remove trailing whitespace

[[Imported from SVN: r9294]]

dune/gfe/localgeodesicfestiffness.hh

@@ -10,18 +10,18 @@
 
 
 template<class GridView, class LocalFiniteElement, class TargetSpace>
-class LocalGeodesicFEStiffness 
+class LocalGeodesicFEStiffness
 {
     // grid types
     typedef typename GridView::Grid::ctype DT;
     typedef typename TargetSpace::ctype RT;
     typedef typename GridView::template Codim<0>::Entity Entity;
-    
+
     // some other sizes
     enum {gridDim=GridView::dimension};
 
 public:
-    
+
     //! Dimension of a tangent space
     enum { blocksize = TargetSpace::TangentVector::dimension };
 
@@ -50,17 +50,17 @@ public:
                        const LocalFiniteElement& localFiniteElement,
                        const std::vector<TargetSpace>& localSolution) const = 0;
 
-    /** \brief Assemble the element gradient of the energy functional 
+    /** \brief Assemble the element gradient of the energy functional
 
     The default implementation in this class uses a finite difference approximation */
     virtual void assembleGradient(const Entity& element,
                                   const LocalFiniteElement& localFiniteElement,
                                   const std::vector<TargetSpace>& solution,
                                   std::vector<typename TargetSpace::TangentVector>& gradient) const;
-    
+
     // assembled data
     Dune::Matrix<Dune::FieldMatrix<double,blocksize,blocksize> > A_;
-    
+
 };
 
 
@@ -84,18 +84,18 @@ assembleGradient(const Entity& element,
     std::vector<TargetSpace> backwardSolution = localSolution;
 
     for (size_t i=0; i<localSolution.size(); i++) {
-        
+
         // basis vectors of the tangent space of the i-th entry of localSolution
         const Dune::FieldMatrix<double,blocksize,embeddedBlocksize> B = localSolution[i].orthonormalFrame();
 
         for (int j=0; j<blocksize; j++) {
-            
+
             typename TargetSpace::EmbeddedTangentVector forwardCorrection = B[j];
             forwardCorrection *= eps;
-            
+
             typename TargetSpace::EmbeddedTangentVector backwardCorrection = B[j];
             backwardCorrection *= -eps;
-            
+
             forwardSolution[i]  = TargetSpace::exp(localSolution[i], forwardCorrection);
             backwardSolution[i] = TargetSpace::exp(localSolution[i], backwardCorrection);
 
@@ -105,7 +105,7 @@ assembleGradient(const Entity& element,
 
         forwardSolution[i]  = localSolution[i];
         backwardSolution[i] = localSolution[i];
-        
+
     }
 
 }
@@ -129,7 +129,7 @@ assembleHessian(const Entity& element,
     A_ = 0;
 
     const double eps = 1e-4;
-        
+
     std::vector<Dune::FieldMatrix<double,blocksize,embeddedBlocksize> > B(localSolution.size());
     for (size_t i=0; i<B.size(); i++)
         B[i] = localSolution[i].orthonormalFrame();
@@ -137,7 +137,7 @@ assembleHessian(const Entity& element,
     // Precompute negative energy at the current configuration
     // (negative because that is how we need it as part of the 2nd-order fd formula)
     double centerValue   = -energy(element, localFiniteElement, localSolution);
-        
+
     // Precompute energy infinitesimal corrections in the directions of the local basis vectors
     std::vector<Dune::array<double,blocksize> > forwardEnergy(nDofs);
     std::vector<Dune::array<double,blocksize> > backwardEnergy(nDofs);
@@ -149,18 +149,18 @@ assembleHessian(const Entity& element,
             epsXi *= eps;
             Dune::FieldVector<double,embeddedBlocksize> minusEpsXi = epsXi;
             minusEpsXi  *= -1;
-            
+
             std::vector<TargetSpace> forwardSolution  = localSolution;
             std::vector<TargetSpace> backwardSolution = localSolution;
-            
+
             forwardSolution[i]  = TargetSpace::exp(localSolution[i],epsXi);
             backwardSolution[i] = TargetSpace::exp(localSolution[i],minusEpsXi);
-    
+
             forwardEnergy[i][i2]  = energy(element, localFiniteElement, forwardSolution);
             backwardEnergy[i][i2] = energy(element, localFiniteElement, backwardSolution);
-    
+
         }
-        
+
     }
 
     // finite-difference approximation
@@ -174,20 +174,20 @@ assembleHessian(const Entity& element,
 
                     std::vector<TargetSpace> forwardSolutionXiEta  = localSolution;
                     std::vector<TargetSpace> backwardSolutionXiEta  = localSolution;
-            
+
                     Dune::FieldVector<double,embeddedBlocksize> epsXi  = B[i][i2];    epsXi *= eps;
                     Dune::FieldVector<double,embeddedBlocksize> epsEta = B[j][j2];   epsEta *= eps;
-            
+
                     Dune::FieldVector<double,embeddedBlocksize> minusEpsXi  = epsXi;   minusEpsXi  *= -1;
                     Dune::FieldVector<double,embeddedBlocksize> minusEpsEta = epsEta;  minusEpsEta *= -1;
-                        
+
                     if (i==j)
                         forwardSolutionXiEta[i] = TargetSpace::exp(localSolution[i],epsXi+epsEta);
                     else {
                         forwardSolutionXiEta[i] = TargetSpace::exp(localSolution[i],epsXi);
                         forwardSolutionXiEta[j] = TargetSpace::exp(localSolution[j],epsEta);
                     }
-                        
+
                     if (i==j)
                         backwardSolutionXiEta[i] = TargetSpace::exp(localSolution[i],minusEpsXi+minusEpsEta);
                     else {
@@ -197,9 +197,9 @@ assembleHessian(const Entity& element,
 
                     double forwardValue  = energy(element, localFiniteElement, forwardSolutionXiEta) - forwardEnergy[i][i2] - forwardEnergy[j][j2];
                     double backwardValue = energy(element, localFiniteElement, backwardSolutionXiEta) - backwardEnergy[i][i2] - backwardEnergy[j][j2];
-            
+
                     A_[i][j][i2][j2] = A_[j][i][j2][i2] = 0.5 * (forwardValue - 2*centerValue + backwardValue) / (eps*eps);
-                    
+
                 }
             }
         }