extern "C" magma_int_t magma_ssygvd_m(magma_int_t nrgpu, 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 1.4.1) -- Univ. of Tennessee, Knoxville Univ. of California, Berkeley Univ. of Colorado, Denver December 2013 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) REAL 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 >= N + 1. If JOBZ = 'V' and N > 1, LWORK >= 2*N*nb + N**2. 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. RWORK (workspace/output) REAL array, dimension (MAX(1,LRWORK)) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. LRWORK (input) INTEGER The dimension of the array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = 'N' and N > 1, LRWORK >= N. If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. If LRWORK = -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: 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; magma_int_t lower; char trans[1]; magma_int_t wantz; magma_int_t lquery; magma_int_t lwmin; magma_int_t liwmin; magma_queue_t stream; magma_queue_create( &stream ); wantz = lapackf77_lsame(jobz_, MagmaVecStr); 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_, MagmaNoVecStr))) { *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 ) { lwmin = 1; liwmin = 1; } else if ( wantz ) { lwmin = 1 + 6*n + 2*n*n; liwmin = 3 + 5*n; } else { lwmin = 2*n + n*nb; liwmin = 1; } work[0] = lwmin * (1. + lapackf77_slamch("Epsilon")); // round up 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; } /* 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); return *info; } // #ifdef ENABLE_TIMER magma_timestr_t start, end; start = get_current_time(); #endif magma_spotrf_m(nrgpu, uplo_[0], n, b, ldb, info); if (*info != 0) { *info = n + *info; return *info; } #ifdef ENABLE_TIMER end = get_current_time(); printf("time spotrf = %6.2f\n", GetTimerValue(start,end)/1000.); start = get_current_time(); #endif /* Transform problem to standard eigenvalue problem and solve. */ magma_ssygst_m(nrgpu, itype, uplo_[0], n, a, lda, b, ldb, info); #ifdef ENABLE_TIMER end = get_current_time(); printf("time ssygst = %6.2f\n", GetTimerValue(start,end)/1000.); start = get_current_time(); #endif magma_ssyevd_m(nrgpu, jobz_[0], uplo_[0], n, a, lda, w, work, lwork, iwork, liwork, info); #ifdef ENABLE_TIMER end = get_current_time(); printf("time ssyevd = %6.2f\n", GetTimerValue(start,end)/1000.); #endif if (wantz && *info == 0) { #ifdef ENABLE_TIMER start = get_current_time(); #endif /* 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_m(nrgpu, MagmaLeft, uplo, *trans, MagmaNonUnit, n, n, 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) { *(unsigned char *)trans = MagmaNoTrans; } else { *(unsigned char *)trans = MagmaTrans; } //magma_strmm(MagmaLeft, uplo_[0], *trans, MagmaNonUnit, // n, n, c_one, db, lddb, da, ldda); } #ifdef ENABLE_TIMER end = get_current_time(); printf("time setmatrices trsm/mm + getmatrices = %6.2f\n", GetTimerValue(start,end)/1000.); #endif } work[0] = lwmin * (1. + lapackf77_slamch("Epsilon")); // round up iwork[0] = liwmin; return *info; } /* magma_ssygvd_m */
/** 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] ngpu INTEGER Number of GPUs to use. ngpu > 0. @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_m( magma_int_t ngpu, 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; magma_int_t lower; magma_trans_t trans; magma_int_t wantz, lquery; magma_int_t lwmin, liwmin; magma_queue_t stream; magma_queue_create( &stream ); 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; } // 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 = -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; } magma_timer_t time=0; timer_start( time ); magma_spotrf_m( ngpu, uplo, n, B, ldb, info ); if (*info != 0) { *info = n + *info; return *info; } timer_stop( time ); timer_printf( "time spotrf = %6.2f\n", time ); timer_start( time ); /* Transform problem to standard eigenvalue problem and solve. */ magma_ssygst_m( ngpu, itype, uplo, n, A, lda, B, ldb, info ); timer_stop( time ); timer_printf( "time ssygst = %6.2f\n", time ); timer_start( time ); magma_ssyevd_m( ngpu, jobz, uplo, n, A, lda, w, work, lwork, iwork, liwork, info ); timer_stop( time ); timer_printf( "time ssyevd = %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_strsm_m( ngpu, MagmaLeft, uplo, trans, MagmaNonUnit, n, n, 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; } printf("--- the multi GPU version is falling back to 1 GPU to perform the last TRMM since there is no TRMM_mgpu --- \n"); float *dA=NULL, *dB=NULL; magma_int_t ldda = roundup( n, 32 ); magma_int_t lddb = ldda; 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_ssetmatrix( n, n, B, ldb, dB, lddb ); magma_ssetmatrix( n, n, A, lda, dA, ldda ); magma_strmm( MagmaLeft, uplo, trans, MagmaNonUnit, n, n, d_one, dB, lddb, dA, ldda ); magma_sgetmatrix( n, n, dA, ldda, A, lda ); magma_free( dA ); magma_free( dB ); } timer_stop( time ); timer_printf( "time setmatrices trsm/mm + getmatrices = %6.2f\n", time ); } work[0] = lwmin * one_eps; // round up iwork[0] = liwmin; return *info; } /* magma_ssygvd_m */
/** 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] ngpu INTEGER Number of GPUs to use. ngpu > 0. @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] 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 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_ssygvdx_m( magma_int_t ngpu, 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 *m, 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) { /* Constants */ float c_one = MAGMA_S_ONE; /* Local variables */ const char* uplo_ = lapack_uplo_const( uplo ); const char* jobz_ = lapack_vec_const( jobz ); 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; 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; } work[0] = magma_smake_lwork( lwmin ); 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; } magma_timer_t time=0; timer_start( time ); magma_spotrf_m(ngpu, uplo, n, B, ldb, info); if (*info != 0) { *info = n + *info; return *info; } timer_stop( time ); timer_printf( "time spotrf = %6.2f\n", time ); timer_start( time ); /* Transform problem to standard eigenvalue problem and solve. */ magma_ssygst_m(ngpu, itype, uplo, n, A, lda, B, ldb, info); timer_stop( time ); timer_printf( "time ssygst = %6.2f\n", time ); timer_start( time ); magma_ssyevdx_m(ngpu, jobz, range, uplo, n, A, lda, vl, vu, il, iu, m, w, work, lwork, iwork, liwork, info); timer_stop( time ); timer_printf( "time ssyevd = %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_strsm_m( ngpu, MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, c_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; } #ifdef ENABLE_DEBUG printf("--- the multi GPU version is falling back to 1 GPU to perform the last TRMM since there is no TRMM_mgpu --- \n"); #endif float *dA=NULL, *dB=NULL; magma_int_t ldda = magma_roundup( n, 32 ); magma_int_t lddb = ldda; if (MAGMA_SUCCESS != magma_smalloc( &dA, ldda*(*m) ) || MAGMA_SUCCESS != magma_smalloc( &dB, lddb*n ) ) { 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 ); magma_ssetmatrix( n, n, B, ldb, dB, lddb, queue ); magma_ssetmatrix( n, (*m), A, lda, dA, ldda, queue ); magma_strmm( MagmaLeft, uplo, trans, MagmaNonUnit, n, (*m), c_one, dB, lddb, dA, ldda, queue ); magma_sgetmatrix( n, (*m), dA, ldda, A, lda, queue ); magma_queue_destroy( queue ); magma_free( dA ); magma_free( dB ); } timer_stop( time ); timer_printf( "time setmatrices trsm/mm + getmatrices = %6.2f\n", time ); } work[0] = magma_smake_lwork( lwmin ); iwork[0] = liwmin; return *info; } /* magma_ssygvd_m */
SEXP smagmaCholeskyFinal_m(SEXP A, SEXP n, SEXP NB, SEXP zeroTri, SEXP ngpu, SEXP lowerTri) { magma_init(); int ndevices; 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); float *sPA = calloc(In*In, sizeof(float)); int i,j; for(i = 0; i < In; i++) { for(j = 0; j < In; j++) { sPA[i*In + j] = (float) PA[i*In + j]; } } magma_int_t N, status, info, nGPUs; N = In; status = 0; nGPUs = ndevices; //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) magma_spotrf_m(nGPUs, MagmaLower, N, sPA, N, &info); else magma_spotrf_m(nGPUs, MagmaUpper, N, sPA, N, &info); if(info != 0) { printf("magma_spotrf 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]); //} magma_finalize(); cublasShutdown(); //caste sPA back to double and set upper or lower triangle to zero if necessary: int IZeroTri = INTEGER_VALUE(zeroTri); int zeroUTri = IZeroTri & lTri; int zeroLTri = IZeroTri & !lTri; if(!IZeroTri) { for(i = 1; i< In; i++) { for(j=1; j < In; j++) { PA[i*In + j] = (double) sPA[i*In + j]; } } } else if(zeroUTri) { for(i = 1; i< In; i++) { for(j=1; j < In; j++) { if(i > j) PA[i*In + j] = 0; else PA[i*In + j] = (double) sPA[i*In + j]; } } } else { for(i = 1; i< In; i++) { for(j=1; j < In; j++) { if(i < j) PA[i*In + j] = 0; else PA[i*In + j] = (double) sPA[i*In + j]; } } } UNPROTECT(1); free(sPA); return(R_NilValue); }
/** Purpose ------- SPOTRF 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**T * U, if uplo = MagmaUpper, or A = L * L**T, 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 user defined 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 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**T * U or A = L * L**T. \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_sposv_comp ********************************************************************/ extern "C" magma_int_t magma_spotrf(magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, magma_int_t *info) { #define A(i, j) (A + (j)*lda + (i)) #define dA(i, j) (work + (j)*ldda + (i)) /* Local variables */ const char* uplo_ = lapack_uplo_const( uplo ); magma_int_t ldda, nb; magma_int_t j, jb; float c_one = MAGMA_S_ONE; float c_neg_one = MAGMA_S_NEG_ONE; float *work; float d_one = 1.0; float 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 num_gpus = magma_num_gpus(); if ( num_gpus > 1 ) { /* call multiple-GPU interface */ return magma_spotrf_m(num_gpus, uplo, n, A, lda, info); } ldda = ((n+31)/32)*32; if (MAGMA_SUCCESS != magma_smalloc( &work, (n)*ldda )) { /* alloc failed so call the non-GPU-resident version */ return magma_spotrf_m(num_gpus, uplo, n, A, lda, info); } /* Define user stream if current stream is NULL */ cudaStream_t stream[3], current_stream; magmablasGetKernelStream(¤t_stream); magma_queue_create( &stream[0] ); magma_queue_create( &stream[2] ); if (current_stream == NULL) { magma_queue_create( &stream[1] ); magmablasSetKernelStream(stream[1]); } else stream[1] = current_stream; nb = magma_get_spotrf_nb(n); if (nb <= 1 || nb >= n) { lapackf77_spotrf(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_ssetmatrix_async( jb, (n-j), A(j, j), lda, dA(j, j), ldda, stream[1]); magma_ssyrk(MagmaUpper, MagmaTrans, jb, j, d_neg_one, dA(0, j), ldda, d_one, dA(j, j), ldda); magma_queue_sync( stream[1] ); magma_sgetmatrix_async( jb, jb, dA(j, j), ldda, A(j, j), lda, stream[0] ); if ( (j+jb) < n) { magma_sgemm(MagmaTrans, 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_sgetmatrix_async( j, jb, dA(0, j), ldda, A (0, j), lda, stream[2] ); magma_queue_sync( stream[0] ); lapackf77_spotrf(MagmaUpperStr, &jb, A(j, j), &lda, info); if (*info != 0) { *info = *info + j; break; } magma_ssetmatrix_async( jb, jb, A(j, j), lda, dA(j, j), ldda, stream[0] ); magma_queue_sync( stream[0] ); if ( (j+jb) < n ) { magma_strsm(MagmaLeft, MagmaUpper, MagmaTrans, 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_ssetmatrix_async( (n-j), jb, A(j, j), lda, dA(j, j), ldda, stream[1]); magma_ssyrk(MagmaLower, MagmaNoTrans, jb, j, d_neg_one, dA(j, 0), ldda, d_one, dA(j, j), ldda); magma_queue_sync( stream[1] ); magma_sgetmatrix_async( jb, jb, dA(j,j), ldda, A(j,j), lda, stream[0] ); if ( (j+jb) < n) { magma_sgemm( MagmaNoTrans, MagmaTrans, (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_sgetmatrix_async( jb, j, dA(j, 0), ldda, A(j, 0), lda, stream[2] ); magma_queue_sync( stream[0] ); lapackf77_spotrf(MagmaLowerStr, &jb, A(j, j), &lda, info); if (*info != 0) { *info = *info + j; break; } magma_ssetmatrix_async( jb, jb, A(j, j), lda, dA(j, j), ldda, stream[0] ); magma_queue_sync( stream[0] ); if ( (j+jb) < n) { magma_strsm(MagmaRight, MagmaLower, MagmaTrans, 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 (current_stream == NULL) { magma_queue_destroy( stream[1] ); magmablasSetKernelStream(NULL); } magma_free( work ); return *info; } /* magma_spotrf */
/***************************************************************************//** Purpose ------- SPOTRF 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 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. \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_potrf *******************************************************************************/ extern "C" magma_int_t magma_spotrf( magma_uplo_t uplo, magma_int_t n, float *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 float c_one = MAGMA_S_ONE; const float c_neg_one = MAGMA_S_NEG_ONE; const float d_one = 1.0; const float 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; magmaFloat_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_spotrf_nb( n ); if (nb <= 1 || nb >= n) { lapackf77_spotrf( 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_spotrf_m( ngpu, uplo, n, A, lda, info ); } if (MAGMA_SUCCESS != magma_smalloc( &dA, n*ldda )) { /* alloc failed so call the non-GPU-resident version */ return magma_spotrf_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_ssetmatrix_async( jb, n-j, A(j, j), lda, dA(j, j), ldda, queues[1] ); magma_ssyrk( 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_sgetmatrix_async( jb, jb, dA(j, j), ldda, A(j, j), lda, queues[0] ); if (j+jb < n) { magma_sgemm( 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_sgetmatrix_async( j, jb, dA(0, j), ldda, A(0, j), lda, queues[0] ); lapackf77_spotrf( MagmaUpperStr, &jb, A(j, j), &lda, info ); if (*info != 0) { *info = *info + j; break; } magma_ssetmatrix_async( jb, jb, A(j, j), lda, dA(j, j), ldda, queues[0] ); magma_queue_sync( queues[0] ); if (j+jb < n) { magma_strsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit, jb, n-j-jb, c_one, dA(j, j ), ldda, dA(j, j+jb), ldda, queues[1] ); } } } 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. jb = min( nb, n-j ); magma_ssetmatrix_async( n-j, jb, A(j, j), lda, dA(j, j), ldda, queues[1] ); magma_ssyrk( 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_sgetmatrix_async( jb, jb, dA(j,j), ldda, A(j,j), lda, queues[0] ); if (j+jb < n) { magma_sgemm( 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] ); } magma_queue_sync( queues[0] ); // this could be on any queue; it isn't needed until exit. magma_sgetmatrix_async( jb, j, dA(j, 0), ldda, A(j, 0), lda, queues[0] ); lapackf77_spotrf( MagmaLowerStr, &jb, A(j, j), &lda, info ); if (*info != 0) { *info = *info + j; break; } magma_ssetmatrix_async( jb, jb, A(j, j), lda, dA(j, j), ldda, queues[0] ); magma_queue_sync( queues[0] ); if (j+jb < n) { magma_strsm( 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_spotrf */
/** 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] 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 COMPLEX_16 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 COMPLEX_16 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] 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 REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. @param[out] work (workspace) COMPLEX_16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) 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 >= N + 1. If JOBZ = MagmaVec and N > 1, LWORK >= 2*N*nb + N**2. \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(1) 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: 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_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, 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) { const char* uplo_ = lapack_uplo_const( uplo ); const char* jobz_ = lapack_vec_const( jobz ); float c_one = MAGMA_S_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; 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 = 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; } /* 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; } magma_timer_t time=0; timer_start( time ); magma_spotrf_m(nrgpu, uplo, n, B, ldb, info); if (*info != 0) { *info = n + *info; return *info; } timer_stop( time ); timer_printf( "time spotrf = %6.2f\n", time ); timer_start( time ); /* Transform problem to standard eigenvalue problem and solve. */ magma_ssygst_m(nrgpu, itype, uplo, n, A, lda, B, ldb, info); timer_stop( time ); timer_printf( "time ssygst = %6.2f\n", time ); timer_start( time ); magma_ssyevdx_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 ssyevd = %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_strsm_m(nrgpu, MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, c_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_strmm(MagmaLeft, uplo, trans, MagmaNonUnit, // n, n, c_one, db, lddb, da, ldda); } timer_stop( time ); timer_printf( "time setmatrices trsm/mm + getmatrices = %6.2f\n", time ); } work[0] = lwmin * one_eps; // round up iwork[0] = liwmin; return *info; } /* magma_ssygvd_m */