/* ////////////////////////////////////////////////////////////////////////////
   -- Testing cheevd
*/
int main( int argc, char** argv) 
{
    TESTING_CUDA_INIT();

    cuFloatComplex *h_A, *h_R, *h_work;
    float *rwork, *w1, *w2;
    magma_int_t *iwork;
    float gpu_time, cpu_time;

    magma_timestr_t start, end;

    /* Matrix size */
    magma_int_t N=0, n2;
    magma_int_t size[8] = {1024,2048,3072,4032,5184,6016,7040,8064};

    magma_int_t i, info;
    magma_int_t ione     = 1, izero = 0;
    magma_int_t ISEED[4] = {0,0,0,1};

    const char *uplo = MagmaLowerStr;
    const char *jobz = MagmaVectorsStr;

    magma_int_t checkres;
    float result[3], eps = lapackf77_slamch( "E" );

    if (argc != 1){
        for(i = 1; i<argc; i++){
            if (strcmp("-N", argv[i])==0) {
                N = atoi(argv[++i]);
            }
            else if ( strcmp("-JV", argv[i]) == 0 ) {
                jobz = MagmaVectorsStr;
            }
            else if ( strcmp("-JN", argv[i]) == 0 ) {
                jobz = MagmaNoVectorsStr;
            }
        }
        if (N>0)
            printf("  testing_cheevd -N %d [-JV] [-JN]\n\n", (int) N);
        else {
            printf("\nUsage: \n");
            printf("  testing_cheevd -N %d [-JV] [-JN]\n\n", (int) N);
            exit(1);
        }
    }
    else {
        printf("\nUsage: \n");
        printf("  testing_cheevd -N %d [-JV] [-JN]\n\n", 1024);
        N = size[7];
    }

    checkres  = getenv("MAGMA_TESTINGS_CHECK") != NULL;
    if ( checkres && jobz[0] == MagmaNoVectors ) {
        printf( "Cannot check results when vectors are not computed (jobz='N')\n" );
        checkres = false;
    }

    /* Query for workspace sizes */
    cuFloatComplex aux_work[1];
    float          aux_rwork[1];
    magma_int_t     aux_iwork[1];
    magma_cheevd( jobz[0], uplo[0],
                  N, h_R, N, w1,
                  aux_work,  -1,
                  aux_rwork, -1,
                  aux_iwork, -1,
                  &info );
    magma_int_t lwork, lrwork, liwork;
    lwork  = (magma_int_t) MAGMA_C_REAL( aux_work[0] );
    lrwork = (magma_int_t) aux_rwork[0];
    liwork = aux_iwork[0];

    /* Allocate host memory for the matrix */
    TESTING_MALLOC(    h_A, cuFloatComplex, N*N );
    TESTING_MALLOC(    w1,  float         , N   );
    TESTING_MALLOC(    w2,  float         , N   );
    TESTING_HOSTALLOC( h_R, cuFloatComplex, N*N );
    TESTING_HOSTALLOC( h_work, cuFloatComplex, lwork  );
    TESTING_MALLOC(    rwork,  float,          lrwork );
    TESTING_MALLOC(    iwork,  magma_int_t,     liwork );
    
    printf("  N     CPU Time(s)    GPU Time(s) \n");
    printf("===================================\n");
    for(i=0; i<8; i++){
        if (argc==1){
            N = size[i];
        }
        n2 = N*N;

        /* Initialize the matrix */
        lapackf77_clarnv( &ione, ISEED, &n2, h_A );
        for( int i=0; i<N; i++) {
            MAGMA_C_SET2REAL( h_A[i*N+i], MAGMA_C_REAL(h_A[i*N+i]) );
        }
        lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );

        /* warm up run */
        magma_cheevd(jobz[0], uplo[0],
                     N, h_R, N, w1,
                     h_work, lwork, 
                     rwork, lrwork, 
                     iwork, liwork, 
                     &info);
        
        lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );

        /* query for optimal workspace sizes */
        magma_cheevd(jobz[0], uplo[0],
                     N, h_R, N, w1,
                     h_work, -1,
                     rwork,  -1,
                     iwork,  -1,
                     &info);
        int lwork_save  = lwork;
        int lrwork_save = lrwork;
        int liwork_save = liwork;
        lwork  = min( lwork,  (magma_int_t) MAGMA_C_REAL( h_work[0] ));
        lrwork = min( lrwork, (magma_int_t) rwork[0] );
        liwork = min( liwork, iwork[0] );
        //printf( "lwork %d, query %d, used %d; liwork %d, query %d, used %d\n",
        //        lwork_save,  (magma_int_t) h_work[0], lwork,
        //        liwork_save, iwork[0], liwork );

        /* ====================================================================
           Performs operation using MAGMA
           =================================================================== */
        start = get_current_time();
        magma_cheevd(jobz[0], uplo[0],
                     N, h_R, N, w1,
                     h_work, lwork,
                     rwork, lrwork,
                     iwork, liwork,
                     &info);
        end = get_current_time();

        gpu_time = GetTimerValue(start,end)/1000.;

        lwork  = lwork_save;
        lrwork = lrwork_save;
        liwork = liwork_save;
        
        if ( checkres ) {
          /* =====================================================================
             Check the results following the LAPACK's [zcds]drvst routine.
             A is factored as A = U S U' and the following 3 tests computed:
             (1)    | A - U S U' | / ( |A| N )
             (2)    | I - U'U | / ( N )
             (3)    | S(with U) - S(w/o U) | / | S |
             =================================================================== */
          float temp1, temp2;
          cuFloatComplex *tau;

          lapackf77_chet21(&ione, uplo, &N, &izero,
                           h_A, &N,
                           w1, w1,
                           h_R, &N,
                           h_R, &N,
                           tau, h_work, rwork, &result[0]);
          
          lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
          magma_cheevd('N', uplo[0],
                       N, h_R, N, w2,
                       h_work, lwork,
                       rwork, lrwork,
                       iwork, liwork,
                       &info);

          temp1 = temp2 = 0;
          for(int j=0; j<N; j++){
            temp1 = max(temp1, absv(w1[j]));
            temp1 = max(temp1, absv(w2[j]));
            temp2 = max(temp2, absv(w1[j]-w2[j]));
          }
          result[2] = temp2 / temp1;
        }

        /* =====================================================================
           Performs operation using LAPACK
           =================================================================== */
        start = get_current_time();
        lapackf77_cheevd(jobz, uplo,
                         &N, h_A, &N, w2,
                         h_work, &lwork,
                         rwork, &lrwork,
                         iwork, &liwork,
                         &info);
        end = get_current_time();
        if (info < 0)
          printf("Argument %d of cheevd had an illegal value.\n", (int) -info);

        cpu_time = GetTimerValue(start,end)/1000.;

        /* =====================================================================
           Print execution time
           =================================================================== */
        printf("%5d     %6.2f         %6.2f\n",
               (int) N, cpu_time, gpu_time);
        if ( checkres ){
          printf("Testing the factorization A = U S U' for correctness:\n");
          printf("(1)    | A - U S U' | / (|A| N) = %e\n", result[0]*eps);
          printf("(2)    | I -   U'U  | /  N      = %e\n", result[1]*eps);
          printf("(3)    | S(w/ U)-S(w/o U)|/ |S| = %e\n\n", result[2]);
        }

        if (argc != 1)
            break;
    }
 
    /* Memory clean up */
    TESTING_FREE(       h_A);
    TESTING_FREE(        w1);
    TESTING_FREE(        w2);
    TESTING_FREE(     rwork);
    TESTING_FREE(     iwork);
    TESTING_HOSTFREE(h_work);
    TESTING_HOSTFREE(   h_R);

    /* Shutdown */
    TESTING_CUDA_FINALIZE();
}
Exemple #2
0
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 */
Exemple #3
0
/**
    Purpose
    -------
    CHEEVDX_GPU computes selected eigenvalues and, optionally, eigenvectors
    of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
    be selected by specifying either a range of values or a range of
    indices for the desired eigenvalues.
    If eigenvectors are desired, it uses a divide and conquer algorithm.

    The divide and conquer algorithm makes very mild assumptions about
    floating point arithmetic. It will work on machines with a guard
    digit in add/subtract, or on those binary machines without guard
    digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
    Cray-2. It could conceivably fail on hexadecimal or decimal machines
    without guard digits, but we know of none.

    Arguments
    ---------
    @param[in]
    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]
    dA      COMPLEX array on the GPU,
            dimension (LDDA, 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]
    ldda    INTEGER
            The leading dimension of the array DA.  LDDA >= 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
    wA      (workspace) COMPLEX array, dimension (LDWA, N)

    @param[in]
    ldwa    INTEGER
            The leading dimension of the array wA.  LDWA >= max(1,N).

    @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 >= N + N*NB.
            If JOBZ = MagmaVec   and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ).
            NB can be obtained through magma_get_chetrd_nb(N).
    \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_gpu(magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo,
                  magma_int_t n,
                  magmaFloatComplex *dA, magma_int_t ldda,
                  float vl, float vu, magma_int_t il, magma_int_t iu,
                  magma_int_t *m, float *w,
                  magmaFloatComplex *wA,  magma_int_t ldwa,
                  magmaFloatComplex *work, magma_int_t lwork,
                  float *rwork, magma_int_t lrwork,
                  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  );
    magma_int_t ione = 1;

    float d__1;

    float eps;
    magma_int_t inde;
    float anrm;
    magma_int_t imax;
    float rmin, rmax;
    float sigma;
    magma_int_t iinfo, lwmin;
    magma_int_t lower;
    magma_int_t llrwk;
    magma_int_t wantz;
    magma_int_t indwk2, llwrk2;
    magma_int_t iscale;
    float safmin;
    float bignum;
    magma_int_t indtau;
    magma_int_t indrwk, indwrk, liwmin;
    magma_int_t lrwmin, llwork;
    float smlnum;
    magma_int_t lquery;
    magma_int_t alleig, valeig, indeig;

    float *dwork;
    magmaFloatComplex *dC;
    magma_int_t lddc = ldda;

    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 (ldda < max(1,n)) {
        *info = -6;
    } else if (ldwa < max(1,n)) {
        *info = -14;
    } 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_chetrd_nb( n );
    if ( n <= 1 ) {
        lwmin  = 1;
        lrwmin = 1;
        liwmin = 1;
    }
    else if ( wantz ) {
        lwmin  = max( n + n*nb, 2*n + n*n );
        lrwmin = 1 + 5*n + 2*n*n;
        liwmin = 3 + 5*n;
    }
    else {
        lwmin  = 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.);
    rwork[0] = lrwmin * one_eps;
    iwork[0] = liwmin;

    if ((lwork < lwmin) && !lquery) {
        *info = -16;
    } else if ((lrwork < lrwmin) && ! lquery) {
        *info = -18;
    } else if ((liwork < liwmin) && ! lquery) {
        *info = -20;
    }

    if (*info != 0) {
        magma_xerbla( __func__, -(*info));
        return *info;
    }
    else if (lquery) {
        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
        magmaFloatComplex *A;
        magma_cmalloc_cpu( &A, n*n );
        magma_cgetmatrix(n, n, dA, ldda, A, n);
        lapackf77_cheevd(jobz_, uplo_,
                         &n, A, &n,
                         w, work, &lwork,
                         rwork, &lrwork,
                         iwork, &liwork, info);
        magma_csetmatrix( n, n, A, n, dA, ldda);
        magma_free_cpu(A);
        *m=n;
        return *info;
    }

    magma_queue_t stream;
    magma_queue_create( &stream );

    // dC and dwork are never used together, so use one buffer for both;
    // unfortunately they're different types (complex and float).
    // (this works better in dsyevd_gpu where they're both float).
    // n*lddc for chetrd2_gpu, *2 for complex
    // n for clanhe
    magma_int_t ldwork = n*lddc*2;
    if ( wantz ) {
        // need 3n^2/2 for cstedx
        ldwork = max( ldwork, 3*n*(n/2 + 1) );
    }
    if (MAGMA_SUCCESS != magma_smalloc( &dwork, ldwork )) {
        *info = MAGMA_ERR_DEVICE_ALLOC;
        return *info;
    }
    dC = (magmaFloatComplex*) dwork;

    /* 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 = magmablas_clanhe(MagmaMaxNorm, uplo, n, dA, ldda, dwork);
    iscale = 0;
    sigma  = 1;
    if (anrm > 0. && anrm < rmin) {
        iscale = 1;
        sigma = rmin / anrm;
    } else if (anrm > rmax) {
        iscale = 1;
        sigma = rmax / anrm;
    }
    if (iscale == 1) {
        magmablas_clascl(uplo, 0, 0, 1., sigma, n, n, dA, ldda, info);
    }

    /* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */
    // chetrd rwork: e (n)
    // cstedx rwork: e (n) + llrwk (1 + 4*N + 2*N**2)  ==>  1 + 5n + 2n^2
    inde   = 0;
    indrwk = inde + n;
    llrwk  = lrwork - indrwk;

    // chetrd work: tau (n) + llwork (n*nb)  ==>  n + n*nb
    // cstedx work: tau (n) + z (n^2)
    // cunmtr work: tau (n) + z (n^2) + llwrk2 (n or n*nb)  ==>  2n + n^2, or n + n*nb + n^2
    indtau = 0;
    indwrk = indtau + n;
    indwk2 = indwrk + n*n;
    llwork = lwork - indwrk;
    llwrk2 = lwork - indwk2;

    magma_timer_t time=0;
    timer_start( time );

#ifdef FAST_HEMV
    magma_chetrd2_gpu(uplo, n, dA, ldda, w, &rwork[inde],
                      &work[indtau], wA, ldwa, &work[indwrk], llwork,
                      dC, n*lddc, &iinfo);
#else
    magma_chetrd_gpu (uplo, n, dA, ldda, w, &rwork[inde],
                      &work[indtau], wA, ldwa, &work[indwrk], llwork, &iinfo);
#endif

    timer_stop( time );
    timer_printf( "time chetrd_gpu = %6.2f\n", time );

    /* 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) {
        lapackf77_ssterf(&n, w, &rwork[inde], info);

        magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
    }
    else {
        timer_start( time );

        magma_cstedx(range, n, vl, vu, il, iu, w, &rwork[inde],
                     &work[indwrk], n, &rwork[indrwk],
                     llrwk, iwork, liwork, dwork, info);

        timer_stop( time );
        timer_printf( "time cstedx = %6.2f\n", time );
        timer_start( time );

        magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);

        magma_csetmatrix( n, *m, &work[indwrk + n * (il-1) ], n, dC, lddc );

        magma_cunmtr_gpu(MagmaLeft, uplo, MagmaNoTrans, n, *m, dA, ldda, &work[indtau],
                         dC, lddc, wA, ldwa, &iinfo);

        magma_ccopymatrix( n, *m, dC, lddc, dA, ldda );

        timer_stop( time );
        timer_printf( "time cunmtr_gpu + copy = %6.2f\n", time );
    }

    /* 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;

    magma_queue_destroy( stream );
    magma_free( dwork );

    return *info;
} /* magma_cheevdx_gpu */
Exemple #4
0
extern "C" magma_int_t
magma_cheevdx(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
    =======
    CHEEVDX computes selected eigenvalues and, optionally, eigenvectors
    of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
    be selected by specifying either a range of values or a range of
    indices for the desired eigenvalues.
    If eigenvectors are desired, it uses a divide and conquer algorithm.

    The divide and conquer algorithm makes very mild assumptions about
    floating point arithmetic. It will work on machines with a guard
    digit in add/subtract, or on those binary machines without guard
    digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
    Cray-2. It could conceivably fail on hexadecimal or decimal machines
    without guard digits, but we know of none.

    Arguments
    =========
    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[0] 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 + N*NB.
            If JOBZ  = 'V' and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ).
            NB can be obtained through magma_get_chetrd_nb(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.

    RWORK   (workspace/output) DOUBLE PRECISION array,
                                           dimension (LRWORK)
            On exit, if INFO = 0, RWORK[0] 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[0] 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};
    magma_int_t ione = 1;
    magma_int_t izero = 0;
    float d_one = 1.;

    float d__1;

    float eps;
    magma_int_t inde;
    float anrm;
    magma_int_t imax;
    float rmin, rmax;
    float sigma;
    magma_int_t iinfo, lwmin;
    magma_int_t lower;
    magma_int_t llrwk;
    magma_int_t wantz;
    magma_int_t indwk2, llwrk2;
    magma_int_t iscale;
    float safmin;
    float bignum;
    magma_int_t indtau;
    magma_int_t indrwk, indwrk, liwmin;
    magma_int_t lrwmin, llwork;
    float smlnum;
    magma_int_t lquery;
    magma_int_t alleig, valeig, indeig;

    float* dwork;

    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_chetrd_nb( n );
    if ( n <= 1 ) {
        lwmin  = 1;
        lrwmin = 1;
        liwmin = 1;
    }
    else if ( wantz ) {
        lwmin  = max( n + n*nb, 2*n + n*n );
        lrwmin = 1 + 5*n + 2*n*n;
        liwmin = 3 + 5*n;
    }
    else {
        lwmin  = n + n*nb;
        lrwmin = n;
        liwmin = 1;
    }
    // multiply by 1+eps to ensure length gets rounded up,
    // if it cannot be exactly represented in floating point.
    work[0]  = MAGMA_C_MAKE( lwmin * (1. + lapackf77_slamch("Epsilon")), 0.);
    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;
    }
    /* 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_cheevd(jobz_, uplo_,
                         &n, a, &lda,
                         w, work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
                         rwork, &lrwork, 
#endif  
                         iwork, &liwork, info);
        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);
    }

    /* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */
    // chetrd rwork: e (n)
    // cstedx rwork: e (n) + llrwk (1 + 4*N + 2*N**2)  ==>  1 + 5n + 2n^2
    inde   = 0;
    indrwk = inde + n;
    llrwk  = lrwork - indrwk;

    // chetrd work: tau (n) + llwork (n*nb)  ==>  n + n*nb
    // cstedx work: tau (n) + z (n^2)
    // cunmtr work: tau (n) + z (n^2) + llwrk2 (n or n*nb)  ==>  2n + n^2, or n + n*nb + n^2
    indtau = 0;
    indwrk = indtau + n;
    indwk2 = indwrk + n*n;
    llwork = lwork - indwrk;
    llwrk2 = lwork - indwk2;

//
#ifdef ENABLE_TIMER
    magma_timestr_t start, end;
    start = get_current_time();
#endif

    magma_chetrd(uplo_[0], n, a, lda, w, &rwork[inde],
                 &work[indtau], &work[indwrk], llwork, &iinfo);

#ifdef ENABLE_TIMER
    end = get_current_time();
    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) {
        lapackf77_ssterf(&n, w, &rwork[inde], info);

        magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);

    } else {

#ifdef ENABLE_TIMER
        start = get_current_time();
#endif

        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 );

#ifdef ENABLE_TIMER
        end = get_current_time();
        printf("time cstedx = %6.2f\n", GetTimerValue(start,end)/1000.);
        start = get_current_time();
#endif

        magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);

        magma_cunmtr(MagmaLeft, uplo, MagmaNoTrans, n, *m, a, lda, &work[indtau],
                     &work[indwrk + n * (il-1) ], n, &work[indwk2], llwrk2, &iinfo);

        lapackf77_clacpy("A", &n, m, &work[indwrk + n * (il-1)] , &n, a, &lda);

#ifdef ENABLE_TIMER
        end = get_current_time();
        printf("time cunmtr + copy = %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( lwmin * (1. + lapackf77_slamch("Epsilon")), 0.);  // round up
    rwork[0] = lrwmin * (1. + lapackf77_slamch("Epsilon"));
    iwork[0] = liwmin;

    return *info;
} /* magma_cheevdx */
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing cheevd
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    real_Double_t   gpu_time, cpu_time;
    magmaFloatComplex *h_A, *h_R, *h_work, aux_work[1];
    float *rwork, *w1, *w2, result[3], eps, aux_rwork[1];
    magma_int_t *iwork, aux_iwork[1];
    magma_int_t N, n2, info, lwork, lrwork, liwork, lda;
    magma_int_t izero    = 0;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    eps = lapackf77_slamch( "E" );
    magma_int_t status = 0;

    magma_opts opts;
    parse_opts( argc, argv, &opts );

    float tol    = opts.tolerance * lapackf77_slamch("E");
    float tolulp = opts.tolerance * lapackf77_slamch("P");
    
    if ( opts.check && opts.jobz == MagmaNoVec ) {
        fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
        opts.jobz = MagmaVec;
    }
    
    printf("using: jobz = %s, uplo = %s\n",
           lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo));

    printf("    N   CPU Time (sec)   GPU Time (sec)\n");
    printf("=======================================\n");
    for( int itest = 0; itest < opts.ntest; ++itest ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            N = opts.nsize[itest];
            n2  = N*N;
            lda = N;
            
            // query for workspace sizes
            magma_cheevd( opts.jobz, opts.uplo,
                          N, NULL, lda, NULL,
                          aux_work,  -1,
                          aux_rwork, -1,
                          aux_iwork, -1,
                          &info );
            lwork  = (magma_int_t) MAGMA_C_REAL( aux_work[0] );
            lrwork = (magma_int_t) aux_rwork[0];
            liwork = aux_iwork[0];
            
            /* Allocate host memory for the matrix */
            TESTING_MALLOC_CPU( h_A,    magmaFloatComplex, N*lda  );
            TESTING_MALLOC_CPU( w1,     float,             N      );
            TESTING_MALLOC_CPU( w2,     float,             N      );
            TESTING_MALLOC_CPU( rwork,  float,             lrwork );
            TESTING_MALLOC_CPU( iwork,  magma_int_t,        liwork );
            
            TESTING_MALLOC_PIN( h_R,    magmaFloatComplex, N*lda  );
            TESTING_MALLOC_PIN( h_work, magmaFloatComplex, lwork  );
            
            /* Initialize the matrix */
            lapackf77_clarnv( &ione, ISEED, &n2, h_A );
            magma_cmake_hermitian( N, h_A, N );
            
            lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
            
            /* warm up run */
            if ( opts.warmup ) {
                magma_cheevd( opts.jobz, opts.uplo,
                              N, h_R, lda, w1,
                              h_work, lwork,
                              rwork, lrwork,
                              iwork, liwork,
                              &info );
                if (info != 0)
                    printf("magma_cheevd returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
                lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
            }
            
            /* ====================================================================
               Performs operation using MAGMA
               =================================================================== */
            gpu_time = magma_wtime();
            magma_cheevd( opts.jobz, opts.uplo,
                          N, h_R, lda, w1,
                          h_work, lwork,
                          rwork, lrwork,
                          iwork, liwork,
                          &info );
            gpu_time = magma_wtime() - gpu_time;
            if (info != 0)
                printf("magma_cheevd returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            
            if ( opts.check ) {
                /* =====================================================================
                   Check the results following the LAPACK's [zcds]drvst routine.
                   A is factored as A = U S U' and the following 3 tests computed:
                   (1)    | A - U S U' | / ( |A| N )
                   (2)    | I - U'U | / ( N )
                   (3)    | S(with U) - S(w/o U) | / | S |
                   =================================================================== */
                float temp1, temp2;
                
                // tau=NULL is unused since itype=1
                lapackf77_chet21( &ione, lapack_uplo_const(opts.uplo), &N, &izero,
                                  h_A, &lda,
                                  w1, w1,
                                  h_R, &lda,
                                  h_R, &lda,
                                  NULL, h_work, rwork, &result[0] );
                
                lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
                magma_cheevd( MagmaNoVec, opts.uplo,
                              N, h_R, lda, w2,
                              h_work, lwork,
                              rwork, lrwork,
                              iwork, liwork,
                              &info );
                if (info != 0)
                    printf("magma_cheevd returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
                
                temp1 = temp2 = 0;
                for( int j=0; j<N; j++ ) {
                    temp1 = max(temp1, fabs(w1[j]));
                    temp1 = max(temp1, fabs(w2[j]));
                    temp2 = max(temp2, fabs(w1[j]-w2[j]));
                }
                result[2] = temp2 / (((float)N)*temp1);
            }
            
            /* =====================================================================
               Performs operation using LAPACK
               =================================================================== */
            if ( opts.lapack ) {
                cpu_time = magma_wtime();
                lapackf77_cheevd( lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
                                  &N, h_A, &lda, w2,
                                  h_work, &lwork,
                                  rwork, &lrwork,
                                  iwork, &liwork,
                                  &info );
                cpu_time = magma_wtime() - cpu_time;
                if (info != 0)
                    printf("lapackf77_cheevd returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
                
                printf("%5d   %7.2f          %7.2f\n",
                       (int) N, cpu_time, gpu_time);
            }
            else {
                printf("%5d     ---            %7.2f\n",
                       (int) N, gpu_time);
            }
            
            /* =====================================================================
               Print execution time
               =================================================================== */
            if ( opts.check ) {
                printf("Testing the factorization A = U S U' for correctness:\n");
                printf("(1)    | A - U S U' | / (|A| N)     = %8.2e   %s\n",   result[0]*eps, (result[0]*eps < tol ? "ok" : "failed") );
                printf("(2)    | I -   U'U  | /  N          = %8.2e   %s\n",   result[1]*eps, (result[1]*eps < tol ? "ok" : "failed") );
                printf("(3)    | S(w/ U) - S(w/o U) | / |S| = %8.2e   %s\n\n", result[2]    , (result[2]  < tolulp ? "ok" : "failed") );
                status += ! (result[0]*eps < tol && result[1]*eps < tol && result[2] < tolulp);
            }
            
            TESTING_FREE_CPU( h_A   );
            TESTING_FREE_CPU( w1    );
            TESTING_FREE_CPU( w2    );
            TESTING_FREE_CPU( rwork );
            TESTING_FREE_CPU( iwork );
            
            TESTING_FREE_PIN( h_R    );
            TESTING_FREE_PIN( h_work );
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }
    
    TESTING_FINALIZE();
    return status;
}
Exemple #6
0
/***************************************************************************//**
    Purpose
    -------
    CHEEVD computes all eigenvalues and, optionally, eigenvectors of a
    complex Hermitian matrix A.  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]
    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, A contains the
            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 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 >= N + N*NB.
     -      If JOBZ = MagmaVec   and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ).
            NB can be obtained through magma_get_chetrd_nb(N).
    \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_heevdx
*******************************************************************************/
extern "C" magma_int_t
magma_cheevdx_m(
    magma_int_t ngpu,
    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)
{
    const char* uplo_  = lapack_uplo_const( uplo  );
    const char* jobz_  = lapack_vec_const( jobz  );
    magma_int_t ione = 1;
    magma_int_t izero = 0;
    float d_one = 1.;
    
    float d__1;
    
    float eps;
    magma_int_t inde;
    float anrm;
    magma_int_t imax;
    float rmin, rmax;
    float sigma;
    magma_int_t iinfo, lwmin;
    magma_int_t lower;
    magma_int_t llrwk;
    magma_int_t wantz;
    magma_int_t indwk2, llwrk2;
    magma_int_t iscale;
    float safmin;
    float bignum;
    magma_int_t indtau;
    magma_int_t indrwk, indwrk, liwmin;
    magma_int_t lrwmin, llwork;
    float smlnum;
    magma_int_t lquery;
    magma_int_t alleig, valeig, indeig;
    
    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_chetrd_nb( n );
    if ( n <= 1 ) {
        lwmin  = 1;
        lrwmin = 1;
        liwmin = 1;
    }
    else if ( wantz ) {
        lwmin  = max( n + n*nb, 2*n + n*n );
        lrwmin = 1 + 5*n + 2*n*n;
        liwmin = 3 + 5*n;
    }
    else {
        lwmin  = n + n*nb;
        lrwmin = n;
        liwmin = 1;
    }
    
    work[0]  = magma_cmake_lwork( lwmin );
    rwork[0] = magma_smake_lwork( lrwmin );
    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;
    }
    /* 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=%lld NB=%lld, calling lapack on CPU\n", (long long) n, (long long) nb );
        printf("--------------------------------------------------------------\n");
        #endif
        lapackf77_cheevd(jobz_, uplo_,
                         &n, A, &lda,
                         w, work, &lwork,
                         #ifdef COMPLEX
                         rwork, &lrwork,
                         #endif
                         iwork, &liwork, info);
        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);
    }

    /* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */
    inde = 0;
    indtau = 0;
    indwrk = indtau + n;
    indrwk = inde + n;
    indwk2 = indwrk + n * n;
    llwork = lwork - indwrk;
    llwrk2 = lwork - indwk2;
    llrwk = lrwork - indrwk;

    magma_timer_t time=0;
    timer_start( time );

    magma_chetrd_mgpu(ngpu, 1, uplo, n, A, lda, w, &rwork[inde],
                      &work[indtau], &work[indwrk], llwork, &iinfo);

    timer_stop( time );
    timer_printf( "time chetrd = %6.2f\n", time );

    /* 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) {
        lapackf77_ssterf(&n, w, &rwork[inde], info);
        magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
    }
    else {
        timer_start( time );

        magma_cstedx_m(ngpu, range, n, vl, vu, il, iu, w, &rwork[inde],
                       &work[indwrk], n, &rwork[indrwk],
                       llrwk, iwork, liwork, info);

        timer_stop( time );
        timer_printf( "time cstedc = %6.2f\n", time );
        timer_start( time );

        magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);

        magma_cunmtr_m(ngpu, MagmaLeft, uplo, MagmaNoTrans, n, *m, A, lda, &work[indtau],
                       &work[indwrk + n * (il-1)], n, &work[indwk2], llwrk2, &iinfo);

        lapackf77_clacpy("A", &n, m, &work[indwrk + n * (il-1)], &n, A, &lda);
        
        timer_stop( time );
        timer_printf( "time cunmtr + copy = %6.2f\n", time );
    }

    /* 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_cmake_lwork( lwmin );
    rwork[0] = magma_smake_lwork( lrwmin );
    iwork[0] = liwmin;

    return *info;
} /* magma_cheevd_m */
Exemple #7
0
/**
    Purpose
    -------
    CHEEVD computes all eigenvalues and, optionally, eigenvectors of a
    complex Hermitian matrix A.  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]
    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, A contains the
            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[out]
    w       REAL array, dimension (N)
            If INFO = 0, the 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 >= N + N*NB.
            If JOBZ = MagmaVec   and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ).
            NB can be obtained through magma_get_chetrd_nb(N).
    \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_cheevd(
    magma_vec_t jobz, magma_uplo_t uplo,
    magma_int_t n,
    magmaFloatComplex *A, magma_int_t lda,
    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)
{
    const char* uplo_ = lapack_uplo_const( uplo );
    const char* jobz_ = lapack_vec_const( jobz );
    magma_int_t ione = 1;
    magma_int_t izero = 0;
    float d_one = 1.;

    float d__1;

    float eps;
    magma_int_t inde;
    float anrm;
    magma_int_t imax;
    float rmin, rmax;
    float sigma;
    magma_int_t iinfo, lwmin;
    magma_int_t lower;
    magma_int_t llrwk;
    magma_int_t wantz;
    magma_int_t indwk2, llwrk2;
    magma_int_t iscale;
    float safmin;
    float bignum;
    magma_int_t indtau;
    magma_int_t indrwk, indwrk, liwmin;
    magma_int_t lrwmin, llwork;
    float smlnum;
    magma_int_t lquery;

    float* dwork;

    wantz = (jobz == MagmaVec);
    lower = (uplo == MagmaLower);
    lquery = (lwork == -1 || lrwork == -1 || liwork == -1);

    *info = 0;

    if (! (wantz || (jobz == MagmaNoVec))) {
        *info = -1;
    } else if (! (lower || (uplo == MagmaUpper))) {
        *info = -2;
    } else if (n < 0) {
        *info = -3;
    } else if (lda < max(1,n)) {
        *info = -5;
    }

    magma_int_t nb = magma_get_chetrd_nb( n );
    if ( n <= 1 ) {
        lwmin  = 1;
        lrwmin = 1;
        liwmin = 1;
    }
    else if ( wantz ) {
        lwmin  = max( n + n*nb, 2*n + n*n );
        lrwmin = 1 + 5*n + 2*n*n;
        liwmin = 3 + 5*n;
    }
    else {
        lwmin  = 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 );
    rwork[0] = lrwmin * one_eps;
    iwork[0] = liwmin;

    if ((lwork < lwmin) && !lquery) {
        *info = -8;
    } else if ((lrwork < lrwmin) && ! lquery) {
        *info = -10;
    } else if ((liwork < liwmin) && ! lquery) {
        *info = -12;
    }

    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;
    }

    /* If matrix is very small, then just call LAPACK on CPU, no need for GPU */
    if (n <= 128) {
        lapackf77_cheevd( jobz_, uplo_,
                          &n, A, &lda,
                          w, work, &lwork,
                          #ifdef COMPLEX
                          rwork, &lrwork,
                          #endif
                          iwork, &liwork, info );
        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 );
    }

    /* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */
    // chetrd rwork: e (n)
    // cstedx rwork: e (n) + llrwk (1 + 4*N + 2*N**2)  ==>  1 + 5n + 2n^2
    inde   = 0;
    indrwk = inde + n;
    llrwk  = lrwork - indrwk;

    // chetrd work: tau (n) + llwork (n*nb)  ==>  n + n*nb
    // cstedx work: tau (n) + z (n^2)
    // cunmtr work: tau (n) + z (n^2) + llwrk2 (n or n*nb)  ==>  2n + n^2, or n + n*nb + n^2
    indtau = 0;
    indwrk = indtau + n;
    indwk2 = indwrk + n*n;
    llwork = lwork - indwrk;
    llwrk2 = lwork - indwk2;

    magma_timer_t time=0;
    timer_start( time );

    magma_chetrd( uplo, n, A, lda, w, &rwork[inde],
                  &work[indtau], &work[indwrk], llwork, &iinfo );

    timer_stop( time );
    timer_printf( "time chetrd = %6.2f\n", time );

    /* 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) {
        lapackf77_ssterf( &n, w, &rwork[inde], info );
    }
    else {
        timer_start( time );

        if (MAGMA_SUCCESS != magma_smalloc( &dwork, 3*n*(n/2 + 1) )) {
            *info = MAGMA_ERR_DEVICE_ALLOC;
            return *info;
        }

        magma_cstedx( MagmaRangeAll, n, 0., 0., 0, 0, 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 );

        magma_cunmtr( MagmaLeft, uplo, MagmaNoTrans, n, n, A, lda, &work[indtau],
                      &work[indwrk], n, &work[indwk2], llwrk2, &iinfo );

        lapackf77_clacpy( "A", &n, &n, &work[indwrk], &n, A, &lda );

        timer_stop( time );
        timer_printf( "time cunmtr + copy = %6.2f\n", time );
    }

    /* 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_cheevd */
Exemple #8
0
/**
    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 */
Exemple #9
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing cheevd
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    /* Constants */
    const float d_zero = 0;
    const magma_int_t izero = 0;
    const magma_int_t ione  = 1;
    
    /* Local variables */
    real_Double_t   gpu_time, cpu_time;
    magmaFloatComplex *h_A, *h_R, *h_Z, *h_work, aux_work[1];
    #ifdef COMPLEX
    float *rwork, aux_rwork[1];
    magma_int_t lrwork;
    #endif
    float *w1, *w2, result[4]={0, 0, 0, 0}, eps, abstol;
    magma_int_t *iwork, *isuppz, *ifail, aux_iwork[1];
    magma_int_t N, n2, info, lwork, liwork, lda;
    magma_int_t ISEED[4] = {0,0,0,1};
    eps = lapackf77_slamch( "E" );
    magma_int_t status = 0;

    magma_opts opts;
    opts.parse_opts( argc, argv );

    // checking NoVec requires LAPACK
    opts.lapack |= (opts.check && opts.jobz == MagmaNoVec);
    
    magma_range_t range = MagmaRangeAll;
    if (opts.fraction != 1)
        range = MagmaRangeI;
    
    #ifdef REAL
    if (opts.version == 3 || opts.version == 4) {
        printf("%% magma_cheevr and magma_cheevx are not available for real precisions (single, float).\n");
        return status;
    }
    #endif
    
    float tol    = opts.tolerance * lapackf77_slamch("E");
    float tolulp = opts.tolerance * lapackf77_slamch("P");
    
    // pass ngpu = -1 to test multi-GPU code using 1 gpu
    magma_int_t abs_ngpu = abs( opts.ngpu );
    
    printf("%% jobz = %s, range = %s, uplo = %s, fraction = %6.4f, ngpu = %d\n",
           lapack_vec_const(opts.jobz), lapack_range_const(range), lapack_uplo_const(opts.uplo),
           opts.fraction, int(abs_ngpu) );

    printf("%%   N   CPU Time (sec)   GPU Time (sec)   |S-S_magma|   |A-USU^H|   |I-U^H U|\n");
    printf("%%============================================================================\n");
    for( int itest = 0; itest < opts.ntest; ++itest ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            N = opts.nsize[itest];
            n2  = N*N;
            lda = N;
            abstol = 0;  // auto, in cheevr
            
            // TODO: test vl-vu range
            magma_int_t m1 = 0;
            float vl = 0;
            float 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) );
            }

            // query for workspace sizes
            if ( opts.version == 1 || opts.version == 2 ) {
                magma_cheevd( opts.jobz, opts.uplo,
                              N, NULL, lda, NULL,  // A, w
                              aux_work,  -1,
                              #ifdef COMPLEX
                              aux_rwork, -1,
                              #endif
                              aux_iwork, -1,
                              &info );
            }
            else if ( opts.version == 3 ) {
                #ifdef COMPLEX
                magma_cheevr( opts.jobz, range, opts.uplo,
                              N, NULL, lda,      // A
                              vl, vu, il, iu, abstol,
                              &m1, NULL,         // w
                              NULL, lda, NULL,   // Z, isuppz
                              aux_work,  -1,
                              #ifdef COMPLEX
                              aux_rwork, -1,
                              #endif
                              aux_iwork, -1,
                              &info );
                #endif
            }
            else if ( opts.version == 4 ) {
                #ifdef COMPLEX
                magma_cheevx( opts.jobz, range, opts.uplo,
                              N, NULL, lda,      // A
                              vl, vu, il, iu, abstol,
                              &m1, NULL,         // w
                              NULL, lda,         // Z
                              aux_work,  -1,
                              #ifdef COMPLEX
                              aux_rwork,
                              #endif
                              aux_iwork,
                              NULL,              // ifail
                              &info );
                // cheevx doesn't query rwork, iwork; set them for consistency
                aux_rwork[0] = float(7*N);
                aux_iwork[0] = float(5*N);
                #endif
            }
            lwork  = (magma_int_t) MAGMA_C_REAL( aux_work[0] );
            #ifdef COMPLEX
            lrwork = (magma_int_t) aux_rwork[0];
            #endif
            liwork = aux_iwork[0];
            
            /* Allocate host memory for the matrix */
            TESTING_MALLOC_CPU( h_A,    magmaFloatComplex, N*lda  );
            TESTING_MALLOC_CPU( w1,     float,             N      );
            TESTING_MALLOC_CPU( w2,     float,             N      );
            #ifdef COMPLEX
            TESTING_MALLOC_CPU( rwork,  float,             lrwork );
            #endif
            TESTING_MALLOC_CPU( iwork,  magma_int_t,        liwork );
            
            TESTING_MALLOC_PIN( h_R,    magmaFloatComplex, N*lda  );
            TESTING_MALLOC_PIN( h_work, magmaFloatComplex, lwork  );
            
            if (opts.version == 3) {
                TESTING_MALLOC_CPU( h_Z,    magmaFloatComplex, N*lda      );
                TESTING_MALLOC_CPU( isuppz, magma_int_t,        2*max(1,N) );
            }
            if (opts.version == 4) {
                TESTING_MALLOC_CPU( h_Z,    magmaFloatComplex, N*lda      );
                TESTING_MALLOC_CPU( ifail,  magma_int_t,        N          );
            }
            
            /* Clear eigenvalues, for |S-S_magma| check when fraction < 1. */
            lapackf77_slaset( "Full", &N, &ione, &d_zero, &d_zero, w1, &N );
            lapackf77_slaset( "Full", &N, &ione, &d_zero, &d_zero, w2, &N );
            
            /* Initialize the matrix */
            lapackf77_clarnv( &ione, ISEED, &n2, h_A );
            magma_cmake_hermitian( N, h_A, lda );
            
            lapackf77_clacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
            
            /* ====================================================================
               Performs operation using MAGMA
               =================================================================== */
            gpu_time = magma_wtime();
            if (opts.version == 1) {
                if (opts.ngpu == 1) {
                    magma_cheevd( opts.jobz, opts.uplo,
                                  N, h_R, lda, w1,
                                  h_work, lwork,
                                  #ifdef COMPLEX
                                  rwork, lrwork,
                                  #endif
                                  iwork, liwork,
                                  &info );
                }
                else {
                    //printf( "magma_cheevd_m, ngpu %d (%d)\n", opts.ngpu, abs_ngpu );
                    magma_cheevd_m( abs_ngpu, opts.jobz, opts.uplo,
                                    N, h_R, lda, w1,
                                    h_work, lwork,
                                    #ifdef COMPLEX
                                    rwork, lrwork,
                                    #endif
                                    iwork, liwork,
                                    &info );
                }
            }
            else if ( opts.version == 2 ) {  // version 2: cheevdx computes selected eigenvalues/vectors
                if (opts.ngpu == 1) {
                    magma_cheevdx( opts.jobz, range, opts.uplo,
                                   N, h_R, lda,
                                   vl, vu, il, iu,
                                   &m1, w1,
                                   h_work, lwork,
                                   #ifdef COMPLEX
                                   rwork, lrwork,
                                   #endif
                                   iwork, liwork,
                                   &info );
                }
                else {
                    //printf( "magma_cheevdx_m, ngpu %d (%d)\n", opts.ngpu, abs_ngpu );
                    magma_cheevdx_m( abs_ngpu, opts.jobz, range, opts.uplo,
                                     N, h_R, lda,
                                     vl, vu, il, iu,
                                     &m1, w1,
                                     h_work, lwork,
                                     #ifdef COMPLEX
                                     rwork, lrwork,
                                     #endif
                                     iwork, liwork,
                                     &info );
                }
                //printf( "il %d, iu %d, m1 %d\n", il, iu, m1 );
            }
            else if ( opts.version == 3 ) {  // version 3: MRRR, computes selected eigenvalues/vectors
                // only complex version available
                #ifdef COMPLEX
                magma_cheevr( opts.jobz, range, opts.uplo,
                              N, h_R, lda,
                              vl, vu, il, iu, abstol,
                              &m1, w1,
                              h_Z, lda, isuppz,
                              h_work, lwork,
                              #ifdef COMPLEX
                              rwork, lrwork,
                              #endif
                              iwork, liwork,
                              &info );
                lapackf77_clacpy( "Full", &N, &N, h_Z, &lda, h_R, &lda );
                #endif
            }
            else if ( opts.version == 4 ) {  // version 3: cheevx (QR iteration), computes selected eigenvalues/vectors
                // only complex version available
                #ifdef COMPLEX
                magma_cheevx( opts.jobz, range, opts.uplo,
                              N, h_R, lda,
                              vl, vu, il, iu, abstol,
                              &m1, w1,
                              h_Z, lda,
                              h_work, lwork,
                              #ifdef COMPLEX
                              rwork, /*lrwork,*/
                              #endif
                              iwork, /*liwork,*/
                              ifail,
                              &info );
                lapackf77_clacpy( "Full", &N, &N, h_Z, &lda, h_R, &lda );
                #endif
            }
            gpu_time = magma_wtime() - gpu_time;
            if (info != 0) {
                printf("magma_cheevd returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            }
            
            bool okay = true;
            if ( opts.check && opts.jobz != MagmaNoVec ) {
                /* =====================================================================
                   Check the results following the LAPACK's [zcds]drvst routine.
                   A is factored as A = U S U^H and the following 3 tests computed:
                   (1)    | A - U S U^H | / ( |A| N )
                   (2)    | I - U^H U   | / ( N )
                   (3)    | S(with U) - S(w/o U) | / | S |    // currently disabled, but compares to LAPACK
                   =================================================================== */
                magmaFloatComplex *work;
                TESTING_MALLOC_CPU( work, magmaFloatComplex, 2*N*N );
                
                // e=NULL is unused since kband=0; tau=NULL is unused since itype=1
                lapackf77_chet21( &ione, lapack_uplo_const(opts.uplo), &N, &izero,
                                  h_A, &lda,
                                  w1, NULL,
                                  h_R, &lda,
                                  h_R, &lda,
                                  NULL, work,
                                  #ifdef COMPLEX
                                  rwork,
                                  #endif
                                  &result[0] );
                result[0] *= eps;
                result[1] *= eps;
                
                TESTING_FREE_CPU( work );  work=NULL;
                
                // Disable third eigenvalue check that calls routine again --
                // it obscures whether error occurs in first call above or in this call.
                // But see comparison to LAPACK below.
                //
                //lapackf77_clacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
                //magma_cheevd( MagmaNoVec, opts.uplo,
                //              N, h_R, lda, w2,
                //              h_work, lwork,
                //              #ifdef COMPLEX
                //              rwork, lrwork,
                //              #endif
                //              iwork, liwork,
                //              &info );
                //if (info != 0) {
                //    printf("magma_cheevd returned error %d: %s.\n",
                //           (int) info, magma_strerror( info ));
                //}
                //
                //float maxw=0, diff=0;
                //for( int j=0; j < N; j++ ) {
                //    maxw = max(maxw, fabs(w1[j]));
                //    maxw = max(maxw, fabs(w2[j]));
                //    diff = max(diff, fabs(w1[j]-w2[j]));
                //}
                //result[2] = diff / (N*maxw);
            }
            
            /* =====================================================================
               Performs operation using LAPACK
               =================================================================== */
            if ( opts.lapack ) {
                cpu_time = magma_wtime();
                if ( opts.version == 1 || opts.version == 2 ) {
                    lapackf77_cheevd( lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
                                      &N, h_A, &lda, w2,
                                      h_work, &lwork,
                                      #ifdef COMPLEX
                                      rwork, &lrwork,
                                      #endif
                                      iwork, &liwork,
                                      &info );
                }
                else if ( opts.version == 3 ) {
                    lapackf77_cheevr( lapack_vec_const(opts.jobz),
                                      lapack_range_const(range),
                                      lapack_uplo_const(opts.uplo),
                                      &N, h_A, &lda,
                                      &vl, &vu, &il, &iu, &abstol,
                                      &m1, w2,
                                      h_Z, &lda, isuppz,
                                      h_work, &lwork,
                                      #ifdef COMPLEX
                                      rwork, &lrwork,
                                      #endif
                                      iwork, &liwork,
                                      &info );
                    lapackf77_clacpy( "Full", &N, &N, h_Z, &lda, h_A, &lda );
                }
                else if ( opts.version == 4 ) {
                    lapackf77_cheevx( lapack_vec_const(opts.jobz),
                                      lapack_range_const(range),
                                      lapack_uplo_const(opts.uplo),
                                      &N, h_A, &lda,
                                      &vl, &vu, &il, &iu, &abstol,
                                      &m1, w2,
                                      h_Z, &lda,
                                      h_work, &lwork,
                                      #ifdef COMPLEX
                                      rwork,
                                      #endif
                                      iwork,
                                      ifail,
                                      &info );
                    lapackf77_clacpy( "Full", &N, &N, h_Z, &lda, h_A, &lda );
                }
                cpu_time = magma_wtime() - cpu_time;
                if (info != 0) {
                    printf("lapackf77_cheevd returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
                }
                
                // compare eigenvalues
                float maxw=0, diff=0;
                for( int j=0; j < N; j++ ) {
                    maxw = max(maxw, fabs(w1[j]));
                    maxw = max(maxw, fabs(w2[j]));
                    diff = max(diff, fabs(w1[j] - w2[j]));
                }
                result[3] = diff / (N*maxw);
                
                okay = okay && (result[3] < tolulp);
                printf("%5d   %9.4f        %9.4f         %8.2e  ",
                       (int) N, cpu_time, gpu_time, result[3] );
            }
            else {
                printf("%5d      ---           %9.4f           ---     ",
                       (int) N, gpu_time);
            }
            
            // print error checks
            if ( opts.check && opts.jobz != MagmaNoVec ) {
                okay = okay && (result[0] < tol) && (result[1] < tol);
                printf("    %8.2e    %8.2e", result[0], result[1] );
            }
            else {
                printf("      ---         ---   ");
            }
            printf("   %s\n", (okay ? "ok" : "failed"));
            status += ! okay;
            
            TESTING_FREE_CPU( h_A   );
            TESTING_FREE_CPU( w1    );
            TESTING_FREE_CPU( w2    );
            #ifdef COMPLEX
            TESTING_FREE_CPU( rwork );
            #endif
            TESTING_FREE_CPU( iwork );
            
            TESTING_FREE_PIN( h_R    );
            TESTING_FREE_PIN( h_work );
            
            if ( opts.version == 3 ) {
                TESTING_FREE_CPU( h_Z    );
                TESTING_FREE_CPU( isuppz );
            }
            if ( opts.version == 4 ) {
                TESTING_FREE_CPU( h_Z    );
                TESTING_FREE_CPU( ifail  );
            }
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }
    
    opts.cleanup();
    TESTING_FINALIZE();
    return status;
}
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing chegvdx
*/
int main( int argc, char** argv)
{

    TESTING_INIT();

    real_Double_t gpu_time;

    magmaFloatComplex *h_A, *h_R, *h_work;

#if defined(PRECISION_z) || defined(PRECISION_c)
    float *rwork;
    magma_int_t lrwork;
#endif

    /* Matrix size */
    float *w1, *w2;
    magma_int_t *iwork;
    magma_int_t N, n2, info, lwork, liwork;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};;
    magma_int_t info_ortho     = 0;
    magma_int_t info_solution  = 0;
    magma_int_t info_reduction = 0;

    magma_timestr_t start, end;

    magma_opts opts;
    parse_opts( argc, argv, &opts );

    magma_int_t ngpu = opts.ngpu;
    char jobz = opts.jobz;
    magma_int_t checkres = opts.check;

    char range = 'A';
    char uplo = opts.uplo;
    magma_int_t itype = opts.itype;
    float f = opts.fraction;

    if (f != 1)
        range='I';

    if ( checkres && jobz == MagmaNoVec ) {
        fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
        jobz = MagmaVec;
    }

    printf("using: itype = %d, jobz = %c, range = %c, uplo = %c, checkres = %d, fraction = %6.4f\n",
           (int) itype, jobz, range, uplo, (int) checkres, f);

    printf("  N     M     GPU Time(s) \n");
    printf("==========================\n");
    magma_int_t threads = magma_get_numthreads();
    for( magma_int_t i = 0; i < opts.ntest; ++i ) {
        for( magma_int_t iter = 0; iter < opts.niter; ++iter ) {
            N = opts.nsize[i];
            n2     = N*N;
#if defined(PRECISION_z) || defined(PRECISION_c)
            lwork  = magma_cbulge_get_lq2(N, threads) + 2*N + N*N;
            lrwork = 1 + 5*N +2*N*N;
#else
            lwork  = magma_cbulge_get_lq2(N, threads) + 1 + 6*N + 2*N*N;
#endif
            liwork = 3 + 5*N;

            /* Allocate host memory for the matrix */
            TESTING_MALLOC(   h_A, magmaFloatComplex, n2);
            TESTING_MALLOC(    w1, float         ,  N);
            TESTING_MALLOC(    w2, float         ,  N);
            TESTING_HOSTALLOC(h_R, magmaFloatComplex, n2);
            TESTING_HOSTALLOC(h_work, magmaFloatComplex,  lwork);
#if defined(PRECISION_z) || defined(PRECISION_c)
            TESTING_HOSTALLOC( rwork,          float, lrwork);
#endif
            TESTING_MALLOC(    iwork,     magma_int_t, liwork);


            /* Initialize the matrix */
            lapackf77_clarnv( &ione, ISEED, &n2, h_A );
            /* Make diagonal real */
            for(int i=0; i<N; i++) {
                MAGMA_C_SET2REAL( h_A[i*N+i], MAGMA_C_REAL(h_A[i*N+i]) );
            }


            magma_int_t m1 = 0;
            float vl = 0;
            float vu = 0;
            magma_int_t il = 0;
            magma_int_t iu = 0;
            if (range == 'I'){
                il = 1;
                iu = (int) (f*N);
            }

            if(opts.warmup){
                // ==================================================================
                // Warmup using MAGMA
                // ==================================================================
                lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
                if(ngpu==1){
                    printf("calling cheevdx_2stage 1 GPU\n");
                    magma_cheevdx_2stage(jobz, range, uplo, N, 
                                    h_R, N, 
                                    vl, vu, il, iu, 
                                    &m1, w1, 
                                    h_work, lwork, 
#if defined(PRECISION_z) || defined(PRECISION_c)
                                    rwork, lrwork, 
#endif         
                                    iwork, liwork, 
                                    &info);
               
                }else{
                    printf("calling cheevdx_2stage_m %d GPU\n", (int) ngpu);
                    magma_cheevdx_2stage_m(ngpu, jobz, range, uplo, N, 
                                    h_R, N, 
                                    vl, vu, il, iu, 
                                    &m1, w1, 
                                    h_work, lwork, 
#if defined(PRECISION_z) || defined(PRECISION_c)
                                    rwork, lrwork, 
#endif         
                                    iwork, liwork, 
                                    &info);
                }
            }


            // ===================================================================
            // Performs operation using MAGMA
            // ===================================================================
            lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
            start = get_current_time();
            if(ngpu==1){
                printf("calling cheevdx_2stage 1 GPU\n");
                magma_cheevdx_2stage(jobz, range, uplo, N, 
                                h_R, N, 
                                vl, vu, il, iu, 
                                &m1, w1, 
                                h_work, lwork, 
#if defined(PRECISION_z) || defined(PRECISION_c)
                                rwork, lrwork, 
#endif     
                                iwork, liwork, 
                                &info);
           
            }else{
                printf("calling cheevdx_2stage_m %d GPU\n", (int) ngpu);
                magma_cheevdx_2stage_m(ngpu, jobz, range, uplo, N, 
                                h_R, N, 
                                vl, vu, il, iu, 
                                &m1, w1, 
                                h_work, lwork, 
#if defined(PRECISION_z) || defined(PRECISION_c)
                                rwork, lrwork, 
#endif     
                                iwork, liwork, 
                                &info);
            }
            end = get_current_time();
            gpu_time = GetTimerValue(start,end)/1000.;

            if ( checkres ) {
                float eps   = lapackf77_slamch("E");
                printf("\n");
                printf("------ TESTS FOR MAGMA CHEEVD ROUTINE -------  \n");
                printf("        Size of the Matrix %d by %d\n", (int) N, (int) N);
                printf("\n");
                printf(" The matrix A is randomly generated for each test.\n");
                printf("============\n");
                printf(" The relative machine precision (eps) is %8.2e\n",eps);
                printf(" Computational tests pass if scaled residuals are less than 60.\n");
              
                /* Check the orthogonality, reduction and the eigen solutions */
                if (jobz == MagmaVec) {
                    info_ortho = check_orthogonality(N, N, h_R, N, eps);
                    info_reduction = check_reduction(uplo, N, 1, h_A, w1, N, h_R, eps);
                }
                printf("------ CALLING LAPACK CHEEVD TO COMPUTE only eigenvalue and verify elementswise -------  \n");
                lapackf77_cheevd("N", "L", &N, 
                                h_A, &N, w2, 
                                h_work, &lwork, 
#if defined(PRECISION_z) || defined(PRECISION_c)
                                rwork, &lrwork, 
#endif     
                                iwork, &liwork, 
                                &info);
                info_solution = check_solution(N, w2, w1, eps);
              
                if ( (info_solution == 0) & (info_ortho == 0) & (info_reduction == 0) ) {
                    printf("***************************************************\n");
                    printf(" ---- TESTING CHEEVD ...................... PASSED !\n");
                    printf("***************************************************\n");
                }
                else {
                    printf("************************************************\n");
                    printf(" - TESTING CHEEVD ... FAILED !\n");
                    printf("************************************************\n");
                }
            }


            /* =====================================================================
             Print execution time
             =================================================================== */
            printf("%5d %5d     %6.2f\n",
                   (int) N, (int) m1, gpu_time);

            TESTING_FREE(       h_A);
            TESTING_FREE(        w1);
            TESTING_FREE(        w2);
#if defined(PRECISION_z) || defined(PRECISION_c)
            TESTING_HOSTFREE( rwork);
#endif
            TESTING_FREE(     iwork);
            TESTING_HOSTFREE(h_work);
            TESTING_HOSTFREE(   h_R);
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }

    /* Shutdown */
    TESTING_FINALIZE();

    return 0;
}