STKUNIT_UNIT_TEST(UnitTestLinsysFunctions, test1)
{
static const size_t spatial_dimension = 3;
MPI_Barrier( MPI_COMM_WORLD );
MPI_Comm comm = MPI_COMM_WORLD;
//First create and fill MetaData and BulkData objects:
const unsigned bucket_size = 100; //for a real application mesh, bucket_size would be much bigger...
stk::mesh::fem::FEMMetaData fem_meta;
stk::mesh::fem::FEMMetaData fem_meta2;
fem_meta.FEM_initialize(spatial_dimension);
fem_meta2.FEM_initialize(spatial_dimension);
stk::mesh::MetaData & meta_data = stk::mesh::fem::FEMMetaData::get_meta_data(fem_meta);
stk::mesh::MetaData & meta_data2 = stk::mesh::fem::FEMMetaData::get_meta_data(fem_meta2);
const stk::mesh::EntityRank element_rank = fem_meta.element_rank();
stk::mesh::BulkData bulk_data( meta_data, comm, bucket_size );
stk::mesh::BulkData bulk_data2( meta_data2, comm, bucket_size );
//create a boundary-condition part for testing later:
stk::mesh::Part& bcpart = fem_meta.declare_part("bcpart");
fill_utest_mesh_meta_data( fem_meta );
bool use_temperature=false;
fill_utest_mesh_meta_data( fem_meta2, use_temperature );
fill_utest_mesh_bulk_data( bulk_data );
fill_utest_mesh_bulk_data( bulk_data2 );
//set owner-processors to lowest-sharing (stk::mesh defaults to
//highest-sharing) If highest-sharing owns, then it isn't correct for the
//way the fei library sets ownership of shared nodes for vectors etc.
stk::mesh::set_owners<stk::mesh::LowestRankSharingProcOwns>( bulk_data );
//put a node in our boundary-condition part. arbitrarily choose the
//first locally-owned node:
bulk_data.modification_begin();
std::vector<stk::mesh::Entity*> local_nodes;
stk::mesh::Selector select_owned(meta_data.locally_owned_part());
stk::mesh::get_selected_entities(select_owned,
bulk_data.buckets(NODE_RANK),
local_nodes);
stk::mesh::EntityId bc_node_id = 0;
if (local_nodes.size() > 0) {
stk::mesh::PartVector partvector;
partvector.push_back(&bcpart);
bulk_data.change_entity_parts(*local_nodes[0], partvector);
bc_node_id = stk::linsys::impl::entityid_to_int(local_nodes[0]->identifier());
}
bulk_data.modification_end();
stk::mesh::Selector selector = ( meta_data.locally_owned_part() | meta_data.globally_shared_part() ) & *meta_data.get_part("block_1");
std::vector<unsigned> count;
stk::mesh::count_entities(selector, bulk_data, count);
STKUNIT_ASSERT_EQUAL( count[element_rank], (unsigned)4 );
STKUNIT_ASSERT_EQUAL( count[NODE_RANK], (unsigned)20 );
ScalarField* temperature_field = meta_data.get_field<ScalarField>("temperature");
//Create a fei Factory and stk::linsys::LinearSystem object:
fei::SharedPtr<fei::Factory> factory(new Factory_Trilinos(comm));
stk::linsys::LinearSystem ls(comm, factory);
stk::linsys::add_connectivities(ls, element_rank, NODE_RANK,
*temperature_field, selector, bulk_data);
fei::SharedPtr<fei::MatrixGraph> matgraph = ls.get_fei_MatrixGraph();
int num_blocks = matgraph->getNumConnectivityBlocks();
STKUNIT_ASSERT_EQUAL( num_blocks, (int)1 );
ls.synchronize_mappings_and_structure();
ls.create_fei_LinearSystem();
//put 0 throughout the matrix and 3 throughout the rhs:
fei::SharedPtr<fei::Matrix> mat = ls.get_fei_LinearSystem()->getMatrix();
ls.get_fei_LinearSystem()->getMatrix()->putScalar(0);
ls.get_fei_LinearSystem()->getRHS()->putScalar(3.0);
//put 10 on the matrix diagonal to ensure it will be easy to solve later.
fei::SharedPtr<fei::VectorSpace> vspace = ls.get_fei_LinearSystem()->getRHS()->getVectorSpace();
int numLocalRows = vspace->getNumIndices_Owned();
std::vector<int> local_rows(numLocalRows);
vspace->getIndices_Owned(numLocalRows, &local_rows[0], numLocalRows);
for(size_t i=0; i<local_rows.size(); ++i) {
int col = local_rows[i];
double coef = 10;
double* coefPtr = &coef;
mat->sumIn(1, &local_rows[i], 1, &col, &coefPtr);
}
//now we'll impose a dirichlet bc on our one-node bcpart:
stk::linsys::dirichlet_bc(ls, bulk_data, bcpart, NODE_RANK,
*temperature_field, 0, 9.0);
ls.finalize_assembly();
//now confirm that the rhs value for the equation corresponding to our
//bc node is 9.0:
fei::SharedPtr<fei::Vector> rhsvec = ls.get_fei_LinearSystem()->getRHS();
double rhs_bc_val = 0;
int bc_eqn_index = ls.get_DofMapper().get_global_index(NODE_RANK,
bc_node_id, *temperature_field);
rhsvec->copyOut(1, &bc_eqn_index, &rhs_bc_val);
bool bc_val_is_correct = std::abs(rhs_bc_val - 9.0) < 1.e-13;
STKUNIT_ASSERT( bc_val_is_correct );
stk::linsys::copy_vector_to_mesh( *rhsvec, ls.get_DofMapper(), bulk_data);
stk::mesh::Entity* bc_node = bulk_data.get_entity(NODE_RANK, local_nodes[0]->identifier());
stk::mesh::FieldTraits<ScalarField>::data_type* bc_node_data = stk::mesh::field_data(*temperature_field, *bc_node);
bool bc_node_data_is_correct = std::abs(bc_node_data[0] - 9.0) < 1.e-13;
STKUNIT_ASSERT( bc_node_data_is_correct );
//now make sure we get a throw if we use the wrong bulk-data (that doesn't have the
//temperature field defined)
STKUNIT_ASSERT_THROW(stk::linsys::copy_vector_to_mesh( *rhsvec, ls.get_DofMapper(), bulk_data2), std::runtime_error);
//obtain and zero the solution vector
fei::SharedPtr<fei::Vector> solnvec = ls.get_fei_LinearSystem()->getSolutionVector();
solnvec->putScalar(0);
//copy the vector of zeros into the mesh:
stk::linsys::copy_vector_to_mesh( *solnvec, ls.get_DofMapper(), bulk_data);
//assert that our bc node's data is now zero.
bc_node_data_is_correct = std::abs(bc_node_data[0] - 0) < 1.e-13;
STKUNIT_ASSERT( bc_node_data_is_correct );
//call the linear-system solve function.
//(note that when we add options to the solve method, we'll need to enhance this
//testing to exercise various specific solves.)
Teuchos::ParameterList params;
int status = 0;
ls.solve(status, params);
//copy the solution-vector into the mesh:
stk::linsys::copy_vector_to_mesh( *solnvec, ls.get_DofMapper(), bulk_data);
//now assert that the value 9 (bc value) produced by the solve is in this
//node's data.
//note that we use a loose tolerance, because the default solver tolerance
//is (I think) only 1.e-6.
bc_node_data_is_correct = std::abs(bc_node_data[0] - 9.0) < 1.e-6;
STKUNIT_ASSERT( bc_node_data_is_correct );
STKUNIT_ASSERT(bc_node_data_is_correct);
}
/// 计算结果存储在矩阵a中
/// n_global: the order of the matrix
static void inv_driver(blas_idx_t n_global)
{
auto grid = std::make_shared<blacs_grid_t>();
//// self code
//n_global = 3;
//double *aaa = new double(n_global*n_global);
//for (int i = 0; i < 9; i++)
//{
// aaa[i] = i + 1;
//}
//aaa[8] = 10;
//auto a = block_cyclic_mat_t::createWithArray(grid, n_global, n_global, aaa);
// Create a NxN random matrix A
auto a = block_cyclic_mat_t::random(grid, n_global, n_global);
// Create a NxN matrix to hold A^{-1}
auto ai = block_cyclic_mat_t::constant(grid, n_global, n_global);
// Copy A to A^{-1} since it will be overwritten during factorization
std::copy_n(a->local_data(), a->local_size(), ai->local_data());
MPI_Barrier (MPI_COMM_WORLD);
double t0 = MPI_Wtime();
// Factorize A
blas_idx_t ia = 1, ja = 1;
std::vector<blas_idx_t> ipiv(a->local_rows() + a->row_block_size() + 100);
blas_idx_t info;
//含义应该是D-GE-TRF。
//第一个D表示我们的矩阵是double类型的
//GE表示我们的矩阵是General类型的
//TRF表示对矩阵进行三角分解也就是我们通常所说的LU分解。
pdgetrf_(n_global, n_global,
ai->local_data(), ia, ja, ai->descriptor(),
ipiv.data(),
info);
assert(info == 0);
double t_factor = MPI_Wtime() - t0;
// Compute A^{-1} based on the LU factorization
// Compute workspace for double and integer work arrays on each process
blas_idx_t lwork = 10;
blas_idx_t liwork = 10;
std::vector<double> work (lwork);
std::vector<blas_idx_t> iwork(liwork);
lwork = liwork = -1;
// 计算lwork与liwork的值
pdgetri_(n_global,
ai->local_data(), ia, ja, ai->descriptor(),
ipiv.data(),
work.data(), lwork, iwork.data(), liwork, info);
assert(info == 0);
lwork = static_cast<blas_idx_t>(work[0]);
liwork = static_cast<size_t>(iwork[0]);
work.resize(lwork);
iwork.resize(liwork);
// Now compute the inverse
t0 = MPI_Wtime();
pdgetri_(n_global,
ai->local_data(), ia, ja, ai->descriptor(),
ipiv.data(),
work.data(), lwork, iwork.data(), liwork, info);
assert(info == 0);
double t_solve = MPI_Wtime() - t0;
// Verify that the inverse is correct using A*A^{-1} = I
auto identity = block_cyclic_mat_t::diagonal(grid, n_global, n_global);
// Compute I = A * A^{-1} - I and verify that the ||I|| is small
char nein = 'N';
double alpha = 1.0, beta = -1.0;
pdgemm_(nein, nein, n_global, n_global, n_global, alpha,
a->local_data() , ia, ja, a->descriptor(),
ai->local_data(), ia, ja, ai->descriptor(),
beta,
identity->local_data(), ia, ja, identity->descriptor());
// Compute 1-norm of the result
char norm='1';
work.resize(identity->local_cols());
double err = pdlange_(norm, n_global, n_global,
identity->local_data(), ia, ja, identity->descriptor(), work.data());
double t_total = t_factor + t_solve;
double t_glob;
MPI_Reduce(&t_total, &t_glob, 1, MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD);
if (grid->iam() == 0)
{
double gflops = getri_flops(n_global)/t_glob/grid->nprocs();
printf("\n"
"MATRIX INVERSE BENCHMARK SUMMARY\n"
"================================\n"
"N = %d\tNP = %d\tNP_ROW = %d\tNP_COL = %d\n"
"Time for PxGETRF + PxGETRI = %10.7f seconds\tGflops/Proc = %10.7f, Error = %f\n",
n_global, grid->nprocs(), grid->nprows(), grid->npcols(),
t_glob, gflops, err);fflush(stdout);
}
}