--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2017 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+
+// this BlockVector<Number>::scalar_product().
+// same as parallel_block_vector_05, but uses LAPACKFUllMatrix and tests
+// that internally we set it to be symmetric and so, for example, one can
+// immediately run Cholesky factorization
+
+#include "../tests.h"
+
+#include <deal.II/base/utilities.h>
+#include <deal.II/base/function.h>
+#include <deal.II/distributed/tria.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/dofs/dof_tools.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/matrix_free/operators.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/numerics/vector_tools.h>
+#include <deal.II/lac/la_parallel_block_vector.h>
+#include <deal.II/lac/lapack_full_matrix.h>
+
+#include <iostream>
+
+
+
+
+template <int dim, int fe_degree>
+void test (const unsigned int n_blocks = 5)
+{
+ typedef double number;
+
+ parallel::distributed::Triangulation<dim> tria (MPI_COMM_WORLD);
+ GridGenerator::hyper_cube (tria);
+ tria.refine_global(1);
+ typename Triangulation<dim>::active_cell_iterator
+ cell = tria.begin_active (),
+ endc = tria.end();
+ cell = tria.begin_active ();
+ for (; cell!=endc; ++cell)
+ if (cell->is_locally_owned())
+ if (cell->center().norm()<0.2)
+ cell->set_refine_flag();
+ tria.execute_coarsening_and_refinement();
+ if (dim < 3 && fe_degree < 2)
+ tria.refine_global(2);
+ else
+ tria.refine_global(1);
+ if (tria.begin(tria.n_levels()-1)->is_locally_owned())
+ tria.begin(tria.n_levels()-1)->set_refine_flag();
+ if (tria.last()->is_locally_owned())
+ tria.last()->set_refine_flag();
+ tria.execute_coarsening_and_refinement();
+ cell = tria.begin_active ();
+ for (unsigned int i=0; i<10-3*dim; ++i)
+ {
+ cell = tria.begin_active ();
+ unsigned int counter = 0;
+ for (; cell!=endc; ++cell, ++counter)
+ if (cell->is_locally_owned())
+ if (counter % (7-i) == 0)
+ cell->set_refine_flag();
+ tria.execute_coarsening_and_refinement();
+ }
+
+ FE_Q<dim> fe (fe_degree);
+ DoFHandler<dim> dof (tria);
+ dof.distribute_dofs(fe);
+
+ IndexSet owned_set = dof.locally_owned_dofs();
+ IndexSet relevant_set;
+ DoFTools::extract_locally_relevant_dofs (dof, relevant_set);
+
+ ConstraintMatrix constraints (relevant_set);
+ DoFTools::make_hanging_node_constraints(dof, constraints);
+ VectorTools::interpolate_boundary_values (dof, 0, Functions::ZeroFunction<dim>(),
+ constraints);
+ constraints.close();
+
+ std::shared_ptr<MatrixFree<dim,number> > mf_data(new MatrixFree<dim,number> ());
+ {
+ const QGauss<1> quad (fe_degree+2);
+ typename MatrixFree<dim,number>::AdditionalData data;
+ data.tasks_parallel_scheme =
+ MatrixFree<dim,number>::AdditionalData::none;
+ data.tasks_block_size = 7;
+ mf_data->reinit (dof, constraints, quad, data);
+ }
+
+ MatrixFreeOperators::MassOperator<dim,fe_degree, fe_degree+2, 1, LinearAlgebra::distributed::Vector<number> > mf;
+ mf.initialize(mf_data);
+ mf.compute_diagonal();
+
+ LinearAlgebra::distributed::BlockVector<number> left(n_blocks), right(n_blocks);
+ for (unsigned int b = 0; b < n_blocks; ++b)
+ {
+ mf_data->initialize_dof_vector (left.block(b));
+ mf_data->initialize_dof_vector (right.block(b));
+
+ for (unsigned int i=0; i<right.block(b).local_size(); ++i)
+ {
+ const unsigned int glob_index =
+ owned_set.nth_index_in_set (i);
+ if (constraints.is_constrained(glob_index))
+ continue;
+ right.block(b).local_element(i) = (double)Testing::rand()/RAND_MAX;
+ }
+
+ mf.vmult (left.block(b), right.block(b));
+ }
+
+ {
+ // general lapack matrices:
+ LAPACKFullMatrix<number> product(n_blocks,n_blocks), diff(n_blocks,n_blocks);
+
+ deallog << "Symmetric:" << std::endl;
+
+ // inside LAPACK matrix should have its Property set as symmetric
+ // and so we can call compute_cholesky_factorization() below.
+ left.multivector_inner_product(product, right, true);
+
+ for (unsigned int i = 0; i < n_blocks; ++i)
+ for (unsigned int j = 0; j < n_blocks; ++j)
+ diff(i,j) = left.block(i) * right.block(j) - product(i,j);
+
+ const double diff_norm = diff.frobenius_norm();
+
+ deallog << "Norm of difference: " << diff_norm << std::endl;
+ deallog << "Cholesky: " << std::flush;
+ product.compute_cholesky_factorization();
+ deallog << "Ok" << std::endl;
+ }
+
+ // Non-symmetric case
+ {
+ const unsigned int n_blocks_2 = n_blocks+3;
+ LinearAlgebra::distributed::BlockVector<number> left2(n_blocks_2);
+ for (unsigned int b = 0; b < left2.n_blocks(); ++b)
+ {
+ mf_data->initialize_dof_vector (left2.block(b));
+ for (unsigned int i=0; i<left2.block(b).local_size(); ++i)
+ {
+ const unsigned int glob_index =
+ owned_set.nth_index_in_set (i);
+ if (constraints.is_constrained(glob_index))
+ continue;
+ left2.block(b).local_element(i) = (double)Testing::rand()/RAND_MAX;
+ }
+ }
+
+ LAPACKFullMatrix<number> product2(n_blocks_2,n_blocks), diff2(n_blocks_2,n_blocks);
+
+ deallog << "Non-Symmetric:" << std::endl;
+
+ left2.multivector_inner_product(product2, right, false);
+
+ for (unsigned int i = 0; i < n_blocks_2; ++i)
+ for (unsigned int j = 0; j < n_blocks; ++j)
+ diff2(i,j) = left2.block(i) * right.block(j) - product2(i,j);
+
+ const double diff_norm2 = diff2.frobenius_norm();
+
+ deallog << "Norm of difference: " << diff_norm2 << std::endl;
+ }
+
+
+}
+
+
+int main (int argc, char **argv)
+{
+ Utilities::MPI::MPI_InitFinalize mpi_initialization (argc, argv, testing_max_num_threads());
+
+ unsigned int myid = Utilities::MPI::this_mpi_process (MPI_COMM_WORLD);
+ deallog.push(Utilities::int_to_string(myid));
+
+ if (myid == 0)
+ {
+ initlog();
+ deallog << std::setprecision(4);
+
+ test<2,1>();
+ }
+ else
+ {
+ test<2,1>();
+ }
+}