_sgetmatrix_async( n, n, db, lddb, b, ldb, stream ); /* Transform problem to standard eigenvalue problem and solve. */ magma_ssygst_gpu(itype, uplo_[0], n, da, ldda, db, lddb, info); magma_ssyevd_gpu(jobz_[0], uplo_[0], n, da, ldda, w, a, lda, work, lwork, iwork, liwork, info); lopt = max( lopt, (magma_int_t) work[0]); liopt = max(liopt, iwork[0]); if (wantz && *info == 0) { /* 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) { *(unsigned char *)trans = MagmaTrans; } else { *(unsigned char *)trans = MagmaNoTrans; } magma_strsm(MagmaLeft, uplo_[0], *trans, MagmaNonUnit, n, n, d_one, db, lddb, da, ldda); } else if (itype == 3) { /* For B*A*x=(lambda)*x; backtransform eigenvectors: x = L*y or U'*y */ if (lower) { *(unsigned char *)trans = MagmaNoTrans; } else { *(unsigned char *)trans = MagmaTrans; } magma_strmm(MagmaLeft, uplo_[0], *trans, MagmaNonUnit, n, n, d_one, db, lddb, da, ldda); } magma_sgetmatrix( n, n, da, ldda, a, lda ); } magma_queue_sync( stream ); magma_queue_destroy( stream ); work[0] = (float) lopt; iwork[0] = liopt; magma_free( da ); magma_free( db ); return MAGMA_SUCCESS; } /* magma_ssygvd */
extern "C" magma_err_t magma_sposv_gpu( magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaFloat_ptr dA, size_t dA_offset, magma_int_t ldda, magmaFloat_ptr dB, size_t dB_offset, magma_int_t lddb, magma_err_t *info, magma_queue_t queue ) { /* -- clMagma (version 0.1) -- Univ. of Tennessee, Knoxville Univ. of California, Berkeley Univ. of Colorado, Denver @date January 2014 Purpose ======= SPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices. The Cholesky decomposition is used to factor A as A = U**T * U, if UPLO = 'U', or A = L * L**T, if UPLO = 'L', where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B. Arguments ========= UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. dA (input/output) REAL array on the GPU, dimension (LDDA,N) On entry, the symmetric matrix dA. If UPLO = 'U', the leading N-by-N upper triangular part of dA contains the upper triangular part of the matrix dA, and the strictly lower triangular part of dA is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of dA contains the lower triangular part of the matrix dA, and the strictly upper triangular part of dA is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization dA = U**T*U or dA = L*L**T. LDDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). dB (input/output) REAL array on the GPU, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value ===================================================================== */ magma_err_t ret; *info = 0 ; if( (uplo != MagmaUpper) && (uplo != MagmaLower) ) *info = -1; if( n < 0 ) *info = -2; if( nrhs < 0) *info = -3; if ( ldda < max(1, n) ) *info = -5; if ( lddb < max(1, n) ) *info = -7; if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } /* Quick return if possible */ if ( (n == 0) || (nrhs == 0) ) { return *info; } ret = magma_spotrf_gpu(uplo, n, dA, 0, ldda, info, queue); if ( (ret != MAGMA_SUCCESS) || ( *info != 0 ) ) { return ret; } ret = magma_spotrs_gpu(uplo, n, nrhs, dA, 0, ldda, dB, 0, lddb, info, queue); if ( (ret != MAGMA_SUCCESS) || ( *info != 0 ) ) { return ret; } return *info; }
/* //////////////////////////////////////////////////////////////////////////// -- Testing spotrf */ int main( int argc, char** argv) { TESTING_INIT(); real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time; float *h_A, *h_R; magmaFloat_ptr d_A; magma_int_t N, n2, lda, ldda, info; float c_neg_one = MAGMA_S_NEG_ONE; magma_int_t ione = 1; magma_int_t ISEED[4] = {0,0,0,1}; float work[1], error; magma_int_t status = 0; magma_opts opts; parse_opts( argc, argv, &opts ); opts.lapack |= opts.check; // check (-c) implies lapack (-l) float tol = opts.tolerance * lapackf77_slamch("E"); printf("uplo = %s\n", lapack_uplo_const(opts.uplo) ); printf(" N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R_magma - R_lapack||_F / ||R_lapack||_F\n"); printf("========================================================\n"); for( int itest = 0; itest < opts.ntest; ++itest ) { for( int iter = 0; iter < opts.niter; ++iter ) { N = opts.nsize[itest]; lda = N; n2 = lda*N; ldda = ((N+31)/32)*32; gflops = FLOPS_SPOTRF( N ) / 1e9; TESTING_MALLOC_CPU( h_A, float, n2 ); TESTING_MALLOC_PIN( h_R, float, n2 ); TESTING_MALLOC_DEV( d_A, float, ldda*N ); /* Initialize the matrix */ lapackf77_slarnv( &ione, ISEED, &n2, h_A ); magma_smake_hpd( N, h_A, lda ); lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda ); magma_ssetmatrix( N, N, h_A, lda, d_A, ldda ); /* ==================================================================== Performs operation using MAGMA =================================================================== */ gpu_time = magma_wtime(); magma_spotrf_gpu( opts.uplo, N, d_A, ldda, &info ); gpu_time = magma_wtime() - gpu_time; gpu_perf = gflops / gpu_time; if (info != 0) printf("magma_spotrf_gpu returned error %d: %s.\n", (int) info, magma_strerror( info )); if ( opts.lapack ) { /* ===================================================================== Performs operation using LAPACK =================================================================== */ cpu_time = magma_wtime(); lapackf77_spotrf( lapack_uplo_const(opts.uplo), &N, h_A, &lda, &info ); cpu_time = magma_wtime() - cpu_time; cpu_perf = gflops / cpu_time; if (info != 0) printf("lapackf77_spotrf returned error %d: %s.\n", (int) info, magma_strerror( info )); /* ===================================================================== Check the result compared to LAPACK =================================================================== */ magma_sgetmatrix( N, N, d_A, ldda, h_R, lda ); error = lapackf77_slange("f", &N, &N, h_A, &lda, work); blasf77_saxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione); error = lapackf77_slange("f", &N, &N, h_R, &lda, work) / error; printf("%5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n", (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time, error, (error < tol ? "ok" : "failed") ); status += ! (error < tol); } else { printf("%5d --- ( --- ) %7.2f (%7.2f) --- \n", (int) N, gpu_perf, gpu_time ); } TESTING_FREE_CPU( h_A ); TESTING_FREE_PIN( h_R ); TESTING_FREE_DEV( d_A ); fflush( stdout ); } if ( opts.niter > 1 ) { printf( "\n" ); } } TESTING_FINALIZE(); return status; }
/** Purpose ------- SSYGVDX computes selected eigenvalues and, optionally, eigenvectors of a real generalized symmetric-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 symmetric and B is also positive definite. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. 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] 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 REAL 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. 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**T * B * Z = I; if ITYPE = 3, Z**T * 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 REAL array, dimension (LDB, N) On entry, the symmetric 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**T * U or B = L * L**T. @param[in] ldb INTEGER The leading dimension of the array B. LDB >= max(1,N). @param[in] vl REAL @param[in] vu REAL 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] mout INTEGER The total number of eigenvalues found. 0 <= MOUT <= N. If RANGE = MagmaRangeAll, MOUT = N, and if RANGE = MagmaRangeI, MOUT = IU-IL+1. @param[out] w REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. @param[out] work (workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. @param[out] work (workspace) REAL 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 >= 2*N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ). NB can be obtained through magma_get_ssytrd_nb(N). \n If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK 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 and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK 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: SPOTRF or SSYEVD 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 SSYEVD 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_ssygv_driver ********************************************************************/ extern "C" magma_int_t magma_ssygvdx( magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, float *B, magma_int_t ldb, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *mout, float *w, float *work, magma_int_t lwork, #ifdef COMPLEX float *rwork, magma_int_t lrwork, #endif 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 ); float d_one = MAGMA_S_ONE; float *dA=NULL, *dB=NULL; magma_int_t ldda = roundup( n, 32 ); magma_int_t lddb = ldda; magma_int_t lower; magma_trans_t trans; magma_int_t wantz, lquery; magma_int_t alleig, valeig, indeig; magma_int_t lwmin, liwmin; magma_queue_t stream; magma_queue_create( &stream ); 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_ssytrd_nb( n ); if ( n <= 1 ) { lwmin = 1; liwmin = 1; } else if ( wantz ) { lwmin = max( 2*n + n*nb, 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_slamch("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; } /* If matrix is very small, then just call LAPACK on CPU, no need for GPU */ if (n <= 128) { lapackf77_ssygvd( &itype, jobz_, uplo_, &n, A, &lda, B, &ldb, w, work, &lwork, iwork, &liwork, info ); *mout = n; return *info; } if (MAGMA_SUCCESS != magma_smalloc( &dA, n*ldda ) || MAGMA_SUCCESS != magma_smalloc( &dB, n*lddb )) { magma_free( dA ); magma_free( dB ); *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } /* Form a Cholesky factorization of B. */ magma_ssetmatrix( n, n, B, ldb, dB, lddb ); magma_ssetmatrix_async( n, n, A, lda, dA, ldda, stream ); magma_timer_t time=0; timer_start( time ); magma_spotrf_gpu( uplo, n, dB, lddb, info ); if (*info != 0) { *info = n + *info; return *info; } timer_stop( time ); timer_printf( "time spotrf_gpu = %6.2f\n", time ); magma_queue_sync( stream ); magma_sgetmatrix_async( n, n, dB, lddb, B, ldb, stream ); timer_start( time ); /* Transform problem to standard eigenvalue problem and solve. */ magma_ssygst_gpu( itype, uplo, n, dA, ldda, dB, lddb, info ); timer_stop( time ); timer_printf( "time ssygst_gpu = %6.2f\n", time ); /* simple fix to be able to run bigger size. * set dB=NULL so we know to re-allocate below * TODO: have dwork here that will be used as dB and then passed to ssyevd. */ if (n > 5000) { magma_queue_sync( stream ); magma_free( dB ); dB=NULL; } timer_start( time ); magma_ssyevdx_gpu( jobz, range, uplo, n, dA, ldda, vl, vu, il, iu, mout, w, A, lda, work, lwork, iwork, liwork, info ); timer_stop( time ); timer_printf( "time ssyevdx_gpu = %6.2f\n", time ); if (wantz && *info == 0) { timer_start( time ); /* allocate and copy dB back */ if (dB == NULL) { if (MAGMA_SUCCESS != magma_smalloc( &dB, n*lddb ) ) { magma_free( dA ); dA=NULL; *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magma_ssetmatrix( n, n, B, ldb, dB, lddb ); } /* 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_strsm( MagmaLeft, uplo, trans, MagmaNonUnit, n, *mout, d_one, dB, lddb, dA, ldda ); } 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_strmm( MagmaLeft, uplo, trans, MagmaNonUnit, n, *mout, d_one, dB, lddb, dA, ldda ); } magma_sgetmatrix( n, *mout, dA, ldda, A, lda ); timer_stop( time ); timer_printf( "time strsm/mm + getmatrix = %6.2f\n", time ); } magma_queue_sync( stream ); magma_queue_destroy( stream ); work[0] = lwmin * one_eps; // round up iwork[0] = liwmin; magma_free( dA ); dA=NULL; magma_free( dB ); dB=NULL; return *info; } /* magma_ssygvd */
extern "C" magma_int_t magma_ssygvdx_2stage(magma_int_t itype, char jobz, char range, char uplo, magma_int_t n, float *a, magma_int_t lda, float *b, magma_int_t ldb, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *m, float *w, float *work, magma_int_t lwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) { /* -- MAGMA (version 1.4.0) -- Univ. of Tennessee, Knoxville Univ. of California, Berkeley Univ. of Colorado, Denver August 2013 Purpose ======= SSYGVDX_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 ========= ITYPE (input) 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 RANGE (input) CHARACTER*1 = 'A': all eigenvalues will be found. = 'V': all eigenvalues in the half-open interval (VL,VU] will be found. = 'I': the IL-th through IU-th eigenvalues will be found. JOBZ (input) CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO (input) CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored. N (input) INTEGER The order of the matrices A and B. N >= 0. A (input/output) DOUBLE PRECISION array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', 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 = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). B (input/output) DOUBLE PRECISION array, dimension (LDB, N) On entry, the Hermitian matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B. 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. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). VL (input) DOUBLE PRECISION VU (input) DOUBLE PRECISION If RANGE='V', the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'. IL (input) INTEGER IU (input) INTEGER If RANGE='I', 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 = 'A' or 'V'. M (output) INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. W (output) DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= LQ2 + N * (NB + 2). If JOBZ = 'V' 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. 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. IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. LIWORK (input) INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = 'N' and N > 1, LIWORK >= 1. If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*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. INFO (output) 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 = 'N', 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 = 'V', 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. ===================================================================== */ char uplo_[2] = {uplo, 0}; char jobz_[2] = {jobz, 0}; char range_[2] = {range, 0}; float d_one = MAGMA_S_ONE; float *da; float *db; magma_int_t ldda = n; magma_int_t lddb = n; magma_int_t lower; char trans[1]; magma_int_t wantz; magma_int_t lquery; magma_int_t alleig, valeig, indeig; magma_int_t lwmin; magma_int_t liwmin; magma_queue_t stream; magma_queue_create( &stream ); /* determine the number of threads */ magma_int_t threads = magma_get_numthreads(); magma_setlapack_numthreads(threads); wantz = lapackf77_lsame(jobz_, MagmaVecStr); lower = lapackf77_lsame(uplo_, MagmaLowerStr); alleig = lapackf77_lsame(range_, "A"); valeig = lapackf77_lsame(range_, "V"); indeig = lapackf77_lsame(range_, "I"); lquery = lwork == -1 || liwork == -1; *info = 0; if (itype < 1 || itype > 3) { *info = -1; } else if (! (alleig || valeig || indeig)) { *info = -2; } else if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) { *info = -3; } else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) { *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_sbulge_nb(n, threads); magma_int_t lq2 = magma_sbulge_get_lq2(n, threads); if (wantz) { lwmin = lq2 + 1 + 6*n + 2*n*n; liwmin = 3 + 5*n; } else { lwmin = n * (nb + 2); liwmin = 1; } work[0] = lwmin * (1. + lapackf77_slamch("Epsilon")); 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_ssygvd(&itype, jobz_, uplo_, &n, a, &lda, b, &ldb, w, work, &lwork, iwork, &liwork, info); *m = n; return *info; } if (MAGMA_SUCCESS != magma_smalloc( &da, n*ldda ) || MAGMA_SUCCESS != magma_smalloc( &db, n*lddb )) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } /* Form a Cholesky factorization of B. */ magma_ssetmatrix( n, n, b, ldb, db, lddb ); magma_ssetmatrix_async( n, n, a, lda, da, ldda, stream ); #ifdef ENABLE_TIMER magma_timestr_t start, end; start = get_current_time(); #endif magma_spotrf_gpu(uplo_[0], n, db, lddb, info); if (*info != 0) { *info = n + *info; return *info; } #ifdef ENABLE_TIMER end = get_current_time(); printf("time spotrf_gpu = %6.2f\n", GetTimerValue(start,end)/1000.); #endif magma_queue_sync( stream ); magma_sgetmatrix_async( n, n, db, lddb, b, ldb, stream ); #ifdef ENABLE_TIMER start = get_current_time(); #endif /* Transform problem to standard eigenvalue problem and solve. */ magma_ssygst_gpu(itype, uplo, n, da, ldda, db, lddb, info); #ifdef ENABLE_TIMER end = get_current_time(); printf("time ssygst_gpu = %6.2f\n", GetTimerValue(start,end)/1000.); #endif magma_sgetmatrix( n, n, da, ldda, a, lda ); magma_queue_sync( stream ); magma_free( da ); magma_free( db ); #ifdef ENABLE_TIMER start = get_current_time(); #endif magma_ssyevdx_2stage(jobz, range, uplo, n, a, lda, vl, vu, il, iu, m, w, work, lwork, iwork, liwork, info); #ifdef ENABLE_TIMER end = get_current_time(); printf("time ssyevdx_2stage = %6.2f\n", GetTimerValue(start,end)/1000.); #endif if (wantz && *info == 0) { if (MAGMA_SUCCESS != magma_smalloc( &da, n*ldda ) || MAGMA_SUCCESS != magma_smalloc( &db, n*lddb )) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } #ifdef ENABLE_TIMER start = get_current_time(); #endif magma_ssetmatrix( n, *m, a, lda, da, ldda ); magma_ssetmatrix( n, n, b, ldb, db, lddb ); /* 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) { *(unsigned char *)trans = MagmaConjTrans; } else { *(unsigned char *)trans = MagmaNoTrans; } magma_strsm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, d_one, db, lddb, da, ldda); } else if (itype == 3) { /* For B*A*x=(lambda)*x; backtransform eigenvectors: x = L*y or U'*y */ if (lower) { *(unsigned char *)trans = MagmaNoTrans; } else { *(unsigned char *)trans = MagmaConjTrans; } magma_strmm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, d_one, db, lddb, da, ldda); } magma_sgetmatrix( n, *m, da, ldda, a, lda ); #ifdef ENABLE_TIMER end = get_current_time(); printf("time strsm/mm + getmatrix = %6.2f\n", GetTimerValue(start,end)/1000.); #endif magma_free( da ); magma_free( db ); } magma_queue_destroy( stream ); work[0] = lwmin * (1. + lapackf77_slamch("Epsilon")); iwork[0] = liwmin; return *info; } /* ssygvdx_2stage */
/** Purpose ------- DSPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices. DSPOSV first attempts to factorize the matrix in real SINGLE PRECISION and use this factorization within an iterative refinement procedure to produce a solution with real DOUBLE PRECISION norm-wise backward error quality (see below). If the approach fails the method switches to a real DOUBLE PRECISION factorization and solve. The iterative refinement is not going to be a winning strategy if the ratio real SINGLE PRECISION performance over real DOUBLE PRECISION performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. This might be done with a call to ILAENV in the future. Up to now, we always try iterative refinement. The iterative refinement process is stopped if ITER > ITERMAX or for all the RHS we have: RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX where o ITER is the number of the current iteration in the iterative refinement process o RNRM is the infinity-norm of the residual o XNRM is the infinity-norm of the solution o ANRM is the infinity-operator-norm of the matrix A o EPS is the machine epsilon returned by DLAMCH('Epsilon') The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively. 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 number of linear equations, i.e., the order of the matrix A. N >= 0. @param[in] nrhs INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. @param[in,out] dA DOUBLE PRECISION array on the GPU, dimension (LDDA,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. On exit, if iterative refinement has been successfully used (INFO.EQ.0 and ITER.GE.0, see description below), then A is unchanged, if double factorization has been used (INFO.EQ.0 and ITER.LT.0, see description below), then the array dA contains the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T. @param[in] ldda INTEGER The leading dimension of the array dA. LDDA >= max(1,N). @param[in] dB DOUBLE PRECISION array on the GPU, dimension (LDDB,NRHS) The N-by-NRHS right hand side matrix B. @param[in] lddb INTEGER The leading dimension of the array dB. LDDB >= max(1,N). @param[out] dX DOUBLE PRECISION array on the GPU, dimension (LDDX,NRHS) If INFO = 0, the N-by-NRHS solution matrix X. @param[in] lddx INTEGER The leading dimension of the array dX. LDDX >= max(1,N). @param dworkd (workspace) DOUBLE PRECISION array on the GPU, dimension (N*NRHS) This array is used to hold the residual vectors. @param dworks (workspace) SINGLE PRECISION array on the GPU, dimension (N*(N+NRHS)) This array is used to store the real single precision matrix and the right-hand sides or solutions in single precision. @param[out] iter INTEGER - < 0: iterative refinement has failed, double precision factorization has been performed + -1 : the routine fell back to full precision for implementation- or machine-specific reasons + -2 : narrowing the precision induced an overflow, the routine fell back to full precision + -3 : failure of SPOTRF + -31: stop the iterative refinement after the 30th iteration - > 0: iterative refinement has been successfully used. Returns the number of iterations @param[out] info INTEGER - = 0: successful exit - < 0: if INFO = -i, the i-th argument had an illegal value - > 0: if INFO = i, the leading minor of order i of (DOUBLE PRECISION) A is not positive definite, so the factorization could not be completed, and the solution has not been computed. @ingroup magma_dposv_driver ********************************************************************/ extern "C" magma_int_t magma_dsposv_gpu( magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDouble_ptr dA, magma_int_t ldda, magmaDouble_ptr dB, magma_int_t lddb, magmaDouble_ptr dX, magma_int_t lddx, magmaDouble_ptr dworkd, magmaFloat_ptr dworks, magma_int_t *iter, magma_int_t *info) { #define dB(i,j) (dB + (i) + (j)*lddb) #define dX(i,j) (dX + (i) + (j)*lddx) #define dR(i,j) (dR + (i) + (j)*lddr) #define dSX(i,j) (dSX + (i) + (j)*lddsx) // Constants const double BWDMAX = 1.0; const magma_int_t ITERMAX = 30; const double c_neg_one = MAGMA_D_NEG_ONE; const double c_one = MAGMA_D_ONE; const magma_int_t ione = 1; // Local variables magmaDouble_ptr dR; magmaFloat_ptr dSA, dSX; double Xnrmv, Rnrmv; double Anrm, Xnrm, Rnrm, cte, eps; magma_int_t i, j, iiter, lddsa, lddsx, lddr; /* Check arguments */ *iter = 0; *info = 0; if ( n < 0 ) *info = -1; else if ( nrhs < 0 ) *info = -2; else if ( ldda < max(1,n)) *info = -4; else if ( lddb < max(1,n)) *info = -7; else if ( lddx < max(1,n)) *info = -9; if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } if ( n == 0 || nrhs == 0 ) return *info; lddsa = n; lddsx = n; lddr = n; dSA = dworks; dSX = dSA + lddsa*n; dR = dworkd; magma_queue_t queue; magma_device_t cdev; magma_getdevice( &cdev ); magma_queue_create( cdev, &queue ); eps = lapackf77_dlamch("Epsilon"); Anrm = magmablas_dlansy( MagmaInfNorm, uplo, n, dA, ldda, (double*)dworkd, n*nrhs, queue ); cte = Anrm * eps * magma_dsqrt( n ) * BWDMAX; /* * Convert to single precision */ magmablas_dlag2s( n, nrhs, dB, lddb, dSX, lddsx, queue, info ); if (*info != 0) { *iter = -2; goto fallback; } magmablas_dlat2s( uplo, n, dA, ldda, dSA, lddsa, queue, info ); if (*info != 0) { *iter = -2; goto fallback; } // factor dSA in single precision magma_spotrf_gpu( uplo, n, dSA, lddsa, info ); if (*info != 0) { *iter = -3; goto fallback; } // solve dSA*dSX = dB in single precision magma_spotrs_gpu( uplo, n, nrhs, dSA, lddsa, dSX, lddsx, info ); // residual dR = dB - dA*dX in double precision magmablas_slag2d( n, nrhs, dSX, lddsx, dX, lddx, queue, info ); magmablas_dlacpy( MagmaFull, n, nrhs, dB, lddb, dR, lddr, queue ); if ( nrhs == 1 ) { magma_dsymv( uplo, n, c_neg_one, dA, ldda, dX, 1, c_one, dR, 1, queue ); } else { magma_dsymm( MagmaLeft, uplo, n, nrhs, c_neg_one, dA, ldda, dX, lddx, c_one, dR, lddr, queue ); } // TODO: use MAGMA_D_ABS( dX(i,j) ) instead of dlange? for( j=0; j < nrhs; j++ ) { i = magma_idamax( n, dX(0,j), 1, queue ) - 1; magma_dgetmatrix( 1, 1, dX(i,j), 1, &Xnrmv, 1, queue ); Xnrm = lapackf77_dlange( "F", &ione, &ione, &Xnrmv, &ione, NULL ); i = magma_idamax( n, dR(0,j), 1, queue ) - 1; magma_dgetmatrix( 1, 1, dR(i,j), 1, &Rnrmv, 1, queue ); Rnrm = lapackf77_dlange( "F", &ione, &ione, &Rnrmv, &ione, NULL ); if ( Rnrm > Xnrm*cte ) { goto refinement; } } *iter = 0; goto cleanup; //return *info; refinement: for( iiter=1; iiter < ITERMAX; ) { *info = 0; // convert residual dR to single precision dSX magmablas_dlag2s( n, nrhs, dR, lddr, dSX, lddsx, queue, info ); if (*info != 0) { *iter = -2; goto fallback; } // solve dSA*dSX = R in single precision magma_spotrs_gpu( uplo, n, nrhs, dSA, lddsa, dSX, lddsx, info ); // Add correction and setup residual // dX += dSX [including conversion] --and-- // dR = dB for( j=0; j < nrhs; j++ ) { magmablas_dsaxpycp( n, dSX(0,j), dX(0,j), dB(0,j), dR(0,j), queue ); } // residual dR = dB - dA*dX in double precision if ( nrhs == 1 ) { magma_dsymv( uplo, n, c_neg_one, dA, ldda, dX, 1, c_one, dR, 1, queue ); } else { magma_dsymm( MagmaLeft, uplo, n, nrhs, c_neg_one, dA, ldda, dX, lddx, c_one, dR, lddr, queue ); } // TODO: use MAGMA_D_ABS( dX(i,j) ) instead of dlange? /* Check whether the nrhs normwise backward errors satisfy the * stopping criterion. If yes, set ITER=IITER > 0 and return. */ for( j=0; j < nrhs; j++ ) { i = magma_idamax( n, dX(0,j), 1, queue ) - 1; magma_dgetmatrix( 1, 1, dX(i,j), 1, &Xnrmv, 1, queue ); Xnrm = lapackf77_dlange( "F", &ione, &ione, &Xnrmv, &ione, NULL ); i = magma_idamax( n, dR(0,j), 1, queue ) - 1; magma_dgetmatrix( 1, 1, dR(i,j), 1, &Rnrmv, 1, queue ); Rnrm = lapackf77_dlange( "F", &ione, &ione, &Rnrmv, &ione, NULL ); if ( Rnrm > Xnrm*cte ) { goto L20; } } /* If we are here, the nrhs normwise backward errors satisfy * the stopping criterion, we are good to exit. */ *iter = iiter; goto cleanup; //return *info; L20: iiter++; } /* If we are at this place of the code, this is because we have * performed ITER=ITERMAX iterations and never satisified the * stopping criterion. Set up the ITER flag accordingly and follow * up on double precision routine. */ *iter = -ITERMAX - 1; fallback: /* Single-precision iterative refinement failed to converge to a * satisfactory solution, so we resort to double precision. */ magma_dpotrf_gpu( uplo, n, dA, ldda, info ); if (*info == 0) { magmablas_dlacpy( MagmaFull, n, nrhs, dB, lddb, dX, lddx, queue ); magma_dpotrs_gpu( uplo, n, nrhs, dA, ldda, dX, lddx, info ); } cleanup: magma_queue_destroy( queue ); return *info; }
extern "C" magma_int_t magma_sposv ( char uplo, magma_int_t n, magma_int_t nrhs, float *A, magma_int_t lda, float *B, magma_int_t ldb, magma_int_t *info ) { /* -- MAGMA (version 1.4.0) -- Univ. of Tennessee, Knoxville Univ. of California, Berkeley Univ. of Colorado, Denver August 2013 Purpose ======= SPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices. The Cholesky decomposition is used to factor A as A = U**T * U, if UPLO = 'U', or A = L * L**T, if UPLO = 'L', where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B. Arguments ========= UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input/output) REAL array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = 'U', 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 = 'L', 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. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). B (input/output) REAL array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value ===================================================================== */ magma_int_t num_gpus, ldda, lddb; *info = 0 ; if( (uplo != 'U') && (uplo != 'u') && (uplo != 'L') && (uplo != 'l') ) *info = -1; if( n < 0 ) *info = -2; if( nrhs < 0) *info = -3; if ( lda < max(1, n) ) *info = -5; if ( ldb < max(1, n) ) *info = -7; if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } /* Quick return if possible */ if ( (n==0) || (nrhs == 0) ) { return *info; } /* If single-GPU and allocation suceeds, use GPU interface. */ num_gpus = magma_num_gpus(); float *dA, *dB; if ( num_gpus > 1 ) { goto CPU_INTERFACE; } ldda = ((n+31)/32)*32; lddb = ldda; if ( MAGMA_SUCCESS != magma_smalloc( &dA, ldda*n )) { goto CPU_INTERFACE; } if ( MAGMA_SUCCESS != magma_smalloc( &dB, lddb*nrhs )) { magma_free( dA ); goto CPU_INTERFACE; } magma_ssetmatrix( n, n, A, lda, dA, ldda ); magma_spotrf_gpu( uplo, n, dA, ldda, info ); if ( *info == MAGMA_ERR_DEVICE_ALLOC ) { magma_free( dA ); magma_free( dB ); goto CPU_INTERFACE; } magma_sgetmatrix( n, n, dA, ldda, A, lda ); if ( *info == 0 ) { magma_ssetmatrix( n, nrhs, B, ldb, dB, lddb ); magma_spotrs_gpu( uplo, n, nrhs, dA, ldda, dB, lddb, info ); magma_sgetmatrix( n, nrhs, dB, lddb, B, ldb ); } magma_free( dA ); magma_free( dB ); return *info; CPU_INTERFACE: /* If multi-GPU or allocation failed, use CPU interface and LAPACK. * Faster to use LAPACK for potrs than to copy A to GPU. */ magma_spotrf( uplo, n, A, lda, info ); if ( *info == 0 ) { lapackf77_spotrs( &uplo, &n, &nrhs, A, &lda, B, &ldb, info ); } return *info; }
/** Purpose ------- SSYGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-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 symmetric and B is also positive definite. 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] 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] 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 REAL 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. 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**T * B * Z = I; if ITYPE = 3, Z**T * 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 REAL array, dimension (LDB, N) On entry, the symmetric 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**T * U or B = L * L**T. @param[in] ldb INTEGER The leading dimension of the array B. LDB >= max(1,N). @param[out] w REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. @param[out] work (workspace) REAL 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 >= 2*N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ). NB can be obtained through magma_get_ssytrd_nb(N). \n If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK 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 and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK 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: SPOTRF or SSYEVD 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 SSYEVD 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_ssygv_driver ********************************************************************/ extern "C" magma_int_t magma_ssygvd( magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, float *B, magma_int_t ldb, float *w, float *work, magma_int_t lwork, #ifdef COMPLEX float *rwork, magma_int_t lrwork, #endif 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 ); float d_one = MAGMA_S_ONE; float *dA=NULL, *dB=NULL; magma_int_t ldda = magma_roundup( n, 32 ); magma_int_t lddb = ldda; magma_int_t lower; magma_trans_t trans; magma_int_t wantz, lquery; magma_int_t lwmin, liwmin; wantz = (jobz == MagmaVec); lower = (uplo == MagmaLower); lquery = (lwork == -1 || liwork == -1); *info = 0; if (itype < 1 || itype > 3) { *info = -1; } else if (! (wantz || (jobz == MagmaNoVec))) { *info = -2; } else if (! (lower || (uplo == MagmaUpper))) { *info = -3; } else if (n < 0) { *info = -4; } else if (lda < max(1,n)) { *info = -6; } else if (ldb < max(1,n)) { *info = -8; } magma_int_t nb = magma_get_ssytrd_nb( n ); if ( n <= 1 ) { lwmin = 1; liwmin = 1; } else if ( wantz ) { lwmin = max( 2*n + n*nb, 1 + 6*n + 2*n*n ); liwmin = 3 + 5*n; } else { lwmin = 2*n + n*nb; liwmin = 1; } work[0] = magma_smake_lwork( lwmin ); iwork[0] = liwmin; if (lwork < lwmin && ! lquery) { *info = -11; } else if (liwork < liwmin && ! lquery) { *info = -13; } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } else if (lquery) { return *info; } /* Quick return if possible */ if (n == 0) { return *info; } /* If matrix is very small, then just call LAPACK on CPU, no need for GPU */ if (n <= 128) { lapackf77_ssygvd( &itype, jobz_, uplo_, &n, A, &lda, B, &ldb, w, work, &lwork, iwork, &liwork, info ); return *info; } if (MAGMA_SUCCESS != magma_smalloc( &dA, n*ldda ) || MAGMA_SUCCESS != magma_smalloc( &dB, n*lddb )) { magma_free( dA ); magma_free( dB ); *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magma_queue_t queue; magma_device_t cdev; magma_getdevice( &cdev ); magma_queue_create( cdev, &queue ); /* Form a Cholesky factorization of B. */ magma_ssetmatrix( n, n, B, ldb, dB, lddb, queue ); magma_ssetmatrix_async( n, n, A, lda, dA, ldda, queue ); magma_timer_t time=0; timer_start( time ); magma_spotrf_gpu( uplo, n, dB, lddb, info ); if (*info != 0) { *info = n + *info; return *info; } timer_stop( time ); timer_printf( "time spotrf_gpu = %6.2f\n", time ); magma_queue_sync( queue ); magma_sgetmatrix_async( n, n, dB, lddb, B, ldb, queue ); timer_start( time ); /* Transform problem to standard eigenvalue problem and solve. */ magma_ssygst_gpu( itype, uplo, n, dA, ldda, dB, lddb, info ); timer_stop( time ); timer_printf( "time ssygst_gpu = %6.2f\n", time ); /* simple fix to be able to run bigger size. * set dB=NULL so we know to re-allocate below * TODO: have dwork here that will be used as dB and then passed to ssyevd. */ if (n > 5000) { magma_queue_sync( queue ); magma_free( dB ); dB=NULL; } timer_start( time ); magma_ssyevd_gpu( jobz, uplo, n, dA, ldda, w, A, lda, work, lwork, iwork, liwork, info ); timer_stop( time ); timer_printf( "time ssyevd_gpu = %6.2f\n", time ); if (wantz && *info == 0) { timer_start( time ); /* allocate and copy dB back */ if (dB == NULL) { if (MAGMA_SUCCESS != magma_smalloc( &dB, n*lddb ) ) { magma_free( dA ); *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magma_ssetmatrix( n, n, B, ldb, dB, lddb, queue ); } /* 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_strsm( MagmaLeft, uplo, trans, MagmaNonUnit, n, n, d_one, dB, lddb, dA, ldda, queue ); } 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_strmm( MagmaLeft, uplo, trans, MagmaNonUnit, n, n, d_one, dB, lddb, dA, ldda, queue ); } magma_sgetmatrix( n, n, dA, ldda, A, lda, queue ); timer_stop( time ); timer_printf( "time strsm/mm + getmatrix = %6.2f\n", time ); } magma_queue_sync( queue ); magma_queue_destroy( queue ); work[0] = magma_smake_lwork( lwmin ); iwork[0] = liwmin; magma_free( dA ); dA=NULL; magma_free( dB ); dB=NULL; return *info; } /* magma_ssygvd */
/** Purpose ------- SPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices. The Cholesky decomposition is used to factor A as 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 a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B. 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] nrhs INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. @param[in,out] A REAL 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. @param[in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). @param[in,out] B REAL array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. @param[in] ldb INTEGER The leading dimension of the array B. LDB >= max(1,N). @param[out] info INTEGER - = 0: successful exit - < 0: if INFO = -i, the i-th argument had an illegal value @ingroup magma_sposv_driver ********************************************************************/ extern "C" magma_int_t magma_sposv( magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, float *A, magma_int_t lda, float *B, magma_int_t ldb, magma_int_t *info ) { magma_int_t ngpu, ldda, lddb; *info = 0; if ( uplo != MagmaUpper && uplo != MagmaLower ) *info = -1; if ( n < 0 ) *info = -2; if ( nrhs < 0) *info = -3; if ( lda < max(1, n) ) *info = -5; if ( ldb < max(1, n) ) *info = -7; if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } /* Quick return if possible */ if ( (n == 0) || (nrhs == 0) ) { return *info; } /* If single-GPU and allocation suceeds, use GPU interface. */ ngpu = magma_num_gpus(); float *dA, *dB; if ( ngpu > 1 ) { goto CPU_INTERFACE; } ldda = ((n+31)/32)*32; lddb = ldda; if ( MAGMA_SUCCESS != magma_smalloc( &dA, ldda*n )) { goto CPU_INTERFACE; } if ( MAGMA_SUCCESS != magma_smalloc( &dB, lddb*nrhs )) { magma_free( dA ); goto CPU_INTERFACE; } magma_ssetmatrix( n, n, A, lda, dA, ldda ); magma_spotrf_gpu( uplo, n, dA, ldda, info ); if ( *info == MAGMA_ERR_DEVICE_ALLOC ) { magma_free( dA ); magma_free( dB ); goto CPU_INTERFACE; } magma_sgetmatrix( n, n, dA, ldda, A, lda ); if ( *info == 0 ) { magma_ssetmatrix( n, nrhs, B, ldb, dB, lddb ); magma_spotrs_gpu( uplo, n, nrhs, dA, ldda, dB, lddb, info ); magma_sgetmatrix( n, nrhs, dB, lddb, B, ldb ); } magma_free( dA ); magma_free( dB ); return *info; CPU_INTERFACE: /* If multi-GPU or allocation failed, use CPU interface and LAPACK. * Faster to use LAPACK for potrs than to copy A to GPU. */ magma_spotrf( uplo, n, A, lda, info ); if ( *info == 0 ) { lapackf77_spotrs( lapack_uplo_const(uplo), &n, &nrhs, A, &lda, B, &ldb, info ); } return *info; }
int main( int argc, char** argv) { real_Double_t gflops, gpu_perf, cpu_perf, gpu_time, cpu_time; float *hA, *hR; magmaFloat_ptr dA; magma_int_t N = 0, n2, lda, ldda; magma_int_t size[10] = { 1024, 2048, 3072, 4032, 5184, 6048, 7200, 8064, 8928, 10560 }; magma_int_t i, info; float mz_one = MAGMA_S_NEG_ONE; magma_int_t ione = 1; magma_int_t ISEED[4] = {0,0,0,1}; float work[1], matnorm, diffnorm; if (argc != 1) { for(i = 1; i<argc; i++) { if (strcmp("-N", argv[i])==0) N = atoi(argv[++i]); } if (N>0) size[0] = size[9] = N; else exit(1); } else { printf("\nUsage: \n"); printf(" testing_spotrf_gpu -N %d\n\n", 1024); } /* Initialize */ magma_queue_t queue; magma_device_t device[ MagmaMaxGPUs ]; int num = 0; magma_err_t err; magma_init(); err = magma_get_devices( device, MagmaMaxGPUs, &num ); if ( err != 0 || num < 1 ) { fprintf( stderr, "magma_get_devices failed: %d\n", err ); exit(-1); } err = magma_queue_create( device[0], &queue ); if ( err != 0 ) { fprintf( stderr, "magma_queue_create failed: %d\n", err ); exit(-1); } /* Allocate memory for the largest matrix */ N = size[9]; n2 = N * N; ldda = ((N+31)/32) * 32; TESTING_MALLOC_CPU( hA, float, n2 ); TESTING_MALLOC_PIN( hR, float, n2 ); TESTING_MALLOC_DEV( dA, float, ldda*N ); printf("\n\n"); printf(" N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R_magma-R_lapack||_F / ||R_lapack||_F\n"); printf("========================================================================================\n"); for(i=0; i<10; i++) { N = size[i]; lda = N; n2 = lda*N; ldda = ((N+31)/32)*32; gflops = FLOPS( (float)N ) * 1e-9; /* Initialize the matrix */ lapackf77_slarnv( &ione, ISEED, &n2, hA ); /* Symmetrize and increase the diagonal */ for( int i = 0; i < N; ++i ) { MAGMA_S_SET2REAL( hA(i,i), MAGMA_S_REAL(hA(i,i)) + N ); for( int j = 0; j < i; ++j ) { hA(i, j) = MAGMA_S_CNJG( hA(j,i) ); } } lapackf77_slacpy( MagmaFullStr, &N, &N, hA, &lda, hR, &lda ); /* Warm up to measure the performance */ magma_ssetmatrix( N, N, hA, 0, lda, dA, 0, ldda, queue ); magma_spotrf_gpu( MagmaUpper, N, dA, 0, ldda, &info, queue ); /* ==================================================================== Performs operation using MAGMA =================================================================== */ magma_ssetmatrix( N, N, hA, 0, lda, dA, 0, ldda, queue ); gpu_time = magma_wtime(); magma_spotrf_gpu( MagmaUpper, N, dA, 0, ldda, &info, queue ); gpu_time = magma_wtime() - gpu_time; if (info != 0) printf( "magma_spotrf had error %d.\n", info ); gpu_perf = gflops / gpu_time; /* ===================================================================== Performs operation using LAPACK =================================================================== */ cpu_time = magma_wtime(); lapackf77_spotrf( MagmaUpperStr, &N, hA, &lda, &info ); cpu_time = magma_wtime() - cpu_time; if (info != 0) printf( "lapackf77_spotrf had error %d.\n", info ); cpu_perf = gflops / cpu_time; /* ===================================================================== Check the result compared to LAPACK |R_magma - R_lapack| / |R_lapack| =================================================================== */ magma_sgetmatrix( N, N, dA, 0, ldda, hR, 0, lda, queue ); matnorm = lapackf77_slange("f", &N, &N, hA, &lda, work); blasf77_saxpy(&n2, &mz_one, hA, &ione, hR, &ione); diffnorm = lapackf77_slange("f", &N, &N, hR, &lda, work); printf( "%5d %6.2f (%6.2f) %6.2f (%6.2f) %e\n", N, cpu_perf, cpu_time, gpu_perf, gpu_time, diffnorm / matnorm ); if (argc != 1) break; } /* clean up */ TESTING_FREE_CPU( hA ); TESTING_FREE_PIN( hR ); TESTING_FREE_DEV( dA ); magma_queue_destroy( queue ); magma_finalize(); }