Add test for 1D mass matrix

diff --git a/tests/base/polynomial_hermite_like_mass_1d.cc b/tests/base/polynomial_hermite_like_mass_1d.cc
new file mode 100644 (file)
index 0000000..ce90b46
--- /dev/null
+++ b/tests/base/polynomial_hermite_like_mass_1d.cc
@@ -0,0 +1,53 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2019 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.
+//
+// ---------------------------------------------------------------------
+
+
+// Check the mass matrix of the HermiteLikeInterpolation
+
+#include <deal.II/base/polynomial.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/lac/full_matrix.h>
+
+#include "../tests.h"
+
+
+int
+main()
+{
+  initlog();
+
+  for (unsigned int degree = 1; degree < 11; ++degree)
+    {
+      auto poly =
+        Polynomials::HermiteLikeInterpolation::generate_complete_basis(degree);
+      QGauss<1>          quad(degree + 1);
+      FullMatrix<double> mat(degree + 1, degree + 1);
+      for (unsigned int i = 0; i < degree + 1; ++i)
+        for (unsigned int j = 0; j < degree + 1; ++j)
+          {
+            double sum = 0;
+            for (unsigned int q = 0; q < quad.size(); ++q)
+              sum += poly[i].value(quad.point(q)[0]) *
+                     poly[j].value(quad.point(q)[0]) * quad.weight(q);
+            if (std::abs(sum) > 1e-15)
+              mat(i, j) = sum;
+          }
+
+      deallog << "Mass matrix degree " << degree << std::endl;
+      mat.print_formatted(deallog.get_file_stream());
+      deallog << std::endl;
+    }
+}

diff --git a/tests/base/polynomial_hermite_like_mass_1d.output b/tests/base/polynomial_hermite_like_mass_1d.output
new file mode 100644 (file)
index 0000000..2c5c01c
--- /dev/null
+++ b/tests/base/polynomial_hermite_like_mass_1d.output
@@ -0,0 +1,86 @@
+
+DEAL::Mass matrix degree 1
+3.333e-01  1.667e-01  
+1.667e-01  3.333e-01  
+DEAL::
+DEAL::Mass matrix degree 2
+2.000e-01  1.000e-01  3.333e-02  
+1.000e-01  1.333e-01  1.000e-01  
+3.333e-02  1.000e-01  2.000e-01  
+DEAL::
+DEAL::Mass matrix degree 3
+8.333e-02             -4.583e-02 4.167e-03  
+           2.881e-01  2.161e-01  -4.583e-02 
+-4.583e-02 2.161e-01  2.881e-01             
+4.167e-03  -4.583e-02            8.333e-02  
+DEAL::
+DEAL::Mass matrix degree 4
+4.762e-02                        2.381e-02  -4.762e-03 
+           1.587e-01  6.349e-02  -7.937e-02 2.381e-02  
+           6.349e-02  4.063e-01  6.349e-02             
+2.381e-02  -7.937e-02 6.349e-02  1.587e-01             
+-4.762e-03 2.381e-02                        4.762e-02  
+DEAL::
+DEAL::Mass matrix degree 5
+3.130e-02             -1.780e-03 3.316e-03  -1.271e-02 3.206e-03  
+           1.054e-01  5.107e-02  -2.741e-02 3.764e-02  -1.271e-02 
+-1.780e-03 5.107e-02  2.975e-01             -2.741e-02 3.316e-03  
+3.316e-03  -2.741e-02            2.975e-01  5.107e-02  -1.780e-03 
+-1.271e-02 3.764e-02  -2.741e-02 5.107e-02  1.054e-01             
+3.206e-03  -1.271e-02 3.316e-03  -1.780e-03            3.130e-02  
+DEAL::
+DEAL::Mass matrix degree 6
+2.233e-02             -2.223e-03 3.502e-03  -2.426e-03 7.296e-03  -2.051e-03 
+           7.610e-02  4.074e-02  -2.505e-02 1.430e-02  -2.038e-02 7.296e-03  
+-2.223e-03 4.074e-02  2.286e-01                        1.430e-02  -2.426e-03 
+3.502e-03  -2.505e-02            2.463e-01             -2.505e-02 3.502e-03  
+-2.426e-03 1.430e-02                        2.286e-01  4.074e-02  -2.223e-03 
+7.296e-03  -2.038e-02 1.430e-02  -2.505e-02 4.074e-02  7.610e-02             
+-2.051e-03 7.296e-03  -2.426e-03 3.502e-03  -2.223e-03            2.233e-02  
+DEAL::
+DEAL::Mass matrix degree 7
+1.681e-02             -2.199e-03 3.288e-03  -2.586e-03 1.620e-03  -4.462e-03 1.334e-03  
+           5.785e-02  3.289e-02  -2.172e-02 1.425e-02  -8.289e-03 1.205e-02  -4.462e-03 
+-2.199e-03 3.289e-02  1.809e-01                                   -8.289e-03 1.620e-03  
+3.288e-03  -2.172e-02            2.054e-01                        1.425e-02  -2.586e-03 
+-2.586e-03 1.425e-02                        2.054e-01             -2.172e-02 3.288e-03  
+1.620e-03  -8.289e-03                                  1.809e-01  3.289e-02  -2.199e-03 
+-4.462e-03 1.205e-02  -8.289e-03 1.425e-02  -2.172e-02 3.289e-02  5.785e-02             
+1.334e-03  -4.462e-03 1.620e-03  -2.586e-03 3.288e-03  -2.199e-03            1.681e-02  
+DEAL::
+DEAL::Mass matrix degree 8
+1.315e-02             -2.024e-03 2.960e-03  -2.486e-03 1.791e-03  -1.090e-03 2.875e-03  -8.936e-04 
+           4.559e-02  2.697e-02  -1.860e-02 1.314e-02  -8.805e-03 5.163e-03  -7.598e-03 2.875e-03  
+-2.024e-03 2.697e-02  1.466e-01                                              5.163e-03  -1.090e-03 
+2.960e-03  -1.860e-02            1.724e-01                                   -8.805e-03 1.791e-03  
+-2.486e-03 1.314e-02                        1.819e-01                        1.314e-02  -2.486e-03 
+1.791e-03  -8.805e-03                                  1.724e-01             -1.860e-02 2.960e-03  
+-1.090e-03 5.163e-03                                              1.466e-01  2.697e-02  -2.024e-03 
+2.875e-03  -7.598e-03 5.163e-03  -8.805e-03 1.314e-02  -1.860e-02 2.697e-02  4.559e-02             
+-8.936e-04 2.875e-03  -1.090e-03 1.791e-03  -2.486e-03 2.960e-03  -2.024e-03            1.315e-02  
+DEAL::
+DEAL::Mass matrix degree 9
+1.059e-02             -1.814e-03 2.622e-03  -2.294e-03 1.781e-03  -1.249e-03 7.511e-04  -1.933e-03 6.168e-04  
+           3.691e-02  2.245e-02  -1.594e-02 1.179e-02  -8.523e-03 5.763e-03  -3.393e-03 5.033e-03  -1.933e-03 
+-1.814e-03 2.245e-02  1.211e-01                                                         -3.393e-03 7.511e-04  
+2.622e-03  -1.594e-02            1.460e-01                                              5.763e-03  -1.249e-03 
+-2.294e-03 1.179e-02                        1.598e-01                                   -8.523e-03 1.781e-03  
+1.781e-03  -8.523e-03                                  1.598e-01                        1.179e-02  -2.294e-03 
+-1.249e-03 5.763e-03                                              1.460e-01             -1.594e-02 2.622e-03  
+7.511e-04  -3.393e-03                                                        1.211e-01  2.245e-02  -1.814e-03 
+-1.933e-03 5.033e-03  -3.393e-03 5.763e-03  -8.523e-03 1.179e-02  -1.594e-02 2.245e-02  3.691e-02             
+6.168e-04  -1.933e-03 7.511e-04  -1.249e-03 1.781e-03  -2.294e-03 2.622e-03  -1.814e-03            1.059e-02  
+DEAL::
+DEAL::Mass matrix degree 10
+8.720e-03             -1.611e-03 2.313e-03  -2.080e-03 1.691e-03  -1.281e-03 8.892e-04  -5.315e-04 1.346e-03  -4.378e-04 
+           3.052e-02  1.894e-02  -1.373e-02 1.048e-02  -7.942e-03 5.800e-03  -3.941e-03 2.325e-03  -3.469e-03 1.346e-03  
+-1.611e-03 1.894e-02  1.016e-01                                                                    2.325e-03  -5.315e-04 
+2.313e-03  -1.373e-02            1.248e-01                                                         -3.941e-03 8.892e-04  
+-2.080e-03 1.048e-02                        1.402e-01                                              5.800e-03  -1.281e-03 
+1.691e-03  -7.942e-03                                  1.455e-01                                   -7.942e-03 1.691e-03  
+-1.281e-03 5.800e-03                                              1.402e-01                        1.048e-02  -2.080e-03 
+8.892e-04  -3.941e-03                                                        1.248e-01             -1.373e-02 2.313e-03  
+-5.315e-04 2.325e-03                                                                    1.016e-01  1.894e-02  -1.611e-03 
+1.346e-03  -3.469e-03 2.325e-03  -3.941e-03 5.800e-03  -7.942e-03 1.048e-02  -1.373e-02 1.894e-02  3.052e-02             
+-4.378e-04 1.346e-03  -5.315e-04 8.892e-04  -1.281e-03 1.691e-03  -2.080e-03 2.313e-03  -1.611e-03            8.720e-03  
+DEAL::