Implement block_linop

diff --git a/include/deal.II/lac/linear_operator.h b/include/deal.II/lac/linear_operator.h
index fb5c1d90280999986b4683f10be181a12f820f37..d95e21dcf2b2a05a701b8fabaaa1484a153e54b9 100644 (file)
--- a/include/deal.II/lac/linear_operator.h
+++ b/include/deal.II/lac/linear_operator.h
@@ -23,6 +23,7 @@
 #ifdef DEAL_II_WITH_CXX11
 
 #include <functional>
+#include <array>
 
 DEAL_II_NAMESPACE_OPEN
 
@@ -582,6 +583,115 @@ inverse_linop(Solver &solver,
 }
 
 
+
+/**
+ * A function that encapsulates a given collection @p ops of
+ * LinearOperators into a block structure. Hereby, it is assumed that Range
+ * and Domain are blockvectors, i.e., derived from @ref
+ * BlockVectorBase<typename Vector>. The individual linear operators in @p
+ * ops must act on a the underlying vector type of the block vectors, i.e.,
+ * on Domain::BlockType yielding a result in Range::BlockType.
+ *
+ * The list @p ops is best passed as an initializer list. Consider for
+ * example a linear operator block (acting on Vector<double>)
+ * @code
+ *  op_a00 | op_a01
+ *         |
+ *  ---------------
+ *         |
+ *  op_a10 | op_a11
+ * @endcode
+ * the coresponding block_linop invocation takes the form
+ * @code
+ * block_linop<2, 2, BlockVector<double>>({op_a00, op_a01, op_a10, op_a11});
+ * @endcode
+ */
+template <unsigned int m, unsigned int n,
+          typename Range = BlockVector<double>,
+          typename Domain = Range>
+LinearOperator<Range, Domain>
+block_linop(const std::array<std::array<LinearOperator<typename Range::BlockType, typename Domain::BlockType>, n>, m> &ops)
+{
+  static_assert(m > 0 && n > 0,
+                "a blocked LinearOperator must consist of at least one block");
+
+  LinearOperator<Range, Domain> return_op;
+
+  return_op.reinit_range_vector = [ops](Range &v, bool fast)
+  {
+    // Reinitialize the block vector to m blocks:
+    v.reinit(m);
+
+    // And reinitialize every individual block with reinit_range_vectors:
+    for (unsigned int i = 0; i < m; ++i)
+      ops[i][0].reinit_range_vector(v.block(i), fast);
+
+    v.collect_sizes();
+  };
+
+  return_op.reinit_domain_vector = [ops](Domain &v, bool fast)
+  {
+    // Reinitialize the block vector to n blocks:
+    v.reinit(n);
+
+    // And reinitialize every individual block with reinit_domain_vectors:
+    for (unsigned int i = 0; i < n; ++i)
+      ops[0][i].reinit_domain_vector(v.block(i), fast);
+
+    v.collect_sizes();
+  };
+
+  return_op.vmult = [ops](Range &v, const Domain &u)
+  {
+    Assert(v.n_blocks() == m, ExcDimensionMismatch(v.n_blocks(), m));
+    Assert(u.n_blocks() == n, ExcDimensionMismatch(u.n_blocks(), n));
+
+    for (unsigned int i = 0; i < m; ++i)
+      {
+        ops[i][0].vmult(v.block(i), u.block(0));
+        for (unsigned int j = 1; j < n; ++j)
+          ops[i][j].vmult_add(v.block(i), u.block(j));
+      }
+  };
+
+  return_op.vmult_add = [ops](Range &v, const Domain &u)
+  {
+    Assert(v.n_blocks() == m, ExcDimensionMismatch(v.n_blocks(), m));
+    Assert(u.n_blocks() == n, ExcDimensionMismatch(u.n_blocks(), n));
+
+    for (unsigned int i = 0; i < m; ++i)
+      for (unsigned int j = 0; j < n; ++j)
+        ops[i][j].vmult_add(v.block(i), u.block(j));
+  };
+
+  return_op.Tvmult = [ops](Domain &v, const Range &u)
+  {
+    Assert(v.n_blocks() == n, ExcDimensionMismatch(v.n_blocks(), n));
+    Assert(u.n_blocks() == m, ExcDimensionMismatch(u.n_blocks(), m));
+
+    for (unsigned int i = 0; i < n; ++i)
+      {
+        ops[0][i].Tvmult(v.block(i), u.block(0));
+        for (unsigned int j = 1; j < m; ++j)
+          ops[j][i].Tvmult_add(v.block(i), u.block(j));
+      }
+  };
+
+  return_op.Tvmult_add = [ops](Domain &v, const Range &u)
+  {
+    Assert(v.n_blocks() == n, ExcDimensionMismatch(v.n_blocks(), n));
+    Assert(u.n_blocks() == m, ExcDimensionMismatch(u.n_blocks(), m));
+
+    for (unsigned int i = 0; i < n; ++i)
+      for (unsigned int j = 0; j < m; ++j)
+        ops[j][i].Tvmult_add(v.block(i), u.block(j));
+  };
+
+  return return_op;
+}
+
+
+
 /**
  * A factory class that is responsible for the creation of a
  * reinit_range_vector object for a given pair of vector type Range and matrix

diff --git a/tests/lac/linear_operator_05.cc b/tests/lac/linear_operator_05.cc
new file mode 100644 (file)
index 0000000..0a66e89
--- /dev/null
+++ b/tests/lac/linear_operator_05.cc
@@ -0,0 +1,218 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2015 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.
+//
+// ---------------------------------------------------------------------
+
+// Tests for block_linop
+
+#include "../tests.h"
+
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/dofs/dof_tools.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.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_vector.h>
+#include <deal.II/lac/dynamic_sparsity_pattern.h>
+#include <deal.II/lac/linear_operator.h>
+
+#define PRINTME(name, var) \
+  deallog << "Block vector: " name << ":" << std::endl; \
+  for (unsigned int i = 0; i < var.n_blocks(); ++i) \
+    deallog << "[block " << i << " ]  " << var.block(i);
+
+
+using namespace dealii;
+
+int main()
+{
+  initlog();
+  deallog << std::setprecision(10);
+
+  static const int dim = 2;
+
+  Triangulation<dim> triangulation;
+  GridGenerator::hyper_cube (triangulation);
+  triangulation.refine_global(2);
+
+  MappingQ1<dim> mapping_q1;
+  FESystem<dim> fe(FE_Q<dim>(2), 1, FE_Q<dim>(1), 1);
+  DoFHandler<dim> dof_handler(triangulation);
+
+  dof_handler.distribute_dofs(fe);
+
+  std::vector<types::global_dof_index> dofs_per_component (2);
+  DoFTools::count_dofs_per_component (dof_handler, dofs_per_component);
+  const unsigned int n_u = dofs_per_component[0],
+                     n_p = dofs_per_component[1];
+
+  BlockDynamicSparsityPattern dsp(2, 2);
+  dsp.block(0, 0).reinit (n_u, n_u);
+  dsp.block(1, 0).reinit (n_p, n_u);
+  dsp.block(0, 1).reinit (n_u, n_p);
+  dsp.block(1, 1).reinit (n_p, n_p);
+
+  for (unsigned int i = 0; i < n_u; ++i) {
+    for (unsigned int j = 0; j < n_u; ++j)
+      dsp.block(0, 0).add(i, j);
+    for (unsigned int j = 0; j < n_p; ++j) {
+      dsp.block(0, 1).add(i, j);
+      dsp.block(1, 0).add(j, i);
+    }
+  }
+  for (unsigned int i = 0; i < n_p; ++i)
+    for (unsigned int j = 0; j < n_p; ++j)
+      dsp.block(1, 1).add(i, j);
+  dsp.collect_sizes ();
+
+  BlockSparsityPattern sparsity_pattern;
+  sparsity_pattern.copy_from(dsp);
+  sparsity_pattern.compress();
+
+  BlockSparseMatrix<double> a (sparsity_pattern);
+
+  // Come up with some simple, but non-trivial structure:
+
+  for(unsigned int i = 0; i < a.block(0, 0).n(); ++i)
+    a.block(0, 0).set(i, i, 10.);
+
+  for(unsigned int i = 0; i < a.block(1, 1).n(); ++i)
+    a.block(1, 1).set(i, i, 5.);
+
+  for(unsigned int i = 0; i < a.block(1, 0).m(); ++i)
+    a.block(0, 1).set(i, i, 3.);
+
+  for(unsigned int i = 0; i < a.block(0, 1).n(); ++i)
+    a.block(1, 0).set(i, i, 1.);
+
+
+  auto op_a = linop<BlockVector<double>>(a);
+
+  auto op_b00 = linop(a.block(0, 0));
+  auto op_b01 = linop(a.block(0, 1));
+  auto op_b10 = linop(a.block(1, 0));
+  auto op_b11 = linop(a.block(1, 1));
+
+  auto op_b =
+      block_linop<2, 2, BlockVector<double>>({op_b00, op_b01, op_b10, op_b11});
+
+  // vmult:
+
+  BlockVector<double> u;
+  op_a.reinit_domain_vector(u, false);
+  for (unsigned int i = 0; i < u.size(); ++i) {
+    u[i] = (double)(i+1);
+  }
+
+  PRINTME("u", u);
+
+  BlockVector<double> v;
+  op_a.reinit_domain_vector(v, false);
+  BlockVector<double> w;
+  op_a.reinit_domain_vector(w, false);
+  BlockVector<double> x;
+  op_a.reinit_domain_vector(x, false);
+
+  op_a.vmult(v, u);
+  PRINTME("Au", v);
+
+  op_b.vmult(w, u);
+  PRINTME("Bu", w);
+
+  x = v;
+  x -= w;
+  PRINTME("Au-Bu", x);
+
+  // Test that both objects give the same results:
+
+  auto op_x = op_a - op_b;
+
+  op_x.vmult(x, u);
+  PRINTME("vmult", x);
+
+  x = 0.;
+  op_x.vmult_add(x, u);
+  PRINTME("vmult_add", x);
+
+  op_x.Tvmult(x, u);
+  PRINTME("Tvmult", x);
+
+  x = 0.;
+  op_x.Tvmult_add(x, u);
+  PRINTME("Tvmult_add", x);
+
+
+  // Test vector reinitalization:
+
+  op_x = op_b * op_b * op_b;
+  op_x.vmult(x, u);
+  PRINTME("(B*B*B) vmult", x);
+
+  x = 0.;
+  op_x.vmult_add(x, u);
+  PRINTME("(B*B*B) vmult_add", x);
+
+  op_x.Tvmult(x, u);
+  PRINTME("(B*B*B) Tvmult", x);
+
+  x = 0.;
+  op_x.Tvmult_add(x, u);
+  PRINTME("(B*B*B) Tvmult_add", x);
+
+  // And finally complicated block structures:
+
+  auto op_upp_x_upu = block_linop<3, 3, BlockVector<double>>(
+      {op_b00, op_b01, op_b00, op_b10, op_b11, op_b10, op_b10, op_b11, op_b10});
+
+  op_upp_x_upu.reinit_domain_vector(u, false);
+  for (unsigned int i = 0; i < u.size(); ++i) {
+    u[i] = (double)(i+1);
+  }
+  PRINTME("u", u);
+
+  op_upp_x_upu.reinit_range_vector(v, false);
+  op_upp_x_upu.vmult(v, u);
+  PRINTME("v", v);
+
+  v = 0.;
+  op_upp_x_upu.vmult_add(v, u);
+  PRINTME("v", v);
+
+  auto op_upp_x_p =
+      block_linop<3, 1, BlockVector<double>>({op_b01, op_b11, op_b11});
+
+  auto op_u_x_upu =
+      block_linop<1, 3, BlockVector<double>>({op_b00, op_b01, op_b00});
+
+  auto op_long = op_u_x_upu * transpose_linop(op_upp_x_upu) * op_upp_x_p;
+
+  op_long.reinit_domain_vector(u, false);
+  for (unsigned int i = 0; i < u.size(); ++i) {
+    u[i] = (double)(i+1);
+  }
+  PRINTME("u", u);
+
+  op_long.reinit_range_vector(v, false);
+  op_long.vmult(v, u);
+  PRINTME("v", v);
+
+  v = 0.;
+  op_long.vmult_add(v, u);
+  PRINTME("v", v);
+
+}
+
+
+

diff --git a/tests/lac/linear_operator_05.with_cxx11=on.output b/tests/lac/linear_operator_05.with_cxx11=on.output
new file mode 100644 (file)
index 0000000..0841217
--- /dev/null
+++ b/tests/lac/linear_operator_05.with_cxx11=on.output
@@ -0,0 +1,55 @@
+
+DEAL::Block vector: u:
+DEAL::[block 0 ]  1.000000000 2.000000000 3.000000000 4.000000000 5.000000000 6.000000000 7.000000000 8.000000000 9.000000000 10.00000000 11.00000000 12.00000000 13.00000000 14.00000000 15.00000000 16.00000000 17.00000000 18.00000000 19.00000000 20.00000000 21.00000000 22.00000000 23.00000000 24.00000000 25.00000000 26.00000000 27.00000000 28.00000000 29.00000000 30.00000000 31.00000000 32.00000000 33.00000000 34.00000000 35.00000000 36.00000000 37.00000000 38.00000000 39.00000000 40.00000000 41.00000000 42.00000000 43.00000000 44.00000000 45.00000000 46.00000000 47.00000000 48.00000000 49.00000000 50.00000000 51.00000000 52.00000000 53.00000000 54.00000000 55.00000000 56.00000000 57.00000000 58.00000000 59.00000000 60.00000000 61.00000000 62.00000000 63.00000000 64.00000000 65.00000000 66.00000000 67.00000000 68.00000000 69.00000000 70.00000000 71.00000000 72.00000000 73.00000000 74.00000000 75.00000000 76.00000000 77.00000000 78.00000000 79.00000000 80.00000000 81.00000000 
+DEAL::[block 1 ]  82.00000000 83.00000000 84.00000000 85.00000000 86.00000000 87.00000000 88.00000000 89.00000000 90.00000000 91.00000000 92.00000000 93.00000000 94.00000000 95.00000000 96.00000000 97.00000000 98.00000000 99.00000000 100.0000000 101.0000000 102.0000000 103.0000000 104.0000000 105.0000000 106.0000000 
+DEAL::Block vector: Au:
+DEAL::[block 0 ]  256.0000000 269.0000000 282.0000000 295.0000000 308.0000000 321.0000000 334.0000000 347.0000000 360.0000000 373.0000000 386.0000000 399.0000000 412.0000000 425.0000000 438.0000000 451.0000000 464.0000000 477.0000000 490.0000000 503.0000000 516.0000000 529.0000000 542.0000000 555.0000000 568.0000000 260.0000000 270.0000000 280.0000000 290.0000000 300.0000000 310.0000000 320.0000000 330.0000000 340.0000000 350.0000000 360.0000000 370.0000000 380.0000000 390.0000000 400.0000000 410.0000000 420.0000000 430.0000000 440.0000000 450.0000000 460.0000000 470.0000000 480.0000000 490.0000000 500.0000000 510.0000000 520.0000000 530.0000000 540.0000000 550.0000000 560.0000000 570.0000000 580.0000000 590.0000000 600.0000000 610.0000000 620.0000000 630.0000000 640.0000000 650.0000000 660.0000000 670.0000000 680.0000000 690.0000000 700.0000000 710.0000000 720.0000000 730.0000000 740.0000000 750.0000000 760.0000000 770.0000000 780.0000000 790.0000000 800.0000000 810.0000000 
+DEAL::[block 1 ]  411.0000000 417.0000000 423.0000000 429.0000000 435.0000000 441.0000000 447.0000000 453.0000000 459.0000000 465.0000000 471.0000000 477.0000000 483.0000000 489.0000000 495.0000000 501.0000000 507.0000000 513.0000000 519.0000000 525.0000000 531.0000000 537.0000000 543.0000000 549.0000000 555.0000000 
+DEAL::Block vector: Bu:
+DEAL::[block 0 ]  256.0000000 269.0000000 282.0000000 295.0000000 308.0000000 321.0000000 334.0000000 347.0000000 360.0000000 373.0000000 386.0000000 399.0000000 412.0000000 425.0000000 438.0000000 451.0000000 464.0000000 477.0000000 490.0000000 503.0000000 516.0000000 529.0000000 542.0000000 555.0000000 568.0000000 260.0000000 270.0000000 280.0000000 290.0000000 300.0000000 310.0000000 320.0000000 330.0000000 340.0000000 350.0000000 360.0000000 370.0000000 380.0000000 390.0000000 400.0000000 410.0000000 420.0000000 430.0000000 440.0000000 450.0000000 460.0000000 470.0000000 480.0000000 490.0000000 500.0000000 510.0000000 520.0000000 530.0000000 540.0000000 550.0000000 560.0000000 570.0000000 580.0000000 590.0000000 600.0000000 610.0000000 620.0000000 630.0000000 640.0000000 650.0000000 660.0000000 670.0000000 680.0000000 690.0000000 700.0000000 710.0000000 720.0000000 730.0000000 740.0000000 750.0000000 760.0000000 770.0000000 780.0000000 790.0000000 800.0000000 810.0000000 
+DEAL::[block 1 ]  411.0000000 417.0000000 423.0000000 429.0000000 435.0000000 441.0000000 447.0000000 453.0000000 459.0000000 465.0000000 471.0000000 477.0000000 483.0000000 489.0000000 495.0000000 501.0000000 507.0000000 513.0000000 519.0000000 525.0000000 531.0000000 537.0000000 543.0000000 549.0000000 555.0000000 
+DEAL::Block vector: Au-Bu:
+DEAL::[block 0 ]  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::[block 1 ]  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::Block vector: vmult:
+DEAL::[block 0 ]  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::[block 1 ]  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::Block vector: vmult_add:
+DEAL::[block 0 ]  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::[block 1 ]  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::Block vector: Tvmult:
+DEAL::[block 0 ]  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::[block 1 ]  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::Block vector: Tvmult_add:
+DEAL::[block 0 ]  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::[block 1 ]  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::Block vector: (B*B*B) vmult:
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