Beispiel #1
0
/**
    Purpose
    -------
    ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to
    Hermitian tridiagonal form by an orthogonal similarity
    transformation Q' * A * Q, and returns the matrices V and W which are
    needed to apply the transformation to the unreduced part of A.

    If UPLO = MagmaUpper, ZLATRD reduces the last NB rows and columns of a
    matrix, of which the upper triangle is supplied;
    if UPLO = MagmaLower, ZLATRD reduces the first NB rows and columns of a
    matrix, of which the lower triangle is supplied.

    This is an auxiliary routine called by ZHETRD.

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

    @param[in]
    uplo    magma_uplo_t
            Specifies whether the upper or lower triangular part of the
            Hermitian matrix A is stored:
      -     = MagmaUpper: Upper triangular
      -     = MagmaLower: Lower triangular

    @param[in]
    n       INTEGER
            The order of the matrix A.

    @param[in]
    nb      INTEGER
            The number of rows and columns to be reduced.

    @param[in]
    nb0     INTEGER
            The block size used for the matrix distribution.
            nb and nb0 can be different for the final step of zhetrd.

    @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, and the strictly lower
            triangular part of A is not referenced.  If UPLO = MagmaLower, the
            leading n-by-n lower triangular part of A contains the lower
            triangular part of the matrix A, and the strictly upper
            triangular part of A is not referenced.
            On exit:
      -     if UPLO = MagmaUpper, the last NB columns have been reduced to
              tridiagonal form, with the diagonal elements overwriting
              the diagonal elements of A; the elements above the diagonal
              with the array TAU, represent the orthogonal matrix Q as a
              product of elementary reflectors;
      -     if UPLO = MagmaLower, the first NB columns have been reduced to
              tridiagonal form, with the diagonal elements overwriting
              the diagonal elements of A; the elements below the diagonal
              with the array TAU, represent the  orthogonal matrix Q as a
              product of elementary reflectors.
            See Further Details.

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

    @param[out]
    e       COMPLEX_16 array, dimension (N-1)
            If UPLO = MagmaUpper, E(n-nb:n-1) contains the superdiagonal
            elements of the last NB columns of the reduced matrix;
            if UPLO = MagmaLower, E(1:nb) contains the subdiagonal elements of
            the first NB columns of the reduced matrix.

    @param[out]
    tau     COMPLEX_16 array, dimension (N-1)
            The scalar factors of the elementary reflectors, stored in
            TAU(n-nb:n-1) if UPLO = MagmaUpper, and in TAU(1:nb) if UPLO = MagmaLower.
            See Further Details.

    @param[out]
    W       COMPLEX_16 array, dimension (LDW,NB)
            The n-by-nb matrix W required to update the unreduced part
            of A.

    @param[in]
    ldw     INTEGER
            The leading dimension of the array W. LDW >= max(1,N).

    @param
    dA

    @param[in]
    ldda

    @param[in]
    offset

    @param
    dW

    @param[in]
    lddw

    @param
    hwork

    @param[in]
    lhwork

    @param
    dwork

    @param[in]
    ldwork
             
    @param[in]
    queues  magma_queue_t array of dimension (ngpu).
            queues[dev] is an execution queue on GPU dev.
    
    Further Details
    ---------------
    If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary
    reflectors

       Q = H(n) H(n-1) . . . H(n-nb+1).

    Each H(i) has the form

       H(i) = I - tau * v * v'

    where tau is a complex scalar, and v is a complex vector with
    v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
    and tau in TAU(i-1).

    If UPLO = MagmaLower, the matrix Q is represented as a product of elementary
    reflectors

       Q = H(1) H(2) . . . H(nb).

    Each H(i) has the form

       H(i) = I - tau * v * v'

    where tau is a complex scalar, and v is a complex vector with
    v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
    and tau in TAU(i).

    The elements of the vectors v together form the n-by-nb matrix V
    which is needed, with W, to apply the transformation to the unreduced
    part of the matrix, using a Hermitian rank-2k update of the form:
    A := A - V*W' - W*V'.

    The contents of A on exit are illustrated by the following examples
    with n = 5 and nb = 2:

    if UPLO = MagmaUpper:                       if UPLO = MagmaLower:

      (  a   a   a   v4  v5 )              (  d                  )
      (      a   a   v4  v5 )              (  1   d              )
      (          a   1   v5 )              (  v1  1   a          )
      (              d   1  )              (  v1  v2  a   a      )
      (                  d  )              (  v1  v2  a   a   a  )

    where d denotes a diagonal element of the reduced matrix, a denotes
    an element of the original matrix that is unchanged, and vi denotes
    an element of the vector defining H(i).

    @ingroup magma_zheev_aux
    ********************************************************************/
extern "C" magma_int_t
magma_zlatrd_mgpu(
    magma_int_t ngpu,
    magma_uplo_t uplo,
    magma_int_t n, magma_int_t nb, magma_int_t nb0,
    magmaDoubleComplex *A,  magma_int_t lda,
    double *e, magmaDoubleComplex *tau,
    magmaDoubleComplex *W,          magma_int_t ldw,
    magmaDoubleComplex_ptr dA[],    magma_int_t ldda, magma_int_t offset,
    magmaDoubleComplex_ptr dW[],    magma_int_t lddw,
    magmaDoubleComplex    *hwork,   magma_int_t lhwork,
    magmaDoubleComplex_ptr dwork[], magma_int_t ldwork,
    magma_queue_t queues[] )
{
#define A(i, j) (A + (j)*lda + (i))
#define W(i, j) (W + (j)*ldw + (i))

#define dA(dev, i, j)  (dA[(dev)] + ((j)+loffset)*ldda + (i) + offset)
#define dW(dev, i, j)  (dW[(dev)] + (j)          *lddw + (i))
#define dW1(dev, i, j) (dW[(dev)] + ((j)+nb)     *lddw + (i))

    /* Constants */
    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;

    /* Local variables */
    magmaDoubleComplex alpha, value;
    magma_int_t dev;
    magma_int_t i, n_i, n_i_1, ip1, iw;

    // TODO check arguments
    magma_int_t info = 0;
    if (n <= 0) {
        return info;
    }
    
    // TODO allocate f in zhetrd and pass into zlatrd. (e.g., expand hwork a bit)
    magmaDoubleComplex *f;
    magma_zmalloc_cpu( &f, n );
    if ( f == NULL ) {
        info = MAGMA_ERR_HOST_ALLOC;
        return info;
    }

    magma_device_t orig_dev;
    magma_getdevice( &orig_dev );
    
    if (uplo == MagmaUpper) {
        /* Reduce last NB columns of upper triangle */
        for (i = n-1; i >= n - nb; --i) {
            ip1 = i + 1;
            n_i_1 = n - i - 1;
            iw = i - n + nb;
            if (i < n-1) {
                /* Update A(1:i,i) */
                magmaDoubleComplex wii = -conj( *W(i, iw+1) );
                blasf77_zaxpy( &ip1, &wii, A(0, i+1), &ione, A(0, i), &ione );

                wii = -conj( *A(i, i+1) );
                blasf77_zaxpy( &ip1, &wii, W(0, iw+1), &ione, A(0, i), &ione );
            }
            if (i > 0) {
                /* Generate elementary reflector H(i) to annihilate A(1:i-2,i) */
                alpha = *A(i-1, i);
                lapackf77_zlarfg( &i, &alpha, A(0, i), &ione, &tau[i - 1] );

                e[i-1] = MAGMA_Z_REAL( alpha );
                *A(i-1,i) = MAGMA_Z_ONE;
                
                // TODO Previously, this set dx2[dev] = dW1(dev, 0, iw); and used dx2 in zhemv.
                // TODO Now zhemv handles broadcasting x to the GPUs, but data in dW1 is
                // TODO apparently still used in zhetrd_mgpu / zher2k_mgpu.
                for( dev=0; dev < ngpu; dev++ ) {
                    magma_setdevice( dev );
                    magma_zsetvector_async( n, A(0,i), 1, dW1(dev, 0, iw), 1, queues[dev] );
                }
                magmablas_zhemv_mgpu( 
                    MagmaUpper, i, c_one, dA, ldda, 0,
                    A(0,i), 1, c_zero, W(0, iw), 1,
                    hwork, lhwork, dwork, ldwork, ngpu, nb0, queues );

                if (i < n-1) {
                    blasf77_zgemv( MagmaConjTransStr, &i, &n_i_1, &c_one,
                                   W(0,   iw+1), &ldw,
                                   A(0,   i),    &ione, &c_zero,
                                   W(i+1, iw),   &ione );
                }

                /* overlap update */
                if ( i < n-1 && i-1 >= n - nb ) {
                    /* Update A(1:i,i) */
                    #ifdef COMPLEX
                    lapackf77_zlacgv( &n_i_1, W(i-1, iw+1), &ldw );
                    #endif
                    blasf77_zgemv( "No transpose", &i, &n_i_1, &c_neg_one,
                                   A(0,   i+1),  &lda,
                                   W(i-1, iw+1), &ldw, &c_one,
                                   A(0,   i-1),  &ione );
                    #ifdef COMPLEX
                    lapackf77_zlacgv( &n_i_1, W(i-1, iw+1), &ldw );
                    lapackf77_zlacgv( &n_i_1, A(i-1, i +1), &lda );
                    #endif
                    blasf77_zgemv( "No transpose", &i, &n_i_1, &c_neg_one,
                                   W(0,   iw+1), &ldw,
                                   A(i-1, i+1),  &lda, &c_one,
                                   A(0,   i-1),  &ione );
                    #ifdef COMPLEX
                    lapackf77_zlacgv( &n_i_1, A(i-1, i+1), &lda );
                    #endif
                }

                // synchronize to get zhemv result W(0, iw)
                magmablas_zhemv_mgpu_sync( 
                    MagmaUpper, i, c_one, dA, ldda, 0,
                    A(0,i), 1, c_zero, W(0, iw), 1,
                    hwork, lhwork, dwork, ldwork, ngpu, nb0, queues );

                if (i < n-1) {
                    blasf77_zgemv( "No transpose", &i, &n_i_1, &c_neg_one,
                                   A(0,   i+1), &lda,
                                   W(i+1, iw),  &ione, &c_one,
                                   W(0,   iw),  &ione );

                    blasf77_zgemv( MagmaConjTransStr, &i, &n_i_1, &c_one,
                                   A(0,   i+1), &lda,
                                   A(0,   i),   &ione, &c_zero,
                                   W(i+1, iw),  &ione );

                    blasf77_zgemv( "No transpose", &i, &n_i_1, &c_neg_one,
                                   W(0,   iw+1), &ldw,
                                   W(i+1, iw),   &ione, &c_one,
                                   W(0,   iw),   &ione );
                }

                blasf77_zscal( &i, &tau[i - 1], W(0, iw), &ione );

                value = magma_cblas_zdotc( i, W(0,iw), ione, A(0,i), ione );
                alpha = tau[i - 1] * -0.5f * value;
                blasf77_zaxpy( &i, &alpha, A(0, i), &ione, W(0, iw), &ione );

                for( dev=0; dev < ngpu; dev++ ) {
                    magma_setdevice( dev );
                    magma_zsetvector_async( n, W(0,iw), 1, dW(dev, 0, iw), 1, queues[dev] );
                }
            }
        }
    } else {
        /*  Reduce first NB columns of lower triangle */
        for (i = 0; i < nb; ++i) {
            /* Update A(i:n,i) */
            n_i = n - i;
            //idw = ((offset+i)/nb)%ngpu;
            if ( i > 0 ) {
                trace_cpu_start( 0, "gemv", "gemv" );
                magmaDoubleComplex wii = -conj( *W(i, i-1) );
                blasf77_zaxpy( &n_i, &wii, A(i, i-1), &ione, A(i, i), &ione );

                wii = -conj( *A(i, i-1) );
                blasf77_zaxpy( &n_i, &wii, W(i, i-1), &ione, A(i, i), &ione );
            }

            if (i < n-1) {
                /* Generate elementary reflector H(i) to annihilate A(i+2:n,i) */
                n_i_1 = n - i - 1;
                trace_cpu_start( 0, "larfg", "larfg" );
                alpha = *A(i+1, i);
                lapackf77_zlarfg( &n_i_1, &alpha, A(min(i+2,n-1), i), &ione, &tau[i] );
                e[i] = MAGMA_Z_REAL( alpha );
                *A(i+1,i) = MAGMA_Z_ONE;
                trace_cpu_end( 0 );

                /* Compute W(i+1:n,i) */
                // TODO Previously, this set dx2[id] = dW1(id, 0, i)-offset; and used dx2 in zhemv.
                // TODO Now zhemv handles broadcasting x to the GPUs, but data in dW1 is
                // TODO apparently still used in zhetrd_mgpu / zher2k_mgpu.
                for( dev=0; dev < ngpu; dev++ ) {
                    magma_setdevice( dev );
                    magma_zsetvector_async( n, A(0,i), 1, dW1(dev, 0, i), 1, queues[dev] );
                }
                
                magmablas_zhemv_mgpu( 
                    MagmaLower, n_i_1, c_one, dA, ldda, offset+i+1,
                    A(i+1, i), 1, c_zero, W(i+1, i), 1,
                    hwork, lhwork, dwork, ldwork, ngpu, nb0, queues );
                
                trace_cpu_start( 0, "gemv", "gemv" );
                blasf77_zgemv( MagmaConjTransStr, &n_i_1, &i, &c_one,
                               W(i+1, 0), &ldw,
                               A(i+1, i), &ione, &c_zero,
                               W(0,   i), &ione );
                
                blasf77_zgemv( "No transpose", &n_i_1, &i, &c_neg_one,
                               A(i+1, 0), &lda,
                               W(0,   i), &ione, &c_zero,
                               f,         &ione );
                
                blasf77_zgemv( MagmaConjTransStr, &n_i_1, &i, &c_one,
                               A(i+1, 0), &lda,
                               A(i+1, i), &ione, &c_zero,
                               W(0,   i), &ione );
                trace_cpu_end( 0 );

                /* overlap update */
                if ( i > 0 && i+1 < n ) {
                    trace_cpu_start( 0, "gemv", "gemv" );
                    #ifdef COMPLEX
                    lapackf77_zlacgv( &i, W(i+1, 0), &ldw );
                    #endif
                    blasf77_zgemv( "No transpose", &n_i_1, &i, &c_neg_one,
                                   A(i+1, 0),   &lda,
                                   W(i+1, 0),   &ldw, &c_one,
                                   A(i+1, i+1), &ione );
                    #ifdef COMPLEX
                    lapackf77_zlacgv( &i, W(i+1, 0), &ldw );
                    lapackf77_zlacgv( &i, A(i+1, 0), &lda );
                    #endif
                    blasf77_zgemv( "No transpose", &n_i_1, &i, &c_neg_one,
                                   W(i+1, 0),   &ldw,
                                   A(i+1, 0),   &lda, &c_one,
                                   A(i+1, i+1), &ione );
                    #ifdef COMPLEX
                    lapackf77_zlacgv( &i, A(i+1, 0), &lda );
                    #endif
                    trace_cpu_end( 0 );
                }

                // synchronize to get zhemv result W(i+1, i)
                magmablas_zhemv_mgpu_sync( 
                    MagmaLower, n_i_1, c_one, dA, ldda, offset+i+1,
                    A(i+1, i), 1, c_zero, W(i+1, i), 1,
                    hwork, lhwork, dwork, ldwork, ngpu, nb0, queues );
                
                trace_cpu_start( 0, "axpy", "axpy" );
                if (i != 0) {
                    blasf77_zaxpy( &n_i_1, &c_one, f, &ione, W(i+1, i), &ione );
                }

                blasf77_zgemv( "No transpose", &n_i_1, &i, &c_neg_one,
                               W(i+1, 0), &ldw,
                               W(0,   i), &ione, &c_one,
                               W(i+1, i), &ione );
                blasf77_zscal( &n_i_1, &tau[i], W(i+1,i), &ione );

                value = magma_cblas_zdotc( n_i_1, W(i+1,i), ione, A(i+1,i), ione );
                alpha = tau[i] * -0.5f * value;
                blasf77_zaxpy( &n_i_1, &alpha, A(i+1, i), &ione, W(i+1,i), &ione );
                trace_cpu_end( 0 );
                for( dev=0; dev < ngpu; dev++ ) {
                    magma_setdevice( dev );
                    magma_zsetvector_async( n, W(0,i), 1, dW(dev, 0, i), 1, queues[dev] );
                }
            }
        }
    }

    magma_free_cpu( f );

    magma_setdevice( orig_dev );
    
    return info;
} /* magma_zlatrd_mgpu */
Beispiel #2
0
// --------------------
int main(int argc, char **argv)
{
    TESTING_INIT();

    real_Double_t gflops, cpu_time=0, cpu_perf=0, gpu_time, gpu_perf, mgpu_time, mgpu_perf, cuda_time, cuda_perf;
    double      Ynorm, error=0, error2=0, work[1];
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
    magma_int_t n_local[MagmaMaxGPUs];

    magma_int_t N, Noffset, lda, ldda, blocks, lhwork, ldwork, matsize, vecsize;
    magma_int_t incx = 1;

    magmaDoubleComplex alpha = MAGMA_Z_MAKE(  1.5, -2.3 );
    magmaDoubleComplex beta  = MAGMA_Z_MAKE( -0.6,  0.8 );
    magmaDoubleComplex *A, *X, *Y, *Ylapack, *Ycublas, *Ymagma, *Ymagma1, *hwork;
    magmaDoubleComplex_ptr dA, dX, dY;
    magmaDoubleComplex_ptr d_lA[MagmaMaxGPUs], dwork[MagmaMaxGPUs];

    magma_device_t dev;
    magma_queue_t queues[MagmaMaxGPUs];
    magma_int_t     status = 0;
    
    magma_opts opts;
    opts.parse_opts( argc, argv );
    opts.ngpu = abs( opts.ngpu );  // always uses multi-GPU code
    
    double tol = opts.tolerance * lapackf77_dlamch("E");

    magma_int_t nb = 64;  // required by magmablas_zhemv_mgpu implementation

    for( dev=0; dev < opts.ngpu; ++dev ) {
        magma_queue_create( dev, &queues[dev] );
    }
    
    // currently, tests all offsets in the offsets array;
    // comment out loop below to test a specific offset.
    magma_int_t offset = opts.offset;
    magma_int_t offsets[] = { 0, 1, 31, 32, 33, 63, 64, 65, 100, 200 };
    magma_int_t noffsets = sizeof(offsets) / sizeof(*offsets);
    
    printf("%% uplo = %s, ngpu %d, block size = %d, offset %d\n",
            lapack_uplo_const(opts.uplo), (int) opts.ngpu, (int) nb, (int) offset );
    printf( "%%                 BLAS                CUBLAS              MAGMA 1 GPU         MAGMA MGPU       Error rel  Error rel\n"
            "%%   N  offset     Gflop/s (msec)      Gflop/s (msec)      Gflop/s (msec)      Gflop/s (msec)   to CUBLAS  to LAPACK\n"
            "%%==================================================================================================================\n" );
    for( int itest = 0; itest < opts.ntest; ++itest ) {
      
      // comment out these two lines & end of loop to test a specific offset
      for( int ioffset=0; ioffset < noffsets; ioffset += 1 ) {
        offset = offsets[ioffset];
        
        for( int iter = 0; iter < opts.niter; ++iter ) {
            N       = opts.nsize[itest];
            Noffset = N + offset;
            lda     = Noffset;
            ldda    = magma_roundup( Noffset, opts.align );  // multiple of 32 by default
            matsize = Noffset*ldda;
            vecsize = (Noffset-1)*incx + 1;
            gflops  = FLOPS_ZHEMV( N ) / 1e9;
            
            blocks = magma_ceildiv( N + (offset % nb), nb );
            lhwork = N*opts.ngpu;
            ldwork = ldda*(blocks + 1);

            TESTING_MALLOC_CPU( A,       magmaDoubleComplex, matsize );
            TESTING_MALLOC_CPU( Y,       magmaDoubleComplex, vecsize );
            TESTING_MALLOC_CPU( Ycublas, magmaDoubleComplex, vecsize );
            TESTING_MALLOC_CPU( Ymagma,  magmaDoubleComplex, vecsize );
            TESTING_MALLOC_CPU( Ymagma1, magmaDoubleComplex, vecsize );
            TESTING_MALLOC_CPU( Ylapack, magmaDoubleComplex, vecsize );

            TESTING_MALLOC_PIN( X,       magmaDoubleComplex, vecsize );
            TESTING_MALLOC_PIN( hwork,   magmaDoubleComplex, lhwork  );
            
            magma_setdevice( opts.device );
            TESTING_MALLOC_DEV( dA, magmaDoubleComplex, matsize );
            TESTING_MALLOC_DEV( dX, magmaDoubleComplex, vecsize );
            TESTING_MALLOC_DEV( dY, magmaDoubleComplex, vecsize );
            
            // TODO make magma_zmalloc_bcyclic helper function?
            for( dev=0; dev < opts.ngpu; dev++ ) {
                n_local[dev] = ((Noffset/nb)/opts.ngpu)*nb;
                if (dev < (Noffset/nb) % opts.ngpu)
                    n_local[dev] += nb;
                else if (dev == (Noffset/nb) % opts.ngpu)
                    n_local[dev] += Noffset % nb;
                
                magma_setdevice( dev );
                TESTING_MALLOC_DEV( d_lA[dev],  magmaDoubleComplex, ldda*n_local[dev] );
                TESTING_MALLOC_DEV( dwork[dev], magmaDoubleComplex, ldwork );
            }
            
            //////////////////////////////////////////////////////////////////////////
            
            /* Initialize the matrix */
            lapackf77_zlarnv( &ione, ISEED, &matsize, A );
            magma_zmake_hermitian( Noffset, A, lda );
            
            lapackf77_zlarnv( &ione, ISEED, &vecsize, X );
            lapackf77_zlarnv( &ione, ISEED, &vecsize, Y );
            
            /* =====================================================================
               Performs operation using CUBLAS
               =================================================================== */
            magma_setdevice( opts.device );
            magma_zsetmatrix( Noffset, Noffset, A, lda, dA, ldda, opts.queue );
            magma_zsetvector( Noffset, X, incx, dX, incx, opts.queue );
            magma_zsetvector( Noffset, Y, incx, dY, incx, opts.queue );
            
            cuda_time = magma_sync_wtime(0);
            cublasZhemv( opts.handle, cublas_uplo_const(opts.uplo), N,
                         &alpha, dA + offset + offset*ldda, ldda,
                                 dX + offset, incx,
                         &beta,  dY + offset, incx );
            cuda_time = magma_sync_wtime(0) - cuda_time;
            cuda_perf = gflops / cuda_time;
            
            magma_zgetvector( Noffset, dY, incx, Ycublas, incx, opts.queue );
            
            /* =====================================================================
               Performs operation using MAGMABLAS (1 GPU)
               =================================================================== */
            magma_setdevice( opts.device );
            magma_zsetvector( Noffset, Y, incx, dY, incx, opts.queue );
            
            gpu_time = magma_sync_wtime( opts.queue );
            
            magmablas_zhemv_work( opts.uplo, N,
                                  alpha, dA + offset + offset*ldda, ldda,
                                         dX + offset, incx,
                                  beta,  dY + offset, incx, dwork[ opts.device ], ldwork,
                                  opts.queue );
            
            gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
            gpu_perf = gflops / gpu_time;
            magma_zgetvector( Noffset, dY, incx, Ymagma1, incx, opts.queue );
            
            /* =====================================================================
               Performs operation using MAGMABLAS (multi-GPU)
               =================================================================== */
            magma_zsetmatrix_1D_col_bcyclic( Noffset, Noffset, A, lda, d_lA, ldda, opts.ngpu, nb, queues );
            blasf77_zcopy( &Noffset, Y, &incx, Ymagma, &incx );
            
            // workspaces do NOT need to be zero -- set to NAN to prove
            for( dev=0; dev < opts.ngpu; ++dev ) {
                magma_setdevice( dev );
                magmablas_zlaset( MagmaFull, ldwork, 1, MAGMA_Z_NAN, MAGMA_Z_NAN, dwork[dev], ldwork, opts.queue );
            }
            lapackf77_zlaset( "Full", &lhwork, &ione, &MAGMA_Z_NAN, &MAGMA_Z_NAN, hwork, &lhwork );
            
            mgpu_time = magma_sync_wtime(0);
            
            magma_int_t info;
            info = magmablas_zhemv_mgpu(
                opts.uplo, N,
                alpha,
                d_lA, ldda, offset,
                X + offset, incx,
                beta,
                Ymagma + offset, incx,
                hwork, lhwork,
                dwork, ldwork,
                opts.ngpu, nb, queues );
            if (info != 0) {
                printf("magmablas_zhemv_mgpu returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            }
            
            info = magmablas_zhemv_mgpu_sync(
                opts.uplo, N,
                alpha,
                d_lA, ldda, offset,
                X + offset, incx,
                beta,
                Ymagma + offset, incx,
                hwork, lhwork,
                dwork, ldwork,
                opts.ngpu, nb, queues );
            if (info != 0) {
                printf("magmablas_zhemv_sync returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            }
            
            mgpu_time = magma_sync_wtime(0) - mgpu_time;
            mgpu_perf = gflops / mgpu_time;
            
            /* =====================================================================
               Performs operation using LAPACK
               =================================================================== */
            if ( opts.lapack ) {
                blasf77_zcopy( &Noffset, Y, &incx, Ylapack, &incx );
                
                cpu_time = magma_wtime();
                blasf77_zhemv( lapack_uplo_const(opts.uplo), &N,
                               &alpha, A + offset + offset*lda, &lda,
                                       X + offset, &incx,
                               &beta,  Ylapack + offset, &incx );
                cpu_time = magma_wtime() - cpu_time;
                cpu_perf = gflops / cpu_time;
    
                /* =====================================================================
                   Compute the Difference LAPACK vs. Magma
                   =================================================================== */
                Ynorm  = lapackf77_zlange( "F", &Noffset, &ione, Ylapack, &Noffset, work );
                blasf77_zaxpy( &Noffset, &c_neg_one, Ymagma, &incx, Ylapack, &incx );
                error2 = lapackf77_zlange( "F", &Noffset, &ione, Ylapack, &Noffset, work ) / Ynorm;
            }
            
            /* =====================================================================
               Compute the Difference Cublas vs. Magma
               =================================================================== */
            Ynorm = lapackf77_zlange( "F", &Noffset, &ione, Ycublas, &Noffset, work );
            blasf77_zaxpy( &Noffset, &c_neg_one, Ymagma, &incx, Ycublas, &incx );
            error = lapackf77_zlange( "F", &Noffset, &ione, Ycublas, &Noffset, work ) / Ynorm;
            
            bool okay = (error < tol && error2 < tol);
            status += ! okay;
            if ( opts.lapack ) {
                printf( "%5d  %5d   %7.2f (%7.2f)   %7.2f (%7.2f)   %7.2f (%7.2f)   %7.2f (%7.2f)   %8.2e   %8.2e   %s\n",
                        (int) N, (int) offset,
                         cpu_perf,  cpu_time*1000.,
                        cuda_perf, cuda_time*1000.,
                         gpu_perf,  gpu_time*1000.,
                        mgpu_perf, mgpu_time*1000.,
                        error, error2, (okay ? "ok" : "failed") );
            }
            else {
                printf( "%5d  %5d     ---   (  ---  )   %7.2f (%7.2f)   %7.2f (%7.2f)   %7.2f (%7.2f)   %8.2e     ---      %s\n",
                        (int) N, (int) offset,
                        cuda_perf, cuda_time*1000.,
                         gpu_perf,  gpu_time*1000.,
                        mgpu_perf, mgpu_time*1000.,
                        error, (okay ? "ok" : "failed") );
            }
            
            /* Free Memory */
            TESTING_FREE_CPU( A );
            TESTING_FREE_CPU( Y );
            TESTING_FREE_CPU( Ycublas );
            TESTING_FREE_CPU( Ymagma  );
            TESTING_FREE_CPU( Ymagma1 );
            TESTING_FREE_CPU( Ylapack );

            TESTING_FREE_PIN( X );
            TESTING_FREE_PIN( hwork   );
            
            magma_setdevice( opts.device );
            TESTING_FREE_DEV( dA );
            TESTING_FREE_DEV( dX );
            TESTING_FREE_DEV( dY );
            
            for( dev=0; dev < opts.ngpu; dev++ ) {
                magma_setdevice( dev );
                TESTING_FREE_DEV( d_lA[dev]  );
                TESTING_FREE_DEV( dwork[dev] );
            }
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
        
      // comment out these two lines line & top of loop test a specific offset
      }  // end for ioffset
      printf( "\n" );
    }
    
    for( dev=0; dev < opts.ngpu; ++dev ) {
        magma_queue_destroy( queues[dev] );
    }
    
    opts.cleanup();
    TESTING_FINALIZE();
    return status;
}
Beispiel #3
0
extern "C" double
magma_zlatrd_mgpu(magma_int_t num_gpus, char uplo,
                  magma_int_t n0, magma_int_t n, magma_int_t nb, magma_int_t nb0,
                  magmaDoubleComplex *a,  magma_int_t lda,
                  double *e, magmaDoubleComplex *tau,
                  magmaDoubleComplex *w,   magma_int_t ldw,
                  magmaDoubleComplex **da, magma_int_t ldda, magma_int_t offset,
                  magmaDoubleComplex **dw, magma_int_t lddw,
                  magmaDoubleComplex *dwork[MagmaMaxGPUs], magma_int_t ldwork,
                  magma_int_t k,
                  magmaDoubleComplex  *dx[MagmaMaxGPUs], magmaDoubleComplex *dy[MagmaMaxGPUs],
                  magmaDoubleComplex *work,
                  magma_queue_t stream[][10],
                  double *times)
{
/*  -- MAGMA (version 1.4.1) --
       Univ. of Tennessee, Knoxville
       Univ. of California, Berkeley
       Univ. of Colorado, Denver
       December 2013

    Purpose
    =======
    ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to
    Hermitian tridiagonal form by an orthogonal similarity
    transformation Q' * A * Q, and returns the matrices V and W which are
    needed to apply the transformation to the unreduced part of A.

    If UPLO = 'U', ZLATRD reduces the last NB rows and columns of a
    matrix, of which the upper triangle is supplied;
    if UPLO = 'L', ZLATRD reduces the first NB rows and columns of a
    matrix, of which the lower triangle is supplied.

    This is an auxiliary routine called by ZHETRD.

    Arguments
    =========
    UPLO    (input) CHARACTER*1
            Specifies whether the upper or lower triangular part of the
            Hermitian matrix A is stored:
            = 'U': Upper triangular
            = 'L': Lower triangular

    N       (input) INTEGER
            The order of the matrix A.

    NB      (input) INTEGER
            The number of rows and columns to be reduced.

    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, and the strictly lower
            triangular part of A is not referenced.  If UPLO = 'L', the
            leading n-by-n lower triangular part of A contains the lower
            triangular part of the matrix A, and the strictly upper
            triangular part of A is not referenced.
            On exit:
            if UPLO = 'U', the last NB columns have been reduced to
              tridiagonal form, with the diagonal elements overwriting
              the diagonal elements of A; the elements above the diagonal
              with the array TAU, represent the orthogonal matrix Q as a
              product of elementary reflectors;
            if UPLO = 'L', the first NB columns have been reduced to
              tridiagonal form, with the diagonal elements overwriting
              the diagonal elements of A; the elements below the diagonal
              with the array TAU, represent the  orthogonal matrix Q as a
              product of elementary reflectors.
            See Further Details.

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

    E       (output) COMPLEX_16 array, dimension (N-1)
            If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal
            elements of the last NB columns of the reduced matrix;
            if UPLO = 'L', E(1:nb) contains the subdiagonal elements of
            the first NB columns of the reduced matrix.

    TAU     (output) COMPLEX_16 array, dimension (N-1)
            The scalar factors of the elementary reflectors, stored in
            TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.
            See Further Details.

    W       (output) COMPLEX_16 array, dimension (LDW,NB)
            The n-by-nb matrix W required to update the unreduced part
            of A.

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

    Further Details
    ===============
    If UPLO = 'U', the matrix Q is represented as a product of elementary
    reflectors

       Q = H(n) H(n-1) . . . H(n-nb+1).

    Each H(i) has the form

       H(i) = I - tau * v * v'

    where tau is a complex scalar, and v is a complex vector with
    v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
    and tau in TAU(i-1).

    If UPLO = 'L', the matrix Q is represented as a product of elementary
    reflectors

       Q = H(1) H(2) . . . H(nb).

    Each H(i) has the form

       H(i) = I - tau * v * v'

    where tau is a complex scalar, and v is a complex vector with
    v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
    and tau in TAU(i).

    The elements of the vectors v together form the n-by-nb matrix V
    which is needed, with W, to apply the transformation to the unreduced
    part of the matrix, using a Hermitian rank-2k update of the form:
    A := A - V*W' - W*V'.

    The contents of A on exit are illustrated by the following examples
    with n = 5 and nb = 2:

    if UPLO = 'U':                       if UPLO = 'L':

      (  a   a   a   v4  v5 )              (  d                  )
      (      a   a   v4  v5 )              (  1   d              )
      (          a   1   v5 )              (  v1  1   a          )
      (              d   1  )              (  v1  v2  a   a      )
      (                  d  )              (  v1  v2  a   a   a  )

    where d denotes a diagonal element of the reduced matrix, a denotes
    an element of the original matrix that is unchanged, and vi denotes
    an element of the vector defining H(i).
    =====================================================================    */

    char uplo_[2]  = {uplo, 0};

    double mv_time = 0.0;
    magma_int_t i;
#ifndef MAGMABLAS_ZHEMV_MGPU
    magma_int_t loffset = nb0*((offset/nb0)/num_gpus);
#endif

    magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
    magmaDoubleComplex c_one     = MAGMA_Z_ONE;
    magmaDoubleComplex c_zero    = MAGMA_Z_ZERO;
    magmaDoubleComplex value     = MAGMA_Z_ZERO;
    magma_int_t id, idw, i_one = 1;

    //magma_int_t kk;
    magma_int_t ione = 1;

    magma_int_t i_n, i_1, iw;

    magmaDoubleComplex alpha;

    magmaDoubleComplex *dx2[MagmaMaxGPUs];
    magmaDoubleComplex *f = (magmaDoubleComplex *)malloc(n*sizeof(magmaDoubleComplex ));

    if (n <= 0) {
        return 0;
    }

//#define PROFILE_SYMV
#ifdef PROFILE_SYMV
    magma_event_t start, stop;
    float etime;
    magma_timestr_t cpu_start, cpu_end;
    magma_setdevice(0);
    magma_event_create( &start );
    magma_event_create( &stop  );
#endif

    if (lapackf77_lsame(uplo_, "U")) {
        /* Reduce last NB columns of upper triangle */
        for (i = n-1; i >= n - nb ; --i) {
            i_1 = i + 1;
            i_n = n - i - 1;
            iw = i - n + nb;
            if (i < n-1) {
                /* Update A(1:i,i) */
                magmaDoubleComplex wii = *W(i, iw+1);
                #if defined(PRECISION_z) || defined(PRECISION_c)
                    lapackf77_zlacgv(&i_one, &wii, &ldw);
                #endif
                wii = -wii;
                blasf77_zaxpy(&i_1, &wii, A(0, i+1), &i_one, A(0, i), &ione);

                wii = *A(i, i+1);
                #if defined(PRECISION_z) || defined(PRECISION_c)
                    lapackf77_zlacgv(&i_one, &wii, &ldw);
                #endif
                wii = -wii;
                blasf77_zaxpy(&i_1, &wii, W(0, iw+1), &i_one, A(0, i), &ione);
            }
            if (i > 0) {
                /* Generate elementary reflector H(i) to annihilate A(1:i-2,i) */
                alpha = *A(i-1, i);
                lapackf77_zlarfg(&i, &alpha, A(0, i), &ione, &tau[i - 1]);

                e[i-1] = MAGMA_Z_REAL( alpha );
                *A(i-1,i) = MAGMA_Z_MAKE( 1, 0 );
                for( id=0; id<num_gpus; id++ ) {
                    magma_setdevice(id);
                    dx2[id] = dW1(id, 0, iw);
                    magma_zsetvector_async( n, A(0,i), 1, dW1(id, 0, iw), 1, stream[id][0]);
#ifndef  MAGMABLAS_ZHEMV_MGPU
                    magma_zsetvector_async( i, A(0,i), 1, dx[id], 1, stream[id][0] );
#endif
                }
                magmablas_zhemv_mgpu(num_gpus, k, 'U', i, nb0, c_one, da, ldda, 0,
                                     dx2, ione, c_zero, dy, ione, dwork, ldwork,
                                     work, W(0, iw), stream );

                if (i < n-1) {
                    blasf77_zgemv(MagmaConjTransStr, &i, &i_n, &c_one, W(0, iw+1), &ldw,
                                  A(0, i), &ione, &c_zero, W(i+1, iw), &ione);
                }

                /* overlap update */
                if( i < n-1 && i-1 >= n - nb )
                {
                    magma_int_t im1_1 = i_1 - 1;
                    magma_int_t im1   = i-1;
                    /* Update A(1:i,i) */
                    #if defined(PRECISION_z) || defined(PRECISION_c)
                        magma_int_t im1_n = i_n + 1;
                        lapackf77_zlacgv(&im1_n, W(im1, iw+1), &ldw);
                    #endif
                    blasf77_zgemv("No transpose", &im1_1, &i_n, &c_neg_one, A(0, i+1), &lda,
                                  W(im1, iw+1), &ldw, &c_one, A(0, i-1), &ione);
                    #if defined(PRECISION_z) || defined(PRECISION_c)
                        lapackf77_zlacgv(&im1_n, W(im1, iw+1), &ldw);
                        lapackf77_zlacgv(&im1_n, A(im1, i +1), &lda);
                    #endif
                    blasf77_zgemv("No transpose", &im1_1, &i_n, &c_neg_one, W(0, iw+1), &ldw,
                                  A(im1, i+1), &lda, &c_one, A(0, i-1), &ione);
                    #if defined(PRECISION_z) || defined(PRECISION_c)
                        lapackf77_zlacgv(&im1_n, A(im1, i+1), &lda);
                    #endif
                }

                // 3. Here is where we need it // TODO find the right place
                magmablas_zhemv_sync(num_gpus, k, i, work, W(0, iw), stream );

                if (i < n-1) {
                    blasf77_zgemv("No transpose", &i, &i_n, &c_neg_one, A(0, i+1), &lda,
                                  W(i+1, iw), &ione, &c_one, W(0, iw), &ione);

                    blasf77_zgemv(MagmaConjTransStr, &i, &i_n, &c_one, A(0, i+1), &lda,
                                  A(0, i), &ione, &c_zero, W(i+1, iw), &ione);

                    blasf77_zgemv("No transpose", &i, &i_n, &c_neg_one, W(0, iw+1), &ldw,
                                  W(i+1, iw), &ione, &c_one, W(0, iw), &ione);
                }

                blasf77_zscal(&i, &tau[i - 1], W(0, iw), &ione);

                #if defined(PRECISION_z) || defined(PRECISION_c)
                cblas_zdotc_sub( i, W(0,iw), ione, A(0,i), ione, &value );
                #else
                value = cblas_zdotc( i, W(0,iw), ione, A(0,i), ione );
                #endif
                alpha = tau[i - 1] * -.5f * value;
                blasf77_zaxpy(&i, &alpha, A(0, i), &ione, W(0, iw), &ione);

                for( id=0; id<num_gpus; id++ ) {
                    magma_setdevice(id);
                    if( k > 1 ) {
                        magma_zsetvector_async( n, W(0,iw), 1, dW(id, 0, iw), 1, stream[id][1] );
                    } else {
                        magma_zsetvector_async( n, W(0,iw), 1, dW(id, 0, iw), 1, stream[id][0] );
                    }
                }
            }
        }
    } else {
        /*  Reduce first NB columns of lower triangle */
        for (i = 0; i < nb; ++i) {
            /* Update A(i:n,i) */
            i_n = n - i;
            idw = ((offset+i)/nb)%num_gpus;
            if( i > 0 ) {
                trace_cpu_start( 0, "gemv", "gemv" );
                magmaDoubleComplex wii = *W(i, i-1);
                #if defined(PRECISION_z) || defined(PRECISION_c)
                    lapackf77_zlacgv(&i_one, &wii, &ldw);
                #endif
                wii = -wii;
                blasf77_zaxpy( &i_n, &wii, A(i, i-1), &ione, A(i, i), &ione);

                wii = *A(i, i-1);
                #if defined(PRECISION_z) || defined(PRECISION_c)
                    lapackf77_zlacgv(&i_one, &wii, &lda);
                #endif
                wii = -wii;
                blasf77_zaxpy( &i_n, &wii, W(i, i-1), &ione, A(i, i), &ione);
            }

            if (i < n-1) {
                /* Generate elementary reflector H(i) to annihilate A(i+2:n,i) */
                i_n = n - i - 1;
                trace_cpu_start( 0, "larfg", "larfg" );
                alpha = *A(i+1, i);
#ifdef PROFILE_SYMV
                cpu_start = get_current_time();
#endif
                lapackf77_zlarfg(&i_n, &alpha, A(min(i+2,n-1), i), &ione, &tau[i]);
#ifdef PROFILE_SYMV
                cpu_end = get_current_time();
                times[0] += GetTimerValue(cpu_start,cpu_end)/1000.0;
#endif
                e[i] = MAGMA_Z_REAL( alpha );
                *A(i+1,i) = MAGMA_Z_MAKE( 1, 0 );
                trace_cpu_end( 0 );

                /* Compute W(i+1:n,i) */
                // 1. Send the block reflector  A(i+1:n,i) to the GPU
                //trace_gpu_start(  idw, 0, "comm", "comm1" );
#ifndef  MAGMABLAS_ZHEMV_MGPU
                magma_setdevice(idw);
                magma_zsetvector( i_n, A(i+1,i), 1, dA(idw, i+1, i), 1 );
#endif
                for( id=0; id<num_gpus; id++ ) {
                    magma_setdevice(id);
                    trace_gpu_start( id, 0, "comm", "comm" );
#ifdef MAGMABLAS_ZHEMV_MGPU
                    dx2[id] = dW1(id, 0, i)-offset;
#else
                    dx2[id] = dx[id];
                    magma_zsetvector( i_n, A(i+1,i), 1, dx[id], 1 );
#endif
                    magma_zsetvector_async( n, A(0,i), 1, dW1(id, 0, i), 1, stream[id][0] );
                    trace_gpu_end( id, 0 );
                }
                /* mat-vec on multiple GPUs */
#ifdef PROFILE_SYMV
                magma_setdevice(0);
                magma_event_record(start, stream[0][0]);
#endif
                magmablas_zhemv_mgpu(num_gpus, k, 'L', i_n, nb0, c_one, da, ldda, offset+i+1,
                                       dx2, ione, c_zero, dy, ione, dwork, ldwork,
                                       work, W(i+1,i), stream );
#ifdef PROFILE_SYMV
                magma_setdevice(0);
                magma_event_record(stop, stream[0][0]);
#endif
                trace_cpu_start( 0, "gemv", "gemv" );
                blasf77_zgemv(MagmaConjTransStr, &i_n, &i, &c_one, W(i+1, 0), &ldw,
                              A(i+1, i), &ione, &c_zero, W(0, i), &ione);
                blasf77_zgemv("No transpose", &i_n, &i, &c_neg_one, A(i+1, 0), &lda,
                              W(0, i), &ione, &c_zero, f, &ione);
                blasf77_zgemv(MagmaConjTransStr, &i_n, &i, &c_one, A(i+1, 0), &lda,
                              A(i+1, i), &ione, &c_zero, W(0, i), &ione);
                trace_cpu_end( 0 );

                /* overlap update */
                if( i > 0 && i+1 < n )
                {
                    magma_int_t ip1 = i+1;
                    trace_cpu_start( 0, "gemv", "gemv" );
                    #if defined(PRECISION_z) || defined(PRECISION_c)
                        lapackf77_zlacgv(&i, W(ip1, 0), &ldw);
                    #endif
                    blasf77_zgemv("No transpose", &i_n, &i, &c_neg_one, A(ip1, 0), &lda,
                                  W(ip1, 0), &ldw, &c_one, A(ip1, ip1), &ione);
                    #if defined(PRECISION_z) || defined(PRECISION_c)
                        lapackf77_zlacgv(&i, W(ip1, 0), &ldw);
                        lapackf77_zlacgv(&i, A(ip1 ,0), &lda);
                    #endif
                    blasf77_zgemv("No transpose", &i_n, &i, &c_neg_one, W(ip1, 0), &ldw,
                                  A(ip1, 0), &lda, &c_one, A(ip1, ip1), &ione);
                    #if defined(PRECISION_z) || defined(PRECISION_c)
                        lapackf77_zlacgv(&i, A(ip1, 0), &lda);
                    #endif
                    trace_cpu_end( 0 );
                }

                /* synchronize */
                magmablas_zhemv_sync(num_gpus, k, i_n, work, W(i+1,i), stream );
#ifdef PROFILE_SYMV
                cudaEventElapsedTime(&etime, start, stop);
                mv_time += (etime/1000.0);
                times[1+(i_n/(n0/10))] += (etime/1000.0);
#endif
                trace_cpu_start( 0, "axpy", "axpy" );
                if (i!=0)
                    blasf77_zaxpy(&i_n, &c_one, f, &ione, W(i+1, i), &ione);

                blasf77_zgemv("No transpose", &i_n, &i, &c_neg_one, W(i+1, 0), &ldw,
                              W(0, i), &ione, &c_one, W(i+1, i), &ione);
                blasf77_zscal(&i_n, &tau[i], W(i+1,i), &ione);

                #if defined(PRECISION_z) || defined(PRECISION_c)
                    cblas_zdotc_sub( i_n, W(i+1,i), ione, A(i+1,i), ione, &value );
                #else
                    value = cblas_zdotc( i_n, W(i+1,i), ione, A(i+1,i), ione );
                #endif
                alpha = tau[i]* -.5f * value;
                blasf77_zaxpy(&i_n, &alpha, A(i+1, i), &ione, W(i+1,i), &ione);
                trace_cpu_end( 0 );
                for( id=0; id<num_gpus; id++ ) {
                    magma_setdevice(id);
                    if( k > 1 ) {
                        magma_zsetvector_async( n, W(0,i), 1, dW(id, 0, i), 1, stream[id][1] );
                    } else {
                        magma_zsetvector_async( n, W(0,i), 1, dW(id, 0, i), 1, stream[id][0] );
                    }
                }
            }
        }
    }

#ifdef PROFILE_SYMV
    magma_setdevice(0);
    magma_event_destory( start );
    magma_event_destory( stop  );
#endif
    for( id=0; id<num_gpus; id++ ) {
        magma_setdevice(id);
        if( k > 1) magma_queue_sync(stream[id][1]);
    }
    free(f);

    return mv_time;
} /* zlatrd_ */