Beispiel #1
0
extern "C" magma_int_t
magma_chegvdx_m(magma_int_t nrgpu, magma_int_t itype, char jobz, char range, char uplo, magma_int_t n,
                magmaFloatComplex *a, magma_int_t lda, magmaFloatComplex *b, magma_int_t ldb,
                float vl, float vu, magma_int_t il, magma_int_t iu,
                magma_int_t *m, float *w, magmaFloatComplex *work, magma_int_t lwork,
                float *rwork, magma_int_t lrwork,
                magma_int_t *iwork, magma_int_t liwork, magma_int_t *info)
{
/*  -- MAGMA (version 1.4.0) --
       Univ. of Tennessee, Knoxville
       Univ. of California, Berkeley
       Univ. of Colorado, Denver
       August 2013

    Purpose
    =======
    CHEGVD computes all the eigenvalues, and optionally, the eigenvectors
    of a complex generalized Hermitian-definite eigenproblem, of the form
    A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and
    B are assumed to be Hermitian and B is also positive definite.
    If eigenvectors are desired, it uses a divide and conquer algorithm.

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

    Arguments
    =========
    ITYPE   (input) INTEGER
            Specifies the problem type to be solved:
            = 1:  A*x = (lambda)*B*x
            = 2:  A*B*x = (lambda)*x
            = 3:  B*A*x = (lambda)*x

    RANGE   (input) CHARACTER*1
            = 'A': all eigenvalues will be found.
            = 'V': all eigenvalues in the half-open interval (VL,VU]
                   will be found.
            = 'I': the IL-th through IU-th eigenvalues will be found.

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

    UPLO    (input) CHARACTER*1
            = 'U':  Upper triangles of A and B are stored;
            = 'L':  Lower triangles of A and B are stored.

    N       (input) INTEGER
            The order of the matrices A and B.  N >= 0.

    A       (input/output) COMPLEX*16 array, dimension (LDA, N)
            On entry, the Hermitian matrix A.  If UPLO = 'U', the
            leading N-by-N upper triangular part of A contains the
            upper triangular part of the matrix A.  If UPLO = 'L',
            the leading N-by-N lower triangular part of A contains
            the lower triangular part of the matrix A.

            On exit, if JOBZ = 'V', then if INFO = 0, A contains the
            matrix Z of eigenvectors.  The eigenvectors are normalized
            as follows:
            if ITYPE = 1 or 2, Z**H*B*Z = I;
            if ITYPE = 3, Z**H*inv(B)*Z = I.
            If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
            or the lower triangle (if UPLO='L') of A, including the
            diagonal, is destroyed.

    LDA     (input) INTEGER
            The leading dimension of the array A.  LDA >= max(1,N).

    B       (input/output) COMPLEX*16 array, dimension (LDB, N)
            On entry, the Hermitian matrix B.  If UPLO = 'U', the
            leading N-by-N upper triangular part of B contains the
            upper triangular part of the matrix B.  If UPLO = 'L',
            the leading N-by-N lower triangular part of B contains
            the lower triangular part of the matrix B.

            On exit, if INFO <= N, the part of B containing the matrix is
            overwritten by the triangular factor U or L from the Cholesky
            factorization B = U**H*U or B = L*L**H.

    LDB     (input) INTEGER
            The leading dimension of the array B.  LDB >= max(1,N).

    VL      (input) DOUBLE PRECISION
    VU      (input) DOUBLE PRECISION
            If RANGE='V', the lower and upper bounds of the interval to
            be searched for eigenvalues. VL < VU.
            Not referenced if RANGE = 'A' or 'I'.

    IL      (input) INTEGER
    IU      (input) INTEGER
            If RANGE='I', the indices (in ascending order) of the
            smallest and largest eigenvalues to be returned.
            1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
            Not referenced if RANGE = 'A' or 'V'.

    M       (output) INTEGER
            The total number of eigenvalues found.  0 <= M <= N.
            If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

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

    WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK   (input) INTEGER
            The length of the array WORK.
            If N <= 1,                LWORK >= 1.
            If JOBZ  = 'N' and N > 1, LWORK >= N + 1.
            If JOBZ  = 'V' and N > 1, LWORK >= 2*N*nb + N**2.

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

    RWORK   (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
            On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

    LRWORK  (input) INTEGER
            The dimension of the array RWORK.
            If N <= 1,                LRWORK >= 1.
            If JOBZ  = 'N' and N > 1, LRWORK >= N.
            If JOBZ  = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.

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

    IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
            On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

    LIWORK  (input) INTEGER
            The dimension of the array IWORK.
            If N <= 1,                LIWORK >= 1.
            If JOBZ  = 'N' and N > 1, LIWORK >= 1.
            If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.

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

    INFO    (output) INTEGER
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            > 0:  CPOTRF or CHEEVD returned an error code:
               <= N:  if INFO = i and JOBZ = 'N', then the algorithm
                      failed to converge; i off-diagonal elements of an
                      intermediate tridiagonal form did not converge to
                      zero;
                      if INFO = i and JOBZ = 'V', then the algorithm
                      failed to compute an eigenvalue while working on
                      the submatrix lying in rows and columns INFO/(N+1)
                      through mod(INFO,N+1);
               > N:   if INFO = N + i, for 1 <= i <= N, then the leading
                      minor of order i of B is not positive definite.
                      The factorization of B could not be completed and
                      no eigenvalues or eigenvectors were computed.

    Further Details
    ===============
    Based on contributions by
       Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

    Modified so that no backsubstitution is performed if CHEEVD fails to
    converge (NEIG in old code could be greater than N causing out of
    bounds reference to A - reported by Ralf Meyer).  Also corrected the
    description of INFO and the test on ITYPE. Sven, 16 Feb 05.
    =====================================================================  */

    char uplo_[2] = {uplo, 0};
    char jobz_[2] = {jobz, 0};
    char range_[2] = {range, 0};
    
    magmaFloatComplex c_one = MAGMA_C_ONE;
    
    magma_int_t lower;
    char trans[1];
    magma_int_t wantz;
    magma_int_t lquery;
    magma_int_t alleig, valeig, indeig;
    
    magma_int_t lwmin;
    magma_int_t liwmin;
    magma_int_t lrwmin;
    
    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 (itype < 1 || itype > 3) {
        *info = -1;
    } else if (! (alleig || valeig || indeig)) {
        *info = -2;
    } else if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) {
        *info = -3;
    } else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
        *info = -4;
    } else if (n < 0) {
        *info = -5;
    } else if (lda < max(1,n)) {
        *info = -7;
    } else if (ldb < max(1,n)) {
        *info = -9;
    } else {
        if (valeig) {
            if (n > 0 && vu <= vl) {
                *info = -11;
            }
        } else if (indeig) {
            if (il < 1 || il > max(1,n)) {
                *info = -12;
            } else if (iu < min(n,il) || iu > n) {
                *info = -13;
            }
        }
    }
    
    magma_int_t nb = magma_get_chetrd_nb( n );
    if ( n <= 1 ) {
        lwmin  = 1;
        lrwmin = 1;
        liwmin = 1;
    }
    else if ( wantz ) {
        lwmin  = 2*n + n*n;
        lrwmin = 1 + 5*n + 2*n*n;
        liwmin = 3 + 5*n;
    }
    else {
        lwmin  = n + n*nb;
        lrwmin = n;
        liwmin = 1;
    }
    
    work[0]  = MAGMA_C_MAKE( lwmin * (1. + lapackf77_slamch("Epsilon")), 0.);  // round up
    rwork[0] = lrwmin * (1. + lapackf77_slamch("Epsilon"));
    iwork[0] = liwmin;
    
    if (lwork < lwmin && ! lquery) {
        *info = -17;
    } else if (lrwork < lrwmin && ! lquery) {
        *info = -19;
    } else if (liwork < liwmin && ! lquery) {
        *info = -21;
    }
    
    if (*info != 0) {
        magma_xerbla( __func__, -(*info));
        return *info;
    }
    else if (lquery) {
        return *info;
    }
    
    /*  Quick return if possible */
    if (n == 0) {
        return *info;
    }

    /* 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_chegvd(&itype, jobz_, uplo_,
                         &n, a, &lda, b, &ldb,
                         w, work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
                         rwork, &lrwork, 
#endif  
                         iwork, &liwork, info);
        *m = n;
        return *info;
    }

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

    magma_cpotrf_m(nrgpu, uplo_[0], n, b, ldb, info);
    if (*info != 0) {
        *info = n + *info;
        return *info;
    }

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

    /*  Transform problem to standard eigenvalue problem and solve. */
    magma_chegst_m(nrgpu, itype, uplo_[0], n, a, lda, b, ldb, info);

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

    magma_cheevdx_m(nrgpu, jobz, range, uplo, n, a, lda, vl, vu, il, iu, m, w, work, lwork, rwork, lrwork, iwork, liwork, info);

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

    if (wantz && *info == 0)
    {

#ifdef ENABLE_TIMER
        start = get_current_time();
#endif

        /* Backtransform eigenvectors to the original problem. */
        if (itype == 1 || itype == 2)
        {
            /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
             backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
            if (lower) {
                *(unsigned char *)trans = MagmaConjTrans;
            } else {
                *(unsigned char *)trans = MagmaNoTrans;
            }

            magma_ctrsm_m(nrgpu, MagmaLeft, uplo_[0], *trans, MagmaNonUnit,
                          n, *m, c_one, b, ldb, a, lda);

        }
        else if (itype == 3)
        {
            /*  For B*A*x=(lambda)*x;
             backtransform eigenvectors: x = L*y or U'*y */
            if (lower) {
                *(unsigned char *)trans = MagmaNoTrans;
            } else {
                *(unsigned char *)trans = MagmaConjTrans;
            }

            //magma_ctrmm(MagmaLeft, uplo_[0], *trans, MagmaNonUnit,
            //            n, n, c_one, db, lddb, da, ldda);
        }

#ifdef ENABLE_TIMER
        end = get_current_time();
        printf("time setmatrices trsm/mm + getmatrices = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
    }

    work[0]  = MAGMA_C_MAKE( lwmin * (1. + lapackf77_slamch("Epsilon")), 0.);  // round up
    rwork[0] = lrwmin * (1. + lapackf77_slamch("Epsilon"));
    iwork[0] = liwmin;


    return *info;
} /* magma_chegvd_m */
Beispiel #2
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing ctrsm
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    real_Double_t   gflops, magma_perf=0, magma_time=0, cublas_perf, cublas_time, cpu_perf=0, cpu_time=0;
    float          magma_error=0, cublas_error, lapack_error, work[1];
    magma_int_t M, N, info;
    magma_int_t Ak;
    magma_int_t sizeA, sizeB;
    magma_int_t lda, ldb, ldda, lddb;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    magma_int_t *ipiv;
    
    magmaFloatComplex *h_A, *h_B, *h_Bcublas, *h_Bmagma, *h_Blapack, *h_X;
    magmaFloatComplex_ptr d_A, d_B;
    magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
    magmaFloatComplex c_one = MAGMA_C_ONE;
    magmaFloatComplex alpha = MAGMA_C_MAKE(  0.29, -0.86 );
    magma_int_t status = 0;
    
    magma_opts opts;
    opts.parse_opts( argc, argv );
    
    float tol = opts.tolerance * lapackf77_slamch("E");

    // pass ngpu = -1 to test multi-GPU code using 1 gpu
    magma_int_t abs_ngpu = abs( opts.ngpu );
    
    printf("%% side = %s, uplo = %s, transA = %s, diag = %s, ngpu = %d\n",
           lapack_side_const(opts.side), lapack_uplo_const(opts.uplo),
           lapack_trans_const(opts.transA), lapack_diag_const(opts.diag), int(abs_ngpu) );
    
    printf("%%   M     N  MAGMA Gflop/s (ms)  CUBLAS Gflop/s (ms)   CPU Gflop/s (ms)      MAGMA     CUBLAS   LAPACK error\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];
            gflops = FLOPS_CTRSM(opts.side, M, N) / 1e9;

            if ( opts.side == MagmaLeft ) {
                lda = M;
                Ak  = M;
            } else {
                lda = N;
                Ak  = N;
            }
            
            ldb = M;
            
            ldda = magma_roundup( lda, opts.align );  // multiple of 32 by default
            lddb = magma_roundup( ldb, opts.align );  // multiple of 32 by default
            
            sizeA = lda*Ak;
            sizeB = ldb*N;
            
            TESTING_MALLOC_CPU( h_A,       magmaFloatComplex, lda*Ak  );
            TESTING_MALLOC_CPU( h_B,       magmaFloatComplex, ldb*N   );
            TESTING_MALLOC_CPU( h_X,       magmaFloatComplex, ldb*N   );
            TESTING_MALLOC_CPU( h_Blapack, magmaFloatComplex, ldb*N   );
            TESTING_MALLOC_CPU( h_Bcublas, magmaFloatComplex, ldb*N   );
            TESTING_MALLOC_CPU( h_Bmagma,  magmaFloatComplex, ldb*N   );
            TESTING_MALLOC_CPU( ipiv,      magma_int_t,        Ak      );
            
            TESTING_MALLOC_DEV( d_A,       magmaFloatComplex, ldda*Ak );
            TESTING_MALLOC_DEV( d_B,       magmaFloatComplex, lddb*N  );
            
            /* Initialize the matrices */
            /* Factor A into LU to get well-conditioned triangular matrix.
             * Copy L to U, since L seems okay when used with non-unit diagonal
             * (i.e., from U), while U fails when used with unit diagonal. */
            lapackf77_clarnv( &ione, ISEED, &sizeA, h_A );
            lapackf77_cgetrf( &Ak, &Ak, h_A, &lda, ipiv, &info );
            for( int j = 0; j < Ak; ++j ) {
                for( int i = 0; i < j; ++i ) {
                    *h_A(i,j) = *h_A(j,i);
                }
            }
            
            lapackf77_clarnv( &ione, ISEED, &sizeB, h_B );
            memcpy( h_Blapack, h_B, sizeB*sizeof(magmaFloatComplex) );
            magma_csetmatrix( Ak, Ak, h_A, lda, d_A, ldda, opts.queue );
            
            /* =====================================================================
               Performs operation using MAGMABLAS
               =================================================================== */
            #if defined(HAVE_CUBLAS)
                magma_csetmatrix( M, N, h_B, ldb, d_B, lddb, opts.queue );
                
                magma_time = magma_sync_wtime( opts.queue );
                if (opts.ngpu == 1) {
                    magmablas_ctrsm( opts.side, opts.uplo, opts.transA, opts.diag,
                                     M, N,
                                     alpha, d_A, ldda,
                                            d_B, lddb, opts.queue );
                }
                else {
                    magma_ctrsm_m( abs_ngpu, opts.side, opts.uplo, opts.transA, opts.diag,
                                   M, N,
                                   alpha, d_A, ldda,
                                          d_B, lddb );
                }
                magma_time = magma_sync_wtime( opts.queue ) - magma_time;
                magma_perf = gflops / magma_time;
                
                magma_cgetmatrix( M, N, d_B, lddb, h_Bmagma, ldb, opts.queue );
            #endif
            
            /* =====================================================================
               Performs operation using CUBLAS
               =================================================================== */
            magma_csetmatrix( M, N, h_B, ldb, d_B, lddb, opts.queue );
            
            cublas_time = magma_sync_wtime( opts.queue );
            #if defined(HAVE_CUBLAS)
                // opts.handle also uses opts.queue 
                cublasCtrsm( opts.handle,
                             cublas_side_const(opts.side), cublas_uplo_const(opts.uplo),
                             cublas_trans_const(opts.transA), cublas_diag_const(opts.diag),
                             M, N,
                             &alpha, d_A, ldda,
                                     d_B, lddb );
            #elif defined(HAVE_clBLAS)
                clblasCtrsm( clblasColumnMajor,
                             clblas_side_const(opts.side), clblas_uplo_const(opts.uplo),
                             clblas_trans_const(opts.transA), clblas_diag_const(opts.diag),
                             M, N,
                             alpha, d_A, 0, ldda,
                                    d_B, 0, lddb,
                             1, &opts.queue, 0, NULL, NULL );
            #endif
            cublas_time = magma_sync_wtime( opts.queue ) - cublas_time;
            cublas_perf = gflops / cublas_time;
            
            magma_cgetmatrix( M, N, d_B, lddb, h_Bcublas, ldb, opts.queue );
            
            /* =====================================================================
               Performs operation using CPU BLAS
               =================================================================== */
            if ( opts.lapack ) {
                cpu_time = magma_wtime();
                blasf77_ctrsm( lapack_side_const(opts.side), lapack_uplo_const(opts.uplo),
                               lapack_trans_const(opts.transA), lapack_diag_const(opts.diag),
                               &M, &N,
                               &alpha, h_A, &lda,
                                       h_Blapack, &ldb );
                cpu_time = magma_wtime() - cpu_time;
                cpu_perf = gflops / cpu_time;
            }
            
            /* =====================================================================
               Check the result
               =================================================================== */
            // ||b - 1/alpha*A*x|| / (||A||*||x||)
            magmaFloatComplex inv_alpha = MAGMA_C_DIV( c_one, alpha );
            float normR, normX, normA;
            normA = lapackf77_clange( "M", &Ak, &Ak, h_A, &lda, work );
            
            #if defined(HAVE_CUBLAS)
                // check magma
                memcpy( h_X, h_Bmagma, sizeB*sizeof(magmaFloatComplex) );
                blasf77_ctrmm( lapack_side_const(opts.side), lapack_uplo_const(opts.uplo),
                               lapack_trans_const(opts.transA), lapack_diag_const(opts.diag),
                               &M, &N,
                               &inv_alpha, h_A, &lda,
                                           h_X, &ldb );
                
                blasf77_caxpy( &sizeB, &c_neg_one, h_B, &ione, h_X, &ione );
                normR = lapackf77_clange( "M", &M, &N, h_X,      &ldb, work );
                normX = lapackf77_clange( "M", &M, &N, h_Bmagma, &ldb, work );
                magma_error = normR/(normX*normA);
            #endif

            // check cublas
            memcpy( h_X, h_Bcublas, sizeB*sizeof(magmaFloatComplex) );
            blasf77_ctrmm( lapack_side_const(opts.side), lapack_uplo_const(opts.uplo),
                           lapack_trans_const(opts.transA), lapack_diag_const(opts.diag),
                           &M, &N,
                           &inv_alpha, h_A, &lda,
                                       h_X, &ldb );

            blasf77_caxpy( &sizeB, &c_neg_one, h_B, &ione, h_X, &ione );
            normR = lapackf77_clange( "M", &M, &N, h_X,       &ldb, work );
            normX = lapackf77_clange( "M", &M, &N, h_Bcublas, &ldb, work );
            cublas_error = normR/(normX*normA);

            if ( opts.lapack ) {
                // check lapack
                // this verifies that the matrix wasn't so bad that it couldn't be solved accurately.
                memcpy( h_X, h_Blapack, sizeB*sizeof(magmaFloatComplex) );
                blasf77_ctrmm( lapack_side_const(opts.side), lapack_uplo_const(opts.uplo),
                               lapack_trans_const(opts.transA), lapack_diag_const(opts.diag),
                               &M, &N,
                               &inv_alpha, h_A, &lda,
                                           h_X, &ldb );
    
                blasf77_caxpy( &sizeB, &c_neg_one, h_B, &ione, h_X, &ione );
                normR = lapackf77_clange( "M", &M, &N, h_X,       &ldb, work );
                normX = lapackf77_clange( "M", &M, &N, h_Blapack, &ldb, work );
                lapack_error = normR/(normX*normA);
                
                printf("%5d %5d   %7.2f (%7.2f)   %7.2f (%7.2f)   %7.2f (%7.2f)   %8.2e   %8.2e   %8.2e   %s\n",
                        (int) M, (int) N,
                        magma_perf,  1000.*magma_time,
                        cublas_perf, 1000.*cublas_time,
                        cpu_perf,    1000.*cpu_time,
                        magma_error, cublas_error, lapack_error,
                        (magma_error < tol && cublas_error < tol? "ok" : "failed"));
                status += ! (magma_error < tol && cublas_error < tol);
            }
            else {
                printf("%5d %5d   %7.2f (%7.2f)   %7.2f (%7.2f)     ---   (  ---  )   %8.2e   %8.2e     ---      %s\n",
                        (int) M, (int) N,
                        magma_perf,  1000.*magma_time,
                        cublas_perf, 1000.*cublas_time,
                        magma_error, cublas_error,
                        (magma_error < tol && cublas_error < tol ? "ok" : "failed"));
                status += ! (magma_error < tol && cublas_error < tol);
            }
            
            TESTING_FREE_CPU( h_A );
            TESTING_FREE_CPU( h_B );
            TESTING_FREE_CPU( h_X );
            TESTING_FREE_CPU( h_Blapack );
            TESTING_FREE_CPU( h_Bcublas );
            TESTING_FREE_CPU( h_Bmagma  );
            TESTING_FREE_CPU( ipiv );
            
            TESTING_FREE_DEV( d_A );
            TESTING_FREE_DEV( d_B );
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }

    opts.cleanup();
    TESTING_FINALIZE();
    return status;
}
Beispiel #3
0
/**
    Purpose
    -------
    CHEGVD computes all the eigenvalues, and optionally, the eigenvectors
    of a complex generalized Hermitian-definite eigenproblem, of the form
    A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and
    B are assumed to be Hermitian and B is also positive definite.
    If eigenvectors are desired, it uses a divide and conquer algorithm.

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

    Arguments
    ---------
    @param[in]
    nrgpu   INTEGER
            Number of GPUs to use.

    @param[in]
    itype   INTEGER
            Specifies the problem type to be solved:
            = 1:  A*x = (lambda)*B*x
            = 2:  A*B*x = (lambda)*x
            = 3:  B*A*x = (lambda)*x

    @param[in]
    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 triangles of A and B are stored;
      -     = MagmaLower:  Lower triangles of A and B are stored.

    @param[in]
    n       INTEGER
            The order of the matrices A and B.  N >= 0.

    @param[in,out]
    A       COMPLEX 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.
    \n
            On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the
            matrix Z of eigenvectors.  The eigenvectors are normalized
            as follows:
            if ITYPE = 1 or 2, Z**H*B*Z = I;
            if ITYPE = 3, Z**H*inv(B)*Z = I.
            If JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper)
            or the lower triangle (if UPLO=MagmaLower) of A, including the
            diagonal, is destroyed.

    @param[in]
    lda     INTEGER
            The leading dimension of the array A.  LDA >= max(1,N).

    @param[in,out]
    B       COMPLEX array, dimension (LDB, N)
            On entry, the Hermitian matrix B.  If UPLO = MagmaUpper, the
            leading N-by-N upper triangular part of B contains the
            upper triangular part of the matrix B.  If UPLO = MagmaLower,
            the leading N-by-N lower triangular part of B contains
            the lower triangular part of the matrix B.
    \n
            On exit, if INFO <= N, the part of B containing the matrix is
            overwritten by the triangular factor U or L from the Cholesky
            factorization B = U**H*U or B = L*L**H.

    @param[in]
    ldb     INTEGER
            The leading dimension of the array B.  LDB >= max(1,N).

    @param[in]
    vl      REAL
    @param[in]
    vu      REAL
            If RANGE=MagmaRangeV, the lower and upper bounds of the interval to
            be searched for eigenvalues. VL < VU.
            Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.

    @param[in]
    il      INTEGER
    @param[in]
    iu      INTEGER
            If RANGE=MagmaRangeI, the indices (in ascending order) of the
            smallest and largest eigenvalues to be returned.
            1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
            Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.

    @param[out]
    m       INTEGER
            The total number of eigenvalues found.  0 <= M <= N.
            If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.

    @param[out]
    w       REAL array, dimension (N)
            If INFO = 0, the eigenvalues in ascending order.

    @param[out]
    work    (workspace) COMPLEX array, dimension (MAX(1,LWORK))
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    @param[in]
    lwork   INTEGER
            The length of the array WORK.
            If N <= 1,                      LWORK >= 1.
            If JOBZ = MagmaNoVec and N > 1, LWORK >= N + 1.
            If JOBZ = MagmaVec   and N > 1, LWORK >= 2*N*nb + N**2.
    \n
            If LWORK = -1, then a workspace query is assumed; the routine
            only calculates the optimal sizes of the WORK, RWORK and
            IWORK arrays, returns these values as the first entries of
            the WORK, RWORK and IWORK arrays, and no error message
            related to LWORK or LRWORK or LIWORK is issued by XERBLA.

    @param[out]
    rwork   (workspace) REAL array, dimension (MAX(1,LRWORK))
            On exit, if INFO = 0, RWORK(1) 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(1) returns the optimal LIWORK.

    @param[in]
    liwork  INTEGER
            The dimension of the array IWORK.
            If N <= 1,                      LIWORK >= 1.
            If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1.
            If JOBZ = MagmaVec   and N > 1, LIWORK >= 3 + 5*N.
    \n
            If LIWORK = -1, then a workspace query is assumed; the
            routine only calculates the optimal sizes of the WORK, RWORK
            and IWORK arrays, returns these values as the first entries
            of the WORK, RWORK and IWORK arrays, and no error message
            related to LWORK or LRWORK or LIWORK is issued by XERBLA.

    @param[out]
    info    INTEGER
      -     = 0:  successful exit
      -     < 0:  if INFO = -i, the i-th argument had an illegal value
      -     > 0:  CPOTRF or CHEEVD returned an error code:
               <= N:  if INFO = i and JOBZ = MagmaNoVec, then the algorithm
                      failed to converge; i off-diagonal elements of an
                      intermediate tridiagonal form did not converge to
                      zero;
                      if INFO = i and JOBZ = MagmaVec, then the algorithm
                      failed to compute an eigenvalue while working on
                      the submatrix lying in rows and columns INFO/(N+1)
                      through mod(INFO,N+1);
               > N:   if INFO = N + i, for 1 <= i <= N, then the leading
                      minor of order i of B is not positive definite.
                      The factorization of B could not be completed and
                      no eigenvalues or eigenvectors were computed.

    Further Details
    ---------------
    Based on contributions by
       Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

    Modified so that no backsubstitution is performed if CHEEVD fails to
    converge (NEIG in old code could be greater than N causing out of
    bounds reference to A - reported by Ralf Meyer).  Also corrected the
    description of INFO and the test on ITYPE. Sven, 16 Feb 05.

    @ingroup magma_chegv_driver
    ********************************************************************/
extern "C" magma_int_t
magma_chegvdx_m(magma_int_t nrgpu, magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n,
                magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *B, magma_int_t ldb,
                float vl, float vu, magma_int_t il, magma_int_t iu,
                magma_int_t *m, float *w, magmaFloatComplex *work, magma_int_t lwork,
                float *rwork, magma_int_t lrwork,
                magma_int_t *iwork, magma_int_t liwork, magma_int_t *info)
{
    const char* uplo_  = lapack_uplo_const( uplo  );
    const char* jobz_  = lapack_vec_const( jobz  );
    
    magmaFloatComplex c_one = MAGMA_C_ONE;
    
    magma_int_t lower;
    magma_trans_t trans;
    magma_int_t wantz;
    magma_int_t lquery;
    magma_int_t alleig, valeig, indeig;
    
    magma_int_t lwmin;
    magma_int_t liwmin;
    magma_int_t lrwmin;
    
    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 (itype < 1 || itype > 3) {
        *info = -1;
    } else if (! (alleig || valeig || indeig)) {
        *info = -2;
    } else if (! (wantz || (jobz == MagmaNoVec))) {
        *info = -3;
    } else if (! (lower || (uplo == MagmaUpper))) {
        *info = -4;
    } else if (n < 0) {
        *info = -5;
    } else if (lda < max(1,n)) {
        *info = -7;
    } else if (ldb < max(1,n)) {
        *info = -9;
    } else {
        if (valeig) {
            if (n > 0 && vu <= vl) {
                *info = -11;
            }
        } else if (indeig) {
            if (il < 1 || il > max(1,n)) {
                *info = -12;
            } else if (iu < min(n,il) || iu > n) {
                *info = -13;
            }
        }
    }
    
    magma_int_t nb = magma_get_chetrd_nb( n );
    if ( n <= 1 ) {
        lwmin  = 1;
        lrwmin = 1;
        liwmin = 1;
    }
    else if ( wantz ) {
        lwmin  = 2*n + n*n;
        lrwmin = 1 + 5*n + 2*n*n;
        liwmin = 3 + 5*n;
    }
    else {
        lwmin  = n + n*nb;
        lrwmin = n;
        liwmin = 1;
    }
    
    // multiply by 1+eps (in Double!) to ensure length gets rounded up,
    // if it cannot be exactly represented in floating point.
    real_Double_t one_eps = 1. + lapackf77_slamch("Epsilon");
    work[0]  = MAGMA_C_MAKE( lwmin * one_eps, 0.);  // round up
    rwork[0] = lrwmin * one_eps;
    iwork[0] = liwmin;
    
    if (lwork < lwmin && ! lquery) {
        *info = -17;
    } else if (lrwork < lrwmin && ! lquery) {
        *info = -19;
    } else if (liwork < liwmin && ! lquery) {
        *info = -21;
    }
    
    if (*info != 0) {
        magma_xerbla( __func__, -(*info));
        return *info;
    }
    else if (lquery) {
        return *info;
    }
    
    /*  Quick return if possible */
    if (n == 0) {
        return *info;
    }

    /* 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_chegvd(&itype, jobz_, uplo_,
                         &n, A, &lda, B, &ldb,
                         w, work, &lwork,
                         #if defined(PRECISION_z) || defined(PRECISION_c)
                         rwork, &lrwork,
                         #endif
                         iwork, &liwork, info);
        *m = n;
        return *info;
    }

    magma_timer_t time=0;
    timer_start( time );

    magma_cpotrf_m(nrgpu, uplo, n, B, ldb, info);
    if (*info != 0) {
        *info = n + *info;
        return *info;
    }

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

    /* Transform problem to standard eigenvalue problem and solve. */
    magma_chegst_m(nrgpu, itype, uplo, n, A, lda, B, ldb, info);

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

    magma_cheevdx_m(nrgpu, jobz, range, uplo, n, A, lda, vl, vu, il, iu, m, w, work, lwork, rwork, lrwork, iwork, liwork, info);

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

    if (wantz && *info == 0) {
        timer_start( time );

        /* Backtransform eigenvectors to the original problem. */
        if (itype == 1 || itype == 2) {
            /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
               backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
            if (lower) {
                trans = MagmaConjTrans;
            } else {
                trans = MagmaNoTrans;
            }

            magma_ctrsm_m(nrgpu, MagmaLeft, uplo, trans, MagmaNonUnit,
                          n, *m, c_one, B, ldb, A, lda);
        }
        else if (itype == 3) {
            /* For B*A*x=(lambda)*x;
               backtransform eigenvectors: x = L*y or U'*y */
            if (lower) {
                trans = MagmaNoTrans;
            } else {
                trans = MagmaConjTrans;
            }

            //magma_ctrmm(MagmaLeft, uplo, trans, MagmaNonUnit,
            //            n, n, c_one, db, lddb, da, ldda);
        }

        timer_stop( time );
        timer_printf( "time setmatrices trsm/mm + getmatrices = %6.2f\n", time );
    }

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

    return *info;
} /* magma_chegvd_m */
Beispiel #4
0
/**
    Purpose
    -------
    CHEGVD computes all the eigenvalues, and optionally, the eigenvectors
    of a complex generalized Hermitian-definite eigenproblem, of the form
    A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and
    B are assumed to be Hermitian and B is also positive definite.
    If eigenvectors are desired, it uses a divide and conquer algorithm.

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

    Arguments
    ---------
    @param[in]
    ngpu    INTEGER
            Number of GPUs to use. ngpu > 0.

    @param[in]
    itype   INTEGER
            Specifies the problem type to be solved:
            = 1:  A*x = (lambda)*B*x
            = 2:  A*B*x = (lambda)*x
            = 3:  B*A*x = (lambda)*x

    @param[in]
    jobz    magma_vec_t
      -     = MagmaNoVec:  Compute eigenvalues only;
      -     = MagmaVec:    Compute eigenvalues and eigenvectors.

    @param[in]
    uplo    magma_uplo_t
      -     = MagmaUpper:  Upper triangles of A and B are stored;
      -     = MagmaLower:  Lower triangles of A and B are stored.

    @param[in]
    n       INTEGER
            The order of the matrices A and B.  N >= 0.

    @param[in,out]
    A       COMPLEX array, dimension (LDA, N)
            On entry, the Hermitian matrix A.  If UPLO = MagmaUpper, the
            leading N-by-N upper triangular part of A contains the
            upper triangular part of the matrix A.  If UPLO = MagmaLower,
            the leading N-by-N lower triangular part of A contains
            the lower triangular part of the matrix A.
    \n
            On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the
            matrix Z of eigenvectors.  The eigenvectors are normalized
            as follows:
            if ITYPE = 1 or 2, Z**H*B*Z = I;
            if ITYPE = 3, Z**H*inv(B)*Z = I.
            If JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper)
            or the lower triangle (if UPLO=MagmaLower) of A, including the
            diagonal, is destroyed.

    @param[in]
    lda     INTEGER
            The leading dimension of the array A.  LDA >= max(1,N).

    @param[in,out]
    B       COMPLEX array, dimension (LDB, N)
            On entry, the Hermitian matrix B.  If UPLO = MagmaUpper, the
            leading N-by-N upper triangular part of B contains the
            upper triangular part of the matrix B.  If UPLO = MagmaLower,
            the leading N-by-N lower triangular part of B contains
            the lower triangular part of the matrix B.
    \n
            On exit, if INFO <= N, the part of B containing the matrix is
            overwritten by the triangular factor U or L from the Cholesky
            factorization B = U**H*U or B = L*L**H.

    @param[in]
    ldb     INTEGER
            The leading dimension of the array B.  LDB >= max(1,N).

    @param[out]
    w       REAL array, dimension (N)
            If INFO = 0, the eigenvalues in ascending order.

    @param[out]
    work    (workspace) COMPLEX array, dimension (MAX(1,LWORK))
            On exit, if INFO = 0, WORK[0] returns the optimal LWORK.

    @param[in]
    lwork   INTEGER
            The length of the array WORK.
            If N <= 1,                      LWORK >= 1.
            If JOBZ = MagmaNoVec and N > 1, LWORK >= N + N*NB.
            If JOBZ = MagmaVec   and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ).
            NB can be obtained through magma_get_chetrd_nb(N).
    \n
            If LWORK = -1, then a workspace query is assumed; the routine
            only calculates the optimal sizes of the WORK, RWORK and
            IWORK arrays, returns these values as the first entries of
            the WORK, RWORK and IWORK arrays, and no error message
            related to LWORK or LRWORK or LIWORK is issued by XERBLA.

    @param[out]
    rwork   (workspace) REAL array, dimension (MAX(1,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:  CPOTRF or CHEEVD returned an error code:
               <= N:  if INFO = i and JOBZ = MagmaNoVec, then the algorithm
                      failed to converge; i off-diagonal elements of an
                      intermediate tridiagonal form did not converge to
                      zero;
                      if INFO = i and JOBZ = MagmaVec, then the algorithm
                      failed to compute an eigenvalue while working on
                      the submatrix lying in rows and columns INFO/(N+1)
                      through mod(INFO,N+1);
               > N:   if INFO = N + i, for 1 <= i <= N, then the leading
                      minor of order i of B is not positive definite.
                      The factorization of B could not be completed and
                      no eigenvalues or eigenvectors were computed.

    Further Details
    ---------------
    Based on contributions by
       Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

    Modified so that no backsubstitution is performed if CHEEVD fails to
    converge (NEIG in old code could be greater than N causing out of
    bounds reference to A - reported by Ralf Meyer).  Also corrected the
    description of INFO and the test on ITYPE. Sven, 16 Feb 05.

    @ingroup magma_chegv_driver
    ********************************************************************/
extern "C" magma_int_t
magma_chegvd_m(
    magma_int_t ngpu,
    magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n,
    magmaFloatComplex *A, magma_int_t lda,
    magmaFloatComplex *B, magma_int_t ldb,
    float *w, magmaFloatComplex *work, magma_int_t lwork,
    #ifdef COMPLEX
    float *rwork, magma_int_t lrwork,
    #endif
    magma_int_t *iwork, magma_int_t liwork,
    magma_int_t *info)
{
    const char* uplo_ = lapack_uplo_const( uplo );
    const char* jobz_ = lapack_vec_const( jobz );

    magmaFloatComplex c_one = MAGMA_C_ONE;

    magma_int_t lower;
    magma_trans_t trans;
    magma_int_t wantz;
    magma_int_t lquery;

    magma_int_t lwmin;
    magma_int_t liwmin;
    magma_int_t lrwmin;

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

    *info = 0;
    if (itype < 1 || itype > 3) {
        *info = -1;
    } else if (! (wantz || (jobz == MagmaNoVec))) {
        *info = -2;
    } else if (! (lower || (uplo == MagmaUpper))) {
        *info = -3;
    } else if (n < 0) {
        *info = -4;
    } else if (lda < max(1,n)) {
        *info = -6;
    } else if (ldb < max(1,n)) {
        *info = -8;
    }

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

    work[0]  = magma_cmake_lwork( lwmin );
    rwork[0] = magma_smake_lwork( lrwmin );
    iwork[0] = liwmin;

    if (lwork < lwmin && ! lquery) {
        *info = -11;
    } else if (lrwork < lrwmin && ! lquery) {
        *info = -13;
    } else if (liwork < liwmin && ! lquery) {
        *info = -15;
    }

    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }
    else if (lquery) {
        return *info;
    }

    /* Quick return if possible */
    if (n == 0) {
        return *info;
    }

    /* If matrix is very small, then just call LAPACK on CPU, no need for GPU */
    if (n <= 128) {
        lapackf77_chegvd( &itype, jobz_, uplo_,
                          &n, A, &lda, B, &ldb,
                          w, work, &lwork,
                          #ifdef COMPLEX
                          rwork, &lrwork,
                          #endif
                          iwork, &liwork, info);
        return *info;
    }

    magma_timer_t time=0;
    timer_start( time );

    magma_cpotrf_m( ngpu, uplo, n, B, ldb, info );
    if (*info != 0) {
        *info = n + *info;
        return *info;
    }

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

    /*  Transform problem to standard eigenvalue problem and solve. */
    magma_chegst_m( ngpu, itype, uplo, n, A, lda, B, ldb, info );

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

    magma_cheevd_m( ngpu, jobz, uplo, n, A, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info );

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

    if (wantz && *info == 0) {
        timer_start( time );

        /* Backtransform eigenvectors to the original problem. */
        if (itype == 1 || itype == 2) {
            /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
               backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
            if (lower) {
                trans = MagmaConjTrans;
            } else {
                trans = MagmaNoTrans;
            }
            magma_ctrsm_m( ngpu, MagmaLeft, uplo, trans, MagmaNonUnit,
                           n, n, c_one, B, ldb, A, lda );
        }
        else if (itype == 3) {
            /* For B*A*x=(lambda)*x;
               backtransform eigenvectors: x = L*y or U'*y */
            if (lower) {
                trans = MagmaNoTrans;
            } else {
                trans = MagmaConjTrans;
            }
            #ifdef ENABLE_DEBUG
            printf("--- the multi GPU version is falling back to 1 GPU to perform the last TRMM since there is no TRMM_mgpu --- \n");
            #endif
            magmaFloatComplex *dA=NULL, *dB=NULL;
            magma_int_t ldda = magma_roundup( n, 32 );
            magma_int_t lddb = ldda;
            
            if (MAGMA_SUCCESS != magma_cmalloc( &dA, n*ldda ) ||
                MAGMA_SUCCESS != magma_cmalloc( &dB, n*lddb )) {
                magma_free( dA );
                magma_free( dB );
                *info = MAGMA_ERR_DEVICE_ALLOC;
                return *info;
            }
            
            magma_queue_t queue;
            magma_device_t cdev;
            magma_getdevice( &cdev );
            magma_queue_create( cdev, &queue );
        
            magma_csetmatrix( n, n, B, ldb, dB, lddb, queue );
            magma_csetmatrix( n, n, A, lda, dA, ldda, queue );
            magma_ctrmm( MagmaLeft, uplo, trans, MagmaNonUnit,
                         n, n, c_one, dB, lddb, dA, ldda, queue );
            magma_cgetmatrix( n, n, dA, ldda, A, lda, queue );
            
            magma_queue_destroy( queue );
            
            magma_free( dA );
            magma_free( dB );
        }

        timer_stop( time );
        timer_printf( "time setmatrices trsm/mm + getmatrices = %6.2f\n", time );
    }

    work[0]  = magma_cmake_lwork( lwmin );
    rwork[0] = magma_smake_lwork( lrwmin );
    iwork[0] = liwmin;
    
    return *info;
} /* magma_chegvd_m */