Add a test for Bessel function values.

This verifies that the upcoming change produces the same results as the present
implementation.

diff --git a/tests/base/bessel_function_values.cc b/tests/base/bessel_function_values.cc
new file mode 100644 (file)
index 0000000..0a0fd45
--- /dev/null
+++ b/tests/base/bessel_function_values.cc
@@ -0,0 +1,43 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 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.
+//
+// ---------------------------------------------------------------------
+
+
+// Verify that the new C++17 Bessel function produces equivalent output to jn.
+
+
+#include <deal.II/base/function_bessel.h>
+
+#include "../tests.h"
+
+
+int
+main()
+{
+  initlog();
+
+  for (unsigned int order = 0; order < 3; order += 1)
+    for (double wave_n = -4.0; wave_n < 4.0; wave_n += 1.5)
+      for (double x = 1.0; x < 2.0; x += 0.5)
+        for (double y = 2.0; y < 3.0; y += 0.5)
+          {
+            Functions::Bessel1<2> bessel(order, wave_n, Point<2>(x, y));
+
+            const Point<2> new_point(x + 0.1, y + 0.1);
+            deallog << "value at (" << new_point[0] << ", " << new_point[1]
+                    << ") = " << bessel.value(new_point) << std::endl;
+            deallog << "gradient at (" << new_point[0] << ", " << new_point[1]
+                    << ") = " << bessel.gradient(new_point) << std::endl;
+          }
+}

diff --git a/tests/base/bessel_function_values.output b/tests/base/bessel_function_values.output
new file mode 100644 (file)
index 0000000..afd64b9
--- /dev/null
+++ b/tests/base/bessel_function_values.output
@@ -0,0 +1,145 @@
+
+DEAL::value at (1.10000, 2.10000) = 0.921586
+DEAL::gradient at (1.10000, 2.10000) = -0.768424 -0.768424
+DEAL::value at (1.10000, 2.60000) = 0.921586
+DEAL::gradient at (1.10000, 2.60000) = -0.768424 -0.768424
+DEAL::value at (1.60000, 2.10000) = 0.921586
+DEAL::gradient at (1.60000, 2.10000) = -0.768424 -0.768424
+DEAL::value at (1.60000, 2.60000) = 0.921586
+DEAL::gradient at (1.60000, 2.60000) = -0.768424 -0.768424
+DEAL::value at (1.10000, 2.10000) = 0.968993
+DEAL::gradient at (1.10000, 2.10000) = -0.307643 -0.307643
+DEAL::value at (1.10000, 2.60000) = 0.968993
+DEAL::gradient at (1.10000, 2.60000) = -0.307643 -0.307643
+DEAL::value at (1.60000, 2.10000) = 0.968993
+DEAL::gradient at (1.60000, 2.10000) = -0.307643 -0.307643
+DEAL::value at (1.60000, 2.60000) = 0.968993
+DEAL::gradient at (1.60000, 2.60000) = -0.307643 -0.307643
+DEAL::value at (1.10000, 2.10000) = 0.995006
+DEAL::gradient at (1.10000, 2.10000) = -0.0498751 -0.0498751
+DEAL::value at (1.10000, 2.60000) = 0.995006
+DEAL::gradient at (1.10000, 2.60000) = -0.0498751 -0.0498751
+DEAL::value at (1.60000, 2.10000) = 0.995006
+DEAL::gradient at (1.60000, 2.10000) = -0.0498751 -0.0498751
+DEAL::value at (1.60000, 2.60000) = 0.995006
+DEAL::gradient at (1.60000, 2.60000) = -0.0498751 -0.0498751
+DEAL::value at (1.10000, 2.10000) = 0.998750
+DEAL::gradient at (1.10000, 2.10000) = -0.0124922 -0.0124922
+DEAL::value at (1.10000, 2.60000) = 0.998750
+DEAL::gradient at (1.10000, 2.60000) = -0.0124922 -0.0124922
+DEAL::value at (1.60000, 2.10000) = 0.998750
+DEAL::gradient at (1.60000, 2.10000) = -0.0124922 -0.0124922
+DEAL::value at (1.60000, 2.60000) = 0.998750
+DEAL::gradient at (1.60000, 2.60000) = -0.0124922 -0.0124922
+DEAL::value at (1.10000, 2.10000) = 0.980100
+DEAL::gradient at (1.10000, 2.10000) = -0.198007 -0.198007
+DEAL::value at (1.10000, 2.60000) = 0.980100
+DEAL::gradient at (1.10000, 2.60000) = -0.198007 -0.198007
+DEAL::value at (1.60000, 2.10000) = 0.980100
+DEAL::gradient at (1.60000, 2.10000) = -0.198007 -0.198007
+DEAL::value at (1.60000, 2.60000) = 0.980100
+DEAL::gradient at (1.60000, 2.60000) = -0.198007 -0.198007
+DEAL::value at (1.10000, 2.10000) = 0.939682
+DEAL::gradient at (1.10000, 2.10000) = -0.593933 -0.593933
+DEAL::value at (1.10000, 2.60000) = 0.939682
+DEAL::gradient at (1.10000, 2.60000) = -0.593933 -0.593933
+DEAL::value at (1.60000, 2.10000) = 0.939682
+DEAL::gradient at (1.60000, 2.10000) = -0.593933 -0.593933
+DEAL::value at (1.60000, 2.60000) = 0.939682
+DEAL::gradient at (1.60000, 2.60000) = -0.593933 -0.593933
+DEAL::value at (1.10000, 2.10000) = -0.271679
+DEAL::gradient at (1.10000, 2.10000) = -1.24824 -1.24824
+DEAL::value at (1.10000, 2.60000) = -0.271679
+DEAL::gradient at (1.10000, 2.60000) = -1.24824 -1.24824
+DEAL::value at (1.60000, 2.10000) = -0.271679
+DEAL::gradient at (1.60000, 2.10000) = -1.24824 -1.24824
+DEAL::value at (1.60000, 2.60000) = -0.271679
+DEAL::gradient at (1.60000, 2.60000) = -1.24824 -1.24824
+DEAL::value at (1.10000, 2.10000) = -0.174029
+DEAL::gradient at (1.10000, 2.10000) = -0.842810 -0.842810
+DEAL::value at (1.10000, 2.60000) = -0.174029
+DEAL::gradient at (1.10000, 2.60000) = -0.842810 -0.842810
+DEAL::value at (1.60000, 2.10000) = -0.174029
+DEAL::gradient at (1.60000, 2.10000) = -0.842810 -0.842810
+DEAL::value at (1.60000, 2.60000) = -0.174029
+DEAL::gradient at (1.60000, 2.60000) = -0.842810 -0.842810
+DEAL::value at (1.10000, 2.10000) = -0.0705340
+DEAL::gradient at (1.10000, 2.10000) = -0.350905 -0.350905
+DEAL::value at (1.10000, 2.60000) = -0.0705340
+DEAL::gradient at (1.10000, 2.60000) = -0.350905 -0.350905
+DEAL::value at (1.60000, 2.10000) = -0.0705340
+DEAL::gradient at (1.60000, 2.10000) = -0.350905 -0.350905
+DEAL::value at (1.60000, 2.60000) = -0.0705340
+DEAL::gradient at (1.60000, 2.60000) = -0.350905 -0.350905
+DEAL::value at (1.10000, 2.10000) = 0.0353332
+DEAL::gradient at (1.10000, 2.10000) = 0.176445 0.176445
+DEAL::value at (1.10000, 2.60000) = 0.0353332
+DEAL::gradient at (1.10000, 2.60000) = 0.176445 0.176445
+DEAL::value at (1.60000, 2.10000) = 0.0353332
+DEAL::gradient at (1.60000, 2.10000) = 0.176445 0.176445
+DEAL::value at (1.60000, 2.60000) = 0.0353332
+DEAL::gradient at (1.60000, 2.60000) = 0.176445 0.176445
+DEAL::value at (1.10000, 2.10000) = 0.140012
+DEAL::gradient at (1.10000, 2.10000) = 0.686011 0.686011
+DEAL::value at (1.10000, 2.60000) = 0.140012
+DEAL::gradient at (1.10000, 2.60000) = 0.686011 0.686011
+DEAL::value at (1.60000, 2.10000) = 0.140012
+DEAL::gradient at (1.60000, 2.10000) = 0.686011 0.686011
+DEAL::value at (1.60000, 2.60000) = 0.140012
+DEAL::gradient at (1.60000, 2.60000) = 0.686011 0.686011
+DEAL::value at (1.10000, 2.10000) = 0.239985
+DEAL::gradient at (1.10000, 2.10000) = 1.12567 1.12567
+DEAL::value at (1.10000, 2.60000) = 0.239985
+DEAL::gradient at (1.10000, 2.60000) = 1.12567 1.12567
+DEAL::value at (1.60000, 2.10000) = 0.239985
+DEAL::gradient at (1.60000, 2.10000) = 1.12567 1.12567
+DEAL::value at (1.60000, 2.60000) = 0.239985
+DEAL::gradient at (1.60000, 2.60000) = 1.12567 1.12567
+DEAL::value at (1.10000, 2.10000) = 0.0389439
+DEAL::gradient at (1.10000, 2.10000) = 0.378984 0.378984
+DEAL::value at (1.10000, 2.60000) = 0.0389439
+DEAL::gradient at (1.10000, 2.60000) = 0.378984 0.378984
+DEAL::value at (1.60000, 2.10000) = 0.0389439
+DEAL::gradient at (1.60000, 2.10000) = 0.378984 0.378984
+DEAL::value at (1.60000, 2.60000) = 0.0389439
+DEAL::gradient at (1.60000, 2.60000) = 0.378984 0.378984
+DEAL::value at (1.10000, 2.10000) = 0.0154629
+DEAL::gradient at (1.10000, 2.10000) = 0.153014 0.153014
+DEAL::value at (1.10000, 2.60000) = 0.0154629
+DEAL::gradient at (1.10000, 2.60000) = 0.153014 0.153014
+DEAL::value at (1.60000, 2.10000) = 0.0154629
+DEAL::gradient at (1.60000, 2.10000) = 0.153014 0.153014
+DEAL::value at (1.60000, 2.60000) = 0.0154629
+DEAL::gradient at (1.60000, 2.60000) = 0.153014 0.153014
+DEAL::value at (1.10000, 2.10000) = 0.00249584
+DEAL::gradient at (1.10000, 2.10000) = 0.0249167 0.0249167
+DEAL::value at (1.10000, 2.60000) = 0.00249584
+DEAL::gradient at (1.10000, 2.60000) = 0.0249167 0.0249167
+DEAL::value at (1.60000, 2.10000) = 0.00249584
+DEAL::gradient at (1.60000, 2.10000) = 0.0249167 0.0249167
+DEAL::value at (1.60000, 2.60000) = 0.00249584
+DEAL::gradient at (1.60000, 2.60000) = 0.0249167 0.0249167
+DEAL::value at (1.10000, 2.10000) = 0.000624740
+DEAL::gradient at (1.10000, 2.10000) = 0.00624479 0.00624479
+DEAL::value at (1.10000, 2.60000) = 0.000624740
+DEAL::gradient at (1.10000, 2.60000) = 0.00624479 0.00624479
+DEAL::value at (1.60000, 2.10000) = 0.000624740
+DEAL::gradient at (1.60000, 2.10000) = 0.00624479 0.00624479
+DEAL::value at (1.60000, 2.60000) = 0.000624740
+DEAL::gradient at (1.60000, 2.60000) = 0.00624479 0.00624479
+DEAL::value at (1.10000, 2.10000) = 0.00993350
+DEAL::gradient at (1.10000, 2.10000) = 0.0986717 0.0986717
+DEAL::value at (1.10000, 2.60000) = 0.00993350
+DEAL::gradient at (1.10000, 2.60000) = 0.0986717 0.0986717
+DEAL::value at (1.60000, 2.10000) = 0.00993350
+DEAL::gradient at (1.60000, 2.10000) = 0.0986717 0.0986717
+DEAL::value at (1.60000, 2.60000) = 0.00993350
+DEAL::gradient at (1.60000, 2.60000) = 0.0986717 0.0986717
+DEAL::value at (1.10000, 2.10000) = 0.0300045
+DEAL::gradient at (1.10000, 2.10000) = 0.293888 0.293888
+DEAL::value at (1.10000, 2.60000) = 0.0300045
+DEAL::gradient at (1.10000, 2.60000) = 0.293888 0.293888
+DEAL::value at (1.60000, 2.10000) = 0.0300045
+DEAL::gradient at (1.60000, 2.10000) = 0.293888 0.293888
+DEAL::value at (1.60000, 2.60000) = 0.0300045
+DEAL::gradient at (1.60000, 2.60000) = 0.293888 0.293888