template <int dim>
void
-test(bool transpose = false)
+test(const bool transpose = false)
{
deallog << dim << 'd' << std::endl;
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2002 - 2018 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.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+
+// Like the _03 test, but with complex matrix and vector. That said,
+// the matrix just so happens to have zero imaginary components, even
+// though we store its entries as complex numbers.
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_values.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/lac/sparse_direct.h>
+#include <deal.II/lac/sparse_matrix.h>
+#include <deal.II/lac/sparsity_pattern.h>
+#include <deal.II/lac/vector.h>
+
+#include <deal.II/numerics/matrix_tools.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include <iostream>
+
+#include "../tests.h"
+
+
+template <int dim>
+void
+test(const bool transpose = false)
+{
+ deallog << dim << 'd' << std::endl;
+
+ Triangulation<dim> tria;
+ GridGenerator::hyper_cube(tria, 0, 1);
+ tria.refine_global(1);
+
+ // destroy the uniformity of the matrix by
+ // refining one cell
+ tria.begin_active()->set_refine_flag();
+ tria.execute_coarsening_and_refinement();
+ tria.refine_global(8 - 2 * dim);
+
+ FE_Q<dim> fe(1);
+ DoFHandler<dim> dof_handler(tria);
+ dof_handler.distribute_dofs(fe);
+
+ deallog << "Number of dofs = " << dof_handler.n_dofs() << std::endl;
+
+ SparsityPattern sparsity_pattern;
+ sparsity_pattern.reinit(dof_handler.n_dofs(),
+ dof_handler.n_dofs(),
+ dof_handler.max_couplings_between_dofs());
+ DoFTools::make_sparsity_pattern(dof_handler, sparsity_pattern);
+ sparsity_pattern.compress();
+
+ SparseMatrix<std::complex<double>> B;
+ B.reinit(sparsity_pattern);
+
+ // Create a real sparse matrix and copy it onto B
+ {
+ SparseMatrix<double> BB;
+ BB.reinit(sparsity_pattern);
+
+ QGauss<dim> qr(2);
+ MatrixTools::create_mass_matrix(dof_handler, qr, BB);
+
+ // scale lower left part of the matrix by
+ // 1/2 and upper right part by 2 to make
+ // matrix nonsymmetric
+ for (SparseMatrix<double>::iterator p = BB.begin(); p != BB.end(); ++p)
+ if (p->column() < p->row())
+ p->value() = p->value() / 2;
+ else if (p->column() > p->row())
+ p->value() = p->value() * 2;
+
+ // check that we've done it right
+ for (SparseMatrix<double>::iterator p = BB.begin(); p != BB.end(); ++p)
+ if (p->column() != p->row())
+ AssertThrow(B(p->row(), p->column()) != BB(p->column(), p->row()),
+ ExcInternalError());
+
+ for (SparseMatrix<double>::iterator p = BB.begin(); p != BB.end(); ++p)
+ B.set(p->row(), p->column(), {p->value(), 0});
+ }
+
+
+ // for a number of different solution
+ // vectors, make up a matching rhs vector
+ // and check what the UMFPACK solver finds
+ for (unsigned int i = 0; i < 3; ++i)
+ {
+ Vector<std::complex<double>> solution(dof_handler.n_dofs());
+ Vector<std::complex<double>> x(dof_handler.n_dofs());
+ Vector<std::complex<double>> b(dof_handler.n_dofs());
+
+ for (unsigned int j = 0; j < dof_handler.n_dofs(); ++j)
+ solution(j) =
+ 1. * (j + j * (i + 1) * (i + 1)) *
+ std::complex<double>(1. / std::sqrt(2.), 1. / std::sqrt(2.));
+
+ if (transpose)
+ B.Tvmult(b, solution);
+ else
+ B.vmult(b, solution);
+
+ x = b;
+ SparseDirectUMFPACK().solve(B, x, transpose);
+
+ x -= solution;
+ deallog << "relative norm distance = " << x.l2_norm() / solution.l2_norm()
+ << std::endl;
+ deallog << "absolute norms = " << x.l2_norm() << ' ' << solution.l2_norm()
+ << std::endl;
+ Assert(x.l2_norm() / solution.l2_norm() < 1e-8, ExcInternalError());
+ }
+}
+
+
+int
+main()
+{
+ initlog();
+
+ test<1>();
+ test<2>();
+ test<3>();
+
+ test<1>(/*transpose =*/true);
+ test<2>(/*transpose =*/true);
+ test<3>(/*transpose =*/true);
+}
--- /dev/null
+
+DEAL::1d
+DEAL::Number of dofs = 193
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 3084.00
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 7709.99
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 15420.0
+DEAL::2d
+DEAL::Number of dofs = 1889
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 94764.3
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 236911.
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 473822.
+DEAL::3d
+DEAL::Number of dofs = 1333
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 56165.6
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 140414.
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 280828.
+DEAL::1d
+DEAL::Number of dofs = 193
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 3084.00
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 7709.99
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 15420.0
+DEAL::2d
+DEAL::Number of dofs = 1889
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 94764.3
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 236911.
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 473822.
+DEAL::3d
+DEAL::Number of dofs = 1333
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 56165.6
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 140414.
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 280828.
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2002 - 2018 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.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+
+// Like the _03_complex, but this time with nonzero real and imaginary
+// parts.
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_values.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/lac/sparse_direct.h>
+#include <deal.II/lac/sparse_matrix.h>
+#include <deal.II/lac/sparsity_pattern.h>
+#include <deal.II/lac/vector.h>
+
+#include <deal.II/numerics/matrix_tools.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include <iostream>
+
+#include "../tests.h"
+
+
+template <int dim>
+void
+test(const bool transpose = false)
+{
+ deallog << dim << 'd' << std::endl;
+
+ Triangulation<dim> tria;
+ GridGenerator::hyper_cube(tria, 0, 1);
+ tria.refine_global(1);
+
+ // destroy the uniformity of the matrix by
+ // refining one cell
+ tria.begin_active()->set_refine_flag();
+ tria.execute_coarsening_and_refinement();
+ tria.refine_global(8 - 2 * dim);
+
+ FE_Q<dim> fe(1);
+ DoFHandler<dim> dof_handler(tria);
+ dof_handler.distribute_dofs(fe);
+
+ deallog << "Number of dofs = " << dof_handler.n_dofs() << std::endl;
+
+ SparsityPattern sparsity_pattern;
+ sparsity_pattern.reinit(dof_handler.n_dofs(),
+ dof_handler.n_dofs(),
+ dof_handler.max_couplings_between_dofs());
+ DoFTools::make_sparsity_pattern(dof_handler, sparsity_pattern);
+ sparsity_pattern.compress();
+
+ SparseMatrix<std::complex<double>> B;
+ B.reinit(sparsity_pattern);
+
+ // Create a real sparse matrix and copy it onto B
+ {
+ SparseMatrix<double> BB;
+ BB.reinit(sparsity_pattern);
+
+ QGauss<dim> qr(2);
+ MatrixTools::create_mass_matrix(dof_handler, qr, BB);
+
+ // scale lower left part of the matrix by
+ // 1/2 and upper right part by 2 to make
+ // matrix nonsymmetric
+ for (SparseMatrix<double>::iterator p = BB.begin(); p != BB.end(); ++p)
+ if (p->column() < p->row())
+ p->value() = p->value() / 2;
+ else if (p->column() > p->row())
+ p->value() = p->value() * 2;
+
+ // check that we've done it right
+ for (SparseMatrix<double>::iterator p = BB.begin(); p != BB.end(); ++p)
+ if (p->column() != p->row())
+ AssertThrow(B(p->row(), p->column()) != BB(p->column(), p->row()),
+ ExcInternalError());
+
+ for (SparseMatrix<double>::iterator p = BB.begin(); p != BB.end(); ++p)
+ B.set(p->row(), p->column(), {p->value(), 2 * p->value()});
+ }
+
+
+ // for a number of different solution
+ // vectors, make up a matching rhs vector
+ // and check what the UMFPACK solver finds
+ for (unsigned int i = 0; i < 3; ++i)
+ {
+ Vector<std::complex<double>> solution(dof_handler.n_dofs());
+ Vector<std::complex<double>> x(dof_handler.n_dofs());
+ Vector<std::complex<double>> b(dof_handler.n_dofs());
+
+ for (unsigned int j = 0; j < dof_handler.n_dofs(); ++j)
+ solution(j) =
+ 1. * (j + j * (i + 1) * (i + 1)) *
+ std::complex<double>(1. / std::sqrt(5.), 2. / std::sqrt(5.));
+
+ if (transpose)
+ B.Tvmult(b, solution);
+ else
+ B.vmult(b, solution);
+
+ x = b;
+ SparseDirectUMFPACK().solve(B, x, transpose);
+
+ x -= solution;
+ deallog << "relative norm distance = " << x.l2_norm() / solution.l2_norm()
+ << std::endl;
+ deallog << "absolute norms = " << x.l2_norm() << ' ' << solution.l2_norm()
+ << std::endl;
+ Assert(x.l2_norm() / solution.l2_norm() < 1e-8, ExcInternalError());
+ }
+}
+
+
+int
+main()
+{
+ initlog();
+
+ test<1>();
+ test<2>();
+ test<3>();
+
+ test<1>(/*transpose =*/true);
+ test<2>(/*transpose =*/true);
+ test<3>(/*transpose =*/true);
+}
--- /dev/null
+
+DEAL::1d
+DEAL::Number of dofs = 193
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 3084.00
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 7709.99
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 15420.0
+DEAL::2d
+DEAL::Number of dofs = 1889
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 94764.3
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 236911.
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 473822.
+DEAL::3d
+DEAL::Number of dofs = 1333
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 56165.6
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 140414.
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 280828.
+DEAL::1d
+DEAL::Number of dofs = 193
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 3084.00
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 7709.99
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 15420.0
+DEAL::2d
+DEAL::Number of dofs = 1889
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 94764.3
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 236911.
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 473822.
+DEAL::3d
+DEAL::Number of dofs = 1333
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 56165.6
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 140414.
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 280828.
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2002 - 2018 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.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+
+// This test is like the _09 test in that it uses a real-valued
+// matrix, but it then solves a linear system with a complex-valued
+// right hand side and corresponding complex-valued solution vector.
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_values.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/lac/block_sparse_matrix.h>
+#include <deal.II/lac/block_sparsity_pattern.h>
+#include <deal.II/lac/sparse_direct.h>
+#include <deal.II/lac/vector.h>
+
+#include <deal.II/numerics/matrix_tools.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include "../tests.h"
+
+
+template <int dim>
+void
+test()
+{
+ deallog << dim << 'd' << std::endl;
+
+ Triangulation<dim> tria;
+ GridGenerator::hyper_cube(tria, 0, 1);
+ tria.refine_global(1);
+
+ // destroy the uniformity of the matrix by
+ // refining one cell
+ tria.begin_active()->set_refine_flag();
+ tria.execute_coarsening_and_refinement();
+ tria.refine_global(8 - 2 * dim);
+
+ FE_Q<dim> fe(1);
+ DoFHandler<dim> dof_handler(tria);
+ dof_handler.distribute_dofs(fe);
+
+ deallog << "Number of dofs = " << dof_handler.n_dofs() << std::endl;
+
+ BlockSparsityPattern sparsity_pattern;
+ sparsity_pattern.reinit(3, 3);
+ for (unsigned int i = 0; i < 3; ++i)
+ for (unsigned int j = 0; j < 3; ++j)
+ sparsity_pattern.block(i, j).reinit(
+ i != 2 ? dof_handler.n_dofs() / 3 :
+ dof_handler.n_dofs() - 2 * (dof_handler.n_dofs() / 3),
+ j != 2 ? dof_handler.n_dofs() / 3 :
+ dof_handler.n_dofs() - 2 * (dof_handler.n_dofs() / 3),
+ dof_handler.max_couplings_between_dofs());
+ sparsity_pattern.collect_sizes();
+ DoFTools::make_sparsity_pattern(dof_handler, sparsity_pattern);
+ sparsity_pattern.compress();
+
+ BlockSparseMatrix<double> B;
+ B.reinit(sparsity_pattern);
+
+ {
+ // for some reason, we can't
+ // create block matrices directly
+ // in matrixtools...
+ SparsityPattern xsparsity_pattern;
+ xsparsity_pattern.reinit(dof_handler.n_dofs(),
+ dof_handler.n_dofs(),
+ dof_handler.max_couplings_between_dofs());
+ DoFTools::make_sparsity_pattern(dof_handler, xsparsity_pattern);
+ xsparsity_pattern.compress();
+
+ SparseMatrix<double> xB;
+ xB.reinit(xsparsity_pattern);
+
+ QGauss<dim> qr(2);
+ MatrixTools::create_mass_matrix(dof_handler, qr, xB);
+
+ // scale lower left part of the matrix by
+ // 1/2 and upper right part by 2 to make
+ // matrix nonsymmetric
+ for (SparseMatrix<double>::iterator p = xB.begin(); p != xB.end(); ++p)
+ if (p->column() < p->row())
+ p->value() = p->value() / 2;
+ else if (p->column() > p->row())
+ p->value() = p->value() * 2;
+
+ // check that we've done it right
+ for (SparseMatrix<double>::iterator p = xB.begin(); p != xB.end(); ++p)
+ if (p->column() != p->row())
+ AssertThrow(xB(p->row(), p->column()) != xB(p->column(), p->row()),
+ ExcInternalError());
+
+ // now copy stuff over
+ for (SparseMatrix<double>::const_iterator i = xB.begin(); i != xB.end();
+ ++i)
+ B.set(i->row(), i->column(), i->value());
+ }
+
+
+ // for a number of different solution
+ // vectors, make up a matching rhs vector
+ // and check what the UMFPACK solver finds
+ for (unsigned int i = 0; i < 3; ++i)
+ {
+ BlockVector<std::complex<double>> solution(3);
+ solution.block(0).reinit(dof_handler.n_dofs() / 3);
+ solution.block(1).reinit(dof_handler.n_dofs() / 3);
+ solution.block(2).reinit(dof_handler.n_dofs() -
+ 2 * (dof_handler.n_dofs() / 3));
+ solution.collect_sizes();
+
+ // Pick a solution vector. Normalize it in such a way that we
+ // get the exact same norm as for the regular _09 test. Since
+ // the actual choice of rhs shouldn't matter for this test, we
+ // are free to normalize as we see fit.
+ for (unsigned int j = 0; j < dof_handler.n_dofs(); ++j)
+ {
+ solution(j) =
+ std::complex<double>(1 + j + j * (i + 1) * (i + 1), // real part
+ 1 + i +
+ i * (j + 1) * (j + 1)); // imaginary part
+ solution(j) *=
+ 1. * (j + j * (i + 1) * (i + 1)) / std::fabs(solution(j));
+ }
+
+ // Then choose as rhs for the linear system the vector
+ // b = B*solution
+ // so that later the solution of the linear system Bx=b
+ // is again
+ // x = solution
+ BlockVector<std::complex<double>> x;
+ x.reinit(solution);
+ BlockVector<std::complex<double>> b;
+ b.reinit(solution);
+
+ B.vmult(b, solution);
+ x = b;
+ SparseDirectUMFPACK().solve(B, x);
+
+ // Check that we really got what we expected
+ x -= solution;
+ deallog << "relative norm distance = " << x.l2_norm() / solution.l2_norm()
+ << std::endl;
+ deallog << "absolute norms = " << x.l2_norm() << ' ' << solution.l2_norm()
+ << std::endl;
+ Assert(x.l2_norm() / solution.l2_norm() < 1e-8, ExcInternalError());
+ }
+}
+
+
+int
+main()
+{
+ initlog();
+
+ test<1>();
+ test<2>();
+ test<3>();
+}
--- /dev/null
+
+DEAL::1d
+DEAL::Number of dofs = 193
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 3084.00
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 7709.99
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 15420.0
+DEAL::2d
+DEAL::Number of dofs = 1889
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 94764.3
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 236911.
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 473822.
+DEAL::3d
+DEAL::Number of dofs = 1333
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 56165.6
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 140414.
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 280828.
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2002 - 2018 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.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+
+// This test is like the _09_complex_complex test, but indeed stores a
+// matrix with complex entries.
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_values.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/lac/block_sparse_matrix.h>
+#include <deal.II/lac/block_sparsity_pattern.h>
+#include <deal.II/lac/sparse_direct.h>
+#include <deal.II/lac/vector.h>
+
+#include <deal.II/numerics/matrix_tools.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include "../tests.h"
+
+
+template <int dim>
+void
+test()
+{
+ deallog << dim << 'd' << std::endl;
+
+ Triangulation<dim> tria;
+ GridGenerator::hyper_cube(tria, 0, 1);
+ tria.refine_global(1);
+
+ // destroy the uniformity of the matrix by
+ // refining one cell
+ tria.begin_active()->set_refine_flag();
+ tria.execute_coarsening_and_refinement();
+ tria.refine_global(8 - 2 * dim);
+
+ FE_Q<dim> fe(1);
+ DoFHandler<dim> dof_handler(tria);
+ dof_handler.distribute_dofs(fe);
+
+ deallog << "Number of dofs = " << dof_handler.n_dofs() << std::endl;
+
+ SparsityPattern sparsity_pattern(dof_handler.n_dofs(),
+ dof_handler.n_dofs(),
+ dof_handler.max_couplings_between_dofs());
+ DoFTools::make_sparsity_pattern(dof_handler, sparsity_pattern);
+ sparsity_pattern.compress();
+
+ SparseMatrix<std::complex<double>> B;
+ B.reinit(sparsity_pattern);
+
+ {
+ SparseMatrix<double> BB;
+ BB.reinit(sparsity_pattern);
+
+ QGauss<dim> qr(2);
+ MatrixTools::create_mass_matrix(dof_handler, qr, BB);
+
+ // // scale lower left part of the matrix by
+ // // 1/2 and upper right part by 2 to make
+ // // matrix nonsymmetric
+ // for (SparseMatrix<double>::iterator p = BB.begin(); p != BB.end(); ++p)
+ // if (p->column() < p->row())
+ // p->value() = p->value() / 2;
+ // else if (p->column() > p->row())
+ // p->value() = p->value() * 2;
+
+ // // check that we've done it right
+ // for (SparseMatrix<double>::iterator p = BB.begin(); p != BB.end(); ++p)
+ // if (p->column() != p->row())
+ // AssertThrow(BB(p->row(), p->column()) != BB(p->column(), p->row()),
+ // ExcInternalError());
+
+ // Now copy stuff over and make sure that what we have is indeed
+ // complex-valued
+ for (auto i = BB.begin(); i != BB.end(); ++i)
+ B.set(i->row(), i->column(), {i->value(), 2. * i->value()});
+ }
+
+
+ // for a number of different solution
+ // vectors, make up a matching rhs vector
+ // and check what the UMFPACK solver finds
+ for (unsigned int i = 0; i < 3; ++i)
+ {
+ Vector<std::complex<double>> solution(dof_handler.n_dofs());
+
+ // Pick a solution vector. Normalize it in such a way that we
+ // get the exact same norm as for the regular _09 test. Since
+ // the actual choice of rhs shouldn't matter for this test, we
+ // are free to normalize as we see fit.
+ for (unsigned int j = 0; j < dof_handler.n_dofs(); ++j)
+ solution(j) =
+ 1. * (j + j * (i + 1) * (i + 1)) *
+ std::complex<double>(1. / std::sqrt(5.), 2. / std::sqrt(5.));
+
+ // Then choose as rhs for the linear system the vector
+ // b = B*solution
+ // so that later the solution of the linear system Bx=b
+ // is again
+ // x = solution
+ Vector<std::complex<double>> x;
+ x.reinit(solution);
+ Vector<std::complex<double>> b;
+ b.reinit(solution);
+
+ B.Tvmult(b, solution);
+ x = b;
+ SparseDirectUMFPACK().solve(B, x, true);
+
+ // Now check that the residual is zero or close to
+ Vector<std::complex<double>> res;
+ res.reinit(solution);
+ B.residual(res, x, b);
+ Assert(res.l2_norm() <= 1e-8 * b.l2_norm(), ExcInternalError());
+
+ // Check that we really got what we expected
+ x -= solution;
+ deallog << "relative norm distance = " << x.l2_norm() / solution.l2_norm()
+ << std::endl;
+ deallog << "absolute norms = " << x.l2_norm() << ' ' << solution.l2_norm()
+ << std::endl;
+ Assert(x.l2_norm() / solution.l2_norm() < 1e-8, ExcInternalError());
+ }
+}
+
+
+int
+main()
+{
+ initlog();
+
+ test<1>();
+ test<2>();
+ test<3>();
+}
--- /dev/null
+
+DEAL::1d
+DEAL::Number of dofs = 193
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 3084.00
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 7709.99
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 15420.0
+DEAL::2d
+DEAL::Number of dofs = 1889
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 94764.3
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 236911.
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 473822.
+DEAL::3d
+DEAL::Number of dofs = 1333
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 56165.6
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 140414.
+DEAL::relative norm distance = 0
+DEAL::absolute norms = 0 280828.
projects / dealii.git / commitdiff