Ejemplo n.º 1
0
// --------------------
// MKL 11.1 has bug in multi-threaded zlanhe; use single thread to work around.
// MKL 11.2 corrects it for inf, one, max norm.
// MKL 11.2 still segfaults for Frobenius norm.
// See testing_zlanhe.cpp
double safe_lapackf77_zlanhe(
    const char *norm, const char *uplo,
    const magma_int_t *n,
    const magmaDoubleComplex *A, const magma_int_t *lda,
    double *work )
{
    #ifdef MAGMA_WITH_MKL
    // work around MKL bug in multi-threaded zlanhe
    magma_int_t la_threads = magma_get_lapack_numthreads();
    magma_set_lapack_numthreads( 1 );
    #endif
    
    double result = lapackf77_zlanhe( norm, uplo, n, A, lda, work );
    
    #ifdef MAGMA_WITH_MKL
    // end single thread to work around MKL bug
    magma_set_lapack_numthreads( la_threads );
    #endif
    
    return result;
}
Ejemplo n.º 2
0
extern "C" magma_int_t
magma_zheevd(char jobz, char uplo,
             magma_int_t n,
             magmaDoubleComplex *a, magma_int_t lda,
             double *w,
             magmaDoubleComplex *work, magma_int_t lwork,
             double *rwork, magma_int_t lrwork,
             magma_int_t *iwork, magma_int_t liwork,
             magma_int_t *info)
{
/*  -- MAGMA (version 1.4.1) --
       Univ. of Tennessee, Knoxville
       Univ. of California, Berkeley
       Univ. of Colorado, Denver
       December 2013

    Purpose
    =======
    ZHEEVD 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
    =========
    JOBZ    (input) CHARACTER*1
            = 'N':  Compute eigenvalues only;
            = 'V':  Compute eigenvalues and eigenvectors.

    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_16 array, dimension (LDA, N)
            On entry, the Hermitian matrix A.  If UPLO = 'U', the
            leading N-by-N upper triangular part of A contains the
            upper triangular part of the matrix A.  If UPLO = 'L',
            the leading N-by-N lower triangular part of A contains
            the lower triangular part of the matrix A.
            On exit, if JOBZ = 'V', then if INFO = 0, A contains the
            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).

    W       (output) DOUBLE PRECISION array, dimension (N)
            If INFO = 0, the eigenvalues in ascending order.

    WORK    (workspace/output) COMPLEX_16 array, dimension (MAX(1,LWORK))
            On exit, if INFO = 0, WORK[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_zhetrd_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};
    magma_int_t ione = 1;
    magma_int_t izero = 0;
    double d_one = 1.;

    double d__1;

    double eps;
    magma_int_t inde;
    double anrm;
    magma_int_t imax;
    double rmin, rmax;
    double 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;
    double safmin;
    double bignum;
    magma_int_t indtau;
    magma_int_t indrwk, indwrk, liwmin;
    magma_int_t lrwmin, llwork;
    double smlnum;
    magma_int_t lquery;

    double* dwork;

    wantz = lapackf77_lsame(jobz_, MagmaVecStr);
    lower = lapackf77_lsame(uplo_, MagmaLowerStr);
    lquery = lwork == -1 || lrwork == -1 || liwork == -1;

    *info = 0;

    if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) {
        *info = -1;
    } else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
        *info = -2;
    } else if (n < 0) {
        *info = -3;
    } else if (lda < max(1,n)) {
        *info = -5;
    }

    magma_int_t nb = magma_get_zhetrd_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_Z_MAKE( lwmin * (1. + lapackf77_dlamch("Epsilon")), 0.);
    rwork[0] = lrwmin * (1. + lapackf77_dlamch("Epsilon"));
    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_Z_REAL(a[0]);
        if (wantz) {
            a[0] = MAGMA_Z_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_zheevd(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_dlamch("Safe minimum");
    eps    = lapackf77_dlamch("Precision");
    smlnum = safmin / eps;
    bignum = 1. / smlnum;
    rmin = magma_dsqrt(smlnum);
    rmax = magma_dsqrt(bignum);

    /* Scale matrix to allowable range, if necessary. */
    anrm = lapackf77_zlanhe("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_zlascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, a,
                         &lda, info);
    }

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

    // zhetrd work: tau (n) + llwork (n*nb)  ==>  n + n*nb
    // zstedx work: tau (n) + z (n^2)
    // zunmtr 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_zhetrd(uplo_[0], n, a, lda, w, &rwork[inde],
                 &work[indtau], &work[indwrk], llwork, &iinfo);

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

    /* For eigenvalues only, call DSTERF.  For eigenvectors, first call
     ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
     tridiagonal matrix, then call ZUNMTR to multiply it to the Householder
     transformations represented as Householder vectors in A. */
    if (! wantz) {
        lapackf77_dsterf(&n, w, &rwork[inde], info);
    } else {

#ifdef ENABLE_TIMER
        start = get_current_time();
#endif

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

        magma_zstedx('A', n, 0., 0., 0, 0, 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 zstedx = %6.2f\n", GetTimerValue(start,end)/1000.);
        start = get_current_time();
#endif

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

        lapackf77_zlacpy("A", &n, &n, &work[indwrk], &n, a, &lda);

#ifdef ENABLE_TIMER
        end = get_current_time();
        printf("time zunmtr + 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_dscal(&imax, &d__1, w, &ione);
    }

    work[0]  = MAGMA_Z_MAKE( lwmin * (1. + lapackf77_dlamch("Epsilon")), 0.);  // round up
    rwork[0] = lrwmin * (1. + lapackf77_dlamch("Epsilon"));
    iwork[0] = liwmin;

    return *info;
} /* magma_zheevd */
Ejemplo n.º 3
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing zgeqlf
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    const double             d_neg_one = MAGMA_D_NEG_ONE;
    const double             d_one     = MAGMA_D_ONE;
    const magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
    const magmaDoubleComplex c_one     = MAGMA_Z_ONE;
    const magmaDoubleComplex c_zero    = MAGMA_Z_ZERO;
    const magma_int_t        ione      = 1;
    
    real_Double_t    gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
    double           Anorm, error=0, error2=0;
    magmaDoubleComplex *h_A, *h_R, *tau, *h_work, tmp[1];
    magma_int_t M, N, n2, lda, lwork, info, min_mn, nb;
    magma_int_t ISEED[4] = {0,0,0,1};
    magma_int_t status = 0;

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

    double tol = opts.tolerance * lapackf77_dlamch("E");
    
    printf("    M     N   CPU GFlop/s (sec)   GPU GFlop/s (sec)   |L - Q^H*A|   |I - Q^H*Q|\n");
    printf("===============================================================================\n");
    for( int itest = 0; itest < opts.ntest; ++itest ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            M = opts.msize[itest];
            N = opts.nsize[itest];
            min_mn = min(M, N);
            lda    = M;
            n2     = lda*N;
            nb     = magma_get_zgeqlf_nb(M);
            gflops = FLOPS_ZGEQLF( M, N ) / 1e9;
            
            // query for workspace size
            lwork = -1;
            lapackf77_zgeqlf(&M, &N, NULL, &M, NULL, tmp, &lwork, &info);
            lwork = (magma_int_t)MAGMA_Z_REAL( tmp[0] );
            lwork = max( lwork, N*nb );
            lwork = max( lwork, 2*nb*nb);
            
            TESTING_MALLOC_CPU( tau,    magmaDoubleComplex, min_mn );
            TESTING_MALLOC_CPU( h_A,    magmaDoubleComplex, n2     );
            TESTING_MALLOC_CPU( h_work, magmaDoubleComplex, lwork  );
            
            TESTING_MALLOC_PIN( h_R,    magmaDoubleComplex, n2     );
            
            /* Initialize the matrix */
            lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
            lapackf77_zlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
            
            /* ====================================================================
               Performs operation using MAGMA
               =================================================================== */
            gpu_time = magma_wtime();
            magma_zgeqlf( M, N, h_R, lda, tau, h_work, lwork, &info);
            gpu_time = magma_wtime() - gpu_time;
            gpu_perf = gflops / gpu_time;
            if (info != 0)
                printf("magma_zgeqlf returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            
            /* =====================================================================
               Check the result, following zqlt01 except using the reduced Q.
               This works for any M,N (square, tall, wide).
               =================================================================== */
            if ( opts.check ) {
                magma_int_t ldq = M;
                magma_int_t ldl = min_mn;
                magmaDoubleComplex *Q, *L;
                double *work;
                TESTING_MALLOC_CPU( Q,    magmaDoubleComplex, ldq*min_mn );  // M by K
                TESTING_MALLOC_CPU( L,    magmaDoubleComplex, ldl*N );       // K by N
                TESTING_MALLOC_CPU( work, double,             min_mn );
                
                // copy M by K matrix V to Q (copying diagonal, which isn't needed) and
                // copy K by N matrix L
                lapackf77_zlaset( "Full", &min_mn, &N, &c_zero, &c_zero, L, &ldl );
                if ( M >= N ) {
                    // for M=5, N=3: A = [ V V V ]  <= V full block (M-N by K)
                    //          K=N      [ V V V ]
                    //                   [ ----- ]
                    //                   [ L V V ]  <= V triangle (N by K, copying diagonal too)
                    //                   [ L L V ]  <= L triangle (K by N)
                    //                   [ L L L ]
                    magma_int_t M_N = M - N;
                    lapackf77_zlacpy( "Full",  &M_N, &min_mn,  h_R,      &lda,  Q,      &ldq );
                    lapackf77_zlacpy( "Upper", &N,   &min_mn, &h_R[M_N], &lda, &Q[M_N], &ldq );
                    
                    lapackf77_zlacpy( "Lower", &min_mn, &N,   &h_R[M_N], &lda,  L,      &ldl );
                }
                else {
                    // for M=3, N=5: A = [ L L | L V V ] <= V triangle (K by K)
                    //     K=M           [ L L | L L V ] <= L triangle (K by M)
                    //                   [ L L | L L L ]
                    //                     ^^^============= L full block (K by N-M)
                    magma_int_t N_M = N - M;
                    lapackf77_zlacpy( "Upper", &M, &min_mn,  &h_R[N_M*lda], &lda,  Q,          &ldq );
                    
                    lapackf77_zlacpy( "Full",  &min_mn, &N_M, h_R,          &lda,  L,          &ldl );
                    lapackf77_zlacpy( "Lower", &min_mn, &M,  &h_R[N_M*lda], &lda, &L[N_M*ldl], &ldl );
                }
                
                // generate M by K matrix Q, where K = min(M,N)
                lapackf77_zungql( &M, &min_mn, &min_mn, Q, &ldq, tau, h_work, &lwork, &info );
                assert( info == 0 );
                
                // error = || L - Q^H*A || / (N * ||A||)
                blasf77_zgemm( "Conj", "NoTrans", &min_mn, &N, &M,
                               &c_neg_one, Q, &ldq, h_A, &lda, &c_one, L, &ldl );
                Anorm = lapackf77_zlange( "1", &M,      &N, h_A, &lda, work );
                error = lapackf77_zlange( "1", &min_mn, &N, L,   &ldl, work );
                if ( N > 0 && Anorm > 0 )
                    error /= (N*Anorm);
                
                // set L = I (K by K identity), then L = I - Q^H*Q
                // error = || I - Q^H*Q || / N
                lapackf77_zlaset( "Upper", &min_mn, &min_mn, &c_zero, &c_one, L, &ldl );
                blasf77_zherk( "Upper", "Conj", &min_mn, &M, &d_neg_one, Q, &ldq, &d_one, L, &ldl );
                error2 = lapackf77_zlanhe( "1", "Upper", &min_mn, L, &ldl, work );
                if ( N > 0 )
                    error2 /= N;
                
                TESTING_FREE_CPU( Q    );  Q    = NULL;
                TESTING_FREE_CPU( L    );  L    = NULL;
                TESTING_FREE_CPU( work );  work = NULL;
            }
            
            /* =====================================================================
               Performs operation using LAPACK
               =================================================================== */
            if ( opts.lapack ) {
                cpu_time = magma_wtime();
                lapackf77_zgeqlf( &M, &N, h_A, &lda, tau, h_work, &lwork, &info );
                cpu_time = magma_wtime() - cpu_time;
                cpu_perf = gflops / cpu_time;
                if (info != 0)
                    printf("lapack_zgeqlf returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
            }
            
            /* =====================================================================
               Print performance and error.
               =================================================================== */
            printf("%5d %5d   ", (int) M, (int) N );
            if ( opts.lapack ) {
                printf( "%7.2f (%7.2f)", cpu_perf, cpu_time );
            }
            else {
                printf("  ---   (  ---  )" );
            }
            printf( "   %7.2f (%7.2f)   ", gpu_perf, gpu_time );
            if ( opts.check ) {
                bool okay = (error < tol && error2 < tol);
                status += ! okay;
                printf( "%11.2e   %11.2e   %s\n", error, error2, (okay ? "ok" : "failed") );
            }
            else {
                printf( "    ---\n" );
            }
            
            TESTING_FREE_CPU( tau    );
            TESTING_FREE_CPU( h_A    );
            TESTING_FREE_CPU( h_work );
            
            TESTING_FREE_PIN( h_R    );
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }

    TESTING_FINALIZE();
    return status;
}
Ejemplo n.º 4
0
extern "C" magma_int_t
magma_zheevdx_2stage(char jobz, char range, char uplo,
                     magma_int_t n,
                     magmaDoubleComplex *a, magma_int_t lda,
                     double vl, double vu, magma_int_t il, magma_int_t iu,
                     magma_int_t *m, double *w,
                     magmaDoubleComplex *work, magma_int_t lwork,
                     double *rwork, magma_int_t lrwork,
                     magma_int_t *iwork, magma_int_t liwork,
                     magma_int_t *info)
{
/*  -- MAGMA (version 1.4.0) --
       Univ. of Tennessee, Knoxville
       Univ. of California, Berkeley
       Univ. of Colorado, Denver
       August 2013

    Purpose
    =======
    ZHEEVD_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_16 array, dimension (LDA, N)
            On entry, the Hermitian matrix A.  If UPLO = 'U', the
            leading N-by-N upper triangular part of A contains the
            upper triangular part of the matrix A.  If UPLO = 'L',
            the leading N-by-N lower triangular part of A contains
            the lower triangular part of the matrix A.
            On exit, if JOBZ = 'V', then if INFO = 0, 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_16 array, dimension (MAX(1,LWORK))
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK   (input) INTEGER
            The length of the array WORK.
            If N <= 1,                LWORK >= 1.
            If JOBZ  = 'N' and N > 1, LWORK >= LQ2 + N * (NB + 1).
            If JOBZ  = 'V' and N > 1, LWORK >= LQ2 + 2*N + N**2.
                                      where LQ2 is the size needed to store
                                      the Q2 matrix and is returned by
                                      MAGMA_BULGE_GET_LQ2.

            If LWORK = -1, then a workspace query is assumed; the routine
            only calculates the optimal sizes of the WORK, RWORK and
            IWORK arrays, returns these values as the first entries of
            the WORK, RWORK and IWORK arrays, and no error message
            related to LWORK or LRWORK or LIWORK is issued by XERBLA.

    RWORK   (workspace/output) DOUBLE PRECISION array,
                                           dimension (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};
    magmaDoubleComplex c_one  = MAGMA_Z_ONE;
    magma_int_t ione = 1;
    magma_int_t izero = 0;
    double d_one = 1.;

    double d__1;

    double eps;
    double anrm;
    magma_int_t imax;
    double rmin, rmax;
    double sigma;
    //magma_int_t iinfo;
    magma_int_t lwmin, lrwmin, liwmin;
    magma_int_t lower;
    magma_int_t wantz;
    magma_int_t iscale;
    double safmin;
    double bignum;
    double smlnum;
    magma_int_t lquery;
    magma_int_t alleig, valeig, indeig;

    double* dwork;

    /* 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_zbulge_nb(n,threads);
    magma_int_t Vblksiz = magma_zbulge_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_zbulge_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_Z_MAKE( lwmin * (1. + lapackf77_dlamch("Epsilon")), 0.);  // round up
    rwork[0] = lrwmin * (1. + lapackf77_dlamch("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_Z_REAL(a[0]);
        if (wantz) {
            a[0] = MAGMA_Z_ONE;
        }
        return *info;
    }


#ifdef ENABLE_TIMER
    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_zheevd(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_dlamch("Safe minimum");
    eps = lapackf77_dlamch("Precision");
    smlnum = safmin / eps;
    bignum = 1. / smlnum;
    rmin = magma_dsqrt(smlnum);
    rmax = magma_dsqrt(bignum);

    /* Scale matrix to allowable range, if necessary. */
    anrm = lapackf77_zlanhe("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_zlascl(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

    magmaDoubleComplex *dT1;
    if (MAGMA_SUCCESS != magma_zmalloc( &dT1, n*nb)) {
        *info = MAGMA_ERR_DEVICE_ALLOC;
        return *info;
    }
    magma_zhetrd_he2hb(uplo, n, nb, a, lda, &work[indtau1], &work[indwrk], llwork, dT1, threads, info);

#ifdef ENABLE_TIMER
    st1 = get_current_time();
    printf("  time zhetrd_he2hb = %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);
    magmaDoubleComplex* A2 = &work[indwrk];
    memset(A2 , 0, n*lda2*sizeof(magmaDoubleComplex));

    for (magma_int_t j = 0; j < n-nb; j++)
    {
        cblas_zcopy(nb+1, &a[j*(lda+1)], 1, &A2[j*lda2], 1);
        memset(&a[j*(lda+1)], 0, (nb+1)*sizeof(magmaDoubleComplex));
        a[nb + j*(lda+1)] = c_one;
    }
    for (magma_int_t j = 0; j < nb; j++)
    {
        cblas_zcopy(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(magmaDoubleComplex));
    }

#ifdef ENABLE_TIMER
    st2 = get_current_time();
    printf("  time zhetrd_convert = %6.2f\n" , GetTimerValue(st1,st2)/1000.);
#endif

    magma_zhetrd_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 zhetrd_hb2st = %6.2f\n" , GetTimerValue(st2,end)/1000.);
    printf("  time zhetrd = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif

    /* For eigenvalues only, call DSTERF.  For eigenvectors, first call
     ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
     tridiagonal matrix, then call ZUNMTR to multiply it to the Householder
     transformations represented as Householder vectors in A. */
    if (! wantz) {
#ifdef ENABLE_TIMER
        start = get_current_time();
#endif

        lapackf77_dsterf(&n, w, &rwork[inde], info);
        magma_dmove_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

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

        magma_zstedx(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 zstedx = %6.2f\n", GetTimerValue(start,end)/1000.);
        start = get_current_time();
#endif
        magmaDoubleComplex *dZ;
        magma_int_t lddz = n;

        magmaDoubleComplex *da;
        magma_int_t ldda = n;

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

        if (MAGMA_SUCCESS != magma_zmalloc( &dZ, *m*lddz)) {
            *info = MAGMA_ERR_DEVICE_ALLOC;
            return *info;
        }
        if (MAGMA_SUCCESS != magma_zmalloc( &da, n*ldda )) {
            *info = MAGMA_ERR_DEVICE_ALLOC;
            return *info;
        }

        magma_zbulge_back(threads, uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n, dZ, lddz,
                          &work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info);

#ifdef ENABLE_TIMER
        st1 = get_current_time();
        printf("  time zbulge_back = %6.2f\n" , GetTimerValue(start,st1)/1000.);
#endif

        magma_zsetmatrix( n, n, a, lda, da, ldda );

        magma_zunmqr_gpu_2stages(MagmaLeft, MagmaNoTrans, n-nb, *m, n-nb, da+nb, ldda,
                                 dZ+nb, n, dT1, nb, info);

        magma_zgetmatrix( n, *m, dZ, lddz, a, lda );
        magma_free(dT1);
        magma_free(dZ);
        magma_free(da);

#ifdef ENABLE_TIMER
        end = get_current_time();
        printf("  time zunmqr + 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_dscal(&imax, &d__1, w, &ione);
    }

    work[0]  = MAGMA_Z_MAKE( lwmin * (1. + lapackf77_dlamch("Epsilon")), 0.);  // round up
    rwork[0] = lrwmin * (1. + lapackf77_dlamch("Epsilon"));
    iwork[0] = liwmin;

    return *info;
} /* magma_zheevdx_2stage */
Ejemplo n.º 5
0
/**
    Purpose
    -------
    ZHEEVDX 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]
    A       COMPLEX_16 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      DOUBLE PRECISION
    @param[in]
    vu      DOUBLE PRECISION
            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       DOUBLE PRECISION array, dimension (N)
            If INFO = 0, the required m eigenvalues in ascending order.

    @param[out]
    work    (workspace) COMPLEX_16 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_zhetrd_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) DOUBLE PRECISION 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_zheev_driver
    ********************************************************************/
extern "C" magma_int_t
magma_zheevdx(
    magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo,
    magma_int_t n,
    magmaDoubleComplex *A, magma_int_t lda,
    double vl, double vu, magma_int_t il, magma_int_t iu,
    magma_int_t *m, double *w,
    magmaDoubleComplex *work, magma_int_t lwork,
    #ifdef COMPLEX
    double *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;
    double d_one = 1.;

    double d__1;

    double eps;
    magma_int_t inde;
    double anrm;
    magma_int_t imax;
    double rmin, rmax;
    double 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;
    double safmin;
    double bignum;
    magma_int_t indtau;
    magma_int_t indrwk, indwrk, liwmin;
    magma_int_t lrwmin, llwork;
    double smlnum;
    magma_int_t lquery;
    magma_int_t alleig, valeig, indeig;

    double* dwork;

    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_zhetrd_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_dlamch("Epsilon");
    work[0]  = MAGMA_Z_MAKE( lwmin * one_eps, 0.);
    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_Z_REAL(A[0]);
        if (wantz) {
            A[0] = MAGMA_Z_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_zheevd(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_dlamch("Safe minimum");
    eps    = lapackf77_dlamch("Precision");
    smlnum = safmin / eps;
    bignum = 1. / smlnum;
    rmin = magma_dsqrt(smlnum);
    rmax = magma_dsqrt(bignum);

    /* Scale matrix to allowable range, if necessary. */
    anrm = lapackf77_zlanhe("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_zlascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, A,
                         &lda, info);
    }

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

    // zhetrd work: tau (n) + llwork (n*nb)  ==>  n + n*nb
    // zstedx work: tau (n) + z (n^2)
    // zunmtr 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_zhetrd(uplo, n, A, lda, w, &rwork[inde],
                 &work[indtau], &work[indwrk], llwork, &iinfo);

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

    /* For eigenvalues only, call DSTERF.  For eigenvectors, first call
     ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
     tridiagonal matrix, then call ZUNMTR to multiply it to the Householder
     transformations represented as Householder vectors in A. */
    if (! wantz) {
        lapackf77_dsterf(&n, w, &rwork[inde], info);

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

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

        magma_zstedx(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 zstedx = %6.2f\n", time );
        timer_start( time );

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

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

        lapackf77_zlacpy("A", &n, m, &work[indwrk + n * (il-1)], &n, A, &lda);

        timer_stop( time );
        timer_printf( "time zunmtr + 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_dscal(&imax, &d__1, w, &ione);
    }

    work[0]  = MAGMA_Z_MAKE( lwmin * one_eps, 0.);  // round up
    rwork[0] = lrwmin * one_eps;
    iwork[0] = liwmin;

    return *info;
} /* magma_zheevdx */
Ejemplo n.º 6
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing zhegvdx
*/
int main( int argc, char** argv)
{

    TESTING_INIT_MGPU();

    real_Double_t   mgpu_time;
    magmaDoubleComplex *h_A, *h_Ainit, *h_B, *h_Binit, *h_work;

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

    double *w1, result;
    magma_int_t *iwork;
    magma_int_t N, n2, info, lwork, liwork;
    magmaDoubleComplex c_zero    = MAGMA_Z_ZERO;
    magmaDoubleComplex c_one     = MAGMA_Z_ONE;
    magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};

    magma_timestr_t start, end;

    magma_opts opts;
    parse_opts( argc, argv, &opts );
    double tol = opts.tolerance * lapackf77_dlamch("E");

    char jobz = opts.jobz;
    int checkres = opts.check;

    char range = 'A';
    char uplo = opts.uplo;
    magma_int_t itype = opts.itype;

    double 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: nrgpu = %d, itype = %d, jobz = %c, range = %c, uplo = %c, checkres = %d, fraction = %6.4f\n",
           (int) opts.ngpu, (int) itype, jobz, range, uplo, (int) checkres, f);
    
    printf("  N     M   nr GPU     MGPU Time(s) \n");
    printf("====================================\n");
    magma_int_t threads = magma_get_numthreads();
    for( int i = 0; i < opts.ntest; ++i ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            N = opts.nsize[i];
            n2     = N*N;
#if defined(PRECISION_z) || defined(PRECISION_c)
            lwork  = magma_zbulge_get_lq2(N, threads) + 2*N + N*N;
            lrwork = 1 + 5*N +2*N*N;
#else
            lwork  = magma_zbulge_get_lq2(N, threads) + 1 + 6*N + 2*N*N;
#endif
            liwork = 3 + 5*N;


            //magma_int_t NB = 96;//magma_bulge_get_nb(N);
            //magma_int_t sizvblg = magma_zbulge_get_lq2(N, threads);        
            //magma_int_t siz = max(sizvblg,n2)+2*(N*NB+N)+24*N; 
            /* Allocate host memory for the matrix */
            TESTING_HOSTALLOC(   h_A, magmaDoubleComplex, n2);
            TESTING_HOSTALLOC(   h_B, magmaDoubleComplex, n2);
            TESTING_MALLOC(    w1, double         ,  N);
            TESTING_HOSTALLOC(h_work, magmaDoubleComplex,  lwork);
#if defined(PRECISION_z) || defined(PRECISION_c)
            TESTING_HOSTALLOC( rwork,          double, lrwork);
#endif
            TESTING_MALLOC(    iwork,     magma_int_t, liwork);

            /* Initialize the matrix */
            lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
            lapackf77_zlarnv( &ione, ISEED, &n2, h_B );
            /* increase the diagonal */
            {
                for(int i=0; i<N; i++) {
                    MAGMA_Z_SET2REAL( h_B[i*N+i], ( MAGMA_Z_REAL(h_B[i*N+i]) + 1.*N ) );
                    MAGMA_Z_SET2REAL( h_A[i*N+i], MAGMA_Z_REAL(h_A[i*N+i]) );
                }
            }

            if((opts.warmup)||( checkres )){
                TESTING_MALLOC(h_Ainit, magmaDoubleComplex, n2);
                TESTING_MALLOC(h_Binit, magmaDoubleComplex, n2);
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_Ainit, &N );
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_Binit, &N );
            }



            magma_int_t m1 = 0;
            double vl = 0;
            double 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. I prefer to use smalltest to warmup A-
                // ==================================================================
                magma_zhegvdx_2stage_m(opts.ngpu, itype, jobz, range, uplo,
                                       N, h_A, N, h_B, N, vl, vu, il, iu, &m1, w1,
                                       h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
                                       rwork, lrwork,
#endif
                                       iwork, liwork,
                                       &info);
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_Ainit, &N, h_A, &N );
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_Binit, &N, h_B, &N );
            }

            // ===================================================================
            // Performs operation using MAGMA
            // ===================================================================

            start = get_current_time();
            magma_zhegvdx_2stage_m(opts.ngpu, itype, jobz, range, uplo,
                                   N, h_A, N, h_B, 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();

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

            if ( checkres ) {
                // ===================================================================
                // Check the results following the LAPACK's [zc]hegvdx routine.
                // A x = lambda B x is solved
                // and the following 3 tests computed:
                // (1)    | A Z - B Z D | / ( |A||Z| N )  (itype = 1)
                // | A B Z - Z D | / ( |A||Z| N )  (itype = 2)
                // | B A Z - Z D | / ( |A||Z| N )  (itype = 3)
                // ===================================================================
#if defined(PRECISION_d) || defined(PRECISION_s)
                double *rwork = h_work + N*N;
#endif
                result = 1.;
                result /= lapackf77_zlanhe("1",&uplo, &N, h_Ainit, &N, rwork);
                result /= lapackf77_zlange("1",&N , &m1, h_A, &N, rwork);

                if (itype == 1){
                    blasf77_zhemm("L", &uplo, &N, &m1, &c_one, h_Ainit, &N, h_A, &N, &c_zero, h_work, &N);
                    for(int i=0; i<m1; ++i)
                        blasf77_zdscal(&N, &w1[i], &h_A[i*N], &ione);
                    blasf77_zhemm("L", &uplo, &N, &m1, &c_neg_one, h_Binit, &N, h_A, &N, &c_one, h_work, &N);
                    result *= lapackf77_zlange("1", &N, &m1, h_work, &N, rwork)/N;
                }
                else if (itype == 2){
                    blasf77_zhemm("L", &uplo, &N, &m1, &c_one, h_Binit, &N, h_A, &N, &c_zero, h_work, &N);
                    for(int i=0; i<m1; ++i)
                        blasf77_zdscal(&N, &w1[i], &h_A[i*N], &ione);
                    blasf77_zhemm("L", &uplo, &N, &m1, &c_one, h_Ainit, &N, h_work, &N, &c_neg_one, h_A, &N);
                    result *= lapackf77_zlange("1", &N, &m1, h_A, &N, rwork)/N;
                }
                else if (itype == 3){
                    blasf77_zhemm("L", &uplo, &N, &m1, &c_one, h_Ainit, &N, h_A, &N, &c_zero, h_work, &N);
                    for(int i=0; i<m1; ++i)
                        blasf77_zdscal(&N, &w1[i], &h_A[i*N], &ione);
                    blasf77_zhemm("L", &uplo, &N, &m1, &c_one, h_Binit, &N, h_work, &N, &c_neg_one, h_A, &N);
                    result *= lapackf77_zlange("1", &N, &m1, h_A, &N, rwork)/N;
                }
            }

            // ===================================================================
            // Print execution time
            // ===================================================================
            printf("%5d %5d %2d    %6.2f\n",
                   (int) N, (int) m1, (int) opts.ngpu, mgpu_time);
            if ( checkres ){
                printf("Testing the eigenvalues and eigenvectors for correctness:\n");
                if(itype==1)
                    printf("(1)    | A Z - B Z D | / (|A| |Z| N) = %8.2e%s\n", result, (result < tol ? "" : "  failed") );
                else if(itype==2)
                    printf("(1)    | A B Z - Z D | / (|A| |Z| N) = %8.2e%s\n", result, (result < tol ? "" : "  failed") );
                else if(itype==3)
                    printf("(1)    | B A Z - Z D | / (|A| |Z| N) = %8.2e%s\n", result, (result < tol ? "" : "  failed") );
            }

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

    /* Shutdown */
    TESTING_FINALIZE_MGPU();

    return 0;
}
Ejemplo n.º 7
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing zhegvdx
*/
int main( int argc, char** argv)
{

//#define USE_MGPU
#ifdef USE_MGPU
    TESTING_CUDA_INIT_MGPU();
#else
    TESTING_CUDA_INIT();
#endif
    magma_int_t nrgpu =1;

    cuDoubleComplex *h_A, *h_R, *h_B, *h_S, *h_work;
    double *rwork, *w1, *w2;
    magma_int_t *iwork;
    double gpu_time, cpu_time;

    magma_timestr_t start, end;

    /* Matrix size */
    magma_int_t N=0, n2;
    magma_int_t size[4] = {1024,2048,4100,6001};

    magma_int_t i, itype, info;
    magma_int_t ione = 1, izero = 0;
    magma_int_t five = 5;

    cuDoubleComplex c_zero    = MAGMA_Z_ZERO;
    cuDoubleComplex c_one     = MAGMA_Z_ONE;
    cuDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;

    double d_one     =  1.;
    double d_neg_one = -1.;
    double d_ten     = 10.;
    magma_int_t ISEED[4] = {0,0,0,1};

    magma_int_t il,iu,m1,m2;
    double vl,vu;

    double fraction_ev = 0;

    //const char *uplo = MagmaLowerStr;
    char *uplo = (char*)MagmaLowerStr;
    //char *uplo = (char*)MagmaUpperStr;
    char *jobz = (char*)MagmaVectorsStr;
    char range = 'A';
    itype = 1;

    magma_int_t checkres;
    double result[2];

    int flagN = 0;

    if (argc != 1){
        for(i = 1; i<argc; i++){
            if (strcmp("-N", argv[i])==0){
                N = atoi(argv[++i]);
                if (N>0){
                   printf("  testing_zhegvdx -N %d\n\n", (int) N);
                   flagN=1;
                }
                else {
                   printf("\nUsage: \n");
                   printf("  testing_zhegvdx -N %d\n\n", (int) N);
                   exit(1);
                }
            }
            if (strcmp("-ngpu", argv[i])==0){
                nrgpu = atoi(argv[++i]);
                if (nrgpu>0){
                   printf("  testing_zhegvdx -ngpu %d\n\n", (int) nrgpu);
                }
                else {
                   printf("\nUsage: \n");
                   printf("  testing_zhegvdx -ngpu %d\n\n", (int) nrgpu);
                   exit(1);
                }
            }
            if (strcmp("-itype", argv[i])==0){
                itype = atoi(argv[++i]);
                if (itype>0 && itype <= 3){
                   printf("  testing_zhegvdx -itype %d\n\n", (int) itype);
                }
                else {
                   printf("\nUsage: \n");
                   printf("  testing_zhegvdx -itype %d\n\n", (int) itype);
                   exit(1);
                }
            }
            if (strcmp("-FE", argv[i])==0){
                fraction_ev = atof(argv[++i]);
                if (fraction_ev > 0 && fraction_ev <= 1){
                    printf("  testing_zhegvdx -FE %f\n\n", fraction_ev);
                }
                else {
                    fraction_ev = 0;
                }
            }
            if (strcmp("-L", argv[i])==0){
              uplo = (char*)MagmaLowerStr;
              printf("  testing_zhegvdx -L");
            }
            if (strcmp("-U", argv[i])==0){
              uplo = (char*)MagmaUpperStr;
              printf("  testing_zhegvdx -U");
            }

        }

    } else {
        printf("\nUsage: \n");
        printf("  testing_zhegvdx -L/U -N %d -itype %d\n\n", 1024, 1);
    }

    if(!flagN)
        N = size[3];

    checkres  = getenv("MAGMA_TESTINGS_CHECK") != NULL;

    n2  = N * N;

    /* Allocate host memory for the matrix */
    TESTING_MALLOC(   h_A, cuDoubleComplex, n2);
    TESTING_MALLOC(   h_B, cuDoubleComplex, n2);
    TESTING_MALLOC(    w1, double         ,  N);
    TESTING_MALLOC(    w2, double         ,  N);
    TESTING_HOSTALLOC(h_R, cuDoubleComplex, n2);
    TESTING_HOSTALLOC(h_S, cuDoubleComplex, n2);

    magma_int_t nb = magma_get_zhetrd_nb(N);
    magma_int_t lwork = magma_zbulge_get_lq2(N) + 2*N + N*N;
    magma_int_t lrwork = 1 + 5*N +2*N*N;
    magma_int_t liwork = 3 + 5*N;

    TESTING_HOSTALLOC(h_work, cuDoubleComplex,  lwork);
    TESTING_HOSTALLOC( rwork,          double, lrwork);
    TESTING_MALLOC(    iwork,     magma_int_t, liwork);

    printf("  N     M     GPU Time(s) \n");
    printf("==========================\n");
    for(i=0; i<4; i++){
        if (!flagN){
            N = size[i];
            n2 = N*N;
        }
        if (fraction_ev == 0){
            il = N / 10;
            iu = N / 5+il;
        }
        else {
            il = 1;
            iu = (int)(fraction_ev*N);
            if (iu < 1) iu = 1;
        }

        /* Initialize the matrix */
        lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
        //lapackf77_zlatms( &N, &N, "U", ISEED, "P", w1, &five, &d_ten,
        //                 &d_one, &N, &N, uplo, h_B, &N, h_work, &info);
        //lapackf77_zlaset( "A", &N, &N, &c_zero, &c_one, h_B, &N);
        lapackf77_zlarnv( &ione, ISEED, &n2, h_B );
        /* increase the diagonal */
        {
          magma_int_t i, j;
          for(i=0; i<N; i++) {
            MAGMA_Z_SET2REAL( h_B[i*N+i], ( MAGMA_Z_REAL(h_B[i*N+i]) + 1.*N ) );
          }
        }
        lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
        lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );

#ifdef USE_MGPU
        magma_zhegvdx_2stage_m(nrgpu, itype, jobz[0], range, uplo[0],
                               N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
                               h_work, lwork,
                               rwork, lrwork,
                               iwork, liwork,
                               &info);
#else
        magma_zhegvdx_2stage(itype, jobz[0], range, uplo[0],
                             N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
                             h_work, lwork,
                             rwork, lrwork,
                             iwork, liwork,
                             &info);
#endif

        lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
        lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );


        /* ====================================================================
           Performs operation using MAGMA
           =================================================================== */
        start = get_current_time();
#ifdef USE_MGPU
        magma_zhegvdx_2stage_m(nrgpu, itype, jobz[0], range, uplo[0],
                               N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
                               h_work, lwork,
                               rwork, lrwork,
                               iwork, liwork,
                               &info);
#else
        magma_zhegvdx_2stage(itype, jobz[0], range, uplo[0],
                             N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
                             h_work, lwork,
                             rwork, lrwork,
                             iwork, liwork,
                             &info);
#endif
        end = get_current_time();

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

        if ( checkres ) {
          /* =====================================================================
             Check the results following the LAPACK's [zc]hegvdx routine.
             A x = lambda B x is solved
             and the following 3 tests computed:
             (1)    | A Z - B Z D | / ( |A||Z| N )  (itype = 1)
                    | A B Z - Z D | / ( |A||Z| N )  (itype = 2)
                    | B A Z - Z D | / ( |A||Z| N )  (itype = 3)
             (2)    | S(with V) - S(w/o V) | / | S |
             =================================================================== */
          double temp1, temp2;
          cuDoubleComplex *tau;

          result[0] = 1.;
          result[0] /= lapackf77_zlanhe("1",uplo, &N, h_A, &N, rwork);
          result[0] /= lapackf77_zlange("1",&N , &m1, h_R, &N, rwork);

          if (itype == 1){
            blasf77_zhemm("L", uplo, &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
            for(int i=0; i<m1; ++i)
              blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
            blasf77_zhemm("L", uplo, &N, &m1, &c_neg_one, h_B, &N, h_R, &N, &c_one, h_work, &N);
            result[0] *= lapackf77_zlange("1", &N, &m1, h_work, &N, rwork)/N;
          }
          else if (itype == 2){
            blasf77_zhemm("L", uplo, &N, &m1, &c_one, h_B, &N, h_R, &N, &c_zero, h_work, &N);
            for(int i=0; i<m1; ++i)
              blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
            blasf77_zhemm("L", uplo, &N, &m1, &c_one, h_A, &N, h_work, &N, &c_neg_one, h_R, &N);
            result[0] *= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork)/N;
          }
          else if (itype == 3){
            blasf77_zhemm("L", uplo, &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
            for(int i=0; i<m1; ++i)
              blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
            blasf77_zhemm("L", uplo, &N, &m1, &c_one, h_B, &N, h_work, &N, &c_neg_one, h_R, &N);
            result[0] *= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork)/N;
          }


          lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
          lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );

          magma_zhegvdx(itype, 'N', range, uplo[0],
                       N, h_R, N, h_S, N, vl, vu, il, iu, &m2, w2,
                       h_work, lwork,
                       rwork, lrwork,
                       iwork, liwork,
                       &info);

          temp1 = temp2 = 0;
          for(int j=0; j<m2; j++){
            temp1 = max(temp1, absv(w1[j]));
            temp1 = max(temp1, absv(w2[j]));
            temp2 = max(temp2, absv(w1[j]-w2[j]));
          }
          result[1] = temp2 / temp1;
        }


        /* =====================================================================
           Print execution time
           =================================================================== */
        printf("%5d %5d     %6.2f\n",
               (int) N, (int) m1, gpu_time);
        if ( checkres ){
          printf("Testing the eigenvalues and eigenvectors for correctness:\n");
          if(itype==1)
             printf("(1)    | A Z - B Z D | / (|A| |Z| N) = %e\n", result[0]);
          else if(itype==2)
             printf("(1)    | A B Z - Z D | / (|A| |Z| N) = %e\n", result[0]);
          else if(itype==3)
             printf("(1)    | B A Z - Z D | / (|A| |Z| N) = %e\n", result[0]);

          printf("(2)    | D(w/ Z)-D(w/o Z)|/ |D| = %e\n\n", result[1]);
        }

        if (flagN)
            break;
    }

    cudaSetDevice(0);
    /* Memory clean up */
    TESTING_FREE(       h_A);
    TESTING_FREE(       h_B);
    TESTING_FREE(        w1);
    TESTING_FREE(        w2);
    TESTING_HOSTFREE( rwork);
    TESTING_FREE(     iwork);
    TESTING_HOSTFREE(h_work);
    TESTING_HOSTFREE(   h_R);
    TESTING_HOSTFREE(   h_S);

    /* Shutdown */
#ifdef USE_MGPU
    TESTING_CUDA_FINALIZE_MGPU();
#else
     TESTING_CUDA_FINALIZE();
#endif
}
Ejemplo n.º 8
0
/**
    Purpose
    -------
    ZHEEVD_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]
    nrgpu   INTEGER
            Number of GPUs to use.

    @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_16 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      DOUBLE PRECISION
    @param[in]
    vu      DOUBLE PRECISION
            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       DOUBLE PRECISION array, dimension (N)
            If INFO = 0, the required m eigenvalues in ascending order.

    @param[out]
    work    (workspace) COMPLEX_16 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) DOUBLE PRECISION 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_zheev_driver
    ********************************************************************/
extern "C" magma_int_t
magma_zheevdx_2stage_m(magma_int_t nrgpu, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo,
                       magma_int_t n,
                       magmaDoubleComplex *A, magma_int_t lda,
                       double vl, double vu, magma_int_t il, magma_int_t iu,
                       magma_int_t *m, double *w,
                       magmaDoubleComplex *work, magma_int_t lwork,
                       double *rwork, magma_int_t lrwork,
                       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  );
    magmaDoubleComplex c_one  = MAGMA_Z_ONE;
    double d_one = 1.;
    magma_int_t ione = 1;
    magma_int_t izero = 0;

    double d__1;

    double eps;
    double anrm;
    magma_int_t imax;
    double rmin, rmax;
    double sigma;
    //magma_int_t iinfo;
    magma_int_t lwmin, lrwmin, liwmin;
    magma_int_t lower;
    magma_int_t wantz;
    magma_int_t iscale;
    double safmin;
    double bignum;
    double smlnum;
    magma_int_t lquery;
    magma_int_t alleig, valeig, indeig;
    magma_int_t len;

    /* 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_zbulge_nb(n, parallel_threads);
    magma_int_t Vblksiz = magma_zbulge_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_zbulge_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_dlamch("Epsilon");
    work[0]  = MAGMA_Z_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_Z_REAL(A[0]);
        if (wantz) {
            A[0] = MAGMA_Z_ONE;
        }
        return *info;
    }

    magma_device_t orig_dev;
    magma_getdevice( &orig_dev );
    
    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_zheevd(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_dlamch("Safe minimum");
    eps = lapackf77_dlamch("Precision");
    smlnum = safmin / eps;
    bignum = 1. / smlnum;
    rmin = magma_dsqrt(smlnum);
    rmax = magma_dsqrt(bignum);

    /* Scale matrix to allowable range, if necessary. */
    anrm = lapackf77_zlanhe("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_zlascl(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, time_alloc=0, time_dist=0, time_band=0;
    timer_start( time_total );

#ifdef HE2HB_SINGLEGPU
    magmaDoubleComplex *dT1;
    if (MAGMA_SUCCESS != magma_zmalloc( &dT1, n*nb)) {
        *info = MAGMA_ERR_DEVICE_ALLOC;
        return *info;
    }
    timer_start( time_band );
    magma_zhetrd_he2hb(uplo, n, nb, A, lda, &work[indtau1], &work[indwrk], llwork, dT1, info);
    timer_stop( time_band );
    timer_printf( "    1 GPU seq code time zhetrd_he2hb only = %7.4f\n", time_band );
    magma_free(dT1);
#else
    magma_int_t nstream = max(3,nrgpu+2);
    magma_queue_t streams[MagmaMaxGPUs][20];
    magmaDoubleComplex *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

    timer_start( time_alloc );
    for( magma_int_t dev = 0; dev < nrgpu; ++dev ) {
        magma_int_t mlocal = ((n / distblk) / nrgpu + 1) * distblk;
        magma_setdevice( dev );
        // TODO check malloc
        magma_zmalloc(&da[dev], ldda*mlocal );
        magma_zmalloc(&dT1[dev], (n*nb) );
        for( int i = 0; i < nstream; ++i ) {
            magma_queue_create( &streams[dev][i] );
        }
    }
    timer_stop( time_alloc );
    
    timer_start( time_dist );
    magma_zsetmatrix_1D_col_bcyclic( n, n, A, lda, da, ldda, nrgpu, distblk );
    magma_setdevice(0);
    timer_stop( time_dist );

    timer_start( time_band );
    if (ver == 30) {
        magma_zhetrd_he2hb_mgpu_spec(uplo, n, nb, A, lda, &work[indtau1], &work[indwrk], llwork, da, ldda, dT1, nb, nrgpu, distblk, streams, nstream, info);
    } else {
        magma_zhetrd_he2hb_mgpu(uplo, n, nb, A, lda, &work[indtau1], &work[indwrk], llwork, da, ldda, dT1, nb, nrgpu, distblk, streams, nstream, info);
    }
    timer_stop( time_band );
    timer_printf("    time alloc %7.4f, ditribution %7.4f, zhetrd_he2hb only = %7.4f\n", time_alloc, time_dist, time_band );

    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 // not HE2HB_SINGLEGPU

    timer_stop( time_total );
    timer_printf( "    time zhetrd_he2hb_mgpu = %6.2f\n", time_total );
    timer_start( time_total );
    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);
    magmaDoubleComplex* A2 = &work[indwrk];
    memset(A2, 0, n*lda2*sizeof(magmaDoubleComplex));

    for (magma_int_t j = 0; j < n-nb; j++) {
        len = nb+1;
        blasf77_zcopy( &len, A(j,j), &ione, A2(0,j), &ione );
        memset(A(j,j), 0, (nb+1)*sizeof(magmaDoubleComplex));
        *A(nb+j,j) = c_one;
    }
    for (magma_int_t j = 0; j < nb; j++) {
        len = nb-j;
        blasf77_zcopy( &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(magmaDoubleComplex));
    }

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

    magma_zhetrd_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 zhetrd_hb2st = %6.2f\n", time );
    timer_printf( "  time zhetrd = %6.2f\n", time_total );

    /* For eigenvalues only, call DSTERF.  For eigenvectors, first call
       ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
       tridiagonal matrix, then call ZUNMTR to multiply it to the Householder
       transformations represented as Householder vectors in A. */
    if (! wantz) {
        timer_start( time );

        lapackf77_dsterf(&n, w, &rwork[inde], info);
        magma_dmove_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 );

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

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

        magma_dmove_eig(range, n, w, &il, &iu, vl, vu, m);
/*
        magmaDoubleComplex *dZ;
        magma_int_t lddz = n;

        if (MAGMA_SUCCESS != magma_zmalloc( &dZ, *m*lddz)) {
            *info = MAGMA_ERR_DEVICE_ALLOC;
            return *info;
        }

        magma_zbulge_back(uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n, dZ, lddz,
                          &work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info);

        magma_zgetmatrix( n, *m, dZ, lddz, &work[indwrk], n);

        magma_free(dZ);

*/

        magma_zbulge_back_m(nrgpu, uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n,
                            &work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info);

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

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

        timer_stop( time );
        timer_stop( time_total );
        timer_printf( "    time zunmqr_m + 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_dscal(&imax, &d__1, w, &ione);
    }

    work[0]  = MAGMA_Z_MAKE( lwmin * one_eps, 0.);  // round up
    rwork[0] = lrwmin * one_eps;
    iwork[0] = liwmin;

    magma_setdevice( orig_dev );
    
    return *info;
} /* magma_zheevdx_2stage_m */
Ejemplo n.º 9
0
int main(int argc, char **argv)
{
    TESTING_INIT();

    real_Double_t   gflopsF, gflopsS, gpu_perf, gpu_time /*cpu_perf, cpu_time*/;
    real_Double_t   gpu_perfdf, gpu_perfds;
    real_Double_t   gpu_perfsf, gpu_perfss;
    double          error, Rnorm, Anorm;
    magmaDoubleComplex c_one     = MAGMA_Z_ONE;
    magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
    magmaDoubleComplex *h_A, *h_B, *h_X;
    magmaDoubleComplex *d_A, *d_B, *d_X, *d_workd;
    magmaFloatComplex  *d_As, *d_Bs, *d_works;
    double          *h_workd;
    magma_int_t lda, ldb, ldx;
    magma_int_t N, nrhs, posv_iter, info, size;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    
    printf("Epsilon(double): %8.6e\n"
           "Epsilon(single): %8.6e\n\n",
           lapackf77_dlamch("Epsilon"), lapackf77_slamch("Epsilon") );
    magma_int_t status = 0;
    
    magma_opts opts;
    parse_opts( argc, argv, &opts );

    double tol = opts.tolerance * lapackf77_dlamch("E");
    
    nrhs = opts.nrhs;
    
    printf("using: uplo = %s\n",
           lapack_uplo_const(opts.uplo));

    printf("    N NRHS   DP-Factor  DP-Solve  SP-Factor  SP-Solve  MP-Solve  Iter   |b-Ax|/|A|\n");
    printf("=====================================================================================\n");
    for( int itest = 0; itest < opts.ntest; ++itest ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            N = opts.nsize[itest];
            ldb = ldx = lda = N;
            gflopsF = FLOPS_ZPOTRF( N ) / 1e9;
            gflopsS = gflopsF + FLOPS_ZPOTRS( N, nrhs ) / 1e9;
            
            TESTING_MALLOC_CPU( h_A,     magmaDoubleComplex, lda*N    );
            TESTING_MALLOC_CPU( h_B,     magmaDoubleComplex, ldb*nrhs );
            TESTING_MALLOC_CPU( h_X,     magmaDoubleComplex, ldx*nrhs );
            TESTING_MALLOC_CPU( h_workd, double,             N        );
            
            TESTING_MALLOC_DEV( d_A,     magmaDoubleComplex, lda*N        );
            TESTING_MALLOC_DEV( d_B,     magmaDoubleComplex, ldb*nrhs     );
            TESTING_MALLOC_DEV( d_X,     magmaDoubleComplex, ldx*nrhs     );
            TESTING_MALLOC_DEV( d_works, magmaFloatComplex,  lda*(N+nrhs) );
            TESTING_MALLOC_DEV( d_workd, magmaDoubleComplex, N*nrhs       );
            
            /* Initialize the matrix */
            size = lda * N ;
            lapackf77_zlarnv( &ione, ISEED, &size, h_A );
            magma_zmake_hpd( N, h_A, lda );
            
            size = ldb * nrhs ;
            lapackf77_zlarnv( &ione, ISEED, &size, h_B );
            
            magma_zsetmatrix( N, N,    h_A, lda, d_A, lda );
            magma_zsetmatrix( N, nrhs, h_B, ldb, d_B, ldb );
            
            //=====================================================================
            //              Mixed Precision Iterative Refinement - GPU
            //=====================================================================
            gpu_time = magma_wtime();
            magma_zcposv_gpu(opts.uplo, N, nrhs, d_A, lda, d_B, ldb, d_X, ldx,
                             d_workd, d_works, &posv_iter, &info);
            gpu_time = magma_wtime() - gpu_time;
            gpu_perf = gflopsS / gpu_time;
            if (info != 0)
                printf("magma_zcposv returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            
            //=====================================================================
            //                 Error Computation
            //=====================================================================
            magma_zgetmatrix( N, nrhs, d_X, ldx, h_X, ldx ) ;
            
            Anorm = lapackf77_zlanhe( "I", lapack_uplo_const(opts.uplo), &N, h_A, &N, h_workd);
            blasf77_zhemm( "L", lapack_uplo_const(opts.uplo), &N, &nrhs,
                           &c_one,     h_A, &lda,
                                       h_X, &ldx,
                           &c_neg_one, h_B, &ldb);
            Rnorm = lapackf77_zlange( "I", &N, &nrhs, h_B, &ldb, h_workd);
            error = Rnorm / Anorm;
            
            //=====================================================================
            //                 Double Precision Factor
            //=====================================================================
            magma_zsetmatrix( N, N, h_A, lda, d_A, lda );
            
            gpu_time = magma_wtime();
            magma_zpotrf_gpu(opts.uplo, N, d_A, lda, &info);
            gpu_time = magma_wtime() - gpu_time;
            gpu_perfdf = gflopsF / gpu_time;
            if (info != 0)
                printf("magma_zpotrf returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            
            //=====================================================================
            //                 Double Precision Solve
            //=====================================================================
            magma_zsetmatrix( N, N,    h_A, lda, d_A, lda );
            magma_zsetmatrix( N, nrhs, h_B, ldb, d_B, ldb );
            
            gpu_time = magma_wtime();
            magma_zpotrf_gpu(opts.uplo, N, d_A, lda, &info);
            magma_zpotrs_gpu(opts.uplo, N, nrhs, d_A, lda, d_B, ldb, &info);
            gpu_time = magma_wtime() - gpu_time;
            gpu_perfds = gflopsS / gpu_time;
            if (info != 0)
                printf("magma_zpotrs returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            
            //=====================================================================
            //                 Single Precision Factor
            //=====================================================================
            d_As = d_works;
            d_Bs = d_works + lda*N;
            magma_zsetmatrix( N, N,    h_A, lda, d_A, lda );
            magma_zsetmatrix( N, nrhs, h_B, ldb, d_B, ldb );
            magmablas_zlag2c( N, N,    d_A, lda, d_As, N, &info );
            magmablas_zlag2c( N, nrhs, d_B, ldb, d_Bs, N, &info );
            
            gpu_time = magma_wtime();
            magma_cpotrf_gpu(opts.uplo, N, d_As, N, &info);
            gpu_time = magma_wtime() - gpu_time;
            gpu_perfsf = gflopsF / gpu_time;
            if (info != 0)
                printf("magma_cpotrf returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            
            //=====================================================================
            //                 Single Precision Solve
            //=====================================================================
            magmablas_zlag2c(N, N,    d_A, lda, d_As, N, &info );
            magmablas_zlag2c(N, nrhs, d_B, ldb, d_Bs, N, &info );
            
            gpu_time = magma_wtime();
            magma_cpotrf_gpu(opts.uplo, N, d_As, lda, &info);
            magma_cpotrs_gpu(opts.uplo, N, nrhs, d_As, N, d_Bs, N, &info);
            gpu_time = magma_wtime() - gpu_time;
            gpu_perfss = gflopsS / gpu_time;
            if (info != 0)
                printf("magma_cpotrs returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            
            printf("%5d %5d   %7.2f   %7.2f   %7.2f   %7.2f   %7.2f    %4d   %8.2e   %s\n",
                   (int) N, (int) nrhs,
                   gpu_perfdf, gpu_perfds, gpu_perfsf, gpu_perfss, gpu_perf,
                   (int) posv_iter, error, (error < tol ? "ok" : "failed"));
            status += ! (error < tol);
            
            TESTING_FREE_CPU( h_A );
            TESTING_FREE_CPU( h_B );
            TESTING_FREE_CPU( h_X );
            TESTING_FREE_CPU( h_workd );
            
            TESTING_FREE_DEV( d_A );
            TESTING_FREE_DEV( d_B );
            TESTING_FREE_DEV( d_X );
            TESTING_FREE_DEV( d_works );
            TESTING_FREE_DEV( d_workd );
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }

    TESTING_FINALIZE();
    return status;
}
Ejemplo n.º 10
0
/**
    Purpose
    -------
    ZHEEVR computes selected eigenvalues and, optionally, eigenvectors
    of a complex Hermitian matrix T.  Eigenvalues and eigenvectors can
    be selected by specifying either a range of values or a range of
    indices for the desired eigenvalues.

    Whenever possible, ZHEEVR calls ZSTEGR to compute the
    eigenspectrum using Relatively Robust Representations.  ZSTEGR
    computes eigenvalues by the dqds algorithm, while orthogonal
    eigenvectors are computed from various "good" L D L^T representations
    (also known as Relatively Robust Representations). Gram-Schmidt
    orthogonalization is avoided as far as possible. More specifically,
    the various steps of the algorithm are as follows. For the i-th
    unreduced block of T,
       1.  Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T
            is a relatively robust representation,
       2.  Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high
           relative accuracy by the dqds algorithm,
       3.  If there is a cluster of close eigenvalues, "choose" sigma_i
           close to the cluster, and go to step (a),
       4.  Given the approximate eigenvalue lambda_j of L_i D_i L_i^T,
           compute the corresponding eigenvector by forming a
           rank-revealing twisted factorization.
    The desired accuracy of the output can be specified by the input
    parameter ABSTOL.

    For more details, see "A new O(n^2) algorithm for the symmetric
    tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon,
    Computer Science Division Technical Report No. UCB//CSD-97-971,
    UC Berkeley, May 1997.


    Note 1 : ZHEEVR calls ZSTEGR when the full spectrum is requested
    on machines which conform to the ieee-754 floating point standard.
    ZHEEVR calls DSTEBZ and ZSTEIN on non-ieee machines and
    when partial spectrum requests are made.

    Normal execution of ZSTEGR may create NaNs and infinities and
    hence may abort due to a floating point exception in environments
    which do not handle NaNs and infinities in the ieee standard default
    manner.

    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_16 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, 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      DOUBLE PRECISION
    @param[in]
    vu      DOUBLE PRECISION
            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[in]
    abstol  DOUBLE PRECISION
            The absolute error tolerance for the eigenvalues.
            An approximate eigenvalue is accepted as converged
            when it is determined to lie in an interval [a,b]
            of width less than or equal to

                    ABSTOL + EPS * max( |a|,|b| ),
    \n
            where EPS is the machine precision.  If ABSTOL is less than
            or equal to zero, then  EPS*|T|  will be used in its place,
            where |T| is the 1-norm of the tridiagonal matrix obtained
            by reducing A to tridiagonal form.
    \n
            See "Computing Small Singular Values of Bidiagonal Matrices
            with Guaranteed High Relative Accuracy," by Demmel and
            Kahan, LAPACK Working Note #3.
    \n
            If high relative accuracy is important, set ABSTOL to
            DLAMCH( 'Safe minimum' ).  Doing so will guarantee that
            eigenvalues are computed to high relative accuracy when
            possible in future releases.  The current code does not
            make any guarantees about high relative accuracy, but
            furutre releases will. See J. Barlow and J. Demmel,
            "Computing Accurate Eigensystems of Scaled Diagonally
            Dominant Matrices", LAPACK Working Note #7, for a discussion
            of which matrices define their eigenvalues to high relative
            accuracy.

    @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       DOUBLE PRECISION array, dimension (N)
            The first M elements contain the selected eigenvalues in
            ascending order.

    @param[out]
    Z       COMPLEX_16 array, dimension (LDZ, max(1,M))
            If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z
            contain the orthonormal eigenvectors of the matrix A
            corresponding to the selected eigenvalues, with the i-th
            column of Z holding the eigenvector associated with W(i).
            If JOBZ = MagmaNoVec, then Z is not referenced.
            Note: the user must ensure that at least max(1,M) columns are
            supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M
            is not known in advance and an upper bound must be used.

    @param[in]
    ldz     INTEGER
            The leading dimension of the array Z.  LDZ >= 1, and if
            JOBZ = MagmaVec, LDZ >= max(1,N).

    @param[out]
    isuppz  INTEGER ARRAY, dimension ( 2*max(1,M) )
            The support of the eigenvectors in Z, i.e., the indices
            indicating the nonzero elements in Z. The i-th eigenvector
            is nonzero only in elements ISUPPZ( 2*i-1 ) through
            ISUPPZ( 2*i ).
            __Implemented only for__ RANGE = MagmaRangeAll or MagmaRangeI and IU - IL = N - 1

    @param[out]
    work    (workspace) COMPLEX_16 array, dimension (LWORK)
            On exit, if INFO = 0, WORK[0] returns the optimal LWORK.

    @param[in]
    lwork   INTEGER
            The length of the array WORK.  LWORK >= max(1,2*N).
            For optimal efficiency, LWORK >= (NB+1)*N,
            where NB is the max of the blocksize for ZHETRD and for
            ZUNMTR as returned by ILAENV.
    \n
            If LWORK = -1, then a workspace query is assumed; the routine
            only calculates the optimal size of the WORK array, returns
            this value as the first entry of the WORK array, and no error
            message related to LWORK is issued by XERBLA.

    @param[out]
    rwork   (workspace) DOUBLE PRECISION array, dimension (LRWORK)
            On exit, if INFO = 0, RWORK[0] returns the optimal
            (and minimal) LRWORK.

    @param[in]
    lrwork  INTEGER
            The length of the array RWORK.  LRWORK >= max(1,24*N).
    \n
            If LRWORK = -1, then a workspace query is assumed; the routine
            only calculates the optimal size of the RWORK array, returns
            this value as the first entry of the RWORK array, and no error
            message related to LRWORK is issued by XERBLA.

    @param[out]
    iwork   (workspace) INTEGER array, dimension (LIWORK)
            On exit, if INFO = 0, IWORK[0] returns the optimal
            (and minimal) LIWORK.

    @param[in]
    liwork  INTEGER
            The dimension of the array IWORK.  LIWORK >= max(1,10*N).
    \n
            If LIWORK = -1, then a workspace query is assumed; the
            routine only calculates the optimal size of the IWORK array,
            returns this value as the first entry of the IWORK array, and
            no error message related to 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:  Internal error

    Further Details
    ---------------
    Based on contributions by
       Inderjit Dhillon, IBM Almaden, USA
       Osni Marques, LBNL/NERSC, USA
       Ken Stanley, Computer Science Division, University of
         California at Berkeley, USA

    @ingroup magma_zheev_driver
    ********************************************************************/
extern "C" magma_int_t
magma_zheevr(
    magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n,
    magmaDoubleComplex *A, magma_int_t lda,
    double vl, double vu,
    magma_int_t il, magma_int_t iu, double abstol, magma_int_t *m,
    double *w,
    magmaDoubleComplex *Z, magma_int_t ldz,
    magma_int_t *isuppz,
    magmaDoubleComplex *work, magma_int_t lwork,
    double *rwork, magma_int_t lrwork,
    magma_int_t *iwork, magma_int_t liwork,
    magma_int_t *info)
{
    /* Constants */
    const magma_int_t izero = 0;
    const magma_int_t ione  = 1;
    const float szero = 0.;
    const float sone  = 1.;
    
    /* Local variables */
    const char* uplo_  = lapack_uplo_const( uplo  );
    const char* jobz_  = lapack_vec_const( jobz  );
    const char* range_ = lapack_range_const( range );
    
    magma_int_t indrd, indre;
    magma_int_t imax;
    magma_int_t lopt, itmp1, indree, indrdd;
    magma_int_t tryrac;
    magma_int_t i, j, jj, i__1;
    magma_int_t iscale, indibl, indifl;
    magma_int_t indiwo, indisp, indtau;
    magma_int_t indrwk, indwk;
    magma_int_t llwork, llrwork, nsplit;
    magma_int_t ieeeok;
    magma_int_t iinfo;
    magma_int_t lwmin, lrwmin, liwmin;
    double safmin;
    double bignum;
    double smlnum;
    double eps, tmp1;
    double anrm;
    double sigma, d__1;
    double rmin, rmax;
    
    bool lower  = (uplo == MagmaLower);
    bool wantz  = (jobz == MagmaVec);
    bool alleig = (range == MagmaRangeAll);
    bool valeig = (range == MagmaRangeV);
    bool indeig = (range == MagmaRangeI);
    bool 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 (ldz < 1 || (wantz && ldz < n)) {
        *info = -15;
    } 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_zhetrd_nb(n);
    
    lwmin =  n * (nb + 1);
    lrwmin = 24 * n;
    liwmin = 10 * n;
    
    work[0] = magma_zmake_lwork( lwmin );
    rwork[0] = magma_dmake_lwork( lrwmin );
    iwork[0] = liwmin;
    
    if (lwork < lwmin && ! lquery) {
        *info = -18;
    } else if ((lrwork < lrwmin) && ! lquery) {
        *info = -20;
    } else if ((liwork < liwmin) && ! lquery) {
        *info = -22;
    }
    
    if (*info != 0) {
        magma_xerbla(__func__, -(*info));
        return *info;
    } else if (lquery) {
        return *info;
    }
    
    *m = 0;
    /* 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_zheevr(jobz_, range_, uplo_,
                         &n, A, &lda, &vl, &vu, &il, &iu, &abstol, m,
                         w, Z, &ldz, isuppz, work, &lwork,
                         rwork, &lrwork, iwork, &liwork, info);
        return *info;
    }
    
    --w;
    --work;
    --rwork;
    --iwork;
    --isuppz;
    
    /* Get machine constants. */
    safmin = lapackf77_dlamch("Safe minimum");
    eps = lapackf77_dlamch("Precision");
    smlnum = safmin / eps;
    bignum = 1. / smlnum;
    rmin = magma_dsqrt(smlnum);
    rmax = magma_dsqrt(bignum);
    
    /* Scale matrix to allowable range, if necessary. */
    anrm = lapackf77_zlanhe("M", uplo_, &n, A, &lda, &rwork[1]);
    iscale = 0;
    if (anrm > 0. && anrm < rmin) {
        iscale = 1;
        sigma = rmin / anrm;
    } else if (anrm > rmax) {
        iscale = 1;
        sigma = rmax / anrm;
    }
    if (iscale == 1) {
        d__1 = 1.;
        lapackf77_zlascl(uplo_, &izero, &izero, &d__1, &sigma, &n, &n, A,
                         &lda, info);
        
        if (abstol > 0.) {
            abstol *= sigma;
        }
        if (valeig) {
            vl *= sigma;
            vu *= sigma;
        }
    }
    
    /* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */
    indtau = 1;
    indwk = indtau + n;
    
    indre = 1;
    indrd = indre + n;
    indree = indrd + n;
    indrdd = indree + n;
    indrwk = indrdd + n;
    llwork = lwork - indwk + 1;
    llrwork = lrwork - indrwk + 1;
    
    indifl = 1;
    indibl = indifl + n;
    indisp = indibl + n;
    indiwo = indisp + n;
    
    magma_zhetrd(uplo, n, A, lda, &rwork[indrd], &rwork[indre], &work[indtau], &work[indwk], llwork, &iinfo);
    
    lopt = n + (magma_int_t)MAGMA_Z_REAL(work[indwk]);
    
    /* If all eigenvalues are desired and ABSTOL is less than or equal to
       zero, then call DSTERF
       or ZUNGTR and ZSTEQR.  If this fails for
       some eigenvalue, then try DSTEBZ. */
    ieeeok = lapackf77_ieeeck( &ione, &szero, &sone);
    
    /* If only the eigenvalues are required call DSTERF for all or DSTEBZ for a part */
    if (! wantz) {
        blasf77_dcopy(&n, &rwork[indrd], &ione, &w[1], &ione);
        i__1 = n - 1;
        if (alleig || (indeig && il == 1 && iu == n)) {
            lapackf77_dsterf(&n, &w[1], &rwork[indre], info);
            *m = n;
        } else {
            lapackf77_dstebz(range_, "E", &n, &vl, &vu, &il, &iu, &abstol,
                             &rwork[indrd], &rwork[indre], m,
                             &nsplit, &w[1], &iwork[indibl], &iwork[indisp],
                             &rwork[indrwk], &iwork[indiwo], info);
        }
        
        /* Otherwise call ZSTEMR if infinite and NaN arithmetic is supported */
    }
    else if (ieeeok == 1) {
        i__1 = n - 1;
        
        blasf77_dcopy(&i__1, &rwork[indre], &ione, &rwork[indree], &ione);
        blasf77_dcopy(&n, &rwork[indrd], &ione, &rwork[indrdd], &ione);
        
        if (abstol < 2*n*eps)
            tryrac = 1;
        else
            tryrac = 0;
        
        lapackf77_zstemr(jobz_, range_, &n, &rwork[indrdd], &rwork[indree], &vl, &vu, &il,
                         &iu, m, &w[1], Z, &ldz, &n, &isuppz[1], &tryrac, &rwork[indrwk],
                         &llrwork, &iwork[1], &liwork, info);
        
        if (*info == 0 && wantz) {
            magma_zunmtr(MagmaLeft, uplo, MagmaNoTrans, n, *m, A, lda, &work[indtau],
                         Z, ldz, &work[indwk], llwork, &iinfo);
        }
    }
    
    
    /* Call DSTEBZ and ZSTEIN if infinite and NaN arithmetic is not supported or ZSTEMR didn't converge. */
    if (wantz && (ieeeok == 0 || *info != 0)) {
        *info = 0;
        
        lapackf77_dstebz(range_, "B", &n, &vl, &vu, &il, &iu, &abstol, &rwork[indrd], &rwork[indre], m,
                         &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &rwork[indrwk], &iwork[indiwo], info);
        
        lapackf77_zstein(&n, &rwork[indrd], &rwork[indre], m, &w[1], &iwork[indibl], &iwork[indisp],
                         Z, &ldz, &rwork[indrwk], &iwork[indiwo], &iwork[indifl], info);
        
        /* Apply unitary matrix used in reduction to tridiagonal
           form to eigenvectors returned by ZSTEIN. */
        magma_zunmtr(MagmaLeft, uplo, MagmaNoTrans, n, *m, A, lda, &work[indtau],
                     Z, ldz, &work[indwk], llwork, &iinfo);
    }
    
    /* If matrix was scaled, then rescale eigenvalues appropriately. */
    if (iscale == 1) {
        if (*info == 0) {
            imax = *m;
        } else {
            imax = *info - 1;
        }
        d__1 = 1. / sigma;
        blasf77_dscal(&imax, &d__1, &w[1], &ione);
    }
    
    /* If eigenvalues are not in order, then sort them, along with
       eigenvectors. */
    if (wantz) {
        for (j = 1; j <= *m-1; ++j) {
            i = 0;
            tmp1 = w[j];
            for (jj = j + 1; jj <= *m; ++jj) {
                if (w[jj] < tmp1) {
                    i = jj;
                    tmp1 = w[jj];
                }
            }
            
            if (i != 0) {
                itmp1 = iwork[indibl + i - 1];
                w[i] = w[j];
                iwork[indibl + i - 1] = iwork[indibl + j - 1];
                w[j] = tmp1;
                iwork[indibl + j - 1] = itmp1;
                blasf77_zswap(&n, Z + (i-1)*ldz, &ione, Z + (j-1)*ldz, &ione);
            }
        }
    }
    
    /* Set WORK[0] to optimal complex workspace size. */
    work[1] = magma_zmake_lwork( lopt );
    rwork[1] = magma_dmake_lwork( lrwmin );
    iwork[1] = liwmin;
    
    return *info;
} /* magma_zheevr */
Ejemplo n.º 11
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing zhegvd
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    real_Double_t   gpu_time, cpu_time;
    magmaDoubleComplex *h_A, *h_R, *h_B, *h_S, *h_work;
    double *rwork, *w1, *w2;
    double result[4] = {0};
    magma_int_t *iwork;
    magma_int_t N, n2, info, nb, lwork, liwork, lda, lrwork;
    magmaDoubleComplex c_zero    = MAGMA_Z_ZERO;
    magmaDoubleComplex c_one     = MAGMA_Z_ONE;
    magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
    double d_one         =  1.;
    double d_neg_one     = -1.;
    //double d_ten         = 10.;
    //magma_int_t izero    = 0;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    magma_int_t status = 0;

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

    double tol    = opts.tolerance * lapackf77_dlamch("E");
    double tolulp = opts.tolerance * lapackf77_dlamch("P");
    
    if ( opts.check && opts.jobz == MagmaNoVec ) {
        fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
        opts.jobz = MagmaVec;
    }
    
    printf("using: itype = %d, jobz = %s, uplo = %s\n",
           (int) opts.itype, 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];
            lda    = N;
            n2     = N*lda;
            nb     = magma_get_zhetrd_nb(N);
            lwork  = 2*N*nb + N*N;
            lrwork = 1 + 5*N +2*N*N;
            liwork = 3 + 5*N;

            TESTING_MALLOC_CPU( h_A,    magmaDoubleComplex,  n2     );
            TESTING_MALLOC_CPU( h_B,    magmaDoubleComplex,  n2     );
            TESTING_MALLOC_CPU( w1,     double,              N      );
            TESTING_MALLOC_CPU( w2,     double,              N      );
            TESTING_MALLOC_CPU( rwork,  double,              lrwork );
            TESTING_MALLOC_CPU( iwork,  magma_int_t,         liwork );
            
            TESTING_MALLOC_PIN( h_R,    magmaDoubleComplex,  n2     );
            TESTING_MALLOC_PIN( h_S,    magmaDoubleComplex,  n2     );
            TESTING_MALLOC_PIN( h_work, magmaDoubleComplex,  lwork  );
            
            /* Initialize the matrix */
            lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
            //lapackf77_zlatms( &N, &N, "U", ISEED, "P", w1, &five, &d_ten,
            //                 &d_one, &N, &N, lapack_uplo_const(opts.uplo), h_B, &lda, h_work, &info);
            //lapackf77_zlaset( "A", &N, &N, &c_zero, &c_one, h_B, &lda);
            lapackf77_zlarnv( &ione, ISEED, &n2, h_B );
            magma_zmake_hpd( N, h_B, lda );
            lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
            lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &lda, h_S, &lda );
            
            /* warmup */
            if ( opts.warmup ) {
                magma_zhegvd( opts.itype, opts.jobz, opts.uplo,
                              N, h_R, lda, h_S, lda, w1,
                              h_work, lwork,
                              rwork, lrwork,
                              iwork, liwork,
                              &info );
                if (info != 0)
                    printf("magma_zhegvd returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
                
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &lda, h_S, &lda );
            }
            
            /* ====================================================================
               Performs operation using MAGMA
               =================================================================== */
            gpu_time = magma_wtime();
            magma_zhegvd( opts.itype, opts.jobz, opts.uplo,
                          N, h_R, lda, h_S, lda, w1,
                          h_work, lwork,
                          rwork, lrwork,
                          iwork, liwork,
                          &info );
            gpu_time = magma_wtime() - gpu_time;
            if (info != 0)
                printf("magma_zhegvd returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            
            if ( opts.check ) {
                /* =====================================================================
                   Check the results following the LAPACK's [zc]hegvd routine.
                   A x = lambda B x is solved
                   and the following 3 tests computed:
                   (1)    | A Z - B Z D | / ( |A||Z| N )   (itype = 1)
                          | A B Z - Z D | / ( |A||Z| N )   (itype = 2)
                          | B A Z - Z D | / ( |A||Z| N )   (itype = 3)
                   (2)    | I - V V' B | / ( N )           (itype = 1,2)
                          | B - V V' | / ( |B| N )         (itype = 3)
                   (3)    | S(with V) - S(w/o V) | / | S |
                   =================================================================== */
                double temp1, temp2;
                //magmaDoubleComplex *tau;
                
                if ( opts.itype == 1 || opts.itype == 2 ) {
                    lapackf77_zlaset( "A", &N, &N, &c_zero, &c_one, h_S, &lda);
                    blasf77_zgemm("N", "C", &N, &N, &N, &c_one, h_R, &lda, h_R, &lda, &c_zero, h_work, &N);
                    blasf77_zhemm("R", lapack_uplo_const(opts.uplo), &N, &N, &c_neg_one, h_B, &lda, h_work, &N, &c_one, h_S, &lda);
                    result[1] = lapackf77_zlange("1", &N, &N, h_S, &lda, rwork) / N;
                }
                else if ( opts.itype == 3 ) {
                    lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &lda, h_S, &lda);
                    blasf77_zherk(lapack_uplo_const(opts.uplo), "N", &N, &N, &d_neg_one, h_R, &lda, &d_one, h_S, &lda);
                    result[1] = lapackf77_zlanhe("1", lapack_uplo_const(opts.uplo), &N, h_S, &lda, rwork) / N
                              / lapackf77_zlanhe("1", lapack_uplo_const(opts.uplo), &N, h_B, &lda, rwork);
                }
                
                result[0] = 1.;
                result[0] /= lapackf77_zlanhe("1", lapack_uplo_const(opts.uplo), &N, h_A, &lda, rwork);
                result[0] /= lapackf77_zlange("1", &N, &N, h_R, &lda, rwork);
                
                if ( opts.itype == 1 ) {
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_A, &lda, h_R, &lda, &c_zero, h_work, &N);
                    for(int i=0; i<N; ++i)
                        blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_neg_one, h_B, &lda, h_R, &lda, &c_one, h_work, &N);
                    result[0] *= lapackf77_zlange("1", &N, &N, h_work, &lda, rwork)/N;
                }
                else if ( opts.itype == 2 ) {
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_B, &lda, h_R, &lda, &c_zero, h_work, &N);
                    for(int i=0; i<N; ++i)
                        blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_A, &lda, h_work, &N, &c_neg_one, h_R, &lda);
                    result[0] *= lapackf77_zlange("1", &N, &N, h_R, &lda, rwork)/N;
                }
                else if ( opts.itype == 3 ) {
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_A, &lda, h_R, &lda, &c_zero, h_work, &N);
                    for(int i=0; i<N; ++i)
                        blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_B, &lda, h_work, &N, &c_neg_one, h_R, &lda);
                    result[0] *= lapackf77_zlange("1", &N, &N, h_R, &lda, rwork)/N;
                }
                
                /*
                lapackf77_zhet21( &ione, lapack_uplo_const(opts.uplo), &N, &izero,
                                  h_A, &lda,
                                  w1, w1,
                                  h_R, &lda,
                                  h_R, &lda,
                                  tau, h_work, rwork, &result[0] );
                */
                
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &lda, h_S, &lda );
                
                magma_zhegvd( opts.itype, MagmaNoVec, opts.uplo,
                              N, h_R, lda, h_S, lda, w2,
                              h_work, lwork,
                              rwork, lrwork,
                              iwork, liwork,
                              &info );
                if (info != 0)
                    printf("magma_zhegvd returned error %d: %s.\n",
                           (int) info, magma_strerror( 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 / (((double)N)*temp1);
            }
            
            /* =====================================================================
               Performs operation using LAPACK
               =================================================================== */
            if ( opts.lapack ) {
                cpu_time = magma_wtime();
                lapackf77_zhegvd( &opts.itype, lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
                                  &N, h_A, &lda, h_B, &lda, w2,
                                  h_work, &lwork,
                                  rwork, &lrwork,
                                  iwork, &liwork,
                                  &info );
                cpu_time = magma_wtime() - cpu_time;
                if (info != 0)
                    printf("lapackf77_zhegvd 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 eigenvalues and eigenvectors for correctness:\n");
                if ( opts.itype==1 ) {
                    printf("(1)    | A Z - B Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed") );
                }
                else if ( opts.itype==2 ) {
                    printf("(1)    | A B Z - Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed") );
                }
                else if ( opts.itype==3 ) {
                    printf("(1)    | B A Z - Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed") );
                }
                if ( opts.itype==1 || opts.itype==2 ) {
                    printf("(2)    | I -   Z Z' B | /  N         = %8.2e   %s\n",   result[1], (result[1] < tol    ? "ok" : "failed") );
                }
                else {
                    printf("(2)    | B -  Z Z' | / (|B| N)       = %8.2e   %s\n",   result[1], (result[1] < tol    ? "ok" : "failed") );
                }
                printf(    "(3)    | D(w/ Z) - D(w/o Z) | / |D|  = %8.2e   %s\n\n", result[2], (result[2] < tolulp ? "ok" : "failed") );
                status += ! (result[0] < tol && result[1] < tol && result[2] < tolulp);
            }
            
            TESTING_FREE_CPU( h_A    );
            TESTING_FREE_CPU( h_B    );
            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_S    );
            TESTING_FREE_PIN( h_work );
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }
    
    TESTING_FINALIZE();
    return status;
}
Ejemplo n.º 12
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing zherk
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    real_Double_t   gflops, cublas_perf, cublas_time, cpu_perf, cpu_time;
    double          cublas_error, Cnorm, work[1];
    magma_int_t N, K;
    magma_int_t Ak, An;
    magma_int_t sizeA, sizeC;
    magma_int_t lda, ldc, ldda, lddc;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    
    magmaDoubleComplex *h_A, *h_C, *h_Ccublas;
    magmaDoubleComplex *d_A, *d_C;
    magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
    double alpha = MAGMA_D_MAKE(  0.29, -0.86 );
    double beta  = MAGMA_D_MAKE( -0.48,  0.38 );
    magma_int_t status = 0;
    
    magma_opts opts;
    parse_opts( argc, argv, &opts );
    opts.lapack |= opts.check;  // check (-c) implies lapack (-l)
    
    double tol = opts.tolerance * lapackf77_dlamch("E");
    
    printf("If running lapack (option --lapack), CUBLAS error is computed\n"
           "relative to CPU BLAS result.\n\n");
    printf("uplo = %s, transA = %s\n",
           lapack_uplo_const(opts.uplo), lapack_trans_const(opts.transA) );
    printf("    N     K   CUBLAS Gflop/s (ms)   CPU Gflop/s (ms)  CUBLAS error\n");
    printf("==================================================================\n");
    for( int itest = 0; itest < opts.ntest; ++itest ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            N = opts.nsize[itest];
            K = opts.ksize[itest];
            gflops = FLOPS_ZHERK(K, N) / 1e9;

            if ( opts.transA == MagmaNoTrans ) {
                lda = An = N;
                Ak = K;
            } else {
                lda = An = K;
                Ak = N;
            }
            
            ldc = N;
            
            ldda = ((lda+31)/32)*32;
            lddc = ((ldc+31)/32)*32;
            
            sizeA = lda*Ak;
            sizeC = ldc*N;
            
            TESTING_MALLOC_CPU( h_A,       magmaDoubleComplex, lda*Ak );
            TESTING_MALLOC_CPU( h_C,       magmaDoubleComplex, ldc*N  );
            TESTING_MALLOC_CPU( h_Ccublas, magmaDoubleComplex, ldc*N  );
            
            TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*Ak );
            TESTING_MALLOC_DEV( d_C, magmaDoubleComplex, lddc*N  );
            
            /* Initialize the matrices */
            lapackf77_zlarnv( &ione, ISEED, &sizeA, h_A );
            lapackf77_zlarnv( &ione, ISEED, &sizeC, h_C );
            
            /* =====================================================================
               Performs operation using CUBLAS
               =================================================================== */
            magma_zsetmatrix( An, Ak, h_A, lda, d_A, ldda );
            magma_zsetmatrix( N, N, h_C, ldc, d_C, lddc );

            cublas_time = magma_sync_wtime( NULL );
            cublasZherk( handle, cublas_uplo_const(opts.uplo), cublas_trans_const(opts.transA), N, K,
                         &alpha, d_A, ldda,
                         &beta,  d_C, lddc );
            cublas_time = magma_sync_wtime( NULL ) - cublas_time;
            cublas_perf = gflops / cublas_time;
            
            magma_zgetmatrix( N, N, d_C, lddc, h_Ccublas, ldc );
            
            /* =====================================================================
               Performs operation using CPU BLAS
               =================================================================== */
            if ( opts.lapack ) {
                cpu_time = magma_wtime();
                blasf77_zherk( lapack_uplo_const(opts.uplo), lapack_trans_const(opts.transA), &N, &K,
                               &alpha, h_A, &lda,
                               &beta,  h_C, &ldc );
                cpu_time = magma_wtime() - cpu_time;
                cpu_perf = gflops / cpu_time;
            }
            
            /* =====================================================================
               Check the result
               =================================================================== */
            if ( opts.lapack ) {
                // compute relative error for both magma & cublas, relative to lapack,
                // |C_magma - C_lapack| / |C_lapack|
                Cnorm = lapackf77_zlanhe("fro", lapack_uplo_const(opts.uplo), &N, h_C, &ldc, work);

                blasf77_zaxpy( &sizeC, &c_neg_one, h_C, &ione, h_Ccublas, &ione );
                cublas_error = lapackf77_zlanhe( "fro", lapack_uplo_const(opts.uplo), &N, h_Ccublas, &ldc, work ) / Cnorm;
                
                printf("%5d %5d   %7.2f (%7.2f)   %7.2f (%7.2f)    %8.2e   %s\n",
                       (int) N, (int) K,
                       cublas_perf, 1000.*cublas_time,
                       cpu_perf,    1000.*cpu_time,
                       cublas_error, (cublas_error < tol ? "ok" : "failed"));
                status += ! (cublas_error < tol);
            }
            else {
                printf("%5d %5d   %7.2f (%7.2f)    ---   (  ---  )    ---     ---\n",
                       (int) N, (int) K,
                       cublas_perf, 1000.*cublas_time);
            }
            
            TESTING_FREE_CPU( h_A );
            TESTING_FREE_CPU( h_C );
            TESTING_FREE_CPU( h_Ccublas );
            
            TESTING_FREE_DEV( d_A );
            TESTING_FREE_DEV( d_C );
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }

    TESTING_FINALIZE();
    return status;
}
Ejemplo n.º 13
0
int main( int argc, char** argv)
{
    TESTING_INIT();

    real_Double_t   gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
    magmaDoubleComplex *h_A, *h_R;
    magmaDoubleComplex *d_A;
    magma_int_t N, n2, lda, ldda, info;
    magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    double      work[1], error;
    magma_int_t status = 0;
    magmaDoubleComplex **d_A_array = NULL;
    magma_int_t *dinfo_magma;

    magma_int_t batchCount;

    magma_queue_t queue = magma_stream;
    magma_opts opts;
    parse_opts( argc, argv, &opts );
    opts.lapack |= opts.check;  // check (-c) implies lapack (-l)
    batchCount = opts.batchcount;
    double tol = opts.tolerance * lapackf77_dlamch("E");

    printf("BatchCount    N      CPU GFlop/s (ms)      GPU GFlop/s (ms)    ||R_magma - R_lapack||_F / ||R_lapack||_F\n");
    printf("========================================================\n");
    for( int i = 0; i < opts.ntest; ++i ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            N   = opts.nsize[i];
            ldda = lda = ((N+31)/32)*32;
            n2  = lda* N  * batchCount;

            gflops = batchCount * FLOPS_ZPOTRF( N ) / 1e9 ;

            TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2);
            TESTING_MALLOC_PIN( h_R, magmaDoubleComplex, n2);
            TESTING_MALLOC_DEV(  d_A, magmaDoubleComplex, ldda * N * batchCount);
            TESTING_MALLOC_DEV(  dinfo_magma,  magma_int_t, batchCount);
            
            magma_malloc((void**)&d_A_array, batchCount * sizeof(*d_A_array));

            /* Initialize the matrix */
            lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
            for(int i=0; i<batchCount; i++)
            {
               magma_zmake_hpd( N, h_A + i * lda * N, lda );// need modification
            }
            
            magma_int_t columns = N * batchCount;
            lapackf77_zlacpy( MagmaUpperLowerStr, &N, &(columns), h_A, &lda, h_R, &lda );
            magma_zsetmatrix( N, columns, h_A, lda, d_A, ldda );


            /* ====================================================================
               Performs operation using MAGMA
               =================================================================== */
            zset_pointer(d_A_array, d_A, ldda, 0, 0, ldda * N, batchCount, queue);
            gpu_time = magma_sync_wtime(NULL);
            info = magma_zpotrf_batched( opts.uplo, N, d_A_array, ldda, dinfo_magma, batchCount, queue);
            gpu_time = magma_sync_wtime(NULL) - gpu_time;
            gpu_perf = gflops / gpu_time;
            magma_int_t *cpu_info = (magma_int_t*) malloc(batchCount*sizeof(magma_int_t));
            magma_getvector( batchCount, sizeof(magma_int_t), dinfo_magma, 1, cpu_info, 1);
            for(int i=0; i<batchCount; i++)
            {
                if(cpu_info[i] != 0 ){
                    printf("magma_zpotrf_batched matrix %d returned internal error %d\n",i, (int)cpu_info[i] );
                }
            }
            if (info != 0)
                printf("magma_zpotrf_batched returned argument error %d: %s.\n", (int) info, magma_strerror( info ));

            if ( opts.lapack ) {

                /* =====================================================================
                   Performs operation using LAPACK
                   =================================================================== */
                cpu_time = magma_wtime();
                for(int i=0; i<batchCount; i++)
                {
                   lapackf77_zpotrf( lapack_uplo_const(opts.uplo), &N, h_A + i * lda * N, &lda, &info );
                }
                cpu_time = magma_wtime() - cpu_time;
                cpu_perf = gflops / cpu_time;
                if (info != 0)
                    printf("lapackf77_zpotrf returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));

                /* =====================================================================
                   Check the result compared to LAPACK
                   =================================================================== */
                 magma_zgetmatrix( N, columns, d_A, ldda, h_R, lda );
                 magma_int_t NN = lda*N;
                 char const uplo = 'l'; // lapack_uplo_const(opts.uplo)
                 double err = 0.0;
                 for(int i=0; i<batchCount; i++)
                 { 
                     error = lapackf77_zlanhe("f", &uplo, &N, h_A + i * lda*N, &lda, work);                
                     blasf77_zaxpy(&NN, &c_neg_one, h_A + i * lda*N, &ione, h_R + i  * lda*N, &ione);
                     error = lapackf77_zlanhe("f", &uplo, &N, h_R + i * lda*N, &lda, work) / error;
                     if ( isnan(error) || isinf(error) ) {
                         err = error;
                         break;
                     }
                     err = max(fabs(error),err);
                 }
              

                printf("%5d      %5d    %7.2f (%7.2f)     %7.2f (%7.2f)     %8.2e   %s\n",
                       (int)batchCount, (int) N, cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000., err,  (error < tol ? "ok" : "failed"));
                status += ! (err < tol);
                
            }
            else {
                printf("%5d      %5d    ---   (  ---  )   %7.2f (%7.2f)     ---  \n",
                       (int)batchCount, (int) N, gpu_perf, gpu_time*1000. );
            }
            TESTING_FREE_CPU( h_A );
            TESTING_FREE_PIN( h_R );
            TESTING_FREE_DEV( d_A );
            TESTING_FREE_DEV( d_A_array );
            TESTING_FREE_DEV( dinfo_magma );
            free(cpu_info);
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }

    TESTING_FINALIZE();
    return status;

}
Ejemplo n.º 14
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing zhegvdx
*/
int main( int argc, char** argv)
{

    TESTING_INIT();

    real_Double_t gpu_time;

    magmaDoubleComplex *h_A, *h_R, *h_B, *h_S, *h_work;

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

    /* Matrix size */
    double *w1, *w2, result[2]={0,0};
    magma_int_t *iwork;
    magma_int_t N, n2, info, lwork, liwork;
    magmaDoubleComplex c_zero    = MAGMA_Z_ZERO;
    magmaDoubleComplex c_one     = MAGMA_Z_ONE;
    magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    magma_int_t status = 0;

    magma_opts opts;
    parse_opts( argc, argv, &opts );
    
    double tol    = opts.tolerance * lapackf77_dlamch("E");
    double tolulp = opts.tolerance * lapackf77_dlamch("P");

    magma_range_t range = MagmaRangeAll;
    if (opts.fraction != 1)
        range = MagmaRangeI;

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

    printf("using: itype = %d, jobz = %s, range = %s, uplo = %s, opts.check = %d, fraction = %6.4f\n",
           (int) opts.itype, lapack_vec_const(opts.jobz), lapack_range_const(range), lapack_uplo_const(opts.uplo),
           (int) opts.check, opts.fraction);

    printf("    N     M   GPU Time (sec)\n");
    printf("============================\n");
    magma_int_t threads = magma_get_parallel_numthreads();
    for( int itest = 0; itest < opts.ntest; ++itest ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            N = opts.nsize[itest];
            n2     = N*N;
            #if defined(PRECISION_z) || defined(PRECISION_c)
            lwork  = magma_zbulge_get_lq2(N, threads) + 2*N + N*N;
            lrwork = 1 + 5*N +2*N*N;
            #else
            lwork  = magma_zbulge_get_lq2(N, threads) + 1 + 6*N + 2*N*N;
            #endif
            liwork = 3 + 5*N;

            /* Allocate host memory for the matrix */
            TESTING_MALLOC_CPU( h_A,    magmaDoubleComplex, n2 );
            TESTING_MALLOC_CPU( h_B,    magmaDoubleComplex, n2 );
            TESTING_MALLOC_CPU( w1,     double, N );
            TESTING_MALLOC_CPU( w2,     double, N );
            TESTING_MALLOC_CPU( iwork,  magma_int_t, liwork );
            
            TESTING_MALLOC_PIN( h_R,    magmaDoubleComplex, n2 );
            TESTING_MALLOC_PIN( h_S,    magmaDoubleComplex, n2 );
            TESTING_MALLOC_PIN( h_work, magmaDoubleComplex, lwork );
            #if defined(PRECISION_z) || defined(PRECISION_c)
            TESTING_MALLOC_PIN( rwork,  double, lrwork);
            #endif

            /* Initialize the matrix */
            lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
            lapackf77_zlarnv( &ione, ISEED, &n2, h_B );
            magma_zmake_hpd( N, h_B, N );
            magma_zmake_hermitian( N, h_A, N );

            magma_int_t m1 = 0;
            double vl = 0;
            double vu = 0;
            magma_int_t il = 0;
            magma_int_t iu = 0;

            if (range == MagmaRangeI) {
                il = 1;
                iu = (int) (opts.fraction*N);
            }

            // ==================================================================
            // Warmup using MAGMA
            // ==================================================================
            if (opts.warmup) {
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );

                magma_zhegvdx_2stage(opts.itype, opts.jobz, range, opts.uplo,
                                     N, h_R, N, h_S, 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_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
            lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );

            gpu_time = magma_wtime();
            magma_zhegvdx_2stage(opts.itype, opts.jobz, range, opts.uplo,
                                 N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
                                 h_work, lwork,
                                 #if defined(PRECISION_z) || defined(PRECISION_c)
                                 rwork, lrwork,
                                 #endif
                                 iwork, liwork,
                                 &info);
            gpu_time = magma_wtime() - gpu_time;


            if ( opts.check && opts.jobz != MagmaNoVec ) {
                /* =====================================================================
                   Check the results following the LAPACK's [zc]hegvdx routine.
                   A x = lambda B x is solved
                   and the following 3 tests computed:
                   (1)    | A Z - B Z D | / ( |A||Z| N )  (itype = 1)
                          | A B Z - Z D | / ( |A||Z| N )  (itype = 2)
                          | B A Z - Z D | / ( |A||Z| N )  (itype = 3)
                   (2)    | S(with V) - S(w/o V) | / | S |
                   =================================================================== */
                #if defined(PRECISION_d) || defined(PRECISION_s)
                double *rwork = h_work + N*N;
                #endif

                result[0] = 1.;
                result[0] /= lapackf77_zlanhe("1", lapack_uplo_const(opts.uplo), &N, h_A, &N, rwork);
                result[0] /= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork);

                if (opts.itype == 1) {
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
                    for(int i=0; i<m1; ++i)
                        blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_neg_one, h_B, &N, h_R, &N, &c_one, h_work, &N);
                    result[0] *= lapackf77_zlange("1", &N, &m1, h_work, &N, rwork)/N;
                }
                else if (opts.itype == 2) {
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_B, &N, h_R, &N, &c_zero, h_work, &N);
                    for(int i=0; i<m1; ++i)
                        blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_work, &N, &c_neg_one, h_R, &N);
                    result[0] *= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork)/N;
                }
                else if (opts.itype == 3) {
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
                    for(int i=0; i<m1; ++i)
                        blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_B, &N, h_work, &N, &c_neg_one, h_R, &N);
                    result[0] *= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork)/N;
                }

                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );

                magma_int_t m2 = m1;
                lapackf77_zhegvd(&opts.itype, "N", lapack_uplo_const(opts.uplo), &N,
                              h_R, &N, h_S, &N, w2,
                              h_work, &lwork,
                              #if defined(PRECISION_z) || defined(PRECISION_c)
                              rwork, &lrwork,
                              #endif
                              iwork, &liwork,
                              &info);

                double maxw=0, diff=0;
                for(int j=0; j<m2; j++) {
                    maxw = max(maxw, fabs(w1[j]));
                    maxw = max(maxw, fabs(w2[j]));
                    diff = max(diff, fabs(w1[j] - w2[j]));
                }
                result[1] = diff / (m2*maxw);
            }


            /* =====================================================================
               Print execution time
               =================================================================== */
            printf("%5d %5d   %7.2f\n",
                   (int) N, (int) m1, gpu_time);
            if ( opts.check && opts.jobz != MagmaNoVec ) {
                printf("Testing the eigenvalues and eigenvectors for correctness:\n");
                if (opts.itype==1) {
                    printf("    | A Z - B Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed"));
                }
                else if (opts.itype==2) {
                    printf("    | A B Z - Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed"));
                }
                else if (opts.itype==3) {
                    printf("    | B A Z - Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed"));
                }
                printf(    "    | D(w/ Z) - D(w/o Z) | / |D|  = %8.2e   %s\n\n", result[1], (result[1] < tolulp ? "ok" : "failed"));
                status += ! (result[0] < tol && result[1] < tolulp);
            }

            TESTING_FREE_CPU( h_A   );
            TESTING_FREE_CPU( h_B   );
            TESTING_FREE_CPU( w1    );
            TESTING_FREE_CPU( w2    );
            TESTING_FREE_CPU( iwork );
            
            TESTING_FREE_PIN( h_R );
            TESTING_FREE_PIN( h_S );
            TESTING_FREE_PIN( h_work );
            #if defined(PRECISION_z) || defined(PRECISION_c)
            TESTING_FREE_PIN( rwork );
            #endif
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }

    /* Shutdown */
    TESTING_FINALIZE();
    return status;
}
Ejemplo n.º 15
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing magma_zher2k_mgpu
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
    magmaDoubleComplex alpha = MAGMA_Z_MAKE( 1.2345, 4.321 );
    double beta = 3.14159;
    
    real_Double_t    gflops, gpu_perf, cpu_perf, gpu_time, cpu_time;
    double           error, work[1];
    magmaDoubleComplex *hA, *hR, *hR2, *hV, *hW;
    magmaDoubleComplex_ptr dV[MagmaMaxGPUs], dW[MagmaMaxGPUs], dA[MagmaMaxGPUs];
    magma_int_t n, k, size, lda, ldda, nb, ngpu, nstream;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};

    magma_queue_t streams[MagmaMaxGPUs][20];
    magma_int_t status = 0;
    
    magma_opts opts;
    parse_opts( argc, argv, &opts );

    double tol = opts.tolerance * lapackf77_dlamch("E");
    
    ngpu    = opts.ngpu;
    nb      = (opts.nb      > 0 ? opts.nb      : 64);
    nstream = (opts.nstream > 0 ? opts.nstream :  2);
    
    printf( "version 1: magmablas_zher2k_mgpu2     %s\n", (opts.version==1 ? "(enabled)" : ""));
    printf( "version 2: magmablas_zher2k_mgpu_spec %s\n", (opts.version==2 ? "(enabled)" : ""));
#ifdef ICHI
    printf( "version 3: magma_zher2k_mgpu (Ichi)   %s\n", (opts.version==3 ? "(enabled)" : ""));
#endif
    printf( "\n" );
    
    printf( "nb %d, ngpu %d, nstream %d\n", (int) nb, (int) ngpu, (int) nstream );
    printf("    n     k    nb offset  CPU GFlop/s (sec)   GPU GFlop/s (sec)   |R|/(|V|*|W|+|A|)\n");
    printf("===================================================================================\n");
    for( int itest = 0; itest < opts.ntest; ++itest ) {
        n = opts.nsize[itest];
        k = opts.ksize[itest];
        
        for( int offset = 0; offset < n; offset += min(k,nb) ) {
            for( int iter = 0; iter < opts.niter; ++iter ) {
                lda    = n;
                ldda   = ((n + 31)/32)*32;
                gflops = FLOPS_ZHER2K( k, n-offset ) / 1e9;
                
                TESTING_MALLOC_CPU( hA,  magmaDoubleComplex, lda*n   );
                TESTING_MALLOC_CPU( hR,  magmaDoubleComplex, lda*n   );
                TESTING_MALLOC_CPU( hR2, magmaDoubleComplex, lda*n   );
                TESTING_MALLOC_CPU( hV,  magmaDoubleComplex, lda*k*2 );
                //TESTING_MALLOC_CPU( hW,  magmaDoubleComplex, lda*k   );
                for( int d = 0; d < ngpu; ++d ) {
                    magma_int_t nlocal = ((n / nb) / ngpu + 1) * nb;
                    magma_setdevice( d );
                    TESTING_MALLOC_DEV( dA[d], magmaDoubleComplex, ldda*nlocal );
                    TESTING_MALLOC_DEV( dV[d], magmaDoubleComplex, ldda*k*2    );
                    //TESTING_MALLOC_DEV( dW[d], magmaDoubleComplex, ldda*k      );
                    for( int i = 0; i < nstream; ++i ) {
                        magma_queue_create( &streams[d][i] );
                    }
                }
                
                size = lda*n;
                lapackf77_zlarnv( &ione, ISEED, &size, hA );
                size = lda*k*2;
                lapackf77_zlarnv( &ione, ISEED, &size, hV );
                hW = hV + lda*k;
                //lapackf77_zlarnv( &ione, ISEED, &size, hW );
                
                /* ====================================================================
                   Performs operation using MAGMA
                   =================================================================== */
                magma_zsetmatrix_1D_col_bcyclic( n, n, hA, lda, dA, ldda, ngpu, nb );
                for( int d = 0; d < ngpu; ++d ) {
                    magma_setdevice( d );
                    dW[d] = dV[d] + ldda*k;
                    magma_zsetmatrix( n, k, hV, lda, dV[d], ldda );
                    magma_zsetmatrix( n, k, hW, lda, dW[d], ldda );
                }
                
                gpu_time = magma_sync_wtime(0);
                
                if ( opts.version == 1 ) {
                    magmablas_zher2k_mgpu2(
                        MagmaLower, MagmaNoTrans, n-offset, k,
                        alpha, dV, ldda, 0,
                               dW, ldda, 0,
                        beta,  dA, ldda, offset,
                        ngpu, nb, streams, nstream );
                }
                else if ( opts.version == 2 ) {
                    magmablas_zher2k_mgpu_spec(
                        MagmaLower, MagmaNoTrans, n-offset, k,
                        alpha, dV, ldda, 0,
                               dW, ldda, 0,
                        beta,  dA, ldda, offset,
                        ngpu, nb, streams, nstream );
                }
                else {
#ifdef ICHI
                    magma_zher2k_mgpu(
                        ngpu, MagmaLower, MagmaNoTrans, nb, n-offset, k,
                        alpha, dV, ldda,
                               //dW, ldda,
                        beta,  dA, ldda, offset,
                        nstream, streams );
#endif
                }
                
                gpu_time = magma_sync_wtime(0) - gpu_time;
                gpu_perf = gflops / gpu_time;
                
                // Get dA back to the CPU to compare with the CPU result.
                magma_zgetmatrix_1D_col_bcyclic( n, n, dA, ldda, hR, lda, ngpu, nb );
                
                /* =====================================================================
                   Performs operation using LAPACK
                   =================================================================== */
                if ( opts.lapack || opts.check ) {
                    // store ||V||*||W|| + ||A||
                    magma_int_t n_offset = n - offset;
                    error  = lapackf77_zlange("f", &n_offset, &k, hV, &lda, work );
                    error *= lapackf77_zlange("f", &n_offset, &k, hW, &lda, work );
                    error += lapackf77_zlange("f", &n_offset, &n_offset, &hA[offset + offset*lda], &lda, work );
                    
                    cpu_time = magma_wtime();
                    blasf77_zher2k( "Lower", "NoTrans", &n_offset, &k,
                                    &alpha, hV, &lda,
                                            hW, &lda,
                                    &beta,  &hA[offset + offset*lda], &lda );
                    cpu_time = magma_wtime() - cpu_time;
                    cpu_perf = gflops / cpu_time;
                    
                    // compute relative error ||R||/||A||, where R := A_magma - A_lapack = R - A
                    size = lda*n;
                    blasf77_zaxpy( &size, &c_neg_one, hA, &ione, hR, &ione );
                    error = lapackf77_zlanhe("fro", "Lower", &n_offset, &hR[offset + offset*lda], &lda, work) / error;
                    
                    printf( "%5d %5d %5d %5d   %7.1f (%7.4f)   %7.1f (%7.4f)   %8.2e   %s\n",
                            (int) n, (int) k, (int) nb, (int) offset,
                            cpu_perf, cpu_time, gpu_perf, gpu_time,
                            error, (error < tol ? "ok" : "failed"));
                            //, gpu_perf2, gpu_time2, error, error2 );
                    status += ! (error < tol);
                }
                else {
                    printf( "%5d %5d %5d %5d     ---   (  ---  )   %7.1f (%7.4f)     ---\n",
                            (int) n, (int) k, (int) nb, (int) offset,
                            gpu_perf, gpu_time );
                }
                
                TESTING_FREE_CPU( hA  );
                TESTING_FREE_CPU( hR  );
                TESTING_FREE_CPU( hR2 );
                TESTING_FREE_CPU( hV  );
                //TESTING_FREE_CPU( hW );
                for( int d = 0; d < ngpu; ++d ) {
                    magma_setdevice( d );
                    TESTING_FREE_DEV( dA[d] );
                    TESTING_FREE_DEV( dV[d] );
                    //TESTING_FREE_DEV( dW[d] );
                    for( int i = 0; i < nstream; ++i ) {
                        magma_queue_destroy( streams[d][i] );
                    }
                }
                fflush( stdout );
            }
            if ( opts.niter > 1 ) {
                printf( "\n" );
            }
        } // offset
        printf( "\n" );
    }
    
    TESTING_FINALIZE();
    return status;
}
Ejemplo n.º 16
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing zlanhe
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    real_Double_t   gbytes, gpu_perf, gpu_time, cpu_perf, cpu_time;
    magmaDoubleComplex *h_A;
    double *h_work;
    magmaDoubleComplex_ptr d_A;
    magmaDouble_ptr d_work;
    magma_int_t i, j, N, n2, lda, ldda;
    magma_int_t idist    = 3;  // normal distribution (otherwise max norm is always ~ 1)
    magma_int_t ISEED[4] = {0,0,0,1};
    double      error, norm_magma, norm_lapack;
    magma_int_t status = 0;
    magma_int_t lapack_nan_fail = 0;
    magma_int_t lapack_inf_fail = 0;
    bool mkl_warning = false;

    magma_opts opts;
    opts.parse_opts( argc, argv );
    
    double tol = opts.tolerance * lapackf77_dlamch("E");
    double tol2;
    
    magma_uplo_t uplo[] = { MagmaLower, MagmaUpper };
    magma_norm_t norm[] = { MagmaInfNorm, MagmaOneNorm, MagmaMaxNorm, MagmaFrobeniusNorm };
    
    // Double-Complex inf-norm not supported on Tesla (CUDA arch 1.x)
#if defined(PRECISION_z)
    magma_int_t arch = magma_getdevice_arch();
    if ( arch < 200 ) {
        printf("!!!! NOTE: Double-Complex %s and %s norm are not supported\n"
               "!!!! on CUDA architecture %d; requires arch >= 200.\n"
               "!!!! It should report \"parameter number 1 had an illegal value\" below.\n\n",
               MagmaInfNormStr, MagmaOneNormStr, (int) arch );
        for( int inorm = 0; inorm < 2; ++inorm ) {
        for( int iuplo = 0; iuplo < 2; ++iuplo ) {
            printf( "Testing that magmablas_zlanhe( %s, %s, ... ) returns -1 error...\n",
                    lapack_norm_const( norm[inorm] ),
                    lapack_uplo_const( uplo[iuplo] ));
            norm_magma = magmablas_zlanhe( norm[inorm], uplo[iuplo], 1, NULL, 1, NULL, 1 );
            if ( norm_magma != -1 ) {
                printf( "expected magmablas_zlanhe to return -1 error, but got %f\n", norm_magma );
                status = 1;
            }
        }}
        printf( "...return values %s\n\n", (status == 0 ? "ok" : "failed") );
    }
#endif

    #ifdef MAGMA_WITH_MKL
    // MKL 11.1 has bug in multi-threaded zlanhe; use single thread to work around.
    // MKL 11.2 corrects it for inf, one, max norm.
    // MKL 11.2 still segfaults for Frobenius norm, which is not tested here
    // because MAGMA doesn't implement Frobenius norm yet.
    MKLVersion mkl_version;
    mkl_get_version( &mkl_version );
    magma_int_t la_threads = magma_get_lapack_numthreads();
    bool mkl_single_thread = (mkl_version.MajorVersion <= 11 && mkl_version.MinorVersion < 2);
    if ( mkl_single_thread ) {
        printf( "\nNote: using single thread to work around MKL zlanhe bug.\n\n" );
    }
    #endif
    
    printf("%%   N   norm   uplo   CPU GByte/s (ms)    GPU GByte/s (ms)        error               nan      inf\n");
    printf("%%=================================================================================================\n");
    for( int itest = 0; itest < opts.ntest; ++itest ) {
      for( int inorm = 0; inorm < 3; ++inorm ) {  /* < 4 for Frobenius */
      for( int iuplo = 0; iuplo < 2; ++iuplo ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            N   = opts.nsize[itest];
            lda = N;
            n2  = lda*N;
            ldda = magma_roundup( N, opts.align );
            // read upper or lower triangle
            gbytes = 0.5*(N+1)*N*sizeof(magmaDoubleComplex) / 1e9;
            
            TESTING_MALLOC_CPU( h_A,    magmaDoubleComplex, n2 );
            TESTING_MALLOC_CPU( h_work, double, N );
            
            TESTING_MALLOC_DEV( d_A,    magmaDoubleComplex, ldda*N );
            TESTING_MALLOC_DEV( d_work, double, N );
            
            /* Initialize the matrix */
            lapackf77_zlarnv( &idist, ISEED, &n2, h_A );
            
            magma_zsetmatrix( N, N, h_A, lda, d_A, ldda );
            
            /* ====================================================================
               Performs operation using MAGMA
               =================================================================== */
            gpu_time = magma_wtime();
            norm_magma = magmablas_zlanhe( norm[inorm], uplo[iuplo], N, d_A, ldda, d_work, N );
            gpu_time = magma_wtime() - gpu_time;
            gpu_perf = gbytes / gpu_time;
            if (norm_magma == -1) {
                printf( "%5d   %4c   skipped because %s norm isn't supported\n",
                        (int) N, lapacke_norm_const( norm[inorm] ), lapack_norm_const( norm[inorm] ));
                goto cleanup;
            }
            else if (norm_magma < 0) {
                printf("magmablas_zlanhe returned error %f: %s.\n",
                       norm_magma, magma_strerror( (int) norm_magma ));
            }
            
            /* =====================================================================
               Performs operation using LAPACK
               =================================================================== */
            #ifdef MAGMA_WITH_MKL
            if ( mkl_single_thread ) {
                // work around MKL bug in multi-threaded zlanhe
                magma_set_lapack_numthreads( 1 );
            }
            #endif
            
            cpu_time = magma_wtime();
            norm_lapack = lapackf77_zlanhe(
                lapack_norm_const( norm[inorm] ),
                lapack_uplo_const( uplo[iuplo] ),
                &N, h_A, &lda, h_work );
            cpu_time = magma_wtime() - cpu_time;
            cpu_perf = gbytes / cpu_time;
            if (norm_lapack < 0) {
                printf("lapackf77_zlanhe returned error %f: %s.\n",
                       norm_lapack, magma_strerror( (int) norm_lapack ));
            }
            
            /* =====================================================================
               Check the result compared to LAPACK
               =================================================================== */
            error = fabs( norm_magma - norm_lapack ) / norm_lapack;
            tol2 = tol;
            if ( norm[inorm] == MagmaMaxNorm ) {
                // max-norm depends on only one element, so for Real precisions,
                // MAGMA and LAPACK should exactly agree (tol2 = 0),
                // while Complex precisions incur roundoff in cuCabs.
                #ifdef REAL
                tol2 = 0;
                #endif
            }
            
            bool okay; okay = (error <= tol2);
            status += ! okay;
            mkl_warning |= ! okay;
            
            /* ====================================================================
               Check for NAN and INF propagation
               =================================================================== */
            #define h_A(i_, j_) (h_A + (i_) + (j_)*lda)
            #define d_A(i_, j_) (d_A + (i_) + (j_)*ldda)
            
            i = rand() % N;
            j = rand() % N;
            magma_int_t tmp;
            if ( uplo[iuplo] == MagmaLower && i < j ) {
                tmp = i;
                i = j;
                j = tmp;
            }
            else if ( uplo[iuplo] == MagmaUpper && i > j ) {
                tmp = i;
                i = j;
                j = tmp;
            }
            
            *h_A(i,j) = MAGMA_Z_NAN;
            magma_zsetvector( 1, h_A(i,j), 1, d_A(i,j), 1 );
            norm_magma  = magmablas_zlanhe( norm[inorm], uplo[iuplo], N, d_A, ldda, d_work, N );
            norm_lapack = lapackf77_zlanhe( lapack_norm_const( norm[inorm] ),
                                            lapack_uplo_const( uplo[iuplo] ),
                                            &N, h_A, &lda, h_work );
            bool nan_okay;    nan_okay    = isnan(norm_magma);
            bool la_nan_okay; la_nan_okay = isnan(norm_lapack);
            lapack_nan_fail += ! la_nan_okay;
            status          += !    nan_okay;
            
            *h_A(i,j) = MAGMA_Z_INF;
            magma_zsetvector( 1, h_A(i,j), 1, d_A(i,j), 1 );
            norm_magma  = magmablas_zlanhe( norm[inorm], uplo[iuplo], N, d_A, ldda, d_work, N );
            norm_lapack = lapackf77_zlanhe( lapack_norm_const( norm[inorm] ),
                                            lapack_uplo_const( uplo[iuplo] ),
                                            &N, h_A, &lda, h_work );
            bool inf_okay;    inf_okay    = isinf(norm_magma);
            bool la_inf_okay; la_inf_okay = isinf(norm_lapack);
            lapack_inf_fail += ! la_inf_okay;
            status          += !    inf_okay;
            
            #ifdef MAGMA_WITH_MKL
            if ( mkl_single_thread ) {
                // end single thread to work around MKL bug
                magma_set_lapack_numthreads( la_threads );
            }
            #endif
            
            printf("%5d   %4c   %4c   %7.2f (%7.2f)   %7.2f (%7.2f)   %#9.3g   %-6s   %6s%1s  %6s%1s\n",
                   (int) N,
                   lapacke_norm_const( norm[inorm] ),
                   lapacke_uplo_const( uplo[iuplo] ),
                   cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
                   error,
                   (okay     ? "ok" : "failed"),
                   (nan_okay ? "ok" : "failed"), (la_nan_okay ? " " : "*"),
                   (inf_okay ? "ok" : "failed"), (la_inf_okay ? " " : "*"));
            
        cleanup:
            TESTING_FREE_CPU( h_A    );
            TESTING_FREE_CPU( h_work );
            
            TESTING_FREE_DEV( d_A    );
            TESTING_FREE_DEV( d_work );
            fflush( stdout );
        } // end iter
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
      }} // end iuplo, inorm
      printf( "\n" );
    }
    
    // don't print "failed" here because then run_tests.py thinks MAGMA failed
    if ( lapack_nan_fail ) {
        printf( "* Warning: LAPACK did not pass NAN propagation test; upgrade to LAPACK version >= 3.4.2 (Sep. 2012)\n" );
    }
    if ( lapack_inf_fail ) {
        printf( "* Warning: LAPACK did not pass INF propagation test\n" );
    }
    if ( mkl_warning ) {
        printf("* MKL (e.g., 11.1) has a bug in zlanhe with multiple threads;\n"
               "  corrected in 11.2 for one, inf, max norms, but still in Frobenius norm.\n"
               "  Try again with MKL_NUM_THREADS=1.\n" );
    }
    
    opts.cleanup();
    TESTING_FINALIZE();
    return status;
}
Ejemplo n.º 17
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing zhegvdx
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    real_Double_t   gpu_time /*cpu_time*/;
    magmaDoubleComplex *h_A, *h_R, *h_B, *h_S, *h_work;
    double *w1, *w2, vl=0, vu=0;
    double result[2] = {0};
    magma_int_t *iwork;
    magma_int_t N, n2, info, il, iu, m1, m2, nb, lwork, liwork;
    magmaDoubleComplex c_zero    = MAGMA_Z_ZERO;
    magmaDoubleComplex c_one     = MAGMA_Z_ONE;
    magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
    #if defined(PRECISION_z) || defined(PRECISION_c)
    double *rwork;
    magma_int_t lrwork;
    #endif
    //double d_one         =  1.;
    //double d_ten         = 10.;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    magma_int_t status = 0;

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

    double tol    = opts.tolerance * lapackf77_dlamch("E");
    double tolulp = opts.tolerance * lapackf77_dlamch("P");
    
    if ( opts.check && opts.jobz == MagmaNoVec ) {
        fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
        opts.jobz = MagmaVec;
    }
    
    printf("using: itype = %d, jobz = %s, uplo = %s, check = %d, fraction = %6.4f\n",
           (int) opts.itype, lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
           (int) opts.check, opts.fraction);

    printf("    N     M   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;
            nb     = magma_get_zhetrd_nb(N);
            #if defined(PRECISION_z) || defined(PRECISION_c)
            lwork  = 2*N*nb + N*N;
            lrwork = 1 + 5*N +2*N*N;
            #else
            lwork  = 1 + 6*N*nb + 2* N*N;
            #endif
            liwork = 3 + 5*N;

            if ( opts.fraction == 0 ) {
                il = N / 10;
                iu = N / 5+il;
            }
            else {
                il = 1;
                iu = (int) (opts.fraction*N);
                if (iu < 1) iu = 1;
            }

            TESTING_MALLOC_CPU( h_A,    magmaDoubleComplex, n2     );
            TESTING_MALLOC_CPU( h_B,    magmaDoubleComplex, n2     );
            TESTING_MALLOC_CPU( w1,     double,             N      );
            TESTING_MALLOC_CPU( w2,     double,             N      );
            TESTING_MALLOC_CPU( iwork,  magma_int_t,        liwork );
            
            TESTING_MALLOC_PIN( h_R,    magmaDoubleComplex, n2     );
            TESTING_MALLOC_PIN( h_S,    magmaDoubleComplex, n2     );
            TESTING_MALLOC_PIN( h_work, magmaDoubleComplex, lwork  );
            #if defined(PRECISION_z) || defined(PRECISION_c)
            TESTING_MALLOC_PIN( rwork, double, lrwork);
            #endif
            
            /* Initialize the matrix */
            lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
            lapackf77_zlarnv( &ione, ISEED, &n2, h_B );
            magma_zmake_hpd( N, h_B, N );
            magma_zmake_hermitian( N, h_A, N );

            // ==================================================================
            // Warmup using MAGMA
            // ==================================================================
            if(opts.warmup){
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
                
                magma_zhegvdx( opts.itype, opts.jobz, MagmaRangeI, opts.uplo,
                               N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
                               h_work, lwork,
                               #if defined(PRECISION_z) || defined(PRECISION_c)
                               rwork, lrwork,
                               #endif      
                               iwork, liwork,
                               &info );
                if (info != 0)
                    printf("magma_zhegvdx returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
            }
            /* ====================================================================
               Performs operation using MAGMA
               =================================================================== */
            lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
            lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );

            gpu_time = magma_wtime();
            magma_zhegvdx( opts.itype, opts.jobz, MagmaRangeI, opts.uplo,
                           N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
                           h_work, lwork,
                           #if defined(PRECISION_z) || defined(PRECISION_c)
                           rwork, lrwork,
                           #endif
                           iwork, liwork,
                           &info );
            gpu_time = magma_wtime() - gpu_time;
            if (info != 0)
                printf("magma_zhegvdx returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            
            if ( opts.check ) {
                /* =====================================================================
                   Check the results following the LAPACK's [zc]hegvdx routine.
                   A x = lambda B x is solved
                   and the following 3 tests computed:
                   (1)    | A Z - B Z D | / ( |A||Z| N )  (itype = 1)
                          | A B Z - Z D | / ( |A||Z| N )  (itype = 2)
                          | B A Z - Z D | / ( |A||Z| N )  (itype = 3)
                   (2)    | S(with V) - S(w/o V) | / | S |
                   =================================================================== */
                #if defined(PRECISION_d) || defined(PRECISION_s)
                double *rwork = h_work + N*N;
                #endif
                double temp1, temp2;
                
                result[0] = 1.;
                result[0] /= lapackf77_zlanhe("1", lapack_uplo_const(opts.uplo), &N, h_A, &N, rwork);
                result[0] /= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork);
                
                if (opts.itype == 1) {
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
                    for(int i=0; i < m1; ++i)
                        blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_neg_one, h_B, &N, h_R, &N, &c_one, h_work, &N);
                    result[0] *= lapackf77_zlange("1", &N, &m1, h_work, &N, rwork)/N;
                }
                else if (opts.itype == 2) {
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_B, &N, h_R, &N, &c_zero, h_work, &N);
                    for(int i=0; i < m1; ++i)
                        blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_work, &N, &c_neg_one, h_R, &N);
                    result[0] *= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork)/N;
                }
                else if (opts.itype == 3) {
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
                    for(int i=0; i < m1; ++i)
                        blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
                    blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_B, &N, h_work, &N, &c_neg_one, h_R, &N);
                    result[0] *= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork)/N;
                }
                
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
                lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
                
                magma_zhegvdx( opts.itype, MagmaNoVec, MagmaRangeI, opts.uplo,
                               N, h_R, N, h_S, N, vl, vu, il, iu, &m2, w2,
                               h_work, lwork,
                               #if defined(PRECISION_z) || defined(PRECISION_c)
                               rwork, lrwork,
                               #endif
                               iwork, liwork,
                               &info );
                if (info != 0)
                    printf("magma_zhegvdx returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
                
                temp1 = temp2 = 0;
                for(int j=0; j < m2; j++) {
                    temp1 = max(temp1, absv(w1[j]));
                    temp1 = max(temp1, absv(w2[j]));
                    temp2 = max(temp2, absv(w1[j]-w2[j]));
                }
                result[1] = temp2 / (((double)m2)*temp1);
            }
            
            /* =====================================================================
               Print execution time
               =================================================================== */
            printf("%5d %5d   %7.2f\n",
                   (int) N, (int) m1, gpu_time);
            if ( opts.check ) {
                printf("Testing the eigenvalues and eigenvectors for correctness:\n");
                if (opts.itype == 1) {
                    printf("(1)    | A Z - B Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed"));
                }
                else if (opts.itype == 2) {
                    printf("(1)    | A B Z - Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed"));
                }
                else if (opts.itype == 3) {
                    printf("(1)    | B A Z - Z D | / (|A| |Z| N) = %8.2e   %s\n",   result[0], (result[0] < tol    ? "ok" : "failed"));
                }
                printf(    "(2)    | D(w/ Z) - D(w/o Z) | / |D|  = %8.2e   %s\n\n", result[1], (result[1] < tolulp ? "ok" : "failed"));
                status += ! (result[0] < tol && result[1] < tolulp);
            }
            
            TESTING_FREE_CPU( h_A );
            TESTING_FREE_CPU( h_B );
            TESTING_FREE_CPU( w1  );
            TESTING_FREE_CPU( w2  );
            TESTING_FREE_CPU( iwork );
            
            TESTING_FREE_PIN( h_R    );
            TESTING_FREE_PIN( h_S    );
            TESTING_FREE_PIN( h_work );
            #if defined(PRECISION_z) || defined(PRECISION_c)
            TESTING_FREE_PIN( rwork );
            #endif
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }

    TESTING_FINALIZE();
    return status;
}