magma_int_t magma_cbulge_get_lq2(magma_int_t n, magma_int_t threads) { magma_int_t nb = magma_get_cbulge_nb(n, threads); magma_int_t Vblksiz = magma_cbulge_get_Vblksiz(n, nb, threads); magma_int_t ldv = nb + Vblksiz; magma_int_t ldt = Vblksiz; return magma_bulge_get_blkcnt(n, nb, Vblksiz) * Vblksiz * (ldt + ldv + 1); }
extern "C" magma_int_t magma_cheevdx_2stage_m(magma_int_t nrgpu, char jobz, char range, char uplo, magma_int_t n, magmaFloatComplex *a, magma_int_t lda, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *m, float *w, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, 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 ======= CHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. 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 ========= JOBZ (input) CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. 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. 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. A (input/output) COMPLEX 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, the first m columns of A contains the required orthonormal eigenvectors of the matrix A. If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed. LDA (input) INTEGER The leading dimension of the array A. LDA >= 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 required m eigenvalues in ascending order. WORK (workspace/output) COMPLEX 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 + 1). If JOBZ = 'V' and N > 1, LWORK >= LQ2 + 2*N + 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. RWORK (workspace/output) DOUBLE PRECISION array, dimension (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: 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). Further Details =============== Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA Modified description of INFO. Sven, 16 Feb 05. ===================================================================== */ char uplo_[2] = {uplo, 0}; char jobz_[2] = {jobz, 0}; char range_[2] = {range, 0}; magmaFloatComplex c_one = MAGMA_C_ONE; magma_int_t ione = 1; magma_int_t izero = 0; float d_one = 1.; float d__1; float eps; float anrm; magma_int_t imax; float rmin, rmax; float sigma; //magma_int_t iinfo; magma_int_t lwmin, lrwmin, liwmin; magma_int_t lower; magma_int_t wantz; magma_int_t iscale; float safmin; float bignum; float smlnum; magma_int_t lquery; magma_int_t alleig, valeig, indeig; /* 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 || lrwork == -1 || liwork == -1; *info = 0; if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) { *info = -1; } else if (! (alleig || valeig || indeig)) { *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 (valeig) { if (n > 0 && vu <= vl) { *info = -8; } } else if (indeig) { if (il < 1 || il > max(1,n)) { *info = -9; } else if (iu < min(n,il) || iu > n) { *info = -10; } } } magma_int_t nb = magma_get_cbulge_nb(n, threads); magma_int_t Vblksiz = magma_cbulge_get_Vblksiz(n, nb, threads); magma_int_t ldt = Vblksiz; magma_int_t ldv = nb + Vblksiz; magma_int_t blkcnt = magma_bulge_get_blkcnt(n, nb, Vblksiz); magma_int_t lq2 = magma_cbulge_get_lq2(n, threads); if (wantz) { lwmin = lq2 + 2 * n + n * n; lrwmin = 1 + 5 * n + 2 * n * n; liwmin = 5 * n + 3; } else { lwmin = lq2 + n * (nb + 1); lrwmin = n; liwmin = 1; } work[0] = MAGMA_C_MAKE( lwmin * (1. + lapackf77_slamch("Epsilon")), 0.); // round up rwork[0] = lrwmin * (1. + lapackf77_slamch("Epsilon")); iwork[0] = liwmin; if ((lwork < lwmin) && !lquery) { *info = -14; } else if ((lrwork < lrwmin) && ! lquery) { *info = -16; } else if ((liwork < liwmin) && ! lquery) { *info = -18; } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } else if (lquery) { return *info; } /* Quick return if possible */ if (n == 0) { return *info; } if (n == 1) { w[0] = MAGMA_C_REAL(a[0]); if (wantz) { a[0] = MAGMA_C_ONE; } return *info; } #ifdef ENABLE_DEBUG printf("using %d threads\n", threads); #endif /* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */ magma_int_t ntiles = n/nb; if( ( ntiles < 2 ) || ( 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_cheevd(jobz_, uplo_, &n, a, &lda, w, work, &lwork, #if defined(PRECISION_z) || defined(PRECISION_c) rwork, &lrwork, #endif iwork, &liwork, info); *m = n; return *info; } /* Get machine constants. */ safmin = lapackf77_slamch("Safe minimum"); eps = lapackf77_slamch("Precision"); smlnum = safmin / eps; bignum = 1. / smlnum; rmin = magma_ssqrt(smlnum); rmax = magma_ssqrt(bignum); /* Scale matrix to allowable range, if necessary. */ anrm = lapackf77_clanhe("M", uplo_, &n, a, &lda, rwork); iscale = 0; if (anrm > 0. && anrm < rmin) { iscale = 1; sigma = rmin / anrm; } else if (anrm > rmax) { iscale = 1; sigma = rmax / anrm; } if (iscale == 1) { lapackf77_clascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, a, &lda, info); } magma_int_t indT2 = 0; magma_int_t indTAU2 = indT2 + blkcnt*ldt*Vblksiz; magma_int_t indV2 = indTAU2+ blkcnt*Vblksiz; magma_int_t indtau1 = indV2 + blkcnt*ldv*Vblksiz; magma_int_t indwrk = indtau1+ n; magma_int_t indwk2 = indwrk + n * n; magma_int_t llwork = lwork - indwrk; magma_int_t llwrk2 = lwork - indwk2; magma_int_t inde = 0; magma_int_t indrwk = inde + n; magma_int_t llrwk = lrwork - indrwk; #ifdef ENABLE_TIMER magma_timestr_t start, st1, st2, end; start = get_current_time(); #endif #ifdef HE2HB_SINGLEGPU magmaFloatComplex *dT1; if (MAGMA_SUCCESS != magma_cmalloc( &dT1, n*nb)) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } #ifdef ENABLE_TIMER tband1 = get_current_time(); #endif magma_chetrd_he2hb(uplo, n, nb, a, lda, &work[indtau1], &work[indwrk], llwork, dT1, threads, info); #ifdef ENABLE_TIMER tband2 = get_current_time(); printf(" 1 GPU seq code time chetrd_he2hb only = %7.4f\n" , GetTimerValue(tband1,tband2)/1000.); #endif magma_free(dT1); #else magma_int_t nstream = max(3,nrgpu+2); magma_queue_t streams[MagmaMaxGPUs][20]; magmaFloatComplex *da[MagmaMaxGPUs],*dT1[MagmaMaxGPUs]; magma_int_t ldda = ((n+31)/32)*32; magma_int_t ver = 0; magma_int_t distblk = max(256, 4*nb); #ifdef ENABLE_DEBUG printf("voici ngpu %d distblk %d NB %d nstream %d version %d \n ",nrgpu,distblk,nb,nstream,ver); #endif #ifdef ENABLE_TIMER magma_timestr_t tband1, tband2, t1, t2, ta1, ta2; t1 = get_current_time(); #endif for( magma_int_t dev = 0; dev < nrgpu; ++dev ) { magma_int_t mlocal = ((n / distblk) / nrgpu + 1) * distblk; magma_setdevice( dev ); magma_cmalloc(&da[dev], ldda*mlocal ); magma_cmalloc(&dT1[dev], (n*nb) ); for( int i = 0; i < nstream; ++i ) { magma_queue_create( &streams[dev][i] ); } } #ifdef ENABLE_TIMER t2 = get_current_time(); #endif magma_csetmatrix_1D_col_bcyclic( n, n, a, lda, da, ldda, nrgpu, distblk); magma_setdevice(0); #ifdef ENABLE_TIMER tband1 = get_current_time(); #endif if(ver==30){ magma_chetrd_he2hb_mgpu_spec(uplo, n, nb, a, lda, &work[indtau1], &work[indwrk], llwork, da, ldda, dT1, nb, nrgpu, distblk, streams, nstream, threads, info); }else{ magma_chetrd_he2hb_mgpu(uplo, n, nb, a, lda, &work[indtau1], &work[indwrk], llwork, da, ldda, dT1, nb, nrgpu, distblk, streams, nstream, threads, info); } #ifdef ENABLE_TIMER tband2 = get_current_time(); printf(" time alloc %7.4f, ditribution %7.4f, chetrd_he2hb only = %7.4f\n" , GetTimerValue(t1,t2)/1000., GetTimerValue(t2,tband1)/1000., GetTimerValue(tband1,tband2)/1000.); #endif for( magma_int_t dev = 0; dev < nrgpu; ++dev ) { magma_setdevice( dev ); magma_free( da[dev] ); magma_free( dT1[dev] ); for( int i = 0; i < nstream; ++i ) { magma_queue_destroy( streams[dev][i] ); } } #endif #ifdef ENABLE_TIMER st1 = get_current_time(); printf(" time chetrd_he2hb_mgpu = %6.2f\n" , GetTimerValue(start,st1)/1000.); #endif /* copy the input matrix into WORK(INDWRK) with band storage */ /* PAY ATTENTION THAT work[indwrk] should be able to be of size lda2*n which it should be checked in any future modification of lwork.*/ magma_int_t lda2 = 2*nb; //nb+1+(nb-1); magmaFloatComplex* A2 = &work[indwrk]; memset(A2 , 0, n*lda2*sizeof(magmaFloatComplex)); for (magma_int_t j = 0; j < n-nb; j++) { cblas_ccopy(nb+1, &a[j*(lda+1)], 1, &A2[j*lda2], 1); memset(&a[j*(lda+1)], 0, (nb+1)*sizeof(magmaFloatComplex)); a[nb + j*(lda+1)] = c_one; } for (magma_int_t j = 0; j < nb; j++) { cblas_ccopy(nb-j, &a[(j+n-nb)*(lda+1)], 1, &A2[(j+n-nb)*lda2], 1); memset(&a[(j+n-nb)*(lda+1)], 0, (nb-j)*sizeof(magmaFloatComplex)); } #ifdef ENABLE_TIMER st2 = get_current_time(); printf(" time chetrd_convert = %6.2f\n" , GetTimerValue(st1,st2)/1000.); #endif magma_chetrd_hb2st(threads, uplo, n, nb, Vblksiz, A2, lda2, w, &rwork[inde], &work[indV2], ldv, &work[indTAU2], wantz, &work[indT2], ldt); #ifdef ENABLE_TIMER end = get_current_time(); printf(" time chetrd_hb2st = %6.2f\n" , GetTimerValue(st2,end)/1000.); printf(" time chetrd = %6.2f\n", GetTimerValue(start,end)/1000.); #endif /* For eigenvalues only, call SSTERF. For eigenvectors, first call CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the tridiagonal matrix, then call CUNMTR to multiply it to the Householder transformations represented as Householder vectors in A. */ if (! wantz) { #ifdef ENABLE_TIMER start = get_current_time(); #endif lapackf77_ssterf(&n, w, &rwork[inde], info); magma_smove_eig(range, n, w, &il, &iu, vl, vu, m); #ifdef ENABLE_TIMER end = get_current_time(); printf(" time dstedc = %6.2f\n", GetTimerValue(start,end)/1000.); #endif } else { #ifdef ENABLE_TIMER start = get_current_time(); #endif magma_cstedx_m(nrgpu, range, n, vl, vu, il, iu, w, &rwork[inde], &work[indwrk], n, &rwork[indrwk], llrwk, iwork, liwork, info); #ifdef ENABLE_TIMER end = get_current_time(); printf(" time cstedx_m = %6.2f\n", GetTimerValue(start,end)/1000.); start = get_current_time(); #endif magma_smove_eig(range, n, w, &il, &iu, vl, vu, m); /* magmaFloatComplex *dZ; magma_int_t lddz = n; if (MAGMA_SUCCESS != magma_cmalloc( &dZ, *m*lddz)) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magma_cbulge_back(threads, uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n, dZ, lddz, &work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info); magma_cgetmatrix( n, *m, dZ, lddz, &work[indwrk], n); magma_free(dZ); */ magma_cbulge_back_m(nrgpu, threads, uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n, &work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info); #ifdef ENABLE_TIMER st1 = get_current_time(); printf(" time cbulge_back_m = %6.2f\n" , GetTimerValue(start,st1)/1000.); #endif magma_cunmqr_m(nrgpu, MagmaLeft, MagmaNoTrans, n-nb, *m, n-nb, a+nb, lda, &work[indtau1], &work[indwrk + n * (il-1) + nb], n, &work[indwk2], llwrk2, info); lapackf77_clacpy("A", &n, m, &work[indwrk + n * (il-1)], &n, a, &lda); #ifdef ENABLE_TIMER end = get_current_time(); printf(" time cunmqr_m + copy = %6.2f\n", GetTimerValue(st1,end)/1000.); printf(" time eigenvectors backtransf. = %6.2f\n" , GetTimerValue(start,end)/1000.); #endif } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { if (*info == 0) { imax = n; } else { imax = *info - 1; } d__1 = 1. / sigma; blasf77_sscal(&imax, &d__1, w, &ione); } work[0] = MAGMA_C_MAKE((float) lwmin, 0.); rwork[0] = (float) lrwmin; iwork[0] = liwmin; return *info; } /* magma_cheevdx_2stage_m */
/** Purpose ------- CHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. It uses a two-stage algorithm for the tridiagonalization. If eigenvectors are desired, it uses a divide and conquer algorithm. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. Arguments --------- @param[in] jobz magma_vec_t - = MagmaNoVec: Compute eigenvalues only; - = MagmaVec: Compute eigenvalues and eigenvectors. @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] 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 COMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = MagmaVec, then if INFO = 0, the first m columns of A contains the required orthonormal eigenvectors of the matrix A. If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. @param[in] lda INTEGER The leading dimension of the array A. LDA >= 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 required m eigenvalues in ascending order. @param[out] work (workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. @param[in] lwork INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LWORK >= LQ2 + N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= LQ2 + 2*N + N**2. where LQ2 is the size needed to store the Q2 matrix and is returned by magma_bulge_get_lq2. \n If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. @param[out] rwork (workspace) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK. @param[in] lrwork INTEGER The dimension of the array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LRWORK >= N. If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2. \n 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. @param[out] iwork (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. @param[in] liwork INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1. If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N. \n If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. @param[out] info INTEGER - = 0: successful exit - < 0: if INFO = -i, the i-th argument had an illegal value - > 0: 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). Further Details --------------- Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA Modified description of INFO. Sven, 16 Feb 05. @ingroup magma_cheev_driver ********************************************************************/ extern "C" magma_int_t magma_cheevdx_2stage( magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *m, float *w, magmaFloatComplex *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) { #define A( i_,j_) (A + (i_) + (j_)*lda) #define A2(i_,j_) (A2 + (i_) + (j_)*lda2) const char* uplo_ = lapack_uplo_const( uplo ); const char* jobz_ = lapack_vec_const( jobz ); magmaFloatComplex c_one = MAGMA_C_ONE; magma_int_t ione = 1; magma_int_t izero = 0; float d_one = 1.; float d__1; float eps; float anrm; magma_int_t imax; float rmin, rmax; float sigma; //magma_int_t iinfo; magma_int_t lwmin, lrwmin, liwmin; magma_int_t lower; magma_int_t wantz; magma_int_t iscale; float safmin; float bignum; float smlnum; magma_int_t lquery; magma_int_t alleig, valeig, indeig; magma_int_t len; float* dwork; /* determine the number of threads */ magma_int_t parallel_threads = magma_get_parallel_numthreads(); wantz = (jobz == MagmaVec); lower = (uplo == MagmaLower); alleig = (range == MagmaRangeAll); valeig = (range == MagmaRangeV); indeig = (range == MagmaRangeI); lquery = (lwork == -1 || lrwork == -1 || liwork == -1); *info = 0; if (! (wantz || (jobz == MagmaNoVec))) { *info = -1; } else if (! (alleig || valeig || indeig)) { *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 (valeig) { if (n > 0 && vu <= vl) { *info = -8; } } else if (indeig) { if (il < 1 || il > max(1,n)) { *info = -9; } else if (iu < min(n,il) || iu > n) { *info = -10; } } } magma_int_t nb = magma_get_cbulge_nb(n,parallel_threads); magma_int_t Vblksiz = magma_cbulge_get_Vblksiz(n, nb, parallel_threads); magma_int_t ldt = Vblksiz; magma_int_t ldv = nb + Vblksiz; magma_int_t blkcnt = magma_bulge_get_blkcnt(n, nb, Vblksiz); magma_int_t lq2 = magma_cbulge_get_lq2(n, parallel_threads); if (wantz) { lwmin = lq2 + 2*n + n*n; lrwmin = 1 + 5*n + 2*n*n; liwmin = 5*n + 3; } else { lwmin = lq2 + n + n*nb; lrwmin = n; 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] = MAGMA_C_MAKE( lwmin * one_eps, 0.); // round up rwork[0] = lrwmin * one_eps; iwork[0] = liwmin; if ((lwork < lwmin) && !lquery) { *info = -14; } else if ((lrwork < lrwmin) && ! lquery) { *info = -16; } else if ((liwork < liwmin) && ! lquery) { *info = -18; } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } else if (lquery) { return *info; } /* Quick return if possible */ if (n == 0) { return *info; } if (n == 1) { w[0] = MAGMA_C_REAL(A[0]); if (wantz) { A[0] = MAGMA_C_ONE; } return *info; } timer_printf("using %d parallel_threads\n", (int) parallel_threads); /* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */ magma_int_t ntiles = n/nb; if ( ( ntiles < 2 ) || ( 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_cheevd(jobz_, uplo_, &n, A, &lda, w, work, &lwork, #if defined(PRECISION_z) || defined(PRECISION_c) rwork, &lrwork, #endif iwork, &liwork, info); *m = n; return *info; } /* Get machine constants. */ safmin = lapackf77_slamch("Safe minimum"); eps = lapackf77_slamch("Precision"); smlnum = safmin / eps; bignum = 1. / smlnum; rmin = magma_ssqrt(smlnum); rmax = magma_ssqrt(bignum); /* Scale matrix to allowable range, if necessary. */ anrm = lapackf77_clanhe("M", uplo_, &n, A, &lda, rwork); iscale = 0; if (anrm > 0. && anrm < rmin) { iscale = 1; sigma = rmin / anrm; } else if (anrm > rmax) { iscale = 1; sigma = rmax / anrm; } if (iscale == 1) { lapackf77_clascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, A, &lda, info); } magma_int_t indT2 = 0; magma_int_t indTAU2 = indT2 + blkcnt*ldt*Vblksiz; magma_int_t indV2 = indTAU2+ blkcnt*Vblksiz; magma_int_t indtau1 = indV2 + blkcnt*ldv*Vblksiz; magma_int_t indwrk = indtau1+ n; //magma_int_t indwk2 = indwrk + n*n; magma_int_t llwork = lwork - indwrk; //magma_int_t llwrk2 = lwork - indwk2; magma_int_t inde = 0; magma_int_t indrwk = inde + n; magma_int_t llrwk = lrwork - indrwk; magma_timer_t time=0, time_total=0; timer_start( time_total ); timer_start( time ); magmaFloatComplex *dT1; if (MAGMA_SUCCESS != magma_cmalloc( &dT1, n*nb)) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magma_chetrd_he2hb(uplo, n, nb, A, lda, &work[indtau1], &work[indwrk], llwork, dT1, info); timer_stop( time ); timer_printf( " time chetrd_he2hb = %6.2f\n", time ); timer_start( time ); /* copy the input matrix into WORK(INDWRK) with band storage */ /* PAY ATTENTION THAT work[indwrk] should be able to be of size lda2*n which it should be checked in any future modification of lwork.*/ magma_int_t lda2 = 2*nb; //nb+1+(nb-1); magmaFloatComplex* A2 = &work[indwrk]; memset(A2, 0, n*lda2*sizeof(magmaFloatComplex)); for (magma_int_t j = 0; j < n-nb; j++) { len = nb+1; blasf77_ccopy( &len, A(j,j), &ione, A2(0,j), &ione ); memset(A(j,j), 0, (nb+1)*sizeof(magmaFloatComplex)); *A(nb+j,j) = c_one; } for (magma_int_t j = 0; j < nb; j++) { len = nb-j; blasf77_ccopy( &len, A(j+n-nb,j+n-nb), &ione, A2(0,j+n-nb), &ione ); memset(A(j+n-nb,j+n-nb), 0, (nb-j)*sizeof(magmaFloatComplex)); } timer_stop( time ); timer_printf( " time chetrd_convert = %6.2f\n", time ); timer_start( time ); magma_chetrd_hb2st(uplo, n, nb, Vblksiz, A2, lda2, w, &rwork[inde], &work[indV2], ldv, &work[indTAU2], wantz, &work[indT2], ldt); timer_stop( time ); timer_stop( time_total ); timer_printf( " time chetrd_hb2st = %6.2f\n", time ); timer_printf( " time chetrd = %6.2f\n", time_total ); /* For eigenvalues only, call SSTERF. For eigenvectors, first call CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the tridiagonal matrix, then call CUNMTR to multiply it to the Householder transformations represented as Householder vectors in A. */ if (! wantz) { timer_start( time ); lapackf77_ssterf(&n, w, &rwork[inde], info); magma_smove_eig(range, n, w, &il, &iu, vl, vu, m); timer_stop( time ); timer_printf( " time dstedc = %6.2f\n", time ); } else { timer_start( time_total ); timer_start( time ); if (MAGMA_SUCCESS != magma_smalloc( &dwork, 3*n*(n/2 + 1) )) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magma_cstedx(range, n, vl, vu, il, iu, w, &rwork[inde], &work[indwrk], n, &rwork[indrwk], llrwk, iwork, liwork, dwork, info); magma_free( dwork ); timer_stop( time ); timer_printf( " time cstedx = %6.2f\n", time ); timer_start( time ); magmaFloatComplex *dZ; magma_int_t lddz = n; magmaFloatComplex *da; magma_int_t ldda = n; magma_smove_eig(range, n, w, &il, &iu, vl, vu, m); if (MAGMA_SUCCESS != magma_cmalloc( &dZ, *m*lddz)) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } if (MAGMA_SUCCESS != magma_cmalloc( &da, n*ldda )) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magma_cbulge_back(uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n, dZ, lddz, &work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info); timer_stop( time ); timer_printf( " time cbulge_back = %6.2f\n", time ); timer_start( time ); magma_csetmatrix( n, n, A, lda, da, ldda ); magma_cunmqr_gpu_2stages(MagmaLeft, MagmaNoTrans, n-nb, *m, n-nb, da+nb, ldda, dZ+nb, n, dT1, nb, info); magma_cgetmatrix( n, *m, dZ, lddz, A, lda ); magma_free(dT1); magma_free(dZ); magma_free(da); timer_stop( time ); timer_stop( time_total ); timer_printf( " time cunmqr + copy = %6.2f\n", time ); timer_printf( " time eigenvectors backtransf. = %6.2f\n", time_total ); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { if (*info == 0) { imax = n; } else { imax = *info - 1; } d__1 = 1. / sigma; blasf77_sscal(&imax, &d__1, w, &ione); } work[0] = MAGMA_C_MAKE( lwmin * one_eps, 0.); // round up rwork[0] = lrwmin * one_eps; iwork[0] = liwmin; return *info; } /* magma_cheevdx_2stage */