// --------------------
int main(int argc, char **argv)
{
TESTING_INIT();
real_Double_t gflops, cpu_time=0, cpu_perf=0, gpu_time, gpu_perf, mgpu_time, mgpu_perf, cuda_time, cuda_perf;
double Ynorm, error=0, error2=0, work[1];
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t n_local[MagmaMaxGPUs];
magma_int_t N, Noffset, lda, ldda, blocks, lhwork, ldwork, matsize, vecsize;
magma_int_t incx = 1;
magmaDoubleComplex alpha = MAGMA_Z_MAKE( 1.5, -2.3 );
magmaDoubleComplex beta = MAGMA_Z_MAKE( -0.6, 0.8 );
magmaDoubleComplex *A, *X, *Y, *Ylapack, *Ycublas, *Ymagma, *Ymagma1, *hwork;
magmaDoubleComplex_ptr dA, dX, dY;
magmaDoubleComplex_ptr d_lA[MagmaMaxGPUs], dwork[MagmaMaxGPUs];
magma_device_t dev;
magma_queue_t queues[MagmaMaxGPUs];
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
opts.ngpu = abs( opts.ngpu ); // always uses multi-GPU code
double tol = opts.tolerance * lapackf77_dlamch("E");
magma_int_t nb = 64; // required by magmablas_zhemv_mgpu implementation
for( dev=0; dev < opts.ngpu; ++dev ) {
magma_queue_create( dev, &queues[dev] );
}
// currently, tests all offsets in the offsets array;
// comment out loop below to test a specific offset.
magma_int_t offset = opts.offset;
magma_int_t offsets[] = { 0, 1, 31, 32, 33, 63, 64, 65, 100, 200 };
magma_int_t noffsets = sizeof(offsets) / sizeof(*offsets);
printf("%% uplo = %s, ngpu %d, block size = %d, offset %d\n",
lapack_uplo_const(opts.uplo), (int) opts.ngpu, (int) nb, (int) offset );
printf( "%% BLAS CUBLAS MAGMA 1 GPU MAGMA MGPU Error rel Error rel\n"
"%% N offset Gflop/s (msec) Gflop/s (msec) Gflop/s (msec) Gflop/s (msec) to CUBLAS to LAPACK\n"
"%%==================================================================================================================\n" );
for( int itest = 0; itest < opts.ntest; ++itest ) {
// comment out these two lines & end of loop to test a specific offset
for( int ioffset=0; ioffset < noffsets; ioffset += 1 ) {
offset = offsets[ioffset];
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
Noffset = N + offset;
lda = Noffset;
ldda = magma_roundup( Noffset, opts.align ); // multiple of 32 by default
matsize = Noffset*ldda;
vecsize = (Noffset-1)*incx + 1;
gflops = FLOPS_ZHEMV( N ) / 1e9;
blocks = magma_ceildiv( N + (offset % nb), nb );
lhwork = N*opts.ngpu;
ldwork = ldda*(blocks + 1);
TESTING_MALLOC_CPU( A, magmaDoubleComplex, matsize );
TESTING_MALLOC_CPU( Y, magmaDoubleComplex, vecsize );
TESTING_MALLOC_CPU( Ycublas, magmaDoubleComplex, vecsize );
TESTING_MALLOC_CPU( Ymagma, magmaDoubleComplex, vecsize );
TESTING_MALLOC_CPU( Ymagma1, magmaDoubleComplex, vecsize );
TESTING_MALLOC_CPU( Ylapack, magmaDoubleComplex, vecsize );
TESTING_MALLOC_PIN( X, magmaDoubleComplex, vecsize );
TESTING_MALLOC_PIN( hwork, magmaDoubleComplex, lhwork );
magma_setdevice( opts.device );
TESTING_MALLOC_DEV( dA, magmaDoubleComplex, matsize );
TESTING_MALLOC_DEV( dX, magmaDoubleComplex, vecsize );
TESTING_MALLOC_DEV( dY, magmaDoubleComplex, vecsize );
// TODO make magma_zmalloc_bcyclic helper function?
for( dev=0; dev < opts.ngpu; dev++ ) {
n_local[dev] = ((Noffset/nb)/opts.ngpu)*nb;
if (dev < (Noffset/nb) % opts.ngpu)
n_local[dev] += nb;
else if (dev == (Noffset/nb) % opts.ngpu)
n_local[dev] += Noffset % nb;
magma_setdevice( dev );
TESTING_MALLOC_DEV( d_lA[dev], magmaDoubleComplex, ldda*n_local[dev] );
TESTING_MALLOC_DEV( dwork[dev], magmaDoubleComplex, ldwork );
}
//////////////////////////////////////////////////////////////////////////
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &matsize, A );
magma_zmake_hermitian( Noffset, A, lda );
lapackf77_zlarnv( &ione, ISEED, &vecsize, X );
lapackf77_zlarnv( &ione, ISEED, &vecsize, Y );
/* =====================================================================
Performs operation using CUBLAS
=================================================================== */
magma_setdevice( opts.device );
magma_zsetmatrix( Noffset, Noffset, A, lda, dA, ldda, opts.queue );
magma_zsetvector( Noffset, X, incx, dX, incx, opts.queue );
magma_zsetvector( Noffset, Y, incx, dY, incx, opts.queue );
cuda_time = magma_sync_wtime(0);
cublasZhemv( opts.handle, cublas_uplo_const(opts.uplo), N,
&alpha, dA + offset + offset*ldda, ldda,
dX + offset, incx,
&beta, dY + offset, incx );
cuda_time = magma_sync_wtime(0) - cuda_time;
cuda_perf = gflops / cuda_time;
magma_zgetvector( Noffset, dY, incx, Ycublas, incx, opts.queue );
/* =====================================================================
Performs operation using MAGMABLAS (1 GPU)
=================================================================== */
magma_setdevice( opts.device );
magma_zsetvector( Noffset, Y, incx, dY, incx, opts.queue );
gpu_time = magma_sync_wtime( opts.queue );
magmablas_zhemv_work( opts.uplo, N,
alpha, dA + offset + offset*ldda, ldda,
dX + offset, incx,
beta, dY + offset, incx, dwork[ opts.device ], ldwork,
opts.queue );
gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
gpu_perf = gflops / gpu_time;
magma_zgetvector( Noffset, dY, incx, Ymagma1, incx, opts.queue );
/* =====================================================================
Performs operation using MAGMABLAS (multi-GPU)
=================================================================== */
magma_zsetmatrix_1D_col_bcyclic( Noffset, Noffset, A, lda, d_lA, ldda, opts.ngpu, nb, queues );
blasf77_zcopy( &Noffset, Y, &incx, Ymagma, &incx );
// workspaces do NOT need to be zero -- set to NAN to prove
for( dev=0; dev < opts.ngpu; ++dev ) {
magma_setdevice( dev );
magmablas_zlaset( MagmaFull, ldwork, 1, MAGMA_Z_NAN, MAGMA_Z_NAN, dwork[dev], ldwork, opts.queue );
}
lapackf77_zlaset( "Full", &lhwork, &ione, &MAGMA_Z_NAN, &MAGMA_Z_NAN, hwork, &lhwork );
mgpu_time = magma_sync_wtime(0);
magma_int_t info;
info = magmablas_zhemv_mgpu(
opts.uplo, N,
alpha,
d_lA, ldda, offset,
X + offset, incx,
beta,
Ymagma + offset, incx,
hwork, lhwork,
dwork, ldwork,
opts.ngpu, nb, queues );
if (info != 0) {
printf("magmablas_zhemv_mgpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
info = magmablas_zhemv_mgpu_sync(
opts.uplo, N,
alpha,
d_lA, ldda, offset,
X + offset, incx,
beta,
Ymagma + offset, incx,
hwork, lhwork,
dwork, ldwork,
opts.ngpu, nb, queues );
if (info != 0) {
printf("magmablas_zhemv_sync returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
mgpu_time = magma_sync_wtime(0) - mgpu_time;
mgpu_perf = gflops / mgpu_time;
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
blasf77_zcopy( &Noffset, Y, &incx, Ylapack, &incx );
cpu_time = magma_wtime();
blasf77_zhemv( lapack_uplo_const(opts.uplo), &N,
&alpha, A + offset + offset*lda, &lda,
X + offset, &incx,
&beta, Ylapack + offset, &incx );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
/* =====================================================================
Compute the Difference LAPACK vs. Magma
=================================================================== */
Ynorm = lapackf77_zlange( "F", &Noffset, &ione, Ylapack, &Noffset, work );
blasf77_zaxpy( &Noffset, &c_neg_one, Ymagma, &incx, Ylapack, &incx );
error2 = lapackf77_zlange( "F", &Noffset, &ione, Ylapack, &Noffset, work ) / Ynorm;
}
/* =====================================================================
Compute the Difference Cublas vs. Magma
=================================================================== */
Ynorm = lapackf77_zlange( "F", &Noffset, &ione, Ycublas, &Noffset, work );
blasf77_zaxpy( &Noffset, &c_neg_one, Ymagma, &incx, Ycublas, &incx );
error = lapackf77_zlange( "F", &Noffset, &ione, Ycublas, &Noffset, work ) / Ynorm;
bool okay = (error < tol && error2 < tol);
status += ! okay;
if ( opts.lapack ) {
printf( "%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e %s\n",
(int) N, (int) offset,
cpu_perf, cpu_time*1000.,
cuda_perf, cuda_time*1000.,
gpu_perf, gpu_time*1000.,
mgpu_perf, mgpu_time*1000.,
error, error2, (okay ? "ok" : "failed") );
}
else {
printf( "%5d %5d --- ( --- ) %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %8.2e --- %s\n",
(int) N, (int) offset,
cuda_perf, cuda_time*1000.,
gpu_perf, gpu_time*1000.,
mgpu_perf, mgpu_time*1000.,
error, (okay ? "ok" : "failed") );
}
/* Free Memory */
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( Y );
TESTING_FREE_CPU( Ycublas );
TESTING_FREE_CPU( Ymagma );
TESTING_FREE_CPU( Ymagma1 );
TESTING_FREE_CPU( Ylapack );
TESTING_FREE_PIN( X );
TESTING_FREE_PIN( hwork );
magma_setdevice( opts.device );
TESTING_FREE_DEV( dA );
TESTING_FREE_DEV( dX );
TESTING_FREE_DEV( dY );
for( dev=0; dev < opts.ngpu; dev++ ) {
magma_setdevice( dev );
TESTING_FREE_DEV( d_lA[dev] );
TESTING_FREE_DEV( dwork[dev] );
}
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
// comment out these two lines line & top of loop test a specific offset
} // end for ioffset
printf( "\n" );
}
for( dev=0; dev < opts.ngpu; ++dev ) {
magma_queue_destroy( queues[dev] );
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zlaset
Code is very similar to testing_zlacpy.cpp
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gbytes, gpu_perf, gpu_time, cpu_perf, cpu_time;
double error, work[1];
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *h_A, *h_R;
magmaDoubleComplex_ptr d_A;
magmaDoubleComplex offdiag, diag;
magma_int_t M, N, size, lda, ldda;
magma_int_t ione = 1;
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
magma_uplo_t uplo[] = { MagmaLower, MagmaUpper, MagmaFull };
printf("%% uplo M N offdiag diag CPU GByte/s (ms) GPU GByte/s (ms) check\n");
printf("%%===================================================================================\n");
for( int iuplo = 0; iuplo < 3; ++iuplo ) {
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
for( int ival = 0; ival < 4; ++ival ) {
// test combinations of zero & non-zero:
// ival offdiag diag
// 0 0 0
// 1 0 3.14
// 2 1.23 0
// 3 1.23 3.14
offdiag = MAGMA_Z_MAKE( 1.2345, 6.7890 ) * (ival / 2);
diag = MAGMA_Z_MAKE( 3.1415, 2.7183 ) * (ival % 2);
M = opts.msize[itest];
N = opts.nsize[itest];
//M += 2; // space for insets
//N += 2;
lda = M;
ldda = magma_roundup( M, opts.align );
size = lda*N;
if ( uplo[iuplo] == MagmaLower ) {
// save lower trapezoid (with diagonal)
if ( M > N ) {
gbytes = sizeof(magmaDoubleComplex) * (1.*M*N - 0.5*N*(N-1)) / 1e9;
} else {
gbytes = sizeof(magmaDoubleComplex) * 0.5*M*(M+1) / 1e9;
}
}
else if ( uplo[iuplo] == MagmaUpper ) {
// save upper trapezoid (with diagonal)
if ( N > M ) {
gbytes = sizeof(magmaDoubleComplex) * (1.*M*N - 0.5*M*(M-1)) / 1e9;
} else {
gbytes = sizeof(magmaDoubleComplex) * 0.5*N*(N+1) / 1e9;
}
}
else {
// save entire matrix
gbytes = sizeof(magmaDoubleComplex) * 1.*M*N / 1e9;
}
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, size );
TESTING_MALLOC_CPU( h_R, magmaDoubleComplex, size );
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N );
/* Initialize the matrix */
for( int j = 0; j < N; ++j ) {
for( int i = 0; i < M; ++i ) {
h_A[i + j*lda] = MAGMA_Z_MAKE( i + j/10000., j );
}
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_zsetmatrix( M, N, h_A, lda, d_A, ldda );
magmablasSetKernelStream( opts.queue );
gpu_time = magma_sync_wtime( opts.queue );
//magmablas_zlaset( uplo[iuplo], M-2, N-2, offdiag, diag, d_A+1+ldda, ldda ); // inset by 1 row & col
magmablas_zlaset( uplo[iuplo], M, N, offdiag, diag, d_A, ldda );
gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
gpu_perf = gbytes / gpu_time;
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
//magma_int_t M2 = M-2; // inset by 1 row & col
//magma_int_t N2 = N-2;
//lapackf77_zlaset( lapack_uplo_const( uplo[iuplo] ), &M2, &N2, &offdiag, &diag, h_A+1+lda, &lda );
lapackf77_zlaset( lapack_uplo_const( uplo[iuplo] ), &M, &N, &offdiag, &diag, h_A, &lda );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gbytes / cpu_time;
if ( opts.verbose ) {
printf( "A= " ); magma_zprint( M, N, h_A, lda );
printf( "dA=" ); magma_zprint_gpu( M, N, d_A, ldda );
}
/* =====================================================================
Check the result
=================================================================== */
magma_zgetmatrix( M, N, d_A, ldda, h_R, lda );
blasf77_zaxpy(&size, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_zlange("f", &M, &N, h_R, &lda, work);
bool okay = (error == 0);
status += ! okay;
printf("%5s %5d %5d %9.4f %6.4f %7.2f (%7.2f) %7.2f (%7.2f) %s\n",
lapack_uplo_const( uplo[iuplo] ), (int) M, (int) N,
real(offdiag), real(diag),
cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
(okay ? "ok" : "failed") );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_R );
TESTING_FREE_DEV( d_A );
fflush( stdout );
}
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
printf( "\n" );
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
extern "C" magma_int_t
magma_zpotrf3_mgpu(magma_int_t num_gpus, char uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
magmaDoubleComplex *d_lA[], magma_int_t ldda,
magmaDoubleComplex *d_lP[], magma_int_t lddp,
magmaDoubleComplex *a, magma_int_t lda, magma_int_t h,
magma_queue_t stream[][3], magma_event_t event[][5],
magma_int_t *info )
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix dA.
Auxiliary subroutine for zpotrf2_ooc. It is multiple gpu interface to compute
Cholesky of a "rectangular" matrix.
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) COMPLEX_16 array on the GPU, dimension (LDDA,N)
On entry, the Hermitian 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
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, nb0, nb2, d, dd, id, j_local, j_local2, buf;
char uplo_[2] = {uplo, 0};
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
double d_one = 1.0;
double d_neg_one = -1.0;
int upper = lapackf77_lsame(uplo_, "U");
magmaDoubleComplex *dlpanel;
magma_int_t n_local[MagmaMaxGPUs], ldpanel;
const magma_int_t stream1 = 0, stream2 = 1, stream3 = 2;
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
/* used by ztrsm_work */
int trsm_nb = 128;
int trsm_n = trsm_nb*((nb+trsm_nb-1)/trsm_nb);
magmaDoubleComplex *d_dinvA[MagmaMaxGPUs];
magmaDoubleComplex *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
*/
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
if ( (MAGMA_SUCCESS != magma_zmalloc( &d_dinvA[d], 2*trsm_nb*trsm_n )) ||
(MAGMA_SUCCESS != magma_zmalloc( &d_x[d], 2*nb*(upper ? n : m) )) ) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
}
magma_setdevice(0);
#endif
*info = 0;
if ( (! upper) && (! lapackf77_lsame(uplo_, "L")) ) {
*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;
}
/* initialization */
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;
}
}
/* == initialize the trace */
trace_init( 1, num_gpus, 3, (CUstream_st**)stream );
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)%num_gpus;
buf = (j/nb)%num_gpus; // right now, we have num_gpu buffers, so id and buf are the same..
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (m-j));
/* Update the current diagonal block on stream1 */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
trace_gpu_start( id, stream1, "syrk", "syrk" );
magma_zherk(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_zgetmatrix_async( jb, jb,
dlA(id, j, nb*j_local), ldda,
Aup(j,j), lda,
stream[id][stream1] );
trace_gpu_end( id, stream1 );
/* update off-diagonal blocks in the panel */
if( j > 0 ) {
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; // number of local columns in the panel, while jb is panel-size (number of rows)
if( n_local[d] > nb0 ) {
magma_setdevice(d);
magmablasSetKernelStream(stream[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( stream[d][stream2], event[d][0] ); // rows arrived at gpu
} else {
dlpanel = dlP(d,nb,0,buf);
ldpanel = lddp;
magma_queue_wait_event( stream[d][stream2], event[d][0] ); // rows arrived at gpu
}
trace_gpu_start( d, stream2, "gemm", "gemm" );
magma_zgemm(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( event[d][2], stream[d][stream2] );
}
d = (d+1)%num_gpus;
}
}
/* wait for panel and factorize it on cpu */
magma_setdevice(id);
magma_queue_sync( stream[id][stream1] );
trace_cpu_start( 0, "getrf", "getrf" );
lapackf77_zpotrf(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)%num_gpus;
for( dd=0; dd<num_gpus; 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_zsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlpanel, ldpanel,
stream[d][stream1] );
trace_gpu_end( d, stream1 );
magma_event_record( event[d][1], stream[d][stream1] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
trace_gpu_start( id, stream1, "comm", "comm" );
magma_zsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlA(id, j, nb*j_local), ldda,
stream[id][stream1] );
trace_gpu_end( id, stream1 );
}
/* 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] - j_local2*nb;
magma_setdevice(d);
if( j+jb < m && d == (j/nb+1)%num_gpus ) {
/* owns the next column, look-ahead next block on stream1 */
nb0 = min(nb, nb2);
magmablasSetKernelStream(stream[d][stream1]);
magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for gemm update
trace_gpu_start( d, stream1, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magmablas_zlaset( MagmaUpperLower, trsm_nb, trsm_n, dinvA(d,0),trsm_nb );
magmablas_zlaset( MagmaUpperLower, nb0,jb, dx(d,0),nb0 );
magmablas_ztrsm_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_ztrsm( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
magma_event_record( event[d][4], stream[d][stream1] );
trace_gpu_end( d, stream1 );
} else if( nb2 > 0 ) {
/* update all the blocks on stream2 */
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for cholesky factor
trace_gpu_start( d, stream2, "trsm", "trsm" );
magmablasSetKernelStream(stream[d][stream2]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magmablas_zlaset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,0),trsm_nb );
magmablas_zlaset( MagmaUpperLower, nb2,jb, dx(d,0),nb2 );
magmablas_ztrsm_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_ztrsm( 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)%num_gpus;
} /* end of for */
/* ========================================================== */
if( j+jb < m ) {
d = (j/nb+1)%num_gpus;
/* 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( stream[d][stream3], event[d][4] );
trace_gpu_start( d, stream3, "comm", "row to CPU" );
magma_zgetmatrix_async( (j+jb), nb0,
dlA(d, 0, nb*j_local2), ldda,
Aup(0,j+jb), lda,
stream[d][stream3] );
trace_gpu_end( d, stream3 );
magma_event_record( event[d][3], stream[d][stream3] );
/* needed on pluto */
//magma_queue_sync( stream[d][stream3] );
/* broadcast rows to gpus on stream2 */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
if( d2 != d )
{
magma_setdevice(d2);
trace_gpu_start( d2, stream3, "comm", "row to GPUs" );
magma_queue_wait_event( stream[d2][stream3], event[d][3] ); // rows arrived at cpu on stream3
magma_zsetmatrix_async( j+jb, nb0,
Aup(0,j+jb), lda,
dlP(d2,nb,0,buf2), lddp,
stream[d2][stream3] );
trace_gpu_end( d2, stream3 );
magma_event_record( event[d2][0], stream[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(stream[d][stream2]);
trace_gpu_start( d, stream2, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
int flag = 0;
if (flag == 0) {
magma_queue_wait_event( stream[d][stream2], event[d][4] ); // lookahead -> diagonal inversion
} else {
magmablas_zlaset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,flag),trsm_nb );
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // panel received
}
magmablas_zlaset( MagmaUpperLower, nb2,jb, dx(d,1),nb2 );
magmablas_ztrsm_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( stream[d][stream2], event[d][1] ); // wait for cholesky factor
magma_ztrsm( 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 ztrsm */
} /* 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)%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));
/* Update the current diagonal block on stream1 */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
magma_zherk(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_zgetmatrix_async( jb, jb,
dlA(id, nb*j_local, j), ldda,
Alo(j,j), lda,
stream[id][stream1] );
/* update off-diagonal blocks of the panel */
if( j > 0 ) {
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] ) {
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
if( d == id ) {
dlpanel = dlA(d, nb*j_local, 0);
ldpanel = ldda;
} else {
dlpanel = dlPT(d,0,nb,buf);
ldpanel = nb;
magma_queue_wait_event( stream[d][stream2], event[d][0] ); // rows arrived at gpu
}
magma_zgemm( 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( event[d][2], stream[d][stream2] );
}
d = (d+1)%num_gpus;
}
}
/* wait for the panel and factorized it on cpu */
magma_setdevice(id);
magma_queue_sync( stream[id][stream1] );
lapackf77_zpotrf(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)%num_gpus;
for( dd=0; dd<num_gpus; 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_zsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlpanel, ldpanel,
stream[d][stream1] );
magma_event_record( event[d][1], stream[d][stream1] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
magma_zsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlA(id, nb*j_local, j), ldda,
stream[id][stream1] );
}
/* panel factorize the off-diagonal */
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);
if( j+nb < n && d == (j/nb+1)%num_gpus ) { /* owns next column, look-ahead next block on stream1 */
if ( j > 0 ) magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for gemm update
magmablasSetKernelStream(stream[d][stream1]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magmablas_zlaset( MagmaUpperLower, trsm_nb, trsm_n, dinvA(d,0),trsm_nb );
magmablas_zlaset( MagmaUpperLower, nb0,jb, dx(d,0),nb0 );
magmablas_ztrsm_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_ztrsm( MagmaRight, MagmaLower,
MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
magma_event_record( event[d][4], stream[d][stream1] );
} else if( nb2 > 0 ) { /* other gpus updating all the blocks on stream2 */
/* update the entire column */
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for the cholesky factor
magmablasSetKernelStream(stream[d][stream2]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magmablas_zlaset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,0),trsm_nb );
magmablas_zlaset( MagmaUpperLower, nb2,jb, dx(d,0),nb2 );
magmablas_ztrsm_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_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
}
d = (d+1)%num_gpus;
} /* end for d */
/* ========================================================== */
if( j+jb < n ) {
d = (j/nb+1)%num_gpus;
/* 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 ZPOTRF_DEVICE_TO_DEVICE
#ifdef ZPOTRF_DEVICE_TO_DEVICE
// lookahead done
/* broadcast the rows to gpus */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
magma_setdevice(d2);
magma_queue_wait_event( stream[d2][stream3], event[d][4] );
if( d2 != d ) {
magma_zcopymatrix_async( nb0, j+jb,
dlPT(d2,0,nb,buf2), nb, // first nbxnb reserved for diagonal block
dlA(d, nb*j_local2, 0), ldda,
stream[d2][stream3] );
magma_event_record( event[d2][0], stream[d2][stream3] );
} else {
magma_zgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
stream[d][stream3] );
}
}
#else
// lookahead done
magma_setdevice(d);
magma_queue_wait_event( stream[d][stream3], event[d][4] );
magma_zgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
stream[d][stream3] );
magma_event_record( event[d][3], stream[d][stream3] );
/* syn on rows on CPU, seem to be needed on Pluto */
//magma_queue_sync( stream[d][stream3] );
/* broadcast the rows to gpus */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
if( d2 != d )
{
magma_setdevice(d2);
magma_queue_wait_event( stream[d2][stream3], event[d][3] ); // getmatrix done
magma_zsetmatrix_async( nb0, j+jb,
Alo(j+jb,0), lda,
dlPT(d2,0,nb,buf2), nb, // first nbxnb reserved for diagonal block
stream[d2][stream3] );
magma_event_record( event[d2][0], stream[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(stream[d][stream2]);
/* update the remaining blocks in the column */
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
int flag = 0;
if (flag == 0) {
magma_queue_wait_event( stream[d][stream2], event[d][4] ); // lookahead -> diagonal inversion
} else {
magmablas_zlaset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,flag),trsm_nb );
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // panel received
}
magmablas_zlaset( MagmaUpperLower, nb2,jb, dx(d,1),nb2 );
magmablas_ztrsm_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( stream[d][stream2], event[d][1] ); // panel received
magma_ztrsm( 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( "zpotrf.svg","trace.css" );
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
for( j=0; j<3; j++ ) {
magma_queue_sync( stream[d][j] );
}
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magma_free( d_dinvA[d] );
magma_free( d_x[d] );
#endif
magmablasSetKernelStream(NULL);
}
magma_setdevice(0);
return *info;
} /* magma_zpotrf_mgpu */
extern "C" magma_int_t
magma_zlahr2_m(
magma_int_t n, magma_int_t k, magma_int_t nb,
magmaDoubleComplex *A, magma_int_t lda,
magmaDoubleComplex *tau,
magmaDoubleComplex *T, magma_int_t ldt,
magmaDoubleComplex *Y, magma_int_t ldy,
struct zgehrd_data* data )
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZLAHR2 reduces the first NB columns of a complex general n-BY-(n-k+1)
matrix A so that elements below the k-th subdiagonal are zero. The
reduction is performed by an orthogonal similarity transformation
Q' * A * Q. The routine returns the matrices V and T which determine
Q as a block reflector I - V*T*V', and also the matrix Y = A * V.
(Note this is different than LAPACK, which computes Y = A * V * T.)
This is an auxiliary routine called by ZGEHRD.
Arguments
=========
N (input) INTEGER
The order of the matrix A.
K (input) INTEGER
The offset for the reduction. Elements below the k-th
subdiagonal in the first NB columns are reduced to zero.
K < N.
NB (input) INTEGER
The number of columns to be reduced.
A (input/output) COMPLEX_16 array, dimension (LDA,N-K+1)
On entry, the n-by-(n-k+1) general matrix A.
On exit, the elements on and above the k-th subdiagonal in
the first NB columns are overwritten with the corresponding
elements of the reduced matrix; the elements below the k-th
subdiagonal, with the array TAU, represent the matrix Q as a
product of elementary reflectors. The other columns of A are
unchanged. See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAU (output) COMPLEX_16 array, dimension (NB)
The scalar factors of the elementary reflectors. See Further
Details.
T (output) COMPLEX_16 array, dimension (LDT,NB)
The upper triangular matrix T.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= NB.
Y (output) COMPLEX_16 array, dimension (LDY,NB)
The n-by-nb matrix Y.
LDY (input) INTEGER
The leading dimension of the array Y. LDY >= N.
dA (input/output) COMPLEX_16 array on the GPU, dimension (LDA,N-K+1)
On entry, the n-by-(n-k+1) general matrix A.
On exit, the elements in rows K:N of the first NB columns are
overwritten with the matrix Y.
DV (output) COMPLEX_16 array on the GPU, dimension (N, NB)
On exit this contains the Householder vectors of the transformation.
Further Details
===============
The matrix Q is represented as a product of nb elementary reflectors
Q = H(1) H(2) . . . H(nb).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
A(i+k+1:n,i), and tau in TAU(i).
The elements of the vectors v together form the (n-k+1)-by-nb matrix
V which is needed, with T and Y, to apply the transformation to the
unreduced part of the matrix, using an update of the form:
A := (I - V*T*V') * (A - Y*T*V').
The contents of A on exit are illustrated by the following example
with n = 7, k = 3 and nb = 2:
( a a a a a )
( a a a a a )
( a a a a a )
( h h a a a )
( v1 h a a a )
( v1 v2 a a a )
( v1 v2 a a a )
where "a" denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
This implementation follows the hybrid algorithm and notations described in
S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg
form through hybrid GPU-based computing," University of Tennessee Computer
Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219),
May 24, 2009.
===================================================================== */
#define A( i, j ) ( A + (i) + (j)*lda)
#define Y( i, j ) ( Y + (i) + (j)*ldy)
#define T( i, j ) ( T + (i) + (j)*ldt)
#define dA( d, i, j ) (data->A [d] + (i) + (j)*ldda)
#define dTi( d ) (data->Ti[d])
#define dV( d, i, j ) (data->V [d] + (i) + (j)*ldv )
#define dVd( d, i, j ) (data->Vd[d] + (i) + (j)*ldvd)
#define dY( d, i, j ) (data->Y [d] + (i) + (j)*ldda)
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex tmp;
magma_int_t ngpu = data->ngpu;
magma_int_t ldda = data->ldda;
magma_int_t ldv = data->ldv;
magma_int_t ldvd = data->ldvd;
magma_int_t ione = 1;
magma_int_t d, dki1, dn, nblocks, gblock, lblock, lgid;
magma_int_t n_k_i_1, n_k;
magmaDoubleComplex scale;
magma_int_t i;
magmaDoubleComplex ei = MAGMA_Z_ZERO;
magma_int_t info_data = 0;
magma_int_t *info = &info_data;
if (n < 0) {
*info = -1;
} else if (k < 0 || k >= n) {
*info = -2;
} else if (nb < 1 || nb > n) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
} else if (ldt < nb) {
*info = -8;
} else if (ldy < max(1,n)) {
*info = -10;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
// adjust from 1-based indexing
k -= 1;
// Function Body
if (n <= 1)
return 0;
// zero out current top block of V on all GPUs
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magmablasSetKernelStream( data->streams[d] );
magmablas_zlaset( MagmaUpperLower, nb, nb, dV(d,k,0), ldv );
}
// set all Y=0
lapackf77_zlaset( "Full", &n, &nb, &c_zero, &c_zero, Y, &ldy );
for (i = 0; i < nb; ++i) {
n_k_i_1 = n - k - i - 1;
n_k = n - k;
if (i > 0) {
// Finish applying I - V * T * V' on right
tmp = MAGMA_Z_NEGATE( tau[i-1] );
blasf77_zaxpy( &n_k, &tmp, Y(k,i-1), &ione, A(k,i), &ione );
// Apply I - V * T' * V' to this column (call it b) from the
// left, using the last column of T as workspace, w.
//
// Let V = ( V1 ) and b = ( b1 ) (first i-1 rows)
// ( V2 ) ( b2 )
// where V1 is unit lower triangular
// w := b1 = A(k+1:k+i, i)
blasf77_zcopy( &i,
A(k+1,i), &ione,
T(0,nb-1), &ione );
// w := V1' * b1 = VA(k+1:k+i, 0:i-1)' * w
blasf77_ztrmv( "Lower", "Conj", "Unit", &i,
A(k+1,0), &lda,
T(0,nb-1), &ione );
// w := w + V2'*b2 = w + VA(k+i+1:n-1, 0:i-1)' * A(k+i+1:n-1, i)
blasf77_zgemv( "Conj", &n_k_i_1, &i,
&c_one, A(k+i+1,0), &lda,
A(k+i+1,i), &ione,
&c_one, T(0,nb-1), &ione );
// w := T'*w = T(0:i-1, 0:i-1)' * w
blasf77_ztrmv( "Upper", "Conj", "Non-unit", &i,
T(0,0), &ldt,
T(0,nb-1), &ione );
// b2 := b2 - V2*w = A(k+i+1:n-1, i) - VA(k+i+1:n-1, 0:i-1) * w
blasf77_zgemv( "No trans", &n_k_i_1, &i,
&c_neg_one, A(k+i+1,0), &lda,
T(0,nb-1), &ione,
&c_one, A(k+i+1,i), &ione );
// w := V1*w = VA(k+1:k+i, 0:i-1) * w
blasf77_ztrmv( "Lower", "No trans", "Unit", &i,
A(k+1,0), &lda,
T(0,nb-1), &ione );
// b1 := b1 - w = A(k+1:k+i-1, i) - w
blasf77_zaxpy( &i,
&c_neg_one, T(0,nb-1), &ione,
A(k+1,i), &ione );
// Restore diagonal element, saved below during previous iteration
*A(k+i,i-1) = ei;
}
// Generate the elementary reflector H(i) to annihilate A(k+i+1:n-1,i)
lapackf77_zlarfg( &n_k_i_1,
A(k+i+1,i),
A(k+i+2,i), &ione, &tau[i] );
// Save diagonal element and set to one, to simplify multiplying by V
ei = *A(k+i+1,i);
*A(k+i+1,i) = c_one;
// compute yi = A vi = sum_g A{d} vi{d}
nblocks = (n-1) / nb / ngpu + 1;
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magmablasSetKernelStream( data->streams[d] );
// dV(k+i+1:n-1, i) = VA(k+i:n, i)
magma_zsetvector_async( n_k_i_1,
A(k+i+1,i), 1,
dV(d, k+i+1, i), 1, data->streams[d] );
// copy column of dV -> dVd, using block cyclic distribution.
// This assumes V and Vd have been padded so that
// a 2D matrix copy doesn't access them out-of-bounds
gblock = k / nb;
lblock = gblock / ngpu;
lgid = gblock % ngpu;
if ( d < lgid ) {
lblock += 1;
}
// treat V as (nb*ngpu) x nblock matrix, and Vd as nb x nblock matrix
magmablas_zlacpy( 'F', nb, nblocks-lblock,
dV (d, d*nb + lblock*nb*ngpu, i), nb*ngpu,
dVd(d, 0 + lblock*nb , i), nb );
// convert global indices (k) to local indices (dk)
magma_indices_1D_bcyclic( nb, ngpu, d, k+i+1, n, &dki1, &dn );
// dY(k:n, i) = dA(k:n, k+i+1:n) * dV(k+i+1:n, i)
// skip if matrix is empty
// each GPU copies to different temporary vector in Y,
// which are summed in separate loop below
if ( dn-dki1 > 0 ) {
magma_zgemv( 'N', n-k, dn-dki1,
c_one, dA (d, k , dki1), ldda,
dVd(d, dki1, i), 1,
c_zero, dY (d, k , i), 1 );
// copy vector to host, storing in column nb+d of Y
// as temporary space (Y has >= nb+ngpu columns)
magma_zgetvector_async( n-k,
dY(d, k, i), 1,
Y(k, nb+d), 1, data->streams[d] );
}
}
// while GPU is doing above Ag*v...
// Compute T(0:i,i) = [ -tau T V' vi ]
// [ tau ]
// T(0:i-1, i) = -tau VA(k+i+1:n-1, 0:i-1)' VA(k+i+1:n-1, i)
scale = MAGMA_Z_NEGATE( tau[i] );
blasf77_zgemv( "Conj", &n_k_i_1, &i,
&scale, A(k+i+1,0), &lda,
A(k+i+1,i), &ione,
&c_zero, T(0,i), &ione );
// T(0:i-1, i) = T(0:i-1, 0:i-1) * T(0:i-1, i)
blasf77_ztrmv( "Upper", "No trans", "Non-unit", &i,
T(0,0), &ldt,
T(0,i), &ione );
*T(i,i) = tau[i];
// apply reflectors to next column, A(i+1), on right only.
// one axpy will be required to finish this, in the next iteration above
if ( i > 0 && i+1 < nb ) {
// Update next column, A(k:n,i+1), applying Q on right.
// One axpy will be required to finish this, in the next iteration
// above, after yi is computed.
// This updates one more row than LAPACK does (row k),
// making block above panel an even multiple of nb.
// Use last column of T as workspace, w.
magma_int_t i1 = i+1;
// If complex, conjugate row of V, and undo afterwards
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_zlacgv( &i1, A(k+i1,0), &lda );
#endif
// w = T(0:i, 0:i+1) * VA(k+i+1, 0:i+1)'
// T is now rectangular, so we use gemv instead of trmv as in lapack.
blasf77_zgemv( "No trans", &i, &i1,
&c_one, T(0,0), &ldt,
A(k+i1,0), &lda,
&c_zero, T(0,nb-1), &ione );
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_zlacgv( &i1, A(k+i1,0), &lda );
#endif
// A(k:n, i+1) -= Y(k:n, 0:i) * w
blasf77_zgemv( "No trans", &n_k, &i,
&c_neg_one, Y(k,0), &ldy,
T(0,nb-1), &ione,
&c_one, A(k,i1), &ione );
}
// yi = sum_g yi{d}
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magma_queue_sync( data->streams[d] );
magma_indices_1D_bcyclic( nb, ngpu, d, k+i+1, n, &dki1, &dn );
if ( dn-dki1 > 0 ) {
// yi = yi + yi{d}
blasf77_zaxpy( &n_k, &c_one, Y(k,nb+d), &ione, Y(k,i), &ione );
}
}
}
// Restore diagonal element
*A(k+nb,nb-1) = ei;
// compute Y = Am V = sum_g Am{d} V{d} --- top part, Y(0:k-1,:)
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magmablasSetKernelStream( data->streams[d] );
// convert global indices (k) to local indices (dk)
magma_indices_1D_bcyclic( nb, ngpu, d, k+1, n, &dki1, &dn );
// dY(0:k, :) = dA(0:k, k+i+1:n-1) * dV(k+i+1:n-1, :)
// skip if matrix is empty
// each GPU copies to different temporary block in Y,
// which are summed in separate loop below
if ( dn-dki1 > 0 ) {
magma_zgemm( 'N', 'N', k, nb, dn-dki1,
c_one, dA (d, 0 , dki1), ldda,
dVd(d, dki1, 0), ldvd,
c_zero, dY (d, 0 , 0), ldda );
// copy result to host, storing in columns [nb + nb*d : nb + nb*(d+1)] of Y
// as temporary space (Y has nb + nb*ngpu columns)
magma_zgetmatrix_async( k, nb,
dY(d, 0, 0), ldda,
Y(0,nb+nb*d), ldy, data->streams[d] );
}
}
// Y = sum_g Y{d}
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magma_queue_sync( 0 );
magma_indices_1D_bcyclic( nb, ngpu, d, k+1, n, &dki1, &dn );
if ( dn-dki1 > 0 ) {
// Y = Y + Am V
for( i = 0; i < nb; ++i ) {
blasf77_zaxpy( &k, &c_one, Y(0,nb+nb*d+i), &ione, Y(0,i), &ione );
}
}
}
// copy Y and T matrices to GPUs
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magma_zsetmatrix_async( n, nb, Y, ldy, dY(d, 0, 0), ldda, data->streams[d] );
magma_zsetmatrix_async( nb, nb, T, nb, dTi(d), nb, data->streams[d] );
}
return 0;
} // magma_zlahr2
extern "C" magma_int_t
magma_zpidr_merge(
magma_z_matrix A, magma_z_matrix b, magma_z_matrix *x,
magma_z_solver_par *solver_par,
magma_z_preconditioner *precond_par,
magma_queue_t queue )
{
magma_int_t info = MAGMA_NOTCONVERGED;
// prepare solver feedback
solver_par->solver = Magma_PIDRMERGE;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
solver_par->init_res = 0.0;
solver_par->final_res = 0.0;
solver_par->iter_res = 0.0;
solver_par->runtime = 0.0;
// constants
const magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
const magmaDoubleComplex c_n_one = MAGMA_Z_NEG_ONE;
// internal user parameters
const magma_int_t smoothing = 1; // 0 = disable, 1 = enable
const double angle = 0.7; // [0-1]
// local variables
magma_int_t iseed[4] = {0, 0, 0, 1};
magma_int_t dof;
magma_int_t s;
magma_int_t distr;
magma_int_t k, i, sk;
magma_int_t innerflag;
magma_int_t ldd;
double residual;
double nrm;
double nrmb;
double nrmr;
double nrmt;
double rho;
magmaDoubleComplex om;
magmaDoubleComplex gamma;
magmaDoubleComplex fk;
// matrices and vectors
magma_z_matrix dxs = {Magma_CSR};
magma_z_matrix dr = {Magma_CSR}, drs = {Magma_CSR};
magma_z_matrix dP = {Magma_CSR}, dP1 = {Magma_CSR};
magma_z_matrix dG = {Magma_CSR}, dGcol = {Magma_CSR};
magma_z_matrix dU = {Magma_CSR};
magma_z_matrix dM = {Magma_CSR}, hMdiag = {Magma_CSR};
magma_z_matrix df = {Magma_CSR};
magma_z_matrix dt = {Magma_CSR}, dtt = {Magma_CSR};
magma_z_matrix dc = {Magma_CSR};
magma_z_matrix dv = {Magma_CSR};
magma_z_matrix dlu = {Magma_CSR};
magma_z_matrix dskp = {Magma_CSR}, hskp = {Magma_CSR};
magma_z_matrix dalpha = {Magma_CSR}, halpha = {Magma_CSR};
magma_z_matrix dbeta = {Magma_CSR}, hbeta = {Magma_CSR};
magmaDoubleComplex *d1 = NULL, *d2 = NULL;
// chronometry
real_Double_t tempo1, tempo2;
// initial s space
// TODO: add option for 's' (shadow space number)
// Hack: uses '--restart' option as the shadow space number.
// This is not a good idea because the default value of restart option is used to detect
// if the user provided a custom restart. This means that if the default restart value
// is changed then the code will think it was the user (unless the default value is
// also updated in the 'if' statement below.
s = 1;
if ( solver_par->restart != 50 ) {
if ( solver_par->restart > A.num_cols ) {
s = A.num_cols;
} else {
s = solver_par->restart;
}
}
solver_par->restart = s;
// set max iterations
solver_par->maxiter = min( 2 * A.num_cols, solver_par->maxiter );
// check if matrix A is square
if ( A.num_rows != A.num_cols ) {
//printf("Matrix A is not square.\n");
info = MAGMA_ERR_NOT_SUPPORTED;
goto cleanup;
}
// |b|
nrmb = magma_dznrm2( b.num_rows, b.dval, 1, queue );
if ( nrmb == 0.0 ) {
magma_zscal( x->num_rows, MAGMA_Z_ZERO, x->dval, 1, queue );
info = MAGMA_SUCCESS;
goto cleanup;
}
// t = 0
// make t twice as large to contain both, dt and dr
ldd = magma_roundup( b.num_rows, 32 );
CHECK( magma_zvinit( &dt, Magma_DEV, ldd, 2, c_zero, queue ));
dt.num_rows = b.num_rows;
dt.num_cols = 1;
dt.nnz = dt.num_rows;
// redirect the dr.dval to the second part of dt
CHECK( magma_zvinit( &dr, Magma_DEV, b.num_rows, 1, c_zero, queue ));
magma_free( dr.dval );
dr.dval = dt.dval + ldd;
// r = b - A x
CHECK( magma_zresidualvec( A, b, *x, &dr, &nrmr, queue ));
// |r|
solver_par->init_res = nrmr;
solver_par->final_res = solver_par->init_res;
solver_par->iter_res = solver_par->init_res;
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = (real_Double_t)nrmr;
}
// check if initial is guess good enough
if ( nrmr <= solver_par->atol ||
nrmr/nrmb <= solver_par->rtol ) {
info = MAGMA_SUCCESS;
goto cleanup;
}
// P = randn(n, s)
// P = ortho(P)
//---------------------------------------
// P = 0.0
CHECK( magma_zvinit( &dP, Magma_CPU, A.num_cols, s, c_zero, queue ));
// P = randn(n, s)
distr = 3; // 1 = unif (0,1), 2 = unif (-1,1), 3 = normal (0,1)
dof = dP.num_rows * dP.num_cols;
lapackf77_zlarnv( &distr, iseed, &dof, dP.val );
// transfer P to device
CHECK( magma_zmtransfer( dP, &dP1, Magma_CPU, Magma_DEV, queue ));
magma_zmfree( &dP, queue );
// P = ortho(P1)
if ( dP1.num_cols > 1 ) {
// P = magma_zqr(P1), QR factorization
CHECK( magma_zqr( dP1.num_rows, dP1.num_cols, dP1, dP1.ld, &dP, NULL, queue ));
} else {
// P = P1 / |P1|
nrm = magma_dznrm2( dof, dP1.dval, 1, queue );
nrm = 1.0 / nrm;
magma_zdscal( dof, nrm, dP1.dval, 1, queue );
CHECK( magma_zmtransfer( dP1, &dP, Magma_DEV, Magma_DEV, queue ));
}
magma_zmfree( &dP1, queue );
//---------------------------------------
// allocate memory for the scalar products
CHECK( magma_zvinit( &hskp, Magma_CPU, 4, 1, c_zero, queue ));
CHECK( magma_zvinit( &dskp, Magma_DEV, 4, 1, c_zero, queue ));
CHECK( magma_zvinit( &halpha, Magma_CPU, s, 1, c_zero, queue ));
CHECK( magma_zvinit( &dalpha, Magma_DEV, s, 1, c_zero, queue ));
CHECK( magma_zvinit( &hbeta, Magma_CPU, s, 1, c_zero, queue ));
CHECK( magma_zvinit( &dbeta, Magma_DEV, s, 1, c_zero, queue ));
// workspace for merged dot product
CHECK( magma_zmalloc( &d1, max(2, s) * b.num_rows ));
CHECK( magma_zmalloc( &d2, max(2, s) * b.num_rows ));
// smoothing enabled
if ( smoothing > 0 ) {
// set smoothing solution vector
CHECK( magma_zmtransfer( *x, &dxs, Magma_DEV, Magma_DEV, queue ));
// tt = 0
// make tt twice as large to contain both, dtt and drs
ldd = magma_roundup( b.num_rows, 32 );
CHECK( magma_zvinit( &dtt, Magma_DEV, ldd, 2, c_zero, queue ));
dtt.num_rows = dr.num_rows;
dtt.num_cols = 1;
dtt.nnz = dtt.num_rows;
// redirect the drs.dval to the second part of dtt
CHECK( magma_zvinit( &drs, Magma_DEV, dr.num_rows, 1, c_zero, queue ));
magma_free( drs.dval );
drs.dval = dtt.dval + ldd;
// set smoothing residual vector
magma_zcopyvector( dr.num_rows, dr.dval, 1, drs.dval, 1, queue );
}
// G(n,s) = 0
if ( s > 1 ) {
ldd = magma_roundup( A.num_rows, 32 );
CHECK( magma_zvinit( &dG, Magma_DEV, ldd, s, c_zero, queue ));
dG.num_rows = A.num_rows;
} else {
CHECK( magma_zvinit( &dG, Magma_DEV, A.num_rows, s, c_zero, queue ));
}
// dGcol represents a single column of dG, array pointer is set inside loop
CHECK( magma_zvinit( &dGcol, Magma_DEV, dG.num_rows, 1, c_zero, queue ));
magma_free( dGcol.dval );
// U(n,s) = 0
if ( s > 1 ) {
ldd = magma_roundup( A.num_cols, 32 );
CHECK( magma_zvinit( &dU, Magma_DEV, ldd, s, c_zero, queue ));
dU.num_rows = A.num_cols;
} else {
CHECK( magma_zvinit( &dU, Magma_DEV, A.num_cols, s, c_zero, queue ));
}
// M(s,s) = I
CHECK( magma_zvinit( &dM, Magma_DEV, s, s, c_zero, queue ));
CHECK( magma_zvinit( &hMdiag, Magma_CPU, s, 1, c_zero, queue ));
magmablas_zlaset( MagmaFull, dM.num_rows, dM.num_cols, c_zero, c_one, dM.dval, dM.ld, queue );
// f = 0
CHECK( magma_zvinit( &df, Magma_DEV, dP.num_cols, 1, c_zero, queue ));
// c = 0
CHECK( magma_zvinit( &dc, Magma_DEV, dM.num_cols, 1, c_zero, queue ));
// v = 0
CHECK( magma_zvinit( &dv, Magma_DEV, dr.num_rows, 1, c_zero, queue ));
// lu = 0
CHECK( magma_zvinit( &dlu, Magma_DEV, dr.num_rows, 1, c_zero, queue ));
//--------------START TIME---------------
// chronometry
tempo1 = magma_sync_wtime( queue );
if ( solver_par->verbose > 0 ) {
solver_par->timing[0] = 0.0;
}
om = MAGMA_Z_ONE;
innerflag = 0;
// start iteration
do
{
solver_par->numiter++;
// new RHS for small systems
// f = P' r
magma_zgemvmdot_shfl( dP.num_rows, dP.num_cols, dP.dval, dr.dval, d1, d2, df.dval, queue );
// shadow space loop
for ( k = 0; k < s; ++k ) {
sk = s - k;
// c(k:s) = M(k:s,k:s) \ f(k:s)
magma_zcopyvector( sk, &df.dval[k], 1, &dc.dval[k], 1, queue );
magma_ztrsv( MagmaLower, MagmaNoTrans, MagmaNonUnit, sk, &dM.dval[k*dM.ld+k], dM.ld, &dc.dval[k], 1, queue );
// v = r - G(:,k:s) c(k:s)
magma_zcopyvector( dr.num_rows, dr.dval, 1, dv.dval, 1, queue );
magmablas_zgemv( MagmaNoTrans, dG.num_rows, sk, c_n_one, &dG.dval[k*dG.ld], dG.ld, &dc.dval[k], 1, c_one, dv.dval, 1, queue );
// preconditioning operation
// v = L \ v;
// v = U \ v;
CHECK( magma_z_applyprecond_left( MagmaNoTrans, A, dv, &dlu, precond_par, queue ));
CHECK( magma_z_applyprecond_right( MagmaNoTrans, A, dlu, &dv, precond_par, queue ));
// U(:,k) = om * v + U(:,k:s) c(k:s)
magmablas_zgemv( MagmaNoTrans, dU.num_rows, sk, c_one, &dU.dval[k*dU.ld], dU.ld, &dc.dval[k], 1, om, dv.dval, 1, queue );
magma_zcopyvector( dU.num_rows, dv.dval, 1, &dU.dval[k*dU.ld], 1, queue );
// G(:,k) = A U(:,k)
dGcol.dval = dG.dval + k * dG.ld;
CHECK( magma_z_spmv( c_one, A, dv, c_zero, dGcol, queue ));
solver_par->spmv_count++;
// bi-orthogonalize the new basis vectors
for ( i = 0; i < k; ++i ) {
// alpha = P(:,i)' G(:,k)
halpha.val[i] = magma_zdotc( dP.num_rows, &dP.dval[i*dP.ld], 1, &dG.dval[k*dG.ld], 1, queue );
// alpha = alpha / M(i,i)
halpha.val[i] = halpha.val[i] / hMdiag.val[i];
// G(:,k) = G(:,k) - alpha * G(:,i)
magma_zaxpy( dG.num_rows, -halpha.val[i], &dG.dval[i*dG.ld], 1, &dG.dval[k*dG.ld], 1, queue );
}
// non-first s iteration
if ( k > 0 ) {
// U update outside of loop using GEMV
// U(:,k) = U(:,k) - U(:,1:k) * alpha(1:k)
magma_zsetvector( k, halpha.val, 1, dalpha.dval, 1, queue );
magmablas_zgemv( MagmaNoTrans, dU.num_rows, k, c_n_one, dU.dval, dU.ld, dalpha.dval, 1, c_one, &dU.dval[k*dU.ld], 1, queue );
}
// new column of M = P'G, first k-1 entries are zero
// M(k:s,k) = P(:,k:s)' G(:,k)
magma_zgemvmdot_shfl( dP.num_rows, sk, &dP.dval[k*dP.ld], &dG.dval[k*dG.ld], d1, d2, &dM.dval[k*dM.ld+k], queue );
magma_zgetvector( 1, &dM.dval[k*dM.ld+k], 1, &hMdiag.val[k], 1, queue );
// check M(k,k) == 0
if ( MAGMA_Z_EQUAL(hMdiag.val[k], MAGMA_Z_ZERO) ) {
innerflag = 1;
info = MAGMA_DIVERGENCE;
break;
}
// beta = f(k) / M(k,k)
magma_zgetvector( 1, &df.dval[k], 1, &fk, 1, queue );
hbeta.val[k] = fk / hMdiag.val[k];
// check for nan
if ( magma_z_isnan( hbeta.val[k] ) || magma_z_isinf( hbeta.val[k] )) {
innerflag = 1;
info = MAGMA_DIVERGENCE;
break;
}
// r = r - beta * G(:,k)
magma_zaxpy( dr.num_rows, -hbeta.val[k], &dG.dval[k*dG.ld], 1, dr.dval, 1, queue );
// smoothing disabled
if ( smoothing <= 0 ) {
// |r|
nrmr = magma_dznrm2( dr.num_rows, dr.dval, 1, queue );
// smoothing enabled
} else {
// x = x + beta * U(:,k)
magma_zaxpy( x->num_rows, hbeta.val[k], &dU.dval[k*dU.ld], 1, x->dval, 1, queue );
// smoothing operation
//---------------------------------------
// t = rs - r
magma_zidr_smoothing_1( drs.num_rows, drs.num_cols, drs.dval, dr.dval, dtt.dval, queue );
// t't
// t'rs
CHECK( magma_zgemvmdot_shfl( dt.ld, 2, dtt.dval, dtt.dval, d1, d2, &dskp.dval[2], queue ));
magma_zgetvector( 2, &dskp.dval[2], 1, &hskp.val[2], 1, queue );
// gamma = (t' * rs) / (t' * t)
gamma = hskp.val[3] / hskp.val[2];
// rs = rs - gamma * (rs - r)
magma_zaxpy( drs.num_rows, -gamma, dtt.dval, 1, drs.dval, 1, queue );
// xs = xs - gamma * (xs - x)
magma_zidr_smoothing_2( dxs.num_rows, dxs.num_cols, -gamma, x->dval, dxs.dval, queue );
// |rs|
nrmr = magma_dznrm2( drs.num_rows, drs.dval, 1, queue );
//---------------------------------------
}
// store current timing and residual
if ( solver_par->verbose > 0 ) {
tempo2 = magma_sync_wtime( queue );
if ( (solver_par->numiter) % solver_par->verbose == 0 ) {
solver_par->res_vec[(solver_par->numiter) / solver_par->verbose]
= (real_Double_t)nrmr;
solver_par->timing[(solver_par->numiter) / solver_par->verbose]
= (real_Double_t)tempo2 - tempo1;
}
}
// check convergence or iteration limit
if ( nrmr <= solver_par->atol ||
nrmr/nrmb <= solver_par->rtol ) {
s = k + 1; // for the x-update outside the loop
innerflag = 2;
info = MAGMA_SUCCESS;
break;
}
// non-last s iteration
if ( (k + 1) < s ) {
// f(k+1:s) = f(k+1:s) - beta * M(k+1:s,k)
magma_zaxpy( sk-1, -hbeta.val[k], &dM.dval[k*dM.ld+(k+1)], 1, &df.dval[k+1], 1, queue );
}
}
// smoothing disabled
if ( smoothing <= 0 && innerflag != 1 ) {
// update solution approximation x
// x = x + U(:,1:s) * beta(1:s)
magma_zsetvector( s, hbeta.val, 1, dbeta.dval, 1, queue );
magmablas_zgemv( MagmaNoTrans, dU.num_rows, s, c_one, dU.dval, dU.ld, dbeta.dval, 1, c_one, x->dval, 1, queue );
}
// check convergence or iteration limit or invalid result of inner loop
if ( innerflag > 0 ) {
break;
}
// v = r
magma_zcopy( dr.num_rows, dr.dval, 1, dv.dval, 1, queue );
// preconditioning operation
// v = L \ v;
// v = U \ v;
CHECK( magma_z_applyprecond_left( MagmaNoTrans, A, dv, &dlu, precond_par, queue ));
CHECK( magma_z_applyprecond_right( MagmaNoTrans, A, dlu, &dv, precond_par, queue ));
// t = A v
CHECK( magma_z_spmv( c_one, A, dv, c_zero, dt, queue ));
solver_par->spmv_count++;
// computation of a new omega
//---------------------------------------
// t't
// t'r
CHECK( magma_zgemvmdot_shfl( dt.ld, 2, dt.dval, dt.dval, d1, d2, dskp.dval, queue ));
magma_zgetvector( 2, dskp.dval, 1, hskp.val, 1, queue );
// |t|
nrmt = magma_dsqrt( MAGMA_Z_REAL(hskp.val[0]) );
// rho = abs((t' * r) / (|t| * |r|))
rho = MAGMA_D_ABS( MAGMA_Z_REAL(hskp.val[1]) / (nrmt * nrmr) );
// om = (t' * r) / (|t| * |t|)
om = hskp.val[1] / hskp.val[0];
if ( rho < angle ) {
om = (om * angle) / rho;
}
//---------------------------------------
if ( MAGMA_Z_EQUAL(om, MAGMA_Z_ZERO) ) {
info = MAGMA_DIVERGENCE;
break;
}
// update approximation vector
// x = x + om * v
magma_zaxpy( x->num_rows, om, dv.dval, 1, x->dval, 1, queue );
// update residual vector
// r = r - om * t
magma_zaxpy( dr.num_rows, -om, dt.dval, 1, dr.dval, 1, queue );
// smoothing disabled
if ( smoothing <= 0 ) {
// residual norm
nrmr = magma_dznrm2( dr.num_rows, dr.dval, 1, queue );
// smoothing enabled
} else {
// smoothing operation
//---------------------------------------
// t = rs - r
magma_zidr_smoothing_1( drs.num_rows, drs.num_cols, drs.dval, dr.dval, dtt.dval, queue );
// t't
// t'rs
CHECK( magma_zgemvmdot_shfl( dt.ld, 2, dtt.dval, dtt.dval, d1, d2, &dskp.dval[2], queue ));
magma_zgetvector( 2, &dskp.dval[2], 1, &hskp.val[2], 1, queue );
// gamma = (t' * rs) / (t' * t)
gamma = hskp.val[3] / hskp.val[2];
// rs = rs - gamma * (rs - r)
magma_zaxpy( drs.num_rows, -gamma, dtt.dval, 1, drs.dval, 1, queue );
// xs = xs - gamma * (xs - x)
magma_zidr_smoothing_2( dxs.num_rows, dxs.num_cols, -gamma, x->dval, dxs.dval, queue );
// |rs|
nrmr = magma_dznrm2( drs.num_rows, drs.dval, 1, queue );
//---------------------------------------
}
// store current timing and residual
if ( solver_par->verbose > 0 ) {
tempo2 = magma_sync_wtime( queue );
if ( (solver_par->numiter) % solver_par->verbose == 0 ) {
solver_par->res_vec[(solver_par->numiter) / solver_par->verbose]
= (real_Double_t)nrmr;
solver_par->timing[(solver_par->numiter) / solver_par->verbose]
= (real_Double_t)tempo2 - tempo1;
}
}
// check convergence
if ( nrmr <= solver_par->atol ||
nrmr/nrmb <= solver_par->rtol ) {
info = MAGMA_SUCCESS;
break;
}
}
while ( solver_par->numiter + 1 <= solver_par->maxiter );
// smoothing enabled
if ( smoothing > 0 ) {
// x = xs
magma_zcopyvector( x->num_rows, dxs.dval, 1, x->dval, 1, queue );
// r = rs
magma_zcopyvector( dr.num_rows, drs.dval, 1, dr.dval, 1, queue );
}
// get last iteration timing
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t)tempo2 - tempo1;
//--------------STOP TIME----------------
// get final stats
solver_par->iter_res = nrmr;
CHECK( magma_zresidualvec( A, b, *x, &dr, &residual, queue ));
solver_par->final_res = residual;
// set solver conclusion
if ( info != MAGMA_SUCCESS && info != MAGMA_DIVERGENCE ) {
if ( solver_par->init_res > solver_par->final_res ) {
info = MAGMA_SLOW_CONVERGENCE;
}
}
cleanup:
// free resources
// smoothing enabled
if ( smoothing > 0 ) {
drs.dval = NULL; // needed because its pointer is redirected to dtt
magma_zmfree( &dxs, queue );
magma_zmfree( &drs, queue );
magma_zmfree( &dtt, queue );
}
dr.dval = NULL; // needed because its pointer is redirected to dt
dGcol.dval = NULL; // needed because its pointer is redirected to dG
magma_zmfree( &dr, queue );
magma_zmfree( &dP, queue );
magma_zmfree( &dP1, queue );
magma_zmfree( &dG, queue );
magma_zmfree( &dGcol, queue );
magma_zmfree( &dU, queue );
magma_zmfree( &dM, queue );
magma_zmfree( &hMdiag, queue );
magma_zmfree( &df, queue );
magma_zmfree( &dt, queue );
magma_zmfree( &dc, queue );
magma_zmfree( &dv, queue );
magma_zmfree( &dlu, queue );
magma_zmfree( &dskp, queue );
magma_zmfree( &dalpha, queue );
magma_zmfree( &dbeta, queue );
magma_zmfree( &hskp, queue );
magma_zmfree( &halpha, queue );
magma_zmfree( &hbeta, queue );
magma_free( d1 );
magma_free( d2 );
solver_par->info = info;
return info;
/* magma_zpidr_merge */
}
extern "C" void magma_zbulge_applyQ(
magma_int_t WANTZ, magma_side_t SIDE, magma_int_t NE, magma_int_t N, magma_int_t NB,
magma_int_t Vblksiz, magmaDoubleComplex *E, magma_int_t LDE,
magmaDoubleComplex *V, magmaDoubleComplex *TAU, magmaDoubleComplex *T,
magma_int_t *INFO, magmaDoubleComplex *dV, magmaDoubleComplex *dT,
magmaDoubleComplex *dE, magma_int_t copytype )
{
//%===========================
//% local variables
//%===========================
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magma_int_t LDT, LDV, firstcolj;
magma_int_t bg, nbGblk, rownbm, k, m, n;
magma_int_t st, ed, fst, vlen, vnb, colj, len;
magma_int_t blkid, vpos, taupos, tpos;
//magmaDoubleComplex *WORK;
magma_int_t LWORK;
magma_int_t cur_blksiz, avai_blksiz, ncolinvolvd;
magma_int_t nbgr, colst, coled, versionL, versionR;
magma_int_t blkcnt=-1;
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
*INFO=0;
versionL = 113;
versionR = 92;
LDT = Vblksiz;
LDV = NB+Vblksiz-1;
//blklen = LDV*Vblksiz;
nbGblk = plasma_ceildiv((N-1), Vblksiz);
//magma_zmalloc_cpu( &WORK, LWORK );
/* find the size of the matrix T V*/
findVTsiz(N, NB, Vblksiz, &blkcnt, &LDV);
/* Copy E & V & T to the GPU in dE and dV and dT
* depending on copytype:
* 1: mean copy only V
* 2: mean copy V and T
* 3: mean copy V, T and E
* */
if (copytype > 0) magma_zsetmatrix( LDV, blkcnt*Vblksiz, V, LDV, dV, LDV );
if (copytype > 1) magma_zsetmatrix( LDT, blkcnt*Vblksiz, T, LDT, dT, LDT );
if (copytype > 2) magma_zsetmatrix( N, NE, E, N, dE, N );
magmaDoubleComplex *dwork;
//ldwork = NE;
LWORK = 2*N*max(Vblksiz, 64);
if (MAGMA_SUCCESS != magma_zmalloc( &dwork, LWORK )) {
printf ("!!!! magma_zbulge_applyQ magma_alloc failed for: dwork\n" );
exit(-1);
}
/* SIDE LEFT meaning apply E = Q*E = (q_1*q_2*.....*q_n) * E ==> so traverse Vs in reverse order (forward) from q_n to q_1
* Also E is splitten by row meaning each apply consist in a block of row (horizontal block) */
/* SIDE RIGHT meaning apply E = E*Q = E * (q_1*q_2*.....*q_n) ==> so tarverse Vs in normal order (forward) from q_1 to q_n
* Also E is splitten by col meaning each apply consist in a block of col (vertical block) */
/* WANTZ = 1 meaning E is IDENTITY so form Q using optimized update.
* So we use the reverse order from small q to large one,
* so from q_n to q_1 so Left update to Identity.
* Use versionL 113 because in 114 we need to update the whole matrix and not in icreasing order.
* WANTZ = 2 meaning E is a full matrix and need to be updated from Left or Right so use normal update
* */
if (WANTZ == 1) {
versionL=113;
SIDE = MagmaLeft;
//set the matrix to Identity here to avoid copying it from the CPU
magmablas_zlaset( MagmaFull, N, N, c_zero, c_one, dE, N );
}
printf(" APPLY Q_v115 GPU with N %d NB %d Vblksiz %d SIDE %c versionL %d versionR %d WANTZ %d \n",
(int) N, (int) NB, (int) Vblksiz, SIDE, (int) versionL, (int) versionR, (int) WANTZ);
#if defined(USESTREAM)
magma_int_t N2=N/2;
magma_int_t N1=N-N2;
printf("using stream\n");
magma_queue_t stream[2];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
#endif
if (SIDE == MagmaLeft) {
if (versionL == 113) {
for (bg = nbGblk; bg > 0; bg--) {
firstcolj = (bg-1)*Vblksiz + 1;
if (bg == nbGblk)
rownbm = plasma_ceildiv((N-(firstcolj)), NB); // last blk has size=1 used for complex to handle A(N,N-1)
else
rownbm = plasma_ceildiv((N-(firstcolj+1)), NB);
for (m = rownbm; m > 0; m--) {
vlen = 0;
vnb = 0;
colj = (bg-1)*Vblksiz; // for k=0; I compute the fst and then can remove it from the loop
fst = (rownbm -m)*NB+colj +1;
for (k=0; k < Vblksiz; k++) {
colj = (bg-1)*Vblksiz + k;
st = (rownbm -m)*NB+colj +1;
ed = min(st+NB-1, N-1);
if (st > ed) break;
if ((st == ed) && (colj != N-2)) break;
vlen=ed-fst+1;
vnb=k+1;
}
colst = (bg-1)*Vblksiz;
findVTpos(N, NB, Vblksiz, colst, fst, &vpos, &taupos, &tpos, &blkid);
printf("voici bg %d m %d vlen %d vnb %d fcolj %d vpos %d taupos %d \n", (int) bg, (int) m, (int) vlen, (int) vnb, (int) colst+1, (int) vpos+1, (int) taupos+1);
if ((vlen > 0) && (vnb > 0)) {
if (WANTZ == 1) {
len = N-colst;
magma_zlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, vlen, len, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(fst,colst), LDE, dwork, len);
} else {
magma_zlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, vlen, NE, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(fst,0), LDE, dwork, NE);
}
}
}
}
} else if (versionL == 114) {
rownbm = plasma_ceildiv((N-1), NB);
for (m = rownbm; m > 0; m--) {
ncolinvolvd = min(N-1, m*NB);
avai_blksiz=min(Vblksiz, ncolinvolvd);
nbgr = plasma_ceildiv(ncolinvolvd, avai_blksiz);
for (n = nbgr; n > 0; n--) {
vlen = 0;
vnb = 0;
cur_blksiz = min(ncolinvolvd-(n-1)*avai_blksiz, avai_blksiz);
colst = (n-1)*avai_blksiz;
coled = colst + cur_blksiz -1;
fst = (rownbm -m)*NB+colst +1;
for (colj=colst; colj <= coled; colj++) {
st = (rownbm -m)*NB+colj +1;
ed = min(st+NB-1, N-1);
if (st > ed) break;
if ((st == ed) && (colj != N-2)) break;
vlen=ed-fst+1;
vnb=vnb+1;
}
findVTpos(N, NB, Vblksiz, colst, fst, &vpos, &taupos, &tpos, &blkid);
//printf("voici bg %d m %d vlen %d vnb %d fcolj %d vpos %d taupos %d \n", bg, m, vlen, vnb, colst+1, vpos+1, taupos+1);
if ((vlen > 0) && (vnb > 0)) {
#if defined(USESTREAM)
magmablasSetKernelStream(stream[0]);
magma_zlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, vlen, N1, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(fst,0), LDE, dwork, N1);
magmablasSetKernelStream(stream[1]);
magma_zlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, vlen, N2, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(fst,N1), LDE, &dwork[N1*Vblksiz], N2);
#else
magma_zlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, vlen, NE, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(fst,0), LDE, dwork, NE);
#endif
}
}
}
}
} else if (SIDE == MagmaRight) {
if (versionR == 91) {
for (bg =1; bg <= nbGblk; bg++) {
firstcolj = (bg-1)*Vblksiz + 1;
rownbm = plasma_ceildiv((N-(firstcolj+1)), NB);
if (bg == nbGblk) rownbm = plasma_ceildiv((N-(firstcolj)), NB); // last blk has size=1 used for complex to handle A(N,N-1)
for (m = 1; m <= rownbm; m++) {
vlen = 0;
vnb = 0;
// for k=0; I compute the fst and then can remove it from the loop
colj = (bg-1)*Vblksiz;
fst = (rownbm -m)*NB+colj +1;
for (k=0; k < Vblksiz; k++) {
colj = (bg-1)*Vblksiz + k;
st = (rownbm -m)*NB+colj +1;
ed = min(st+NB-1, N-1);
if (st > ed) break;
if ((st == ed) && (colj != N-2)) break;
vlen=ed-fst+1;
vnb=k+1;
}
colj = (bg-1)*Vblksiz;
findVTpos(N, NB, Vblksiz, colj, fst, &vpos, &taupos, &tpos, &blkid);
//printf("voici bg %d m %d vlen %d vnb %d fcolj %d vpos %d taupos %d \n", bg, m, vlen, vnb, colj, vpos, taupos);
if ((vlen > 0) && (vnb > 0)) {
#if defined(USESTREAM)
magmablasSetKernelStream(stream[0]);
magma_zlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, N1, vlen, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(0, fst), LDE, dwork, N1);
magmablasSetKernelStream(stream[1]);
magma_zlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, N2, vlen, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(N1, fst), LDE, &dwork[N1*Vblksiz], N2);
#else
magma_zlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, NE, vlen, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(0, fst), LDE, dwork, NE);
#endif
}
}
}
} else if (versionR == 92) {
rownbm = plasma_ceildiv((N-1), NB);
for (m = 1; m <= rownbm; m++) {
ncolinvolvd = min(N-1, m*NB);
avai_blksiz=min(Vblksiz, ncolinvolvd);
nbgr = plasma_ceildiv(ncolinvolvd, avai_blksiz);
for (n = 1; n <= nbgr; n++) {
vlen = 0;
vnb = 0;
cur_blksiz = min(ncolinvolvd-(n-1)*avai_blksiz, avai_blksiz);
colst = (n-1)*avai_blksiz;
coled = colst + cur_blksiz -1;
fst = (rownbm -m)*NB+colst +1;
for (colj=colst; colj <= coled; colj++) {
st = (rownbm -m)*NB+colj +1;
ed = min(st+NB-1, N-1);
if (st > ed) break;
if ((st == ed) && (colj != N-2)) break;
vlen=ed-fst+1;
vnb=vnb+1;
}
findVTpos(N, NB, Vblksiz, colst, fst, &vpos, &taupos, &tpos, &blkid);
if ((vlen > 0) && (vnb > 0)) {
#if defined(USESTREAM)
magmablasSetKernelStream(stream[0]);
magma_zlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, N1, vlen, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(0, fst), LDE, dwork, N1);
magmablasSetKernelStream(stream[1]);
magma_zlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, N2, vlen, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(N1, fst), LDE, &dwork[N1*Vblksiz], N2);
#else
magma_zlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, NE, vlen, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(0, fst), LDE, dwork, NE);
#endif
}
}
}
}
} else {
printf("ERROR SIDE %d\n", SIDE);
}
#if defined(USESTREAM)
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
#endif
magmablasSetKernelStream( orig_stream );
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zlaset
Code is very similar to testing_zlacpy.cpp
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gbytes, gpu_perf, gpu_time, cpu_perf, cpu_time;
double error, work[1];
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *h_A, *h_R;
magmaDoubleComplex *d_A;
magmaDoubleComplex offdiag = MAGMA_Z_MAKE( 1.2000, 6.7000 );
magmaDoubleComplex diag = MAGMA_Z_MAKE( 3.1415, 2.7183 );
magma_int_t M, N, size, lda, ldb, ldda;
magma_int_t ione = 1;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
magma_uplo_t uplo[] = { MagmaLower, MagmaUpper, MagmaFull };
printf("uplo M N CPU GByte/s (ms) GPU GByte/s (ms) check\n");
printf("==================================================================\n");
for( int iuplo = 0; iuplo < 3; ++iuplo ) {
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
//M += 2; // space for insets
//N += 2;
lda = M;
ldb = lda;
ldda = ((M+31)/32)*32;
size = lda*N;
if ( uplo[iuplo] == MagmaLower || uplo[iuplo] == MagmaUpper ) {
// save triangle (with diagonal)
// TODO wrong for trapezoid
gbytes = sizeof(magmaDoubleComplex) * 0.5*N*(N+1) / 1e9;
}
else {
// save entire matrix
gbytes = sizeof(magmaDoubleComplex) * 1.*M*N / 1e9;
}
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, size );
TESTING_MALLOC_CPU( h_R, magmaDoubleComplex, size );
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N );
/* Initialize the matrix */
for( int j = 0; j < N; ++j ) {
for( int i = 0; i < M; ++i ) {
h_A[i + j*lda] = MAGMA_Z_MAKE( i + j/10000., j );
}
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_zsetmatrix( M, N, h_A, lda, d_A, ldda );
gpu_time = magma_sync_wtime( 0 );
//magmablas_zlaset( uplo[iuplo], M-2, N-2, offdiag, diag, d_A+1+ldda, ldda ); // inset by 1 row & col
magmablas_zlaset( uplo[iuplo], M, N, offdiag, diag, d_A, ldda );
gpu_time = magma_sync_wtime( 0 ) - gpu_time;
gpu_perf = gbytes / gpu_time;
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
//magma_int_t M2 = M-2; // inset by 1 row & col
//magma_int_t N2 = N-2;
//lapackf77_zlaset( lapack_uplo_const( uplo[iuplo] ), &M2, &N2, &offdiag, &diag, h_A+1+lda, &lda );
lapackf77_zlaset( lapack_uplo_const( uplo[iuplo] ), &M, &N, &offdiag, &diag, h_A, &lda );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gbytes / cpu_time;
/* =====================================================================
Check the result
=================================================================== */
magma_zgetmatrix( M, N, d_A, ldda, h_R, lda );
blasf77_zaxpy(&size, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_zlange("f", &M, &N, h_R, &lda, work);
printf("%4c %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %s\n",
lapacke_uplo_const( uplo[iuplo] ), (int) M, (int) N,
cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
(error == 0. ? "ok" : "failed") );
status += ! (error == 0.);
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_R );
TESTING_FREE_DEV( d_A );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
printf( "\n" );
}
TESTING_FINALIZE();
return status;
}
extern "C" magma_int_t
magma_zgesv_rbt(
magma_bool_t ref, magma_int_t n, magma_int_t nrhs,
magmaDoubleComplex *A, magma_int_t lda,
magmaDoubleComplex *B, magma_int_t ldb,
magma_int_t *info)
{
/* Function Body */
*info = 0;
if ( ! (ref == MagmaTrue) &&
! (ref == MagmaFalse) ) {
*info = -1;
}
else if (n < 0) {
*info = -2;
} else if (nrhs < 0) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
} else if (ldb < max(1,n)) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (nrhs == 0 || n == 0)
return *info;
magma_int_t nn = n + ((4-(n % 4))%4);
magmaDoubleComplex *dA, *hu, *hv, *db, *dAo, *dBo, *dwork;
magma_int_t n2;
magma_int_t iter;
n2 = nn*nn;
if (MAGMA_SUCCESS != magma_zmalloc( &dA, n2 )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (MAGMA_SUCCESS != magma_zmalloc( &db, nn*nrhs )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (ref == MagmaTrue) {
if (MAGMA_SUCCESS != magma_zmalloc( &dAo, n2 )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (MAGMA_SUCCESS != magma_zmalloc( &dwork, nn*nrhs )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (MAGMA_SUCCESS != magma_zmalloc( &dBo, nn*nrhs )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
}
if (MAGMA_SUCCESS != magma_zmalloc_cpu( &hu, 2*nn )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
if (MAGMA_SUCCESS != magma_zmalloc_cpu( &hv, 2*nn )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magmablas_zlaset(MagmaFull, nn, nn, MAGMA_Z_ZERO, MAGMA_Z_ONE, dA, nn);
/* Send matrix on the GPU*/
magma_zsetmatrix(n, n, A, lda, dA, nn);
/* Send b on the GPU*/
magma_zsetmatrix(n, nrhs, B, ldb, db, nn);
*info = magma_zgerbt_gpu(MagmaTrue, nn, nrhs, dA, nn, db, nn, hu, hv, info);
if (*info != MAGMA_SUCCESS) {
return *info;
}
if (ref == MagmaTrue) {
magma_zcopymatrix(nn, nn, dA, nn, dAo, nn);
magma_zcopymatrix(nn, nrhs, db, nn, dBo, nn);
}
/* Solve the system U^TAV.y = U^T.b on the GPU*/
magma_zgesv_nopiv_gpu( nn, nrhs, dA, nn, db, nn, info);
/* Iterative refinement */
if (ref == MagmaTrue) {
magma_zgerfs_nopiv_gpu(MagmaNoTrans, nn, nrhs, dAo, nn, dBo, nn, db, nn, dwork, dA, &iter, info);
}
//printf("iter = %d\n", iter);
/* The solution of A.x = b is Vy computed on the GPU */
magmaDoubleComplex *dv;
if (MAGMA_SUCCESS != magma_zmalloc( &dv, 2*nn )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_zsetvector(2*nn, hv, 1, dv, 1);
for(int i = 0; i < nrhs; i++) {
magmablas_zprbt_mv(nn, dv, db+(i*nn));
}
magma_zgetmatrix(n, nrhs, db, nn, B, ldb);
magma_free_cpu( hu);
magma_free_cpu( hv);
magma_free( dA );
magma_free( dv );
magma_free( db );
if (ref == MagmaTrue) {
magma_free( dAo );
magma_free( dBo );
magma_free( dwork );
}
return *info;
}
/**
Purpose
-------
ZGEHRD reduces a COMPLEX_16 general matrix A to upper Hessenberg form H by
an orthogonal similarity transformation: Q' * A * Q = H . This version
stores the triangular matrices used in the factorization so that they can
be applied directly (i.e., without being recomputed) later. As a result,
the application of Q is much faster.
Arguments
---------
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in]
ilo INTEGER
@param[in]
ihi INTEGER
It is assumed that A is already upper triangular in rows
and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
set by a previous call to ZGEBAL; otherwise they should be
set to 1 and N respectively. See Further Details.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
@param[in,out]
A COMPLEX_16 array, dimension (LDA,N)
On entry, the N-by-N general matrix to be reduced.
On exit, the upper triangle and the first subdiagonal of A
are overwritten with the upper Hessenberg matrix H, and the
elements below the first subdiagonal, with the array TAU,
represent the orthogonal matrix Q as a product of elementary
reflectors. See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
tau COMPLEX_16 array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
zero.
@param[out]
work (workspace) COMPLEX_16 array, dimension (LWORK)
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
dT COMPLEX_16 array on the GPU, dimension NB*N,
where NB is the optimal blocksize. It stores the NB*NB blocks
of the triangular T matrices used in the reduction.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
---------------
The matrix Q is represented as a product of (ihi-ilo) elementary
reflectors
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
exit in A(i+2:ihi,i), and tau in TAU(i).
The contents of A are illustrated by the following example, with
n = 7, ilo = 2 and ihi = 6:
@verbatim
on entry, on exit,
( a a a a a a a ) ( a a h h h h a )
( a a a a a a ) ( a h h h h a )
( a a a a a a ) ( h h h h h h )
( a a a a a a ) ( v2 h h h h h )
( a a a a a a ) ( v2 v3 h h h h )
( a a a a a a ) ( v2 v3 v4 h h h )
( a ) ( a )
@endverbatim
where a denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
This implementation follows the hybrid algorithm and notations described in
S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg
form through hybrid GPU-based computing," University of Tennessee Computer
Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219),
May 24, 2009.
This version stores the T matrices in dT, for later use in magma_zunghr.
@ingroup magma_zgeev_comp
********************************************************************/
extern "C" magma_int_t
magma_zgehrd(
magma_int_t n, magma_int_t ilo, magma_int_t ihi,
magmaDoubleComplex *A, magma_int_t lda,
magmaDoubleComplex *tau,
magmaDoubleComplex *work, magma_int_t lwork,
magmaDoubleComplex_ptr dT,
magma_int_t *info)
{
#define A(i_,j_) ( A + (i_) + (j_)*lda)
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magma_int_t nb = magma_get_zgehrd_nb(n);
magma_int_t ldda = ((n+31)/32)*32;
magma_int_t i, nh, iws;
magma_int_t iinfo;
magma_int_t lquery;
*info = 0;
iws = n*nb;
work[0] = MAGMA_Z_MAKE( iws, 0 );
lquery = (lwork == -1);
if (n < 0) {
*info = -1;
} else if (ilo < 1 || ilo > max(1,n)) {
*info = -2;
} else if (ihi < min(ilo,n) || ihi > n) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
} else if (lwork < max(1,n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
// Adjust from 1-based indexing
ilo -= 1;
// Quick return if possible
nh = ihi - ilo;
if (nh <= 1) {
work[0] = c_one;
return *info;
}
// If not enough workspace, use unblocked code
if ( lwork < iws ) {
nb = 1;
}
if (nb == 1 || nb > nh) {
// Use unblocked code below
i = ilo;
}
else {
// Use blocked code
// GPU workspace is:
// nb*ldda for dwork for zlahru
// nb*ldda for dV
// n*ldda for dA
magmaDoubleComplex *dwork;
if (MAGMA_SUCCESS != magma_zmalloc( &dwork, 2*nb*ldda + n*ldda )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmaDoubleComplex *dV = dwork + nb*ldda;
magmaDoubleComplex *dA = dwork + nb*ldda*2;
magmaDoubleComplex *dTi;
magmaDoubleComplex *T;
magma_zmalloc_cpu( &T, nb*nb );
if ( T == NULL ) {
magma_free( dwork );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
// zero first block of V, which is lower triangular
magmablas_zlaset( MagmaFull, nb, nb, c_zero, c_zero, dV, ldda );
// Set elements 0:ILO-1 and IHI-1:N-2 of TAU to zero
for (i = 0; i < ilo; ++i)
tau[i] = c_zero;
for (i = max(0,ihi-1); i < n-1; ++i)
tau[i] = c_zero;
assert( nb % 4 == 0 );
for (i=0; i < nb*nb; i += 4)
T[i] = T[i+1] = T[i+2] = T[i+3] = c_zero;
magmablas_zlaset( MagmaFull, nb, n, c_zero, c_zero, dT, nb );
// Copy the matrix to the GPU
magma_zsetmatrix( n, n-ilo, A(0,ilo), lda, dA, ldda );
for (i = ilo; i < ihi-1 - nb; i += nb) {
// Reduce columns i:i+nb-1 to Hessenberg form, returning the
// matrices V and T of the block reflector H = I - V*T*V'
// which performs the reduction, and also the matrix Y = A*V*T
// Get the current panel (no need for the 1st iteration)
magma_zgetmatrix( ihi-i, nb,
dA(i,i-ilo), ldda,
A(i,i), lda );
// add 1 to i for 1-based index
magma_zlahr2( ihi, i+1, nb,
dA(0,i-ilo), ldda,
dV, ldda,
A(0,i), lda,
&tau[i], T, nb, work, n);
// Copy T from the CPU to dT on the GPU
dTi = dT + (i - ilo)*nb;
magma_zsetmatrix( nb, nb, T, nb, dTi, nb );
magma_zlahru( n, ihi, i, nb,
A(0,i), lda,
dA(0,i-ilo), ldda, // dA
dA(i,i-ilo), ldda, // dY, stored over current panel
dV, ldda,
dTi, dwork );
}
// Copy remainder to host
magma_zgetmatrix( n, n-i,
dA(0,i-ilo), ldda,
A(0,i), lda );
magma_free( dwork );
magma_free_cpu( T );
}
// Use unblocked code to reduce the rest of the matrix
// add 1 to i for 1-based index
i += 1;
lapackf77_zgehd2(&n, &i, &ihi, A, &lda, tau, work, &iinfo);
work[0] = MAGMA_Z_MAKE( iws, 0 );
return *info;
} /* magma_zgehrd */
/**
Purpose
-------
ZGETRI computes the inverse of a matrix using the LU factorization
computed by ZGETRF. This method inverts U and then computes inv(A) by
solving the system inv(A)*L = inv(U) for inv(A).
Note that it is generally both faster and more accurate to use ZGESV,
or ZGETRF and ZGETRS, to solve the system AX = B, rather than inverting
the matrix and multiplying to form X = inv(A)*B. Only in special
instances should an explicit inverse be computed with this routine.
Arguments
---------
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
dA COMPLEX_16 array on the GPU, dimension (LDDA,N)
On entry, the factors L and U from the factorization
A = P*L*U as computed by ZGETRF_GPU.
On exit, if INFO = 0, the inverse of the original matrix A.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDDA >= max(1,N).
@param[in]
ipiv INTEGER array, dimension (N)
The pivot indices from ZGETRF; for 1 <= i <= N, row i of the
matrix was interchanged with row IPIV(i).
@param[out]
dwork (workspace) COMPLEX_16 array on the GPU, dimension (MAX(1,LWORK))
@param[in]
lwork INTEGER
The dimension of the array DWORK. LWORK >= N*NB, where NB is
the optimal blocksize returned by magma_get_zgetri_nb(n).
\n
Unlike LAPACK, this version does not currently support a
workspace query, because the workspace is on the GPU.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, U(i,i) is exactly zero; the matrix is
singular and its cannot be computed.
@ingroup magma_zgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_zgetri_gpu( magma_int_t n, magmaDoubleComplex *dA, magma_int_t ldda,
magma_int_t *ipiv, magmaDoubleComplex *dwork, magma_int_t lwork,
magma_int_t *info )
{
#define dA(i, j) (dA + (i) + (j)*ldda)
#define dL(i, j) (dL + (i) + (j)*lddl)
/* Local variables */
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *dL = dwork;
magma_int_t lddl = n;
magma_int_t nb = magma_get_zgetri_nb(n);
magma_int_t j, jmax, jb, jp;
*info = 0;
if (n < 0)
*info = -1;
else if (ldda < max(1,n))
*info = -3;
else if ( lwork < n*nb )
*info = -6;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if ( n == 0 )
return *info;
/* Invert the triangular factor U */
magma_ztrtri_gpu( MagmaUpper, MagmaNonUnit, n, dA, ldda, info );
if ( *info != 0 )
return *info;
jmax = ((n-1) / nb)*nb;
for( j = jmax; j >= 0; j -= nb ) {
jb = min( nb, n-j );
// copy current block column of A to work space dL
// (only needs lower trapezoid, but we also copy upper triangle),
// then zero the strictly lower trapezoid block column of A.
magmablas_zlacpy( MagmaFull, n-j, jb,
dA(j,j), ldda,
dL(j,0), lddl );
magmablas_zlaset( MagmaLower, n-j-1, jb, c_zero, c_zero, dA(j+1,j), ldda );
// compute current block column of Ainv
// Ainv(:, j:j+jb-1)
// = ( U(:, j:j+jb-1) - Ainv(:, j+jb:n) L(j+jb:n, j:j+jb-1) )
// * L(j:j+jb-1, j:j+jb-1)^{-1}
// where L(:, j:j+jb-1) is stored in dL.
if ( j+jb < n ) {
magma_zgemm( MagmaNoTrans, MagmaNoTrans, n, jb, n-j-jb,
c_neg_one, dA(0,j+jb), ldda,
dL(j+jb,0), lddl,
c_one, dA(0,j), ldda );
}
// TODO use magmablas work interface
magma_ztrsm( MagmaRight, MagmaLower, MagmaNoTrans, MagmaUnit,
n, jb, c_one,
dL(j,0), lddl,
dA(0,j), ldda );
}
// Apply column interchanges
for( j = n-2; j >= 0; --j ) {
jp = ipiv[j] - 1;
if ( jp != j ) {
magmablas_zswap( n, dA(0,j), 1, dA(0,jp), 1 );
}
}
return *info;
}
/**
Purpose
-------
ZUNGQR generates an M-by-N COMPLEX_16 matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by ZGEQRF.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix Q. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix Q. M >= N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
@param[in,out]
A COMPLEX_16 array A, dimension (LDDA,N).
On entry, the i-th column must contain the vector
which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by ZGEQRF_GPU in the
first k columns of its array argument A.
On exit, the M-by-N matrix Q.
@param[in]
lda INTEGER
The first dimension of the array A. LDA >= max(1,M).
@param[in]
tau COMPLEX_16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF_GPU.
@param[in]
dT COMPLEX_16 array on the GPU device.
DT contains the T matrices used in blocking the elementary
reflectors H(i), e.g., this can be the 6th argument of
magma_zgeqrf_gpu.
@param[in]
nb INTEGER
This is the block size used in ZGEQRF_GPU, and correspondingly
the size of the T matrices, used in the factorization, and
stored in DT.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_zgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_zungqr(
magma_int_t m, magma_int_t n, magma_int_t k,
magmaDoubleComplex *A, magma_int_t lda,
magmaDoubleComplex *tau,
magmaDoubleComplex_ptr dT, magma_int_t nb,
magma_int_t *info)
{
#define A(i,j) ( A + (i) + (j)*lda )
#define dA(i,j) (dA + (i) + (j)*ldda)
#define dT(j) (dT + (j)*nb)
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magma_int_t m_kk, n_kk, k_kk, mi;
magma_int_t lwork, ldda;
magma_int_t i, ib, ki, kk;
magma_int_t lddwork;
magmaDoubleComplex *dA=NULL, *dV=NULL, *dW=NULL;
magmaDoubleComplex *work=NULL;
magma_queue_t queue=NULL;
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (lda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0) {
return *info;
}
// first kk columns are handled by blocked method.
// ki is start of 2nd-to-last block
if ((nb > 1) && (nb < k)) {
ki = (k - nb - 1) / nb * nb;
kk = min(k, ki + nb);
} else {
ki = 0;
kk = 0;
}
// Allocate GPU work space
// ldda*n for matrix dA
// ldda*nb for dV
// lddwork*nb for dW larfb workspace
ldda = magma_roundup( m, 32 );
lddwork = magma_roundup( n, 32 );
if (MAGMA_SUCCESS != magma_zmalloc( &dA, ldda*n + ldda*nb + lddwork*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto cleanup;
}
dV = dA + ldda*n;
dW = dA + ldda*n + ldda*nb;
// Allocate CPU work space
// n*nb for larfb work
// m*nb for V
// nb*nb for T
lwork = (n + m + nb) * nb;
magma_zmalloc_cpu( &work, lwork );
if (work == NULL) {
*info = MAGMA_ERR_HOST_ALLOC;
goto cleanup;
}
magmaDoubleComplex *work_T, *work_V;
work_T = work + n*nb;
work_V = work + n*nb + nb*nb;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
// Use unblocked code for the last or only block.
if (kk < n) {
m_kk = m - kk;
n_kk = n - kk;
k_kk = k - kk;
// zungqr requires less workspace (n*nb), but is slow if k < zungqr's block size.
// replacing it with the 4 routines below is much faster (e.g., 60x).
//magma_int_t iinfo;
//lapackf77_zungqr( &m_kk, &n_kk, &k_kk,
// A(kk, kk), &lda,
// &tau[kk], work, &lwork, &iinfo );
lapackf77_zlacpy( MagmaFullStr, &m_kk, &k_kk, A(kk,kk), &lda, work_V, &m_kk);
lapackf77_zlaset( MagmaFullStr, &m_kk, &n_kk, &c_zero, &c_one, A(kk, kk), &lda );
lapackf77_zlarft( MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &k_kk,
work_V, &m_kk, &tau[kk], work_T, &k_kk);
lapackf77_zlarfb( MagmaLeftStr, MagmaNoTransStr, MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &n_kk, &k_kk,
work_V, &m_kk, work_T, &k_kk, A(kk, kk), &lda, work, &n_kk );
if (kk > 0) {
magma_zsetmatrix( m_kk, n_kk,
A(kk, kk), lda,
dA(kk, kk), ldda, queue );
// Set A(1:kk,kk+1:n) to zero.
magmablas_zlaset( MagmaFull, kk, n - kk, c_zero, c_zero, dA(0, kk), ldda, queue );
}
}
if (kk > 0) {
// Use blocked code
// queue: set Aii (V) --> laset --> laset --> larfb --> [next]
// CPU has no computation
for (i = ki; i >= 0; i -= nb) {
ib = min(nb, k - i);
// Send current panel to dV on the GPU
mi = m - i;
lapackf77_zlaset( "Upper", &ib, &ib, &c_zero, &c_one, A(i, i), &lda );
magma_zsetmatrix_async( mi, ib,
A(i, i), lda,
dV, ldda, queue );
// set panel to identity
magmablas_zlaset( MagmaFull, i, ib, c_zero, c_zero, dA(0, i), ldda, queue );
magmablas_zlaset( MagmaFull, mi, ib, c_zero, c_one, dA(i, i), ldda, queue );
if (i < n) {
// Apply H to A(i:m,i:n) from the left
magma_zlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
mi, n-i, ib,
dV, ldda, dT(i), nb,
dA(i, i), ldda, dW, lddwork, queue );
}
}
// copy result back to CPU
magma_zgetmatrix( m, n,
dA(0, 0), ldda, A(0, 0), lda, queue );
}
cleanup:
magma_queue_destroy( queue );
magma_free( dA );
magma_free_cpu( work );
return *info;
} /* magma_zungqr */
int main(int argc, char **argv)
{
TESTING_INIT();
real_Double_t gflops, magma_perf, magma_time, cpu_perf, cpu_time;
double magma_error, work[1];
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t N, lda, ldda, sizeA, sizeX, sizeY, blocks, ldwork;
magma_int_t incx = 1;
magma_int_t incy = 1;
magma_int_t nb = 64;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex alpha = MAGMA_Z_MAKE( 1.5, -2.3 );
magmaDoubleComplex beta = MAGMA_Z_MAKE( -0.6, 0.8 );
magmaDoubleComplex *A, *X, *Y, *Ymagma;
magmaDoubleComplex *dA, *dX, *dY, *dwork;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("uplo = %s\n", lapack_uplo_const(opts.uplo) );
printf(" N MAGMA Gflop/s (ms) CPU Gflop/s (ms) MAGMA error\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;
ldda = ((N + 31)/32)*32;
sizeA = N*lda;
sizeX = N*incx;
sizeY = N*incy;
gflops = FLOPS_ZSYMV( N ) / 1e9;
TESTING_MALLOC_CPU( A, magmaDoubleComplex, sizeA );
TESTING_MALLOC_CPU( X, magmaDoubleComplex, sizeX );
TESTING_MALLOC_CPU( Y, magmaDoubleComplex, sizeY );
TESTING_MALLOC_CPU( Ymagma, magmaDoubleComplex, sizeY );
TESTING_MALLOC_DEV( dA, magmaDoubleComplex, ldda*N );
TESTING_MALLOC_DEV( dX, magmaDoubleComplex, sizeX );
TESTING_MALLOC_DEV( dY, magmaDoubleComplex, sizeY );
blocks = (N + nb - 1) / nb;
ldwork = ldda*blocks;
TESTING_MALLOC_DEV( dwork, magmaDoubleComplex, ldwork );
magmablas_zlaset( MagmaFull, ldwork, 1, MAGMA_Z_NAN, MAGMA_Z_NAN, dwork, ldwork );
magmablas_zlaset( MagmaFull, ldda, N, MAGMA_Z_NAN, MAGMA_Z_NAN, dA, ldda );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &sizeA, A );
magma_zmake_hermitian( N, A, lda );
lapackf77_zlarnv( &ione, ISEED, &sizeX, X );
lapackf77_zlarnv( &ione, ISEED, &sizeY, Y );
/* Note: CUBLAS does not implement zsymv */
/* =====================================================================
Performs operation using MAGMABLAS
=================================================================== */
magma_zsetmatrix( N, N, A, lda, dA, ldda );
magma_zsetvector( N, X, incx, dX, incx );
magma_zsetvector( N, Y, incy, dY, incy );
//magma_zprint_gpu( ldda, blocks, dwork, ldda );
magma_time = magma_sync_wtime( 0 );
magmablas_zsymv_work( opts.uplo, N, alpha, dA, ldda, dX, incx, beta, dY, incy, dwork, ldwork );
// TODO provide option to test non-work interface
//magmablas_zsymv( opts.uplo, N, alpha, dA, ldda, dX, incx, beta, dY, incy );
magma_time = magma_sync_wtime( 0 ) - magma_time;
magma_perf = gflops / magma_time;
magma_zgetvector( N, dY, incy, Ymagma, incy );
//magma_zprint_gpu( ldda, blocks, dwork, ldda );
/* =====================================================================
Performs operation using CPU BLAS
=================================================================== */
cpu_time = magma_wtime();
lapackf77_zsymv( lapack_uplo_const(opts.uplo), &N, &alpha, A, &lda, X, &incx, &beta, Y, &incy );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
/* =====================================================================
Check the result
=================================================================== */
blasf77_zaxpy( &N, &c_neg_one, Y, &incy, Ymagma, &incy );
magma_error = lapackf77_zlange( "M", &N, &ione, Ymagma, &N, work ) / N;
printf("%5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) N,
magma_perf, 1000.*magma_time,
cpu_perf, 1000.*cpu_time,
magma_error, (magma_error < tol ? "ok" : "failed"));
status += ! (magma_error < tol);
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( X );
TESTING_FREE_CPU( Y );
TESTING_FREE_CPU( Ymagma );
TESTING_FREE_DEV( dA );
TESTING_FREE_DEV( dX );
TESTING_FREE_DEV( dY );
TESTING_FREE_DEV( dwork );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
int main(int argc, char **argv)
{
TESTING_INIT();
const magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
const magma_int_t ione = 1;
real_Double_t atomics_perf=0, atomics_time=0;
real_Double_t gflops, magma_perf=0, magma_time=0, cublas_perf, cublas_time, cpu_perf, cpu_time;
double magma_error=0, atomics_error=0, cublas_error, work[1];
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t N, lda, ldda, sizeA, sizeX, sizeY, blocks, ldwork;
magma_int_t incx = 1;
magma_int_t incy = 1;
magma_int_t nb = 64;
magmaDoubleComplex alpha = MAGMA_Z_MAKE( 1.5, -2.3 );
magmaDoubleComplex beta = MAGMA_Z_MAKE( -0.6, 0.8 );
magmaDoubleComplex *A, *X, *Y, *Yatomics, *Ycublas, *Ymagma;
magmaDoubleComplex_ptr dA, dX, dY, dwork;
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("%% uplo = %s\n", lapack_uplo_const(opts.uplo) );
printf("%% N MAGMA Gflop/s (ms) Atomics Gflop/s CUBLAS Gflop/s CPU Gflop/s MAGMA error Atomics CUBLAS\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;
ldda = magma_roundup( N, opts.align ); // multiple of 32 by default
sizeA = N*lda;
sizeX = N*incx;
sizeY = N*incy;
gflops = FLOPS_ZHEMV( N ) / 1e9;
TESTING_MALLOC_CPU( A, magmaDoubleComplex, sizeA );
TESTING_MALLOC_CPU( X, magmaDoubleComplex, sizeX );
TESTING_MALLOC_CPU( Y, magmaDoubleComplex, sizeY );
TESTING_MALLOC_CPU( Yatomics, magmaDoubleComplex, sizeY );
TESTING_MALLOC_CPU( Ycublas, magmaDoubleComplex, sizeY );
TESTING_MALLOC_CPU( Ymagma, magmaDoubleComplex, sizeY );
TESTING_MALLOC_DEV( dA, magmaDoubleComplex, ldda*N );
TESTING_MALLOC_DEV( dX, magmaDoubleComplex, sizeX );
TESTING_MALLOC_DEV( dY, magmaDoubleComplex, sizeY );
blocks = magma_ceildiv( N, nb );
ldwork = ldda*blocks;
TESTING_MALLOC_DEV( dwork, magmaDoubleComplex, ldwork );
magmablas_zlaset( MagmaFull, ldwork, 1, MAGMA_Z_NAN, MAGMA_Z_NAN, dwork, ldwork );
magmablas_zlaset( MagmaFull, ldda, N, MAGMA_Z_NAN, MAGMA_Z_NAN, dA, ldda );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &sizeA, A );
magma_zmake_hermitian( N, A, lda );
// should not use data from the opposite triangle -- fill with NAN to check
magma_int_t N1 = N-1;
if ( opts.uplo == MagmaUpper ) {
lapackf77_zlaset( "Lower", &N1, &N1, &MAGMA_Z_NAN, &MAGMA_Z_NAN, &A[1], &lda );
}
else {
lapackf77_zlaset( "Upper", &N1, &N1, &MAGMA_Z_NAN, &MAGMA_Z_NAN, &A[lda], &lda );
}
lapackf77_zlarnv( &ione, ISEED, &sizeX, X );
lapackf77_zlarnv( &ione, ISEED, &sizeY, Y );
/* =====================================================================
Performs operation using CUBLAS
=================================================================== */
magma_zsetmatrix( N, N, A, lda, dA, ldda );
magma_zsetvector( N, X, incx, dX, incx );
magma_zsetvector( N, Y, incy, dY, incy );
magmablasSetKernelStream( opts.queue ); // opts.handle also uses opts.queue
cublas_time = magma_sync_wtime( opts.queue );
#ifdef HAVE_CUBLAS
cublasZhemv( opts.handle, cublas_uplo_const(opts.uplo),
N, &alpha, dA, ldda, dX, incx, &beta, dY, incy );
#else
magma_zhemv( opts.uplo, N, alpha, dA, 0, ldda, dX, 0, incx, beta, dY, 0, incy, opts.queue );
#endif
cublas_time = magma_sync_wtime( opts.queue ) - cublas_time;
cublas_perf = gflops / cublas_time;
magma_zgetvector( N, dY, incy, Ycublas, incy );
/* =====================================================================
Performs operation using CUBLAS - using atomics
=================================================================== */
#ifdef HAVE_CUBLAS
cublasSetAtomicsMode( opts.handle, CUBLAS_ATOMICS_ALLOWED );
magma_zsetvector( N, Y, incy, dY, incy );
// sync on queue doesn't work -- need device sync or use NULL stream -- bug in CUBLAS?
atomics_time = magma_sync_wtime( NULL /*opts.queue*/ );
cublasZhemv( opts.handle, cublas_uplo_const(opts.uplo),
N, &alpha, dA, ldda, dX, incx, &beta, dY, incy );
atomics_time = magma_sync_wtime( NULL /*opts.queue*/ ) - atomics_time;
atomics_perf = gflops / atomics_time;
magma_zgetvector( N, dY, incy, Yatomics, incy );
cublasSetAtomicsMode( opts.handle, CUBLAS_ATOMICS_NOT_ALLOWED );
#endif
/* =====================================================================
Performs operation using MAGMABLAS
=================================================================== */
#ifdef HAVE_CUBLAS
magma_zsetvector( N, Y, incy, dY, incy );
magma_time = magma_sync_wtime( opts.queue );
if ( opts.version == 1 ) {
magmablas_zhemv_work( opts.uplo, N, alpha, dA, ldda, dX, incx, beta, dY, incy, dwork, ldwork, opts.queue );
}
else {
// non-work interface (has added overhead)
magmablas_zhemv( opts.uplo, N, alpha, dA, ldda, dX, incx, beta, dY, incy );
}
magma_time = magma_sync_wtime( opts.queue ) - magma_time;
magma_perf = gflops / magma_time;
magma_zgetvector( N, dY, incy, Ymagma, incy );
#endif
/* =====================================================================
Performs operation using CPU BLAS
=================================================================== */
cpu_time = magma_wtime();
blasf77_zhemv( lapack_uplo_const(opts.uplo), &N, &alpha, A, &lda, X, &incx, &beta, Y, &incy );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
/* =====================================================================
Check the result
=================================================================== */
blasf77_zaxpy( &N, &c_neg_one, Y, &incy, Ycublas, &incy );
cublas_error = lapackf77_zlange( "M", &N, &ione, Ycublas, &N, work ) / N;
#ifdef HAVE_CUBLAS
blasf77_zaxpy( &N, &c_neg_one, Y, &incy, Yatomics, &incy );
atomics_error = lapackf77_zlange( "M", &N, &ione, Yatomics, &N, work ) / N;
blasf77_zaxpy( &N, &c_neg_one, Y, &incy, Ymagma, &incy );
magma_error = lapackf77_zlange( "M", &N, &ione, Ymagma, &N, work ) / N;
#endif
bool okay = (magma_error < tol && cublas_error < tol && atomics_error < tol);
status += ! okay;
printf("%5d %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e %8.2e %s\n",
(int) N,
magma_perf, 1000.*magma_time,
atomics_perf, 1000.*atomics_time,
cublas_perf, 1000.*cublas_time,
cpu_perf, 1000.*cpu_time,
magma_error, cublas_error, atomics_error,
(okay ? "ok" : "failed"));
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( X );
TESTING_FREE_CPU( Y );
TESTING_FREE_CPU( Ycublas );
TESTING_FREE_CPU( Yatomics );
TESTING_FREE_CPU( Ymagma );
TESTING_FREE_DEV( dA );
TESTING_FREE_DEV( dX );
TESTING_FREE_DEV( dY );
TESTING_FREE_DEV( dwork );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/**
Purpose
-------
ZGEGQR orthogonalizes the N vectors given by a complex 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_zgeqr2x3_gpu) and magma_zungqr
3: Modified Gram-Schmidt (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 COMPLEX_16 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) COMPLEX_16 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) COMPLEX_16 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.
- > 0: for ikind = 4, the normal equations were not
positive definite, so the factorization could not be
completed, and the solution has not been computed.
@ingroup magma_zgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_zgegqr_gpu(
magma_int_t ikind, magma_int_t m, magma_int_t n,
magmaDoubleComplex_ptr dA, magma_int_t ldda,
magmaDoubleComplex_ptr dwork, magmaDoubleComplex *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;
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
double 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;
}
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
if (ikind == 1) {
// === Iterative, based on SVD ============================================================
magmaDoubleComplex *U, *VT, *vt, *R, *G, *hwork, *tau;
double *S;
R = work; // Size n * n
G = R + n*n; // Size n * n
VT = G + n*n; // Size n * n
magma_zmalloc_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 = (double*)(U + n*n); // Size n
tau = U + n*n + n; // Size n
#ifdef COMPLEX
double *rwork;
magma_dmalloc_cpu( &rwork, 5*n );
if ( rwork == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
#endif
do {
i++;
magma_zgemm( MagmaConjTrans, MagmaNoTrans, n, n, m, c_one,
dA, ldda, dA, ldda, c_zero, dwork, n, queue );
magma_zgetmatrix( n, n, dwork, n, G, n, queue );
lapackf77_zgesvd( "n", "a", &n, &n, G, &n, S, U, &n, VT, &n,
hwork, &lwork,
#ifdef COMPLEX
rwork,
#endif
info );
mins = 100.f, maxs = 0.f;
for (k=0; k < n; k++) {
S[k] = magma_dsqrt( 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_zgeqrf( &n, &n, VT, &n, tau, hwork, &lwork, info );
if (i == 1)
blasf77_zcopy( &n2, VT, &ione, R, &ione );
else
blasf77_ztrmm( "l", "u", "n", "n", &n, &n, &c_one, VT, &n, R, &n );
magma_zsetmatrix( n, n, VT, n, dwork, n, queue );
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
m, n, c_one, dwork, n, dA, ldda, queue );
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 );
#ifdef COMPLEX
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;
magmaDoubleComplex_ptr dtau = dwork + 2*n*n;
magmaDoubleComplex_ptr d_T = dwork;
magmaDoubleComplex_ptr ddA = dwork + n*n;
magmaDoubleComplex *tau = work+n*n;
magmablas_zlaset( MagmaFull, n, n, c_zero, c_zero, d_T, n, queue );
magma_zgeqr2x3_gpu( m, n, dA, ldda, dtau, d_T, ddA,
(double*)(dwork+min_mn+2*n*n), info );
magma_zgetmatrix( min_mn, 1, dtau, min_mn, tau, min_mn, queue );
magma_zgetmatrix( n, n, ddA, n, work, n, queue );
magma_zungqr_gpu( m, n, n, dA, ldda, tau, d_T, nb, info );
// ================== end of ikind == 2 ===================================================
}
else if (ikind == 3) {
// ================== MGS ===================================================
for (j = 0; j < n; j++) {
for (i = 0; i < j; i++) {
*work(i, j) = magma_zdotc( m, dA(0,i), 1, dA(0,j), 1, queue );
magma_zaxpy( m, -(*work(i,j)), dA(0,i), 1, dA(0,j), 1, queue );
}
for (i = j; i < n; i++) {
*work(i, j) = MAGMA_Z_ZERO;
}
//*work(j,j) = MAGMA_Z_MAKE( magma_dznrm2( m, dA(0,j), 1), 0., queue );
*work(j,j) = magma_zdotc( m, dA(0,j), 1, dA(0,j), 1, queue );
*work(j,j) = MAGMA_Z_MAKE( sqrt(MAGMA_Z_REAL( *work(j,j) )), 0. );
magma_zscal( m, 1./ *work(j,j), dA(0,j), 1, queue );
}
// ================== end of ikind == 3 ===================================================
}
else if (ikind == 4) {
// ================== Cholesky QR ===================================================
magma_zgemm( MagmaConjTrans, MagmaNoTrans, n, n, m, c_one,
dA, ldda, dA, ldda, c_zero, dwork, n, queue );
magma_zgetmatrix( n, n, dwork, n, work, n, queue );
lapackf77_zpotrf( "u", &n, work, &n, info );
magma_zsetmatrix( n, n, work, n, dwork, n, queue );
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
m, n, c_one, dwork, n, dA, ldda, queue );
// ================== end of ikind == 4 ===================================================
}
magma_queue_destroy( queue );
return *info;
} /* magma_zgegqr_gpu */
/**
Purpose
-------
ZUNGQR generates an M-by-N COMPLEX_16 matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by ZGEQRF.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix Q. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix Q. M >= N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
@param[in,out]
A COMPLEX_16 array A, dimension (LDDA,N).
On entry, the i-th column must contain the vector
which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by ZGEQRF_GPU in the
first k columns of its array argument A.
On exit, the M-by-N matrix Q.
@param[in]
lda INTEGER
The first dimension of the array A. LDA >= max(1,M).
@param[in]
tau COMPLEX_16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF_GPU.
@param[in]
T COMPLEX_16 array, dimension (NB, min(M,N)).
T contains the T matrices used in blocking the elementary
reflectors H(i), e.g., this can be the 6th argument of
magma_zgeqrf_gpu (except stored on the CPU, not the GPU).
@param[in]
nb INTEGER
This is the block size used in ZGEQRF_GPU, and correspondingly
the size of the T matrices, used in the factorization, and
stored in T.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument has an illegal value
@ingroup magma_zgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_zungqr_m(
magma_int_t m, magma_int_t n, magma_int_t k,
magmaDoubleComplex *A, magma_int_t lda,
magmaDoubleComplex *tau,
magmaDoubleComplex *T, magma_int_t nb,
magma_int_t *info)
{
#define A(i,j) ( A + (i) + (j)*lda )
#define dA(d,i,j) (dA[d] + (i) + (j)*ldda)
#define dT(d,i,j) (dT[d] + (i) + (j)*nb)
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magma_int_t m_kk, n_kk, k_kk, mi;
magma_int_t lwork, ldwork;
magma_int_t i, ib, ki, kk, iinfo;
magmaDoubleComplex *work;
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (lda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0) {
return *info;
}
magma_int_t di, dn;
magma_int_t dpanel;
magma_int_t ngpu = magma_num_gpus();
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
// Allocate memory on GPUs for A and workspaces
magma_int_t ldda = ((m + 31) / 32) * 32;
magma_int_t lddwork = ((n + 31) / 32) * 32;
magma_int_t min_lblocks = (n / nb) / ngpu; // min. blocks per gpu
magma_int_t last_dev = (n / nb) % ngpu; // device with last block
magma_int_t nlocal[ MagmaMaxGPUs ] = { 0 };
magmaDoubleComplex *dA[ MagmaMaxGPUs ] = { NULL };
magmaDoubleComplex *dT[ MagmaMaxGPUs ] = { NULL };
magmaDoubleComplex *dV[ MagmaMaxGPUs ] = { NULL };
magmaDoubleComplex *dW[ MagmaMaxGPUs ] = { NULL };
magma_queue_t stream[ MagmaMaxGPUs ] = { NULL };
for( int d = 0; d < ngpu; ++d ) {
// example with n = 75, nb = 10, ngpu = 3
// min_lblocks = 2
// last_dev = 1
// gpu 0: 2 blocks, cols: 0- 9, 30-39, 60-69
// gpu 1: 1+ blocks, cols: 10-19, 40-49, 70-74 (partial)
// gpu 2: 1 block, cols: 20-29, 50-59
magma_setdevice( d );
nlocal[d] = min_lblocks*nb;
if ( d < last_dev ) {
nlocal[d] += nb;
}
else if ( d == last_dev ) {
nlocal[d] += (n % nb);
}
ldwork = nlocal[d]*ldda // dA
+ nb*m // dT
+ nb*ldda // dV
+ nb*lddwork; // dW
if ( MAGMA_SUCCESS != magma_zmalloc( &dA[d], ldwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto CLEANUP;
}
dT[d] = dA[d] + nlocal[d]*ldda;
dV[d] = dT[d] + nb*m;
dW[d] = dV[d] + nb*ldda;
magma_queue_create( &stream[d] );
}
trace_init( 1, ngpu, 1, stream );
// first kk columns are handled by blocked method.
// ki is start of 2nd-to-last block
if ((nb > 1) && (nb < k)) {
ki = (k - nb - 1) / nb * nb;
kk = min(k, ki + nb);
} else {
ki = 0;
kk = 0;
}
// Allocate CPU work space
// n*nb for zungqr workspace
lwork = n * nb;
magma_zmalloc_cpu( &work, lwork );
if (work == NULL) {
*info = MAGMA_ERR_HOST_ALLOC;
goto CLEANUP;
}
// Use unblocked code for the last or only block.
if (kk < n) {
trace_cpu_start( 0, "ungqr", "ungqr last block" );
m_kk = m - kk;
n_kk = n - kk;
k_kk = k - kk;
dpanel = (kk / nb) % ngpu;
di = ((kk / nb) / ngpu) * nb;
magma_setdevice( dpanel );
lapackf77_zungqr( &m_kk, &n_kk, &k_kk,
A(kk, kk), &lda,
&tau[kk], work, &lwork, &iinfo );
magma_zsetmatrix( m_kk, n_kk,
A(kk, kk), lda,
dA(dpanel, kk, di), ldda );
// Set A(1:kk,kk+1:n) to zero.
magmablas_zlaset( MagmaFull, kk, n - kk, c_zero, c_zero, dA(dpanel, 0, di), ldda );
trace_cpu_end( 0 );
}
if (kk > 0) {
// Use blocked code
// send T to all GPUs
for( int d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
trace_gpu_start( d, 0, "set", "set T" );
magma_zsetmatrix_async( nb, min(m,n), T, nb, dT[d], nb, stream[d] );
trace_gpu_end( d, 0 );
}
// stream: set Aii (V) --> laset --> laset --> larfb --> [next]
// CPU has no computation
for( i = ki; i >= 0; i -= nb ) {
ib = min(nb, k - i);
mi = m - i;
dpanel = (i / nb) % ngpu;
di = ((i / nb) / ngpu) * nb;
// Send current panel to the GPUs
lapackf77_zlaset( "Upper", &ib, &ib, &c_zero, &c_one, A(i, i), &lda );
for( int d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
trace_gpu_start( d, 0, "set", "set V" );
magma_zsetmatrix_async( mi, ib,
A(i, i), lda,
dV[d], ldda, stream[d] );
trace_gpu_end( d, 0 );
}
// set panel to identity
magma_setdevice( dpanel );
magmablasSetKernelStream( stream[dpanel] );
trace_gpu_start( dpanel, 0, "laset", "laset" );
magmablas_zlaset( MagmaFull, i, ib, c_zero, c_zero, dA(dpanel, 0, di), ldda );
magmablas_zlaset( MagmaFull, mi, ib, c_zero, c_one, dA(dpanel, i, di), ldda );
trace_gpu_end( dpanel, 0 );
if (i < n) {
// Apply H to A(i:m,i:n) from the left
for( int d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magmablasSetKernelStream( stream[d] );
magma_indices_1D_bcyclic( nb, ngpu, d, i, n, &di, &dn );
trace_gpu_start( d, 0, "larfb", "larfb" );
magma_zlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
mi, dn-di, ib,
dV[d], ldda, dT(d,0,i), nb,
dA(d, i, di), ldda, dW[d], lddwork );
trace_gpu_end( d, 0 );
}
}
}
}
// copy result back to CPU
trace_cpu_start( 0, "get", "get A" );
magma_zgetmatrix_1D_col_bcyclic( m, n, dA, ldda, A, lda, ngpu, nb );
trace_cpu_end( 0 );
#ifdef TRACING
char name[80];
snprintf( name, sizeof(name), "zungqr-n%d-ngpu%d.svg", m, ngpu );
trace_finalize( name, "trace.css" );
#endif
CLEANUP:
for( int d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magma_free( dA[d] );
magma_queue_destroy( stream[d] );
}
magma_free_cpu( work );
magma_setdevice( orig_dev );
magmablasSetKernelStream( orig_stream );
return *info;
} /* magma_zungqr */
/**
Purpose:
---------
ZUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
which is defined as the first M rows of a product of K elementary
reflectors of order N
Q = H(k)**H . . . H(2)**H H(1)**H
as returned by ZGELQF.
Arguments:
---------
@param[in]
m INTEGER
The number of rows of the matrix Q. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix Q. N >= M.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
@param[in,out]
A COMPLEX_16 array, dimension (LDA,N)
On entry, the i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by ZGELQF in the first k rows of its array argument A.
On exit, the M-by-N matrix Q.
@param[in]
lda INTEGER
The first dimension of the array A. LDA >= max(1,M).
@param[in]
tau COMPLEX_16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGELQF.
@param[out]
work COMPLEX_16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= NB*NB, where NB is
the optimal blocksize.
If LWORK = -1, a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit;
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_zgelqf_comp
********************************************************************/
extern "C" magma_int_t
magma_zunglq(
magma_int_t m, magma_int_t n, magma_int_t k,
magmaDoubleComplex *A, magma_int_t lda,
magmaDoubleComplex *tau,
magmaDoubleComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i_,j_) ( A + (i_) + (j_)*lda)
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define tau(i_) (tau + (i_))
// Constants
const magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
// Local variables
bool lquery;
magma_int_t i, ib, ki, ldda, lddwork, lwkopt, mib, nb, n_i;
magma_queue_t queue = NULL;
magmaDoubleComplex_ptr dA = NULL;
magmaDoubleComplex* work2 = NULL;
// Test the input arguments
*info = 0;
nb = magma_get_zgelqf_nb( m, n );
lwkopt = nb*nb;
work[0] = magma_zmake_lwork( lwkopt );
lquery = (lwork == -1);
if (m < 0) {
*info = -1;
} else if (n < 0 || n < m) {
*info = -2;
} else if (k < 0 || k > m) {
*info = -3;
} else if (lda < max( 1, m )) {
*info = -5;
} else if (lwork < max( 1, lwkopt ) && ! lquery) {
*info = -8;
//printf( "m %d, n %d, nb %d: lwork %d, required %d\n", m, n, nb, lwork, lwkopt );
//*info = 0;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
// Quick return if possible
if (m <= 0) {
work[0] = c_one;
return *info;
}
//if (lwork < lwkopt) {
// magma_zmalloc_cpu( &work2, lwkopt );
//}
//else {
// work2 = work;
//}
work2 = work;
// Allocate GPU work space
// ldda*n for matrix dA
// nb*n for dV
// lddwork*nb for dW larfb workspace
ldda = magma_roundup( m, 32 );
lddwork = magma_roundup( m, 32 );
if (MAGMA_SUCCESS != magma_zmalloc( &dA, ldda*n + n*nb + lddwork*nb + nb*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto cleanup;
}
magmaDoubleComplex_ptr dV; dV = dA + ldda*n;
magmaDoubleComplex_ptr dW; dW = dA + ldda*n + n*nb;
magmaDoubleComplex_ptr dT; dT = dA + ldda*n + n*nb + lddwork*nb;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
magmablas_zlaset( MagmaFull, m, n, MAGMA_Z_NAN, MAGMA_Z_NAN, dA, ldda, queue );
// all columns are handled by blocked method.
// ki is start of last (partial) block
ki = ((k - 1) / nb) * nb;
// Use blocked code
for( i=ki; i >= 0; i -= nb ) {
ib = min( nb, k-i );
// first block has extra rows to update
mib = ib;
if ( i == ki ) {
mib = m - i;
}
// Send current panel of V (block row) to the GPU
lapackf77_zlaset( "Lower", &ib, &ib, &c_zero, &c_one, A(i,i), &lda );
// TODO: having this _async was causing numerical errors. Why?
magma_zsetmatrix( ib, n-i,
A(i,i), lda,
dV, nb, queue );
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
n_i = n - i;
lapackf77_zlarft( MagmaForwardStr, MagmaRowwiseStr, &n_i, &ib,
A(i,i), &lda, &tau[i], work2, &nb );
magma_zsetmatrix_async( ib, ib,
work2, nb,
dT, nb, queue );
// set panel of A (block row) to identity
magmablas_zlaset( MagmaFull, mib, i, c_zero, c_zero, dA(i,0), ldda, queue );
magmablas_zlaset( MagmaFull, mib, n-i, c_zero, c_one, dA(i,i), ldda, queue );
if (i < m) {
// Apply H**H to A(i:m,i:n) from the right
magma_zlarfb_gpu( MagmaRight, MagmaConjTrans, MagmaForward, MagmaRowwise,
m-i, n-i, ib,
dV, nb, dT, nb,
dA(i,i), ldda, dW, lddwork, queue );
}
}
// copy result back to CPU
magma_zgetmatrix( m, n,
dA(0,0), ldda, A(0,0), lda, queue );
cleanup:
magma_queue_destroy( queue );
magma_free( dA );
//if (work2 != work) {
// magma_free_cpu( work2 );
//}
work[0] = magma_zmake_lwork( lwkopt );
return *info;
}
/**
Purpose
-------
ZHETRD reduces a complex Hermitian matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
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 COMPLEX_16 array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = MagmaLower, the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = MagmaUpper, the diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= MagmaLower, the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
d COMPLEX_16 array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
@param[out]
e COMPLEX_16 array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = MagmaUpper, E(i) = A(i+1,i) if UPLO = MagmaLower.
@param[out]
tau COMPLEX_16 array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) COMPLEX_16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= N*NB, where NB is the
optimal blocksize given by magma_get_zhetrd_nb().
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
Further Details
---------------
If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
@ingroup magma_zheev_comp
********************************************************************/
extern "C" magma_int_t
magma_zhetrd(
magma_uplo_t uplo, magma_int_t n,
magmaDoubleComplex *A, magma_int_t lda,
double *d, double *e, magmaDoubleComplex *tau,
magmaDoubleComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i_, j_) ( A + (i_) + (j_)*lda )
#define dA(i_, j_) (dA + (i_) + (j_)*ldda)
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t ldda = roundup( n, 32 );
magma_int_t nb = magma_get_zhetrd_nb( n );
const magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
const magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
const double d_one = MAGMA_D_ONE;
magma_int_t kk, nx;
magma_int_t i, j, i_n;
magma_int_t iinfo;
magma_int_t ldw, lddw, lwkopt;
magma_int_t lquery;
*info = 0;
int upper = (uplo == MagmaUpper);
lquery = (lwork == -1);
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
} else if (lwork < nb*n && ! lquery) {
*info = -9;
}
/* Determine the block size. */
ldw = n;
lddw = ldda;
lwkopt = n * nb;
if (*info == 0) {
work[0] = MAGMA_Z_MAKE( lwkopt, 0 );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return *info;
}
magmaDoubleComplex *dA;
#ifdef FAST_HEMV
magma_int_t ldwork2 = ldda*ceildiv(n,64);
#else
magma_int_t ldwork2 = 0;
#endif
if (MAGMA_SUCCESS != magma_zmalloc( &dA, ldda*n + 2*lddw*nb + ldwork2 )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmaDoubleComplex *dwork = dA + ldda*n;
#ifdef FAST_HEMV
magmaDoubleComplex *dwork2 = dwork + 2*lddw*nb;
#endif
//if (n < 2048)
// nx = n;
//else
// nx = 512;
nx = min( 128, n ); // nx <= n is required
// clear out dwork in case it has NANs (used as y in zhemv)
// rest of dwork (used as work in magmablas_zhemv) doesn't need to be cleared
magmablas_zlaset( MagmaFull, n, nb, c_zero, c_zero, dwork, lddw );
if (upper) {
/* Copy the matrix to the GPU */
magma_zsetmatrix( n, n, A(0, 0), lda, dA(0, 0), ldda );
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
kk = n - (n - nx + nb - 1) / nb * nb;
for (i = n - nb; i >= kk; i -= nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel (no need for the 1st iteration) */
if (i != n-nb)
magma_zgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), lda );
#ifdef FAST_HEMV
magma_zlatrd2( uplo, i+nb, nb, A(0, 0), lda, e, tau,
work, ldw, dA(0, 0), ldda, dwork, lddw,
dwork2, ldwork2 );
#else
magma_zlatrd( uplo, i+nb, nb, A(0, 0), lda, e, tau,
work, ldw, dA(0, 0), ldda, dwork, lddw );
#endif
/* Update the unreduced submatrix A(0:i-2,0:i-2), using an
update of the form: A := A - V*W' - W*V' */
magma_zsetmatrix( i + nb, nb, work, ldw, dwork, lddw );
magma_zher2k( uplo, MagmaNoTrans, i, nb, c_neg_one,
dA(0, i), ldda, dwork, lddw,
d_one, dA(0, 0), ldda );
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j-1,j) = MAGMA_Z_MAKE( e[j - 1], 0 );
d[j] = MAGMA_Z_REAL( *A(j, j) );
}
}
magma_zgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), lda );
/* Use CPU code to reduce the last or only block */
lapackf77_zhetrd( uplo_, &kk, A(0, 0), &lda, d, e, tau, work, &lwork, &iinfo );
}
else {
/* Copy the matrix to the GPU */
if (1 <= n-nx)
magma_zsetmatrix( n, n, A(0,0), lda, dA(0,0), ldda );
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel (no need for the 1st iteration) */
if (i != 0)
magma_zgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), lda );
#ifdef FAST_HEMV
magma_zlatrd2( uplo, n-i, nb, A(i, i), lda, &e[i], &tau[i],
work, ldw, dA(i, i), ldda, dwork, lddw,
dwork2, ldwork2 );
#else
magma_zlatrd( uplo, n-i, nb, A(i, i), lda, &e[i], &tau[i],
work, ldw, dA(i, i), ldda, dwork, lddw );
#endif
/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W' - W*V' */
magma_zsetmatrix( n-i, nb, work, ldw, dwork, lddw );
magma_zher2k( MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one,
dA(i+nb, i), ldda, &dwork[nb], lddw,
d_one, dA(i+nb, i+nb), ldda );
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j+1,j) = MAGMA_Z_MAKE( e[j], 0 );
d[j] = MAGMA_Z_REAL( *A(j, j) );
}
}
/* Use CPU code to reduce the last or only block */
if (1 <= n-nx)
magma_zgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), lda );
i_n = n-i;
lapackf77_zhetrd( uplo_, &i_n, A(i, i), &lda, &d[i], &e[i],
&tau[i], work, &lwork, &iinfo );
}
magma_free( dA );
work[0] = MAGMA_Z_MAKE( lwkopt, 0 );
return *info;
} /* magma_zhetrd */
extern "C" magma_int_t
magma_zlobpcg(
magma_z_matrix A,
magma_z_solver_par *solver_par,
magma_z_preconditioner *precond_par,
magma_queue_t queue )
{
magma_int_t info = 0;
#define residualNorms(i,iter) ( residualNorms + (i) + (iter)*n )
#define SWAP(x, y) { pointer = x; x = y; y = pointer; }
#define hresidualNorms(i,iter) (hresidualNorms + (i) + (iter)*n )
#define gramA( m, n) (gramA + (m) + (n)*ldgram)
#define gramB( m, n) (gramB + (m) + (n)*ldgram)
#define gevectors(m, n) (gevectors + (m) + (n)*ldgram)
#define h_gramB( m, n) (h_gramB + (m) + (n)*ldgram)
#define magma_z_bspmv_tuned(m, n, alpha, A, X, beta, AX, queue) { \
magma_z_matrix x={Magma_CSR}, ax={Magma_CSR}; \
x.memory_location = Magma_DEV; x.num_rows = m; x.num_cols = n; x.major = MagmaColMajor; x.nnz = m*n; x.dval = X; x.storage_type = Magma_DENSE; \
ax.memory_location= Magma_DEV; ax.num_rows = m; ax.num_cols = n; ax.major = MagmaColMajor; ax.nnz = m*n; ax.dval = AX; ax.storage_type = Magma_DENSE; \
CHECK( magma_z_spmv(alpha, A, x, beta, ax, queue )); \
}
//**************************************************************
// Memory allocation for the eigenvectors, eigenvalues, and workspace
solver_par->solver = Magma_LOBPCG;
magma_int_t m = A.num_rows;
magma_int_t n = (solver_par->num_eigenvalues);
magmaDoubleComplex *blockX = solver_par->eigenvectors;
double *evalues = solver_par->eigenvalues;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
magmaDoubleComplex *dwork=NULL, *hwork=NULL;
magmaDoubleComplex *blockP=NULL, *blockAP=NULL, *blockR=NULL, *blockAR=NULL, *blockAX=NULL, *blockW=NULL;
magmaDoubleComplex *gramA=NULL, *gramB=NULL, *gramM=NULL;
magmaDoubleComplex *gevectors=NULL, *h_gramB=NULL;
dwork = NULL;
hwork = NULL;
blockP = NULL;
blockR = NULL;
blockAP = NULL;
blockAR = NULL;
blockAX = NULL;
blockW = NULL;
gramA = NULL;
gramB = NULL;
gramM = NULL;
gevectors = NULL;
h_gramB = NULL;
magmaDoubleComplex *pointer, *origX = blockX;
double *eval_gpu=NULL;
magma_int_t iterationNumber, cBlockSize, restart = 1, iter;
//Chronometry
real_Double_t tempo1, tempo2, tempop1, tempop2;
magma_int_t lwork = max( 2*n+n*magma_get_dsytrd_nb(n),
1 + 6*3*n + 2* 3*n* 3*n);
magma_int_t *iwork={0}, liwork = 15*n+9;
magma_int_t gramDim, ldgram = 3*n, ikind = 3;
magmaDoubleComplex *hW={0};
// === Set solver parameters ===
double residualTolerance = solver_par->rtol;
magma_int_t maxIterations = solver_par->maxiter;
double tmp;
double r0=0; // set in 1st iteration
// === Set some constants & defaults ===
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
double *residualNorms={0}, *condestGhistory={0}, condestG={0};
double *gevalues={0};
magma_int_t *activeMask={0};
double *hresidualNorms={0};
#ifdef COMPLEX
double *rwork={0};
magma_int_t lrwork = 1 + 5*(3*n) + 2*(3*n)*(3*n);
CHECK( magma_dmalloc_cpu(&rwork, lrwork));
#endif
CHECK( magma_zmalloc_pinned( &hwork , lwork ));
CHECK( magma_zmalloc( &blockAX , m*n ));
CHECK( magma_zmalloc( &blockAR , m*n ));
CHECK( magma_zmalloc( &blockAP , m*n ));
CHECK( magma_zmalloc( &blockR , m*n ));
CHECK( magma_zmalloc( &blockP , m*n ));
CHECK( magma_zmalloc( &blockW , m*n ));
CHECK( magma_zmalloc( &dwork , m*n ));
CHECK( magma_dmalloc( &eval_gpu , 3*n ));
//**********************************************************+
// === Check some parameters for possible quick exit ===
solver_par->info = MAGMA_SUCCESS;
if (m < 2)
info = MAGMA_DIVERGENCE;
else if (n > m)
info = MAGMA_SLOW_CONVERGENCE;
if (solver_par->info != 0) {
magma_xerbla( __func__, -(info) );
goto cleanup;
}
solver_par->info = info; // local info variable;
// === Allocate GPU memory for the residual norms' history ===
CHECK( magma_dmalloc(&residualNorms, (maxIterations+1) * n));
CHECK( magma_malloc( (void **)&activeMask, (n+1) * sizeof(magma_int_t) ));
// === Allocate CPU work space ===
CHECK( magma_dmalloc_cpu(&condestGhistory, maxIterations+1));
CHECK( magma_dmalloc_cpu(&gevalues, 3 * n));
CHECK( magma_malloc_cpu((void **)&iwork, liwork * sizeof(magma_int_t)));
CHECK( magma_zmalloc_pinned(&hW, n*n));
CHECK( magma_zmalloc_pinned(&gevectors, 9*n*n));
CHECK( magma_zmalloc_pinned(&h_gramB , 9*n*n));
// === Allocate GPU workspace ===
CHECK( magma_zmalloc(&gramM, n * n));
CHECK( magma_zmalloc(&gramA, 9 * n * n));
CHECK( magma_zmalloc(&gramB, 9 * n * n));
// === Set activemask to one ===
for(magma_int_t k =0; k<n; k++){
iwork[k]=1;
}
magma_setmatrix(n, 1, sizeof(magma_int_t), iwork, n , activeMask, n, queue);
#if defined(PRECISION_s)
ikind = 3;
#endif
// === Make the initial vectors orthonormal ===
magma_zgegqr_gpu(ikind, m, n, blockX, m, dwork, hwork, &info );
//magma_zorthomgs( m, n, blockX, queue );
magma_z_bspmv_tuned(m, n, c_one, A, blockX, c_zero, blockAX, queue );
solver_par->spmv_count++;
// === Compute the Gram matrix = (X, AX) & its eigenstates ===
magma_zgemm( MagmaConjTrans, MagmaNoTrans, n, n, m,
c_one, blockX, m, blockAX, m, c_zero, gramM, n, queue );
magma_zheevd_gpu( MagmaVec, MagmaUpper,
n, gramM, n, evalues, hW, n, hwork, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork, &info );
// === Update X = X * evectors ===
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockX, m, gramM, n, c_zero, blockW, m, queue );
SWAP(blockW, blockX);
// === Update AX = AX * evectors ===
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockAX, m, gramM, n, c_zero, blockW, m, queue );
SWAP(blockW, blockAX);
condestGhistory[1] = 7.82;
tempo1 = magma_sync_wtime( queue );
// === Main LOBPCG loop ============================================================
for(iterationNumber = 1; iterationNumber < maxIterations; iterationNumber++)
{
// === compute the residuals (R = Ax - x evalues )
magmablas_zlacpy( MagmaFull, m, n, blockAX, m, blockR, m, queue );
/*
for(magma_int_t i=0; i<n; i++) {
magma_zaxpy( m, MAGMA_Z_MAKE(-evalues[i],0), blockX+i*m, 1, blockR+i*m, 1, queue );
}
*/
magma_dsetmatrix( 3*n, 1, evalues, 3*n, eval_gpu, 3*n, queue );
CHECK( magma_zlobpcg_res( m, n, eval_gpu, blockX, blockR, eval_gpu, queue ));
magmablas_dznrm2_cols( m, n, blockR, m, residualNorms(0, iterationNumber), queue );
// === remove the residuals corresponding to already converged evectors
CHECK( magma_zcompact(m, n, blockR, m,
residualNorms(0, iterationNumber), residualTolerance,
activeMask, &cBlockSize, queue ));
if (cBlockSize == 0)
break;
// === apply a preconditioner P to the active residulas: R_new = P R_old
// === for now set P to be identity (no preconditioner => nothing to be done )
//magmablas_zlacpy( MagmaFull, m, cBlockSize, blockR, m, blockW, m, queue );
//SWAP(blockW, blockR);
// preconditioner
magma_z_matrix bWv={Magma_CSR}, bRv={Magma_CSR};
bWv.memory_location = Magma_DEV; bWv.num_rows = m; bWv.num_cols = cBlockSize; bWv.major = MagmaColMajor; bWv.nnz = m*cBlockSize; bWv.dval = blockW;
bRv.memory_location = Magma_DEV; bRv.num_rows = m; bRv.num_cols = cBlockSize; bRv.major = MagmaColMajor; bRv.nnz = m*cBlockSize; bRv.dval = blockR;
tempop1 = magma_sync_wtime( queue );
CHECK( magma_z_applyprecond_left( MagmaNoTrans, A, bRv, &bWv, precond_par, queue ));
CHECK( magma_z_applyprecond_right( MagmaNoTrans, A, bWv, &bRv, precond_par, queue ));
tempop2 = magma_sync_wtime( queue );
precond_par->runtime += tempop2-tempop1;
// === make the preconditioned residuals orthogonal to X
if( precond_par->solver != Magma_NONE){
magma_zgemm( MagmaConjTrans, MagmaNoTrans, n, cBlockSize, m,
c_one, blockX, m, blockR, m, c_zero, gramB(0,0), ldgram, queue );
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, cBlockSize, n,
c_neg_one, blockX, m, gramB(0,0), ldgram, c_one, blockR, m, queue );
}
// === make the active preconditioned residuals orthonormal
magma_zgegqr_gpu(ikind, m, cBlockSize, blockR, m, dwork, hwork, &info );
#if defined(PRECISION_s)
// re-orthogonalization
SWAP(blockX, dwork);
magma_zgegqr_gpu(ikind, m, cBlockSize, blockR, m, dwork, hwork, &info );
#endif
//magma_zorthomgs( m, cBlockSize, blockR, queue );
// === compute AR
magma_z_bspmv_tuned(m, cBlockSize, c_one, A, blockR, c_zero, blockAR, queue );
solver_par->spmv_count++;
if (!restart) {
// === compact P & AP as well
CHECK( magma_zcompactActive(m, n, blockP, m, activeMask, queue ));
CHECK( magma_zcompactActive(m, n, blockAP, m, activeMask, queue ));
/*
// === make P orthogonal to X ?
magma_zgemm( MagmaConjTrans, MagmaNoTrans, n, cBlockSize, m,
c_one, blockX, m, blockP, m, c_zero, gramB(0,0), ldgram, queue );
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, cBlockSize, n,
c_neg_one, blockX, m, gramB(0,0), ldgram, c_one, blockP, m, queue );
// === make P orthogonal to R ?
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockR, m, blockP, m, c_zero, gramB(0,0), ldgram, queue );
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, cBlockSize, cBlockSize,
c_neg_one, blockR, m, gramB(0,0), ldgram, c_one, blockP, m, queue );
*/
// === Make P orthonormal & properly change AP (without multiplication by A)
magma_zgegqr_gpu(ikind, m, cBlockSize, blockP, m, dwork, hwork, &info );
#if defined(PRECISION_s)
// re-orthogonalization
SWAP(blockX, dwork);
magma_zgegqr_gpu(ikind, m, cBlockSize, blockP, m, dwork, hwork, &info );
#endif
//magma_zorthomgs( m, cBlockSize, blockP, queue );
//magma_z_bspmv_tuned(m, cBlockSize, c_one, A, blockP, c_zero, blockAP, queue );
magma_zsetmatrix( cBlockSize, cBlockSize, hwork, cBlockSize, dwork, cBlockSize, queue );
// replacement according to Stan
#if defined(PRECISION_s) || defined(PRECISION_d)
magmablas_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
m, cBlockSize, c_one, dwork, cBlockSize, blockAP, m, queue );
#else
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
m, cBlockSize, c_one, dwork, cBlockSize, blockAP, m, queue );
#endif
}
iter = max( 1, iterationNumber - 10 - int(log(1.*cBlockSize)) );
double condestGmean = 0.;
for(magma_int_t i = 0; i<iterationNumber-iter+1; i++){
condestGmean += condestGhistory[i];
}
condestGmean = condestGmean / (iterationNumber-iter+1);
if (restart)
gramDim = n+cBlockSize;
else
gramDim = n+2*cBlockSize;
/* --- The Raileight-Ritz method for [X R P] -----------------------
[ X R P ]' [AX AR AP] y = evalues [ X R P ]' [ X R P ], i.e.,
GramA GramB
/ X'AX X'AR X'AP \ / X'X X'R X'P \
| R'AX R'AR R'AP | y = evalues | R'X R'R R'P |
\ P'AX P'AR P'AP / \ P'X P'R P'P /
----------------------------------------------------------------- */
// === assemble GramB; first, set it to I
magmablas_zlaset( MagmaFull, ldgram, ldgram, c_zero, c_one, gramB, ldgram, queue ); // identity
if (!restart) {
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockP, m, blockX, m, c_zero, gramB(n+cBlockSize,0), ldgram, queue );
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockP, m, blockR, m, c_zero, gramB(n+cBlockSize,n), ldgram, queue );
}
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockR, m, blockX, m, c_zero, gramB(n,0), ldgram, queue );
// === get GramB from the GPU to the CPU and compute its eigenvalues only
magma_zgetmatrix( gramDim, gramDim, gramB, ldgram, h_gramB, ldgram, queue );
lapackf77_zheev("N", "L", &gramDim, h_gramB, &ldgram, gevalues,
hwork, &lwork,
#ifdef COMPLEX
rwork,
#endif
&info);
// === check stability criteria if we need to restart
condestG = log10( gevalues[gramDim-1]/gevalues[0] ) + 1.;
if ((condestG/condestGmean>2 && condestG>2) || condestG>8) {
// Steepest descent restart for stability
restart=1;
printf("restart at step #%d\n", int(iterationNumber));
}
// === assemble GramA; first, set it to I
magmablas_zlaset( MagmaFull, ldgram, ldgram, c_zero, c_one, gramA, ldgram, queue ); // identity
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockR, m, blockAX, m, c_zero, gramA(n,0), ldgram, queue );
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockR, m, blockAR, m, c_zero, gramA(n,n), ldgram, queue );
if (!restart) {
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockP, m, blockAX, m, c_zero,
gramA(n+cBlockSize,0), ldgram, queue );
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockP, m, blockAR, m, c_zero,
gramA(n+cBlockSize,n), ldgram, queue );
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockP, m, blockAP, m, c_zero,
gramA(n+cBlockSize,n+cBlockSize), ldgram, queue );
}
/*
// === Compute X' AX or just use the eigenvalues below ?
magma_zgemm( MagmaConjTrans, MagmaNoTrans, n, n, m,
c_one, blockX, m, blockAX, m, c_zero,
gramA(0,0), ldgram, queue );
*/
if (restart==0) {
magma_zgetmatrix( gramDim, gramDim, gramA, ldgram, gevectors, ldgram, queue );
}
else {
gramDim = n+cBlockSize;
magma_zgetmatrix( gramDim, gramDim, gramA, ldgram, gevectors, ldgram, queue );
}
for(magma_int_t k=0; k<n; k++)
*gevectors(k,k) = MAGMA_Z_MAKE(evalues[k], 0);
// === the previous eigensolver destroyed what is in h_gramB => must copy it again
magma_zgetmatrix( gramDim, gramDim, gramB, ldgram, h_gramB, ldgram, queue );
magma_int_t itype = 1;
lapackf77_zhegvd(&itype, "V", "L", &gramDim,
gevectors, &ldgram, h_gramB, &ldgram,
gevalues, hwork, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
iwork, &liwork, &info);
for(magma_int_t k =0; k<n; k++)
evalues[k] = gevalues[k];
// === copy back the result to gramA on the GPU and use it for the updates
magma_zsetmatrix( gramDim, gramDim, gevectors, ldgram, gramA, ldgram, queue );
if (restart == 0) {
// === contribution from P to the new X (in new search direction P)
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockP, m, gramA(n+cBlockSize,0), ldgram, c_zero, dwork, m, queue );
SWAP(dwork, blockP);
// === contribution from R to the new X (in new search direction P)
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockR, m, gramA(n,0), ldgram, c_one, blockP, m, queue );
// === corresponding contribution from AP to the new AX (in AP)
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockAP, m, gramA(n+cBlockSize,0), ldgram, c_zero, dwork, m, queue );
SWAP(dwork, blockAP);
// === corresponding contribution from AR to the new AX (in AP)
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockAR, m, gramA(n,0), ldgram, c_one, blockAP, m, queue );
}
else {
// === contribution from R (only) to the new X
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockR, m, gramA(n,0), ldgram, c_zero, blockP, m, queue );
// === corresponding contribution from AR (only) to the new AX
magma_zgemm( MagmaNoTrans, MagmaNoTrans,m, n, cBlockSize,
c_one, blockAR, m, gramA(n,0), ldgram, c_zero, blockAP, m, queue );
}
// === contribution from old X to the new X + the new search direction P
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockX, m, gramA, ldgram, c_zero, dwork, m, queue );
SWAP(dwork, blockX);
//magma_zaxpy( m*n, c_one, blockP, 1, blockX, 1, queue );
CHECK( magma_zlobpcg_maxpy( m, n, blockP, blockX, queue ));
// === corresponding contribution from old AX to new AX + AP
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockAX, m, gramA, ldgram, c_zero, dwork, m, queue );
SWAP(dwork, blockAX);
//magma_zaxpy( m*n, c_one, blockAP, 1, blockAX, 1, queue );
CHECK( magma_zlobpcg_maxpy( m, n, blockAP, blockAX, queue ));
condestGhistory[iterationNumber+1]=condestG;
magma_dgetmatrix( 1, 1, residualNorms(0, iterationNumber), 1, &tmp, 1, queue );
if ( iterationNumber == 1 ) {
solver_par->init_res = tmp;
r0 = tmp * solver_par->rtol;
if ( r0 < ATOLERANCE )
r0 = ATOLERANCE;
}
solver_par->final_res = tmp;
if ( tmp < r0 ) {
break;
}
if (cBlockSize == 0) {
break;
}
if ( solver_par->verbose!=0 ) {
if ( iterationNumber%solver_par->verbose == 0 ) {
// double res;
// magma_zgetmatrix( 1, 1,
// (magmaDoubleComplex*)residualNorms(0, iterationNumber), 1,
// (magmaDoubleComplex*)&res, 1, queue );
//
// printf("Iteration %4d, CBS %4d, Residual: %10.7f\n",
// iterationNumber, cBlockSize, res);
printf("%4d-%2d ", int(iterationNumber), int(cBlockSize));
magma_dprint_gpu(1, n, residualNorms(0, iterationNumber), 1);
}
}
restart = 0;
} // === end for iterationNumber = 1,maxIterations =======================
// fill solver info
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
solver_par->numiter = iterationNumber;
if ( solver_par->numiter < solver_par->maxiter) {
info = MAGMA_SUCCESS;
} else if ( solver_par->init_res > solver_par->final_res )
info = MAGMA_SLOW_CONVERGENCE;
else
info = MAGMA_DIVERGENCE;
// =============================================================================
// === postprocessing;
// =============================================================================
// === compute the real AX and corresponding eigenvalues
magma_z_bspmv_tuned(m, n, c_one, A, blockX, c_zero, blockAX, queue );
magma_zgemm( MagmaConjTrans, MagmaNoTrans, n, n, m,
c_one, blockX, m, blockAX, m, c_zero, gramM, n, queue );
magma_zheevd_gpu( MagmaVec, MagmaUpper,
n, gramM, n, gevalues, dwork, n, hwork, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork, &info );
for(magma_int_t k =0; k<n; k++)
evalues[k] = gevalues[k];
// === update X = X * evectors
SWAP(blockX, dwork);
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, dwork, m, gramM, n, c_zero, blockX, m, queue );
// === update AX = AX * evectors to compute the final residual
SWAP(blockAX, dwork);
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, dwork, m, gramM, n, c_zero, blockAX, m, queue );
// === compute R = AX - evalues X
magmablas_zlacpy( MagmaFull, m, n, blockAX, m, blockR, m, queue );
for(magma_int_t i=0; i<n; i++)
magma_zaxpy( m, MAGMA_Z_MAKE(-evalues[i], 0), blockX+i*m, 1, blockR+i*m, 1, queue );
// === residualNorms[iterationNumber] = || R ||
magmablas_dznrm2_cols( m, n, blockR, m, residualNorms(0, iterationNumber), queue );
// === restore blockX if needed
if (blockX != origX)
magmablas_zlacpy( MagmaFull, m, n, blockX, m, origX, m, queue );
printf("Eigenvalues:\n");
for(magma_int_t i =0; i<n; i++)
printf("%e ", evalues[i]);
printf("\n\n");
printf("Final residuals:\n");
magma_dprint_gpu(1, n, residualNorms(0, iterationNumber), 1);
printf("\n\n");
//=== Prmagma_int_t residual history in a file for plotting ====
CHECK( magma_dmalloc_cpu(&hresidualNorms, (iterationNumber+1) * n));
magma_dgetmatrix( n, iterationNumber,
residualNorms, n,
hresidualNorms, n, queue );
solver_par->iter_res = *hresidualNorms(0, iterationNumber-1);
printf("Residuals are stored in file residualNorms\n");
printf("Plot the residuals using: myplot \n");
FILE *residuals_file;
residuals_file = fopen("residualNorms", "w");
for(magma_int_t i =1; i<iterationNumber; i++) {
for(magma_int_t j = 0; j<n; j++)
fprintf(residuals_file, "%f ", *hresidualNorms(j,i));
fprintf(residuals_file, "\n");
}
fclose(residuals_file);
cleanup:
magma_free_cpu(hresidualNorms);
// === free work space
magma_free( residualNorms );
magma_free_cpu( condestGhistory );
magma_free_cpu( gevalues );
magma_free_cpu( iwork );
magma_free_pinned( hW );
magma_free_pinned( gevectors );
magma_free_pinned( h_gramB );
magma_free( gramM );
magma_free( gramA );
magma_free( gramB );
magma_free( activeMask );
if (blockX != (solver_par->eigenvectors))
magma_free( blockX );
if (blockAX != (solver_par->eigenvectors))
magma_free( blockAX );
if (blockAR != (solver_par->eigenvectors))
magma_free( blockAR );
if (blockAP != (solver_par->eigenvectors))
magma_free( blockAP );
if (blockR != (solver_par->eigenvectors))
magma_free( blockR );
if (blockP != (solver_par->eigenvectors))
magma_free( blockP );
if (blockW != (solver_par->eigenvectors))
magma_free( blockW );
if (dwork != (solver_par->eigenvectors))
magma_free( dwork );
magma_free( eval_gpu );
magma_free_pinned( hwork );
#ifdef COMPLEX
magma_free_cpu( rwork );
rwork = NULL;
#endif
return info;
}
/**
Purpose
-------
ZUNGQR generates an M-by-N COMPLEX_16 matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by ZGEQRF_GPU.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix Q. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix Q. M >= N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
@param[in,out]
dA COMPLEX_16 array A on the GPU, dimension (LDDA,N).
On entry, the i-th column must contain the vector
which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by ZGEQRF_GPU in the
first k columns of its array argument A.
On exit, the M-by-N matrix Q.
@param[in]
ldda INTEGER
The first dimension of the array A. LDDA >= max(1,M).
@param[in]
tau COMPLEX_16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF_GPU.
@param[in]
dT (workspace) COMPLEX_16 work space array on the GPU,
dimension (2*MIN(M, N) + ceil(N/32)*32 )*NB.
This must be the 6th argument of magma_zgeqrf_gpu
[ note that if N here is bigger than N in magma_zgeqrf_gpu,
the workspace requirement DT in magma_zgeqrf_gpu must be
as specified in this routine ].
@param[in]
nb INTEGER
This is the block size used in ZGEQRF_GPU, and correspondingly
the size of the T matrices, used in the factorization, and
stored in DT.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_zgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_zungqr_gpu(
magma_int_t m, magma_int_t n, magma_int_t k,
magmaDoubleComplex_ptr dA, magma_int_t ldda,
magmaDoubleComplex *tau,
magmaDoubleComplex_ptr dT, magma_int_t nb,
magma_int_t *info)
{
#define dA(i,j) (dA + (i) + (j)*ldda)
#define dT(j) (dT + (j)*nb)
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magma_int_t m_kk, n_kk, k_kk, mi;
magma_int_t lwork, lpanel;
magma_int_t i, ib, ki, kk, iinfo;
magma_int_t lddwork;
magmaDoubleComplex_ptr dV, dW;
magmaDoubleComplex *work, *panel;
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (ldda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0) {
return *info;
}
// first kk columns are handled by blocked method.
// ki is start of 2nd-to-last block
if ((nb > 1) && (nb < k)) {
ki = (k - nb - 1) / nb * nb;
kk = min( k, ki+nb );
} else {
ki = 0;
kk = 0;
}
// Allocate CPU work space
// n*nb for zungqr workspace
// (m - kk)*(n - kk) for last block's panel
lwork = n*nb;
lpanel = (m - kk)*(n - kk);
magma_zmalloc_cpu( &work, lwork + lpanel );
if ( work == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
panel = work + lwork;
// Allocate work space on GPU
if (MAGMA_SUCCESS != magma_zmalloc( &dV, ldda*nb )) {
magma_free_cpu( work );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
// dT workspace has:
// 2*min(m,n)*nb for T and R^{-1} matrices from geqrf
// roundup(n,32) * nb for dW larfb workspace.
lddwork = min(m,n);
dW = dT + 2*lddwork*nb;
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
// Use unblocked code for the last or only block.
if (kk < n) {
m_kk = m - kk;
n_kk = n - kk;
k_kk = k - kk;
magma_zgetmatrix( m_kk, k_kk,
dA(kk, kk), ldda, panel, m_kk, queue );
lapackf77_zungqr( &m_kk, &n_kk, &k_kk,
panel, &m_kk,
&tau[kk], work, &lwork, &iinfo );
magma_zsetmatrix( m_kk, n_kk,
panel, m_kk, dA(kk, kk), ldda, queue );
// Set A(1:kk,kk+1:n) to zero.
magmablas_zlaset( MagmaFull, kk, n - kk, c_zero, c_zero, dA(0, kk), ldda, queue );
}
if (kk > 0) {
// Use blocked code
// queue: copy Aii to V --> laset --> laset --> larfb --> [next]
// CPU has no computation
for (i = ki; i >= 0; i -= nb) {
ib = min( nb, k-i );
mi = m - i;
// Copy current panel on the GPU from dA to dV
magma_zcopymatrix_async( mi, ib,
dA(i,i), ldda,
dV, ldda, queue );
// set panel to identity
magmablas_zlaset( MagmaFull, i, ib, c_zero, c_zero, dA(0, i), ldda, queue );
magmablas_zlaset( MagmaFull, mi, ib, c_zero, c_one, dA(i, i), ldda, queue );
if (i < n) {
// Apply H to A(i:m,i:n) from the left
magma_zlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
mi, n-i, ib,
dV, ldda, dT(i), nb,
dA(i, i), ldda, dW, lddwork, queue );
}
}
}
magma_queue_sync( queue );
magma_free( dV );
magma_free_cpu( work );
magma_queue_destroy( queue );
return *info;
} /* magma_zungqr_gpu */
/**
Purpose
-------
ZUNGQR generates an M-by-N COMPLEX_16 matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by ZGEQRF.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix Q. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix Q. M >= N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
@param[in,out]
A COMPLEX_16 array A, dimension (LDDA,N).
On entry, the i-th column must contain the vector
which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by ZGEQRF_GPU in the
first k columns of its array argument A.
On exit, the M-by-N matrix Q.
@param[in]
lda INTEGER
The first dimension of the array A. LDA >= max(1,M).
@param[in]
tau COMPLEX_16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF_GPU.
@param[in]
dT COMPLEX_16 array on the GPU device.
DT contains the T matrices used in blocking the elementary
reflectors H(i), e.g., this can be the 6th argument of
magma_zgeqrf_gpu.
@param[in]
nb INTEGER
This is the block size used in ZGEQRF_GPU, and correspondingly
the size of the T matrices, used in the factorization, and
stored in DT.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument has an illegal value
@ingroup magma_zgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_zungqr(magma_int_t m, magma_int_t n, magma_int_t k,
magmaDoubleComplex *A, magma_int_t lda,
magmaDoubleComplex *tau,
magmaDoubleComplex *dT, magma_int_t nb,
magma_int_t *info)
{
#define A(i,j) ( A + (i) + (j)*lda )
#define dA(i,j) (dA + (i) + (j)*ldda)
#define dT(j) (dT + (j)*nb)
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magma_int_t m_kk, n_kk, k_kk, mi;
magma_int_t lwork, ldda;
magma_int_t i, ib, ki, kk; //, iinfo;
magma_int_t lddwork;
magmaDoubleComplex *dA, *dV, *dW;
magmaDoubleComplex *work;
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (lda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0) {
return *info;
}
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
// first kk columns are handled by blocked method.
// ki is start of 2nd-to-last block
if ((nb > 1) && (nb < k)) {
ki = (k - nb - 1) / nb * nb;
kk = min(k, ki + nb);
} else {
ki = 0;
kk = 0;
}
// Allocate GPU work space
// ldda*n for matrix dA
// ldda*nb for dV
// lddwork*nb for dW larfb workspace
ldda = ((m + 31) / 32) * 32;
lddwork = ((n + 31) / 32) * 32;
if (MAGMA_SUCCESS != magma_zmalloc( &dA, ldda*n + ldda*nb + lddwork*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dV = dA + ldda*n;
dW = dA + ldda*n + ldda*nb;
// Allocate CPU work space
lwork = (n+m+nb) * nb;
magma_zmalloc_cpu( &work, lwork );
if (work == NULL) {
magma_free( dA );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magmaDoubleComplex *V = work + (n+nb)*nb;
magma_queue_t stream;
magma_queue_create( &stream );
// Use unblocked code for the last or only block.
if (kk < n) {
m_kk = m - kk;
n_kk = n - kk;
k_kk = k - kk;
/*
// Replacing this with the following 4 routines works but zungqr is slow for
// k smaller than the zungqr's blocking size (new version can be up to 60x faster)
lapackf77_zungqr( &m_kk, &n_kk, &k_kk,
A(kk, kk), &lda,
&tau[kk], work, &lwork, &iinfo );
*/
lapackf77_zlacpy( MagmaUpperLowerStr, &m_kk, &k_kk, A(kk,kk), &lda, V, &m_kk);
lapackf77_zlaset( MagmaUpperLowerStr, &m_kk, &n_kk, &c_zero, &c_one, A(kk, kk), &lda );
lapackf77_zlarft( MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &k_kk,
V, &m_kk, &tau[kk], work, &k_kk);
lapackf77_zlarfb( MagmaLeftStr, MagmaNoTransStr, MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &n_kk, &k_kk,
V, &m_kk, work, &k_kk, A(kk, kk), &lda, work+k_kk*k_kk, &n_kk );
if (kk > 0) {
magma_zsetmatrix( m_kk, n_kk,
A(kk, kk), lda,
dA(kk, kk), ldda );
// Set A(1:kk,kk+1:n) to zero.
magmablas_zlaset( MagmaFull, kk, n - kk, c_zero, c_zero, dA(0, kk), ldda );
}
}
if (kk > 0) {
// Use blocked code
// stream: set Aii (V) --> laset --> laset --> larfb --> [next]
// CPU has no computation
magmablasSetKernelStream( stream );
for (i = ki; i >= 0; i -= nb) {
ib = min(nb, k - i);
// Send current panel to the GPU
mi = m - i;
lapackf77_zlaset( "Upper", &ib, &ib, &c_zero, &c_one, A(i, i), &lda );
magma_zsetmatrix_async( mi, ib,
A(i, i), lda,
dV, ldda, stream );
// set panel to identity
magmablas_zlaset( MagmaFull, i, ib, c_zero, c_zero, dA(0, i), ldda );
magmablas_zlaset( MagmaFull, mi, ib, c_zero, c_one, dA(i, i), ldda );
if (i < n) {
// Apply H to A(i:m,i:n) from the left
magma_zlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
mi, n-i, ib,
dV, ldda, dT(i), nb,
dA(i, i), ldda, dW, lddwork );
}
}
// copy result back to CPU
magma_zgetmatrix( m, n,
dA(0, 0), ldda, A(0, 0), lda);
}
magma_queue_destroy( stream );
magma_free( dA );
magma_free_cpu( work );
magmablasSetKernelStream( orig_stream );
return *info;
} /* magma_zungqr */
