Example #1
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing spotrf
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    real_Double_t   gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
    float *h_A, *h_R;
    magmaFloat_ptr d_A;
    magma_int_t N, n2, lda, ldda, info;
    float c_neg_one = MAGMA_S_NEG_ONE;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    float      work[1], error;
    magma_int_t     status = 0;

    magma_opts opts;
    parse_opts( argc, argv, &opts );
    opts.lapack |= opts.check;  // check (-c) implies lapack (-l)
    
    float tol = opts.tolerance * lapackf77_slamch("E");
    
    printf("uplo = %s\n", lapack_uplo_const(opts.uplo) );
    printf("  N     CPU GFlop/s (sec)   GPU GFlop/s (sec)   ||R_magma - R_lapack||_F / ||R_lapack||_F\n");
    printf("========================================================\n");
    for( int itest = 0; itest < opts.ntest; ++itest ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            N   = opts.nsize[itest];
            lda = N;
            n2  = lda*N;
            ldda = ((N+31)/32)*32;
            gflops = FLOPS_SPOTRF( N ) / 1e9;
            
            TESTING_MALLOC_CPU( h_A, float, n2     );
            TESTING_MALLOC_PIN( h_R, float, n2     );
            TESTING_MALLOC_DEV( d_A, float, ldda*N );
            
            /* Initialize the matrix */
            lapackf77_slarnv( &ione, ISEED, &n2, h_A );
            magma_smake_hpd( N, h_A, lda );
            lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
            magma_ssetmatrix( N, N, h_A, lda, d_A, ldda );
            
            /* ====================================================================
               Performs operation using MAGMA
               =================================================================== */
            gpu_time = magma_wtime();
            magma_spotrf_gpu( opts.uplo, N, d_A, ldda, &info );
            gpu_time = magma_wtime() - gpu_time;
            gpu_perf = gflops / gpu_time;
            if (info != 0)
                printf("magma_spotrf_gpu returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            
            if ( opts.lapack ) {
                /* =====================================================================
                   Performs operation using LAPACK
                   =================================================================== */
                cpu_time = magma_wtime();
                lapackf77_spotrf( lapack_uplo_const(opts.uplo), &N, h_A, &lda, &info );
                cpu_time = magma_wtime() - cpu_time;
                cpu_perf = gflops / cpu_time;
                if (info != 0)
                    printf("lapackf77_spotrf returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
                
                /* =====================================================================
                   Check the result compared to LAPACK
                   =================================================================== */
                magma_sgetmatrix( N, N, d_A, ldda, h_R, lda );
                error = lapackf77_slange("f", &N, &N, h_A, &lda, work);
                blasf77_saxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
                error = lapackf77_slange("f", &N, &N, h_R, &lda, work) / error;
                
                printf("%5d   %7.2f (%7.2f)   %7.2f (%7.2f)   %8.2e   %s\n",
                       (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time,
                       error, (error < tol ? "ok" : "failed") );
                status += ! (error < tol);
            }
            else {
                printf("%5d     ---   (  ---  )   %7.2f (%7.2f)     ---  \n",
                       (int) N, gpu_perf, gpu_time );
            }
            TESTING_FREE_CPU( h_A );
            TESTING_FREE_PIN( h_R );
            TESTING_FREE_DEV( d_A );
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }

    TESTING_FINALIZE();
    return status;
}
Example #2
0
int main( int argc, char** argv)
{
    real_Double_t gflops, gpu_perf, cpu_perf, gpu_time, cpu_time;
    float *h_R = NULL, *h_P = NULL;
    magmaFloat_ptr d_lA[MagmaMaxSubs * MagmaMaxGPUs];
    magma_int_t N = 0, n2, lda, ldda;
    magma_int_t size[10] =
        { 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000 };
    
    magma_int_t i, j, k, check = 0, info;
    float mz_one = MAGMA_S_NEG_ONE;
    magma_int_t ione     = 1;
   
    magma_int_t num_gpus0 = 1, num_gpus, num_subs0 = 1, num_subs, tot_subs, flag = 0;
    magma_int_t nb, n_local, nk;

    magma_uplo_t uplo = MagmaLower;

    if (argc != 1){
        for(i = 1; i<argc; i++){
            if (strcmp("-N", argv[i]) == 0){
                N = atoi(argv[++i]);
                if (N > 0) {
                    size[0] = size[9] = N;
                    flag = 1;
                }
            }
            if(strcmp("-NGPU", argv[i]) == 0)
                num_gpus0 = atoi(argv[++i]);
            if(strcmp("-NSUB", argv[i]) == 0)
                num_subs0 = atoi(argv[++i]);
            if(strcmp("-UPLO", argv[i]) == 0)
                uplo = (strcmp("L", argv[++i]) == 0 ? MagmaLower :  MagmaUpper);
            if(strcmp("-check", argv[i]) == 0)
                check = 1;
        }
    }

    /* Initialize */
    magma_queue_t  queues[2*MagmaMaxGPUs];
    magma_device_t devices[ MagmaMaxGPUs ];
    magma_int_t num = 0;
    magma_int_t err;
    magma_init();
    err = magma_getdevices( devices, MagmaMaxGPUs, &num );
    if ( err != 0 || num < 1 ) {
        fprintf( stderr, "magma_getdevices failed: %d\n", (int) err );
        exit(-1);
    }
    for(i=0;i<num_gpus0;i++){
        err = magma_queue_create( devices[i], &queues[2*i] );
        if ( err != 0 ) {
            fprintf( stderr, "magma_queue_create failed: %d\n", (int) err );
            exit(-1);
        }
        err = magma_queue_create( devices[i], &queues[2*i+1] );
        if ( err != 0 ) {
            fprintf( stderr, "magma_queue_create failed: %d\n", (int) err );
            exit(-1);
        }
    }

    printf("\nUsing %d GPUs:\n", num_gpus0);
    printf("  testing_spotrf_msub -N %d -NGPU %d -NSUB %d -UPLO %c %s\n\n", size[0], num_gpus0,num_subs0,
           (uplo == MagmaLower ? 'L' : 'U'),(check == 1 ? "-check" : " "));

    printf("  N    CPU GFlop/s (sec)    GPU GFlop/s (sec)    ||R_magma-R_lapack||_F / ||R_lapack||_F\n");
    printf("========================================================================================\n");
    for(i=0; i<10; i++){
        N   = size[i];
        lda = N;
        n2  = lda*N;
        gflops = FLOPS_SPOTRF( N ) / 1e9;;
        nb = magma_get_spotrf_nb(N);
        if (num_subs0*num_gpus0 > N/nb) {
            num_gpus = N/nb;
            num_subs = 1;
            if(N%nb != 0) num_gpus ++;
            printf("too many GPUs for the matrix size, using %d GPUs\n", (int)num_gpus);
        } else {
            num_gpus = num_gpus0;
            num_subs = num_subs0;
        }
        tot_subs = num_subs * num_gpus;
        
        /* Allocate host memory for the matrix */
        #ifdef USE_PINNED_CLMEMORY
        cl_mem buffer1 = clCreateBuffer(gContext, CL_MEM_READ_WRITE | CL_MEM_ALLOC_HOST_PTR, n2*sizeof(float), NULL, NULL);
        cl_mem buffer2 = clCreateBuffer(gContext, CL_MEM_READ_WRITE | CL_MEM_ALLOC_HOST_PTR, lda*nb*sizeof(float), NULL, NULL);
        for (k=0; k<num_gpus; k++) {
            h_R = (float*)clEnqueueMapBuffer(queues[2*k], buffer1, CL_TRUE, CL_MAP_READ | CL_MAP_WRITE, 0, 
                                                          n2*sizeof(float), 0, NULL, NULL, NULL);
            h_P = (float*)clEnqueueMapBuffer(queues[2*k], buffer2, CL_TRUE, CL_MAP_READ | CL_MAP_WRITE, 0, 
                                                          lda*nb*sizeof(float), 0, NULL, NULL, NULL);
        }
        #else
        TESTING_MALLOC_PIN( h_P, float, lda*nb );
        TESTING_MALLOC_PIN( h_R, float, n2     );
        #endif
        /* Initialize the matrix */
        init_matrix( N, h_R, lda );

        /* Allocate GPU memory */
        if (uplo == MagmaUpper) {
            ldda    = ((N+nb-1)/nb)*nb;    
            n_local = ((N+nb*tot_subs-1)/(nb*tot_subs))*nb;
        } else {
            ldda    = ((N+nb*tot_subs-1)/(nb*tot_subs))*nb;
            n_local = ((N+nb-1)/nb)*nb;
        }
        for (j=0; j<tot_subs; j++) {
            TESTING_MALLOC_DEV( d_lA[j], float, n_local*ldda );
        }

        /* Warm up to measure the performance */
        /* distribute matrix to gpus */
        if (uplo == MagmaUpper) {
            for (j=0; j<N; j+=nb) {
                k = (j/nb)%tot_subs;
                nk = min(nb, N-j);
                magma_ssetmatrix( j+nk, nk, 
                                 &h_R[j*lda], lda,
                                 d_lA[k], j/(nb*tot_subs)*nb*ldda, ldda, 
                                 queues[2*(k%num_gpus)]);
            }
        } else {
            for (j=0; j<N; j+=nb) {
                nk = min(nb, N-j);
                for (magma_int_t kk = 0; kk<tot_subs; kk++) {
                    magma_int_t mk = 0;
                    for (magma_int_t ii=j+kk*nb; ii<N; ii+=nb*tot_subs) {
                        magma_int_t mii = min(nb, N-ii);
                        lapackf77_slacpy( MagmaFullStr, &mii, &nk, &h_R[ii+j*lda], &lda, &h_P[mk], &lda );
                        mk += mii;
                    }
                    k = ((j+kk*nb)/nb)%tot_subs;
                    if (mk > 0 && nk > 0) {
                        magma_ssetmatrix( mk, nk, 
                                         h_P, lda,
                                         d_lA[k], j*ldda+(j+kk*nb)/(nb*tot_subs)*nb, ldda, 
                                         queues[2*(k%num_gpus)]);
                    }
                }
            }
            /*for (j=0; j<N; j+=nb) {
                k = (j/nb)%tot_subs;
                nk = min(nb, N-j);
                magma_ssetmatrix( nk, j+nk, &h_R[j], lda,
                                    d_lA[k], j/(nb*tot_subs)*nb, ldda,
                                    queues[2*(k%num_gpus)]);
            }*/
        }
        magma_spotrf_msub( num_subs, num_gpus, uplo, N, d_lA, 0, ldda, queues, &info );

        /* ====================================================================
           Performs operation using MAGMA
           =================================================================== */
        /* distribute matrix to gpus */
        if (uplo == MagmaUpper) {
            for (j=0; j<N; j+=nb) {
                k = (j/nb)%tot_subs;
                nk = min(nb, N-j);
                magma_ssetmatrix( j+nk, nk, 
                                 &h_R[j*lda], lda,
                                 d_lA[k], j/(nb*tot_subs)*nb*ldda, ldda, 
                                 queues[2*(k%num_gpus)]);
            }
        } else {
            for (j=0; j<N; j+=nb) {
                nk = min(nb, N-j);
                for (magma_int_t kk = 0; kk<tot_subs; kk++) {
                    magma_int_t mk = 0;
                    for (magma_int_t ii=j+kk*nb; ii<N; ii+=nb*tot_subs) {
                        magma_int_t mii = min(nb, N-ii);
                        lapackf77_slacpy( MagmaFullStr, &mii, &nk, &h_R[ii+j*lda], &lda, &h_P[mk], &lda );
                        mk += mii;
                    }
                    k = ((j+kk*nb)/nb)%tot_subs;
                    if (mk > 0 && nk > 0) {
                        magma_ssetmatrix( mk, nk, 
                                         h_P, lda,
                                         d_lA[k], j*ldda+(j+kk*nb)/(nb*tot_subs)*nb, ldda, 
                                         queues[2*(k%num_gpus)]);
                    }
                }
            }
            /*for (j=0; j<N; j+=nb) {
                k = (j/nb)%tot_subs;
                nk = min(nb, N-j);
                magma_ssetmatrix( nk, j+nk, &h_R[j], lda,
                                    d_lA[k], (j/(nb*tot_subs)*nb), ldda,
                                    queues[2*(k%num_gpus)]);
            }*/
        }
    
        gpu_time = magma_wtime();
        magma_spotrf_msub( num_subs, num_gpus, uplo, N, d_lA, 0, ldda, queues, &info );
        gpu_time = magma_wtime() - gpu_time;
        gpu_perf = gflops / gpu_time;
        if (info != 0)
            printf( "magma_spotrf had error %d.\n", info );
       
        /* gather matrix from gpus */
        if (uplo==MagmaUpper) {
            for (j=0; j<N; j+=nb) {
                k = (j/nb)%tot_subs;
                nk = min(nb, N-j);
                magma_sgetmatrix( j+nk, nk,
                                 d_lA[k], j/(nb*tot_subs)*nb*ldda, ldda,
                                 &h_R[j*lda], lda, queues[2*(k%num_gpus)]);
            }
        } else {
            for (j=0; j<N; j+=nb) {
                nk = min(nb, N-j);
                for (magma_int_t kk = 0; kk<tot_subs; kk++) {
                    k = ((j+kk*nb)/nb)%tot_subs;
                    magma_int_t mk = 0;
                    mk = 0;
                    for (magma_int_t ii=j+kk*nb; ii<N; ii+=nb*tot_subs) {
                        mk += min(nb, N-ii);
                    }
                    if (mk > 0 && nk > 0) {
                        magma_sgetmatrix( mk, nk, 
                                         d_lA[k], j*ldda+(j+kk*nb)/(nb*tot_subs)*nb, ldda, 
                                         h_P, lda,
                                         queues[2*(k%num_gpus)]);
                    }
                    mk = 0;
                    for (magma_int_t ii=j+kk*nb; ii<N; ii+=nb*tot_subs) {
                        magma_int_t mii = min(nb, N-ii);
                        lapackf77_slacpy( MagmaFullStr, &mii, &nk, &h_P[mk], &lda, &h_R[ii+j*lda], &lda );
                        mk += mii;
                    }
                }
            }
            /*for (j=0; j<N; j+=nb) {
                k = (j/nb)%tot_subs;
                nk = min(nb, N-j);
                magma_sgetmatrix( nk, j+nk, 
                            d_lA[k], (j/(nb*tot_subs)*nb), ldda, 
                            &h_R[j], lda, queues[2*(k%num_gpus)] );
            }*/
        }

        /* =====================================================================
           Performs operation using LAPACK
           =================================================================== */
        if (check == 1) {
            float work[1], matnorm, diffnorm;
            float *h_A;
            TESTING_MALLOC_PIN( h_A, float, n2 );
            init_matrix( N, h_A, lda );

            cpu_time = magma_wtime();
            if (uplo == MagmaLower) {
                lapackf77_spotrf( MagmaLowerStr, &N, h_A, &lda, &info );
            } else {
                lapackf77_spotrf( MagmaUpperStr, &N, h_A, &lda, &info );
            }
            cpu_time = magma_wtime() - cpu_time;
            cpu_perf = gflops / cpu_time;
            if (info != 0)
                printf( "lapackf77_spotrf had error %d.\n", info );
        
            /* =====================================================================
               Check the result compared to LAPACK
               |R_magma - R_lapack| / |R_lapack|
               =================================================================== */
            matnorm = lapackf77_slange("f", &N, &N, h_A, &lda, work);
            blasf77_saxpy(&n2, &mz_one, h_A, &ione, h_R, &ione);
            diffnorm = lapackf77_slange("f", &N, &N, h_R, &lda, work);
            printf( "%5d     %6.2f (%6.2f)     %6.2f (%6.2f)         %e\n",
                    N, cpu_perf, cpu_time, gpu_perf, gpu_time, diffnorm / matnorm );
        
            TESTING_FREE_PIN( h_A );
        } else {
            printf( "%5d      - -     (- -)     %6.2f (%6.2f)          - -\n",
                    N, gpu_perf, gpu_time );
        }
        // free memory
        #ifdef USE_PINNED_CLMEMORY
        for (k=0; k<num_gpus; k++) {
            clEnqueueUnmapMemObject(queues[2*k], buffer1, h_R, 0, NULL, NULL);
            clEnqueueUnmapMemObject(queues[2*k], buffer2, h_P, 0, NULL, NULL);
        }
        clReleaseMemObject(buffer1);
        clReleaseMemObject(buffer2);
        #else
        TESTING_FREE_PIN( h_P );
        TESTING_FREE_PIN( h_R );
        #endif
        for (j=0; j<tot_subs; j++) {
            TESTING_FREE_DEV( d_lA[j] );
        }
        if (flag != 0)
            break;
    }

    /* clean up */
    for (i=0; i<num_gpus; i++) {
        magma_queue_destroy( queues[2*i] );
        magma_queue_destroy( queues[2*i+1] );
    }
    magma_finalize();
    return 0;
}
Example #3
0
/**
    Purpose
    -------
    SGEGQR orthogonalizes the N vectors given by a real M-by-N matrix A:
           
            A = Q * R.

    On exit, if successful, the orthogonal vectors Q overwrite A
    and R is given in work (on the CPU memory).
    The routine is designed for tall-and-skinny matrices: M >> N, N <= 128.
    
    This version uses normal equations and SVD in an iterative process that
    makes the computation numerically accurate.
    
    Arguments
    ---------
    @param[in]
    ikind   INTEGER
            Several versions are implemented indiceted by the ikind value:  
            1:  This version uses normal equations and SVD in an iterative process 
                that makes the computation numerically accurate.
            2:  This version uses a standard LAPACK-based orthogonalization through
                MAGMA's QR panel factorization (magma_sgeqr2x3_gpu) and magma_sorgqr
            3:  MGS
            4.  Cholesky QR [ Note: this method uses the normal equations which 
                                    squares the condition number of A, therefore 
                                    ||I - Q'Q|| < O(eps cond(A)^2)               ]

    @param[in]
    m       INTEGER
            The number of rows of the matrix A.  m >= n >= 0.

    @param[in]
    n       INTEGER
            The number of columns of the matrix A. 128 >= n >= 0.

    @param[in,out]
    dA      REAL array on the GPU, dimension (ldda,n)
            On entry, the m-by-n matrix A.
            On exit, the m-by-n matrix Q with orthogonal columns.

    @param[in]
    ldda     INTEGER
            The leading dimension of the array dA.  LDDA >= max(1,m).
            To benefit from coalescent memory accesses LDDA must be
            divisible by 16.

    @param
    dwork   (GPU workspace) REAL array, dimension: 
            n^2                    for ikind = 1
            3 n^2 + min(m, n) + 2  for ikind = 2 
            0 (not used)           for ikind = 3
            n^2                    for ikind = 4           

    @param[out]
    work    (CPU workspace) REAL array, dimension 3 n^2.
            On exit, work(1:n^2) holds the rectangular matrix R.
            Preferably, for higher performance, work should be in pinned memory.
 
    @param[out]
    info    INTEGER
      -     = 0:  successful exit
      -     < 0:  if INFO = -i, the i-th argument had an illegal value
                  or another error occured, such as memory allocation failed.


    @ingroup magma_sgeqrf_comp
    ********************************************************************/
extern "C" magma_int_t
magma_sgegqr_gpu( magma_int_t ikind, magma_int_t m, magma_int_t n,
                  float *dA,   magma_int_t ldda,
                  float *dwork, float *work,
                  magma_int_t *info )
{
    #define work(i_,j_) (work + (i_) + (j_)*n)
    #define dA(i_,j_)   (dA   + (i_) + (j_)*ldda)
    
    magma_int_t i = 0, j, k, n2 = n*n;
    magma_int_t ione = 1;
    float c_zero = MAGMA_S_ZERO;
    float c_one  = MAGMA_S_ONE;
    float cn = 200., mins, maxs;

    /* check arguments */
    *info = 0;
    if (ikind < 1 || ikind > 4) {
        *info = -1;
    } else if (m < 0 || m < n) {
        *info = -2;
    } else if (n < 0 || n > 128) {
        *info = -3;
    } else if (ldda < max(1,m)) {
        *info = -5;
    }
    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }

    if (ikind == 1) {
        // === Iterative, based on SVD ============================================================
        float *U, *VT, *vt, *R, *G, *hwork, *tau;
        float *S;

        R    = work;             // Size n * n
        G    = R    + n*n;       // Size n * n
        VT   = G    + n*n;       // Size n * n
        
        magma_smalloc_cpu( &hwork, 32 + 2*n*n + 2*n);
        if ( hwork == NULL ) {
            *info = MAGMA_ERR_HOST_ALLOC;
            return *info;
        }
        
        magma_int_t lwork=n*n+32; // First part f hwork; used as workspace in svd
        
        U    = hwork + n*n + 32;  // Size n*n
        S    = (float *)(U+n*n); // Size n
        tau  = U + n*n + n;       // Size n
        
#if defined(PRECISION_c) || defined(PRECISION_z)
        float *rwork;
        magma_smalloc_cpu( &rwork, 5*n);
        if ( rwork == NULL ) {
            *info = MAGMA_ERR_HOST_ALLOC;
            return *info;
        }
#endif
        
        do {
            i++;
            
            magma_sgemm(MagmaConjTrans, MagmaNoTrans, n, n, m, c_one, dA, ldda, dA, ldda, c_zero, dwork, n );
            magma_sgetmatrix(n, n, dwork, n, G, n);
            
#if defined(PRECISION_s) || defined(PRECISION_d)
            lapackf77_sgesvd("n", "a", &n, &n, G, &n, S, U, &n, VT, &n,
                             hwork, &lwork, info);
#else
            lapackf77_sgesvd("n", "a", &n, &n, G, &n, S, U, &n, VT, &n,
                             hwork, &lwork, rwork, info);
#endif
            
            mins = 100.f, maxs = 0.f;
            for (k=0; k < n; k++) {
                S[k] = magma_ssqrt( S[k] );
                
                if (S[k] < mins)  mins = S[k];
                if (S[k] > maxs)  maxs = S[k];
            }
            
            for (k=0; k < n; k++) {
                vt = VT + k*n;
                for (j=0; j < n; j++)
                    vt[j] *= S[j];
            }
            lapackf77_sgeqrf(&n, &n, VT, &n, tau, hwork, &lwork, info);
            
            if (i == 1)
                blasf77_scopy(&n2, VT, &ione, R, &ione);
            else
                blasf77_strmm("l", "u", "n", "n", &n, &n, &c_one, VT, &n, R, &n);
            
            magma_ssetmatrix(n, n, VT, n, dwork, n);
            magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit, m, n, c_one, dwork, n, dA, ldda);
            if (mins > 0.00001f)
                cn = maxs/mins;
            
            //fprintf(stderr, "Iteration %d, cond num = %f \n", i, cn);
        } while (cn > 10.f);
        
        magma_free_cpu( hwork );
#if defined(PRECISION_c) || defined(PRECISION_z)
        magma_free_cpu( rwork );
#endif
        // ================== end of ikind == 1 ===================================================
    }
    else if (ikind == 2) {
        // ================== LAPACK based      ===================================================
        magma_int_t min_mn = min(m, n);
        magma_int_t nb = n;

        float *dtau = dwork + 2*n*n, *d_T = dwork, *ddA = dwork + n*n;
        float *tau  = work+n*n;

        magmablas_slaset( MagmaFull, n, n, c_zero, c_zero, d_T, n );
        magma_sgeqr2x3_gpu(m, n, dA, ldda, dtau, d_T, ddA,
                           (float *)(dwork+min_mn+2*n*n), info);
        magma_sgetmatrix( min_mn, 1, dtau, min_mn, tau, min_mn);
        magma_sgetmatrix( n, n, ddA, n, work, n);
        magma_sorgqr_gpu( m, n, n, dA, ldda, tau, d_T, nb, info );
        // ================== end of ikind == 2 ===================================================       
    }
    else if (ikind == 3) {
        // ================== MGS               ===================================================
        for(magma_int_t j = 0; j<n; j++){
            for(magma_int_t i = 0; i<j; i++){
                *work(i, j) = magma_sdot(m, dA(0,i), 1, dA(0,j), 1);
                magma_saxpy(m, -(*work(i,j)),  dA(0,i), 1, dA(0,j), 1);
            }
            for(magma_int_t i = j; i<n; i++)
                *work(i, j) = MAGMA_S_ZERO;
            //*work(j,j) = MAGMA_S_MAKE( magma_snrm2(m, dA(0,j), 1), 0. );
            *work(j,j) = magma_sdot(m, dA(0,j), 1, dA(0,j), 1);
            *work(j,j) = MAGMA_S_MAKE( sqrt(MAGMA_S_REAL( *work(j,j) )), 0.);
            magma_sscal(m, 1./ *work(j,j), dA(0,j), 1);
        }
        // ================== end of ikind == 3 ===================================================
    }
    else if (ikind == 4) {
        // ================== Cholesky QR       ===================================================
        magma_sgemm(MagmaConjTrans, MagmaNoTrans, n, n, m, c_one, dA, ldda, dA, ldda, c_zero, dwork, n );
        magma_sgetmatrix(n, n, dwork, n, work, n);
        lapackf77_spotrf("u", &n, work, &n, info);
        magma_ssetmatrix(n, n, work, n, dwork, n);
        magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit, m, n, c_one, dwork, n, dA, ldda);
        // ================== end of ikind == 4 ===================================================
    }
             
    return *info;
} /* magma_sgegqr_gpu */
Example #4
0
/**
    Purpose
    -------
    SPOTRF_OOC computes the Cholesky factorization of a real symmetric
    positive definite matrix A. This version does not require work
    space on the GPU passed as input. GPU memory is allocated in the
    routine. The matrix A may exceed the GPU memory.

    The factorization has the form
       A = U**H * U,   if UPLO = MagmaUpper, or
       A = L  * L**H,  if UPLO = MagmaLower,
    where U is an upper triangular matrix and L is lower triangular.

    This is the block version of the algorithm, calling Level 3 BLAS.

    Arguments
    ---------
    @param[in]
    num_gpus INTEGER
             The number of GPUs.  num_gpus > 0.

    @param[in]
    uplo     magma_uplo_t
      -      = MagmaUpper:  Upper triangle of A is stored;
      -      = MagmaLower:  Lower triangle of A is stored.

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

    @param[in,out]
    A        REAL array, dimension (LDA,N)
             On entry, the symmetric 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.
    \n
             On exit, if INFO = 0, the factor U or L from the Cholesky
             factorization A = U**H * U or A = L * L**H.
    \n
             Higher performance is achieved if A is in pinned memory, e.g.
             allocated using magma_malloc_pinned.

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

    @param[out]
    info     INTEGER
      -      = 0:  successful exit
      -      < 0:  if INFO = -i, the i-th argument had an illegal value
                   or another error occured, such as memory allocation failed.
      -      > 0:  if INFO = i, the leading minor of order i is not
                   positive definite, and the factorization could not be
                   completed.

    @ingroup magma_sposv_comp
    ********************************************************************/
extern "C" magma_int_t
magma_spotrf_m(magma_int_t num_gpus, magma_uplo_t uplo, magma_int_t n,
               float *A, magma_int_t lda, magma_int_t *info)
{
#define    A(i, j)    (    A      + (j)*lda   + (i))
#define   dA(d, i, j) (dwork[(d)] + (j)*lddla + (i))
#define   dT(d, i, j) (   dt[(d)] + (j)*ldda  + (i))
#define dAup(d, i, j) (dwork[(d)] + (j)*NB    + (i))
#define dTup(d, i, j) (   dt[(d)] + (j)*nb    + (i))

    /* Local variables */
    float                 d_one     =  1.0;
    float                 d_neg_one = -1.0;
    float     c_one     = MAGMA_S_ONE;
    float     c_neg_one = MAGMA_S_NEG_ONE;
    const char* uplo_  = lapack_uplo_const( uplo  );
    int upper = (uplo == MagmaUpper);

    float *dwork[MagmaMaxGPUs], *dt[MagmaMaxGPUs];
    magma_int_t     ldda, lddla, nb, iinfo, n_local[MagmaMaxGPUs], J2, d, num_gpus0 = num_gpus;
    magma_int_t     j, jj, jb, J, JB, NB, MB, h;
    magma_queue_t   stream[MagmaMaxGPUs][3];
    magma_event_t   event[MagmaMaxGPUs][5];
    magma_timer_t time_total=0, time_sum=0, time=0;
    
    *info = 0;
    if (! upper && uplo != MagmaLower) {
        *info = -1;
    } else if (n < 0) {
        *info = -2;
    } else if (lda < max(1,n)) {
        *info = -4;
    }
    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }

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

    magma_device_t orig_dev;
    magma_getdevice( &orig_dev );
    magma_queue_t orig_stream;
    magmablasGetKernelStream( &orig_stream );
    
    nb = magma_get_dpotrf_nb(n);
    if ( num_gpus0 > n/nb ) {
        num_gpus = n/nb;
        if ( n%nb != 0 ) num_gpus ++;
    } else {
        num_gpus = num_gpus0;
    }
    //ldda  = ((n+31)/32)*32;
    ldda  = ((n+nb-1)/nb)*nb;
    lddla = ((nb*((n+nb*num_gpus-1)/(nb*num_gpus))+31)/32)*32;

    /* figure out NB */
    size_t freeMem, totalMem;
    cudaMemGetInfo( &freeMem, &totalMem );
    freeMem /= sizeof(float);
    
    MB = n;  /* number of rows in the big panel    */
    NB = (magma_int_t)((0.8*freeMem-max(2,num_gpus)*nb*ldda-(n+nb)*nb)/lddla); /* number of columns in the big panel */
    //NB = min(5*nb,n);

    if ( NB >= n ) {
        #ifdef CHECK_SPOTRF_OOC
        printf( "      * still fits in GPU memory.\n" );
        #endif
        NB = n;
    } else {
        #ifdef CHECK_SPOTRF_OOC
        printf( "      * doesn't fit in GPU memory.\n" );
        #endif
        NB = (NB/nb) * nb;   /* making sure it's devisable by nb   */
    }
    #ifdef CHECK_SPOTRF_OOC
    if ( NB != n ) printf( "      * running in out-core mode (n=%d, NB=%d, nb=%d, lddla=%d, freeMem=%.2e).\n", n, NB, nb, lddla, (float)freeMem );
    else           printf( "      * running in in-core mode  (n=%d, NB=%d, nb=%d, lddla=%d, freeMem=%.2e).\n", n, NB, nb, lddla, (float)freeMem );
    fflush(stdout);
    #endif
    for (d=0; d < num_gpus; d++ ) {
        magma_setdevice(d);
        if (MAGMA_SUCCESS != magma_smalloc( &dt[d], NB*lddla + max(2,num_gpus)*nb*ldda )) {
            *info = MAGMA_ERR_DEVICE_ALLOC;
            return *info;
        }
        dwork[d] = &dt[d][max(2,num_gpus)*nb*ldda];
        
        for( j=0; j < 3; j++ )
            magma_queue_create( &stream[d][j] );
        for( j=0; j < 5; j++ )
            magma_event_create( &event[d][j]  );
        magma_device_sync(); // synch the device
    }
    magma_setdevice(0);

    timer_start( time_total );

    if (nb <= 1 || nb >= n) {
        lapackf77_spotrf(uplo_, &n, A, &lda, info);
    } else {

    /* Use hybrid blocked code. */
    if (upper) {
        /* =========================================================== *
         * Compute the Cholesky factorization A = U'*U.                *
         * big panel is divided by block-row and distributed in block  *
         * column cyclic format                                        */
        
        /* for each big-panel */
        for( J=0; J < n; J += NB ) {
            JB = min(NB,n-J);
            if ( num_gpus0 > (n-J)/nb ) {
                num_gpus = (n-J)/nb;
                if ( (n-J)%nb != 0 ) num_gpus ++;
            } else {
                num_gpus = num_gpus0;
            }
            
            /* load the new big-panel by block-rows */
            magma_shtodpo( num_gpus, uplo, JB, n, J, J, nb, A, lda, dwork, NB, stream, &iinfo);
            
            /* update with the previous big-panels */
            timer_start( time );
            for( j=0; j < J; j += nb ) {
                /* upload the diagonal of the block column (broadcast to all GPUs) */
                for( d=0; d < num_gpus; d++ ) {
                    magma_setdevice(d);
                    magma_ssetmatrix_async( nb, JB,
                                            A(j, J),       lda,
                                            dTup(d, 0, J), nb,
                                            stream[d][0] );
                    n_local[d] = 0;
                }
                
                /* distribute off-diagonal blocks to GPUs */
                for( jj=J+JB; jj < n; jj += nb ) {
                    d  = ((jj-J)/nb)%num_gpus;
                    magma_setdevice(d);
                    
                    jb = min(nb, n-jj);
                    magma_ssetmatrix_async( nb, jb,
                                            A(j, jj),                    lda,
                                            dTup(d, 0, J+JB+n_local[d]), nb,
                                            stream[d][0] );
                    n_local[d] += jb;
                }
                
                /* wait for the communication */
                for( d=0; d < num_gpus; d++ ) {
                    magma_setdevice(d);
                    magma_queue_sync( stream[d][0] );
                }
                
                /* update the current big-panel using the previous block-row */
                /* -- process the big diagonal block of the big panel */
                for( jj=0; jj < JB; jj += nb ) { // jj is 'local' column index within the big panel
                    d  = (jj/nb)%num_gpus;
                    J2 = jj/(nb*num_gpus);
                    
                    magma_setdevice(d);
                    magmablasSetKernelStream(stream[d][J2%2]); // the last stream (2) used to process off-diagonal
                    J2 = nb*J2;

                    jb = min(nb,JB-jj); // number of columns in this current block-row
                    magma_sgemm( MagmaConjTrans, MagmaNoTrans,
                                 jj, jb, nb,
                                 c_neg_one, dTup(d, 0, J   ), nb,
                                            dTup(d, 0, J+jj), nb,
                                 c_one,     dAup(d, 0, J2), NB);
                    
                    magma_ssyrk(MagmaUpper, MagmaConjTrans, jb, nb,
                                d_neg_one, dTup(d, 0,  J+jj), nb,
                                d_one,     dAup(d, jj, J2), NB);
                }
                /* -- process the remaining big off-diagonal block of the big panel */
                if ( n > J+JB ) {
                    for( d=0; d < num_gpus; d++ ) {
                        magma_setdevice(d);
                        magmablasSetKernelStream(stream[d][2]);
                        
                        /* local number of columns in the big panel */
                        n_local[d] = ((n-J)/(nb*num_gpus))*nb;
                        if (d < ((n-J)/nb)%num_gpus)
                            n_local[d] += nb;
                        else if (d == ((n-J)/nb)%num_gpus)
                            n_local[d] += (n-J)%nb;
                        
                        /* subtracting the local number of columns in the diagonal */
                        J2 = nb*(JB/(nb*num_gpus));
                        if ( d < (JB/nb)%num_gpus )
                            J2 += nb;

                        n_local[d] -= J2;
                        
                        magma_sgemm( MagmaConjTrans, MagmaNoTrans,
                                     JB, n_local[d], nb,
                                     c_neg_one, dTup(d, 0, J   ), nb,
                                                dTup(d, 0, J+JB), nb,
                                     c_one,     dAup(d, 0, J2), NB);
                    }
                }
                
                /* wait for the previous updates */
                for( d=0; d < num_gpus; d++ ) {
                    magma_setdevice(d);
                    for( jj=0; jj < 3; jj++ )
                        magma_queue_sync( stream[d][jj] );
                    magmablasSetKernelStream(NULL);
                }
                magma_setdevice(0);
            } /* end of updates with previous rows */
            
            /* factor the big panel */
            h  = (JB+nb-1)/nb; // big diagonal of big panel will be on CPU
            // using two streams
            //magma_spotrf2_mgpu(num_gpus, uplo, JB, n-J, J, J, nb,
            //                   dwork, NB, dt, ldda, A, lda, h, stream, event, &iinfo);
            // using three streams
            magma_spotrf3_mgpu(num_gpus, uplo, JB, n-J, J, J, nb,
                               dwork, NB, dt, ldda, A, lda, h, stream, event, &iinfo);
            if ( iinfo != 0 ) {
                *info = J+iinfo;
                break;
            }
            time_sum += timer_stop( time );
            
            /* upload the off-diagonal (and diagonal!!!) big panel */
            magma_sdtohpo(num_gpus, uplo, JB, n, J, J, nb, NB, A, lda, dwork, NB, stream, &iinfo);
            //magma_sdtohpo(num_gpus, uplo, JB, n, J, J, nb, 0, A, lda, dwork, NB, stream, &iinfo);
        }
    } else {
        /* ========================================================= *
         * Compute the Cholesky factorization A = L*L'.              */
        
        /* for each big-panel */
        for( J=0; J < n; J += NB ) {
            JB = min(NB,n-J);
            if ( num_gpus0 > (n-J)/nb ) {
                num_gpus = (n-J)/nb;
                if ( (n-J)%nb != 0 ) num_gpus ++;
            } else {
                num_gpus = num_gpus0;
            }
            
            /* load the new big-panel by block-columns */
            magma_shtodpo( num_gpus, uplo, n, JB, J, J, nb, A, lda, dwork, lddla, stream, &iinfo);
            
            /* update with the previous big-panels */
            timer_start( time );
            for( j=0; j < J; j += nb ) {
                /* upload the diagonal of big panel */
                for( d=0; d < num_gpus; d++ ) {
                    magma_setdevice(d);
                    magma_ssetmatrix_async( JB, nb,
                                            A(J, j),     lda,
                                            dT(d, J, 0), ldda,
                                            stream[d][0] );
                    n_local[d] = 0;
                }
                
                /* upload off-diagonals */
                for( jj=J+JB; jj < n; jj += nb ) {
                    d  = ((jj-J)/nb)%num_gpus;
                    magma_setdevice(d);
                    
                    jb = min(nb, n-jj);
                    magma_ssetmatrix_async( jb, nb,
                                            A(jj, j),                  lda,
                                            dT(d, J+JB+n_local[d], 0), ldda,
                                            stream[d][0] );
                    n_local[d] += jb;
                }
                
                /* wait for the communication */
                for( d=0; d < num_gpus; d++ ) {
                    magma_setdevice(d);
                    magma_queue_sync( stream[d][0] );
                }
                
                /* update the current big-panel using the previous block-row */
                for( jj=0; jj < JB; jj += nb ) { /* diagonal */
                    d  = (jj/nb)%num_gpus;
                    J2 = jj/(nb*num_gpus);
                    
                    magma_setdevice(d);
                    magmablasSetKernelStream(stream[d][J2%2]);
                    
                    J2 = nb*J2;
                    jb = min(nb,JB-jj);
                    magma_sgemm( MagmaNoTrans, MagmaConjTrans,
                                 jb, jj, nb,
                                 c_neg_one, dT(d, J+jj, 0), ldda,
                                            dT(d, J,    0), ldda,
                                 c_one,     dA(d, J2,   0), lddla);
                    
                    magma_ssyrk(MagmaLower, MagmaNoTrans, jb, nb,
                                d_neg_one, dT(d, J+jj, 0), ldda,
                                d_one,     dA(d, J2,  jj), lddla);
                }
                
                if ( n > J+JB ) { /* off-diagonal */
                    for( d=0; d < num_gpus; d++ ) {
                        magma_setdevice(d);
                        magmablasSetKernelStream(stream[d][2]);
                        
                        /* local number of columns in the big panel */
                        n_local[d] = (((n-J)/nb)/num_gpus)*nb;
                        if (d < ((n-J)/nb)%num_gpus)
                            n_local[d] += nb;
                        else if (d == ((n-J)/nb)%num_gpus)
                            n_local[d] += (n-J)%nb;
                        
                        /* subtracting local number of columns in diagonal */
                        J2 = nb*(JB/(nb*num_gpus));
                        if ( d < (JB/nb)%num_gpus )
                            J2 += nb;

                        n_local[d] -= J2;
                        
                        magma_sgemm( MagmaNoTrans, MagmaConjTrans,
                                     n_local[d], JB, nb,
                                     c_neg_one, dT(d, J+JB, 0), ldda,
                                                dT(d, J,    0), ldda,
                                     c_one,     dA(d, J2,   0), lddla);
                    }
                }
                /* wait for the previous updates */
                for( d=0; d < num_gpus; d++ ) {
                    magma_setdevice(d);
                    for( jj=0; jj < 3; jj++ )
                        magma_queue_sync( stream[d][jj] );
                    magmablasSetKernelStream(NULL);
                }
                magma_setdevice(0);
            }
            
            /* factor the big panel */
            h = (JB+nb-1)/nb; // big diagonal of big panel will be on CPU
            // using two streams
            //magma_spotrf2_mgpu(num_gpus, uplo, n-J, JB, J, J, nb,
            //                   dwork, lddla, dt, ldda, A, lda, h, stream, event, &iinfo);
            // using three streams
            magma_spotrf3_mgpu(num_gpus, uplo, n-J, JB, J, J, nb,
                               dwork, lddla, dt, ldda, A, lda, h, stream, event, &iinfo);
            if ( iinfo != 0 ) {
                *info = J+iinfo;
                break;
            }
            time_sum += timer_stop( time );
            
            /* upload the off-diagonal big panel */
            magma_sdtohpo( num_gpus, uplo, n, JB, J, J, nb, JB, A, lda, dwork, lddla, stream, &iinfo);
        
        } /* end of for J */
    } /* if upper */
    } /* if nb */
    timer_stop( time_total );
    
    if ( num_gpus0 > n/nb ) {
        num_gpus = n/nb;
        if ( n%nb != 0 ) num_gpus ++;
    } else {
        num_gpus = num_gpus0;
    }
    for (d=0; d < num_gpus; d++ ) {
        magma_setdevice(d);

        for( j=0; j < 3; j++ ) {
            magma_queue_destroy( stream[d][j] );
        }
        magma_free( dt[d] );

        for( j=0; j < 5; j++ ) {
            magma_event_destroy( event[d][j] );
        }
    }
    magma_setdevice( orig_dev );
    magmablasSetKernelStream( orig_stream );
                 
    timer_printf( "\n n=%d NB=%d nb=%d\n", (int) n, (int) NB, (int) nb );
    timer_printf( " Without memory allocation: %f / %f = %f GFlop/s\n",
                  FLOPS_SPOTRF(n) / 1e9,  time_total,
                  FLOPS_SPOTRF(n) / 1e9 / time_total );
    timer_printf( " Performance %f / %f = %f GFlop/s\n",
                  FLOPS_SPOTRF(n) / 1e9,  time_sum,
                  FLOPS_SPOTRF(n) / 1e9 / time_sum );
    
    return *info;
} /* magma_spotrf_ooc */
Example #5
0
/* ////////////////////////////////////////////////////////////////////////////
   -- Testing spotf2_gpu
*/
int main( int argc, char** argv)
{
    TESTING_INIT();

    real_Double_t   gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
    float *h_A, *h_R;
    magmaFloat_ptr d_A;
    magma_int_t N, n2, lda, ldda, info;
    float c_neg_one = MAGMA_S_NEG_ONE;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    float      Anorm, error, work[1];
    magma_int_t status = 0;

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

    float tol = opts.tolerance * lapackf77_slamch("E");
    opts.lapack |= opts.check;  // check (-c) implies lapack (-l)
    
    printf("%% uplo = %s\n", lapack_uplo_const(opts.uplo) );
    printf("%%   N   CPU Gflop/s (ms)    GPU Gflop/s (ms)    ||R_magma - R_lapack||_F / ||R_lapack||_F\n");
    printf("%%=======================================================\n");
    for( int itest = 0; itest < opts.ntest; ++itest ) {
        for( int iter = 0; iter < opts.niter; ++iter ) {
            N   = opts.nsize[itest];
            lda = N;
            n2  = lda*N;
            ldda = magma_roundup( N, opts.align );  // multiple of 32 by default
            gflops = FLOPS_SPOTRF( N ) / 1e9;
            
            if ( N > 512 ) {
                printf( "%5d   skipping because spotf2 does not support N > 512\n", (int) N );
                continue;
            }
            
            TESTING_MALLOC_CPU( h_A, float, n2     );
            TESTING_MALLOC_PIN( h_R, float, n2     );
            TESTING_MALLOC_DEV( d_A, float, ldda*N );
            
            /* Initialize the matrix */
            lapackf77_slarnv( &ione, ISEED, &n2, h_A );
            magma_smake_hpd( N, h_A, lda );
            lapackf77_slacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
            magma_ssetmatrix( N, N, h_A, lda, d_A, ldda, opts.queue );
            
            /* ====================================================================
               Performs operation using MAGMA
               =================================================================== */
            gpu_time = magma_sync_wtime( opts.queue );
            magma_spotf2_gpu( opts.uplo, N, d_A, ldda, opts.queue, &info );
            gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
            gpu_perf = gflops / gpu_time;
            if (info != 0) {
                printf("magma_spotf2_gpu returned error %d: %s.\n",
                       (int) info, magma_strerror( info ));
            }
            
            if ( opts.lapack ) {
                /* =====================================================================
                   Performs operation using LAPACK
                   =================================================================== */
                cpu_time = magma_wtime();
                lapackf77_spotrf( lapack_uplo_const(opts.uplo), &N, h_A, &lda, &info );
                cpu_time = magma_wtime() - cpu_time;
                cpu_perf = gflops / cpu_time;
                if (info != 0) {
                    printf("lapackf77_spotrf returned error %d: %s.\n",
                           (int) info, magma_strerror( info ));
                }
                
                /* =====================================================================
                   Check the result compared to LAPACK
                   =================================================================== */
                magma_sgetmatrix( N, N, d_A, ldda, h_R, lda, opts.queue );
                blasf77_saxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
                Anorm = lapackf77_slange("f", &N, &N, h_A, &lda, work);
                error = lapackf77_slange("f", &N, &N, h_R, &lda, work) / Anorm;
                
                printf("%5d   %7.2f (%7.2f)   %7.2f (%7.2f)   %8.2e   %s\n",
                       (int) N, cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
                       error, (error < tol ? "ok" : "failed"));
                status += ! (error < tol);
            }
            else {
                printf("%5d     ---   (  ---  )   %7.2f (%7.2f)     ---  \n",
                       (int) N, gpu_perf, gpu_time*1000. );
            }
            TESTING_FREE_CPU( h_A );
            TESTING_FREE_PIN( h_R );
            TESTING_FREE_DEV( d_A );
            fflush( stdout );
        }
        if ( opts.niter > 1 ) {
            printf( "\n" );
        }
    }

    opts.cleanup();
    TESTING_FINALIZE();
    return status;
}
int main( int argc, char** argv)
{
    real_Double_t gflops, gpu_perf, cpu_perf, gpu_time, cpu_time;
    float *h_A, *h_R;
    magmaFloat_ptr d_lA[MagmaMaxGPUs];
    magma_int_t N = 0, n2, lda, ldda;
    magma_int_t size[10] =
        { 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000 };
    
    magma_int_t i, j, k, info;
    float mz_one = MAGMA_S_NEG_ONE;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    float      work[1], matnorm, diffnorm;
   
    magma_int_t num_gpus0 = 1, num_gpus, flag = 0;
    int nb, mb, n_local, nk;

    magma_uplo_t uplo = MagmaLower;

    if (argc != 1){
        for(i = 1; i<argc; i++){
            if (strcmp("-N", argv[i])==0){
                N = atoi(argv[++i]);
                if (N>0) {
                    size[0] = size[9] = N;
                    flag = 1;
                }else exit(1);
            }
            if(strcmp("-NGPU", argv[i])==0)
                num_gpus0 = atoi(argv[++i]);
            if(strcmp("-UPLO", argv[i])==0){
                if(strcmp("L", argv[++i])==0){
                    uplo = MagmaLower;
                }else{
                    uplo = MagmaUpper;
                }            
            }
        }
    }
    else {
        printf("\nUsage: \n");
        printf("  testing_spotrf_mgpu -N %d -NGPU %d -UPLO -L\n\n", 1024, num_gpus0);
    }

    /* looking for max. ldda */
    ldda = 0;
    n2 = 0;
    for(i=0;i<10;i++){
        N = size[i];
        nb = magma_get_spotrf_nb(N);
        mb = nb;
        if(num_gpus0 > N/nb){
            num_gpus = N/nb;
            if(N%nb != 0) num_gpus ++;
        }else{
            num_gpus = num_gpus0;
        }
        n_local = nb*(1+N/(nb*num_gpus))*mb*((N+mb-1)/mb);
        if(n_local > ldda) ldda = n_local;
        if(n2 < N*N) n2 = N*N;
        if(flag != 0) break;
    }

     /* Allocate host memory for the matrix */
    TESTING_MALLOC_PIN( h_A, float, n2 );
    TESTING_MALLOC_PIN( h_R, float, n2 );

    /* Initialize */
    magma_queue_t  queues[MagmaMaxGPUs * 2];
    //magma_queue_t  queues[MagmaMaxGPUs];
    magma_device_t devices[ MagmaMaxGPUs ];
    int num = 0;
    magma_err_t err;
    magma_init();
    err = magma_get_devices( devices, MagmaMaxGPUs, &num );
    if ( err != 0 || num < 1 ) {
        fprintf( stderr, "magma_get_devices failed: %d\n", err );
        exit(-1);
    }
    for(i=0;i<num_gpus;i++){
        err = magma_queue_create( devices[i], &queues[2*i] );
        if ( err != 0 ) {
            fprintf( stderr, "magma_queue_create failed: %d\n", err );
            exit(-1);
        }
        err = magma_queue_create( devices[i], &queues[2*i+1] );
        if ( err != 0 ) {
            fprintf( stderr, "magma_queue_create failed: %d\n", err );
            exit(-1);
        }
    }

    printf("each buffer size: %d\n", ldda);
    /* allocate local matrix on Buffers */
    for(i=0; i<num_gpus0; i++){
        TESTING_MALLOC_DEV( d_lA[i], float, ldda );
    }

    
    printf("\n\n");
    printf("Using GPUs: %d\n", num_gpus0);
    if(uplo == MagmaUpper){
        printf("\n  testing_spotrf_mgpu -N %d -NGPU %d -UPLO U\n\n", N, num_gpus0);
    }else{
        printf("\n  testing_spotrf_mgpu -N %d -NGPU %d -UPLO L\n\n", N, num_gpus0);
    }
            printf("  N    CPU GFlop/s (sec)    GPU GFlop/s (sec)    ||R_magma-R_lapack||_F / ||R_lapack||_F\n");
    printf("========================================================================================\n");
    for(i=0; i<10; i++){
        N   = size[i];
        lda = N;
        n2  = lda*N;
        ldda = ((N+31)/32)*32;
        gflops = FLOPS( (float)N ) * 1e-9;
        
        /* Initialize the matrix */
        lapackf77_slarnv( &ione, ISEED, &n2, h_A );
        /* Symmetrize and increase the diagonal */
        for( int i = 0; i < N; ++i ) {
            MAGMA_S_SET2REAL( h_A(i,i), MAGMA_S_REAL(h_A(i,i)) + N );
            for( int j = 0; j < i; ++j ) {
          h_A(i, j) = MAGMA_S_CNJG( h_A(j,i) );
            }
        }
        lapackf77_slacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );

        /* Warm up to measure the performance */
        nb = magma_get_spotrf_nb(N);
        if(num_gpus0 > N/nb){
            num_gpus = N/nb;
            if(N%nb != 0) num_gpus ++;
            printf("too many GPUs for the matrix size, using %d GPUs\n", (int)num_gpus);
        }else{
            num_gpus = num_gpus0;
        }
        /* distribute matrix to gpus */
        if(uplo == MagmaUpper){
            // Upper
            ldda = ((N+mb-1)/mb)*mb;    
            for(j=0;j<N;j+=nb){
                k = (j/nb)%num_gpus;
                nk = min(nb, N-j);
                magma_ssetmatrix(N, nk, 
                                 &h_A[j*lda], 0, lda,
                                 d_lA[k], j/(nb*num_gpus)*nb*ldda, ldda, 
                                 queues[2*k]);
            }
        }else{
            // Lower
            ldda = (1+N/(nb*num_gpus))*nb;
            for(j=0;j<N;j+=nb){
                k = (j/nb)%num_gpus;
                nk = min(nb, N-j);
                magma_ssetmatrix(nk, N, &h_A[j], 0, lda,
                                    d_lA[k], (j/(nb*num_gpus)*nb), ldda,
                                    queues[2*k]);
            }
        }

        magma_spotrf_mgpu( num_gpus, uplo, N, d_lA, 0, ldda, &info, queues );
        /* ====================================================================
           Performs operation using MAGMA
           =================================================================== */
        /* distribute matrix to gpus */
        if(uplo == MagmaUpper){
            // Upper
            ldda = ((N+mb-1)/mb)*mb;    
            for(j=0;j<N;j+=nb){
                k = (j/nb)%num_gpus;
                nk = min(nb, N-j);
                magma_ssetmatrix(N, nk, 
                                 &h_A[j*lda], 0, lda,
                                 d_lA[k], j/(nb*num_gpus)*nb*ldda, ldda, 
                                 queues[2*k]);
            }
        }else{
            // Lower
            ldda = (1+N/(nb*num_gpus))*nb;
            for(j=0;j<N;j+=nb){
                k = (j/nb)%num_gpus;
                nk = min(nb, N-j);
                magma_ssetmatrix(nk, N, &h_A[j], 0, lda,
                                    d_lA[k], (j/(nb*num_gpus)*nb), ldda,
                                    queues[2*k]);
            }
        }
    
        gpu_time = magma_wtime();
        magma_spotrf_mgpu( num_gpus, uplo, N, d_lA, 0, ldda, &info, queues );
        gpu_time = magma_wtime() - gpu_time;
        if (info != 0)
            printf( "magma_spotrf had error %d.\n", info );

        gpu_perf = gflops / gpu_time;
       
        /* gather matrix from gpus */
        if(uplo==MagmaUpper){
            // Upper
            for(j=0;j<N;j+=nb){
                k = (j/nb)%num_gpus;
                nk = min(nb, N-j);
                magma_sgetmatrix(N, nk,
                                 d_lA[k], j/(nb*num_gpus)*nb*ldda, ldda,
                                 &h_R[j*lda], 0, lda, queues[2*k]);
            }
        }else{
            // Lower
            for(j=0; j<N; j+=nb){
                k = (j/nb)%num_gpus;
                nk = min(nb, N-j);
                magma_sgetmatrix( nk, N, 
                            d_lA[k], (j/(nb*num_gpus)*nb), ldda, 
                            &h_R[j], 0, lda, queues[2*k] );
            }
        }

        /* =====================================================================
           Performs operation using LAPACK
           =================================================================== */
        cpu_time = magma_wtime();
        if(uplo == MagmaLower){
            lapackf77_spotrf( MagmaLowerStr, &N, h_A, &lda, &info );
        }else{
            lapackf77_spotrf( MagmaUpperStr, &N, h_A, &lda, &info );
        }
        cpu_time = magma_wtime() - cpu_time;
        if (info != 0)
            printf( "lapackf77_spotrf had error %d.\n", info );
        
        cpu_perf = gflops / cpu_time;
        /* =====================================================================
           Check the result compared to LAPACK
           |R_magma - R_lapack| / |R_lapack|
           =================================================================== */
        matnorm = lapackf77_slange("f", &N, &N, h_A, &lda, work);
        blasf77_saxpy(&n2, &mz_one, h_A, &ione, h_R, &ione);
        diffnorm = lapackf77_slange("f", &N, &N, h_R, &lda, work);
        printf( "%5d     %6.2f (%6.2f)     %6.2f (%6.2f)         %e\n",
                N, cpu_perf, cpu_time, gpu_perf, gpu_time, diffnorm / matnorm );
        
        if (flag != 0)
            break;
    }

    /* clean up */
    TESTING_FREE_PIN( h_A );
    TESTING_FREE_PIN( h_R );
    for(i=0;i<num_gpus;i++){
        TESTING_FREE_DEV( d_lA[i] );
        magma_queue_destroy( queues[2*i]   );
        magma_queue_destroy( queues[2*i+1] );
    }
    magma_finalize();
}
Example #7
0
/***************************************************************************//**
    Purpose
    -------
    SPOTRF computes the Cholesky factorization of a real symmetric
    positive definite matrix dA.

    The factorization has the form
        dA = U**H * U,   if UPLO = MagmaUpper, or
        dA = L  * L**H,  if UPLO = MagmaLower,
    where U is an upper triangular matrix and L is lower triangular.

    This is the block version of the algorithm, calling Level 3 BLAS.

    Arguments
    ---------
    @param[in]
    uplo    magma_uplo_t
      -     = MagmaUpper:  Upper triangle of dA is stored;
      -     = MagmaLower:  Lower triangle of dA is stored.

    @param[in]
    n       INTEGER
            The order of the matrix dA.  N >= 0.

    @param[in,out]
    dA      REAL array on the GPU, dimension (LDDA,N)
            On entry, the symmetric matrix dA.  If UPLO = MagmaUpper, the leading
            N-by-N upper triangular part of dA contains the upper
            triangular part of the matrix dA, and the strictly lower
            triangular part of dA is not referenced.  If UPLO = MagmaLower, the
            leading N-by-N lower triangular part of dA contains the lower
            triangular part of the matrix dA, and the strictly upper
            triangular part of dA is not referenced.
    \n
            On exit, if INFO = 0, the factor U or L from the Cholesky
            factorization dA = U**H * U or dA = L * L**H.

    @param[in]
    ldda     INTEGER
            The leading dimension of the array dA.  LDDA >= max(1,N).
            To benefit from coalescent memory accesses LDDA must be
            divisible by 16.

    @param[out]
    info    INTEGER
      -     = 0:  successful exit
      -     < 0:  if INFO = -i, the i-th argument had an illegal value
      -     > 0:  if INFO = i, the leading minor of order i is not
                  positive definite, and the factorization could not be
                  completed.

    @ingroup magma_potrf
*******************************************************************************/
extern "C" magma_int_t
magma_spotrf_gpu(
    magma_uplo_t uplo, magma_int_t n,
    magmaFloat_ptr dA, magma_int_t ldda,
    magma_int_t *info )
{
    #ifdef HAVE_clBLAS
    #define dA(i_, j_)  dA, ((i_) + (j_)*ldda + dA_offset)
    #else
    #define dA(i_, j_) (dA + (i_) + (j_)*ldda)
    #endif

    /* Constants */
    const float c_one     = MAGMA_S_ONE;
    const float c_neg_one = MAGMA_S_NEG_ONE;
    const float d_one     =  1.0;
    const float d_neg_one = -1.0;
    
    /* Local variables */
    const char* uplo_ = lapack_uplo_const( uplo );
    bool upper = (uplo == MagmaUpper);
    
    magma_int_t j, jb, nb;
    float *work;

    *info = 0;
    if (! upper && uplo != MagmaLower) {
        *info = -1;
    } else if (n < 0) {
        *info = -2;
    } else if (ldda < max(1,n)) {
        *info = -4;
    }
    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }
    
    nb = magma_get_spotrf_nb( n );
    
    if (MAGMA_SUCCESS != magma_smalloc_pinned( &work, nb*nb )) {
        *info = MAGMA_ERR_HOST_ALLOC;
        return *info;
    }
    
    magma_queue_t queues[2];
    magma_device_t cdev;
    magma_getdevice( &cdev );
    magma_queue_create( cdev, &queues[0] );
    magma_queue_create( cdev, &queues[1] );
    
    if (nb <= 1 || nb >= n) {
        /* Use unblocked code. */
        magma_sgetmatrix( n, n, dA(0,0), ldda, work, n, queues[0] );
        lapackf77_spotrf( uplo_, &n, work, &n, info );
        magma_ssetmatrix( n, n, work, n, dA(0,0), ldda, queues[0] );
    }
    else {
        /* Use blocked code. */
        if (upper) {
            //=========================================================
            /* Compute the Cholesky factorization A = U'*U. */
            for (j=0; j < n; j += nb) {
                // apply all previous updates to diagonal block,
                // then transfer it to CPU
                jb = min( nb, n-j );
                magma_ssyrk( MagmaUpper, MagmaConjTrans, jb, j,
                             d_neg_one, dA(0, j), ldda,
                             d_one,     dA(j, j), ldda, queues[1] );
                
                magma_queue_sync( queues[1] );
                magma_sgetmatrix_async( jb, jb,
                                        dA(j, j), ldda,
                                        work,     jb, queues[0] );
                
                // apply all previous updates to block row right of diagonal block
                if (j+jb < n) {
                    magma_sgemm( MagmaConjTrans, MagmaNoTrans,
                                 jb, n-j-jb, j,
                                 c_neg_one, dA(0, j   ), ldda,
                                            dA(0, j+jb), ldda,
                                 c_one,     dA(j, j+jb), ldda, queues[1] );
                }
                
                // simultaneous with above sgemm, transfer diagonal block,
                // factor it on CPU, and test for positive definiteness
                magma_queue_sync( queues[0] );
                lapackf77_spotrf( MagmaUpperStr, &jb, work, &jb, info );
                magma_ssetmatrix_async( jb, jb,
                                        work,     jb,
                                        dA(j, j), ldda, queues[1] );
                if (*info != 0) {
                    *info = *info + j;
                    break;
                }
                
                // apply diagonal block to block row right of diagonal block
                if (j+jb < n) {
                    magma_strsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
                                 jb, n-j-jb,
                                 c_one, dA(j, j),    ldda,
                                        dA(j, j+jb), ldda, queues[1] );
                }
            }
        }
        else {
            //=========================================================
            // Compute the Cholesky factorization A = L*L'.
            for (j=0; j < n; j += nb) {
                // apply all previous updates to diagonal block,
                // then transfer it to CPU
                jb = min( nb, n-j );
                magma_ssyrk( MagmaLower, MagmaNoTrans, jb, j,
                             d_neg_one, dA(j, 0), ldda,
                             d_one,     dA(j, j), ldda, queues[1] );
                
                magma_queue_sync( queues[1] );
                magma_sgetmatrix_async( jb, jb,
                                        dA(j, j), ldda,
                                        work,     jb, queues[0] );
                
                // apply all previous updates to block column below diagonal block
                if (j+jb < n) {
                    magma_sgemm( MagmaNoTrans, MagmaConjTrans,
                                 n-j-jb, jb, j,
                                 c_neg_one, dA(j+jb, 0), ldda,
                                            dA(j,    0), ldda,
                                 c_one,     dA(j+jb, j), ldda, queues[1] );
                }
                
                // simultaneous with above sgemm, transfer diagonal block,
                // factor it on CPU, and test for positive definiteness
                magma_queue_sync( queues[0] );
                lapackf77_spotrf( MagmaLowerStr, &jb, work, &jb, info );
                magma_ssetmatrix_async( jb, jb,
                                        work,     jb,
                                        dA(j, j), ldda, queues[1] );
                if (*info != 0) {
                    *info = *info + j;
                    break;
                }
                
                // apply diagonal block to block column below diagonal
                if (j+jb < n) {
                    magma_strsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
                                 n-j-jb, jb,
                                 c_one, dA(j,    j), ldda,
                                        dA(j+jb, j), ldda, queues[1] );
                }
            }
        }
    }
    
    magma_queue_destroy( queues[0] );
    magma_queue_destroy( queues[1] );
    
    magma_free_pinned( work );
    
    return *info;
} /* magma_spotrf_gpu */
Example #8
0
extern "C" magma_int_t
magma_spotrf_gpu(char uplo, magma_int_t n,
                 float *dA, magma_int_t ldda, magma_int_t *info)
{
/*  -- MAGMA (version 1.4.0) --
       Univ. of Tennessee, Knoxville
       Univ. of California, Berkeley
       Univ. of Colorado, Denver
       August 2013

    Purpose
    =======
    SPOTRF computes the Cholesky factorization of a real symmetric
    positive definite matrix dA.

    The factorization has the form
       dA = U**T * U,  if UPLO = 'U', or
       dA = L  * L**T,  if UPLO = 'L',
    where U is an upper triangular matrix and L is lower triangular.

    This is the block version of the algorithm, calling Level 3 BLAS.
    If the current stream is NULL, this version replaces it with user defined
    stream to overlap computation with communication.

    Arguments
    =========
    UPLO    (input) CHARACTER*1
            = 'U':  Upper triangle of dA is stored;
            = 'L':  Lower triangle of dA is stored.

    N       (input) INTEGER
            The order of the matrix dA.  N >= 0.

    dA      (input/output) REAL array on the GPU, dimension (LDDA,N)
            On entry, the symmetric matrix dA.  If UPLO = 'U', the leading
            N-by-N upper triangular part of dA contains the upper
            triangular part of the matrix dA, and the strictly lower
            triangular part of dA is not referenced.  If UPLO = 'L', the
            leading N-by-N lower triangular part of dA contains the lower
            triangular part of the matrix dA, and the strictly upper
            triangular part of dA is not referenced.

            On exit, if INFO = 0, the factor U or L from the Cholesky
            factorization dA = U**T * U or dA = L * L**T.

    LDDA     (input) INTEGER
            The leading dimension of the array dA.  LDDA >= max(1,N).
            To benefit from coalescent memory accesses LDDA must be
            dividable by 16.

    INFO    (output) INTEGER
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            > 0:  if INFO = i, the leading minor of order i is not
                  positive definite, and the factorization could not be
                  completed.
    =====================================================================   */


    magma_int_t     j, jb, nb;
    char            uplo_[2] = {uplo, 0};
    float c_one     = MAGMA_S_ONE;
    float c_neg_one = MAGMA_S_NEG_ONE;
    float *work;
    float          d_one     =  1.0;
    float          d_neg_one = -1.0;
    int upper = lapackf77_lsame(uplo_, "U");

    *info = 0;
    if ( (! upper) && (! lapackf77_lsame(uplo_, "L")) ) {
        *info = -1;
    } else if (n < 0) {
        *info = -2;
    } else if (ldda < max(1,n)) {
        *info = -4;
    }
    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }

    nb = magma_get_spotrf_nb(n);

    if (MAGMA_SUCCESS != magma_smalloc_pinned( &work, nb*nb )) {
        *info = MAGMA_ERR_HOST_ALLOC;
        return *info;
    }

    /* Define user stream if current stream is NULL */
    cudaStream_t stream[2], current_stream;
    magmablasGetKernelStream(&current_stream);

    magma_queue_create( &stream[0] );
    if (current_stream == NULL) {
      magma_queue_create( &stream[1] );
      magmablasSetKernelStream(stream[1]);
    }
    else
      stream[1] = current_stream;

    if ((nb <= 1) || (nb >= n)) {
        /*  Use unblocked code. */
        magma_sgetmatrix_async( n, n, dA, ldda, work, n, stream[1] );
        magma_queue_sync( stream[1] );
        lapackf77_spotrf(uplo_, &n, work, &n, info);
        magma_ssetmatrix_async( n, n, work, n, dA, ldda, stream[1] );
    }
    else {

        /* Use blocked code. */
        if (upper) {
            
            /* Compute the Cholesky factorization A = U'*U. */
            for (j=0; j<n; j+=nb) {
                
                /* Update and factorize the current diagonal block and test
                   for non-positive-definiteness. Computing MIN */
                jb = min(nb, (n-j));
                
                magma_ssyrk(MagmaUpper, MagmaTrans, jb, j,
                            d_neg_one, dA(0, j), ldda,
                            d_one,     dA(j, j), ldda);

                magma_queue_sync( stream[1] );
                magma_sgetmatrix_async( jb, jb,
                                        dA(j, j), ldda,
                                        work,     jb, stream[0] );
                
                if ( (j+jb) < n) {
                    /* Compute the current block row. */
                    magma_sgemm(MagmaTrans, MagmaNoTrans,
                                jb, (n-j-jb), j,
                                c_neg_one, dA(0, j   ), ldda,
                                           dA(0, j+jb), ldda,
                                c_one,     dA(j, j+jb), ldda);
                }
                
                magma_queue_sync( stream[0] );
                lapackf77_spotrf(MagmaUpperStr, &jb, work, &jb, info);
                magma_ssetmatrix_async( jb, jb,
                                        work,     jb,
                                        dA(j, j), ldda, stream[1] );
                if (*info != 0) {
                    *info = *info + j;
                    break;
                }

                if ( (j+jb) < n) {
                    magma_strsm( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
                                 jb, (n-j-jb),
                                 c_one, dA(j, j   ), ldda,
                                        dA(j, j+jb), ldda);
                }
            }
        }
        else {
            //=========================================================
            // Compute the Cholesky factorization A = L*L'.
            for (j=0; j<n; j+=nb) {

                //  Update and factorize the current diagonal block and test
                //  for non-positive-definiteness. Computing MIN
                jb = min(nb, (n-j));

                magma_ssyrk(MagmaLower, MagmaNoTrans, jb, j,
                            d_neg_one, dA(j, 0), ldda,
                            d_one,     dA(j, j), ldda);
                
                magma_queue_sync( stream[1] );
                magma_sgetmatrix_async( jb, jb,
                                        dA(j, j), ldda,
                                        work,     jb, stream[0] );
                
                if ( (j+jb) < n) {
                    magma_sgemm( MagmaNoTrans, MagmaTrans,
                                 (n-j-jb), jb, j,
                                 c_neg_one, dA(j+jb, 0), ldda,
                                            dA(j,    0), ldda,
                                 c_one,     dA(j+jb, j), ldda);
                }

                magma_queue_sync( stream[0] );
                lapackf77_spotrf(MagmaLowerStr, &jb, work, &jb, info);
                magma_ssetmatrix_async( jb, jb,
                                        work,     jb,
                                        dA(j, j), ldda, stream[1] );
                if (*info != 0) {
                    *info = *info + j;
                    break;
                }
                
                if ( (j+jb) < n) {
                    magma_strsm(MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
                                (n-j-jb), jb,
                                c_one, dA(j,    j), ldda,
                                       dA(j+jb, j), ldda);
                }
            }
        }
    }

    magma_free_pinned( work );

    magma_queue_destroy( stream[0] );
    if (current_stream == NULL) {
      magma_queue_destroy( stream[1] );
      magmablasSetKernelStream(NULL);
    }

    return *info;
} /* magma_spotrf_gpu */
Example #9
0
/**
    Purpose
    -------
    SPOTRF computes the Cholesky factorization of a real symmetric
    positive definite matrix dA.

    The factorization has the form
        dA = U**H * U,   if UPLO = MagmaUpper, or
        dA = L  * L**H,  if UPLO = MagmaLower,
    where U is an upper triangular matrix and L is lower triangular.

    This is the block version of the algorithm, calling Level 3 BLAS.
    If the current stream is NULL, this version replaces it with a new
    stream to overlap computation with communication.

    Arguments
    ---------
    @param[in]
    uplo    magma_uplo_t
      -     = MagmaUpper:  Upper triangle of dA is stored;
      -     = MagmaLower:  Lower triangle of dA is stored.

    @param[in]
    n       INTEGER
            The order of the matrix dA.  N >= 0.

    @param[in,out]
    dA      REAL array on the GPU, dimension (LDDA,N)
            On entry, the symmetric matrix dA.  If UPLO = MagmaUpper, the leading
            N-by-N upper triangular part of dA contains the upper
            triangular part of the matrix dA, and the strictly lower
            triangular part of dA is not referenced.  If UPLO = MagmaLower, the
            leading N-by-N lower triangular part of dA contains the lower
            triangular part of the matrix dA, and the strictly upper
            triangular part of dA is not referenced.
    \n
            On exit, if INFO = 0, the factor U or L from the Cholesky
            factorization dA = U**H * U or dA = L * L**H.

    @param[in]
    ldda     INTEGER
            The leading dimension of the array dA.  LDDA >= max(1,N).
            To benefit from coalescent memory accesses LDDA must be
            divisible by 16.

    @param[out]
    info    INTEGER
      -     = 0:  successful exit
      -     < 0:  if INFO = -i, the i-th argument had an illegal value
      -     > 0:  if INFO = i, the leading minor of order i is not
                  positive definite, and the factorization could not be
                  completed.

    @ingroup magma_sposv_comp
    ********************************************************************/
extern "C" magma_int_t
magma_spotrf_gpu(
    magma_uplo_t uplo, magma_int_t n,
    magmaFloat_ptr dA, magma_int_t ldda,
    magma_int_t *info)
{
#define dA(i, j) (dA + (j)*ldda + (i))

    magma_int_t     j, jb, nb;
    const char* uplo_ = lapack_uplo_const( uplo );
    float c_one     = MAGMA_S_ONE;
    float c_neg_one = MAGMA_S_NEG_ONE;
    float *work;
    float          d_one     =  1.0;
    float          d_neg_one = -1.0;
    int upper = (uplo == MagmaUpper);

    *info = 0;
    if (! upper && uplo != MagmaLower) {
        *info = -1;
    } else if (n < 0) {
        *info = -2;
    } else if (ldda < max(1,n)) {
        *info = -4;
    }
    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }

    nb = magma_get_spotrf_nb(n);

    if (MAGMA_SUCCESS != magma_smalloc_pinned( &work, nb*nb )) {
        *info = MAGMA_ERR_HOST_ALLOC;
        return *info;
    }

    /* Define user stream if current stream is NULL */
    magma_queue_t stream[2];
    
    magma_queue_t orig_stream;
    magmablasGetKernelStream( &orig_stream );
    
    magma_queue_create( &stream[0] );
    if (orig_stream == NULL) {
        magma_queue_create( &stream[1] );
        magmablasSetKernelStream(stream[1]);
    }
    else {
        stream[1] = orig_stream;
    }
    
    if ((nb <= 1) || (nb >= n)) {
        /* Use unblocked code. */
        magma_sgetmatrix_async( n, n, dA, ldda, work, n, stream[1] );
        magma_queue_sync( stream[1] );
        lapackf77_spotrf(uplo_, &n, work, &n, info);
        magma_ssetmatrix_async( n, n, work, n, dA, ldda, stream[1] );
    }
    else {
        /* Use blocked code. */
        if (upper) {
            
            /* Compute the Cholesky factorization A = U'*U. */
            for (j=0; j < n; j += nb) {
                
                /* Update and factorize the current diagonal block and test
                   for non-positive-definiteness. Computing MIN */
                jb = min(nb, (n-j));
                
                magma_ssyrk(MagmaUpper, MagmaConjTrans, jb, j,
                            d_neg_one, dA(0, j), ldda,
                            d_one,     dA(j, j), ldda);

                magma_queue_sync( stream[1] );
                magma_sgetmatrix_async( jb, jb,
                                        dA(j, j), ldda,
                                        work,     jb, stream[0] );
                
                if ( (j+jb) < n) {
                    /* Compute the current block row. */
                    magma_sgemm(MagmaConjTrans, MagmaNoTrans,
                                jb, (n-j-jb), j,
                                c_neg_one, dA(0, j   ), ldda,
                                           dA(0, j+jb), ldda,
                                c_one,     dA(j, j+jb), ldda);
                }
                
                magma_queue_sync( stream[0] );
                lapackf77_spotrf(MagmaUpperStr, &jb, work, &jb, info);
                magma_ssetmatrix_async( jb, jb,
                                        work,     jb,
                                        dA(j, j), ldda, stream[1] );
                if (*info != 0) {
                    *info = *info + j;
                    break;
                }

                if ( (j+jb) < n) {
                    magma_strsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
                                 jb, (n-j-jb),
                                 c_one, dA(j, j   ), ldda,
                                        dA(j, j+jb), ldda);
                }
            }
        }
        else {
            //=========================================================
            // Compute the Cholesky factorization A = L*L'.
            for (j=0; j < n; j += nb) {
                //  Update and factorize the current diagonal block and test
                //  for non-positive-definiteness. Computing MIN
                jb = min(nb, (n-j));

                magma_ssyrk(MagmaLower, MagmaNoTrans, jb, j,
                            d_neg_one, dA(j, 0), ldda,
                            d_one,     dA(j, j), ldda);
                
                magma_queue_sync( stream[1] );
                magma_sgetmatrix_async( jb, jb,
                                        dA(j, j), ldda,
                                        work,     jb, stream[0] );
                
                if ( (j+jb) < n) {
                    magma_sgemm( MagmaNoTrans, MagmaConjTrans,
                                 (n-j-jb), jb, j,
                                 c_neg_one, dA(j+jb, 0), ldda,
                                            dA(j,    0), ldda,
                                 c_one,     dA(j+jb, j), ldda);
                }

                magma_queue_sync( stream[0] );
                lapackf77_spotrf(MagmaLowerStr, &jb, work, &jb, info);
                magma_ssetmatrix_async( jb, jb,
                                        work,     jb,
                                        dA(j, j), ldda, stream[1] );
                if (*info != 0) {
                    *info = *info + j;
                    break;
                }
                
                if ( (j+jb) < n) {
                    magma_strsm(MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
                                (n-j-jb), jb,
                                c_one, dA(j,    j), ldda,
                                       dA(j+jb, j), ldda);
                }
            }
        }
    }

    magma_free_pinned( work );

    magma_queue_destroy( stream[0] );
    if (orig_stream == NULL) {
        magma_queue_destroy( stream[1] );
    }
    magmablasSetKernelStream( orig_stream );

    return *info;
} /* magma_spotrf_gpu */
Example #10
0
/***************************************************************************//**
    Purpose
    -------
    SPOTRF computes the Cholesky factorization of a real symmetric
    positive definite matrix A. This version does not require work
    space on the GPU passed as input. GPU memory is allocated in the
    routine.

    The factorization has the form
        A = U**H * U,  if uplo = MagmaUpper, or
        A = L  * L**H, if uplo = MagmaLower,
    where U is an upper triangular matrix and L is lower triangular.

    This is the block version of the algorithm, calling Level 3 BLAS.

    This uses multiple queues to overlap communication and computation.

    Arguments
    ---------
    @param[in]
    uplo    magma_uplo_t
      -     = MagmaUpper:  Upper triangle of A is stored;
      -     = MagmaLower:  Lower triangle of A is stored.

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

    @param[in,out]
    A       REAL array, dimension (LDA,N)
            On entry, the symmetric 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.
    \n
            On exit, if INFO = 0, the factor U or L from the Cholesky
            factorization A = U**H * U or A = L * L**H.
    \n
            Higher performance is achieved if A is in pinned memory, e.g.
            allocated using magma_malloc_pinned.

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

    @param[out]
    info    INTEGER
      -     = 0:  successful exit
      -     < 0:  if INFO = -i, the i-th argument had an illegal value
                  or another error occured, such as memory allocation failed.
      -     > 0:  if INFO = i, the leading minor of order i is not
                  positive definite, and the factorization could not be
                  completed.

    @ingroup magma_potrf
*******************************************************************************/
extern "C" magma_int_t
magma_spotrf(
    magma_uplo_t uplo, magma_int_t n,
    float *A, magma_int_t lda,
    magma_int_t *info )
{
    #define  A(i_, j_)  (A + (i_) + (j_)*lda)
    
    #ifdef HAVE_clBLAS
    #define dA(i_, j_)  dA, ((i_) + (j_)*ldda)
    #else
    #define dA(i_, j_) (dA + (i_) + (j_)*ldda)
    #endif
    
    /* Constants */
    const float c_one     = MAGMA_S_ONE;
    const float c_neg_one = MAGMA_S_NEG_ONE;
    const float d_one     =  1.0;
    const float d_neg_one = -1.0;
    
    /* Local variables */
    const char* uplo_ = lapack_uplo_const( uplo );
    bool upper = (uplo == MagmaUpper);
    
    magma_int_t j, jb, ldda, nb;
    magmaFloat_ptr dA = NULL;
    
    /* Check arguments */
    *info = 0;
    if (! upper && uplo != MagmaLower) {
        *info = -1;
    } else if (n < 0) {
        *info = -2;
    } else if (lda < max(1,n)) {
        *info = -4;
    }
    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }
    
    /* Quick return */
    if ( n == 0 )
        return *info;
    
    nb = magma_get_spotrf_nb( n );
    
    if (nb <= 1 || nb >= n) {
        lapackf77_spotrf( uplo_, &n, A, &lda, info );
    }
    else {
        /* Use hybrid blocked code. */
        ldda = magma_roundup( n, 32 );
        
        magma_int_t ngpu = magma_num_gpus();
        if ( ngpu > 1 ) {
            /* call multi-GPU non-GPU-resident interface */
            return magma_spotrf_m( ngpu, uplo, n, A, lda, info );
        }
        
        if (MAGMA_SUCCESS != magma_smalloc( &dA, n*ldda )) {
            /* alloc failed so call the non-GPU-resident version */
            return magma_spotrf_m( ngpu, uplo, n, A, lda, info );
        }
        
        magma_queue_t queues[2] = { NULL, NULL };
        magma_device_t cdev;
        magma_getdevice( &cdev );
        magma_queue_create( cdev, &queues[0] );
        magma_queue_create( cdev, &queues[1] );
        
        if (upper) {
            /* Compute the Cholesky factorization A = U'*U. */
            for (j=0; j < n; j += nb) {
                /* Update and factorize the current diagonal block and test
                   for non-positive-definiteness. */
                jb = min( nb, n-j );
                magma_ssetmatrix_async( jb, n-j,
                                         A(j, j), lda,
                                        dA(j, j), ldda, queues[1] );
                
                magma_ssyrk( MagmaUpper, MagmaConjTrans, jb, j,
                             d_neg_one, dA(0, j), ldda,
                             d_one,     dA(j, j), ldda, queues[1] );
                magma_queue_sync( queues[1] );
                
                magma_sgetmatrix_async( jb, jb,
                                        dA(j, j), ldda,
                                         A(j, j), lda, queues[0] );
                
                if (j+jb < n) {
                    magma_sgemm( MagmaConjTrans, MagmaNoTrans,
                                 jb, n-j-jb, j,
                                 c_neg_one, dA(0, j   ), ldda,
                                            dA(0, j+jb), ldda,
                                 c_one,     dA(j, j+jb), ldda, queues[1] );
                }
                
                magma_queue_sync( queues[0] );
                
                // this could be on any queue; it isn't needed until exit.
                magma_sgetmatrix_async( j, jb,
                                        dA(0, j), ldda,
                                         A(0, j), lda, queues[0] );
                
                lapackf77_spotrf( MagmaUpperStr, &jb, A(j, j), &lda, info );
                if (*info != 0) {
                    *info = *info + j;
                    break;
                }
                magma_ssetmatrix_async( jb, jb,
                                         A(j, j), lda,
                                        dA(j, j), ldda, queues[0] );
                magma_queue_sync( queues[0] );
                
                if (j+jb < n) {
                    magma_strsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
                                 jb, n-j-jb,
                                 c_one, dA(j, j   ), ldda,
                                        dA(j, j+jb), ldda, queues[1] );
                }
            }
        }
        else {
            //=========================================================
            // Compute the Cholesky factorization A = L*L'.
            for (j=0; j < n; j += nb) {
                //  Update and factorize the current diagonal block and test
                //  for non-positive-definiteness.
                jb = min( nb, n-j );
                magma_ssetmatrix_async( n-j, jb,
                                         A(j, j), lda,
                                        dA(j, j), ldda, queues[1] );
                
                magma_ssyrk( MagmaLower, MagmaNoTrans, jb, j,
                             d_neg_one, dA(j, 0), ldda,
                             d_one,     dA(j, j), ldda, queues[1] );
                magma_queue_sync( queues[1] );
                
                magma_sgetmatrix_async( jb, jb,
                                        dA(j,j), ldda,
                                         A(j,j), lda, queues[0] );
                
                if (j+jb < n) {
                    magma_sgemm( MagmaNoTrans, MagmaConjTrans,
                                 n-j-jb, jb, j,
                                 c_neg_one, dA(j+jb, 0), ldda,
                                            dA(j,    0), ldda,
                                 c_one,     dA(j+jb, j), ldda, queues[1] );
                }
                
                magma_queue_sync( queues[0] );
                
                // this could be on any queue; it isn't needed until exit.
                magma_sgetmatrix_async( jb, j,
                                        dA(j, 0), ldda,
                                         A(j, 0), lda, queues[0] );
                
                lapackf77_spotrf( MagmaLowerStr, &jb, A(j, j), &lda, info );
                if (*info != 0) {
                    *info = *info + j;
                    break;
                }
                magma_ssetmatrix_async( jb, jb,
                                         A(j, j), lda,
                                        dA(j, j), ldda, queues[0] );
                magma_queue_sync( queues[0] );
                
                if (j+jb < n) {
                    magma_strsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
                                 n-j-jb, jb,
                                 c_one, dA(j,    j), ldda,
                                        dA(j+jb, j), ldda, queues[1] );
                }
            }
        }
        magma_queue_destroy( queues[0] );
        magma_queue_destroy( queues[1] );
        
        magma_free( dA );
    }
    
    return *info;
} /* magma_spotrf */
Example #11
0
extern "C" magma_int_t
magma_spotrf_m(magma_int_t num_gpus0, char uplo, magma_int_t n,
               float *a, magma_int_t lda, magma_int_t *info)
{
/*  -- MAGMA (version 1.4.0) --
       Univ. of Tennessee, Knoxville
       Univ. of California, Berkeley
       Univ. of Colorado, Denver
       August 2013

    Purpose
    =======
    SPOTRF_OOC computes the Cholesky factorization of a real symmetric
    positive definite matrix A. This version does not require work
    space on the GPU passed as input. GPU memory is allocated in the
    routine. The matrix A may not fit entirely in the GPU memory.

    The factorization has the form
       A = U**T * U,  if UPLO = 'U', or
       A = L  * L**T, if UPLO = 'L',
    where U is an upper triangular matrix and L is lower triangular.

    This is the block version of the algorithm, calling Level 3 BLAS.

    Arguments
    =========
    UPLO    (input) CHARACTER*1
            = 'U':  Upper triangle of A is stored;
            = 'L':  Lower triangle of A is stored.

    N       (input) INTEGER
            The order of the matrix A.  N >= 0.

    A       (input/output) REAL array, dimension (LDA,N)
            On entry, the symmetric 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 INFO = 0, the factor U or L from the Cholesky
            factorization A = U**T * U or A = L * L**T.

            Higher performance is achieved if A is in pinned memory, e.g.
            allocated using magma_malloc_pinned.

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

    INFO    (output) INTEGER
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
                  or another error occured, such as memory allocation failed.
            > 0:  if INFO = i, the leading minor of order i is not
                  positive definite, and the factorization could not be
                  completed.

    =====================================================================    */


    /* Local variables */
    float                 d_one     =  1.0;
    float                 d_neg_one = -1.0;
    float     c_one     = MAGMA_S_ONE;
    float     c_neg_one = MAGMA_S_NEG_ONE;
    char                   uplo_[2]  = {uplo, 0};
    int                    upper     = lapackf77_lsame(uplo_, "U");

    float *dwork[MagmaMaxGPUs], *dt[MagmaMaxGPUs];
    magma_int_t     ldda, lddla, nb, iinfo, n_local[MagmaMaxGPUs], J2, d, num_gpus;
    magma_int_t     j, jj, jb, J, JB, NB, MB, h;
    magma_queue_t   stream[MagmaMaxGPUs][3];
    magma_event_t   event[MagmaMaxGPUs][5];
    #ifdef ROW_MAJOR_PROFILE
    magma_timestr_t start, end, start0, end0;
    float chol_time = 1.0;
    #endif
    *info = 0;
    if ((! upper) && (! lapackf77_lsame(uplo_, "L"))) {
        *info = -1;
    } else if (n < 0) {
        *info = -2;
    } else if (lda < max(1,n)) {
        *info = -4;
    }
    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }

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

    nb = magma_get_dpotrf_nb(n);
    if( num_gpus0 > n/nb ) {
        num_gpus = n/nb;
        if( n%nb != 0 ) num_gpus ++;
    } else {
        num_gpus = num_gpus0;
    }
    //ldda  = ((n+31)/32)*32;
    ldda  = ((n+nb-1)/nb)*nb;
    lddla = ((nb*((n+nb*num_gpus-1)/(nb*num_gpus))+31)/32)*32;

    /* figure out NB */
    size_t freeMem, totalMem;
    cudaMemGetInfo( &freeMem, &totalMem );
    freeMem /= sizeof(float);
    
    MB = n;  /* number of rows in the big panel    */
    NB = (magma_int_t)((0.8*freeMem-max(2,num_gpus)*nb*ldda-(n+nb)*nb)/lddla); /* number of columns in the big panel */
    //NB = min(5*nb,n);

    if( NB >= n ) {
        #ifdef CHECK_SPOTRF_OOC
        printf( "      * still fit in GPU memory.\n" );
        #endif
        NB = n;
    } else {
        #ifdef CHECK_SPOTRF_OOC
        printf( "      * don't fit in GPU memory.\n" );
        #endif
        NB = (NB/nb) * nb;   /* making sure it's devisable by nb   */
    }
    #ifdef CHECK_SPOTRF_OOC
    if( NB != n ) printf( "      * running in out-core mode (n=%d, NB=%d, nb=%d, lddla=%d, freeMem=%.2e).\n",n,NB,nb,lddla,(float)freeMem );
    else          printf( "      * running in in-core mode  (n=%d, NB=%d, nb=%d, lddla=%d, freeMem=%.2e).\n",n,NB,nb,lddla,(float)freeMem );
    fflush(stdout);
    #endif
    for (d=0; d<num_gpus; d++ ) {
        magma_setdevice(d);
        if (MAGMA_SUCCESS != magma_smalloc( &dt[d], NB*lddla + max(2,num_gpus)*nb*ldda )) {
            *info = MAGMA_ERR_DEVICE_ALLOC;
            return *info;
        }
        dwork[d] = &dt[d][max(2,num_gpus)*nb*ldda];
        
        for( j=0; j<3; j++ )
            magma_queue_create( &stream[d][j] );
        for( j=0; j<5; j++ )
            magma_event_create( &event[d][j]  );
        magma_device_sync(); // synch the device
    }
    magma_setdevice(0);

    #ifdef ROW_MAJOR_PROFILE
    start0 = get_current_time();
    #endif

    if (nb <= 1 || nb >= n) {
        lapackf77_spotrf(uplo_, &n, a, &lda, info);
    } else {

    /* Use hybrid blocked code. */
    if (upper) {
        /* =========================================================== *
         * Compute the Cholesky factorization A = U'*U.                *
         * big panel is divided by block-row and distributed in block  *
         * column cyclic format                                        */
        
        /* for each big-panel */
        for( J=0; J<n; J+=NB ) {
            JB = min(NB,n-J);
            if( num_gpus0 > (n-J)/nb ) {
                num_gpus = (n-J)/nb;
                if( (n-J)%nb != 0 ) num_gpus ++;
            } else {
                num_gpus = num_gpus0;
            }
            
            /* load the new big-panel by block-rows */
            magma_shtodpo( num_gpus, &uplo, JB, n, J, J, nb, a, lda, dwork, NB, stream, &iinfo);
            
            #ifdef ROW_MAJOR_PROFILE
            start = get_current_time();
            #endif      
            /* update with the previous big-panels */
            for( j=0; j<J; j+=nb ) {
                /* upload the diagonal of the block column (broadcast to all GPUs) */
                for( d=0; d<num_gpus; d++ ) {
                    magma_setdevice(d);
                    magma_ssetmatrix_async( nb, JB,
                                            A(j, J),       lda,
                                            dTup(d, 0, J), nb,
                                            stream[d][0] );
                    n_local[d] = 0;
                }
                
                /* distribute off-diagonal blocks to GPUs */
                for( jj=J+JB; jj<n; jj+=nb ) {
                    d  = ((jj-J)/nb)%num_gpus;
                    magma_setdevice(d);
                    
                    jb = min(nb, n-jj);
                    magma_ssetmatrix_async( nb, jb,
                                            A(j, jj),                    lda,
                                            dTup(d, 0, J+JB+n_local[d]), nb,
                                            stream[d][0] );
                    n_local[d] += jb;
                }
                
                /* wait for the communication */
                for( d=0; d<num_gpus; d++ ) {
                    magma_setdevice(d);
                    magma_queue_sync( stream[d][0] );
                }
                
                /* update the current big-panel using the previous block-row */
                /* -- process the big diagonal block of the big panel */
                for( jj=0; jj<JB; jj+=nb ) { // jj is 'local' column index within the big panel
                    d  = (jj/nb)%num_gpus;
                    J2 = jj/(nb*num_gpus);
                    
                    magma_setdevice(d);
                    magmablasSetKernelStream(stream[d][J2%2]); // the last stream (2) used to process off-diagonal
                    J2 = nb*J2;

                    jb = min(nb,JB-jj); // number of columns in this current block-row
                    magma_sgemm( MagmaTrans, MagmaNoTrans,
                                 jj, jb, nb,
                                 c_neg_one, dTup(d, 0, J   ), nb,
                                            dTup(d, 0, J+jj), nb,
                                 c_one,     dAup(d, 0, J2), NB);
                    
                    magma_ssyrk(MagmaUpper, MagmaTrans, jb, nb,
                                d_neg_one, dTup(d, 0,  J+jj), nb,
                                d_one,     dAup(d, jj, J2), NB);
                }
                /* -- process the remaining big off-diagonal block of the big panel */
                if( n > J+JB ) { 
                    for( d=0; d<num_gpus; d++ ) {
                        magma_setdevice(d);
                        magmablasSetKernelStream(stream[d][2]);
                        
                        /* local number of columns in the big panel */
                        n_local[d] = ((n-J)/(nb*num_gpus))*nb;
                        if (d < ((n-J)/nb)%num_gpus)
                            n_local[d] += nb;
                        else if (d == ((n-J)/nb)%num_gpus)
                            n_local[d] += (n-J)%nb;
                        
                        /* subtracting the local number of columns in the diagonal */
                        J2 = nb*(JB/(nb*num_gpus));
                        if( d < (JB/nb)%num_gpus ) J2+=nb;

                        n_local[d] -= J2;
                        
                        magma_sgemm( MagmaTrans, MagmaNoTrans,
                                     JB, n_local[d], nb,
                                     c_neg_one, dTup(d, 0, J   ), nb,
                                                dTup(d, 0, J+JB), nb,
                                     c_one,     dAup(d, 0, J2), NB);
                    }
                }
                
                /* wait for the previous updates */
                for( d=0; d<num_gpus; d++ ) {
                    magma_setdevice(d);
                    for( jj=0; jj<3; jj++ )
                        magma_queue_sync( stream[d][jj] );
                    magmablasSetKernelStream(NULL);
                }
                magma_setdevice(0);
            } /* end of updates with previous rows */
            
            /* factor the big panel */
            h  = (JB+nb-1)/nb; // big diagonal of big panel will be on CPU
            // using two streams
            //magma_spotrf2_mgpu(num_gpus, uplo, JB, n-J, J, J, nb,
            //                   dwork, NB, dt, ldda, a, lda, h, stream, event, &iinfo);
            // using three streams
            magma_spotrf3_mgpu(num_gpus, uplo, JB, n-J, J, J, nb,
                               dwork, NB, dt, ldda, a, lda, h, stream, event, &iinfo);
            if( iinfo != 0 ) {
                *info = J+iinfo;
                break;
            }
            #ifdef ROW_MAJOR_PROFILE
            end = get_current_time();
            chol_time += GetTimerValue(start, end);
            #endif      
            
            /* upload the off-diagonal (and diagonal!!!) big panel */
            magma_sdtohpo(num_gpus, &uplo, JB, n, J, J, nb, NB, a, lda, dwork, NB, stream, &iinfo);
            //magma_sdtohpo(num_gpus, &uplo, JB, n, J, J, nb, 0, a, lda, dwork, NB, stream, &iinfo);
        }
    } else {
        /* ========================================================= *
         * Compute the Cholesky factorization A = L*L'.              */
        
        /* for each big-panel */
        for( J=0; J<n; J+=NB ) {
            JB = min(NB,n-J);
            if( num_gpus0 > (n-J)/nb ) {
                num_gpus = (n-J)/nb;
                if( (n-J)%nb != 0 ) num_gpus ++;
            } else {
                num_gpus = num_gpus0;
            }
            
            /* load the new big-panel by block-columns */
            magma_shtodpo( num_gpus, &uplo, n, JB, J, J, nb, a, lda, dwork, lddla, stream, &iinfo);
            
            /* update with the previous big-panels */
            #ifdef ROW_MAJOR_PROFILE
            start = get_current_time();
            #endif      
            for( j=0; j<J; j+=nb ) {
                /* upload the diagonal of big panel */
                for( d=0; d<num_gpus; d++ ) {
                    magma_setdevice(d);
                    magma_ssetmatrix_async( JB, nb,
                                            A(J, j),     lda,
                                            dT(d, J, 0), ldda,
                                            stream[d][0] );
                    n_local[d] = 0;
                }
                
                /* upload off-diagonals */
                for( jj=J+JB; jj<n; jj+=nb ) {
                    d  = ((jj-J)/nb)%num_gpus;
                    magma_setdevice(d);
                    
                    jb = min(nb, n-jj);
                    magma_ssetmatrix_async( jb, nb,
                                            A(jj, j),                  lda,
                                            dT(d, J+JB+n_local[d], 0), ldda,
                                            stream[d][0] );
                    n_local[d] += jb;
                }
                
                /* wait for the communication */
                for( d=0; d<num_gpus; d++ ) {
                    magma_setdevice(d);
                    magma_queue_sync( stream[d][0] );
                }
                
                /* update the current big-panel using the previous block-row */
                for( jj=0; jj<JB; jj+=nb ) { /* diagonal */
                    d  = (jj/nb)%num_gpus;
                    J2 = jj/(nb*num_gpus);
                    
                    magma_setdevice(d);
                    magmablasSetKernelStream(stream[d][J2%2]);
                    
                    J2 = nb*J2;
                    jb = min(nb,JB-jj);
                    magma_sgemm( MagmaNoTrans, MagmaTrans,
                                 jb, jj, nb,
                                 c_neg_one, dT(d, J+jj, 0), ldda,
                                            dT(d, J,    0), ldda,
                                 c_one,     dA(d, J2,   0), lddla);
                    
                    magma_ssyrk(MagmaLower, MagmaNoTrans, jb, nb,
                                d_neg_one, dT(d, J+jj, 0), ldda,
                                d_one,     dA(d, J2,  jj), lddla);
                }
                
                if( n > J+JB ) { /* off-diagonal */
                    for( d=0; d<num_gpus; d++ ) {
                        magma_setdevice(d);
                        magmablasSetKernelStream(stream[d][2]);
                        
                        /* local number of columns in the big panel */
                        n_local[d] = (((n-J)/nb)/num_gpus)*nb;
                        if (d < ((n-J)/nb)%num_gpus)
                            n_local[d] += nb;
                        else if (d == ((n-J)/nb)%num_gpus)
                            n_local[d] += (n-J)%nb;
                        
                        /* subtracting local number of columns in diagonal */
                        J2 = nb*(JB/(nb*num_gpus));
                        if( d < (JB/nb)%num_gpus ) J2+=nb;

                        n_local[d] -= J2;
                        
                        magma_sgemm( MagmaNoTrans, MagmaTrans,
                                     n_local[d], JB, nb,
                                     c_neg_one, dT(d, J+JB, 0), ldda,
                                                dT(d, J,    0), ldda,
                                     c_one,     dA(d, J2,   0), lddla);
                    }
                }
                /* wait for the previous updates */
                for( d=0; d<num_gpus; d++ ) {
                    magma_setdevice(d);
                    for( jj=0; jj<3; jj++ ) 
                        magma_queue_sync( stream[d][jj] );
                    magmablasSetKernelStream(NULL);
                }
                magma_setdevice(0);
            }
            
            /* factor the big panel */
            h = (JB+nb-1)/nb; // big diagonal of big panel will be on CPU
            // using two streams
            //magma_spotrf2_mgpu(num_gpus, uplo, n-J, JB, J, J, nb,
            //                   dwork, lddla, dt, ldda, a, lda, h, stream, event, &iinfo);
            // using three streams
            magma_spotrf3_mgpu(num_gpus, uplo, n-J, JB, J, J, nb,
                               dwork, lddla, dt, ldda, a, lda, h, stream, event, &iinfo);
            if( iinfo != 0 ) {
                *info = J+iinfo;
                break;
            }
            #ifdef ROW_MAJOR_PROFILE
            end = get_current_time();
            chol_time += GetTimerValue(start, end);
            #endif      
            /* upload the off-diagonal big panel */
            magma_sdtohpo( num_gpus, &uplo, n, JB, J, J, nb, JB, a, lda, dwork, lddla, stream, &iinfo);
        
        } /* end of for J */
    } /* if upper */
    } /* if nb */
    #ifdef ROW_MAJOR_PROFILE
    end0 = get_current_time();
    #endif
    if( num_gpus0 > n/nb ) {
        num_gpus = n/nb;
        if( n%nb != 0 ) num_gpus ++;
    } else {
        num_gpus = num_gpus0;
    }
    for (d=0; d<num_gpus; d++ ) {
        magma_setdevice(d);

        for( j=0; j<3; j++ ) {
            if( stream[d][j] != NULL ) magma_queue_destroy( stream[d][j] );
        }
        magma_free( dt[d] );

        for( j=0; j<5; j++ ) {
            magma_event_destroy( event[d][j] );
        }
    }
    magma_setdevice(0);

    #ifdef ROW_MAJOR_PROFILE
    printf("\n n=%d NB=%d nb=%d\n",n,NB,nb);
    printf(" Without memory allocation: %f / %f = %f GFlop/s\n",
           FLOPS_SPOTRF(n)/1000000, GetTimerValue(start0, end0),
           FLOPS_SPOTRF(n)/(1000000*GetTimerValue(start0, end0)));
    printf(" Performance %f / %f = %f GFlop/s\n",
           FLOPS_SPOTRF(n)/1000000, chol_time,
           FLOPS_SPOTRF(n)/(1000000*chol_time));
    #endif
    return *info;
} /* magma_spotrf_ooc */
Example #12
0
int main( int argc, char** argv)
{
    real_Double_t gflops, gpu_perf, cpu_perf, gpu_time, cpu_time;
    float *hA, *hR;
    magmaFloat_ptr dA;
    magma_int_t N = 0, n2, lda, ldda;
    magma_int_t size[10] =
    { 1024, 2048, 3072, 4032, 5184, 6048, 7200, 8064, 8928, 10560 };

    magma_int_t i, info;
    float mz_one = MAGMA_S_NEG_ONE;
    magma_int_t ione     = 1;
    magma_int_t ISEED[4] = {0,0,0,1};
    float      work[1], matnorm, diffnorm;

    if (argc != 1) {
        for(i = 1; i<argc; i++) {
            if (strcmp("-N", argv[i])==0)
                N = atoi(argv[++i]);
        }
        if (N>0) size[0] = size[9] = N;
        else exit(1);
    }
    else {
        printf("\nUsage: \n");
        printf("  testing_spotrf_gpu -N %d\n\n", 1024);
    }

    /* Initialize */
    magma_queue_t  queue;
    magma_device_t device[ MagmaMaxGPUs ];
    int num = 0;
    magma_err_t err;
    magma_init();
    err = magma_get_devices( device, MagmaMaxGPUs, &num );
    if ( err != 0 || num < 1 ) {
        fprintf( stderr, "magma_get_devices failed: %d\n", err );
        exit(-1);
    }
    err = magma_queue_create( device[0], &queue );
    if ( err != 0 ) {
        fprintf( stderr, "magma_queue_create failed: %d\n", err );
        exit(-1);
    }

    /* Allocate memory for the largest matrix */
    N    = size[9];
    n2   = N * N;
    ldda = ((N+31)/32) * 32;
    TESTING_MALLOC_CPU( hA, float, n2 );
    TESTING_MALLOC_PIN( hR, float, n2 );
    TESTING_MALLOC_DEV( dA, float, ldda*N );

    printf("\n\n");
    printf("  N    CPU GFlop/s (sec)    GPU GFlop/s (sec)    ||R_magma-R_lapack||_F / ||R_lapack||_F\n");
    printf("========================================================================================\n");
    for(i=0; i<10; i++) {
        N   = size[i];
        lda = N;
        n2  = lda*N;
        ldda = ((N+31)/32)*32;
        gflops = FLOPS( (float)N ) * 1e-9;

        /* Initialize the matrix */
        lapackf77_slarnv( &ione, ISEED, &n2, hA );
        /* Symmetrize and increase the diagonal */
        for( int i = 0; i < N; ++i ) {
            MAGMA_S_SET2REAL( hA(i,i), MAGMA_S_REAL(hA(i,i)) + N );
            for( int j = 0; j < i; ++j ) {
                hA(i, j) = MAGMA_S_CNJG( hA(j,i) );
            }
        }
        lapackf77_slacpy( MagmaFullStr, &N, &N, hA, &lda, hR, &lda );

        /* Warm up to measure the performance */
        magma_ssetmatrix( N, N, hA, 0, lda, dA, 0, ldda, queue );
        magma_spotrf_gpu( MagmaUpper, N, dA, 0, ldda, &info, queue );

        /* ====================================================================
           Performs operation using MAGMA
           =================================================================== */
        magma_ssetmatrix( N, N, hA, 0, lda, dA, 0, ldda, queue );
        gpu_time = magma_wtime();
        magma_spotrf_gpu( MagmaUpper, N, dA, 0, ldda, &info, queue );
        gpu_time = magma_wtime() - gpu_time;
        if (info != 0)
            printf( "magma_spotrf had error %d.\n", info );

        gpu_perf = gflops / gpu_time;

        /* =====================================================================
           Performs operation using LAPACK
           =================================================================== */
        cpu_time = magma_wtime();
        lapackf77_spotrf( MagmaUpperStr, &N, hA, &lda, &info );
        cpu_time = magma_wtime() - cpu_time;
        if (info != 0)
            printf( "lapackf77_spotrf had error %d.\n", info );

        cpu_perf = gflops / cpu_time;

        /* =====================================================================
           Check the result compared to LAPACK
           |R_magma - R_lapack| / |R_lapack|
           =================================================================== */
        magma_sgetmatrix( N, N, dA, 0, ldda, hR, 0, lda, queue );
        matnorm = lapackf77_slange("f", &N, &N, hA, &lda, work);
        blasf77_saxpy(&n2, &mz_one, hA, &ione, hR, &ione);
        diffnorm = lapackf77_slange("f", &N, &N, hR, &lda, work);
        printf( "%5d     %6.2f (%6.2f)     %6.2f (%6.2f)         %e\n",
                N, cpu_perf, cpu_time, gpu_perf, gpu_time, diffnorm / matnorm );

        if (argc != 1)
            break;
    }

    /* clean up */
    TESTING_FREE_CPU( hA );
    TESTING_FREE_PIN( hR );
    TESTING_FREE_DEV( dA );
    magma_queue_destroy( queue );
    magma_finalize();
}
Example #13
0
/**
    Purpose
    -------
    SPOTRF computes the Cholesky factorization of a real symmetric
    positive definite matrix dA.
    Auxiliary subroutine for spotrf2_ooc. It is multiple gpu interface to compute
    Cholesky of a "rectangular" matrix.

    The factorization has the form
       dA = U**H * U,   if UPLO = MagmaUpper, or
       dA = L  * L**H,  if UPLO = MagmaLower,
    where U is an upper triangular matrix and L is lower triangular.

    This is the block version of the algorithm, calling Level 3 BLAS.

    Arguments
    ---------
    @param[in]
    uplo    magma_uplo_t
      -     = MagmaUpper:  Upper triangle of dA is stored;
      -     = MagmaLower:  Lower triangle of dA is stored.

    @param[in]
    n       INTEGER
            The order of the matrix dA.  N >= 0.

    @param[in,out]
    dA      REAL array on the GPU, dimension (LDDA,N)
            On entry, the symmetric matrix dA.  If UPLO = MagmaUpper, the leading
            N-by-N upper triangular part of dA contains the upper
            triangular part of the matrix dA, and the strictly lower
            triangular part of dA is not referenced.  If UPLO = MagmaLower, the
            leading N-by-N lower triangular part of dA contains the lower
            triangular part of the matrix dA, and the strictly upper
            triangular part of dA is not referenced.
    \n
            On exit, if INFO = 0, the factor U or L from the Cholesky
            factorization dA = U**H * U or dA = L * L**H.

    @param[in]
    ldda     INTEGER
            The leading dimension of the array dA.  LDDA >= max(1,N).
            To benefit from coalescent memory accesses LDDA must be
            divisible by 16.

    @param[out]
    info    INTEGER
      -     = 0:  successful exit
      -     < 0:  if INFO = -i, the i-th argument had an illegal value
      -     > 0:  if INFO = i, the leading minor of order i is not
                  positive definite, and the factorization could not be
                  completed.

    @ingroup magma_sposv_comp
    ********************************************************************/
extern "C" magma_int_t
magma_spotrf3_mgpu(
    magma_int_t ngpu,
    magma_uplo_t uplo, magma_int_t m, magma_int_t n,
    magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
    magmaFloat_ptr d_lA[],  magma_int_t ldda,
    magmaFloat_ptr d_lP[],  magma_int_t lddp,
    float *A,          magma_int_t lda, magma_int_t h,
    magma_queue_t queues[][3], magma_event_t events[][5],
    magma_int_t *info )
{
#define Alo(i, j)  (A +             ((j)+off_j)*lda  + (nb*(((i)/nb)%h)+off_i))
#define Aup(i, j)  (A + (nb*(((j)/nb)%h)+off_j)*lda  +               (i+off_i))

#define dlA(id, i, j)     (d_lA[(id)] + (j)*ldda + (i))
#define dlP(id, i, j, k)  (d_lP[(id)] + (k)*nb*lddp + (j)*lddp + (i))
#define dlPT(id, i, j, k) (d_lP[(id)] + (k)*nb*lddp + (j)*nb   + (i))

    magma_int_t     j, jb, nb0, nb2, d, dd, id, j_local, j_local2, buf;
    float c_one     = MAGMA_S_ONE;
    float c_neg_one = MAGMA_S_NEG_ONE;
    float          d_one     =  1.0;
    float          d_neg_one = -1.0;
    int upper = (uplo == MagmaUpper);
    float *dlpanel;
    magma_int_t n_local[MagmaMaxGPUs], ldpanel;
    const magma_int_t stream1 = 0, stream2 = 1, stream3 = 2;
    
    *info = 0;
    if (! upper && uplo != MagmaLower) {
        *info = -1;
    } else if (n < 0) {
        *info = -2;
    } else if (!upper && ngpu*ldda < max(1,n)) {
        *info = -4;
    } else if (upper && ldda < max(1,m)) {
        *info = -4;
    }
    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }

    magma_device_t orig_dev;
    magma_getdevice( &orig_dev );
    magma_queue_t orig_stream;
    magmablasGetKernelStream( &orig_stream );
    
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
    /* used by strsm_work */
    float c_zero    = MAGMA_S_ZERO;
    int trsm_nb = 128;
    int trsm_n = trsm_nb*((nb+trsm_nb-1)/trsm_nb);
    float *d_dinvA[MagmaMaxGPUs];
    float *d_x[MagmaMaxGPUs];
    #define dinvA(d,j) &(d_dinvA[(d)][(j)*trsm_nb*trsm_n])
    #define dx(d,j) &(d_x[(d)][(j)*nb*m])
    /*
     * Allocate device memory for the inversed diagonal blocks, size=N*BLOCK_SIZE
     */
    // TODO free memory on failure.
    for( d=0; d < ngpu; d++ ) {
        magma_setdevice(d);
        if ( (MAGMA_SUCCESS != magma_smalloc( &d_dinvA[d], 2*trsm_nb*trsm_n )) ||
             (MAGMA_SUCCESS != magma_smalloc( &d_x[d],     2*nb*(upper ? n : m) )) ) {
            *info = MAGMA_ERR_DEVICE_ALLOC;
            return *info;
        }
    }
    magma_setdevice(0);
#endif
    
    /* initialization */
    for( d=0; d < ngpu; d++ ) {
        /* local-n and local-ld */
        if (upper) {
            n_local[d] = (n/(nb*ngpu))*nb;
            if (d < (n/nb)%ngpu)
                n_local[d] += nb;
            else if (d == (n/nb)%ngpu)
                n_local[d] += n%nb;
        } else {
            n_local[d] = (m/(nb*ngpu))*nb;
            if (d < (m/nb)%ngpu)
                n_local[d] += nb;
            else if (d == (m/nb)%ngpu)
                n_local[d] += m%nb;
        }
    }

    /* == initialize the trace */
    trace_init( 1, ngpu, 3, (CUstream_st**)queues );

    if (upper) {
        /* ---------------------------------------------- */
        /* Upper-triangular case                          */
        /* > Compute the Cholesky factorization A = U'*U. */
        /* ---------------------------------------------- */
        for (j=0; j < m; j += nb) {
            /* Set the GPU number that holds the current panel */
            id  = (j/nb)%ngpu;
            buf = (j/nb)%ngpu; // right now, we have ngpu buffers, so id and buf are the same..
            
            /* Set the local index where the current panel is */
            j_local = j/(nb*ngpu);
            jb = min(nb, (m-j));
 
            /* Update the current diagonal block on stream1 */
            magma_setdevice(id);
            if ( j > 0 ) {
                magmablasSetKernelStream( queues[id][stream1] );
                trace_gpu_start( id, stream1, "syrk", "syrk" );
                magma_ssyrk(MagmaUpper, MagmaConjTrans, jb, j,
                            d_neg_one, dlA(id, 0, nb*j_local), ldda,
                            d_one,     dlA(id, j, nb*j_local), ldda);
                trace_gpu_end( id, stream1 );
            }
            
            /* send the diagonal to cpu on stream1 */
            trace_gpu_start( id, stream1, "comm", "D to CPU" );
            magma_sgetmatrix_async( jb, jb,
                                    dlA(id, j, nb*j_local), ldda,
                                    Aup(j,j),               lda,
                                    queues[id][stream1] );
            trace_gpu_end( id, stream1 );

            /* update off-diagonal blocks in the panel */
            if ( j > 0 ) {
                d = (j/nb+1)%ngpu;
                for( dd=0; dd < ngpu; dd++ ) {
                    j_local2 = j_local+1;
                    if ( d > id ) j_local2 --;
                    nb0 = nb*j_local2; // number of local columns in the panel, while jb is panel-size (number of rows)
            
                    if ( n_local[d] > nb0 ) {
                        magma_setdevice(d);
                        magmablasSetKernelStream( queues[d][stream2] );
                        if ( d == id ) {
                            dlpanel = dlA(d,0,nb*j_local);
                            ldpanel = ldda;
                            // the GPU owns the row from start, and no need of synch.
                            //magma_queue_wait_event( queues[d][stream2], events[d][0] ); // rows arrived at gpu
                            magma_queue_wait_event( queues[d][stream2], events[d][4] ); // wait for look-ahead trsm to finish
                        } else {
                            dlpanel = dlP(d,nb,0,buf);
                            ldpanel = lddp;
                            magma_queue_wait_event( queues[d][stream2], events[d][0] ); // rows arrived at gpu
                        }
                        trace_gpu_start( d, stream2, "gemm", "gemm" );
                        magma_sgemm(MagmaConjTrans, MagmaNoTrans,
                                    jb, n_local[d]-nb0, j,
                                    c_neg_one, dlpanel,        ldpanel,
                                               dlA(d, 0, nb0), ldda,
                                    c_one,     dlA(d, j, nb0), ldda);
                        trace_gpu_end( d, stream2 );
                        magma_event_record( events[d][2], queues[d][stream2] );
                    }
                    d = (d+1)%ngpu;
                }
            }

            /* wait for panel and factorize it on cpu */
            magma_setdevice(id);
            magma_queue_sync( queues[id][stream1] );
            trace_cpu_start( 0, "getrf", "getrf" );
            lapackf77_spotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
            trace_cpu_end( 0 );
            if (*info != 0) {
                *info = *info + j;
                break;
            }
            
            /* send the diagonal to gpus on stream1 */
            if ( (j+jb) < n) {
                d = (j/nb+1)%ngpu;
                for( dd=0; dd < ngpu; dd++ ) {
                    if ( d == id ) {
                        dlpanel = dlA(d, j, nb*j_local);
                        ldpanel = ldda;
                    } else {
                        dlpanel = dlP(d,0,0,buf);
                        ldpanel = lddp;
                    }
                    magma_setdevice(d);
                    trace_gpu_start( d, stream1, "comm", "comm" );
                    magma_ssetmatrix_async( jb, jb,
                                            Aup(j,j), lda,
                                            dlpanel,  ldpanel,
                                            queues[d][stream1] );
                    trace_gpu_end( d, stream1 );
                    magma_event_record( events[d][1], queues[d][stream1] );
                    d = (d+1)%ngpu;
                }
            } else {
                magma_setdevice(id);
                trace_gpu_start( id, stream1, "comm", "comm" );
                magma_ssetmatrix_async( jb, jb,
                                        Aup(j,j),               lda,
                                        dlA(id, j, nb*j_local), ldda,
                                        queues[id][stream1] );
                trace_gpu_end( id, stream1 );
            }
            
            /* panel-factorize the off-diagonal */
            if ( (j+jb) < n) {
                d = (j/nb+1)%ngpu;
                for( dd=0; dd < ngpu; dd++ ) {
                    /* next column */
                    j_local2 = j_local+1;
                    if ( d > id ) j_local2--;
                    if ( d == id ) {
                        dlpanel = dlA(d,j,nb*j_local);
                        ldpanel = ldda;
                    } else {
                        dlpanel = dlP(d,0,0,buf);
                        ldpanel = lddp;
                    }
                    nb2 = n_local[d] - j_local2*nb;
                    
                    magma_setdevice(d);
                    if ( j+jb < m && d == (j/nb+1)%ngpu ) {
                        /* owns the next column, look-ahead next block on stream1 */
                        nb0 = min(nb, nb2);
                        magmablasSetKernelStream( queues[d][stream1] );
                        magma_queue_wait_event( queues[d][stream1], events[d][2] ); // wait for gemm update
                        trace_gpu_start( d, stream1, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
                        magmablas_slaset( MagmaFull, trsm_nb, trsm_n, c_zero, c_zero, dinvA(d,0), trsm_nb );
                        magmablas_slaset( MagmaFull, nb0,     jb,     c_zero, c_zero, dx(d,0), nb0 );
                        magmablas_strsm_work( MagmaLeft, MagmaUpper,
                                              MagmaConjTrans, MagmaNonUnit,
                                              jb, nb0, c_one,
                                              dlpanel, ldpanel,
                                              dlA(d, j, nb*j_local2), ldda,
                                              1, dinvA(d,0), dx(d,0) );
#else
                        magma_strsm( MagmaLeft, MagmaUpper,
                                     MagmaConjTrans, MagmaNonUnit,
                                     jb, nb0, c_one,
                                     dlpanel,                ldpanel,
                                     dlA(d, j, nb*j_local2), ldda);
#endif
                        magma_event_record( events[d][4], queues[d][stream1] );
                        trace_gpu_end( d, stream1 );
                    } else if ( nb2 > 0 ) {
                        /* update all the blocks on stream2 */
                        magma_queue_wait_event( queues[d][stream2], events[d][1] ); // wait for cholesky factor
                        trace_gpu_start( d, stream2, "trsm", "trsm" );
                        magmablasSetKernelStream( queues[d][stream2] );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
                        magmablas_slaset( MagmaFull, trsm_nb, trsm_n, c_zero, c_zero, dinvA(d,0), trsm_nb );
                        magmablas_slaset( MagmaFull, nb2,     jb,     c_zero, c_zero, dx(d,0), nb2 );
                        magmablas_strsm_work( MagmaLeft, MagmaUpper,
                                              MagmaConjTrans, MagmaNonUnit,
                                              jb, nb2, c_one,
                                              dlpanel, ldpanel,
                                              dlA(d, j, nb*j_local2), ldda,
                                              1, dinvA(d,0), dx(d,0) );
#else
                        magma_strsm( MagmaLeft, MagmaUpper,
                                     MagmaConjTrans, MagmaNonUnit,
                                     jb, nb2, c_one,
                                     dlpanel,                ldpanel,
                                     dlA(d, j, nb*j_local2), ldda);
#endif
                        trace_gpu_end( d, stream2 );
                    }
                    d = (d+1)%ngpu;
                } /* end of for */

                /* ========================================================== */
                if ( j+jb < m ) {
                    d = (j/nb+1)%ngpu;
                    /* next column */
                    j_local2 = j_local+1;
                    if ( d > id ) j_local2--;
                    nb0 = min(nb, n_local[d]-nb*j_local2 );
                
                    /* even on 1 gpu, off-diagonals are copied to cpu (synchronize at the end).      *
                     * so we have the Cholesky factor, but only diagonal submatrix of the big panel, *
                     * on cpu at the end.                                                            */
                    int d2, buf2;
                    magma_setdevice(d);
                    /* lookahead done */
                    magma_queue_wait_event( queues[d][stream3], events[d][4] );
                
                    trace_gpu_start( d, stream3, "comm", "row to CPU" );
                    magma_sgetmatrix_async( (j+jb), nb0,
                                            dlA(d, 0, nb*j_local2), ldda,
                                            Aup(0,j+jb),            lda,
                                            queues[d][stream3] );
                    trace_gpu_end( d, stream3 );
                    magma_event_record( events[d][3], queues[d][stream3] );
                    /* needed on pluto */
                    //magma_queue_sync( queues[d][stream3] );
                
                    /* broadcast rows to gpus on stream2 */
                    buf2 = ((j+jb)/nb)%ngpu;
                    for( d2=0; d2 < ngpu; d2++ ) {
                        if ( d2 != d ) {
                            magma_setdevice(d2);
                            trace_gpu_start( d2, stream3, "comm", "row to GPUs" );
                            magma_queue_wait_event( queues[d2][stream3], events[d][3] ); // rows arrived at cpu on stream3
                            magma_ssetmatrix_async( j+jb, nb0,
                                                    Aup(0,j+jb),       lda,
                                                    dlP(d2,nb,0,buf2), lddp,
                                                    queues[d2][stream3] );
                            trace_gpu_end( d2, stream3 );
                            magma_event_record( events[d2][0], queues[d2][stream3] );
                        }
                    }

                    /* =========================== */
                    /* update the remaining blocks */
                    nb2 = n_local[d]-(nb*j_local2 + nb0);
                    if ( nb2 > 0 ) {
                        if ( d == id ) {
                            dlpanel = dlA(d, j, nb*j_local);
                            ldpanel = ldda;
                        } else {
                            dlpanel = dlP(d,0,0,buf);
                            ldpanel = lddp;
                        }
                        magma_setdevice(d);
                        magmablasSetKernelStream( queues[d][stream2] );
                        trace_gpu_start( d, stream2, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
                        int flag = 0;
                        if (flag == 0) {
                            magma_queue_wait_event( queues[d][stream2], events[d][4] ); // lookahead -> diagonal inversion
                        } else {
                            magmablas_slaset( MagmaFull, trsm_nb, trsm_n, c_zero, c_zero, dinvA(d,flag), trsm_nb );
                            magma_queue_wait_event( queues[d][stream2], events[d][1] ); // panel received
                        }
                        magmablas_slaset( MagmaFull, nb2, jb, c_zero, c_zero, dx(d,1), nb2 );
                        magmablas_strsm_work( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
                                              jb, nb2, c_one,
                                              dlpanel, ldpanel,
                                              dlA(d, j, nb*j_local2+nb0), ldda,
                                              flag, dinvA(d,flag), dx(d,1) );
#else
                        magma_queue_wait_event( queues[d][stream2], events[d][1] ); // wait for cholesky factor
                        magma_strsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
                                     jb, nb2, c_one,
                                     dlpanel, ldpanel,
                                     dlA(d, j, nb*j_local2+nb0), ldda);
#endif
                        trace_gpu_end( d, stream2 );
                    }
                }
            } /* end of strsm */
        } /* end of for j=1, .., n */
    } else {
        /* ---------------------------------------------- */
        /* Lower-triangular case                          */
        /* > Compute the Cholesky factorization A = L*L'. */
        /* ---------------------------------------------- */
        for (j=0; j < n; j += nb) {
        
            /* Set the GPU number that holds the current panel */
            id  = (j/nb)%ngpu;
            buf = (j/nb)%ngpu;
            
            /* Set the local index where the current panel is */
            j_local = j/(nb*ngpu);
            jb = min(nb, (n-j));

            /* Update the current diagonal block on stream1 */
            magma_setdevice(id);
            if ( j > 0 ) {
                magmablasSetKernelStream( queues[id][stream1] );
                magma_ssyrk(MagmaLower, MagmaNoTrans, jb, j,
                            d_neg_one, dlA(id, nb*j_local, 0), ldda,
                            d_one,     dlA(id, nb*j_local, j), ldda);
            }

            /* send the diagonal to cpu on stream1 */
            magma_sgetmatrix_async( jb, jb,
                                    dlA(id, nb*j_local, j), ldda,
                                    Alo(j,j),               lda,
                                    queues[id][stream1] );

            /* update off-diagonal blocks of the panel */
            if ( j > 0 ) {
                d = (j/nb+1)%ngpu;
                for( dd=0; dd < ngpu; dd++ ) {
                    j_local2 = j_local+1;
                    if ( d > id ) j_local2 --;
                    nb0 = nb*j_local2;
            
                    if ( nb0 < n_local[d] ) {
                        magma_setdevice(d);
                        magmablasSetKernelStream( queues[d][stream2] );
                        if ( d == id ) {
                            dlpanel = dlA(d, nb*j_local, 0);
                            ldpanel = ldda;
                            magma_queue_wait_event( queues[d][stream2], events[d][4] ); // wait for look-ahead trsm to finish
                        } else {
                            dlpanel = dlPT(d,0,nb,buf);
                            ldpanel = nb;
                            magma_queue_wait_event( queues[d][stream2], events[d][0] ); // rows arrived at gpu
                        }
                        magma_sgemm( MagmaNoTrans, MagmaConjTrans,
                                     n_local[d]-nb0, jb, j,
                                     c_neg_one, dlA(d, nb0, 0), ldda,
                                                dlpanel,        ldpanel,
                                     c_one,     dlA(d, nb0, j), ldda);
                        magma_event_record( events[d][2], queues[d][stream2] );
                    }
                    d = (d+1)%ngpu;
                }
            }

            /* wait for the panel and factorized it on cpu */
            magma_setdevice(id);
            magma_queue_sync( queues[id][stream1] );
            lapackf77_spotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
            if (*info != 0) {
                *info = *info + j;
                break;
            }

            /* send the diagonal to gpus on stream1 */
            if ( (j+jb) < m) {
                d = (j/nb+1)%ngpu;
                for( dd=0; dd < ngpu; dd++ ) {
                    if ( d == id ) {
                        dlpanel = dlA(d, nb*j_local, j);
                        ldpanel = ldda;
                    } else {
                        dlpanel = dlPT(d, 0, 0, buf);
                        ldpanel = nb;
                    }
                    magma_setdevice(d);
                    magma_ssetmatrix_async( jb, jb,
                                            Alo(j,j), lda,
                                            dlpanel,  ldpanel,
                                            queues[d][stream1] );
                    magma_event_record( events[d][1], queues[d][stream1] );
                    d = (d+1)%ngpu;
                }
            } else {
                magma_setdevice(id);
                magma_ssetmatrix_async( jb, jb,
                                        Alo(j,j),               lda,
                                        dlA(id, nb*j_local, j), ldda,
                                        queues[id][stream1] );
            }

            /* panel factorize the off-diagonal */
            if ( (j+jb) < m) {
                d = (j/nb+1)%ngpu;
                for( dd=0; dd < ngpu; dd++ ) {
                    /* next column */
                    j_local2 = j_local+1;
                    if ( d > id ) j_local2--;
                    if ( d == id ) {
                        dlpanel = dlA(d, nb*j_local, j);
                        ldpanel = ldda;
                    } else {
                        dlpanel = dlPT(d, 0, 0, buf);
                        ldpanel = nb;
                    }
                    nb2 = n_local[d] - j_local2*nb;
                    nb0 = min(nb, nb2);
                    
                    magma_setdevice(d);
                    if ( j+nb < n && d == (j/nb+1)%ngpu ) { /* owns next column, look-ahead next block on stream1 */
                        if ( j > 0 ) magma_queue_wait_event( queues[d][stream1], events[d][2] ); // wait for gemm update
                        magmablasSetKernelStream( queues[d][stream1] );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
                        magmablas_slaset( MagmaFull, trsm_nb, trsm_n, c_zero, c_zero, dinvA(d,0), trsm_nb );
                        magmablas_slaset( MagmaFull, nb0,     jb,     c_zero, c_zero, dx(d,0), nb0 );
                        magmablas_strsm_work( MagmaRight, MagmaLower,
                                              MagmaConjTrans, MagmaNonUnit,
                                              nb0, jb, c_one,
                                              dlpanel, ldpanel,
                                              dlA(d, nb*j_local2, j), ldda,
                                              1, dinvA(d,0), dx(d,0) );
#else
                        magma_strsm( MagmaRight, MagmaLower,
                                     MagmaConjTrans, MagmaNonUnit,
                                     nb0, jb, c_one,
                                     dlpanel, ldpanel,
                                     dlA(d, nb*j_local2, j), ldda);
#endif
                        magma_event_record( events[d][4], queues[d][stream1] );
                    } else if ( nb2 > 0 ) { /* other gpus updating all the blocks on stream2 */
                        /* update the entire column */
                        magma_queue_wait_event( queues[d][stream2], events[d][1] ); // wait for the cholesky factor
                        magmablasSetKernelStream( queues[d][stream2] );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
                        magmablas_slaset( MagmaFull, trsm_nb, trsm_n, c_zero, c_zero, dinvA(d,0), trsm_nb );
                        magmablas_slaset( MagmaFull, nb2,     jb,     c_zero, c_zero, dx(d,0), nb2 );
                        magmablas_strsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
                                              nb2, jb, c_one,
                                              dlpanel,                ldpanel,
                                              dlA(d, nb*j_local2, j), ldda,
                                              1, dinvA(d,0), dx(d,0) );
#else
                        magma_strsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
                                     nb2, jb, c_one,
                                     dlpanel,                ldpanel,
                                     dlA(d, nb*j_local2, j), ldda);
#endif
                    }
                    d = (d+1)%ngpu;
                } /* end for d */

                /* ========================================================== */
                if ( j+jb < n ) {
                    d = (j/nb+1)%ngpu;
                    /* next column */
                    j_local2 = j_local+1;
                    if ( d > id ) j_local2--;
                    nb0 = min(nb, n_local[d]-nb*j_local2 );
                
                    /* even on 1 gpu, we copy off-diagonal to cpu (but don't synchronize).  */
                    /* so we have the Cholesky factor on cpu at the end.                    */
                    int d2, buf2;
//#define SPOTRF_DEVICE_TO_DEVICE
#ifdef SPOTRF_DEVICE_TO_DEVICE
                    // lookahead done
                
                    /* broadcast the rows to gpus */
                    buf2 = ((j+jb)/nb)%ngpu;
                    for( d2=0; d2 < ngpu; d2++ ) {
                        magma_setdevice(d2);
                        magma_queue_wait_event( queues[d2][stream3], events[d][4] );
                        if ( d2 != d ) {
                            magma_scopymatrix_async( nb0, j+jb,
                                                     dlPT(d2,0,nb,buf2), nb, // first nbxnb reserved for diagonal block
                                                     dlA(d, nb*j_local2, 0), ldda,
                                                     queues[d2][stream3] );
                            magma_event_record( events[d2][0], queues[d2][stream3] );
                        } else {
                            magma_sgetmatrix_async( nb0, j+jb,
                                                    dlA(d, nb*j_local2, 0), ldda,
                                                    Alo(j+jb,0),            lda,
                                                    queues[d][stream3] );
                        }
                    }
#else
                    // lookahead done
                    magma_setdevice(d);
                    magma_queue_wait_event( queues[d][stream3], events[d][4] );
                    magma_sgetmatrix_async( nb0, j+jb,
                                            dlA(d, nb*j_local2, 0), ldda,
                                            Alo(j+jb,0),            lda,
                                            queues[d][stream3] );
                    magma_event_record( events[d][3], queues[d][stream3] );
                    /* syn on rows on CPU, seem to be needed on Pluto */
                    //magma_queue_sync( queues[d][stream3] );
                
                    /* broadcast the rows to gpus */
                    buf2 = ((j+jb)/nb)%ngpu;
                    for( d2=0; d2 < ngpu; d2++ ) {
                        if ( d2 != d ) {
                            magma_setdevice(d2);
                            magma_queue_wait_event( queues[d2][stream3], events[d][3] ); // getmatrix done
                            magma_ssetmatrix_async( nb0, j+jb,
                                                    Alo(j+jb,0),        lda,
                                                    dlPT(d2,0,nb,buf2), nb, // first nbxnb reserved for diagonal block
                                                    queues[d2][stream3] );
                            magma_event_record( events[d2][0], queues[d2][stream3] );
                        }
                    }
#endif
                    /* =================================== */
                    /* updates remaining blocks on stream2 */
                    nb2 = n_local[d] - (j_local2*nb + nb0);
                    if ( nb2 > 0 ) {
                        if ( d == id ) {
                            dlpanel = dlA(d, nb*j_local, j);
                            ldpanel = ldda;
                        } else {
                            dlpanel = dlPT(d,0,0,buf);
                            ldpanel = nb;
                        }
                        magma_setdevice(d);
                        magmablasSetKernelStream( queues[d][stream2] );
                        /* update the remaining blocks in the column */
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
                        int flag = 0;
                        if (flag == 0) {
                            magma_queue_wait_event( queues[d][stream2], events[d][4] ); // lookahead -> diagonal inversion
                        } else {
                            magmablas_slaset( MagmaFull, trsm_nb, trsm_n, c_zero, c_zero, dinvA(d,flag), trsm_nb );
                            magma_queue_wait_event( queues[d][stream2], events[d][1] ); // panel received
                        }
                        magmablas_slaset( MagmaFull, nb2, jb, c_zero, c_zero, dx(d,1), nb2 );
                        magmablas_strsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
                                              nb2, jb, c_one,
                                              dlpanel,                    ldpanel,
                                              dlA(d, nb*j_local2+nb0, j), ldda,
                                              flag, dinvA(d,flag), dx(d,1) );
#else
                        magma_queue_wait_event( queues[d][stream2], events[d][1] ); // panel received
                        magma_strsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
                                     nb2, jb, c_one,
                                     dlpanel,                    ldpanel,
                                     dlA(d, nb*j_local2+nb0, j), ldda);
#endif
                    }
                }
            }
        }
    } /* end of else not upper */

    /* == finalize the trace == */
    trace_finalize( "spotrf.svg", "trace.css" );
    for( d=0; d < ngpu; d++ ) {
        magma_setdevice(d);
        for( j=0; j < 3; j++ ) {
            magma_queue_sync( queues[d][j] );
        }
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
        magma_free( d_dinvA[d] );
        magma_free( d_x[d] );
#endif
    }
    magma_setdevice( orig_dev );
    magmablasSetKernelStream( orig_stream );

    return *info;
} /* magma_spotrf_mgpu */
Example #14
0
/**
    Purpose
    -------
    SPOTRF computes the Cholesky factorization of a real symmetric
    positive definite matrix dA.

    The factorization has the form
       dA = U**H * U,   if UPLO = MagmaUpper, or
       dA = L  * L**H,  if UPLO = MagmaLower,
    where U is an upper triangular matrix and L is lower triangular.

    This is the block version of the algorithm, calling Level 3 BLAS.

    Arguments
    ---------
    @param[in]
    uplo    magma_uplo_t
      -     = MagmaUpper:  Upper triangle of dA is stored;
      -     = MagmaLower:  Lower triangle of dA is stored.

    @param[in]
    n       INTEGER
            The order of the matrix dA.  N >= 0.

    @param[in,out]
    d_lA    REAL array of pointers on the GPU, dimension (ngpu)
            On entry, the symmetric matrix dA distributed over GPUs
            (dl_A[d] points to the local matrix on the d-th GPU).
            It is distributed in 1D block column or row cyclic (with the
            block size of nb) if UPLO = MagmaUpper or MagmaLower, respectively.
            If UPLO = MagmaUpper, the leading N-by-N upper triangular
            part of dA contains the upper triangular part of the matrix dA,
            and the strictly lower triangular part of dA is not referenced.
            If UPLO = MagmaLower, the leading N-by-N lower triangular part
            of dA contains the lower triangular part of the matrix dA, and
            the strictly upper triangular part of dA is not referenced.
    \n
            On exit, if INFO = 0, the factor U or L from the Cholesky
            factorization dA = U**H * U or dA = L * L**H.

    @param[in]
    ldda     INTEGER
            The leading dimension of the array dA.  LDDA >= max(1,N).
            To benefit from coalescent memory accesses LDDA must be
            divisible by 16.

    @param[out]
    info    INTEGER
      -     = 0:  successful exit
      -     < 0:  if INFO = -i, the i-th argument had an illegal value
      -     > 0:  if INFO = i, the leading minor of order i is not
                  positive definite, and the factorization could not be
                  completed.

    @ingroup magma_sposv_comp
    ********************************************************************/
extern "C" magma_int_t
magma_spotrf_mgpu_right(
    magma_int_t ngpu,
    magma_uplo_t uplo, magma_int_t n,
    magmaFloat_ptr d_lA[], magma_int_t ldda,
    magma_int_t *info )
{
    #define dlA(id, i, j)  (d_lA[(id)] + (j) * ldda + (i))
    #define dlP(id, i, j)  (d_lP[(id)] + (j) * ldda + (i))

    #define panel(j)  (panel + (j))
    #define tmppanel(j)  (tmppanel + (j))
    #define tmpprevpanel(j)  (tmpprevpanel + (j))
    #define STREAM_ID(i) (nqueue > 1 ? 1+((i)/nb)%(nqueue-1) : 0)

    float z_one = MAGMA_S_MAKE(  1.0, 0.0 );
    float mz_one = MAGMA_S_MAKE( -1.0, 0.0 );
    float             one =  1.0;
    float             m_one = -1.0;
    const char* uplo_ = lapack_uplo_const( uplo );

    magma_int_t j, nb, d, id, j_local, blkid, crosspoint, prevtrsmrows=0, nqueue = 5;
    float *panel, *tmppanel0, *tmppanel1, *tmppanel, *tmpprevpanel;
    float *d_lP[MagmaMaxGPUs], *dlpanel, *dlpanels[MagmaMaxGPUs];
    magma_int_t rows, trsmrows, igpu, n_local[MagmaMaxGPUs], ldpanel;
    magma_queue_t queues[MagmaMaxGPUs][10];

    *info = 0;
    if ( uplo != MagmaUpper && uplo != MagmaLower ) {
        *info = -1;
    } else if (n < 0) {
        *info = -2;
    } else if (ldda < max(1,n)) {
        *info = -4;
    }
    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }

    magma_device_t orig_dev;
    magma_getdevice( &orig_dev );
    magma_queue_t orig_stream;
    magmablasGetKernelStream( &orig_stream );

    nb = magma_get_spotrf_nb(n);

    ldpanel = ldda;
    magma_setdevice(0);
    if (MAGMA_SUCCESS != magma_smalloc_pinned( &panel, 2 * nb * ldpanel )) {
        *info = MAGMA_ERR_HOST_ALLOC;
        return *info;
    }

    tmppanel0 = panel;
    tmppanel1 = tmppanel0 + nb * ldpanel;

    if ((nb <= 1) || (nb >= n)) {
        // Use unblocked code.
        magma_sgetmatrix( n, n, dlA(0, 0, 0), ldda, panel, ldpanel);
        lapackf77_spotrf( uplo_, &n, panel, &ldpanel, info);
        magma_ssetmatrix( n, n, panel, ldpanel, dlA(0, 0, 0), ldda );
    } else {
        for( d = 0; d < ngpu; d++ ) {
            // local-n and local-ld
            n_local[d] = ((n / nb) / ngpu) * nb;
            if (d < (n / nb) % ngpu)
                n_local[d] += nb;
            else if (d == (n / nb) % ngpu)
                n_local[d] += n % nb;

            magma_setdevice(d);
            magma_device_sync();
            if (MAGMA_SUCCESS != magma_smalloc( &d_lP[d], nb * ldda )) {
                for( j = 0; j < d; j++ ) {
                    magma_setdevice(j);
                    magma_free( d_lP[d] );
                }
                *info = MAGMA_ERR_DEVICE_ALLOC;
                return *info;
            }
            for( j=0; j < nqueue; j++ ) {
                magma_queue_create( &queues[d][j] );
            }
        }

        //#define ENABLE_TIMER
        #if defined (ENABLE_TIMER)
        real_Double_t therk[4], tmtc, tcchol, tctrsm, tctm, tmnp, tcnp;
        real_Double_t ttot_herk[4] = {0,0,0,0}, ttot_mtc = 0, ttot_cchol = 0, ttot_ctrsm = 0, ttot_ctm = 0, ttot_mnp = 0, ttot_cnp = 0;
        printf("\n\n %10s %10s %10s %10s %10s %10s %10s %10s %10s %10s %10s %10s %10s %10s %10s\n",
                "j", "nb", "row", "mtc", "CPU_np", "panel", "ctrsm", "CH+TRSM", "CPU", "dsyrk[0]", "dsyrk[1]", "dsyrk[2]", "dsyrk[3]", "ctm P", "gpu_np");
        printf("     ====================================================================================================\n");
        #endif

        // Use blocked code.
        if (uplo == MagmaUpper) {
            printf( " === not supported, yet ===\n" );
        } else {
            blkid = -1;
            if (ngpu == 4)
                crosspoint = n;
            else if (ngpu == 3)
                crosspoint = n;
            else if (ngpu == 2)
                crosspoint = 20160;
            else
                crosspoint = 0;
            crosspoint = 0; //n; //n -- > gpu always does next panel, 0 --> cpu always does next panel
            crosspoint = n;

            #if defined (ENABLE_TIMER)
            real_Double_t tget = magma_wtime(), tset = 0.0, ttot = 0.0;
            #endif
            if ( n > nb ) {
                // send first panel to cpu
                magma_setdevice(0);
                tmppanel = tmppanel0;
                magma_sgetmatrix_async(n, nb,
                        dlA(0, 0, 0), ldda,
                        tmppanel(0),  ldpanel,
                        queues[0][0] );
            }
            #if defined (ENABLE_TIMER)
            for( d=0; d < ngpu; d++ ) {
                magma_setdevice(d);
                magma_device_sync();
            }
            tget = magma_wtime()-tget;
            #endif

            // Compute the Cholesky factorization A = L*L'
            for (j = 0; (j + nb) < n; j += nb) {
                #if defined (ENABLE_TIMER)
                therk[0] = therk[1] = therk[2] = therk[3] = tmtc = tcchol = tctrsm = tctm = tmnp = tcnp = 0.0;
                #endif

                blkid += 1;
                tmppanel = (blkid % 2 == 0) ? tmppanel0 : tmppanel1;
                // Set the gpu number that holds the current panel
                id = (j / nb) % ngpu;
                magma_setdevice(id);

                // Set the local index where the current panel is
                j_local = j / (nb * ngpu) * nb;
                
                rows = n - j;
                // Wait for the panel on cpu
                magma_queue_sync( queues[id][0] );
                if (j > 0 && prevtrsmrows > crosspoint) {
                    #if defined (ENABLE_TIMER)
                    tcnp = magma_wtime();
                    #endif

                    tmpprevpanel = ((blkid - 1) % 2) == 0 ? tmppanel0 : tmppanel1;

                    blasf77_sgemm( MagmaNoTransStr, MagmaConjTransStr,
                            &rows, &nb, &nb,
                            &mz_one, tmpprevpanel(j), &ldpanel,
                                     tmpprevpanel(j), &ldpanel,
                            &z_one,      tmppanel(j), &ldpanel );

                    #if defined (ENABLE_TIMER)
                    tcnp = magma_wtime() - tcnp;
                    ttot_cnp += tcnp;
                    #endif
                }

                #if defined (ENABLE_TIMER)
                tcchol = magma_wtime();
                #endif
                lapackf77_spotrf(MagmaLowerStr, &nb, tmppanel(j), &ldpanel, info);
                if (*info != 0) {
                    *info = *info + j;
                    break;
                }

                #if defined (ENABLE_TIMER)
                tcchol = magma_wtime() - tcchol;
                ttot_cchol += tcchol;
                tctrsm = magma_wtime();
                #endif

                trsmrows = rows - nb;

                if (trsmrows > 0) {
                    blasf77_strsm(MagmaRightStr, MagmaLowerStr, MagmaConjTransStr, MagmaNonUnitStr,
                                  &trsmrows, &nb,
                                  &z_one, tmppanel(j), &ldpanel,
                                          tmppanel(j + nb), &ldpanel);
                }

                #if defined (ENABLE_TIMER)
                tctrsm = magma_wtime() - tctrsm;
                ttot_ctrsm += tctrsm;
                tctm = magma_wtime();
                #endif

                d = (id + 1) % ngpu;
                // send current panel to gpus
                for (igpu = 0; igpu < ngpu; igpu++, d = (d + 1) % ngpu ) {
                    magma_int_t myrows = 0;
                    magma_int_t row_offset = 0;
                    if ( d == id ) {
                        dlpanel = dlA(d, j, j_local);
                        myrows = rows;
                        row_offset = 0;
                    } else {
                        dlpanel = dlP(d, 0, 0);
                        myrows = trsmrows;
                        row_offset = nb;
                    }

                    if (myrows > 0) {
                        magma_setdevice(d);
                        magma_ssetmatrix_async(myrows, nb,
                                tmppanel(j + row_offset),    ldpanel,
                                dlpanel, ldda, queues[d][0] );
                    }
                }
                /* make sure panel is on GPUs */
                d = (id + 1) % ngpu;
                for (igpu = 0; igpu < ngpu; igpu++, d = (d + 1) % ngpu ) {
                    magma_setdevice(d);
                    magma_queue_sync( queues[d][0] );
                }

                #if defined (ENABLE_TIMER)
                tctm = magma_wtime() - tctm;
                ttot_ctm += tctm;
                #endif

                if ( (j + nb) < n) {
                    magma_int_t offset = 0;
                    magma_int_t row_offset = 0;
                    if (j + nb + nb < n) {
                        d = (id + 1) % ngpu;
                        magma_setdevice(d);
                        magma_int_t j_local2 = (j + nb) / (nb * ngpu) * nb;
                        if (trsmrows <= crosspoint) {
                            #if defined (ENABLE_TIMER)
                            tmnp = magma_wtime();
                            #endif

                            // do gemm on look ahead panel
                            if ( d == id ) {
                                dlpanel = dlA(d, j + nb, j_local);
                            } else {
                                dlpanel = dlP(d, 0, 0);
                            }

                            magmablasSetKernelStream( queues[d][STREAM_ID(j_local2)] );
                            #define SSYRK_ON_DIAG
                            #ifdef  SSYRK_ON_DIAG
                            magma_ssyrk( MagmaLower, MagmaNoTrans,
                                    nb, nb,
                                    m_one, dlpanel, ldda,
                                     one,  dlA(d, j + nb, j_local2), ldda);
                            magma_sgemm( MagmaNoTrans, MagmaConjTrans,
                                    trsmrows-nb, nb, nb,
                                    mz_one, dlpanel+nb, ldda,
                                            dlpanel,    ldda,
                                     z_one, dlA(d, j + nb +nb, j_local2), ldda);
                            #else
                            magma_sgemm( MagmaNoTrans, MagmaConjTrans,
                                    trsmrows, nb, nb,
                                    mz_one, dlpanel, ldda,
                                            dlpanel, ldda,
                                     z_one, dlA(d, j + nb, j_local2), ldda);
                            #endif

                            #if defined (ENABLE_TIMER)
                            magma_device_sync();
                            tmnp = magma_wtime() - tmnp;
                            ttot_mnp += tmnp;
                            #endif
                        }
                        // send next panel to cpu
                        magma_queue_sync( queues[d][STREAM_ID(j_local2)] ); // make sure lookahead is done
                        tmppanel = ((blkid+1) % 2 == 0) ? tmppanel0 : tmppanel1;
                        magma_sgetmatrix_async(rows-nb, nb,
                                dlA(d, j+nb, j_local2), ldda,
                                tmppanel(j+nb),  ldpanel,
                                queues[d][0] );
                        tmppanel = (blkid % 2 == 0) ? tmppanel0 : tmppanel1;

                        offset = j + nb + nb;
                        row_offset = nb;
                    } else {
                        offset = j + nb;
                        row_offset = 0;
                    }

                    if (n - offset > 0) {
                        // syrk on multiple gpu
                        for (d = 0; d < ngpu; d++ ) {
                            if ( d == id ) {
                                dlpanels[d] = dlA(d, j + nb + row_offset, j_local);
                            } else {
                                dlpanels[d] = dlP(d, row_offset, 0);
                            }
                        }

                        #if defined (ENABLE_TIMER)
                        for( d=0; d < ngpu; d++ ) therk[d] = magma_wtime();
                        #endif

                        //magmablasSetKernelStream( queues[d] );
                        //magma_ssyrk(MagmaLower, MagmaNoTrans, n - offset, nb,
                        //        m_one, dlpanel, ldda,
                        //        one, &d_lA[d][offset + offset*ldda], ldda );
                        #ifdef  SSYRK_ON_DIAG
                        magma_ssyrk_mgpu
                        #else
                        magma_ssyrk_mgpu2
                        #endif
                                        (ngpu, MagmaLower, MagmaNoTrans,
                                         nb, n - offset, nb,
                                         m_one, dlpanels, ldda, 0,
                                         one,   d_lA,     ldda, offset,
                                         nqueue, queues );
                        #if defined (ENABLE_TIMER)
                        for( d=0; d < ngpu; d++ ) {
                            magma_setdevice(d);
                            magma_device_sync();
                            therk[d] = magma_wtime() - therk[d];
                            ttot_herk[d] += therk[d];
                        }
                        #endif
                    }

                    prevtrsmrows = trsmrows;

                    #if defined (ENABLE_TIMER)
                    ttot += (tcnp+tcchol+tctrsm+therk[0]+therk[1]+therk[2]+tctm+tmnp);
                    printf("%10d %10d %10d %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf(%d) %10.3lf\n",
                            j, nb, rows, tmtc,
                            tcnp,     // gemm
                            tcchol,   // potrf
                            tctrsm,   // trsm
                            (tcchol + tctrsm),
                            (tmtc+tcnp+tcchol+tctrsm),
                            therk[0], therk[1], therk[2], therk[3], // syrk
                            tctm, // copy panel to GPU
                            tmnp, // lookahead on GPU
                            (id + 1) % ngpu,
                            (tcnp+tcchol+tctrsm+therk[0]+therk[1]+therk[2]+tctm+tmnp));
                    fflush(0);
                    #endif
                }
            }
            for( d = 0; d < ngpu; d++ ) {
                magma_setdevice(d);
                for( id=0; id < nqueue; id++ ) {
                    magma_queue_sync( queues[d][id] );
                }
            }
            #if defined (ENABLE_TIMER)
            printf("\n%10d %10d %10d %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf(-) %10.3lf\n",
                    n, n, 0, ttot_mtc,
                    ttot_cnp,     // gemm
                    ttot_cchol,   // potrf
                    ttot_ctrsm,   // trsm
                    (ttot_cchol + ttot_ctrsm),
                    (ttot_mtc+ttot_cnp+ttot_cchol+ttot_ctrsm),
                    ttot_herk[0], ttot_herk[1], ttot_herk[2], ttot_herk[3], // syrk
                    ttot_ctm, // copy panel to GPU
                    ttot_mnp, // lookahead on GPU
                    (ttot_cnp+ttot_cchol+ttot_ctrsm+ttot_herk[0]+ttot_herk[1]+ttot_herk[2]+ttot_ctm+ttot_mnp));
            printf("%10d %10d %10d %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf(-) %10.3lf (ratio)\n",
                    n, n, 0, ttot_mtc/ttot,
                    ttot_cnp/ttot,     // gemm
                    ttot_cchol/ttot,   // potrf
                    ttot_ctrsm/ttot,   // trsm
                    (ttot_cchol + ttot_ctrsm)/ttot,
                    (ttot_mtc+ttot_cnp+ttot_cchol+ttot_ctrsm)/ttot,
                    ttot_herk[0]/ttot, ttot_herk[1]/ttot, ttot_herk[2]/ttot, ttot_herk[3]/ttot, // syrk
                    ttot_ctm/ttot, // copy panel to GPU
                    ttot_mnp/ttot, // lookahead on GPU
                    (ttot_cnp+ttot_cchol+ttot_ctrsm+ttot_herk[0]+ttot_herk[1]+ttot_herk[2]+ttot_ctm+ttot_mnp)/ttot);
            #endif

            // cholesky for the last block
            if (j < n && *info == 0) {
                rows = n - j;
                id = (j / nb) % ngpu;

                // Set the local index where the current panel is
                j_local = j / (nb * ngpu) * nb;
                
                magma_setdevice(id);
                #if defined (ENABLE_TIMER)
                tset = magma_wtime();
                #endif
                magma_sgetmatrix(rows, rows, dlA(id, j, j_local), ldda, panel(j), ldpanel);
                lapackf77_spotrf(MagmaLowerStr, &rows, panel(j), &ldpanel, info);
                magma_ssetmatrix(rows, rows, panel(j), ldpanel, dlA(id, j, j_local), ldda);
                #if defined (ENABLE_TIMER)
                tset = magma_wtime() - tset;
                #endif
            }
            #if defined (ENABLE_TIMER)
            printf( " matrix_get,set: %10.3lf %10.3lf -> %10.3lf\n",tget,tset,ttot+tget+tset );
            #endif
        } // end of else not upper

        // clean up
        for( d = 0; d < ngpu; d++ ) {
            magma_setdevice(d);
            for( j=0; j < nqueue; j++ ) {
                magma_queue_destroy( queues[d][j] );
            }
            magma_free( d_lP[d] );
        }
    } // end of not lapack

    // free workspace
    magma_free_pinned( panel );
    magma_setdevice( orig_dev );
    magmablasSetKernelStream( orig_stream );

    return *info;
} /* magma_spotrf_mgpu_right */
Example #15
0
/**
    Purpose
    -------
    SPOTRF computes the Cholesky factorization of a real symmetric
    positive definite matrix A. This version does not require work
    space on the GPU passed as input. GPU memory is allocated in the
    routine.

    The factorization has the form
        A = U**T * U,  if uplo = MagmaUpper, or
        A = L  * L**T, if uplo = MagmaLower,
    where U is an upper triangular matrix and L is lower triangular.

    This is the block version of the algorithm, calling Level 3 BLAS.
    If the current stream is NULL, this version replaces it with user defined
    stream to overlap computation with communication.

    Arguments
    ---------
    @param[in]
    uplo    magma_uplo_t
      -     = MagmaUpper:  Upper triangle of A is stored;
      -     = MagmaLower:  Lower triangle of A is stored.

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

    @param[in,out]
    A       REAL array, dimension (LDA,N)
            On entry, the symmetric 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.
    \n
            On exit, if INFO = 0, the factor U or L from the Cholesky
            factorization A = U**T * U or A = L * L**T.
    \n
            Higher performance is achieved if A is in pinned memory, e.g.
            allocated using magma_malloc_pinned.

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

    @param[out]
    info    INTEGER
      -     = 0:  successful exit
      -     < 0:  if INFO = -i, the i-th argument had an illegal value
                  or another error occured, such as memory allocation failed.
      -     > 0:  if INFO = i, the leading minor of order i is not
                  positive definite, and the factorization could not be
                  completed.

    @ingroup magma_sposv_comp
    ********************************************************************/
extern "C" magma_int_t
magma_spotrf(magma_uplo_t uplo, magma_int_t n,
             float *A, magma_int_t lda, magma_int_t *info)
{
#define A(i, j)  (A    + (j)*lda  + (i))
#define dA(i, j) (work + (j)*ldda + (i))

    /* Local variables */
    const char* uplo_ = lapack_uplo_const( uplo );
    magma_int_t        ldda, nb;
    magma_int_t j, jb;
    float    c_one     = MAGMA_S_ONE;
    float    c_neg_one = MAGMA_S_NEG_ONE;
    float   *work;
    float             d_one     =  1.0;
    float             d_neg_one = -1.0;
    int upper = (uplo == MagmaUpper);

    *info = 0;
    if (! upper && uplo != MagmaLower) {
        *info = -1;
    } else if (n < 0) {
        *info = -2;
    } else if (lda < max(1,n)) {
        *info = -4;
    }
    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }

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

    magma_int_t num_gpus = magma_num_gpus();
    if ( num_gpus > 1 ) {
        /* call multiple-GPU interface  */
        return magma_spotrf_m(num_gpus, uplo, n, A, lda, info);
    }

    ldda = ((n+31)/32)*32;

    if (MAGMA_SUCCESS != magma_smalloc( &work, (n)*ldda )) {
        /* alloc failed so call the non-GPU-resident version */
        return magma_spotrf_m(num_gpus, uplo, n, A, lda, info);
    }

    /* Define user stream if current stream is NULL */
    cudaStream_t stream[3], current_stream;
    magmablasGetKernelStream(&current_stream);

    magma_queue_create( &stream[0] );
    magma_queue_create( &stream[2] );

    if (current_stream == NULL) {
        magma_queue_create( &stream[1] );
        magmablasSetKernelStream(stream[1]);
    }
    else
        stream[1] = current_stream;

    nb = magma_get_spotrf_nb(n);

    if (nb <= 1 || nb >= n) {
        lapackf77_spotrf(uplo_, &n, A, &lda, info);
    } else {
        /* Use hybrid blocked code. */
        if (upper) {
            /* Compute the Cholesky factorization A = U'*U. */
            for (j=0; j < n; j += nb) {
                /* Update and factorize the current diagonal block and test
                   for non-positive-definiteness. Computing MIN */
                jb = min(nb, (n-j));
                magma_ssetmatrix_async( jb, (n-j), A(j, j), lda, dA(j, j), ldda, stream[1]);

                magma_ssyrk(MagmaUpper, MagmaTrans, jb, j,
                            d_neg_one, dA(0, j), ldda,
                            d_one,     dA(j, j), ldda);
                magma_queue_sync( stream[1] );

                magma_sgetmatrix_async( jb, jb,
                                        dA(j, j), ldda,
                                        A(j, j),  lda, stream[0] );

                if ( (j+jb) < n) {
                    magma_sgemm(MagmaTrans, MagmaNoTrans,
                                jb, (n-j-jb), j,
                                c_neg_one, dA(0, j   ), ldda,
                                dA(0, j+jb), ldda,
                                c_one,     dA(j, j+jb), ldda);
                }

                magma_sgetmatrix_async( j, jb,
                                        dA(0, j), ldda,
                                        A (0, j),  lda, stream[2] );

                magma_queue_sync( stream[0] );
                lapackf77_spotrf(MagmaUpperStr, &jb, A(j, j), &lda, info);
                if (*info != 0) {
                    *info = *info + j;
                    break;
                }
                magma_ssetmatrix_async( jb, jb,
                                        A(j, j),  lda,
                                        dA(j, j), ldda, stream[0] );
                magma_queue_sync( stream[0] );

                if ( (j+jb) < n ) {
                    magma_strsm(MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
                                jb, (n-j-jb),
                                c_one, dA(j, j   ), ldda,
                                dA(j, j+jb), ldda);
                }
            }
        }
        else {
            //=========================================================
            // Compute the Cholesky factorization A = L*L'.
            for (j=0; j < n; j += nb) {
                //  Update and factorize the current diagonal block and test
                //  for non-positive-definiteness. Computing MIN
                jb = min(nb, (n-j));
                magma_ssetmatrix_async( (n-j), jb, A(j, j), lda, dA(j, j), ldda, stream[1]);

                magma_ssyrk(MagmaLower, MagmaNoTrans, jb, j,
                            d_neg_one, dA(j, 0), ldda,
                            d_one,     dA(j, j), ldda);
                magma_queue_sync( stream[1] );

                magma_sgetmatrix_async( jb, jb,
                                        dA(j,j), ldda,
                                        A(j,j),  lda, stream[0] );

                if ( (j+jb) < n) {
                    magma_sgemm( MagmaNoTrans, MagmaTrans,
                                 (n-j-jb), jb, j,
                                 c_neg_one, dA(j+jb, 0), ldda,
                                 dA(j,    0), ldda,
                                 c_one,     dA(j+jb, j), ldda);
                }

                magma_sgetmatrix_async( jb, j,
                                        dA(j, 0), ldda,
                                        A(j, 0),  lda, stream[2] );

                magma_queue_sync( stream[0] );
                lapackf77_spotrf(MagmaLowerStr, &jb, A(j, j), &lda, info);
                if (*info != 0) {
                    *info = *info + j;
                    break;
                }
                magma_ssetmatrix_async( jb, jb,
                                        A(j, j),  lda,
                                        dA(j, j), ldda, stream[0] );
                magma_queue_sync( stream[0] );

                if ( (j+jb) < n) {
                    magma_strsm(MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
                                (n-j-jb), jb,
                                c_one, dA(j,    j), ldda,
                                dA(j+jb, j), ldda);
                }
            }
        }
    }

    magma_queue_destroy( stream[0] );
    magma_queue_destroy( stream[2] );
    if (current_stream == NULL) {
        magma_queue_destroy( stream[1] );
        magmablasSetKernelStream(NULL);
    }

    magma_free( work );

    return *info;
} /* magma_spotrf */
Example #16
0
/**
    Purpose
    -------
    SPOTRF computes the Cholesky factorization of a real symmetric
    positive definite matrix dA.

    The factorization has the form
       dA = U**T * U,   if UPLO = MagmaUpper, or
       dA = L  * L**T,  if UPLO = MagmaLower,
    where U is an upper triangular matrix and L is lower triangular.

    This is the block version of the algorithm, calling Level 3 BLAS.

    Arguments
    ---------
    @param[in]
    uplo    magma_uplo_t
      -     = MagmaUpper:  Upper triangle of dA is stored;
      -     = MagmaLower:  Lower triangle of dA is stored.

    @param[in]
    n       INTEGER
            The order of the matrix dA.  N >= 0.

    @param[in,out]
    dA      REAL array on the GPU, dimension (LDDA,N)
            On entry, the symmetric matrix dA.  If UPLO = MagmaUpper, the leading
            N-by-N upper triangular part of dA contains the upper
            triangular part of the matrix dA, and the strictly lower
            triangular part of dA is not referenced.  If UPLO = MagmaLower, the
            leading N-by-N lower triangular part of dA contains the lower
            triangular part of the matrix dA, and the strictly upper
            triangular part of dA is not referenced.
    \n
            On exit, if INFO = 0, the factor U or L from the Cholesky
            factorization dA = U**T * U or dA = L * L**T.

    @param[in]
    ldda     INTEGER
            The leading dimension of the array dA.  LDDA >= max(1,N).
            To benefit from coalescent memory accesses LDDA must be
            divisible by 16.

    @param[out]
    info    INTEGER
      -     = 0:  successful exit
      -     < 0:  if INFO = -i, the i-th argument had an illegal value
      -     > 0:  if INFO = i, the leading minor of order i is not
                  positive definite, and the factorization could not be
                  completed.

    @ingroup magma_sposv_comp
    ********************************************************************/
extern "C" magma_int_t
magma_spotrf2_mgpu(int num_gpus, magma_uplo_t uplo, magma_int_t m, magma_int_t n,
                   magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
                   float **d_lA,  magma_int_t ldda,
                   float **d_lP,  magma_int_t lddp,
                   float *A,      magma_int_t lda,   magma_int_t h,
                   magma_queue_t stream[][3], magma_event_t event[][5],
                   magma_int_t *info )
{
#define Alo(i, j)  (A +             ((j)+off_j)*lda  + (nb*(((i)/nb)%h)+off_i))
#define Aup(i, j)  (A + (nb*(((j)/nb)%h)+off_j)*lda  +               (i+off_i))

#define  dlA(id, i, j)    (d_lA[(id)] + (j)*ldda + (i))
#define  dlP(id, i, j, k) (d_lP[(id)] + (k)*nb*lddp + (j)*lddp + (i))
#define dlPT(id, i, j, k) (d_lP[(id)] + (k)*nb*lddp + (j)*nb   + (i))

    magma_int_t     j, jb, nb0, nb2, dd, d, id, j_local, j_local2, buf;
    float c_one     = MAGMA_S_ONE;
    float c_neg_one = MAGMA_S_NEG_ONE;
    float          d_one     =  1.0;
    float          d_neg_one = -1.0;
    int upper = (uplo == MagmaUpper);
    float *dlpanel;
    //magma_event_t event0[MagmaMaxGPUs], // syrk
    //            event1[MagmaMaxGPUs], // send off-diagonal
    //            event2[MagmaMaxGPUs], // send diagonal
    //            event3[MagmaMaxGPUs]; // trsm
    magma_int_t n_local[MagmaMaxGPUs], ldpanel;
    int stream0 = 0, stream1 = 1;
    #ifdef STRSM_WORK
    float *d_dinvA[MagmaMaxGPUs][2], *d_x[MagmaMaxGPUs][2]; /* used by strsm_work */
    #endif
    
    *info = 0;
    if (! upper && uplo != MagmaLower) {
        *info = -1;
    } else if (n < 0) {
        *info = -2;
    } else if (!upper && num_gpus*ldda < max(1,n)) {
        *info = -4;
    } else if (upper && ldda < max(1,m)) {
        *info = -4;
    }
    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }

    for( d=0; d < num_gpus; d++ ) {
        /* local-n and local-ld */
        if (upper) {
            n_local[d] = ((n/nb)/num_gpus)*nb;
            if (d < (n/nb)%num_gpus)
                n_local[d] += nb;
            else if (d == (n/nb)%num_gpus)
                n_local[d] += n%nb;
        } else {
            n_local[d] = ((m/nb)/num_gpus)*nb;
            if (d < (m/nb)%num_gpus)
                n_local[d] += nb;
            else if (d == (m/nb)%num_gpus)
                n_local[d] += m%nb;
        }
        //magma_setdevice(d);
        //magma_event_create( &event0[d] );
        //magma_event_create( &event1[d] );
        //magma_event_create( &event2[d] );
        //magma_event_create( &event3[d] );
    }
    magma_setdevice(0);

    /* == initialize the trace */
    trace_init( 1, num_gpus, 3, (magma_queue_t*)stream );

    /* Use blocked code. */
    if (upper) {
        /* ---------------------------------------------- */
        /* Upper-triangular case                          */
        /* > Compute the Cholesky factorization A = U'*U. */
        /* ---------------------------------------------- */
        
#if defined(PRECISION_d) && defined(STRSM_WORK)
        /* invert the diagonals
         * Allocate device memory for the inversed diagonal blocks, size=m*NB
         */
        for( d=0; d < num_gpus; d++ ) {
            magma_setdevice(d);
            for( j=0; j < 2; j++ ) {
                magma_smalloc( &d_dinvA[d][j], nb*nb );
                magma_smalloc( &d_x[d][j],      n*nb );
                cudaMemset(d_dinvA[d][j], 0, nb*nb*sizeof(float));
                cudaMemset(d_x[d][j],     0,  n*nb*sizeof(float));
            }
        }
        magma_setdevice(0);
#endif
        
        for (j=0; j < m; j += nb) {
            /* Set the GPU number that holds the current panel */
            id  = (j/nb)%num_gpus;
            buf = (j/nb)%num_gpus;
            
            /* Set the local index where the current panel is */
            j_local = j/(nb*num_gpus);
            jb = min(nb, (m-j));
            
            if ( j > 0 ) {
                /* needed on pluto... */
                magma_setdevice(id);
                magma_queue_sync( stream[id][stream0] ); // wait for the column on CPU

                /* broadcast off-diagonal column to all gpus */
                d = (j/nb+1)%num_gpus;
                for( dd=0; dd < num_gpus; dd++ ) {
                    if ( d != id ) {
                        magma_setdevice(d);
                
                        /* wait for it on CPU */
                        magma_queue_wait_event( stream[d][stream0], event[id][1] );
                
                        /* send it to GPU */
                        trace_gpu_start( d, stream0, "comm", "rows to GPUs" );
                        magma_ssetmatrix_async( j, jb,
                                                Aup(0,j),        lda,
                                                dlP(d,jb,0,buf), lddp,
                                                stream[d][stream0] );
                        trace_gpu_end( d, stream0 );
                        magma_event_record( event[d][1], stream[d][stream0] );
                    }
                    d = (d+1)%num_gpus;
                }
            }
            
            /* Update the current diagonal block */
            magma_setdevice(id);
            if ( j > 0 ) {
                magmablasSetKernelStream(stream[id][stream1]);
                trace_gpu_start( id, stream1, "syrk", "syrk" );
                magma_ssyrk(MagmaUpper, MagmaTrans, jb, j,
                            d_neg_one, dlA(id, 0, nb*j_local), ldda,
                            d_one,     dlA(id, j, nb*j_local), ldda);
                trace_gpu_end( id, stream1 );
                magma_event_record( event[id][0], stream[id][stream1] );
            }

            /* send the diagonal to cpu */
            magma_queue_wait_event( stream[id][stream0], event[id][0] ); // wait for syrk
            trace_gpu_start( id, stream0, "comm", "D to CPU" );
            magma_sgetmatrix_async( jb, jb,
                                    dlA(id, j, nb*j_local), ldda,
                                    Aup(j,j),               lda,
                                    stream[id][stream0] );
            trace_gpu_end( id, stream0 );

            if ( j > 0 ) {
                /* Compute the local block column of the panel. */
                d = (j/nb+1)%num_gpus;
                for( dd=0; dd < num_gpus; dd++ ) {
                    j_local2 = j_local+1;
                    if ( d > id ) j_local2 --;
                    nb0 = nb*j_local2;
                
                    if ( n_local[d] > nb0 ) {
                        /* wait for the off-diagonal */
                        if ( d != id ) {
                            //magma_queue_sync( stream[id][3] );
                            dlpanel = dlP(d, jb, 0, buf);
                            ldpanel = lddp;
                
                            /* wait for the offdiagonal column */
                            magma_queue_wait_event( stream[d][stream1], event[d][1] );
                        } else {
                            dlpanel = dlA(d, 0, nb*j_local);
                            ldpanel = ldda;
                        }
                        
                        /* update the panel */
                        magma_setdevice(d);
                        magmablasSetKernelStream(stream[d][stream1]);
                        trace_gpu_start( d, stream1, "gemm", "gemm" );
                        magma_sgemm(MagmaTrans, MagmaNoTrans,
                                    jb, n_local[d]-nb0, j,
                                    c_neg_one, dlpanel,        ldpanel,
                                               dlA(d, 0, nb0), ldda,
                                    c_one,     dlA(d, j, nb0), ldda);
                        trace_gpu_end( d, stream1 );
                    }
                    d = (d+1)%num_gpus;
                }
            }
            
            /* factor the diagonal */
            magma_setdevice(id);
            magma_queue_sync( stream[id][stream0] ); // wait for the diagonal
            trace_cpu_start( 0, "getrf", "getrf" );
            lapackf77_spotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
            trace_cpu_end( 0 );
            if (*info != 0) {
                *info = *info + j;
                break;
            }

            /* send the diagonal to gpus */
            if ( (j+jb) < n) {
                d = (j/nb+1)%num_gpus;
                for( dd=0; dd < num_gpus; dd++ ) {
                    magma_setdevice(d);
                    if ( d == id ) {
                        dlpanel = dlA(d, j, nb*j_local);
                        ldpanel = ldda;
                    } else {
                        dlpanel = dlP(d, 0, 0, buf);
                        ldpanel = lddp;
                    }
                    
                    trace_gpu_start( d, stream0, "comm", "D to GPUs" );
                    magma_ssetmatrix_async( jb, jb,
                                            Aup(j,j), lda,
                                            dlpanel,  ldpanel,
                                            stream[d][stream0] );
                    trace_gpu_end( d, stream0 );
                    magma_event_record( event[d][2], stream[d][stream0] );
                    d = (d+1)%num_gpus;
                }
            } else {
                magma_setdevice(id);
                trace_gpu_start( id, stream0, "comm", "D to GPUs" );
                magma_ssetmatrix_async( jb, jb,
                                        Aup(j,j),               lda,
                                        dlA(id, j, nb*j_local), ldda,
                                        stream[id][stream0] );
                trace_gpu_end( id, stream0 );
            }
            
            /* panel-factorize the off-diagonal */
            if ( (j+jb) < n) {
                d = (j/nb+1)%num_gpus;
                for( dd=0; dd < num_gpus; dd++ ) {
                    /* next column */
                    j_local2 = j_local+1;
                    if ( d > id ) j_local2--;
                    if ( d == id ) {
                        dlpanel = dlA(d, j, nb*j_local);
                        ldpanel = ldda;
                    } else {
                        dlpanel = dlP(d, 0, 0, buf);
                        ldpanel = lddp;
                    }
                    nb2 = n_local[d]-nb*j_local2;
                    nb0 = min(nb, nb2 );
                    
                    magma_setdevice(d);
                    magmablasSetKernelStream(stream[d][stream1]);
                    magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for the diagonal
                    if ( j+jb < m && d == (j/nb+1)%num_gpus ) {
                        /* owns the next column, look-ahead the column */
                        trace_gpu_start( d, stream1, "trsm", "trsm" );
#if defined(PRECISION_d) && defined(STRSM_WORK)
                        magmablas_strsm_work( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
                                              jb, nb0, c_one,
                                              dlpanel,                ldpanel,
                                              dlA(d, j, nb*j_local2), ldda,
                                              d_dinvA[d][0], d_x[d][0] );
                        /*nb2 = n_local[d] - j_local2*nb;
                        magmablas_strsm_work( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
                                              jb, nb2, c_one,
                                              dlpanel,                ldpanel,
                                              dlA(d, j, nb*j_local2), ldda,
                                              d_dinvA[d], d_x[d] ); */
#else
                        /*nb2 = n_local[d] - j_local2*nb;
                        magma_strsm( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
                                     jb, nb2, c_one,
                                     dlpanel,                ldda,
                                     dlA(d, j, nb*j_local2), ldda);
                        */
                        magma_strsm( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
                                     jb, nb0, c_one,
                                     dlpanel,                ldpanel,
                                     dlA(d, j, nb*j_local2), ldda);
#endif
                        trace_gpu_end( d, stream1 );
                        magma_event_record( event[d][3], stream[d][stream1] );
                        
                        /* send the column to cpu */
                        if ( j+jb < m ) {
                            trace_gpu_start( d, stream0, "comm", "rows to CPU" );
                            magma_queue_wait_event( stream[d][stream0], event[d][3] ); // wait for lookahead
                            magma_sgetmatrix_async( (j+jb), nb0,
                                                    dlA(d, 0, nb*j_local2), ldda,
                                                    Aup(0,j+jb),            lda,
                                                    stream[d][stream0] );
                            trace_gpu_end( d, stream0 );
                            magma_event_record( event[d][1], stream[d][stream0] );
                        }
                        
                        /* update the remaining blocks */
                        nb2 = nb2 - nb0;
#if defined(PRECISION_d) && defined(STRSM_WORK)
                        magmablas_strsm_work( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
                                              jb, nb2, c_one,
                                              dlpanel,                    ldpanel,
                                              dlA(d, j, nb*j_local2+nb0), ldda,
                                              d_dinvA[d][1], d_x[d][1] );
#else
                        magma_strsm( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
                                     jb, nb2, c_one,
                                     dlpanel,                    ldpanel,
                                     dlA(d, j, nb*j_local2+nb0), ldda);
#endif
                    } else if ( nb2 > 0 ) {
                        /* update the entire trailing matrix */
                        trace_gpu_start( d, stream1, "trsm", "trsm" );
#if defined(PRECISION_d) && defined(STRSM_WORK)
                        magmablas_strsm_work( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
                                              jb, nb2, c_one,
                                              dlpanel,                ldpanel,
                                              dlA(d, j, nb*j_local2), ldda,
                                    d_dinvA[d][1], d_x[d][1] );
#else
                        magma_strsm( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
                                     jb, nb2, c_one,
                                     dlpanel,                ldpanel,
                                     dlA(d, j, nb*j_local2), ldda);
#endif
                        trace_gpu_end( d, stream1 );
                    }
                    d = (d+1)%num_gpus;
                }
            } /* end of strsm */
        } /* end of for j=1, .., n */
    } else {
        /* -------------------------------------------- */
        /* Lower-triangular case                        */
        /* Compute the Cholesky factorization A = L*L'. */
        /* -------------------------------------------- */
#if defined(PRECISION_d) && defined(STRSM_WORK)
        /*
         * Allocate device memory for the inversed diagonal blocks, size=N*BLOCK_SIZE
         */
        for( d=0; d < num_gpus; d++ ) {
            magma_setdevice(d);
            for( j=0; j < 2; j++ ) {
                magma_smalloc( &d_dinvA[d][j], nb*nb );
                magma_smalloc( &d_x[d][j],     nb*m  );
                cudaMemset(d_dinvA[d][j], 0, nb*nb*sizeof(float));
                cudaMemset(d_x[d][j],     0, nb* m*sizeof(float));
            }
        }
        magma_setdevice(0);
#endif

        for (j=0; j < n; j += nb) {
            /* Set the GPU number that holds the current panel */
            id  = (j/nb)%num_gpus;
            buf = (j/nb)%num_gpus;
            
            /* Set the local index where the current panel is */
            j_local = j/(nb*num_gpus);
            jb = min(nb, (n-j));
            
            if ( j > 0 ) {
                /* needed on pluto... */
                magma_setdevice(id);
                magma_queue_sync( stream[id][stream0] ); // wait for the column on CPU

                /* broadcast offdiagonal row to all gpus */
                d = (j/nb+1)%num_gpus;
                for( dd=0; dd < num_gpus; dd++ ) {
                    if ( d != id ) {
                        magma_setdevice(d);
                        /* wait for it on CPU */
                        magma_queue_wait_event( stream[d][stream0], event[id][1] );
            
                        /* send it to GPU */
                        magma_ssetmatrix_async( jb, j,
                                                Alo(j,0),         lda,
                                                dlPT(d,0,jb,buf), nb,
                                                stream[d][stream0] );
                        magma_event_record( event[d][1], stream[d][stream0] );
                    }
                    d = (d+1)%num_gpus;
                }
            }

            /* Update the current diagonal block */
            magma_setdevice(id);
            if ( j > 0 ) {
                magmablasSetKernelStream(stream[id][stream1]);
                magma_ssyrk(MagmaLower, MagmaNoTrans, jb, j,
                            d_neg_one, dlA(id, nb*j_local, 0), ldda,
                            d_one,     dlA(id, nb*j_local, j), ldda);
                magma_event_record( event[id][0], stream[id][stream1] );
            }
            
            /* send the diagonal to cpu */
            magma_queue_wait_event( stream[id][stream0], event[id][0] ); // wait for syrk
            magma_sgetmatrix_async( jb, jb,
                                    dlA(id, nb*j_local, j), ldda,
                                    Alo(j,j),               lda,
                                    stream[id][stream0] );

            /* update the offdiagonal blocks */
            if ( j > 0 ) {
                /* compute the block-rows of the panel */
                d = (j/nb+1)%num_gpus;
                for( dd=0; dd < num_gpus; dd++ ) {
                    j_local2 = j_local+1;
                    if ( d > id ) j_local2 --;
                    nb0 = nb*j_local2;
            
                    if ( nb0 < n_local[d] ) {
                        if ( d != id ) {
                            dlpanel = dlPT(d, 0, jb, buf);
                            ldpanel = nb;
            
                            /* wait for offdiagonal row */
                            magma_queue_wait_event( stream[d][stream1], event[d][1] );
                        } else {
                            dlpanel = dlA(d, nb*j_local, 0);
                            ldpanel = ldda;
                        }
            
                        magma_setdevice(d);
                        magmablasSetKernelStream(stream[d][stream1]);
                        magma_sgemm( MagmaNoTrans, MagmaTrans,
                                     n_local[d]-nb0, jb, j,
                                     c_neg_one, dlA(d, nb0, 0), ldda,
                                                dlpanel,        ldpanel,
                                     c_one,     dlA(d, nb0, j), ldda);
                    }
                    d = (d+1)%num_gpus;
                }
            }

            /* factor the diagonal */
            magma_setdevice(id);
            magma_queue_sync( stream[id][stream0] );
            lapackf77_spotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
            if (*info != 0) {
                *info = *info + j;
                break;
            }

            /* send the diagonal to gpus */
            if ( (j+jb) < m ) {
                d = (j/nb+1)%num_gpus;
                for( dd=0; dd < num_gpus; dd++ ) {
                    magma_setdevice(d);
                    if ( d == id ) {
                        dlpanel = dlA(d, nb*j_local, j);
                        ldpanel = ldda;
                    } else {
                        dlpanel = dlPT(d, 0, 0, buf);
                        ldpanel = nb;
                    }
                    magma_ssetmatrix_async( jb, jb,
                                            Alo(j,j), lda,
                                            dlpanel,  ldpanel,
                                            stream[d][stream0] );
                    magma_event_record( event[d][2], stream[d][stream0] );
                    d = (d+1)%num_gpus;
                }
            } else {
                magma_setdevice(id);
                magma_ssetmatrix_async( jb, jb,
                                        Alo(j,j),               lda,
                                        dlA(id, nb*j_local, j), ldda,
                                        stream[id][stream0] );
            }

            /* factorize off-diagonal blocks */
            if ( (j+jb) < m ) {
                d = (j/nb+1)%num_gpus;
                for( dd=0; dd < num_gpus; dd++ ) {
                    /* next column */
                    j_local2 = j_local+1;
                    if ( d > id ) j_local2--;
                    if ( d == id ) {
                        dlpanel = dlA(d, nb*j_local, j);
                        ldpanel = ldda;
                    } else {
                        dlpanel = dlPT(d, 0, 0, buf);
                        ldpanel = nb;
                    }
                    nb2 = n_local[d] - j_local2*nb;
                    nb0 = min(nb, nb2 );
            
                    magma_setdevice(d);
                    magmablasSetKernelStream(stream[d][stream1]);
                    magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for the diagonal
                    if ( j+jb < n && d == (j/nb+1)%num_gpus ) {
                        /* owns the next column, look-ahead the column */
#if defined(PRECISION_d) && defined(STRSM_WORK)
                        magmablas_strsm_work( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
                                              nb0, jb, c_one,
                                              dlpanel,                ldpanel,
                                              dlA(d, nb*j_local2, j), ldda,
                                              d_dinvA[d][0], d_x[d][0]);
#else
                        magma_strsm( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
                                     nb0, jb, c_one,
                                     dlpanel,                ldpanel,
                                     dlA(d, nb*j_local2, j), ldda);
#endif
                        magma_event_record( event[d][3], stream[d][stream1] );

                        /* send the column to cpu */
                        if ( j+jb < n ) {
                            magma_queue_wait_event( stream[d][stream0], event[d][3] ); // wait for lookahead
                            magma_sgetmatrix_async( nb0, j+jb,
                                                    dlA(d, nb*j_local2, 0), ldda,
                                                    Alo(j+jb,0),            lda,
                                                    stream[d][stream0] );
                            magma_event_record( event[d][1], stream[d][stream0] );
                        }

                        /* update the remaining blocks */
                        nb2 = nb2 - nb0;
#if defined(PRECISION_d) && defined(STRSM_WORK)
                        magmablas_strsm_work( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
                                              nb2, jb, c_one,
                                              dlpanel,                    ldpanel,
                                              dlA(d, nb*j_local2+nb0, j), ldda,
                                              d_dinvA[d][1], d_x[d][1] );
#else
                        magma_strsm( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
                                     nb2, jb, c_one,
                                     dlpanel,                    ldpanel,
                                     dlA(d, nb*j_local2+nb0, j), ldda);
#endif
                    } else if ( nb2 > 0 ) {
                        /* update the entire trailing matrix */
#if defined(PRECISION_d) && defined(STRSM_WORK)
                        magmablas_strsm_work( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
                                              nb2, jb, c_one,
                                              dlpanel,                ldpanel,
                                              dlA(d, nb*j_local2, j), ldda,
                                              d_dinvA[d][1], d_x[d][1] );
#else
                        magma_strsm( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
                                     nb2, jb, c_one,
                                     dlpanel,                ldpanel,
                                     dlA(d, nb*j_local2, j), ldda);
#endif
                    }
                    d = (d+1)%num_gpus;
                }
            }
        }
    } /* end of else not upper */

    /* == finalize the trace == */
    trace_finalize( "spotrf.svg", "trace.css" );

    /* clean up */
    for( d=0; d < num_gpus; d++ ) {
        magma_setdevice(d);
        magma_queue_sync( stream[d][0] );
        magma_queue_sync( stream[d][1] );
        magmablasSetKernelStream(NULL);

        //magma_event_destroy( event0[d] );
        //magma_event_destroy( event1[d] );
        //magma_event_destroy( event2[d] );
        //magma_event_destroy( event3[d] );
    }
    magma_setdevice(0);

    return *info;
} /* magma_spotrf_mgpu */
Example #17
0
extern "C" magma_int_t
magma_spotrf2_mgpu(
    magma_int_t num_gpus, magma_uplo_t uplo, magma_int_t m, magma_int_t n, 
    magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
    magmaFloat_ptr *d_lA, size_t d_lA_offset, magma_int_t ldda, 
    magmaFloat_ptr *d_lP,  magma_int_t lddp, 
    float *a,      magma_int_t lda,   magma_int_t h,
    magma_queue_t *queues,
    magma_int_t *info )
{
/*  -- clMAGMA (version 1.3.0) --
       Univ. of Tennessee, Knoxville
       Univ. of California, Berkeley
       Univ. of Colorado, Denver
       @date November 2014

    Purpose   
    =======   
    SPOTRF computes the Cholesky factorization of a real symmetric   
    positive definite matrix dA.   

    The factorization has the form   
       dA = U**H * U,  if UPLO = 'U', or   
       dA = L  * L**H,  if UPLO = 'L',   
    where U is an upper triangular matrix and L is lower triangular.   

    This is the block version of the algorithm, calling Level 3 BLAS.   

    Arguments   
    =========   
    UPLO    (input) CHARACTER*1   
            = 'U':  Upper triangle of dA is stored;   
            = 'L':  Lower triangle of dA is stored.   

    N       (input) INTEGER   
            The order of the matrix dA.  N >= 0.   

    dA      (input/output) REAL array on the GPU, dimension (LDDA,N)   
            On entry, the symmetric matrix dA.  If UPLO = 'U', the leading   
            N-by-N upper triangular part of dA contains the upper   
            triangular part of the matrix dA, and the strictly lower   
            triangular part of dA is not referenced.  If UPLO = 'L', the   
            leading N-by-N lower triangular part of dA contains the lower   
            triangular part of the matrix dA, and the strictly upper   
            triangular part of dA is not referenced.   

            On exit, if INFO = 0, the factor U or L from the Cholesky   
            factorization dA = U**H * U or dA = L * L**H.   

    LDDA     (input) INTEGER   
            The leading dimension of the array dA.  LDDA >= max(1,N).
            To benefit from coalescent memory accesses LDDA must be
            divisible by 16.

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   
            > 0:  if INFO = i, the leading minor of order i is not   
                  positive definite, and the factorization could not be   
                  completed.   
    =====================================================================   */

    magma_int_t     j, jb, nb0, nb2, dd, d, id, j_local, j_local2, buf;
    float c_one     = MAGMA_S_ONE;
    float c_neg_one = MAGMA_S_NEG_ONE;
    float          d_one     =  1.0;
    float          d_neg_one = -1.0;
    magmaFloat_ptr dlpanel;
    size_t dlpanel_offset;
    magma_int_t n_local[MagmaMaxGPUs], ldpanel;
    magma_event_t events[MagmaMaxGPUs];

    *info = 0;
    if ( (uplo != MagmaUpper) && (uplo != MagmaLower) ) {
        *info = -1;
    } else if (n < 0) {
        *info = -2;
    } else if ((uplo != MagmaUpper) && num_gpus*ldda < max(1,n)) {
        *info = -4;
    } else if ((uplo == MagmaUpper) && ldda < max(1,m)) {
        *info = -4;
    }
    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }

    {

      for( d=0; d<num_gpus; d++ ) {
        /* local-n and local-ld */
        if (uplo == MagmaUpper) {
            n_local[d] = ((n/nb)/num_gpus)*nb;
            if (d < (n/nb)%num_gpus)
               n_local[d] += nb;
            else if (d == (n/nb)%num_gpus)
              n_local[d] += n%nb;
        } else {
            n_local[d] = ((m/nb)/num_gpus)*nb;
            if (d < (m/nb)%num_gpus)
               n_local[d] += nb;
            else if (d == (m/nb)%num_gpus)
              n_local[d] += m%nb;
        }
      }

      /* Use blocked code. */
      if (uplo == MagmaUpper) 
        {
          /* ---------------------------------------------- */
          /* Upper-triangular case                          */
          /* > Compute the Cholesky factorization A = U'*U. */
          /* ---------------------------------------------- */
            for(j=0;j<m;j+=nb){
                /* Set the GPU number that holds the current panel */
                id  = (j/nb)%num_gpus;
                buf = (j/nb)%num_gpus;
                
                /* Set the local index where the current panel is */
                j_local = j/(nb*num_gpus);
                jb = min(nb, (m-j));

                if(j>0){
                    magma_queue_sync(queues[id*2]); // wait for the column on CPU
                    /* broadcast off-diagonal column to all gpus */
                    d = (j/nb+1)%num_gpus;
                    for(dd=0;dd<num_gpus;dd++){
                        if(d != id){
                            //magma_queue_sync(queues[2*d]);
                            magma_ssetmatrix_async( j, jb, 
                                                    Aup(0,j), lda, 
                                                    dlP(d,jb,0,buf), lddp, 
                                                    queues[d*2], NULL );
                        }
                        d = (d+1)%num_gpus;
                    }
                }
                /* Update the current diagonal block */
                if( j > 0 ) {
                    magma_ssyrk(MagmaUpper, MagmaConjTrans, jb, j, 
                                d_neg_one, dlA(id, 0, nb*j_local), ldda,
                                d_one,     dlA(id, j, nb*j_local), ldda,
                                queues[2*id+1]);
                                                                                                }
                /* send the diagonal to cpu */
                magma_queue_sync(queues[2*id+1]);// wait for syrk
                magma_sgetmatrix_async( jb, jb, 
                                        dlA(id, j, nb*j_local), ldda,
                                        Aup(j,j), lda,
                                        queues[2*id], NULL);
                if(j>0){
                    /* Compute the local block column of the panel. */
                    d = (j/nb+1)%num_gpus;
                    for(dd=0;dd<num_gpus;dd++){
                        j_local2 = j_local+1;
                        if(d>id) j_local2 --;
                        nb0 = nb*j_local2;

                        if(n_local[d]>nb0){
                            /* wait for the off-diagonal */
                            if(d!=id){
                                dlpanel = d_lP[d];
                                dlpanel_offset = dlP_offset(jb, 0, buf);
                                ldpanel = lddp;
                        
                                /* wait for the offdiagonal column */
                                magma_queue_sync(queues[d*2]);
                            }else{
                                dlpanel = d_lA[d];
                                dlpanel_offset = dlA_offset(0, nb*j_local);
                                ldpanel = ldda;
                            }

                            /* update the panel */
                            magma_sgemm(MagmaConjTrans, MagmaNoTrans, 
                                        jb, n_local[d]-nb0, j, 
                                        c_neg_one, dlpanel, dlpanel_offset, ldpanel,
                                        dlA(d, 0, nb0), ldda, 
                                        c_one, dlA(d, j, nb0), ldda,
                                        queues[2*d+1]);

                        }
                        d = (d+1)%num_gpus;
                    }
                }

                /* factor the diagonal */
                magma_queue_sync( queues[id*2] ); // wait for the diagonal
                lapackf77_spotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
                if (*info != 0) {
                    *info = *info + j;
                    break;
                }

                /* send the diagonal to gpus */
                if ( (j+jb) < n) {
                    d = (j/nb+1)%num_gpus;
                    for( dd=0; dd<num_gpus; dd++ ) {
                        if( d == id ) {
                            dlpanel = d_lA[d];
                            dlpanel_offset = dlA_offset(j, nb*j_local);
                            ldpanel = ldda;
                        } else {
                            dlpanel = d_lP[d];
                            dlpanel_offset = dlP_offset(0, 0, buf);                                            
                            ldpanel = lddp;
                        }
                        magma_ssetmatrix_async( jb, jb, 
                                                Aup(j,j), lda,
                                                dlpanel, dlpanel_offset,  ldpanel, 
                                                queues[d*2], NULL);
                        d = (d+1)%num_gpus;
                    }
                } else {
                    magma_ssetmatrix_async( jb, jb, 
                                            Aup(j,j), lda, 
                                            dlA(id, j, nb*j_local), ldda,
                                            queues[id*2], NULL );
                }

                /* panel-factorize the off-diagonal */
                if((j+jb)<n){
                    d = (j/nb+1)%num_gpus;
                    for(dd=0;dd<num_gpus;dd++){
                        /* next column */
                        j_local2 = j_local+1;
                        if(d>id) j_local2--;
                        if( d == id ) {
                            dlpanel = d_lA[d];
                            dlpanel_offset = dlA_offset(j, nb*j_local);
                            ldpanel = ldda;
                        } else {
                            dlpanel = d_lP[d];
                            dlpanel_offset = dlP_offset(0, 0, buf);
                            ldpanel = lddp;
                        }
                        nb2 = n_local[d]-nb*j_local2;
                        nb0 = min(nb, nb2 );
                        magma_queue_sync( queues[2*d]); // wait for the diagonal
                        if(j+jb < m && d == (j/nb+1)%num_gpus){
                            /* owns the next column, look-ahead the column */
                            magma_strsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
                                         jb, nb0, c_one,
                                         dlpanel, dlpanel_offset, ldpanel,
                                         dlA(d, j, nb*j_local2), ldda, 
                                         queues[2*d+1]);
                            /* send the column to cpu */
                            if(j+jb < m){
                                magma_queue_sync(queues[2*d+1]);  // wait for lookahead
                                 magma_sgetmatrix_async( (j+jb), nb0, 
                                                         dlA(d, 0, nb*j_local2), ldda, 
                                                         Aup(0,j+jb), lda,
                                                         queues[2*d], NULL);
                            }

                            /* update the remaining blocks */
                            nb2 = nb2 - nb0;

                            magma_strsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
                                         jb, nb2, c_one, 
                                         dlpanel, dlpanel_offset, ldpanel,
                                         dlA(d, j, nb*j_local2+nb0), ldda, 
                                         queues[2*d+1]);
                        }else if(nb2 > 0){
                            /* update the entire trailing matrix */
                            magma_strsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit, 
                                         jb, nb2, c_one, 
                                         dlpanel, dlpanel_offset, ldpanel,
                                         dlA(d, j, nb*j_local2), ldda,
                                         queues[d*2+1]);
                        }
                        d = (d+1)%num_gpus;
                    }
                }
            }            
        } else { 
            /* -------------------------------------------- */
            /* Lower-triangular case                        */
            /* Compute the Cholesky factorization A = L*L'. */
            /* -------------------------------------------- */
            for (j=0; j<n; j+=nb) {

              /* Set the GPU number that holds the current panel */
              id  = (j/nb)%num_gpus;
              buf = (j/nb)%num_gpus;

              /* Set the local index where the current panel is */
              j_local = j/(nb*num_gpus);
              jb = min(nb, (n-j));

              if( j > 0 ) {
/* needed on pluto... */
//magma_setdevice(id);
                   magma_queue_sync( queues[id*2] ); // wait for the column on CPU

                  /* broadcast offdiagonal row to all gpus */
                  d = (j/nb+1)%num_gpus;
                  for( dd=0; dd<num_gpus; dd++ ) {
                      if( d != id ) {
                          /* wait for it on CPU */
                          //magma_queue_sync( queues[d*2] );

                          /* send it to GPU */
                          magma_ssetmatrix_async( jb, j,
                                                  Alo(j,0), lda,
                                                  dlPT(d,0,jb,buf), nb, 
                                                  queues[d*2], NULL );
                         clFlush(queues[d*2]);
                      }
                      d = (d+1)%num_gpus;
                  }
              }

              /* Update the current diagonal block */
              if( j > 0 ) {
                  magma_ssyrk(MagmaLower, MagmaNoTrans, jb, j,
                              d_neg_one, dlA(id, nb*j_local, 0), ldda,
                              d_one,     dlA(id, nb*j_local, j), ldda,
                              queues[id*2+1]);
                magma_queue_sync( queues[id*2+1] ); // wait for syrk
              }

              /* update the offdiagonal blocks */
              if ( j > 0 ) {
                  /* compute the block-rows of the panel */
                  d = (j/nb+1)%num_gpus;
                  for( dd=0; dd<num_gpus; dd++ ) {
                      j_local2 = j_local+1;
                      if( d > id ) j_local2 --;
                      nb0 = nb*j_local2;

                      if( nb0 < n_local[d] ) {
                          if( d != id ) {
                              //dlpanel = dlPT(d);
                              dlpanel = d_lP[d];
                              dlpanel_offset = dlPT_offset(0, jb, buf);
                              ldpanel = nb;

                              /* wait for offdiagonal row */
                              magma_queue_sync(queues[d*2]);
                          } else {
                              dlpanel = d_lA[d];
                              dlpanel_offset = dlA_offset(nb*j_local, 0);
                              ldpanel = ldda;
                          }

                          magma_sgemm( MagmaNoTrans, MagmaConjTrans,
                                       n_local[d]-nb0, jb, j,
                                       c_neg_one, dlA(d, nb0, 0), ldda,
                                                  dlpanel, dlpanel_offset, ldpanel,
                                       c_one,     dlA(d, nb0, j), ldda, 
                                       queues[d*2+1]);
                      }
                      d = (d+1)%num_gpus;
                  }
              }

              /* send the diagonal to cpu */
              magma_sgetmatrix_async( jb, jb,
                                      dlA(id, nb*j_local, j), ldda,
                                      Alo(j,j),               lda, 
                                      queues[id*2], &events[id] );
              clFlush(queues[id*2]);
              /* factor the diagonal */
              magma_queue_sync( queues[id*2] );
              lapackf77_spotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
              if (*info != 0) {
                  printf("row number: %d\n", (int) j);
                  *info = *info + j;
                  break;
              }

              /* send the diagonal to gpus */
              if ( (j+jb) < m ) {
                  d = (j/nb+1)%num_gpus;
                  for( dd=0; dd<num_gpus; dd++ ) {
                      if( d == id ) {
                          dlpanel = d_lA[d];
                          dlpanel_offset = dlA_offset(nb*j_local, j);
                          ldpanel = ldda;
                      } else {
                          //dlpanel = dlPT(d);
                          dlpanel = d_lP[d];
                          dlpanel_offset = dlPT_offset(0, 0, buf);
                          ldpanel = nb;
                      }
                      magma_ssetmatrix_async( jb, jb,
                                              Alo(j,j), lda,
                                              dlpanel,  dlpanel_offset, ldpanel, 
                                              queues[d*2], NULL );
                      clFlush(queues[d*2]);
                      d = (d+1)%num_gpus;
                  }
              } else {
                  magma_ssetmatrix_async( jb, jb,
                                          Alo(j,j),       lda,
                                          dlA(id, nb*j_local, j), ldda, 
                                          queues[id*2], NULL );
                  clFlush(queues[id*2]);
              }

              /* factorize off-diagonal blocks */
              if ( (j+jb) < m ) {
                  d = (j/nb+1)%num_gpus;
                  for( dd=0; dd<num_gpus; dd++ ) {
                      /* next column */
                      j_local2 = j_local+1;
                      if( d > id ) j_local2--;
                      if( d == id ) {
                          dlpanel = d_lA[d];
                          dlpanel_offset = dlA_offset(nb*j_local, j);
                          ldpanel = ldda;
                      } else {         
                          //dlpanel = dlPT(d);
                          dlpanel = d_lP[d];
                          dlpanel_offset = dlPT_offset(0, 0, buf);
                          ldpanel = nb;
                      }
                      nb2 = n_local[d] - j_local2*nb;
                      nb0 = min(nb, nb2 );
                        
                      magma_queue_sync(queues[d*2]);
                      // wait for the diagonal
                      if( j+jb < n && d == (j/nb+1)%num_gpus ) {
                          /* owns the next column, look-ahead the column */
                          magma_strsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit, 
                                       nb0, jb, c_one,
                                       dlpanel,  dlpanel_offset, ldpanel, 
                                       dlA(d, nb*j_local2, j), ldda,
                                       queues[d*2+1]);
                          /* send the column to cpu */
                          if( j+jb < n ) {
                              magma_queue_sync( queues[d*2+1] ); // wait for lookahead
                              magma_sgetmatrix_async( nb0, j+jb,
                                                      dlA(d, nb*j_local2, 0), ldda,
                                                      Alo(j+jb,0),            lda, 
                                                      queues[d*2], NULL);
                              clFlush(queues[d*2]);
                          }
                          /* update the remaining blocks */
                          nb2 = nb2 - nb0;
                          magma_strsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit, 
                                       nb2, jb, c_one,
                                       dlpanel, dlpanel_offset, ldpanel, 
                                       dlA(d, nb*j_local2+nb0, j), ldda, 
                                       queues[d*2+1]);
                      } else if( nb2 > 0 ) {
                          /* update the entire trailing matrix */
                          magma_strsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit, 
                                       nb2, jb, c_one,
                                       dlpanel, dlpanel_offset, ldpanel, 
                                       dlA(d, nb*j_local2, j), ldda, 
                                       queues[d*2+1]);
                      }
                      d = (d+1)%num_gpus;
                  }
              }
            }
          } /* end of else not upper */

          /* clean up */
          for( d=0; d<num_gpus; d++ ) {
              magma_queue_sync( queues[d*2] );
              magma_queue_sync( queues[d*2+1] );
          }

    } /* end of not lapack */

    return *info;
} /* magma_spotrf_mgpu */