int exampleDenseCholByBlocks(const ordinal_type mmin,
const ordinal_type mmax,
const ordinal_type minc,
const ordinal_type mb,
const int max_concurrency,
const int max_task_dependence,
const int team_size,
const int mkl_nthreads,
const bool check,
const bool verbose) {
typedef typename
Kokkos::Impl::is_space<DeviceSpaceType>::host_mirror_space::execution_space HostSpaceType ;
const bool detail = false;
std::cout << "DeviceSpace:: "; DeviceSpaceType::print_configuration(std::cout, detail);
std::cout << "HostSpace:: "; HostSpaceType::print_configuration(std::cout, detail);
typedef Kokkos::Experimental::TaskPolicy<DeviceSpaceType> PolicyType;
typedef DenseMatrixBase<value_type,ordinal_type,size_type,HostSpaceType> DenseMatrixBaseHostType;
typedef DenseMatrixView<DenseMatrixBaseHostType> DenseMatrixViewHostType;
typedef DenseMatrixBase<value_type,ordinal_type,size_type,DeviceSpaceType> DenseMatrixBaseDeviceType;
typedef DenseMatrixView<DenseMatrixBaseDeviceType> DenseMatrixViewDeviceType;
typedef TaskView<DenseMatrixViewDeviceType> DenseTaskViewDeviceType;
typedef DenseMatrixBase<DenseTaskViewDeviceType,ordinal_type,size_type,DeviceSpaceType> DenseHierMatrixBaseDeviceType;
typedef DenseMatrixView<DenseHierMatrixBaseDeviceType> DenseHierMatrixViewDeviceType;
typedef TaskView<DenseHierMatrixViewDeviceType> DenseHierTaskViewDeviceType;
int r_val = 0;
Kokkos::Impl::Timer timer;
double t = 0.0;
std::cout << "DenseCholByBlocks:: test matrices "
<<":: mmin = " << mmin << " , mmax = " << mmax << " , minc = " << minc
<< " , mb = " << mb << std::endl;
const size_t max_task_size = (3*sizeof(DenseTaskViewDeviceType)+sizeof(PolicyType)+128);
PolicyType policy(max_concurrency,
max_task_size,
max_task_dependence,
team_size);
std::ostringstream os;
os.precision(3);
os << std::scientific;
for (ordinal_type m=mmin;m<=mmax;m+=minc) {
os.str("");
// host matrices
DenseMatrixBaseHostType AA_host("AA_host", m, m), AB_host("AB_host"), TT_host("TT_host");
// random T matrix
{
TT_host.createConfTo(AA_host);
for (ordinal_type j=0;j<TT_host.NumCols();++j) {
for (ordinal_type i=0;i<TT_host.NumRows();++i)
TT_host.Value(i,j) = 2.0*((value_type)rand()/(RAND_MAX)) - 1.0;
TT_host.Value(j,j) = std::fabs(TT_host.Value(j,j));
}
}
// create SPD matrix
{
Teuchos::BLAS<ordinal_type,value_type> blas;
blas.HERK(ArgUplo == Uplo::Upper ? Teuchos::UPPER_TRI : Teuchos::LOWER_TRI,
Teuchos::CONJ_TRANS,
m, m,
1.0,
TT_host.ValuePtr(), TT_host.ColStride(),
0.0,
AA_host.ValuePtr(), AA_host.ColStride());
// preserve a copy of A
AB_host.createConfTo(AA_host);
DenseMatrixTools::copy(AB_host, AA_host);
}
const double flop = DenseFlopCount<value_type>::Chol(m);
#ifdef HAVE_SHYLUTACHO_MKL
mkl_set_num_threads(mkl_nthreads);
#endif
os << "DenseCholByBlocks:: m = " << m << " ";
int ierr = 0;
if (check) {
timer.reset();
DenseMatrixViewHostType A_host(AB_host);
ierr = Chol<ArgUplo,AlgoChol::ExternalLapack,Variant::One>::invoke
(policy, policy.member_single(),
A_host);
t = timer.seconds();
TACHO_TEST_FOR_ABORT( ierr, "Fail to perform Cholesky (serial)");
os << ":: Serial Performance = " << (flop/t/1.0e9) << " [GFLOPs] ";
}
DenseMatrixBaseDeviceType AA_device("AA_device");
{
timer.reset();
AA_device.mirror(AA_host);
t = timer.seconds();
os << ":: Mirror = " << t << " [sec] ";
}
{
DenseHierMatrixBaseDeviceType HA_device("HA_device");
DenseMatrixTools::createHierMatrix(HA_device, AA_device, mb, mb);
DenseHierTaskViewDeviceType TA_device(HA_device);
timer.reset();
auto future = policy.proc_create_team
(Chol<ArgUplo,AlgoChol::DenseByBlocks,ArgVariant>
::createTaskFunctor(policy, TA_device),
0);
policy.spawn(future);
Kokkos::Experimental::wait(policy);
t = timer.seconds();
os << ":: Parallel Performance = " << (flop/t/1.0e9) << " [GFLOPs] ";
}
AA_host.mirror(AA_device);
if (!ierr && check) {
double err = 0.0, norm = 0.0;
for (ordinal_type j=0;j<AA_host.NumCols();++j)
for (ordinal_type i=0;i<=j;++i) {
const double diff = abs(AA_host.Value(i,j) - AB_host.Value(i,j));
const double val = AB_host.Value(i,j);
err += diff*diff;
norm += val*val;
}
os << ":: Check result ::norm = " << sqrt(norm) << ", error = " << sqrt(err);
}
std::cout << os.str() << std::endl;
}
return r_val;
}
int exampleDenseGemmByBlocks(const ordinal_type mmin,
const ordinal_type mmax,
const ordinal_type minc,
const ordinal_type k,
const ordinal_type mb,
const int max_concurrency,
const int max_task_dependence,
const int team_size,
const int mkl_nthreads,
const bool check,
const bool verbose) {
typedef typename
Kokkos::Impl::is_space<DeviceSpaceType>::host_mirror_space::execution_space HostSpaceType ;
const bool detail = false;
std::cout << "DeviceSpace:: "; DeviceSpaceType::print_configuration(std::cout, detail);
std::cout << "HostSpace:: "; HostSpaceType::print_configuration(std::cout, detail);
typedef Kokkos::Experimental::TaskPolicy<DeviceSpaceType> PolicyType;
typedef DenseMatrixBase<value_type,ordinal_type,size_type,HostSpaceType> DenseMatrixBaseHostType;
typedef DenseMatrixView<DenseMatrixBaseHostType> DenseMatrixViewHostType;
typedef DenseMatrixBase<value_type,ordinal_type,size_type,DeviceSpaceType> DenseMatrixBaseDeviceType;
typedef DenseMatrixView<DenseMatrixBaseDeviceType> DenseMatrixViewDeviceType;
typedef TaskView<DenseMatrixViewDeviceType> DenseTaskViewDeviceType;
typedef DenseMatrixBase<DenseTaskViewDeviceType,ordinal_type,size_type,DeviceSpaceType> DenseHierMatrixBaseDeviceType;
typedef DenseMatrixView<DenseHierMatrixBaseDeviceType> DenseHierMatrixViewDeviceType;
typedef TaskView<DenseHierMatrixViewDeviceType> DenseHierTaskViewDeviceType;
int r_val = 0;
Kokkos::Impl::Timer timer;
double t = 0.0;
std::cout << "DenseGemmByBlocks:: test matrices "
<<":: mmin = " << mmin << " , mmax = " << mmax << " , minc = " << minc
<< " , k = "<< k << " , mb = " << mb << std::endl;
const size_t max_task_size = (3*sizeof(DenseTaskViewDeviceType)+sizeof(PolicyType)+128);
PolicyType policy(max_concurrency,
max_task_size,
max_task_dependence,
team_size);
std::ostringstream os;
os.precision(3);
os << std::scientific;
for (ordinal_type m=mmin;m<=mmax;m+=minc) {
os.str("");
// host matrices
DenseMatrixBaseHostType AA_host, BB_host, CC_host("CC_host", m, m), CB_host("CB_host", m, m);
{
if (ArgTransA == Trans::NoTranspose)
AA_host = DenseMatrixBaseHostType("AA_host", m, k);
else
AA_host = DenseMatrixBaseHostType("AA_host", k, m);
if (ArgTransB == Trans::NoTranspose)
BB_host = DenseMatrixBaseHostType("BB_host", k, m);
else
BB_host = DenseMatrixBaseHostType("BB_host", m, k);
for (ordinal_type j=0;j<AA_host.NumCols();++j)
for (ordinal_type i=0;i<AA_host.NumRows();++i)
AA_host.Value(i,j) = 2.0*((value_type)rand()/(RAND_MAX)) - 1.0;
for (ordinal_type j=0;j<BB_host.NumCols();++j)
for (ordinal_type i=0;i<BB_host.NumRows();++i)
BB_host.Value(i,j) = 2.0*((value_type)rand()/(RAND_MAX)) - 1.0;
for (ordinal_type j=0;j<CC_host.NumCols();++j)
for (ordinal_type i=0;i<CC_host.NumRows();++i)
CC_host.Value(i,j) = 2.0*((value_type)rand()/(RAND_MAX)) - 1.0;
DenseMatrixTools::copy(CB_host, CC_host);
}
const double flop = DenseFlopCount<value_type>::Gemm(m, m, k);
#ifdef HAVE_SHYLUTACHO_MKL
mkl_set_num_threads(mkl_nthreads);
#endif
os << "DenseGemmByBlocks:: m = " << m << " n = " << m << " k = " << k << " ";
if (check) {
timer.reset();
DenseMatrixViewHostType A_host(AA_host), B_host(BB_host), C_host(CB_host);
Gemm<ArgTransA,ArgTransB,AlgoGemm::ExternalBlas,Variant::One>::invoke
(policy, policy.member_single(),
1.0, A_host, B_host, 1.0, C_host);
t = timer.seconds();
os << ":: Serial Performance = " << (flop/t/1.0e9) << " [GFLOPs] ";
}
DenseMatrixBaseDeviceType AA_device("AA_device"), BB_device("BB_device"), CC_device("CC_device");
{
timer.reset();
AA_device.mirror(AA_host);
BB_device.mirror(BB_host);
CC_device.mirror(CC_host);
t = timer.seconds();
os << ":: Mirror = " << t << " [sec] ";
}
{
DenseHierMatrixBaseDeviceType HA_device("HA_device"), HB_device("HB_device"), HC_device("HC_device");
DenseMatrixTools::createHierMatrix(HA_device, AA_device, mb, mb);
DenseMatrixTools::createHierMatrix(HB_device, BB_device, mb, mb);
DenseMatrixTools::createHierMatrix(HC_device, CC_device, mb, mb);
DenseHierTaskViewDeviceType TA_device(HA_device), TB_device(HB_device), TC_device(HC_device);
timer.reset();
auto future = policy.proc_create_team
(Gemm<ArgTransA,ArgTransB,AlgoGemm::DenseByBlocks,ArgVariant>
::createTaskFunctor(policy, 1.0, TA_device, TB_device, 1.0, TC_device),
0);
policy.spawn(future);
Kokkos::Experimental::wait(policy);
t = timer.seconds();
os << ":: Parallel Performance = " << (flop/t/1.0e9) << " [GFLOPs] ";
}
CC_host.mirror(CC_device);
if (check) {
double err = 0.0, norm = 0.0;
for (ordinal_type j=0;j<CC_host.NumCols();++j)
for (ordinal_type i=0;i<CC_host.NumRows();++i) {
const double diff = abs(CC_host.Value(i,j) - CB_host.Value(i,j));
const double val = CB_host.Value(i,j);
err += diff*diff;
norm += val*val;
}
os << ":: Check result ::norm = " << sqrt(norm) << ", error = " << sqrt(err);
}
std::cout << os.str() << std::endl;
}
return r_val;
}
int exampleCholUnblocked(const std::string file_input,
const int treecut,
const int prunecut,
const int fill_level,
const int rows_per_team,
const bool verbose) {
typedef typename
Kokkos::Impl::is_space<DeviceSpaceType>::host_mirror_space::execution_space HostSpaceType ;
const bool detail = false;
std::cout << "DeviceSpace:: "; DeviceSpaceType::print_configuration(std::cout, detail);
std::cout << "HostSpace:: "; HostSpaceType::print_configuration(std::cout, detail);
typedef CrsMatrixBase<value_type,ordinal_type,size_type,HostSpaceType> CrsMatrixBaseHostType;
typedef GraphTools<ordinal_type,size_type,HostSpaceType> GraphToolsHostType;
typedef GraphTools_Scotch<ordinal_type,size_type,HostSpaceType> GraphToolsHostType_Scotch;
typedef GraphTools_CAMD<ordinal_type,size_type,HostSpaceType> GraphToolsHostType_CAMD;
typedef IncompleteSymbolicFactorization<CrsMatrixBaseHostType> IncompleteSymbolicFactorizationType;
typedef Kokkos::Experimental::TaskPolicy<DeviceSpaceType> PolicyType;
typedef CrsMatrixBase<value_type,ordinal_type,size_type,DeviceSpaceType> CrsMatrixBaseDeviceType;
typedef CrsMatrixView<CrsMatrixBaseDeviceType> CrsMatrixViewDeviceType;
typedef TaskView<CrsMatrixViewDeviceType> CrsTaskViewDeviceType;
int r_val = 0;
Kokkos::Impl::Timer timer;
CrsMatrixBaseHostType AA_host("AA_host");
timer.reset();
{
std::ifstream in;
in.open(file_input);
if (!in.good()) {
std::cout << "Failed in open the file: " << file_input << std::endl;
return -1;
}
MatrixMarket::read(AA_host, in);
}
double t_read = timer.seconds();
if (verbose)
AA_host.showMe(std::cout) << std::endl;
typename GraphToolsHostType::size_type_array rptr("Graph::RowPtrArray", AA_host.NumRows() + 1);
typename GraphToolsHostType::ordinal_type_array cidx("Graph::ColIndexArray", AA_host.NumNonZeros());
timer.reset();
GraphToolsHostType::getGraph(rptr, cidx, AA_host);
double t_graph = timer.seconds();
GraphToolsHostType_Scotch S;
S.setGraph(AA_host.NumRows(), rptr, cidx);
S.setSeed(0);
S.setTreeLevel();
S.setStrategy( SCOTCH_STRATSPEED
| SCOTCH_STRATLEVELMAX
| SCOTCH_STRATLEVELMIN
| SCOTCH_STRATLEAFSIMPLE
| SCOTCH_STRATSEPASIMPLE
);
timer.reset();
S.computeOrdering(treecut);
double t_scotch = timer.seconds();
S.pruneTree(prunecut);
if (verbose)
S.showMe(std::cout) << std::endl;
CrsMatrixBaseHostType BB_host("BB_host");
BB_host.createConfTo(AA_host);
CrsMatrixTools::copy(BB_host,
S.PermVector(),
S.InvPermVector(),
AA_host);
if (verbose)
BB_host.showMe(std::cout) << std::endl;
timer.reset();
GraphToolsHostType::getGraph(rptr, cidx, BB_host);
t_graph += timer.seconds();
GraphToolsHostType_CAMD C;
C.setGraph(BB_host.NumRows(),
rptr, cidx,
S.NumBlocks(),
S.RangeVector());
timer.reset();
C.computeOrdering();
double t_camd = timer.seconds();
if (verbose)
C.showMe(std::cout) << std::endl;
CrsMatrixBaseHostType CC_host("CC_host");
CC_host.createConfTo(BB_host);
CrsMatrixTools::copy(CC_host,
C.PermVector(),
C.InvPermVector(),
BB_host);
if (verbose)
CC_host.showMe(std::cout) << std::endl;
CrsMatrixBaseHostType DD_host("DD_host");
timer.reset();
IncompleteSymbolicFactorizationType::createNonZeroPattern(DD_host,
fill_level,
Uplo::Upper,
CC_host,
rows_per_team);
double t_symbolic = timer.seconds();
if (verbose)
DD_host.showMe(std::cout) << std::endl;
// ==================================================================================
CrsMatrixBaseDeviceType AA_device("AA_device");
AA_device.mirror(DD_host);
const size_type max_concurrency = 10;
const size_type max_task_size = (3*sizeof(CrsTaskViewDeviceType)+sizeof(PolicyType)+128);
const size_type max_task_dependence = 0;
const size_type team_size = 1;
PolicyType policy(max_concurrency,
max_task_size,
max_task_dependence,
team_size);
CrsMatrixViewDeviceType A_device(AA_device);
Kokkos::View<typename CrsMatrixViewDeviceType::row_view_type*,DeviceSpaceType>
rowviews("RowViewInMatView", A_device.NumRows());
A_device.setRowViewArray(rowviews);
timer.reset();
int ierr = Chol<Uplo::Upper,AlgoChol::Unblocked,Variant::One>::invoke
(policy, policy.member_single(),
A_device);
double t_chol = timer.seconds();
TACHO_TEST_FOR_ABORT( ierr, "Fail to perform Cholesky (serial)");
if (verbose) {
DD_host.mirror(AA_device);
DD_host.showMe(std::cout) << std::endl;
}
{
const auto prec = std::cout.precision();
std::cout.precision(4);
std::cout << std::scientific;
std::cout << "SymbolicFactorization:: Given matrix dimension = " << AA_host.NumRows() << " x " << AA_host.NumCols()
<< ", " << " nnz = " << AA_host.NumNonZeros() << std::endl;
std::cout << "SymbolicFactorization:: Upper factors dimension = " << DD_host.NumRows() << " x " << DD_host.NumCols()
<< ", " << " nnz = " << DD_host.NumNonZeros() << std::endl;
std::cout << "SymbolicFactorization:: "
<< "read = " << t_read << " [sec], "
<< "graph generation = " << (t_graph/2.0) << " [sec] "
<< "scotch reordering = " << t_scotch << " [sec] "
<< "camd reordering = " << t_camd << " [sec] "
<< "symbolic factorization = " << t_symbolic << " [sec] "
<< "Cholesky factorization = " << t_chol << " [sec] "
<< std::endl;
std::cout.unsetf(std::ios::scientific);
std::cout.precision(prec);
}
return r_val;
}
