Test case

diff --git a/tests/mappings/mapping_q_quadrature_points.cc b/tests/mappings/mapping_q_quadrature_points.cc
new file mode 100644 (file)
index 0000000..1f4a9c1
--- /dev/null
+++ b/tests/mappings/mapping_q_quadrature_points.cc
@@ -0,0 +1,95 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2020 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.
+//
+// ---------------------------------------------------------------------
+
+
+// Show positions of quadrature points with various degrees of MappingQGeneric
+// and quadrature formulas, including the collocation case where quadrature
+// points coincide with the mapping support points and going to the tensor
+// product and non-tensor product path of MappingQGeneric
+
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/fe/fe_nothing.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_q.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria.h>
+
+#include "../tests.h"
+
+
+template <int dim>
+void
+test(const unsigned int degree, const unsigned int n_q_points)
+{
+  MappingQGeneric<dim> mapping(degree);
+  FE_Nothing<dim>      dummy;
+  QGaussLobatto<dim>   quadrature(n_q_points);
+  Quadrature<dim>      quadrature_copy(quadrature.get_points());
+
+  Triangulation<dim> tria;
+  GridGenerator::hyper_ball(tria);
+
+  deallog << "Checking " << dim << "D with mapping degree " << degree
+          << " with " << n_q_points << " points per coordinate direction"
+          << std::endl;
+
+  // for QGaussLobatto, MappingQGeneric will choose the tensor product code
+  // path, whereas for the copy it will not as we do not know the tensor
+  // product property on general points
+  FEValues<dim> fe_val(mapping, dummy, quadrature, update_quadrature_points);
+  FEValues<dim> fe_val_copy(mapping,
+                            dummy,
+                            quadrature_copy,
+                            update_quadrature_points);
+
+  for (const auto &cell : tria.active_cell_iterators())
+    {
+      fe_val.reinit(cell);
+      fe_val_copy.reinit(cell);
+
+      for (unsigned int q = 0; q < quadrature.size(); ++q)
+        {
+          deallog << "GL: " << fe_val.quadrature_point(q)
+                  << "  copy: " << fe_val_copy.quadrature_point(q)
+                  << "  difference: "
+                  << fe_val.quadrature_point(q) -
+                       fe_val_copy.quadrature_point(q)
+                  << std::endl;
+        }
+      deallog << std::endl;
+    }
+}
+
+
+
+int
+main()
+{
+  initlog();
+  deallog << std::setprecision(8) << std::fixed;
+
+  for (unsigned int degree = 1; degree < 5; ++degree)
+    {
+      test<2>(degree, degree + 1);
+      test<2>(degree, degree + 2);
+    }
+
+  for (unsigned int degree = 1; degree < 4; ++degree)
+    test<3>(degree, degree + 1);
+
+  return 0;
+}

diff --git a/tests/mappings/mapping_q_quadrature_points.output b/tests/mappings/mapping_q_quadrature_points.output
new file mode 100644 (file)
index 0000000..1a61e5e
--- /dev/null
+++ b/tests/mappings/mapping_q_quadrature_points.output
@@ -0,0 +1,1466 @@
+
+DEAL::Checking 2D with mapping degree 1 with 2 points per coordinate direction
+DEAL::GL: -0.70710678 -0.70710678  copy: -0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.70710678 -0.70710678  copy: 0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 -0.29289322  copy: -0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 -0.29289322  copy: 0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.70710678 -0.70710678  copy: -0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 -0.29289322  copy: -0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: -0.70710678 0.70710678  copy: -0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.29289322  copy: -0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.29289322 -0.29289322  copy: -0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 -0.29289322  copy: 0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.29289322  copy: -0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.29289322  copy: 0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: 0.70710678 -0.70710678  copy: 0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.70710678 0.70710678  copy: 0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 -0.29289322  copy: 0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.29289322  copy: 0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.70710678 0.70710678  copy: -0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.29289322  copy: -0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.70710678 0.70710678  copy: 0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.29289322  copy: 0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::Checking 2D with mapping degree 1 with 3 points per coordinate direction
+DEAL::GL: -0.70710678 -0.70710678  copy: -0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.70710678  copy: 0.00000000 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.70710678 -0.70710678  copy: 0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.50000000 -0.50000000  copy: -0.50000000 -0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.50000000  copy: 0.00000000 -0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.50000000 -0.50000000  copy: 0.50000000 -0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 -0.29289322  copy: -0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.29289322  copy: 0.00000000 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 -0.29289322  copy: 0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.70710678 -0.70710678  copy: -0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.50000000 -0.50000000  copy: -0.50000000 -0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 -0.29289322  copy: -0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: -0.70710678 0.00000000  copy: -0.70710678 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.50000000 0.00000000  copy: -0.50000000 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.00000000  copy: -0.29289322 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.70710678 0.70710678  copy: -0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.50000000 0.50000000  copy: -0.50000000 0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.29289322  copy: -0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.29289322 -0.29289322  copy: -0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.29289322  copy: 0.00000000 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 -0.29289322  copy: 0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.00000000  copy: -0.29289322 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.00000000  copy: 0.00000000 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.00000000  copy: 0.29289322 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.29289322  copy: -0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.29289322  copy: 0.00000000 0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.29289322  copy: 0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: 0.70710678 -0.70710678  copy: 0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.70710678 0.00000000  copy: 0.70710678 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.70710678 0.70710678  copy: 0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.50000000 -0.50000000  copy: 0.50000000 -0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.50000000 0.00000000  copy: 0.50000000 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.50000000 0.50000000  copy: 0.50000000 0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 -0.29289322  copy: 0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.00000000  copy: 0.29289322 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.29289322  copy: 0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.70710678 0.70710678  copy: -0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.50000000 0.50000000  copy: -0.50000000 0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.29289322  copy: -0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.70710678  copy: 0.00000000 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.50000000  copy: 0.00000000 0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.29289322  copy: 0.00000000 0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.70710678 0.70710678  copy: 0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.50000000 0.50000000  copy: 0.50000000 0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.29289322  copy: 0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::Checking 2D with mapping degree 2 with 3 points per coordinate direction
+DEAL::GL: -0.70710678 -0.70710678  copy: -0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -1.00000000  copy: 0.00000000 -1.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.70710678 -0.70710678  copy: 0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.50000000 -0.50000000  copy: -0.50000000 -0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.64644661  copy: 0.00000000 -0.64644661  difference: 0.00000000 0.00000000
+DEAL::GL: 0.50000000 -0.50000000  copy: 0.50000000 -0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 -0.29289322  copy: -0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.29289322  copy: 0.00000000 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 -0.29289322  copy: 0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.70710678 -0.70710678  copy: -0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.50000000 -0.50000000  copy: -0.50000000 -0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 -0.29289322  copy: -0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: -1.00000000 0.00000000  copy: -1.00000000 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.64644661 0.00000000  copy: -0.64644661 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.00000000  copy: -0.29289322 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.70710678 0.70710678  copy: -0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.50000000 0.50000000  copy: -0.50000000 0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.29289322  copy: -0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.29289322 -0.29289322  copy: -0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.29289322  copy: 0.00000000 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 -0.29289322  copy: 0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.00000000  copy: -0.29289322 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.00000000  copy: 0.00000000 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.00000000  copy: 0.29289322 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.29289322  copy: -0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.29289322  copy: 0.00000000 0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.29289322  copy: 0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: 0.70710678 -0.70710678  copy: 0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 1.00000000 0.00000000  copy: 1.00000000 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.70710678 0.70710678  copy: 0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.50000000 -0.50000000  copy: 0.50000000 -0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.64644661 0.00000000  copy: 0.64644661 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.50000000 0.50000000  copy: 0.50000000 0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 -0.29289322  copy: 0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.00000000  copy: 0.29289322 0.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.29289322  copy: 0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.70710678 0.70710678  copy: -0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.50000000 0.50000000  copy: -0.50000000 0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.29289322  copy: -0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 1.00000000  copy: 0.00000000 1.00000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.64644661  copy: 0.00000000 0.64644661  difference: 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.29289322  copy: 0.00000000 0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.70710678 0.70710678  copy: 0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.50000000 0.50000000  copy: 0.50000000 0.50000000  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.29289322  copy: 0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::Checking 2D with mapping degree 2 with 4 points per coordinate direction
+DEAL::GL: -0.70710678 -0.70710678  copy: -0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.31622777 -0.94142136  copy: -0.31622777 -0.94142136  difference: 0.00000000 0.00000000
+DEAL::GL: 0.31622777 -0.94142136  copy: 0.31622777 -0.94142136  difference: 0.00000000 0.00000000
+DEAL::GL: 0.70710678 -0.70710678  copy: 0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.59262097 -0.59262097  copy: -0.59262097 -0.59262097  difference: 0.00000000 0.00000000
+DEAL::GL: -0.26502815 -0.76217259  copy: -0.26502815 -0.76217259  difference: 0.00000000 0.00000000
+DEAL::GL: 0.26502815 -0.76217259  copy: 0.26502815 -0.76217259  difference: 0.00000000 0.00000000
+DEAL::GL: 0.59262097 -0.59262097  copy: 0.59262097 -0.59262097  difference: 0.00000000 0.00000000
+DEAL::GL: -0.40737903 -0.40737903  copy: -0.40737903 -0.40737903  difference: 0.00000000 0.00000000
+DEAL::GL: -0.18218544 -0.47214199  copy: -0.18218544 -0.47214199  difference: 0.00000000 0.00000000
+DEAL::GL: 0.18218544 -0.47214199  copy: 0.18218544 -0.47214199  difference: 0.00000000 0.00000000
+DEAL::GL: 0.40737903 -0.40737903  copy: 0.40737903 -0.40737903  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 -0.29289322  copy: -0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: -0.13098583 -0.29289322  copy: -0.13098583 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.13098583 -0.29289322  copy: 0.13098583 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 -0.29289322  copy: 0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.70710678 -0.70710678  copy: -0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.59262097 -0.59262097  copy: -0.59262097 -0.59262097  difference: 0.00000000 0.00000000
+DEAL::GL: -0.40737903 -0.40737903  copy: -0.40737903 -0.40737903  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 -0.29289322  copy: -0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: -0.94142136 -0.31622777  copy: -0.94142136 -0.31622777  difference: 0.00000000 0.00000000
+DEAL::GL: -0.76217259 -0.26502815  copy: -0.76217259 -0.26502815  difference: 0.00000000 0.00000000
+DEAL::GL: -0.47214199 -0.18218544  copy: -0.47214199 -0.18218544  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 -0.13098583  copy: -0.29289322 -0.13098583  difference: 0.00000000 0.00000000
+DEAL::GL: -0.94142136 0.31622777  copy: -0.94142136 0.31622777  difference: 0.00000000 0.00000000
+DEAL::GL: -0.76217259 0.26502815  copy: -0.76217259 0.26502815  difference: 0.00000000 0.00000000
+DEAL::GL: -0.47214199 0.18218544  copy: -0.47214199 0.18218544  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.13098583  copy: -0.29289322 0.13098583  difference: 0.00000000 0.00000000
+DEAL::GL: -0.70710678 0.70710678  copy: -0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: -0.59262097 0.59262097  copy: -0.59262097 0.59262097  difference: 0.00000000 0.00000000
+DEAL::GL: -0.40737903 0.40737903  copy: -0.40737903 0.40737903  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.29289322  copy: -0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.29289322 -0.29289322  copy: -0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: -0.13098583 -0.29289322  copy: -0.13098583 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.13098583 -0.29289322  copy: 0.13098583 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 -0.29289322  copy: 0.29289322 -0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 -0.13098583  copy: -0.29289322 -0.13098583  difference: 0.00000000 0.00000000
+DEAL::GL: -0.13098583 -0.13098583  copy: -0.13098583 -0.13098583  difference: 0.00000000 0.00000000
+DEAL::GL: 0.13098583 -0.13098583  copy: 0.13098583 -0.13098583  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 -0.13098583  copy: 0.29289322 -0.13098583  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.13098583  copy: -0.29289322 0.13098583  difference: 0.00000000 0.00000000
+DEAL::GL: -0.13098583 0.13098583  copy: -0.13098583 0.13098583  difference: 0.00000000 0.00000000
+DEAL::GL: 0.13098583 0.13098583  copy: 0.13098583 0.13098583  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.13098583  copy: 0.29289322 0.13098583  difference: 0.00000000 0.00000000
+DEAL::GL: -0.29289322 0.29289322  copy: -0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: -0.13098583 0.29289322  copy: -0.13098583 0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.13098583 0.29289322  copy: 0.13098583 0.29289322  difference: 0.00000000 0.00000000
+DEAL::GL: 0.29289322 0.29289322  copy: 0.29289322 0.29289322  difference: 0.00000000 0.00000000
+DEAL::
+DEAL::GL: 0.70710678 -0.70710678  copy: 0.70710678 -0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.94142136 -0.31622777  copy: 0.94142136 -0.31622777  difference: 0.00000000 0.00000000
+DEAL::GL: 0.94142136 0.31622777  copy: 0.94142136 0.31622777  difference: 0.00000000 0.00000000
+DEAL::GL: 0.70710678 0.70710678  copy: 0.70710678 0.70710678  difference: 0.00000000 0.00000000
+DEAL::GL: 0.59262097 -0.59262097  copy: 0.59262097 -0.59262097  difference: 0.00000000 0.00000000
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+DEAL::
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+DEAL::
+DEAL::Checking 3D with mapping degree 1 with 2 points per coordinate direction
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+DEAL::
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+DEAL::
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+DEAL::GL: 0.57735027 -0.57735027 0.57735027  copy: 0.57735027 -0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 -0.21132487 0.21132487  copy: -0.21132487 -0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 -0.21132487 0.21132487  copy: 0.21132487 -0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.57735027 0.57735027 0.57735027  copy: -0.57735027 0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.57735027 0.57735027 0.57735027  copy: 0.57735027 0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.21132487 0.21132487  copy: -0.21132487 0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.21132487 0.21132487  copy: 0.21132487 0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.57735027 -0.57735027 -0.57735027  copy: -0.57735027 -0.57735027 -0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 -0.21132487 -0.21132487  copy: -0.21132487 -0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.57735027 0.57735027 -0.57735027  copy: -0.57735027 0.57735027 -0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.21132487 -0.21132487  copy: -0.21132487 0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.57735027 -0.57735027 0.57735027  copy: -0.57735027 -0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 -0.21132487 0.21132487  copy: -0.21132487 -0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.57735027 0.57735027 0.57735027  copy: -0.57735027 0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.21132487 0.21132487  copy: -0.21132487 0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.57735027 -0.57735027 -0.57735027  copy: -0.57735027 -0.57735027 -0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.57735027 -0.57735027 -0.57735027  copy: 0.57735027 -0.57735027 -0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 -0.21132487 -0.21132487  copy: -0.21132487 -0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 -0.21132487 -0.21132487  copy: 0.21132487 -0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.57735027 -0.57735027 0.57735027  copy: -0.57735027 -0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.57735027 -0.57735027 0.57735027  copy: 0.57735027 -0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 -0.21132487 0.21132487  copy: -0.21132487 -0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 -0.21132487 0.21132487  copy: 0.21132487 -0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.57735027 0.57735027 -0.57735027  copy: -0.57735027 0.57735027 -0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.21132487 -0.21132487  copy: -0.21132487 0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.57735027 0.57735027 -0.57735027  copy: 0.57735027 0.57735027 -0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.21132487 -0.21132487  copy: 0.21132487 0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.57735027 0.57735027 0.57735027  copy: -0.57735027 0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.21132487 0.21132487  copy: -0.21132487 0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.57735027 0.57735027 0.57735027  copy: 0.57735027 0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.21132487 0.21132487  copy: 0.21132487 0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::
+DEAL::Checking 3D with mapping degree 2 with 3 points per coordinate direction
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+DEAL::GL: 0.00000000 -0.21132487 -0.21132487  copy: 0.00000000 -0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 -0.21132487 -0.21132487  copy: 0.21132487 -0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.00000000 -0.21132487  copy: -0.21132487 0.00000000 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.00000000 -0.21132487  copy: 0.00000000 0.00000000 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.00000000 -0.21132487  copy: 0.21132487 0.00000000 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.21132487 -0.21132487  copy: -0.21132487 0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.21132487 -0.21132487  copy: 0.00000000 0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.21132487 -0.21132487  copy: 0.21132487 0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 -0.21132487 0.00000000  copy: -0.21132487 -0.21132487 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.21132487 0.00000000  copy: 0.00000000 -0.21132487 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 -0.21132487 0.00000000  copy: 0.21132487 -0.21132487 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.00000000 0.00000000  copy: -0.21132487 0.00000000 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.00000000 0.00000000  copy: 0.00000000 0.00000000 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.00000000 0.00000000  copy: 0.21132487 0.00000000 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.21132487 0.00000000  copy: -0.21132487 0.21132487 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.21132487 0.00000000  copy: 0.00000000 0.21132487 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.21132487 0.00000000  copy: 0.21132487 0.21132487 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 -0.21132487 0.21132487  copy: -0.21132487 -0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.21132487 0.21132487  copy: 0.00000000 -0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 -0.21132487 0.21132487  copy: 0.21132487 -0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.00000000 0.21132487  copy: -0.21132487 0.00000000 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.00000000 0.21132487  copy: 0.00000000 0.00000000 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.00000000 0.21132487  copy: 0.21132487 0.00000000 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.21132487 0.21132487  copy: -0.21132487 0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.21132487 0.21132487  copy: 0.00000000 0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.21132487 0.21132487  copy: 0.21132487 0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.57735027 -0.57735027 -0.57735027  copy: -0.57735027 -0.57735027 -0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.70710678 -0.70710678  copy: 0.00000000 -0.70710678 -0.70710678  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.57735027 -0.57735027 -0.57735027  copy: 0.57735027 -0.57735027 -0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.70710678 0.00000000 -0.70710678  copy: -0.70710678 0.00000000 -0.70710678  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.00000000 -1.00000000  copy: 0.00000000 0.00000000 -1.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.70710678 0.00000000 -0.70710678  copy: 0.70710678 0.00000000 -0.70710678  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.57735027 0.57735027 -0.57735027  copy: -0.57735027 0.57735027 -0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.70710678 -0.70710678  copy: 0.00000000 0.70710678 -0.70710678  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.57735027 0.57735027 -0.57735027  copy: 0.57735027 0.57735027 -0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.39433757 -0.39433757 -0.39433757  copy: -0.39433757 -0.39433757 -0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.45921582 -0.45921582  copy: 0.00000000 -0.45921582 -0.45921582  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.39433757 -0.39433757 -0.39433757  copy: 0.39433757 -0.39433757 -0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.45921582 0.00000000 -0.45921582  copy: -0.45921582 0.00000000 -0.45921582  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.00000000 -0.60566243  copy: 0.00000000 0.00000000 -0.60566243  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.45921582 0.00000000 -0.45921582  copy: 0.45921582 0.00000000 -0.45921582  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.39433757 0.39433757 -0.39433757  copy: -0.39433757 0.39433757 -0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.45921582 -0.45921582  copy: 0.00000000 0.45921582 -0.45921582  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.39433757 0.39433757 -0.39433757  copy: 0.39433757 0.39433757 -0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 -0.21132487 -0.21132487  copy: -0.21132487 -0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.21132487 -0.21132487  copy: 0.00000000 -0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 -0.21132487 -0.21132487  copy: 0.21132487 -0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.00000000 -0.21132487  copy: -0.21132487 0.00000000 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.00000000 -0.21132487  copy: 0.00000000 0.00000000 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.00000000 -0.21132487  copy: 0.21132487 0.00000000 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.21132487 -0.21132487  copy: -0.21132487 0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.21132487 -0.21132487  copy: 0.00000000 0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.21132487 -0.21132487  copy: 0.21132487 0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::
+DEAL::GL: 0.57735027 -0.57735027 -0.57735027  copy: 0.57735027 -0.57735027 -0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.70710678 0.00000000 -0.70710678  copy: 0.70710678 0.00000000 -0.70710678  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.57735027 0.57735027 -0.57735027  copy: 0.57735027 0.57735027 -0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.39433757 -0.39433757 -0.39433757  copy: 0.39433757 -0.39433757 -0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.45921582 0.00000000 -0.45921582  copy: 0.45921582 0.00000000 -0.45921582  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.39433757 0.39433757 -0.39433757  copy: 0.39433757 0.39433757 -0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 -0.21132487 -0.21132487  copy: 0.21132487 -0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.00000000 -0.21132487  copy: 0.21132487 0.00000000 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.21132487 -0.21132487  copy: 0.21132487 0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.70710678 -0.70710678 0.00000000  copy: 0.70710678 -0.70710678 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 1.00000000 0.00000000 0.00000000  copy: 1.00000000 0.00000000 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.70710678 0.70710678 0.00000000  copy: 0.70710678 0.70710678 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.45921582 -0.45921582 0.00000000  copy: 0.45921582 -0.45921582 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.60566243 0.00000000 0.00000000  copy: 0.60566243 0.00000000 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.45921582 0.45921582 0.00000000  copy: 0.45921582 0.45921582 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 -0.21132487 0.00000000  copy: 0.21132487 -0.21132487 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.00000000 0.00000000  copy: 0.21132487 0.00000000 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.21132487 0.00000000  copy: 0.21132487 0.21132487 0.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.57735027 -0.57735027 0.57735027  copy: 0.57735027 -0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.70710678 0.00000000 0.70710678  copy: 0.70710678 0.00000000 0.70710678  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.57735027 0.57735027 0.57735027  copy: 0.57735027 0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.39433757 -0.39433757 0.39433757  copy: 0.39433757 -0.39433757 0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.45921582 0.00000000 0.45921582  copy: 0.45921582 0.00000000 0.45921582  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.39433757 0.39433757 0.39433757  copy: 0.39433757 0.39433757 0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 -0.21132487 0.21132487  copy: 0.21132487 -0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.00000000 0.21132487  copy: 0.21132487 0.00000000 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.21132487 0.21132487  copy: 0.21132487 0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::
+DEAL::GL: -0.57735027 -0.57735027 0.57735027  copy: -0.57735027 -0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.70710678 0.70710678  copy: 0.00000000 -0.70710678 0.70710678  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.57735027 -0.57735027 0.57735027  copy: 0.57735027 -0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.39433757 -0.39433757 0.39433757  copy: -0.39433757 -0.39433757 0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.45921582 0.45921582  copy: 0.00000000 -0.45921582 0.45921582  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.39433757 -0.39433757 0.39433757  copy: 0.39433757 -0.39433757 0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 -0.21132487 0.21132487  copy: -0.21132487 -0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 -0.21132487 0.21132487  copy: 0.00000000 -0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 -0.21132487 0.21132487  copy: 0.21132487 -0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.70710678 0.00000000 0.70710678  copy: -0.70710678 0.00000000 0.70710678  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.00000000 1.00000000  copy: 0.00000000 0.00000000 1.00000000  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.70710678 0.00000000 0.70710678  copy: 0.70710678 0.00000000 0.70710678  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.45921582 0.00000000 0.45921582  copy: -0.45921582 0.00000000 0.45921582  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.00000000 0.60566243  copy: 0.00000000 0.00000000 0.60566243  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.45921582 0.00000000 0.45921582  copy: 0.45921582 0.00000000 0.45921582  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.00000000 0.21132487  copy: -0.21132487 0.00000000 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.00000000 0.21132487  copy: 0.00000000 0.00000000 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.00000000 0.21132487  copy: 0.21132487 0.00000000 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.57735027 0.57735027 0.57735027  copy: -0.57735027 0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.70710678 0.70710678  copy: 0.00000000 0.70710678 0.70710678  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.57735027 0.57735027 0.57735027  copy: 0.57735027 0.57735027 0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.39433757 0.39433757 0.39433757  copy: -0.39433757 0.39433757 0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.45921582 0.45921582  copy: 0.00000000 0.45921582 0.45921582  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.39433757 0.39433757 0.39433757  copy: 0.39433757 0.39433757 0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.21132487 0.21132487  copy: -0.21132487 0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.00000000 0.21132487 0.21132487  copy: 0.00000000 0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: 0.21132487 0.21132487 0.21132487  copy: 0.21132487 0.21132487 0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::
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+DEAL::GL: -0.39433757 -0.39433757 -0.39433757  copy: -0.39433757 -0.39433757 -0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 -0.21132487 -0.21132487  copy: -0.21132487 -0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.70710678 0.00000000 -0.70710678  copy: -0.70710678 0.00000000 -0.70710678  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.45921582 0.00000000 -0.45921582  copy: -0.45921582 0.00000000 -0.45921582  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.00000000 -0.21132487  copy: -0.21132487 0.00000000 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.57735027 0.57735027 -0.57735027  copy: -0.57735027 0.57735027 -0.57735027  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.39433757 0.39433757 -0.39433757  copy: -0.39433757 0.39433757 -0.39433757  difference: 0.00000000 0.00000000 0.00000000
+DEAL::GL: -0.21132487 0.21132487 -0.21132487  copy: -0.21132487 0.21132487 -0.21132487  difference: 0.00000000 0.00000000 0.00000000
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