From: Jean-Paul Pelteret <jppelteret@gmail.com>
Date: Thu, 16 Nov 2017 16:13:43 +0000 (+0100)
Subject: Test to show that a zero-valued function can have non-zero derivatives.
X-Git-Tag: v9.0.0-rc1~765^2
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=d38352beebe4d1ddd6c551a78233598a2fca5c5e;p=dealii.git

Test to show that a zero-valued function can have non-zero derivatives.
---

diff --git a/tests/sacado/zero_val_nonzero_deriv_01.cc b/tests/sacado/zero_val_nonzero_deriv_01.cc
new file mode 100644
index 0000000000..f82ff75ef6
--- /dev/null
+++ b/tests/sacado/zero_val_nonzero_deriv_01.cc
@@ -0,0 +1,89 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2017 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 the computation of the first derivatives of a function with zero
+// input can have a non-zero first derivative.
+
+
+#include "../tests.h"
+
+#include <deal.II/grid/tria.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/fe_values_extractors.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/lac/vector.h>
+
+#include <deal.II/differentiation/ad.h>
+#include <Sacado.hpp>
+
+int main()
+{
+  initlog();
+
+  const unsigned int dim = 2;
+  Triangulation<dim> triangulation;
+  FE_Q<dim>          fe (1);
+  QGauss<dim>        quadrature_formula(2);
+  DoFHandler<dim>    dof_handler (triangulation);
+  Vector<double>     zero_solution;
+
+  FEValues<dim> fe_values (fe, quadrature_formula,
+                           update_values | update_gradients | update_JxW_values);
+
+  GridGenerator::hyper_cube (triangulation, -1, 1);
+  dof_handler.distribute_dofs (fe);
+  zero_solution.reinit (dof_handler.n_dofs());
+
+  const FEValuesExtractors::Scalar extractor_sclr(0);
+
+  typedef Sacado::Fad::DFad<double> ad_type;
+  DoFHandler<dim>::active_cell_iterator cell = dof_handler.begin_active();
+  DoFHandler<dim>::active_cell_iterator endc = dof_handler.end();
+  for (; cell!=endc; ++cell)
+    {
+      fe_values.reinit (cell);
+
+      // Extract (zero'd) DoF values
+      Vector<double> local_dof_values(cell->get_fe().dofs_per_cell);
+      cell->get_dof_values(zero_solution, local_dof_values);
+
+      // Configure AD-equivalent DoF values. These
+      // are the independent variables "x".
+      std::vector<ad_type> local_ad_dof_values (fe.n_dofs_per_cell());
+      for (unsigned int i=0; i<fe.n_dofs_per_cell(); ++i)
+        local_ad_dof_values[i] = ad_type(fe.n_dofs_per_cell(), i, local_dof_values[i]);
+
+      // Get solution values while tracking the influence
+      // that perturbing the DoF values may have on the
+      // derivative of the dependent variable "f(x)".
+      std::vector<ad_type> local_qp_soln_values_ad (fe.n_dofs_per_cell());
+      fe_values[extractor_sclr].get_function_values_from_local_dof_values(local_ad_dof_values,local_qp_soln_values_ad);
+
+      // Compute the dependent variable "f(x)".
+      ad_type f_x = 0.0;
+      for (unsigned int i=0; i<fe.n_dofs_per_cell(); ++i)
+        f_x += local_qp_soln_values_ad[i];
+
+      deallog << "f(x): " << f_x.val() << std::endl;
+      for (unsigned int i=0; i<fe.n_dofs_per_cell(); ++i)
+        deallog << "df/dx_" << i << ": " << f_x.dx(i) << std::endl;
+
+    }
+
+  deallog << "OK" << std::endl;
+}
diff --git a/tests/sacado/zero_val_nonzero_deriv_01.output b/tests/sacado/zero_val_nonzero_deriv_01.output
new file mode 100644
index 0000000000..57628a0f59
--- /dev/null
+++ b/tests/sacado/zero_val_nonzero_deriv_01.output
@@ -0,0 +1,7 @@
+
+DEAL::f(x): 0.00000
+DEAL::df/dx_0: 1.00000
+DEAL::df/dx_1: 1.00000
+DEAL::df/dx_2: 1.00000
+DEAL::df/dx_3: 1.00000
+DEAL::OK