static double factorization( const multivector_type Q ,
const multivector_type R )
{
const size_type count = Q.dimension_1();
value_view tmp("tmp");
value_view one("one");
KokkosArray::deep_copy( one , (Scalar) 1 );
KokkosArray::Impl::Timer timer ;
for ( size_type j = 0 ; j < count ; ++j ) {
// Reduction : tmp = dot( Q(:,j) , Q(:,j) );
// PostProcess : tmp = sqrt( tmp ); R(j,j) = tmp ; tmp = 1 / tmp ;
const vector_type Qj( Q , j );
const value_view Rjj( R , j , j );
KokkosArray::dot( Qj , InvNorm2( Rjj , tmp ) );
// Q(:,j) *= ( 1 / R(j,j) ); => Q(:,j) *= tmp ;
KokkosArray::scale( tmp , Qj );
for ( size_t k = j + 1 ; k < count ; ++k ) {
const vector_type Qk( Q , k );
const value_view Rjk( R , j , k );
// Reduction : R(j,k) = dot( Q(:,j) , Q(:,k) );
// PostProcess : tmp = - R(j,k);
KokkosArray::dot( Qj , Qk , DotM( Rjk , tmp ) );
// Q(:,k) -= R(j,k) * Q(:,j); => Q(:,k) += tmp * Q(:,j)
KokkosArray::axpby( tmp , Qj , one , Qk );
}
}
device_type::fence();
return timer.seconds();
}
std::vector<double>
test_product_tensor_legendre(
const std::vector<int> & arg_var_degree ,
const int nGrid ,
const int iterCount ,
const bool check )
{
typedef TensorType tensor_type ;
typedef typename tensor_type::device_type device_type ;
typedef KokkosArray::View< VectorScalar** ,
KokkosArray::LayoutLeft ,
device_type > vector_type ;
typedef KokkosArray::BlockCrsMatrix< tensor_type , MatrixScalar , device_type > matrix_type ;
typedef typename matrix_type::graph_type graph_type ;
//------------------------------
// Generate graph for "FEM" box structure:
std::vector< std::vector<size_t> > fem_graph ;
const size_t fem_length = nGrid * nGrid * nGrid ;
const size_t fem_graph_length = unit_test::generate_fem_graph( nGrid , fem_graph );
//------------------------------
// Generate CRS block-tensor matrix:
const std::vector<unsigned> var_degree( arg_var_degree.begin() , arg_var_degree.end() );
const KokkosArray::TripleProductTensorLegendreCombinatorialEvaluation
tensor( var_degree );
const size_t stoch_length = tensor.bases_count();
std::vector< std::vector< size_t > > stoch_graph( stoch_length );
for ( size_t i = 0 ; i < stoch_length ; ++i ) {
for ( size_t j = 0 ; j < stoch_length ; ++j ) {
if ( KokkosArray::matrix_nonzero(tensor,i,j) ) {
stoch_graph[i].push_back(j);
}
}
}
//------------------------------
// Generate input multivector:
vector_type x = vector_type( "x" , stoch_length , fem_length );
vector_type y = vector_type( "y" , stoch_length , fem_length );
typename vector_type::HostMirror hx = KokkosArray::create_mirror( x );
typename vector_type::HostMirror hy_result = KokkosArray::create_mirror( y );
for ( size_t iColFEM = 0 ; iColFEM < fem_length ; ++iColFEM ) {
for ( size_t iColStoch = 0 ; iColStoch < stoch_length ; ++iColStoch ) {
hx(iColStoch,iColFEM) =
generate_vector_coefficient( fem_length , stoch_length ,
iColFEM , iColStoch );
}}
KokkosArray::deep_copy( x , hx );
//------------------------------
matrix_type matrix ;
matrix.block = tensor_type( var_degree );
matrix.graph = KokkosArray::create_crsarray<graph_type>( std::string("test crs graph") , fem_graph );
if ( stoch_length != matrix.block.dimension() ) {
throw std::runtime_error("test_crs_product_tensor_legendre matrix sizing error");
}
matrix.values = vector_type( "matrix" , stoch_length , fem_graph_length );
typename vector_type::HostMirror hM = KokkosArray::create_mirror( matrix.values );
for ( size_t iRowFEM = 0 , iEntryFEM = 0 ; iRowFEM < fem_length ; ++iRowFEM ) {
for ( size_t iRowEntryFEM = 0 ; iRowEntryFEM < fem_graph[iRowFEM].size() ; ++iRowEntryFEM , ++iEntryFEM ) {
const size_t iColFEM = fem_graph[iRowFEM][iRowEntryFEM] ;
for ( size_t k = 0 ; k < stoch_length ; ++k ) {
hM(k,iEntryFEM) = generate_matrix_coefficient( fem_length , stoch_length , iRowFEM , iColFEM , k );
}
}
}
KokkosArray::deep_copy( matrix.values , hM );
//------------------------------
if (check) {
for ( size_t iRowStoch = 0 ; iRowStoch < stoch_length ; ++iRowStoch ) {
for ( size_t iRowFEM = 0 , iEntryFEM = 0 ; iRowFEM < fem_length ; ++iRowFEM ) {
double y = 0 ;
for ( size_t iRowEntryFEM = 0 ; iRowEntryFEM < fem_graph[ iRowFEM ].size() ; ++iRowEntryFEM , ++iEntryFEM ) {
const size_t iColFEM = fem_graph[iRowFEM][iRowEntryFEM] ;
for ( size_t iRowEntryStoch = 0 ; iRowEntryStoch < stoch_graph[iRowStoch].size() ; ++iRowEntryStoch ) {
const size_t iColStoch = stoch_graph[iRowStoch][iRowEntryStoch];
double value = 0 ;
for ( unsigned k = 0 ; k < stoch_length ; ++k ) {
const double A_fem_k = generate_matrix_coefficient( fem_length , stoch_length , iRowFEM , iColFEM , k );
if ( 1.0e-6 < std::abs( hM(k,iEntryFEM) - A_fem_k ) ) {
std::cout << "test_crs_product_tensor_legendre error: Matrix entry"
<< " A(" << k << ",(" << iRowFEM << "," << iColFEM << ")) = " << hM(k,iEntryFEM)
<< " , error = " << hM(k,iEntryFEM) - A_fem_k
<< std::endl ;
}
value += tensor(iRowStoch,iColStoch,k) * A_fem_k ;
}
y += value * hx( iColStoch , iColFEM );
}
}
hy_result( iRowStoch , iRowFEM ) = y ;
}
}
}
//------------------------------
const KokkosArray::Impl::Multiply< matrix_type , vector_type , vector_type > op( matrix , x , y );
KokkosArray::Impl::Timer clock ;
for ( int iter = 0 ; iter < iterCount ; ++iter ) {
op.run();
}
device_type::fence();
const double seconds_per_iter = clock.seconds() / ((double) iterCount );
const double flops_per_block = matrix.block.multiply_add_flops();
const double flops = 1.0e-9*fem_graph_length*flops_per_block / seconds_per_iter;
//------------------------------
// Verify result
if (check)
{
const double tol = KokkosArray::Impl::is_same<double,VectorScalar>::value ? 1.0e-13 : 1.0e-5 ;
const size_t error_max = 10 ;
KokkosArray::deep_copy( hx , y );
size_t error_count = 0 ;
for ( size_t iRowFEM = 0 ; iRowFEM < fem_length ; ++iRowFEM ) {
for ( size_t iRowStoch = 0 ; iRowStoch < stoch_length ; ++iRowStoch ) {
const double mag = std::abs( hy_result(iRowStoch,iRowFEM) );
const double error = std::abs( hx(iRowStoch,iRowFEM) - hy_result(iRowStoch,iRowFEM) );
if ( tol < error && tol < error / mag ) {
if ( error_count < error_max ) {
std::cout << "test_product_tensor_legendre error:"
<< " y(" << iRowStoch << "," << iRowFEM << ") = " << hx(iRowStoch,iRowFEM)
<< " , error = " << ( hx(iRowStoch,iRowFEM) - hy_result(iRowStoch,iRowFEM) )
<< std::endl ;
}
++error_count ;
}
}
}
if ( error_count ) {
std::cout << "test_crs_product_tensor_legendre error_count = " << error_count << std::endl ;
}
}
//------------------------------
std::vector<double> perf(3) ;
perf[0] = fem_length * stoch_length ;
perf[1] = seconds_per_iter ;
perf[2] = flops ;
return perf ;
}
void test( const std::string & label ,
const size_t elem_count ,
const size_t iter_count )
{
KokkosArray::Impl::Timer timer ;
double seconds_scalar ;
double seconds_multi ;
double seconds_array1 ;
double seconds_array4 ;
double seconds_array16 ;
{ // Loop 16 times:
Explicit::TestHexGrad<double,float,Device> test_scalar( elem_count );
timer.reset();
for ( size_t i = 0 ; i < iter_count * 16 ; ++i ) {
test_scalar.apply();
}
Device::fence();
seconds_scalar = timer.seconds() / ( 16 * iter_count * elem_count );
}
{ // 16 x elements
Explicit::TestHexGrad<double,float,Device> test_multiple( elem_count * 16 );
timer.reset();
for ( size_t i = 0 ; i < iter_count ; ++i ) {
test_multiple.apply();
}
Device::fence();
seconds_multi = timer.seconds() / ( 16 * iter_count * elem_count );
}
{ // 16 x elements with Array<1>
typedef KokkosArray::Array<double,1> coord_scalar_type ;
typedef KokkosArray::Array<float,1> grad_scalar_type ;
Explicit::TestHexGrad<coord_scalar_type,grad_scalar_type,Device>
test_array( elem_count * 16 );
timer.reset();
for ( size_t i = 0 ; i < iter_count ; ++i ) {
test_array.apply();
}
Device::fence();
seconds_array1 = timer.seconds() / ( 16 * iter_count * elem_count );
}
{ // 4 x elements with Array<4>
typedef KokkosArray::Array<double,4> coord_scalar_type ;
typedef KokkosArray::Array<float,4> grad_scalar_type ;
Explicit::TestHexGrad<coord_scalar_type,grad_scalar_type,Device>
test_array( elem_count * 4 );
timer.reset();
for ( size_t i = 0 ; i < iter_count ; ++i ) {
test_array.apply();
}
Device::fence();
seconds_array4 = timer.seconds() / ( 16 * iter_count * elem_count );
}
{ // 1 x elements with Array<16>
typedef KokkosArray::Array<double,16> coord_scalar_type ;
typedef KokkosArray::Array<float,16> grad_scalar_type ;
Explicit::TestHexGrad<coord_scalar_type,grad_scalar_type,Device> test_array( elem_count );
timer.reset();
for ( size_t i = 0 ; i < iter_count ; ++i ) {
test_array.apply();
}
Device::fence();
seconds_array16 = timer.seconds() / ( 16 * iter_count * elem_count );
}
std::cout << label
<< " scalar( " << seconds_scalar
<< " ) multi( " << seconds_multi << " )"
<< " ) array1( " << seconds_array1 << " )"
<< " ) array4( " << seconds_array4 << " )"
<< " ) array16( " << seconds_array16 << " )"
<< std::endl ;
}