From 218437027429af8846991b823b1e92c7db22eb26 Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Thu, 3 Jan 2013 09:38:06 +0000
Subject: [PATCH] Move second derivative of F wrt q to a separate method
[[Imported from SVN: r9095]]
---
dune/gfe/hyperbolichalfspacepoint.hh | 134 ++++++++++-----------------
1 file changed, 47 insertions(+), 87 deletions(-)
diff --git a/dune/gfe/hyperbolichalfspacepoint.hh b/dune/gfe/hyperbolichalfspacepoint.hh
index c3919be7..8239f157 100644
--- a/dune/gfe/hyperbolichalfspacepoint.hh
+++ b/dune/gfe/hyperbolichalfspacepoint.hh
@@ -78,6 +78,48 @@ class HyperbolicHalfspacePoint
return result;
}
+ /** \brief Compute second derivative of $F(p,q) = 1 + ||p-q||^2 / 2p_nq_n with respect to q
+ \param[in] diffNormSquared Expected to be ||p-q||^2, taken from the caller for efficiency reasons
+ */
+ static Dune::FieldMatrix<T,N,N> computeDFdqdq(const HyperbolicHalfspacePoint& a, const HyperbolicHalfspacePoint& b, const T& diffNormSquared)
+ {
+ // abbreviate notation
+ const Dune::FieldVector<T,N>& p = a.data_;
+ const Dune::FieldVector<T,N>& q = b.data_;
+
+ Dune::FieldMatrix<T,N,N> dFdqdq;
+
+ for (size_t i=0; i<N; i++) {
+
+ for (size_t j=0; j<N; j++) {
+
+ if (i!=N-1 and j!=N-1) {
+
+ dFdqdq[i][j] = (i==j) / (p[N-1]*q[N-1]);
+
+ } else if (i!=N-1 and j==N-1) {
+
+ dFdqdq[i][j] = (p[i] - q[i]) / (p[N-1]*q[N-1]*q[N-1]);
+
+ } else if (i!=N-1 and j==N-1) {
+
+ dFdqdq[i][j] = (p[j] - q[j]) / (p[N-1]*q[N-1]*q[N-1]);
+
+ } else if (i==N-1 and j==N-1) {
+
+ dFdqdq[i][j] = 1/(q[N-1]*q[N-1]) + (p[N-1]-q[N-1]) / (p[N-1]*q[N-1]*q[N-1]) + diffNormSquared / (p[N-1]*q[N-1]*q[N-1]*q[N-1]);
+
+ }
+
+ }
+
+ }
+
+ return dFdqdq;
+ }
+
+
+
public:
/** \brief The type used for coordinates */
@@ -191,46 +233,16 @@ public:
*/
static Dune::FieldMatrix<T,N,N> secondDerivativeOfDistanceSquaredWRTSecondArgument(const HyperbolicHalfspacePoint& a, const HyperbolicHalfspacePoint& b) {
- // abbreviate notation
- const Dune::FieldVector<T,N>& p = a.data_;
- const Dune::FieldVector<T,N>& q = b.data_;
-
- T diffNormSquared = (p-q).two_norm2();
+ T diffNormSquared = (a.data_-b.data_).two_norm2();
// Compute first derivative of F
Dune::FieldVector<T,N> dFdq = computeDFdq(a,b,diffNormSquared);
// Compute second derivatives of F
- Dune::FieldMatrix<T,N,N> dFdqdq;
-
- for (size_t i=0; i<N; i++) {
-
- for (size_t j=0; j<N; j++) {
-
- if (i!=N-1 and j!=N-1) {
-
- dFdqdq[i][j] = (i==j) / (p[N-1]*q[N-1]);
-
- } else if (i!=N-1 and j==N-1) {
-
- dFdqdq[i][j] = (p[i] - q[i]) / (p[N-1]*q[N-1]*q[N-1]);
-
- } else if (i!=N-1 and j==N-1) {
-
- dFdqdq[i][j] = (p[j] - q[j]) / (p[N-1]*q[N-1]*q[N-1]);
-
- } else if (i==N-1 and j==N-1) {
-
- dFdqdq[i][j] = 1/(q[N-1]*q[N-1]) + (p[N-1]-q[N-1]) / (p[N-1]*q[N-1]*q[N-1]) + diffNormSquared / (p[N-1]*q[N-1]*q[N-1]*q[N-1]);
-
- }
-
- }
-
- }
+ Dune::FieldMatrix<T,N,N> dFdqdq = computeDFdqdq(a,b,diffNormSquared);
//
- T x = 1 + diffNormSquared/ (2*p[N-1]*q[N-1]);
+ T x = 1 + diffNormSquared/ (2*a.data_[N-1]*b.data_[N-1]);
T alphaPrime = derivativeOfArcCosHSquared(x);
T alphaPrimePrime = secondDerivativeOfArcCosHSquared(x);
@@ -320,33 +332,7 @@ public:
Dune::FieldVector<T,N> dFdq = computeDFdq(a,b,diffNormSquared);
// Compute second derivatives of F
- Dune::FieldMatrix<T,N,N> dFdqdq;
-
- for (size_t i=0; i<N; i++) {
-
- for (size_t j=0; j<N; j++) {
-
- if (i!=N-1 and j!=N-1) {
-
- dFdqdq[i][j] = (i==j) / (p[N-1]*q[N-1]);
-
- } else if (i!=N-1 and j==N-1) {
-
- dFdqdq[i][j] = (p[i] - q[i]) / (p[N-1]*q[N-1]*q[N-1]);
-
- } else if (i!=N-1 and j==N-1) {
-
- dFdqdq[i][j] = (p[j] - q[j]) / (p[N-1]*q[N-1]*q[N-1]);
-
- } else if (i==N-1 and j==N-1) {
-
- dFdqdq[i][j] = 1/(q[N-1]*q[N-1]) + (p[N-1]-q[N-1]) / (p[N-1]*q[N-1]*q[N-1]) + diffNormSquared / (p[N-1]*q[N-1]*q[N-1]*q[N-1]);
-
- }
-
- }
-
- }
+ Dune::FieldMatrix<T,N,N> dFdqdq = computeDFdqdq(a,b,diffNormSquared);
// Compute third derivatives of F
Tensor3<T,N,N,N> dFdqdqdq;
@@ -434,33 +420,7 @@ public:
Dune::FieldVector<T,N> dFdq = computeDFdq(a,b,diffNormSquared);
// Compute second derivatives of F
- Dune::FieldMatrix<T,N,N> dFdqdq;
-
- for (size_t i=0; i<N; i++) {
-
- for (size_t j=0; j<N; j++) {
-
- if (i!=N-1 and j!=N-1) {
-
- dFdqdq[i][j] = (i==j) / (p[N-1]*q[N-1]);
-
- } else if (i!=N-1 and j==N-1) {
-
- dFdqdq[i][j] = (p[i] - q[i]) / (p[N-1]*q[N-1]*q[N-1]);
-
- } else if (i!=N-1 and j==N-1) {
-
- dFdqdq[i][j] = (p[j] - q[j]) / (p[N-1]*q[N-1]*q[N-1]);
-
- } else if (i==N-1 and j==N-1) {
-
- dFdqdq[i][j] = 1/(q[N-1]*q[N-1]) + (p[N-1]-q[N-1]) / (p[N-1]*q[N-1]*q[N-1]) + diffNormSquared / (p[N-1]*q[N-1]*q[N-1]*q[N-1]);
-
- }
-
- }
-
- }
+ Dune::FieldMatrix<T,N,N> dFdqdq = computeDFdqdq(a,b,diffNormSquared);
Dune::FieldMatrix<T,N,N> dFdpdq;
--
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