From edb3e93c3110e3d4d54fc46d0c697754c4ca29c7 Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Thu, 3 Jan 2013 09:38:03 +0000
Subject: [PATCH] remove unused derivatives of arccos squared
[[Imported from SVN: r9091]]
---
dune/gfe/hyperbolichalfspacepoint.hh | 35 ----------------------------
1 file changed, 35 deletions(-)
diff --git a/dune/gfe/hyperbolichalfspacepoint.hh b/dune/gfe/hyperbolichalfspacepoint.hh
index 2db09578..c6302d53 100644
--- a/dune/gfe/hyperbolichalfspacepoint.hh
+++ b/dune/gfe/hyperbolichalfspacepoint.hh
@@ -19,17 +19,6 @@ class HyperbolicHalfspacePoint
{
dune_static_assert(N>=2, "A hyperbolic half-space needs to be at least two-dimensional!");
- /** \brief Compute the derivative of arccos^2 without getting unstable for x close to 1 */
- static T derivativeOfArcCosSquared(const T& x) {
- const T eps = 1e-4;
- if (x > 1-eps) { // regular expression is unstable, use the series expansion instead
- return -2 + 2*(x-1)/3 - 4/15*(x-1)*(x-1);
- } else if (x < -1+eps) { // The function is not differentiable
- DUNE_THROW(Dune::Exception, "arccos^2 is not differentiable at x==-1!");
- } else
- return -2*std::acos(x) / std::sqrt(1-x*x);
- }
-
/** \brief Compute the derivative of arccosh^2 without getting unstable for x close to 1 */
static T derivativeOfArcCosHSquared(const T& x) {
const T eps = 1e-4;
@@ -39,17 +28,6 @@ class HyperbolicHalfspacePoint
return 2*std::acosh(x) / std::sqrt(x*x-1);
}
- /** \brief Compute the second derivative of arccos^2 without getting unstable for x close to 1 */
- static T secondDerivativeOfArcCosSquared(const T& x) {
- const T eps = 1e-4;
- if (x > 1-eps) { // regular expression is unstable, use the series expansion instead
- return 2.0/3 - 8*(x-1)/15;
- } else if (x < -1+eps) { // The function is not differentiable
- DUNE_THROW(Dune::Exception, "arccos^2 is not differentiable at x==-1!");
- } else
- return 2/(1-x*x) - 2*x*std::acos(x) / std::pow(1-x*x,1.5);
- }
-
/** \brief Compute the second derivative of arccosh^2 without getting unstable for x close to 1 */
static T secondDerivativeOfArcCosHSquared(const T& x) {
const T eps = 1e-4;
@@ -59,19 +37,6 @@ class HyperbolicHalfspacePoint
return 2/(x*x-1) - 2*x*std::acosh(x) / std::pow(x*x-1,1.5);
}
- /** \brief Compute the third derivative of arccos^2 without getting unstable for x close to 1 */
- static T thirdDerivativeOfArcCosSquared(const T& x) {
- const T eps = 1e-4;
- if (x > 1-eps) { // regular expression is unstable, use the series expansion instead
- return -8.0/15 + 24*(x-1)/35;
- } else if (x < -1+eps) { // The function is not differentiable
- DUNE_THROW(Dune::Exception, "arccos^2 is not differentiable at x==-1!");
- } else {
- T d = 1-x*x;
- return 6*x/(d*d) - 6*x*x*std::acos(x)/(d*d*std::sqrt(d)) - 2*std::acos(x)/(d*std::sqrt(d));
- }
- }
-
/** \brief Compute the third derivative of arccos^2 without getting unstable for x close to 1 */
static T thirdDerivativeOfArcCosHSquared(const T& x) {
const T eps = 1e-4;
--
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