/**
Purpose
-------
ZGETRF_m computes an LU factorization of a general M-by-N matrix A
using partial pivoting with row interchanges. This version does not
require work space on the GPU passed as input. GPU memory is allocated
in the routine. The matrix may exceed the GPU memory.
The factorization has the form
A = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if m > n), and U is upper
triangular (upper trapezoidal if m < n).
This is the right-looking Level 3 BLAS version of the algorithm.
Note: The factorization of big panel is done calling multiple-gpu-interface.
Pivots are applied on GPU within the big panel.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
A COMPLEX_16 array, dimension (LDA,N)
On entry, the M-by-N matrix to be factored.
On exit, the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
\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,M).
@param[out]
ipiv INTEGER array, dimension (min(M,N))
The pivot indices; for 1 <= i <= min(M,N), row i of the
matrix was interchanged with row IPIV(i).
@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, U(i,i) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.
@ingroup magma_zgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_zgetrf_m(
magma_int_t ngpu,
magma_int_t m, magma_int_t n,
magmaDoubleComplex *A, magma_int_t lda, magma_int_t *ipiv,
magma_int_t *info)
{
#define A(i,j) (A + (j)*lda + (i))
#define dAT(d,i,j) (dAT[d] + (i)*nb*ldn_local + (j)*nb)
#define dPT(d,i,j) (dPT[d] + (i)*nb*nb + (j)*nb*maxm)
magma_timer_t time=0, time_total=0, time_alloc=0, time_set=0, time_get=0, time_comp=0;
timer_start( time_total );
real_Double_t flops;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *dAT[MagmaMaxGPUs], *dA[MagmaMaxGPUs], *dPT[MagmaMaxGPUs];
magma_int_t iinfo = 0, nb, nbi, maxm, n_local[MagmaMaxGPUs], ldn_local;
magma_int_t N, M, NB, NBk, I, d, ngpu0 = ngpu;
magma_int_t ii, jj, h, offset, ib, rows;
magma_queue_t stream[MagmaMaxGPUs][2];
magma_event_t event[MagmaMaxGPUs][2];
*info = 0;
if (m < 0)
*info = -1;
else if (n < 0)
*info = -2;
else if (lda < max(1,m))
*info = -4;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0)
return *info;
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
/* initialize nb */
nb = magma_get_zgetrf_nb(m);
maxm = ((m + 31)/32)*32;
/* figure out NB */
size_t freeMem, totalMem;
cudaMemGetInfo( &freeMem, &totalMem );
freeMem /= sizeof(magmaDoubleComplex);
/* number of columns in the big panel */
h = 1+(2+ngpu0);
NB = (magma_int_t)(0.8*freeMem/maxm-h*nb);
const char* ngr_nb_char = getenv("MAGMA_NGR_NB");
if ( ngr_nb_char != NULL )
NB = max( nb, min( NB, atoi(ngr_nb_char) ) );
//NB = 5*max(nb,32);
if ( ngpu0 > ceil((double)NB/nb) ) {
ngpu = (int)ceil((double)NB/nb);
h = 1+(2+ngpu);
NB = (magma_int_t)(0.8*freeMem/maxm-h*nb);
} else {
ngpu = ngpu0;
}
if ( ngpu*NB >= n ) {
#ifdef CHECK_ZGETRF_OOC
printf( " * still fit in GPU memory.\n" );
#endif
NB = n;
} else {
#ifdef CHECK_ZGETRF_OOC
printf( " * don't fit in GPU memory.\n" );
#endif
NB = ngpu*NB;
NB = max( nb, (NB / nb) * nb); /* making sure it's devisable by nb (x64) */
}
#ifdef CHECK_ZGETRF_OOC
if ( NB != n ) printf( " * running in out-core mode (n=%d, NB=%d, nb=%d, freeMem=%.2e).\n", n, NB, nb, (double)freeMem );
else printf( " * running in in-core mode (n=%d, NB=%d, nb=%d, freeMem=%.2e).\n", n, NB, nb, (double)freeMem );
#endif
if ( (nb <= 1) || (nb >= min(m,n)) ) {
/* Use CPU code for scalar of one tile. */
lapackf77_zgetrf(&m, &n, A, &lda, ipiv, info);
} else {
/* Use hybrid blocked code. */
/* allocate memory on GPU to store the big panel */
timer_start( time_alloc );
n_local[0] = (NB/nb)/ngpu;
if ( NB%(nb*ngpu) != 0 )
n_local[0]++;
n_local[0] *= nb;
ldn_local = ((n_local[0]+31)/32)*32;
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
if (MAGMA_SUCCESS != magma_zmalloc( &dA[d], (ldn_local+h*nb)*maxm )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dPT[d] = dA[d] + nb*maxm; /* for storing the previous panel from CPU */
dAT[d] = dA[d] + h*nb*maxm; /* for storing the big panel */
magma_queue_create( &stream[d][0] );
magma_queue_create( &stream[d][1] );
magma_event_create( &event[d][0] );
magma_event_create( &event[d][1] );
}
//magma_setdevice(0);
timer_stop( time_alloc );
for( I=0; I < n; I += NB ) {
M = m;
N = min( NB, n-I ); /* number of columns in this big panel */
//s = min( max(m-I,0), N )/nb; /* number of small block-columns in this big panel */
maxm = ((M + 31)/32)*32;
if ( ngpu0 > ceil((double)N/nb) ) {
ngpu = (int)ceil((double)N/nb);
} else {
ngpu = ngpu0;
}
for( d=0; d < ngpu; d++ ) {
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;
}
ldn_local = ((n_local[0]+31)/32)*32;
/* upload the next big panel into GPU, transpose (A->A'), and pivot it */
timer_start( time );
magmablas_zsetmatrix_transpose_mgpu(ngpu, stream, A(0,I), lda,
dAT, ldn_local, dA, maxm, M, N, nb);
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
magma_queue_sync( stream[d][0] );
magma_queue_sync( stream[d][1] );
magmablasSetKernelStream(NULL);
}
time_set += timer_stop( time );
timer_start( time );
/* == --------------------------------------------------------------- == */
/* == loop around the previous big-panels to update the new big-panel == */
for( offset = 0; offset < min(m,I); offset += NB ) {
NBk = min( m-offset, NB );
/* start sending the first tile from the previous big-panels to gpus */
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
nbi = min( nb, NBk );
magma_zsetmatrix_async( (M-offset), nbi,
A(offset,offset), lda,
dA[d], (maxm-offset), stream[d][0] );
/* make sure the previous update finished */
magmablasSetKernelStream(stream[d][0]);
//magma_queue_sync( stream[d][1] );
magma_queue_wait_event( stream[d][0], event[d][0] );
/* transpose */
magmablas_ztranspose( M-offset, nbi, dA[d], maxm-offset, dPT(d,0,0), nb );
}
/* applying the pivot from the previous big-panel */
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
magmablas_zlaswp_q( ldn_local, dAT(d,0,0), ldn_local, offset+1, offset+NBk, ipiv, 1, stream[d][1] );
}
/* == going through each block-column of previous big-panels == */
for( jj=0, ib=offset/nb; jj < NBk; jj += nb, ib++ ) {
ii = offset+jj;
rows = maxm - ii;
nbi = min( nb, NBk-jj );
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
/* wait for a block-column on GPU */
magma_queue_sync( stream[d][0] );
/* start sending next column */
if ( jj+nb < NBk ) {
magma_zsetmatrix_async( (M-ii-nb), min(nb,NBk-jj-nb),
A(ii+nb,ii+nb), lda,
dA[d], (rows-nb), stream[d][0] );
/* make sure the previous update finished */
magmablasSetKernelStream(stream[d][0]);
//magma_queue_sync( stream[d][1] );
magma_queue_wait_event( stream[d][0], event[d][(1+jj/nb)%2] );
/* transpose next column */
magmablas_ztranspose( M-ii-nb, nb, dA[d], rows-nb, dPT(d,0,(1+jj/nb)%2), nb );
}
/* update with the block column */
magmablasSetKernelStream(stream[d][1]);
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n_local[d], nbi, c_one, dPT(d,0,(jj/nb)%2), nb, dAT(d,ib,0), ldn_local );
if ( M > ii+nb ) {
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
n_local[d], M-(ii+nb), nbi, c_neg_one, dAT(d,ib,0), ldn_local,
dPT(d,1,(jj/nb)%2), nb, c_one, dAT(d,ib+1,0), ldn_local );
}
magma_event_record( event[d][(jj/nb)%2], stream[d][1] );
} /* end of for each block-columns in a big-panel */
}
} /* end of for each previous big-panels */
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
magma_queue_sync( stream[d][0] );
magma_queue_sync( stream[d][1] );
magmablasSetKernelStream(NULL);
}
/* calling magma-gpu interface to panel-factorize the big panel */
if ( M > I ) {
magma_zgetrf2_mgpu(ngpu, M-I, N, nb, I, dAT, ldn_local, ipiv+I, dA, A(0,I), lda,
stream, &iinfo);
if ( iinfo < 0 ) {
*info = iinfo;
break;
} else if ( iinfo != 0 ) {
*info = iinfo + I * NB;
//break;
}
/* adjust pivots */
for( ii=I; ii < min(I+N,m); ii++ )
ipiv[ii] += I;
}
time_comp += timer_stop( time );
/* download the current big panel to CPU */
timer_start( time );
magmablas_zgetmatrix_transpose_mgpu(ngpu, stream, dAT, ldn_local, A(0,I), lda, dA, maxm, M, N, nb);
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
magma_queue_sync( stream[d][0] );
magma_queue_sync( stream[d][1] );
magmablasSetKernelStream(NULL);
}
time_get += timer_stop( time );
} /* end of for */
timer_stop( time_total );
flops = FLOPS_ZGETRF( m, n ) / 1e9;
timer_printf(" memory-allocation time: %e\n", time_alloc );
timer_printf(" NB=%d nb=%d\n", (int) NB, (int) nb );
timer_printf(" memcopy and transpose %e seconds\n", time_set );
timer_printf(" total time %e seconds\n", time_total );
timer_printf(" Performance %f GFlop/s, %f seconds without htod and dtoh\n", flops / (time_comp), time_comp );
timer_printf(" Performance %f GFlop/s, %f seconds with htod\n", flops / (time_comp + time_set), time_comp + time_set );
timer_printf(" Performance %f GFlop/s, %f seconds with dtoh\n", flops / (time_comp + time_get), time_comp + time_get );
timer_printf(" Performance %f GFlop/s, %f seconds without memory-allocation\n", flops / (time_total - time_alloc), time_total - time_alloc );
for( d=0; d < ngpu0; d++ ) {
magma_setdevice(d);
magma_free( dA[d] );
magma_event_destroy( event[d][0] );
magma_event_destroy( event[d][1] );
magma_queue_destroy( stream[d][0] );
magma_queue_destroy( stream[d][1] );
}
magma_setdevice( orig_dev );
magmablasSetKernelStream( orig_stream );
}
if ( *info >= 0 )
magma_zgetrf_piv(m, n, NB, A, lda, ipiv, info);
return *info;
} /* magma_zgetrf_m */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgetri_batched
*/
int main( int argc, char** argv)
{
TESTING_INIT();
// constants
const magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
const magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
magmaDoubleComplex *h_A, *h_Ainv, *h_R, *work;
magmaDoubleComplex_ptr d_A, d_invA;
magmaDoubleComplex_ptr *dA_array;
magmaDoubleComplex_ptr *dinvA_array;
magma_int_t **dipiv_array;
magma_int_t *dinfo_array;
magma_int_t *ipiv, *cpu_info;
magma_int_t *d_ipiv, *d_info;
magma_int_t N, n2, lda, ldda, info, info1, info2, lwork;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magmaDoubleComplex tmp;
double error, rwork[1];
magma_int_t columns;
magma_int_t status = 0;
magma_opts opts( MagmaOptsBatched );
opts.parse_opts( argc, argv );
magma_int_t batchCount = opts.batchcount;
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("%% batchCount N CPU Gflop/s (ms) GPU Gflop/s (ms) ||I - A*A^{-1}||_1 / (N*cond(A))\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 * batchCount;
ldda = magma_roundup( N, opts.align ); // multiple of 32 by default
// This is the correct flops but since this getri_batched is based on
// 2 trsm = getrs and to know the real flops I am using the getrs one
//gflops = (FLOPS_ZGETRF( N, N ) + FLOPS_ZGETRI( N ))/ 1e9 * batchCount;
gflops = (FLOPS_ZGETRF( N, N ) + FLOPS_ZGETRS( N, N ))/ 1e9 * batchCount;
// query for workspace size
lwork = -1;
lapackf77_zgetri( &N, NULL, &lda, NULL, &tmp, &lwork, &info );
if (info != 0) {
printf("lapackf77_zgetri returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
lwork = magma_int_t( MAGMA_Z_REAL( tmp ));
TESTING_MALLOC_CPU( cpu_info, magma_int_t, batchCount );
TESTING_MALLOC_CPU( ipiv, magma_int_t, N * batchCount );
TESTING_MALLOC_CPU( work, magmaDoubleComplex, lwork*batchCount );
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( h_Ainv, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( h_R, magmaDoubleComplex, n2 );
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N * batchCount );
TESTING_MALLOC_DEV( d_invA, magmaDoubleComplex, ldda*N * batchCount );
TESTING_MALLOC_DEV( d_ipiv, magma_int_t, N * batchCount );
TESTING_MALLOC_DEV( d_info, magma_int_t, batchCount );
TESTING_MALLOC_DEV( dA_array, magmaDoubleComplex*, batchCount );
TESTING_MALLOC_DEV( dinvA_array, magmaDoubleComplex*, batchCount );
TESTING_MALLOC_DEV( dinfo_array, magma_int_t, batchCount );
TESTING_MALLOC_DEV( dipiv_array, magma_int_t*, batchCount );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
columns = N * batchCount;
lapackf77_zlacpy( MagmaFullStr, &N, &columns, h_A, &lda, h_R, &lda );
lapackf77_zlacpy( MagmaFullStr, &N, &columns, h_A, &lda, h_Ainv, &lda );
magma_zsetmatrix( N, columns, h_R, lda, d_A, ldda, opts.queue );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_zset_pointer( dA_array, d_A, ldda, 0, 0, ldda * N, batchCount, opts.queue );
magma_zset_pointer( dinvA_array, d_invA, ldda, 0, 0, ldda * N, batchCount, opts.queue );
magma_iset_pointer( dipiv_array, d_ipiv, 1, 0, 0, N, batchCount, opts.queue );
gpu_time = magma_sync_wtime( opts.queue );
info1 = magma_zgetrf_batched( N, N, dA_array, ldda, dipiv_array, dinfo_array, batchCount, opts.queue);
info2 = magma_zgetri_outofplace_batched( N, dA_array, ldda, dipiv_array, dinvA_array, ldda, dinfo_array, batchCount, opts.queue);
gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
gpu_perf = gflops / gpu_time;
// check correctness of results throught "dinfo_magma" and correctness of argument throught "info"
magma_getvector( batchCount, sizeof(magma_int_t), dinfo_array, 1, cpu_info, 1, opts.queue );
for (magma_int_t i=0; i < batchCount; i++)
{
if (cpu_info[i] != 0 ) {
printf("magma_zgetrf_batched matrix %d returned error %d\n", (int) i, (int)cpu_info[i] );
}
}
if (info1 != 0) printf("magma_zgetrf_batched returned argument error %d: %s.\n", (int) info1, magma_strerror( info1 ));
if (info2 != 0) printf("magma_zgetri_batched returned argument error %d: %s.\n", (int) info2, magma_strerror( info2 ));
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
#if !defined (BATCHED_DISABLE_PARCPU) && defined(_OPENMP)
magma_int_t nthreads = magma_get_lapack_numthreads();
magma_set_lapack_numthreads(1);
magma_set_omp_numthreads(nthreads);
#pragma omp parallel for schedule(dynamic)
#endif
for (int i=0; i < batchCount; i++)
{
magma_int_t locinfo;
lapackf77_zgetrf(&N, &N, h_Ainv + i*lda*N, &lda, ipiv + i*N, &locinfo);
if (locinfo != 0) {
printf("lapackf77_zgetrf returned error %d: %s.\n",
(int) locinfo, magma_strerror( locinfo ));
}
lapackf77_zgetri(&N, h_Ainv + i*lda*N, &lda, ipiv + i*N, work + i*lwork, &lwork, &locinfo );
if (locinfo != 0) {
printf("lapackf77_zgetri returned error %d: %s.\n",
(int) locinfo, magma_strerror( locinfo ));
}
}
#if !defined (BATCHED_DISABLE_PARCPU) && defined(_OPENMP)
magma_set_lapack_numthreads(nthreads);
#endif
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
printf("%10d %5d %7.2f (%7.2f) %7.2f (%7.2f)",
(int) batchCount, (int) N, cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000. );
}
else {
printf("%10d %5d --- ( --- ) %7.2f (%7.2f)",
(int) batchCount, (int) N, gpu_perf, gpu_time*1000. );
}
/* =====================================================================
Check the result
=================================================================== */
if ( opts.check ) {
magma_igetvector( N*batchCount, d_ipiv, 1, ipiv, 1, opts.queue );
magma_zgetmatrix( N, N*batchCount, d_invA, ldda, h_Ainv, lda, opts.queue );
error = 0;
for (magma_int_t i=0; i < batchCount; i++)
{
for (magma_int_t k=0; k < N; k++) {
if (ipiv[i*N+k] < 1 || ipiv[i*N+k] > N )
{
printf("error for matrix %d ipiv @ %d = %d\n", (int) i, (int) k, (int) ipiv[i*N+k]);
error = -1;
}
}
if (error == -1) {
break;
}
// compute 1-norm condition number estimate, following LAPACK's zget03
double normA, normAinv, rcond, err;
normA = lapackf77_zlange( "1", &N, &N, h_A + i*lda*N, &lda, rwork );
normAinv = lapackf77_zlange( "1", &N, &N, h_Ainv + i*lda*N, &lda, rwork );
if ( normA <= 0 || normAinv <= 0 ) {
rcond = 0;
err = 1 / (tol/opts.tolerance); // == 1/eps
}
else {
rcond = (1 / normA) / normAinv;
// R = I
// R -= A*A^{-1}
// err = ||I - A*A^{-1}|| / ( N ||A||*||A^{-1}|| ) = ||R|| * rcond / N, using 1-norm
lapackf77_zlaset( "full", &N, &N, &c_zero, &c_one, h_R + i*lda*N, &lda );
blasf77_zgemm( "no", "no", &N, &N, &N, &c_neg_one,
h_A + i*lda*N, &lda,
h_Ainv + i*lda*N, &lda, &c_one,
h_R + i*lda*N, &lda );
err = lapackf77_zlange( "1", &N, &N, h_R + i*lda*N, &lda, rwork );
err = err * rcond / N;
}
if ( isnan(err) || isinf(err) ) {
error = err;
break;
}
error = max( err, error );
}
bool okay = (error < tol);
status += ! okay;
printf(" %8.2e %s\n", error, (okay ? "ok" : "failed") );
}
else {
printf("\n");
}
TESTING_FREE_CPU( cpu_info );
TESTING_FREE_CPU( ipiv );
TESTING_FREE_CPU( work );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_Ainv );
TESTING_FREE_CPU( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_invA );
TESTING_FREE_DEV( d_ipiv );
TESTING_FREE_DEV( d_info );
TESTING_FREE_DEV( dA_array );
TESTING_FREE_DEV( dinvA_array );
TESTING_FREE_DEV( dinfo_array );
TESTING_FREE_DEV( dipiv_array );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgesv
*/
int main(int argc, char **argv)
{
real_Double_t gflops, cpu_perf, cpu_time, gpu_perf, gpu_time;
double error, Rnorm, Anorm, Xnorm, *work;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *h_A, *h_LU, *h_B, *h_X;
magma_int_t *ipiv;
magma_int_t N, nrhs, lda, ldb, info, sizeA, sizeB;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
/* Initialize */
magma_queue_t queue[2];
magma_device_t device[ MagmaMaxGPUs ];
int num = 0;
magma_err_t err;
magma_init();
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
nrhs = opts.nrhs;
err = magma_get_devices( device, MagmaMaxGPUs, &num );
if ( err != 0 || num < 1 ) {
fprintf( stderr, "magma_get_devices failed: %d\n", err );
exit(-1);
}
// Create two queues on device opts.device
err = magma_queue_create( device[ opts.device ], &queue[0] );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create failed: %d\n", err );
exit(-1);
}
err = magma_queue_create( device[ opts.device ], &queue[1] );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create failed: %d\n", err );
exit(-1);
}
printf("ngpu %d\n", (int) opts.ngpu );
printf(" N NRHS CPU Gflop/s (sec) GPU GFlop/s (sec) ||B - AX|| / N*||A||*||X||\n");
printf("================================================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[i];
lda = N;
ldb = lda;
gflops = ( FLOPS_ZGETRF( N, N ) + FLOPS_ZGETRS( N, nrhs ) ) / 1e9;
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, lda*N );
TESTING_MALLOC_CPU( h_LU, magmaDoubleComplex, lda*N );
TESTING_MALLOC_CPU( h_B, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC_CPU( h_X, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC_CPU( work, double, N );
TESTING_MALLOC_CPU( ipiv, magma_int_t, N );
/* Initialize the matrices */
sizeA = lda*N;
sizeB = ldb*nrhs;
lapackf77_zlarnv( &ione, ISEED, &sizeA, h_A );
lapackf77_zlarnv( &ione, ISEED, &sizeB, h_B );
// copy A to LU and B to X; save A and B for residual
lapackf77_zlacpy( "F", &N, &N, h_A, &lda, h_LU, &lda );
lapackf77_zlacpy( "F", &N, &nrhs, h_B, &ldb, h_X, &ldb );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_zgesv( N, nrhs, h_LU, lda, ipiv, h_X, ldb, &info, queue );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zgesv returned error %d: %s.\n",
(int) info, magma_strerror( info ));
//=====================================================================
// Residual
//=====================================================================
Anorm = lapackf77_zlange("I", &N, &N, h_A, &lda, work);
Xnorm = lapackf77_zlange("I", &N, &nrhs, h_X, &ldb, work);
blasf77_zgemm( MagmaNoTransStr, MagmaNoTransStr, &N, &nrhs, &N,
&c_one, h_A, &lda,
h_X, &ldb,
&c_neg_one, h_B, &ldb);
Rnorm = lapackf77_zlange("I", &N, &nrhs, h_B, &ldb, work);
error = Rnorm/(N*Anorm*Xnorm);
status |= ! (error < tol);
/* ====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_zgesv( &N, &nrhs, h_A, &lda, ipiv, h_B, &ldb, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zgesv returned error %d: %s.\n",
(int) info, magma_strerror( info ));
printf( "%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e%s\n",
(int) N, (int) nrhs, cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "" : " failed"));
}
else {
printf( "%5d %5d --- ( --- ) %7.2f (%7.2f) %8.2e%s\n",
(int) N, (int) nrhs, gpu_perf, gpu_time,
error, (error < tol ? "" : " failed"));
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_LU );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_X );
TESTING_FREE_CPU( work );
TESTING_FREE_CPU( ipiv );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
magma_queue_destroy( queue[0] );
magma_queue_destroy( queue[1] );
magma_finalize();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgetrf_mgpu
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
double error;
magmaDoubleComplex *h_A;
magmaDoubleComplex_ptr d_lA[ MagmaMaxGPUs ];
magma_int_t *ipiv;
magma_int_t M, N, n2, lda, ldda, n_local, ngpu;
magma_int_t info, min_mn, nb, ldn_local;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("ngpu %d\n", (int) opts.ngpu );
if ( opts.check == 2 ) {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) |Ax-b|/(N*|A|*|x|)\n");
}
else {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) |PA-LU|/(N*|A|)\n");
}
printf("=========================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
min_mn = min(M, N);
lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
nb = magma_get_zgetrf_nb( M );
gflops = FLOPS_ZGETRF( M, N ) / 1e9;
// ngpu must be at least the number of blocks
ngpu = min( opts.ngpu, int((N+nb-1)/nb) );
if ( ngpu < opts.ngpu ) {
printf( " * too many GPUs for the matrix size, using %d GPUs\n", (int) ngpu );
}
// Allocate host memory for the matrix
TESTING_MALLOC_CPU( ipiv, magma_int_t, min_mn );
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
// Allocate device memory
for( int dev=0; dev < ngpu; dev++ ) {
n_local = ((N/nb)/ngpu)*nb;
if (dev < (N/nb) % ngpu)
n_local += nb;
else if (dev == (N/nb) % ngpu)
n_local += N % nb;
ldn_local = ((n_local+31)/32)*32; // TODO why?
magma_setdevice( dev );
TESTING_MALLOC_DEV( d_lA[dev], magmaDoubleComplex, ldda*ldn_local );
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
init_matrix( M, N, h_A, lda );
cpu_time = magma_wtime();
lapackf77_zgetrf( &M, &N, h_A, &lda, ipiv, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zgetrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
init_matrix( M, N, h_A, lda );
magma_zsetmatrix_1D_col_bcyclic( M, N, h_A, lda, d_lA, ldda, ngpu, nb );
gpu_time = magma_wtime();
magma_zgetrf_mgpu( ngpu, M, N, d_lA, ldda, ipiv, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zgetrf_mgpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
magma_zgetmatrix_1D_col_bcyclic( M, N, d_lA, ldda, h_A, lda, ngpu, nb );
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f)",
(int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f)",
(int) M, (int) N, gpu_perf, gpu_time );
}
if ( opts.check == 2 ) {
error = get_residual( M, N, h_A, lda, ipiv );
printf(" %8.2e %s\n", error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
}
else if ( opts.check ) {
error = get_LU_error( M, N, h_A, lda, ipiv );
printf(" %8.2e %s\n", error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
}
else {
printf( " ---\n" );
}
TESTING_FREE_CPU( ipiv );
TESTING_FREE_CPU( h_A );
for( int dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
TESTING_FREE_DEV( d_lA[dev] );
}
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgetrf_mgpu
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
double error;
magmaDoubleComplex *h_A, *h_P;
magmaDoubleComplex_ptr d_lA[ MagmaMaxSubs * MagmaMaxGPUs ];
magma_int_t *ipiv;
magma_int_t M, N, n2, lda, ldda, info, min_mn;
magma_int_t dev, j, k, ngpu, nsub, n_local, nb, nk, ldn_local, maxm;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
/* Initialize queues */
magma_queue_t queues[MagmaMaxGPUs * 2];
magma_device_t devices[MagmaMaxGPUs];
magma_int_t num = 0;
magma_int_t err;
err = magma_getdevices( devices, MagmaMaxGPUs, &num );
if ( err != 0 || num < 1 ) {
fprintf( stderr, "magma_getdevices failed: %d\n", (int) err );
exit(-1);
}
for( dev=0; dev < opts.ngpu; dev++ ) {
err = magma_queue_create( devices[dev], &queues[2*dev] );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create failed: %d (device %d)\n", (int) err, dev );
exit(-1);
}
err = magma_queue_create( devices[dev], &queues[2*dev+1] );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create failed: %d (device %d)\n", (int) err, dev );
exit(-1);
}
}
printf("trans %s, ngpu %d, nsub %d\n",
lapack_trans_const(opts.transA), (int) opts.ngpu, (int) opts.nsub );
if ( opts.check == 2 ) {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) |Ax-b|/(N*|A|*|x|)\n");
}
else {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) |PA-LU|/(N*|A|)\n");
}
printf("=========================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
min_mn = min(M, N);
maxm = 32*((M+31)/32);
lda = M;
n2 = lda*N;
nb = magma_get_zgetrf_nb(M);
gflops = FLOPS_ZGETRF( M, N ) / 1e9;
// nsubs * ngpu must be at least the number of blocks
ngpu = opts.ngpu;
nsub = opts.nsub;
if ( nsub*ngpu > N/nb ) {
nsub = 1;
ngpu = 1;
printf( " * too many GPUs for the matrix size, using %d GPUs and %d submatrices\n", (int) ngpu, (int) nsub );
}
/* Allocate host memory for the matrix */
TESTING_MALLOC_CPU( ipiv, magma_int_t, min_mn );
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( h_P, magmaDoubleComplex, lda*nb );
/* Allocate device memory */
if ( opts.transA == MagmaNoTrans ) {
ldda = N/nb; /* number of block columns */
ldda = ldda/(ngpu*nsub); /* number of block columns per GPU */
ldda = nb*ldda; /* number of columns per GPU */
if ( ldda * ngpu*nsub < N ) {
/* left over */
if ( N-ldda*ngpu*nsub >= nb ) {
ldda += nb;
} else {
ldda += (N-ldda*ngpu*nsub)%nb;
}
}
ldda = ((ldda+31)/32)*32; /* make it a multiple of 32 */
for( j=0; j < nsub * ngpu; j++ ) {
TESTING_MALLOC_DEV( d_lA[j], magmaDoubleComplex, ldda*maxm );
}
} else {
ldda = ((M+31)/32)*32;
for( j=0; j < nsub * ngpu; j++ ) {
n_local = ((N/nb)/(nsub*ngpu))*nb;
if ( j < (N/nb)%(nsub*ngpu) ) {
n_local += nb;
} else if ( j == (N/nb)%(nsub*ngpu) ) {
n_local += N%nb;
}
TESTING_MALLOC_DEV( d_lA[j], magmaDoubleComplex, ldda*n_local );
}
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
init_matrix( M, N, h_A, lda );
cpu_time = magma_wtime();
lapackf77_zgetrf( &M, &N, h_A, &lda, ipiv, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if ( info != 0 )
printf("lapackf77_zgetrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
init_matrix( M, N, h_A, lda );
if ( opts.transA == MagmaNoTrans ) {
for( j=0; j < N; j += nb ) {
k = (j/nb)%(nsub*ngpu);
nk = min(nb, N-j);
/* transpose on CPU, then copy to GPU */
int ii,jj;
for( ii=0; ii < M; ii++ ) {
for( jj=0; jj < nk; jj++ ) {
h_P[jj+ii*nk] = h_A[j*lda + ii+jj*lda];
}
}
magma_zsetmatrix( nk, M,
h_P, nk,
d_lA[k], j/(nb*nsub*ngpu)*nb, ldda,
queues[2*(k%ngpu)] );
}
} else {
ldda = ((M+31)/32)*32;
for( j=0; j < N; j += nb ) {
k = (j/nb)%(nsub*ngpu);
nk = min(nb, N-j);
magma_zsetmatrix( M, nk,
h_A + j*lda, lda,
d_lA[k], j/(nb*nsub*ngpu)*nb*ldda, ldda,
queues[2*(k%ngpu)] );
}
}
gpu_time = magma_wtime();
magma_zgetrf_msub( opts.transA, nsub, ngpu, M, N, d_lA, 0, ldda, ipiv, queues, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zgetrf_mgpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* get the matrix from GPUs */
if ( opts.transA == MagmaNoTrans ) {
for (j=0; j < N; j+=nb) {
k = (j/nb)%(nsub*ngpu);
nk = min(nb, N-j);
/* copy to CPU and then transpose */
magma_zgetmatrix( nk, M,
d_lA[k], j/(nb*nsub*ngpu)*nb, ldda,
h_P, nk, queues[2*(k%ngpu)] );
int ii, jj;
for( ii=0; ii < M; ii++ ) {
for( jj=0; jj < nk; jj++ ) {
h_A[j*lda + ii+jj*lda] = h_P[jj+ii*nk];
}
}
}
} else {
for (j=0; j < N; j+=nb) {
k = (j/nb)%(nsub*ngpu);
nk = min(nb, N-j);
magma_zgetmatrix( M, nk,
d_lA[k], j/(nb*nsub*ngpu)*nb*ldda, ldda,
h_A + j*lda, lda, queues[2*(k%ngpu)] );
}
}
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f)",
(int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f)",
(int) M, (int) N, gpu_perf, gpu_time );
}
if ( opts.check == 2 ) {
error = get_residual( M, N, h_A, lda, ipiv );
printf(" %8.2e %s\n", error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
}
else if ( opts.check ) {
error = get_LU_error( M, N, h_A, lda, ipiv );
printf(" %8.2e %s\n", error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
}
else {
printf(" --- \n");
}
TESTING_FREE_CPU( ipiv );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_P );
for( dev=0; dev < ngpu; dev++ ) {
for( k=0; k < nsub; k++ ) {
TESTING_FREE_DEV( d_lA[dev*nsub + k] );
}
}
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
/* Free queues */
for( dev=0; dev < opts.ngpu; dev++ ) {
magma_queue_destroy( queues[2*dev] );
magma_queue_destroy( queues[2*dev+1] );
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgetrf_batched
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, magma_perf, magma_time, cublas_perf=0., cublas_time=0., cpu_perf=0, cpu_time=0;
double error;
magma_int_t cublas_enable = 0;
magmaDoubleComplex *h_A, *h_R;
magmaDoubleComplex *dA_magma;
magmaDoubleComplex **dA_array = NULL;
magma_int_t **dipiv_array = NULL;
magma_int_t *ipiv, *cpu_info;
magma_int_t *dipiv_magma, *dinfo_magma;
magma_int_t M, N, n2, lda, ldda, min_mn, info;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t batchCount;
magma_int_t status = 0;
magma_opts opts( MagmaOptsBatched );
opts.parse_opts( argc, argv );
//opts.lapack |= opts.check;
batchCount = opts.batchcount;
magma_int_t columns;
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("%% BatchCount M N CPU Gflop/s (ms) MAGMA Gflop/s (ms) CUBLAS Gflop/s (ms) ||PA-LU||/(||A||*N)\n");
printf("%%==========================================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
min_mn = min(M, N);
lda = M;
n2 = lda*N * batchCount;
ldda = magma_roundup( M, opts.align ); // multiple of 32 by default
gflops = FLOPS_ZGETRF( M, N ) / 1e9 * batchCount;
TESTING_MALLOC_CPU( cpu_info, magma_int_t, batchCount );
TESTING_MALLOC_CPU( ipiv, magma_int_t, min_mn * batchCount );
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( h_R, magmaDoubleComplex, n2 );
TESTING_MALLOC_DEV( dA_magma, magmaDoubleComplex, ldda*N * batchCount );
TESTING_MALLOC_DEV( dipiv_magma, magma_int_t, min_mn * batchCount );
TESTING_MALLOC_DEV( dinfo_magma, magma_int_t, batchCount );
TESTING_MALLOC_DEV( dA_array, magmaDoubleComplex*, batchCount );
TESTING_MALLOC_DEV( dipiv_array, magma_int_t*, batchCount );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
// make A diagonally dominant, to not need pivoting
for( int s=0; s < batchCount; ++s ) {
for( int i=0; i < min_mn; ++i ) {
h_A[ i + i*lda + s*lda*N ] = MAGMA_Z_MAKE(
MAGMA_Z_REAL( h_A[ i + i*lda + s*lda*N ] ) + N,
MAGMA_Z_IMAG( h_A[ i + i*lda + s*lda*N ] ));
}
}
columns = N * batchCount;
lapackf77_zlacpy( MagmaFullStr, &M, &columns, h_A, &lda, h_R, &lda );
magma_zsetmatrix( M, columns, h_R, lda, dA_magma, ldda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_zset_pointer( dA_array, dA_magma, ldda, 0, 0, ldda*N, batchCount, opts.queue );
magma_time = magma_sync_wtime( opts.queue );
info = magma_zgetrf_nopiv_batched( M, N, dA_array, ldda, dinfo_magma, batchCount, opts.queue);
magma_time = magma_sync_wtime( opts.queue ) - magma_time;
magma_perf = gflops / magma_time;
// check correctness of results throught "dinfo_magma" and correctness of argument throught "info"
magma_getvector( batchCount, sizeof(magma_int_t), dinfo_magma, 1, cpu_info, 1);
for (int i=0; i < batchCount; i++)
{
if (cpu_info[i] != 0 ) {
printf("magma_zgetrf_batched matrix %d returned internal error %d\n", i, (int)cpu_info[i] );
}
}
if (info != 0) {
printf("magma_zgetrf_batched returned argument error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
for (int i=0; i < batchCount; i++) {
lapackf77_zgetrf(&M, &N, h_A + i*lda*N, &lda, ipiv + i * min_mn, &info);
assert( info == 0 );
}
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_zgetrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
}
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.lapack ) {
printf("%10d %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f)",
(int) batchCount, (int) M, (int) N, cpu_perf, cpu_time*1000., magma_perf, magma_time*1000., cublas_perf*cublas_enable, cublas_time*1000.*cublas_enable );
}
else {
printf("%10d %5d %5d --- ( --- ) %7.2f (%7.2f) %7.2f (%7.2f)",
(int) batchCount, (int) M, (int) N, magma_perf, magma_time*1000., cublas_perf*cublas_enable, cublas_time*1000.*cublas_enable );
}
if ( opts.check ) {
// initialize ipiv to 1, 2, 3, ...
for (int i=0; i < batchCount; i++)
{
for (int k=0; k < min_mn; k++) {
ipiv[i*min_mn+k] = k+1;
}
}
magma_zgetmatrix( M, N*batchCount, dA_magma, ldda, h_A, lda );
error = 0;
for (int i=0; i < batchCount; i++)
{
double err;
err = get_LU_error( M, N, h_R + i * lda*N, lda, h_A + i * lda*N, ipiv + i * min_mn);
if ( isnan(err) || isinf(err) ) {
error = err;
break;
}
error = max( err, error );
}
bool okay = (error < tol);
status += ! okay;
printf(" %8.2e %s\n", error, (okay ? "ok" : "failed") );
}
else {
printf(" --- \n");
}
TESTING_FREE_CPU( cpu_info );
TESTING_FREE_CPU( ipiv );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_R );
TESTING_FREE_DEV( dA_magma );
TESTING_FREE_DEV( dinfo_magma );
TESTING_FREE_DEV( dipiv_magma );
TESTING_FREE_DEV( dipiv_array );
TESTING_FREE_DEV( dA_array );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/**
Purpose
-------
ZGETRF computes an LU factorization of a general M-by-N matrix A
using partial pivoting with row interchanges.
The factorization has the form
A = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if m > n), and U is upper
triangular (upper trapezoidal if m < n).
This is the right-looking Level 3 BLAS version of the algorithm.
Use two buffer to send panels.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
d_lAT COMPLEX_16 array of pointers on the GPU, dimension (ngpu).
On entry, the M-by-N matrix A distributed over GPUs
(d_lAT[d] points to the local matrix on d-th GPU).
It uses a 1D block column cyclic format (with the block size
nb), and each local matrix is stored by row.
On exit, the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
@param[in]
lddat INTEGER
The leading dimension of the array d_lAT[d]. LDDA >= max(1,M).
@param[out]
ipiv INTEGER array, dimension (min(M,N))
The pivot indices; for 1 <= i <= min(M,N), row i of the
matrix was interchanged with row IPIV(i).
@param (workspace) on device
d_lAP COMPLEX_16 array of pointers on the GPU, dimension (ngpu).
d_lAP[d] is the workspace on d-th GPU. Each local workspace
must be of size (3+ngpu)*nb*maxm, where maxm is m rounded
up to a multiple of 32 and nb is the block size.
@param (workspace)
W COMPLEX_16 array, dimension (ngpu*nb*maxm).
It is used to store panel on CPU.
@param[in]
ldw INTEGER
The leading dimension of the workspace w.
@param[in]
queues magma_queue_t
queues[d] points to the streams for the d-th GPU to execute
in. Each GPU require two streams.
@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, U(i,i) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.
@ingroup magma_zgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_zgetrf2_mgpu(
magma_int_t ngpu,
magma_int_t m, magma_int_t n, magma_int_t nb, magma_int_t offset,
magmaDoubleComplex_ptr d_lAT[], magma_int_t lddat, magma_int_t *ipiv,
magmaDoubleComplex_ptr d_lAP[],
magmaDoubleComplex *W, magma_int_t ldw,
magma_queue_t queues[][2],
magma_int_t *info)
{
#define dAT(id,i,j) (d_lAT[(id)] + ((offset)+(i)*nb)*lddat + (j)*nb)
#define W(j) (W + ((j)%ngpu)*nb*ldw)
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t block_size = 32;
magma_int_t iinfo, n_local[MagmaMaxGPUs];
magma_int_t maxm, mindim;
magma_int_t i, j, d, dd, rows, cols, s, ldpan[MagmaMaxGPUs];
magma_int_t id, j_local, j_local2, nb0, nb1, h = 2+ngpu;
magmaDoubleComplex *d_panel[MagmaMaxGPUs], *panel_local[MagmaMaxGPUs];
/* Check arguments */
*info = 0;
if (m < 0)
*info = -2;
else if (n < 0)
*info = -3;
else if (ngpu*lddat < max(1,n))
*info = -5;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0)
return *info;
/* Function Body */
mindim = min(m, n);
if ( ngpu > ceil((double)n/nb) ) {
*info = -1;
return *info;
}
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
/* Use hybrid blocked code. */
maxm = ((m + block_size-1)/block_size)*block_size;
/* some initializations */
for (d=0; d < ngpu; d++) {
magma_setdevice(d);
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;
/* workspaces */
d_panel[d] = &(d_lAP[d][h*nb*maxm]); /* temporary panel storage */
}
trace_init( 1, ngpu, 2, (CUstream_st**)queues );
/* start sending the panel to cpu */
nb0 = min(mindim, nb);
magma_setdevice(0);
magmablasSetKernelStream(queues[0][1]);
trace_gpu_start( 0, 1, "comm", "get" );
magmablas_ztranspose( nb0, m, dAT(0,0,0), lddat, d_lAP[0], maxm );
magma_zgetmatrix_async( m, nb0,
d_lAP[0], maxm,
W(0), ldw, queues[0][1] );
trace_gpu_end( 0, 1 );
/* ------------------------------------------------------------------------------------- */
magma_timer_t time=0;
timer_start( time );
s = mindim / nb;
for( j=0; j < s; j++ ) {
/* Set the GPU number that holds the current panel */
id = j % ngpu;
magma_setdevice(id);
/* Set the local index where the current panel is */
j_local = j/ngpu;
cols = maxm - j*nb;
rows = m - j*nb;
/* synchronize j-th panel from id-th gpu into work */
magma_queue_sync( queues[id][1] );
/* j-th panel factorization */
trace_cpu_start( 0, "getrf", "getrf" );
lapackf77_zgetrf( &rows, &nb, W(j), &ldw, ipiv+j*nb, &iinfo);
if ( (*info == 0) && (iinfo > 0) ) {
*info = iinfo + j*nb;
}
trace_cpu_end( 0 );
/* start sending the panel to all the gpus */
d = (j+1) % ngpu;
for( dd=0; dd < ngpu; dd++ ) {
magma_setdevice(d);
trace_gpu_start( 0, 1, "comm", "set" );
magma_zsetmatrix_async( rows, nb,
W(j), ldw,
&d_lAP[d][(j%h)*nb*maxm], cols,
queues[d][1] );
trace_gpu_end( 0, 1 );
d = (d+1) % ngpu;
}
/* apply the pivoting */
d = (j+1) % ngpu;
for( dd=0; dd < ngpu; dd++ ) {
magma_setdevice(d);
trace_gpu_start( d, 1, "pivot", "pivot" );
if ( dd == 0 ) {
for( i=j*nb; i < j*nb + nb; ++i ) {
ipiv[i] += j*nb;
}
}
magmablas_zlaswp_q( lddat, dAT(d,0,0), lddat, j*nb + 1, j*nb + nb, ipiv, 1, queues[d][0] );
trace_gpu_end( d, 1 );
d = (d+1) % ngpu;
}
/* update the trailing-matrix/look-ahead */
d = (j+1) % ngpu;
for( dd=0; dd < ngpu; dd++ ) {
magma_setdevice(d);
/* storage for panel */
if ( d == id ) {
/* the panel belond to this gpu */
panel_local[d] = dAT(d,j,j_local);
ldpan[d] = lddat;
/* next column */
j_local2 = j_local+1;
} else {
/* the panel belong to another gpu */
panel_local[d] = d_panel[d];
ldpan[d] = nb;
/* next column */
j_local2 = j_local;
if ( d < id ) j_local2 ++;
}
/* the size of the next column */
if ( s > (j+1) ) {
nb0 = nb;
} else {
nb0 = n_local[d]-nb*(s/ngpu);
if ( d < s % ngpu ) nb0 -= nb;
}
if ( d == (j+1) % ngpu) {
/* owns the next column, look-ahead the column */
nb1 = nb0;
magmablasSetKernelStream(queues[d][1]);
/* make sure all the pivoting has been applied */
magma_queue_sync(queues[d][0]);
trace_gpu_start( d, 1, "gemm", "gemm" );
/* transpose panel on GPU */
magmablas_ztranspose( rows, nb, &d_lAP[d][(j%h)*nb*maxm], cols, panel_local[d], ldpan[d] );
/* synch for remaining update */
magma_queue_sync(queues[d][1]);
} else {
/* update the entire trailing matrix */
nb1 = n_local[d] - j_local2*nb;
magmablasSetKernelStream(queues[d][0]);
/* synchronization to make sure panel arrived on gpu */
magma_queue_sync(queues[d][1]);
trace_gpu_start( d, 0, "gemm", "gemm" );
/* transpose panel on GPU */
magmablas_ztranspose( rows, nb, &d_lAP[d][(j%h)*nb*maxm], cols, panel_local[d], ldpan[d] );
}
/* gpu updating the trailing matrix */
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb1, nb, c_one,
panel_local[d], ldpan[d],
dAT(d, j, j_local2), lddat);
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
nb1, m-(j+1)*nb, nb,
c_neg_one, dAT(d, j, j_local2), lddat,
&(panel_local[d][nb*ldpan[d]]), ldpan[d],
c_one, dAT(d, j+1, j_local2), lddat );
if ( d == (j+1) % ngpu ) {
/* Set the local index where the current panel is */
int loff = j+1;
int j_local = (j+1)/ngpu;
int ldda = maxm - (j+1)*nb;
int cols = m - (j+1)*nb;
nb0 = min(nb, mindim - (j+1)*nb); /* size of the diagonal block */
trace_gpu_end( d, 1 );
if ( nb0 > 0 ) {
/* transpose the panel for sending it to cpu */
trace_gpu_start( d, 1, "comm", "get" );
magmablas_ztranspose( nb0, m-(j+1)*nb, dAT(d,loff,j_local), lddat, &d_lAP[d][((j+1)%h)*nb*maxm], ldda );
/* send the panel to cpu */
magma_zgetmatrix_async( cols, nb0,
&d_lAP[d][((j+1)%h)*nb*maxm], ldda,
W(j+1), ldw, queues[d][1] );
trace_gpu_end( d, 1 );
}
} else {
trace_gpu_end( d, 0 );
}
d = (d+1) % ngpu;
}
/* update the remaining matrix by gpu owning the next panel */
if ( (j+1) < s ) {
int j_local = (j+1)/ngpu;
int rows = m - (j+1)*nb;
d = (j+1) % ngpu;
magma_setdevice(d);
magmablasSetKernelStream(queues[d][0]);
trace_gpu_start( d, 0, "gemm", "gemm" );
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n_local[d] - (j_local+1)*nb, nb,
c_one, panel_local[d], ldpan[d],
dAT(d,j,j_local+1), lddat );
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
n_local[d]-(j_local+1)*nb, rows, nb,
c_neg_one, dAT(d,j,j_local+1), lddat,
&(panel_local[d][nb*ldpan[d]]), ldpan[d],
c_one, dAT(d,j+1, j_local+1), lddat );
trace_gpu_end( d, 0 );
}
} /* end of for j=1..s */
/* ------------------------------------------------------------------------------ */
/* Set the GPU number that holds the last panel */
id = s % ngpu;
/* Set the local index where the last panel is */
j_local = s/ngpu;
/* size of the last diagonal-block */
nb0 = min(m - s*nb, n - s*nb);
rows = m - s*nb;
cols = maxm - s*nb;
if ( nb0 > 0 ) {
magma_setdevice(id);
/* wait for the last panel on cpu */
magma_queue_sync( queues[id][1] );
/* factor on cpu */
lapackf77_zgetrf( &rows, &nb0, W(s), &ldw, ipiv+s*nb, &iinfo);
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + s*nb;
/* send the factor to gpus */
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
j_local2 = j_local;
if ( d < id ) j_local2 ++;
if ( d == id || n_local[d] > j_local2*nb ) {
magma_zsetmatrix_async( rows, nb0,
W(s), ldw,
&d_lAP[d][(s%h)*nb*maxm],
cols, queues[d][1] );
}
}
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
if ( d == 0 ) {
for( i=s*nb; i < s*nb + nb0; ++i ) {
ipiv[i] += s*nb;
}
}
magmablas_zlaswp_q( lddat, dAT(d,0,0), lddat, s*nb + 1, s*nb + nb0, ipiv, 1, queues[d][0] );
}
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
magmablasSetKernelStream(queues[d][1]);
/* wait for the pivoting to be done */
magma_queue_sync( queues[d][0] );
j_local2 = j_local;
if ( d < id ) j_local2++;
if ( d == id ) {
/* the panel belond to this gpu */
panel_local[d] = dAT(d,s,j_local);
/* next column */
nb1 = n_local[d] - j_local*nb-nb0;
magmablas_ztranspose( rows, nb0, &d_lAP[d][(s%h)*nb*maxm], cols, panel_local[d], lddat );
if ( nb1 > 0 ) {
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb1, nb0, c_one,
panel_local[d], lddat,
dAT(d,s,j_local)+nb0, lddat);
}
} else if ( n_local[d] > j_local2*nb ) {
/* the panel belong to another gpu */
panel_local[d] = d_panel[d];
/* next column */
nb1 = n_local[d] - j_local2*nb;
magmablas_ztranspose( rows, nb0, &d_lAP[d][(s%h)*nb*maxm], cols, panel_local[d], nb );
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb1, nb0, c_one,
panel_local[d], nb,
dAT(d,s,j_local2), lddat);
}
}
} /* if ( nb0 > 0 ) */
/* clean up */
trace_finalize( "zgetrf_mgpu.svg","trace.css" );
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
magma_queue_sync( queues[d][0] );
magma_queue_sync( queues[d][1] );
}
magma_setdevice( orig_dev );
magmablasSetKernelStream( orig_stream );
timer_start( time );
timer_printf("\n Performance %f GFlop/s\n", FLOPS_ZGETRF(m,n) / 1e9 / time );
return *info;
} /* magma_zgetrf2_mgpu */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgesv_gpu
*/
int main(int argc, char **argv)
{
TESTING_INIT();
real_Double_t gflops, cpu_perf, cpu_time, gpu_perf, gpu_time;
double error, Rnorm, Anorm, Xnorm, *work;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *h_A, *h_B, *h_X;
magmaDoubleComplex *d_A, *d_B;
magma_int_t *ipiv;
magma_int_t N, nrhs, lda, ldb, ldda, lddb, info, sizeA, sizeB;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
nrhs = opts.nrhs;
printf(" N NRHS CPU GFlop/s (sec) GPU GFlop/s (sec) ||B - AX|| / N*||A||*||X||\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;
ldb = lda;
ldda = ((N+31)/32)*32;
lddb = ldda;
gflops = ( FLOPS_ZGETRF( N, N ) + FLOPS_ZGETRS( N, nrhs ) ) / 1e9;
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, lda*N );
TESTING_MALLOC_CPU( h_B, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC_CPU( h_X, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC_CPU( work, double, N );
TESTING_MALLOC_CPU( ipiv, magma_int_t, N );
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N );
TESTING_MALLOC_DEV( d_B, magmaDoubleComplex, lddb*nrhs );
/* Initialize the matrices */
sizeA = lda*N;
sizeB = ldb*nrhs;
lapackf77_zlarnv( &ione, ISEED, &sizeA, h_A );
lapackf77_zlarnv( &ione, ISEED, &sizeB, h_B );
magma_zsetmatrix( N, N, h_A, lda, d_A, ldda );
magma_zsetmatrix( N, nrhs, h_B, ldb, d_B, lddb );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_zgesv_gpu( N, nrhs, d_A, ldda, ipiv, d_B, lddb, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zgesv_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
//=====================================================================
// Residual
//=====================================================================
magma_zgetmatrix( N, nrhs, d_B, lddb, h_X, ldb );
Anorm = lapackf77_zlange("I", &N, &N, h_A, &lda, work);
Xnorm = lapackf77_zlange("I", &N, &nrhs, h_X, &ldb, work);
blasf77_zgemm( MagmaNoTransStr, MagmaNoTransStr, &N, &nrhs, &N,
&c_one, h_A, &lda,
h_X, &ldb,
&c_neg_one, h_B, &ldb);
Rnorm = lapackf77_zlange("I", &N, &nrhs, h_B, &ldb, work);
error = Rnorm/(N*Anorm*Xnorm);
status += ! (error < tol);
/* ====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_zgesv( &N, &nrhs, h_A, &lda, ipiv, h_B, &ldb, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zgesv returned error %d: %s.\n",
(int) info, magma_strerror( info ));
printf( "%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) N, (int) nrhs, cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed"));
}
else {
printf( "%5d %5d --- ( --- ) %7.2f (%7.2f) %8.2e %s\n",
(int) N, (int) nrhs, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed"));
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_X );
TESTING_FREE_CPU( work );
TESTING_FREE_CPU( ipiv );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgetrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
double error;
magmaDoubleComplex *h_A;
magma_int_t *ipiv;
magma_int_t M, N, n2, lda, info, min_mn;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("ngpu %d\n", (int) opts.ngpu );
if ( opts.check == 2 ) {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) |Ax-b|/(N*|A|*|x|)\n");
}
else {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) |PA-LU|/(N*|A|)\n");
}
printf("=========================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
min_mn = min(M, N);
lda = M;
n2 = lda*N;
gflops = FLOPS_ZGETRF( M, N ) / 1e9;
TESTING_MALLOC_CPU( ipiv, magma_int_t, min_mn );
TESTING_MALLOC_PIN( h_A, magmaDoubleComplex, n2 );
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
init_matrix( M, N, h_A, lda );
cpu_time = magma_wtime();
lapackf77_zgetrf(&M, &N, h_A, &lda, ipiv, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zgetrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
init_matrix( M, N, h_A, lda );
gpu_time = magma_wtime();
magma_zgetrf( M, N, h_A, lda, ipiv, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zgetrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f)",
(int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f)",
(int) M, (int) N, gpu_perf, gpu_time );
}
if ( opts.check == 2 ) {
error = get_residual( M, N, h_A, lda, ipiv );
printf(" %8.2e %s\n", error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
}
else if ( opts.check ) {
error = get_LU_error( M, N, h_A, lda, ipiv );
printf(" %8.2e %s\n", error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
}
else {
printf(" --- \n");
}
TESTING_FREE_CPU( ipiv );
TESTING_FREE_PIN( h_A );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
