extern "C" magma_int_t magma_zhegvdx_2stage_m(magma_int_t nrgpu, magma_int_t itype, char jobz, char range, char uplo, magma_int_t n, cuDoubleComplex *a, magma_int_t lda, cuDoubleComplex *b, magma_int_t ldb, double vl, double vu, magma_int_t il, magma_int_t iu, magma_int_t *m, double *w, cuDoubleComplex *work, magma_int_t lwork, double *rwork, magma_int_t lrwork, 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 ======= ZHEGVDX_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) COMPLEX*16 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) COMPLEX*16 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) 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 >= 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 (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: 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}; cuDoubleComplex c_one = MAGMA_Z_ONE; magma_int_t lower; char trans[1]; magma_int_t wantz; magma_int_t lquery; magma_int_t alleig, valeig, indeig; // magma_int_t lopt; magma_int_t lwmin; // magma_int_t liopt; magma_int_t liwmin; // magma_int_t lropt; magma_int_t lrwmin; cudaStream_t stream; magma_queue_create( &stream ); wantz = lapackf77_lsame(jobz_, MagmaVectorsStr); 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 (itype < 1 || itype > 3) { *info = -1; } else if (! (alleig || valeig || indeig)) { *info = -2; } else if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVectorsStr))) { *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_bulge_get_nb(n); magma_int_t lq2 = magma_zbulge_get_lq2(n); 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; } MAGMA_Z_SET2REAL(work[0],(double)lwmin); rwork[0] = lrwmin; iwork[0] = liwmin; if (lwork < lwmin && ! lquery) { *info = -17; } else if (lrwork < lrwmin && ! lquery) { *info = -19; } else if (liwork < liwmin && ! lquery) { *info = -21; } if (*info != 0) { magma_xerbla( __func__, -(*info)); return *info; } else if (lquery) { return *info; } /* Quick return if possible */ if (n == 0) { return *info; } /* Form a Cholesky factorization of B. */ #define ENABLE_TIMER #ifdef ENABLE_TIMER magma_timestr_t start, end; start = get_current_time(); #endif magma_zpotrf_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 zpotrf_m = %6.2f\n", GetTimerValue(start,end)/1000.); #endif #ifdef ENABLE_TIMER start = get_current_time(); #endif /* Transform problem to standard eigenvalue problem and solve. */ magma_zhegst_m(nrgpu, itype, uplo, n, a, lda, b, ldb, info); #ifdef ENABLE_TIMER end = get_current_time(); printf("time zhegst_m = %6.2f\n", GetTimerValue(start,end)/1000.); start = get_current_time(); #endif magma_zheevdx_2stage_m(nrgpu, jobz, range, uplo, n, a, lda, vl, vu, il, iu, m, w, work, lwork, rwork, lrwork, iwork, liwork, info); #ifdef ENABLE_TIMER end = get_current_time(); printf("time zheevdx_2stage_m = %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 = MagmaConjTrans; } else { *(unsigned char *)trans = MagmaNoTrans; } magma_ztrsm_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) { *(unsigned char *)trans = MagmaNoTrans; } else { *(unsigned char *)trans = MagmaConjTrans; } //magma_ztrmm_m(nrgpu, MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, c_one, b, ldb, a, lda); } #ifdef ENABLE_TIMER end = get_current_time(); printf("time trsm/mm_m = %6.2f\n", GetTimerValue(start,end)/1000.); #endif } /*work[0].r = (doublereal) lopt, work[0].i = 0.; rwork[0] = (doublereal) lropt; iwork[0] = liopt;*/ printf("\n\n\n"); return *info; } /* zhegvdx_2stage_m */
/* //////////////////////////////////////////////////////////////////////////// -- Testing zhetrd_he2hb */ int main( int argc, char** argv) { TESTING_INIT(); real_Double_t gpu_time, gpu_perf, gflops; magmaDoubleComplex *h_A, *h_R, *h_work, *dT1; magmaDoubleComplex *tau; double *D, *E; /* Matrix size */ magma_int_t N, n2, lda, lwork, lwork0; //ldt magma_int_t info; magma_int_t ione = 1; magma_int_t ISEED[4] = {0,0,0,1}; #if defined(CHECKEIG) #if defined(PRECISION_z) || defined(PRECISION_d) magma_int_t WANTZ=0; magma_int_t THREADS=1; #endif #endif magma_int_t NE = 0; magma_int_t NB = 0; magma_int_t ngpu = 1; magma_opts opts; opts.parse_opts( argc, argv ); NB = opts.nb; if (NB < 1) NB = 64; //64; //magma_get_zhetrd_he2hb_nb(N); // what is NE ? if (NE < 1) NE = 64; //N; //magma_get_zhetrd_he2hb_nb(N); // N not yet initialized printf("%% N GPU GFlop/s \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; //ldt = N; n2 = lda*N; gflops = FLOPS_ZHETRD( N ) / 1e9; /* We suppose the magma NB is bigger than lapack NB */ lwork0 = N*NB; /* Allocate host memory for the matrix */ TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, lda*N ); TESTING_MALLOC_CPU( tau, magmaDoubleComplex, N-1 ); TESTING_MALLOC_PIN( h_R, magmaDoubleComplex, lda*N ); TESTING_MALLOC_PIN( h_work, magmaDoubleComplex, lwork0 ); TESTING_MALLOC_PIN( D, double, N ); TESTING_MALLOC_PIN( E, double, N ); //TESTING_MALLOC_DEV( dT1, magmaDoubleComplex, (2*min(N,N) + roundup( N, 32 ))*NB ); TESTING_MALLOC_DEV( dT1, magmaDoubleComplex, (N*NB) ); // if (WANTZ) gflops = 2.0*gflops; /* ==================================================================== Initialize the matrix =================================================================== */ lapackf77_zlarnv( &ione, ISEED, &n2, h_A ); magma_zmake_hermitian( N, h_A, lda ); lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda ); /* ==================================================================== Performs operation using MAGMA =================================================================== */ magma_device_t cdev; magma_getdevice( &cdev ); gpu_time = magma_wtime(); /* magma_zhetrd_he2hb( opts.uplo, N, NB, h_R, lda, tau, h_work, lwork0, dT1, THREADS, &info); tband = magma_wtime - gpu_time(); printf(" Finish BAND N %d NB %d ngpu %d timing= %f\n", N, NB, ngpu, tband); magma_zhetrd_bhe2trc_v5(THREADS, WANTZ, opts.uplo, NE, N, NB, h_R, lda, D, E, dT1, ldt); */ /* magma_zhetrd_he2hb( opts.uplo, N, NB, h_R, lda, tau, h_work, lwork, dT1, THREADS, &info); tband = magma_wtime - gpu_time(); printf(" Finish BAND N %d NB %d ngpu %d timing= %f\n", N, NB, ngpu, tband); magma_zhetrd_bhe2trc(THREADS, WANTZ, opts.uplo, NE, N, NB, h_R, lda, D, E, dT1, ldt); */ magma_range_t range = MagmaRangeAll; magma_int_t m1 = 0; double vl = 0; double vu = 0; magma_int_t il = 0; magma_int_t iu = 0; if (opts.fraction == 0) { il = max( 1, magma_int_t(0.1*N) ); iu = max( 1, magma_int_t(0.3*N) ); } else { il = 1; iu = max( 1, magma_int_t(opts.fraction*N) ); } magmaDoubleComplex *hh_work; magma_int_t *iwork; magma_int_t /*nb,*/ /*lwork,*/ liwork; magma_int_t threads = magma_get_parallel_numthreads(); #ifdef COMPLEX double *rwork; magma_int_t lrwork; #endif magma_zheevdx_getworksize(N, threads, (opts.jobz == MagmaVec), &lwork, #ifdef COMPLEX &lrwork, #endif &liwork); TESTING_MALLOC_PIN( hh_work, magmaDoubleComplex, lwork ); TESTING_MALLOC_CPU( iwork, magma_int_t, liwork ); #ifdef COMPLEX TESTING_MALLOC_PIN( rwork, double, lrwork ); #endif if (ngpu == 1) { printf("calling zheevdx_2stage 1 GPU\n"); magma_zheevdx_2stage( opts.jobz, range, opts.uplo, N, h_R, lda, vl, vu, il, iu, &m1, D, hh_work, lwork, #ifdef COMPLEX rwork, lrwork, #endif iwork, liwork, &info); } else { printf("calling zheevdx_2stage_m %d GPU\n", (int) ngpu); magma_zheevdx_2stage_m(ngpu, opts.jobz, range, opts.uplo, N, h_R, lda, vl, vu, il, iu, &m1, D, hh_work, lwork, #ifdef COMPLEX rwork, lrwork, #endif iwork, liwork, &info); } magma_setdevice( cdev ); gpu_time = magma_wtime() - gpu_time; gpu_perf = gflops / gpu_time; /* ===================================================================== Check the factorization =================================================================== */ /* if ( opts.check ) { FILE *fp; printf("Writing input matrix in matlab_i_mat.txt ...\n"); fp = fopen ("matlab_i_mat.txt", "w"); if ( fp == NULL ) { printf("Couldn't open output file\n"); return -1; } for (j=0; j < N; j++) { for (k=0; k < N; k++) { #ifdef COMPLEX fprintf(fp, "%5d %5d %11.8f %11.8f\n", k+1, j+1, h_A[k+j*lda].x, h_A[k+j*lda].y); #else fprintf(fp, "%5d %5d %11.8f\n", k+1, j+1, h_A[k+j*lda]); #endif } } fclose( fp ); printf("Writing output matrix in matlab_o_mat.txt ...\n"); fp = fopen ("matlab_o_mat.txt", "w"); if ( fp == NULL ) { printf("Couldn't open output file\n"); return -1; } for (j=0; j < N; j++) { for (k=0; k < N; k++) { #ifdef COMPLEX fprintf(fp, "%5d %5d %11.8f %11.8f\n", k+1, j+1, h_R[k+j*lda].x, h_R[k+j*lda].y); #else fprintf(fp, "%5d %5d %11.8f\n", k+1, j+1, h_R[k+j*lda]); #endif } } fclose( fp ); } */ /* ===================================================================== Print performance and error. =================================================================== */ #if defined(CHECKEIG) #if defined(PRECISION_z) || defined(PRECISION_d) if ( opts.check ) { printf(" Total N %5d gflops %6.2f timing %6.2f seconds\n", (int) N, gpu_perf, gpu_time ); const char* JOBZ; if (WANTZ == 0) JOBZ = MagmaNoVecStr; else JOBZ = MagmaVecStr; double nrmI=0.0, nrm1=0.0, nrm2=0.0; int lwork2 = 256*N; magmaDoubleComplex *work2, *AINIT; double *rwork2, *D2; // TODO free this memory ! magma_zmalloc_cpu( &work2, lwork2 ); magma_dmalloc_cpu( &rwork2, N ); magma_dmalloc_cpu( &D2, N ); magma_zmalloc_cpu( &AINIT, N*lda ); memcpy(AINIT, h_A, N*lda*sizeof(magmaDoubleComplex)); /* compute the eigenvalues using lapack routine to be able to compare to it and used as ref */ cpu_time = magma_wtime(); i= min(12, THREADS); magma_set_lapack_numthreads( i ); lapackf77_zheev( "N", "L", &N, h_A, &lda, D2, work2, &lwork2, #ifdef COMPLEX rwork2, #endif &info ); ///* call eigensolver for our resulting tridiag [D E] and for Q */ //dstedc_withZ('V', N, D, E, h_R, lda); ////dsterf_( &N, D, E, &info); //// cpu_time = magma_wtime() - cpu_time; printf(" Finish CHECK - EIGEN timing= %f threads %d\n", cpu_time, i); /* for (i=0; i < 10; i++) printf(" voici lpk D[%d] %8.2e\n", i, D2[i]); */ //magmaDoubleComplex mydz=0.0, mydo=1.0; //magmaDoubleComplex *Z; // magma_zmalloc_cpu( &Z, N*lda ); // dgemm_("N", "N", &N, &N, &N, &mydo, h_R, &lda, h_A, &lda, &mydz, Z, &lda); /* compare result */ cmp_vals(N, D2, D, &nrmI, &nrm1, &nrm2); magmaDoubleComplex *WORKAJETER; double *RWORKAJETER, *RESU; // TODO free this memory ! magma_zmalloc_cpu( &WORKAJETER, (2* N * N + N) ); magma_dmalloc_cpu( &RWORKAJETER, N ); magma_dmalloc_cpu( &RESU, 10 ); int MATYPE; memset(RESU, 0, 10*sizeof(double)); MATYPE=3; double NOTHING=0.0; cpu_time = magma_wtime(); // check results zcheck_eig_( JOBZ, &MATYPE, &N, &NB, AINIT, &lda, &NOTHING, &NOTHING, D2, D, h_R, &lda, WORKAJETER, RWORKAJETER, RESU ); cpu_time = magma_wtime() - cpu_time; printf(" Finish CHECK - results timing= %f\n", cpu_time); magma_set_lapack_numthreads( 1 ); printf("\n"); printf(" ================================================================================================================\n"); printf(" ==> INFO voici threads=%d N=%d NB=%d WANTZ=%d\n", (int) THREADS, (int) N, (int) NB, (int) WANTZ); printf(" ================================================================================================================\n"); printf(" DSBTRD : %15s \n", "STATblgv9withQ "); printf(" ================================================================================================================\n"); if (WANTZ > 0) printf(" | A - U S U' | / ( |A| n ulp ) : %15.3E \n", RESU[0]); if (WANTZ > 0) printf(" | I - U U' | / ( n ulp ) : %15.3E \n", RESU[1]); printf(" | D1 - EVEIGS | / (|D| ulp) : %15.3E \n", RESU[2]); printf(" max | D1 - EVEIGS | : %15.3E \n", RESU[6]); printf(" ================================================================================================================\n\n\n"); printf(" ****************************************************************************************************************\n"); printf(" * Hello here are the norm Infinite (max)=%8.2e norm one (sum)=%8.2e norm2(sqrt)=%8.2e *\n", nrmI, nrm1, nrm2); printf(" ****************************************************************************************************************\n\n"); } #endif #endif printf(" Total N %5d gflops %6.2f timing %6.2f seconds\n", (int) N, gpu_perf, gpu_time ); printf("%%===========================================================================\n\n\n"); /* Memory clean up */ TESTING_FREE_CPU( h_A ); TESTING_FREE_CPU( tau ); TESTING_FREE_PIN( h_R ); TESTING_FREE_PIN( h_work ); TESTING_FREE_PIN( D ); TESTING_FREE_PIN( E ); TESTING_FREE_DEV( dT1 ); /* TODO - not all memory has been freed inside loop */ fflush( stdout ); } if ( opts.niter > 1 ) { printf( "\n" ); } } TESTING_FINALIZE(); return EXIT_SUCCESS; }