From 29b23acf1f940c51765e421357343b549b0dc4c7 Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Thu, 14 Oct 2010 13:10:43 +0000
Subject: [PATCH] add mixed derivatives of the squared distance
[[Imported from SVN: r6426]]
---
dune/gfe/realtuple.hh | 22 ++++++++++++++++++++++
1 file changed, 22 insertions(+)
diff --git a/dune/gfe/realtuple.hh b/dune/gfe/realtuple.hh
index c4abeed2..fc426780 100644
--- a/dune/gfe/realtuple.hh
+++ b/dune/gfe/realtuple.hh
@@ -86,6 +86,28 @@ public:
return result;
}
+ /** \brief Compute the mixed second derivate \partial d^2 / \partial da db
+
+ Unlike the distance itself the squared distance is differentiable at zero
+ */
+ static Dune::FieldMatrix<double,N,N> secondDerivativeOfDistanceSquaredWRTFirstAndSecondArgument(const RealTuple& a, const RealTuple& b) {
+
+ Dune::FieldMatrix<double,N,N> result;
+ for (int i=0; i<N; i++)
+ for (int j=0; j<N; j++)
+ result[i][j] = -2*(i==j);
+
+ return result;
+ }
+
+ /** \brief Compute the mixed third derivative \partial d^3 / \partial da db^2
+
+ The result is the constant zero-tensor.
+ */
+ static Tensor3<double,N,N,N> thirdDerivativeOfDistanceSquaredWRTFirst1AndSecond2Argument(const RealTuple& a, const RealTuple& b) {
+ return Tensor3<double,N,N,N>(0);
+ }
+
/** \brief Project tangent vector of R^n onto the tangent space */
EmbeddedTangentVector projectOntoTangentSpace(const EmbeddedTangentVector& v) const {
return v;
--
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