From 8b343d922a40c6b4f531ba9b0efd1a5b9972822e Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Thu, 2 Sep 2010 08:36:09 +0000
Subject: [PATCH] test mixed second derivative
[[Imported from SVN: r6312]]
---
test/unitvectortest.cc | 31 +++++++++++++++++++++++++++++++
1 file changed, 31 insertions(+)
diff --git a/test/unitvectortest.cc b/test/unitvectortest.cc
index e13ac291..26cfe8ac 100644
--- a/test/unitvectortest.cc
+++ b/test/unitvectortest.cc
@@ -23,6 +23,12 @@ double energy(const UnitVector<dim>& a, const FieldVector<double,dim>& b)
return UnitVector<dim>::distance(a,b) * UnitVector<dim>::distance(a,b);
}
+template <int dim>
+double energy(const FieldVector<double,dim>& a, const FieldVector<double,dim>& b)
+{
+ return UnitVector<dim>::distance(a,b) * UnitVector<dim>::distance(a,b);
+}
+
template <int dim>
void testDerivativesOfSquaredDistance(const UnitVector<dim>& a, const UnitVector<dim>& b)
{
@@ -92,6 +98,31 @@ void testDerivativesOfSquaredDistance(const UnitVector<dim>& a, const UnitVector
FieldMatrix<double,dim,dim> d1d2 = UnitVector<dim>::secondDerivativeOfDistanceSquaredWRTFirstAndSecondArgument(a, b);
+ // finite-difference approximation
+ FieldMatrix<double,dim,dim> d1d2_fd;
+
+ for (size_t i=0; i<dim; i++) {
+ for (size_t j=0; j<dim; j++) {
+
+ FieldVector<double,dim> aPlus = a.globalCoordinates();
+ FieldVector<double,dim> aMinus = a.globalCoordinates();
+ aPlus[i] += eps;
+ aMinus[i] -= eps;
+
+ FieldVector<double,dim> bPlus = b.globalCoordinates();
+ FieldVector<double,dim> bMinus = b.globalCoordinates();
+ bPlus[i] += eps;
+ bMinus[i] -= eps;
+
+ d1d2_fd[i][j] = (energy(aPlus,bPlus) + energy(aMinus,bMinus)
+ - energy(aPlus,bMinus) - energy(aMinus,bPlus)) / (4*eps*eps);
+
+ }
+ }
+
+ std::cout << "Analytical:\n" << d1d2 << std::endl;
+ std::cout << "FD :\n" << d1d2_fd << std::endl;
+
/////////////////////////////////////////////////////////////////////////////////////////////
// Test mixed third derivative with respect to first (once) and second (twice) argument
--
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