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  • osander/dune-gfe
  • lnebel/dune-gfe
  • spraetor/dune-gfe
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dune/gfe/riemanniantrsolver.cc
View file @ 48b9358e
......@@ -27,7 +27,7 @@
#include <dune/gfe/parallel/vectorcommunicator.hh>
template <class Basis, class TargetSpace, class Assembler>
void RiemannianTrustRegionSolver<Basis, TargetSpace, Assembler>::
void Dune::GFE::RiemannianTrustRegionSolver<Basis, TargetSpace, Assembler>::
setup(const GridType& grid,
const Assembler* assembler,
const SolutionType& x,
......@@ -36,7 +36,7 @@ setup(const GridType& grid,
{
if(parameterSet.get("norm", "infinity") == "infinity")
normType_ = ErrorNormType::infinity;
else if(parameterSet.get("norm", "infinity") == "H1-Semi")
else if(parameterSet.get("norm", "infinity") == "H1semi")
normType_ = ErrorNormType::H1semi;
else
DUNE_THROW(Dune::Exception, "Unknown norm type for stopping criterion!");
......@@ -66,7 +66,7 @@ setup(const GridType& grid,
}
template <class Basis, class TargetSpace, class Assembler>
void RiemannianTrustRegionSolver<Basis,TargetSpace,Assembler>::
void Dune::GFE::RiemannianTrustRegionSolver<Basis,TargetSpace,Assembler>::
setup(const GridType& grid,
const Assembler* assembler,
const SolutionType& x,
......@@ -121,11 +121,11 @@ setup(const GridType& grid,
// Hack: the two-norm may not scale all that well, but it is fast!
auto baseNorm = std::make_shared<TwoNorm<CorrectionType> >();
auto baseSolver = std::make_shared<::LoopSolver<CorrectionType> >(baseSolverStep,
baseIterations,
baseTolerance,
baseNorm,
Solver::QUIET);
auto baseSolver = std::make_shared<Solvers::LoopSolver<CorrectionType> >(baseSolverStep,
baseIterations,
baseTolerance,
baseNorm,
Solver::QUIET);
#endif
#if HAVE_MPI
......@@ -179,11 +179,11 @@ setup(const GridType& grid,
#endif
h1SemiNorm_ = std::make_shared<H1SemiNorm<CorrectionType> >(A);
innerSolver_ = std::make_shared<::LoopSolver<CorrectionType> >(mmgStep,
innerIterations_,
innerTolerance_,
h1SemiNorm_,
Solver::QUIET);
innerSolver_ = std::make_shared<Solvers::LoopSolver<CorrectionType> >(mmgStep,
innerIterations_,
innerTolerance_,
h1SemiNorm_,
Solver::QUIET);
// //////////////////////////////////////////////////////////////////////////////////////
// Assemble a mass matrix to create a norm that's equivalent to the L2-norm
......@@ -204,8 +204,8 @@ setup(const GridType& grid,
// Write all intermediate solutions, if requested
if (instrumented_
&& dynamic_cast<IterativeSolver<CorrectionType>*>(innerSolver_.get()))
dynamic_cast<IterativeSolver<CorrectionType>*>(innerSolver_.get())->historyBuffer_ = instrumentedPath_ + "/mgHistory";
&& dynamic_cast<Solvers::IterativeSolver<CorrectionType>*>(innerSolver_.get()))
dynamic_cast<Solvers::IterativeSolver<CorrectionType>*>(innerSolver_.get())->historyBuffer_ = instrumentedPath_ + "/mgHistory";
// ////////////////////////////////////////////////////////////
// Create Hessian matrix and its occupation structure
......@@ -248,7 +248,7 @@ setup(const GridType& grid,
#if HAVE_MPI
// If we are on more than 1 processors, join all local transfer matrices on rank 0,
// and construct a single global transfer operator there.
typedef Dune::GlobalP1Mapper<Dune::Functions::LagrangeBasis<typename Basis::GridView,1> > GlobalLeafP1Mapper;
typedef GFE::GlobalP1Mapper<Dune::Functions::LagrangeBasis<typename Basis::GridView,1> > GlobalLeafP1Mapper;
GlobalLeafP1Mapper p1Index(grid_->leafGridView());
typedef Dune::MultipleCodimMultipleGeomTypeMapper<typename GridType::LeafGridView> LeafP1LocalMapper;
......@@ -282,7 +282,7 @@ setup(const GridType& grid,
// If we are on more than 1 processors, join all local transfer matrices on rank 0,
// and construct a single global transfer operator there.
typedef Dune::Functions::LagrangeBasis<typename GridType::LevelGridView, 1> FEBasis;
typedef Dune::GlobalP1Mapper<FEBasis> GlobalLevelP1Mapper;
typedef GFE::GlobalP1Mapper<FEBasis> GlobalLevelP1Mapper;
GlobalLevelP1Mapper fineGUIndex(grid_->levelGridView(i+1));
GlobalLevelP1Mapper coarseGUIndex(grid_->levelGridView(i));
......@@ -328,15 +328,15 @@ setup(const GridType& grid,
template <class Basis, class TargetSpace, class Assembler>
void RiemannianTrustRegionSolver<Basis,TargetSpace,Assembler>::solve()
void Dune::GFE::RiemannianTrustRegionSolver<Basis,TargetSpace,Assembler>::solve()
{
int rank = grid_->comm().rank();
MonotoneMGStep<MatrixType,CorrectionType>* mgStep = nullptr; // Non-shared pointer -- the innerSolver keeps the ownership
// if the inner solver is a monotone multigrid set up a max-norm trust-region
if (dynamic_cast<LoopSolver<CorrectionType>*>(innerSolver_.get())) {
auto loopSolver = std::dynamic_pointer_cast<LoopSolver<CorrectionType> >(innerSolver_);
if (dynamic_cast<Solvers::LoopSolver<CorrectionType>*>(innerSolver_.get())) {
auto loopSolver = std::dynamic_pointer_cast<Solvers::LoopSolver<CorrectionType> >(innerSolver_);
mgStep = dynamic_cast<MonotoneMGStep<MatrixType,CorrectionType>*>(&loopSolver->getIterationStep());
}
......
dune/gfe/riemanniantrsolver.hh
View file @ 48b9358e
......@@ -20,164 +20,169 @@
#include <dune/gfe/parallel/mapperfactory.hh>
/** \brief Riemannian trust-region solver for geodesic finite-element problems */
template <class Basis, class TargetSpace, class Assembler = GeodesicFEAssembler<Basis,TargetSpace> >
class RiemannianTrustRegionSolver
: public IterativeSolver<std::vector<TargetSpace>,
Dune::BitSetVector<TargetSpace::TangentVector::dimension> >
namespace Dune::GFE
{
typedef typename Basis::GridView::Grid GridType;
const static int blocksize = TargetSpace::TangentVector::dimension;
const static int gridDim = GridType::dimension;
// Centralize the field type here
typedef double field_type;
// Some types that I need
typedef Dune::BCRSMatrix<Dune::FieldMatrix<field_type, blocksize, blocksize> > MatrixType;
typedef Dune::BlockVector<Dune::FieldVector<field_type, blocksize> > CorrectionType;
typedef std::vector<TargetSpace> SolutionType;
#if HAVE_MPI
typedef typename Dune::GFE::MapperFactory<Basis>::GlobalMapper GlobalMapper;
typedef typename Dune::GFE::MapperFactory<Basis>::LocalMapper LocalMapper;
#endif
/** \brief Records information about the last run of the RiemannianTrustRegionSolver
*
* This is used primarily for unit testing.
*/
struct Statistics
/** \brief Riemannian trust-region solver for geodesic finite-element problems */
template <class Basis, class TargetSpace, class Assembler = GeodesicFEAssembler<Basis,TargetSpace> >
class RiemannianTrustRegionSolver
: public ::IterativeSolver<std::vector<TargetSpace>,
Dune::BitSetVector<TargetSpace::TangentVector::dimension> >
{
std::size_t finalIteration;
typedef typename Basis::GridView::Grid GridType;
field_type finalEnergy;
};
const static int blocksize = TargetSpace::TangentVector::dimension;
public:
const static int gridDim = GridType::dimension;
RiemannianTrustRegionSolver()
: IterativeSolver<std::vector<TargetSpace>, Dune::BitSetVector<blocksize> >(0,100,NumProc::FULL),
hessianMatrix_(nullptr), h1SemiNorm_(NULL)
{
std::fill(scaling_.begin(), scaling_.end(), 1.0);
}
/** \brief Set up the solver using a monotone multigrid method as the inner solver */
void setup(const GridType& grid,
const Assembler* assembler,
const SolutionType& x,
const Dune::BitSetVector<blocksize>& dirichletNodes,
double tolerance,
int maxTrustRegionSteps,
double initialTrustRegionRadius,
int multigridIterations,
double mgTolerance,
int mu,
int nu1,
int nu2,
int baseIterations,
double baseTolerance,
bool instrumented);
/** \brief Set up the solver using a monotone multigrid method as the inner solver */
void setup(const GridType& grid,
const Assembler* assembler,
const SolutionType& x,
const Dune::BitSetVector<blocksize>& dirichletNodes,
const Dune::ParameterTree& parameterSet);
void setScaling(const Dune::FieldVector<double,blocksize>& scaling)
{
scaling_ = scaling;
}
// Centralize the field type here
typedef double field_type;
void setIgnoreNodes(const Dune::BitSetVector<blocksize>& ignoreNodes)
{
ignoreNodes_ = &ignoreNodes;
std::shared_ptr<LoopSolver<CorrectionType> > loopSolver = std::dynamic_pointer_cast<LoopSolver<CorrectionType> >(innerSolver_);
assert(loopSolver);
loopSolver->iterationStep_->ignoreNodes_ = ignoreNodes_;
}
void solve();
[[deprecated]]
void setInitialSolution(const SolutionType& x) {
x_ = x;
}
void setInitialIterate(const SolutionType& x) {
x_ = x;
}
SolutionType getSol() const {return x_;}
// Some types that I need
typedef Dune::BCRSMatrix<Dune::FieldMatrix<field_type, blocksize, blocksize> > MatrixType;
typedef Dune::BlockVector<Dune::FieldVector<field_type, blocksize> > CorrectionType;
typedef std::vector<TargetSpace> SolutionType;
const Statistics& getStatistics() const {return statistics_;}
#if HAVE_MPI
typedef typename Dune::GFE::MapperFactory<Basis>::GlobalMapper GlobalMapper;
typedef typename Dune::GFE::MapperFactory<Basis>::LocalMapper LocalMapper;
#endif
protected:
/** \brief Records information about the last run of the RiemannianTrustRegionSolver
*
* This is used primarily for unit testing.
*/
struct Statistics
{
std::size_t finalIteration;
field_type finalEnergy;
};
public:
RiemannianTrustRegionSolver()
: ::IterativeSolver<std::vector<TargetSpace>, Dune::BitSetVector<blocksize> >(0,100,NumProc::FULL),
hessianMatrix_(nullptr), h1SemiNorm_(NULL)
{
std::fill(scaling_.begin(), scaling_.end(), 1.0);
}
/** \brief Set up the solver using a monotone multigrid method as the inner solver */
void setup(const GridType& grid,
const Assembler* assembler,
const SolutionType& x,
const Dune::BitSetVector<blocksize>& dirichletNodes,
double tolerance,
int maxTrustRegionSteps,
double initialTrustRegionRadius,
int multigridIterations,
double mgTolerance,
int mu,
int nu1,
int nu2,
int baseIterations,
double baseTolerance,
bool instrumented);
/** \brief Set up the solver using a monotone multigrid method as the inner solver */
void setup(const GridType& grid,
const Assembler* assembler,
const SolutionType& x,
const Dune::BitSetVector<blocksize>& dirichletNodes,
const Dune::ParameterTree& parameterSet);
void setScaling(const Dune::FieldVector<double,blocksize>& scaling)
{
scaling_ = scaling;
}
void setIgnoreNodes(const Dune::BitSetVector<blocksize>& ignoreNodes)
{
ignoreNodes_ = &ignoreNodes;
std::shared_ptr<LoopSolver<CorrectionType> > loopSolver = std::dynamic_pointer_cast<LoopSolver<CorrectionType> >(innerSolver_);
assert(loopSolver);
loopSolver->iterationStep_->ignoreNodes_ = ignoreNodes_;
}
void solve();
[[deprecated]]
void setInitialSolution(const SolutionType& x) {
x_ = x;
}
void setInitialIterate(const SolutionType& x) {
x_ = x;
}
SolutionType getSol() const {return x_;}
const Statistics& getStatistics() const {return statistics_;}
protected:
#if HAVE_MPI
std::unique_ptr<GlobalMapper> globalMapper_;
std::unique_ptr<GlobalMapper> globalMapper_;
#endif
/** \brief The grid */
const GridType* grid_;
/** \brief The grid */
const GridType* grid_;
/** \brief The solution vector */
SolutionType x_;
/** \brief The solution vector */
SolutionType x_;
/** \brief The initial trust-region radius in the maximum-norm */
double initialTrustRegionRadius_;
/** \brief The initial trust-region radius in the maximum-norm */
double initialTrustRegionRadius_;
/** \brief Trust-region norm scaling */
Dune::FieldVector<double,blocksize> scaling_;
/** \brief Trust-region norm scaling */
Dune::FieldVector<double,blocksize> scaling_;
/** \brief Maximum number of trust-region steps */
std::size_t maxTrustRegionSteps_;
/** \brief Maximum number of trust-region steps */
std::size_t maxTrustRegionSteps_;
/** \brief Maximum number of multigrid iterations */
int innerIterations_;
/** \brief Maximum number of multigrid iterations */
int innerIterations_;
/** \brief Error tolerance of the multigrid QP solver */
double innerTolerance_;
/** \brief Error tolerance of the multigrid QP solver */
double innerTolerance_;
/** \brief Hessian matrix */
std::unique_ptr<MatrixType> hessianMatrix_;
/** \brief Hessian matrix */
std::unique_ptr<MatrixType> hessianMatrix_;
/** \brief The assembler for the material law */
const Assembler* assembler_;
/** \brief The assembler for the material law */
const Assembler* assembler_;
/** \brief The solver for the quadratic inner problems */
std::shared_ptr<Solver> innerSolver_;
/** \brief The solver for the quadratic inner problems */
std::shared_ptr<Solver> innerSolver_;
/** \brief Contains 'true' everywhere -- the trust-region is bounded */
Dune::BitSetVector<blocksize> hasObstacle_;
/** \brief Contains 'true' everywhere -- the trust-region is bounded */
Dune::BitSetVector<blocksize> hasObstacle_;
/** \brief The Dirichlet nodes */
const Dune::BitSetVector<blocksize>* ignoreNodes_;
/** \brief The Dirichlet nodes */
const Dune::BitSetVector<blocksize>* ignoreNodes_;
/** \brief The norm used to measure multigrid convergence */
std::shared_ptr<H1SemiNorm<CorrectionType> > h1SemiNorm_;
/** \brief The norm used to measure multigrid convergence */
std::shared_ptr<H1SemiNorm<CorrectionType> > h1SemiNorm_;
/** \brief An L2-norm, really. The H1SemiNorm class is badly named */
std::shared_ptr<H1SemiNorm<CorrectionType> > l2Norm_;
/** \brief An L2-norm, really. The H1SemiNorm class is badly named */
std::shared_ptr<H1SemiNorm<CorrectionType> > l2Norm_;
/** \brief If set to true we log convergence speed and other stuff */
bool instrumented_;
/** \brief If set to true we log convergence speed and other stuff */
bool instrumented_;
/** \brief Output path for instrumented log */
std::string instrumentedPath_ = "/tmp";
/** \brief Output path for instrumented log */
std::string instrumentedPath_ = "/tmp";
/** \brief Norm type used for stopping criterion (default is infinity norm) */
enum class ErrorNormType {infinity, H1semi} normType_ = ErrorNormType::infinity;
/** \brief Norm type used for stopping criterion (default is infinity norm) */
enum class ErrorNormType {infinity, H1semi} normType_ = ErrorNormType::infinity;
/** \brief Store information about solver runs for unit testing */
Statistics statistics_;
/** \brief Store information about solver runs for unit testing */
Statistics statistics_;
};
};
} // namespace Dune::GFE
#include "riemanniantrsolver.cc"
......
dune/gfe/rodfactory.hh
View file @ 48b9358e
......@@ -15,222 +15,228 @@
#include <dune/gfe/spaces/realtuple.hh>
#include <dune/gfe/spaces/rotation.hh>
/** \brief A factory class that implements various ways to create rod configurations
*/
template <class GridView>
class RodFactory
namespace Dune::GFE
{
static_assert(GridView::dimensionworld==1, "RodFactory is only implemented for grids in a 1d world");
public:
RodFactory(const GridView& gridView)
: gridView_(gridView)
{}
/** \brief Make a straight, unsheared rod from two given endpoints
\param[out] rod The new rod
\param[in] n The number of vertices
/** \brief A factory class that implements various ways to create rod configurations
*/
template <int dim>
void create(std::vector<Dune::GFE::ProductManifold<RealTuple<double,dim>,Rotation<double,dim> > >& rod,
const Dune::FieldVector<double,3>& beginning, const Dune::FieldVector<double,3>& end)
{
// Compute the correct orientation
Rotation<double,dim> orientation = Rotation<double,dim>::identity();
Dune::FieldVector<double,3> zAxis(0);
zAxis[2] = 1;
Dune::FieldVector<double,3> axis = MatrixVector::crossProduct(Dune::FieldVector<double,3>(end-beginning), zAxis);
if (axis.two_norm() != 0)
axis /= -axis.two_norm();
Dune::FieldVector<double,3> d3 = end-beginning;
d3 /= d3.two_norm();
double angle = std::acos(zAxis * d3);
if (angle != 0)
orientation = Rotation<double,3>(axis, angle);
template <class GridView>
class RodFactory
{
static_assert(GridView::dimensionworld==1, "RodFactory is only implemented for grids in a 1d world");
// Set the values
create(rod,
Dune::GFE::ProductManifold<RealTuple<double,dim>,Rotation<double,dim> > (beginning,orientation),
Dune::GFE::ProductManifold<RealTuple<double,dim>,Rotation<double,dim> > (end,orientation));
}
public:
RodFactory(const GridView& gridView)
: gridView_(gridView)
{}
/** \brief Make a rod by interpolating between two end configurations
/** \brief Make a straight, unsheared rod from two given endpoints
\param[out] rod The new rod
*/
template <int spaceDim>
void create(std::vector<Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > >& rod,
const Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > & beginning,
const Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > & end)
{
\param[out] rod The new rod
\param[in] n The number of vertices
*/
template <int dim>
void create(std::vector<Dune::GFE::ProductManifold<RealTuple<double,dim>,Rotation<double,dim> > >& rod,
const Dune::FieldVector<double,3>& beginning, const Dune::FieldVector<double,3>& end)
{
// Compute the correct orientation
Rotation<double,dim> orientation = Rotation<double,dim>::identity();
static const int dim = GridView::dimension; // de facto: 1
Dune::FieldVector<double,3> zAxis(0);
zAxis[2] = 1;
Dune::FieldVector<double,3> axis = MatrixVector::crossProduct(Dune::FieldVector<double,3>(end-beginning), zAxis);
if (axis.two_norm() != 0)
axis /= -axis.two_norm();
//////////////////////////////////////////////////////////////////////////////////////////////
// Get smallest and largest coordinate, in order to create an arc-length parametrization
//////////////////////////////////////////////////////////////////////////////////////////////
Dune::FieldVector<double,3> d3 = end-beginning;
d3 /= d3.two_norm();
typename GridView::template Codim<dim>::Iterator vIt = gridView_.template begin<dim>();
typename GridView::template Codim<dim>::Iterator vEndIt = gridView_.template end<dim>();
double angle = std::acos(zAxis * d3);
double min = std::numeric_limits<double>::max();
double max = -std::numeric_limits<double>::max();
if (angle != 0)
orientation = Rotation<double,3>(axis, angle);
for (; vIt != vEndIt; ++vIt) {
min = std::min(min, vIt->geometry().corner(0)[0]);
max = std::max(max, vIt->geometry().corner(0)[0]);
// Set the values
create(rod,
Dune::GFE::ProductManifold<RealTuple<double,dim>,Rotation<double,dim> > (beginning,orientation),
Dune::GFE::ProductManifold<RealTuple<double,dim>,Rotation<double,dim> > (end,orientation));
}
////////////////////////////////////////////////////////////////////////////////////
// Interpolate according to arc-length
////////////////////////////////////////////////////////////////////////////////////
rod.resize(gridView_.size(dim));
/** \brief Make a rod by interpolating between two end configurations
for (vIt = gridView_.template begin<dim>(); vIt != vEndIt; ++vIt) {
int idx = gridView_.indexSet().index(*vIt);
Dune::FieldVector<double,1> local = (vIt->geometry().corner(0)[0] - min) / (max - min);
\param[out] rod The new rod
*/
template <int spaceDim>
void create(std::vector<Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > >& rod,
const Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > & beginning,
const Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > & end)
{
for (int i=0; i<3; i++)
rod[idx].r[i] = (1-local)*beginning.r[i] + local*end.r[i];
rod[idx].q = Rotation<double,3>::interpolate(beginning.q, end.q, local);
}
}
static const int dim = GridView::dimension; // de facto: 1
/** \brief Make a rod by setting each entry to the same value
//////////////////////////////////////////////////////////////////////////////////////////////
// Get smallest and largest coordinate, in order to create an arc-length parametrization
//////////////////////////////////////////////////////////////////////////////////////////////
\param[out] rod The new rod
*/
template <int spaceDim>
void create(std::vector<Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > >& rod,
const Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > & value)
{
rod.resize(gridView_.size(1));
std::fill(rod.begin(), rod.end(), value);
}
typename GridView::template Codim<dim>::Iterator vIt = gridView_.template begin<dim>();
typename GridView::template Codim<dim>::Iterator vEndIt = gridView_.template end<dim>();
/** \brief Make a rod by linearly interpolating between the end values
double min = std::numeric_limits<double>::max();
double max = -std::numeric_limits<double>::max();
\note The end values are expected to be in the input container!
\param[in,out] rod The new rod
*/
template <int spaceDim>
void create(std::vector<Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > >& rod)
{
static const int dim = GridView::dimension; // de facto: 1
assert(gridView_.size(dim)==rod.size());
for (; vIt != vEndIt; ++vIt) {
min = std::min(min, vIt->geometry().corner(0)[0]);
max = std::max(max, vIt->geometry().corner(0)[0]);
}
//////////////////////////////////////////////////////////////////////////////////////////////
// Get smallest and largest coordinate, in order to create an arc-length parametrization
//////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////
// Interpolate according to arc-length
////////////////////////////////////////////////////////////////////////////////////
typename GridView::template Codim<dim>::Iterator vIt = gridView_.template begin<dim>();
typename GridView::template Codim<dim>::Iterator vEndIt = gridView_.template end<dim>();
rod.resize(gridView_.size(dim));
double min = std::numeric_limits<double>::max();
double max = -std::numeric_limits<double>::max();
Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > beginning, end;
for (vIt = gridView_.template begin<dim>(); vIt != vEndIt; ++vIt) {
int idx = gridView_.indexSet().index(*vIt);
Dune::FieldVector<double,1> local = (vIt->geometry().corner(0)[0] - min) / (max - min);
for (; vIt != vEndIt; ++vIt) {
if (vIt->geometry().corner(0)[0] < min) {
min = vIt->geometry().corner(0)[0];
beginning = rod[gridView_.indexSet().index(*vIt)];
}
if (vIt->geometry().corner(0)[0] > max) {
max = vIt->geometry().corner(0)[0];
end = rod[gridView_.indexSet().index(*vIt)];
for (int i=0; i<3; i++)
rod[idx].r[i] = (1-local)*beginning.r[i] + local*end.r[i];
rod[idx].q = Rotation<double,3>::interpolate(beginning.q, end.q, local);
}
}
////////////////////////////////////////////////////////////////////////////////////
// Interpolate according to arc-length
////////////////////////////////////////////////////////////////////////////////////
rod.resize(gridView_.size(dim));
/** \brief Make a rod by setting each entry to the same value
for (vIt = gridView_.template begin<dim>(); vIt != vEndIt; ++vIt) {
int idx = gridView_.indexSet().index(*vIt);
Dune::FieldVector<double,1> local = (vIt->geometry().corner(0)[0] - min) / (max - min);
for (int i=0; i<3; i++)
rod[idx].r[i] = (1-local)*beginning.r[i] + local*end.r[i];
rod[idx].q = Rotation<double,3>::interpolate(beginning.q, end.q, local);
\param[out] rod The new rod
*/
template <int spaceDim>
void create(std::vector<Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > >& rod,
const Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > & value)
{
rod.resize(gridView_.size(1));
std::fill(rod.begin(), rod.end(), value);
}
}
/** \brief Make a rod by linearly interpolating between the end values
\note The end values are expected to be in the input container!
\param[in,out] rod The new rod
*/
template <int spaceDim>
void create(std::vector<Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > >& rod)
{
static const int dim = GridView::dimension; // de facto: 1
assert(gridView_.size(dim)==rod.size());
//////////////////////////////////////////////////////////////////////////////////////////////
// Get smallest and largest coordinate, in order to create an arc-length parametrization
//////////////////////////////////////////////////////////////////////////////////////////////
typename GridView::template Codim<dim>::Iterator vIt = gridView_.template begin<dim>();
typename GridView::template Codim<dim>::Iterator vEndIt = gridView_.template end<dim>();
double min = std::numeric_limits<double>::max();
double max = -std::numeric_limits<double>::max();
Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > beginning, end;
for (; vIt != vEndIt; ++vIt) {
if (vIt->geometry().corner(0)[0] < min) {
min = vIt->geometry().corner(0)[0];
beginning = rod[gridView_.indexSet().index(*vIt)];
}
if (vIt->geometry().corner(0)[0] > max) {
max = vIt->geometry().corner(0)[0];
end = rod[gridView_.indexSet().index(*vIt)];
}
}
/** \brief Make a rod solving a static Dirichlet problem
////////////////////////////////////////////////////////////////////////////////////
// Interpolate according to arc-length
////////////////////////////////////////////////////////////////////////////////////
\param rod The configuration to be computed
\param radius The rod's radius
\param E The rod's elastic modulus
\param nu The rod's Poisson modulus
\param beginning The prescribed Dirichlet values
\param end The prescribed Dirichlet values
\param[out] rod The new rod
*/
template <int spaceDim>
void create(std::vector<Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > >& rod,
double radius, double E, double nu,
const Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > & beginning,
const Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > & end)
{
rod.resize(gridView_.size(dim));
// Make Dirichlet bitfields for the rods as well
Dune::BitSetVector<6> rodDirichletNodes(gridView_.size(GridView::dimension),false);
for (vIt = gridView_.template begin<dim>(); vIt != vEndIt; ++vIt) {
int idx = gridView_.indexSet().index(*vIt);
Dune::FieldVector<double,1> local = (vIt->geometry().corner(0)[0] - min) / (max - min);
for (int j=0; j<6; j++) {
rodDirichletNodes[0][j] = true;
rodDirichletNodes.back()[j] = true;
for (int i=0; i<3; i++)
rod[idx].r[i] = (1-local)*beginning.r[i] + local*end.r[i];
rod[idx].q = Rotation<double,3>::interpolate(beginning.q, end.q, local);
}
}
// Create local assembler for the static elastic problem
RodLocalStiffness<GridView,double> rodLocalStiffness(gridView_, radius*radius*M_PI,
std::pow(radius,4) * 0.25* M_PI, std::pow(radius,4) * 0.25* M_PI, E, nu);
typedef Dune::Functions::PQKNodalBasis<GridView,1> RodP1Basis;
RodP1Basis p1Basis(gridView_);
RodAssembler<RodP1Basis,spaceDim> assembler(p1Basis, &rodLocalStiffness);
/** \brief Make a rod solving a static Dirichlet problem
\param rod The configuration to be computed
\param radius The rod's radius
\param E The rod's elastic modulus
\param nu The rod's Poisson modulus
\param beginning The prescribed Dirichlet values
\param end The prescribed Dirichlet values
\param[out] rod The new rod
*/
template <int spaceDim>
void create(std::vector<Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > >& rod,
double radius, double E, double nu,
const Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > & beginning,
const Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > & end)
{
// Make Dirichlet bitfields for the rods as well
Dune::BitSetVector<6> rodDirichletNodes(gridView_.size(GridView::dimension),false);
for (int j=0; j<6; j++) {
rodDirichletNodes[0][j] = true;
rodDirichletNodes.back()[j] = true;
}
// Create local assembler for the static elastic problem
RodLocalStiffness<GridView,double> rodLocalStiffness(gridView_, radius*radius*M_PI,
std::pow(radius,4) * 0.25* M_PI, std::pow(radius,4) * 0.25* M_PI, E, nu);
// Create initial iterate using the straight rod interpolation method
create(rod, beginning.r, end.r);
typedef Dune::Functions::PQKNodalBasis<GridView,1> RodP1Basis;
RodP1Basis p1Basis(gridView_);
RodAssembler<RodP1Basis,spaceDim> assembler(p1Basis, &rodLocalStiffness);
// Set reference configuration
rodLocalStiffness.setReferenceConfiguration(rod);
// Create initial iterate using the straight rod interpolation method
create(rod, beginning.r, end.r);
// Set Dirichlet values
rod[0] = beginning;
rod.back() = end;
// Set reference configuration
rodLocalStiffness.setReferenceConfiguration(rod);
// Trust--Region solver
RiemannianTrustRegionSolver<RodP1Basis, Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > > rodSolver;
rodSolver.setup(gridView_.grid(), &assembler, rod,
rodDirichletNodes,
1e-10, 100, // TR tolerance and iterations
20, // init TR radius
200, 1e-00, 1, 3, 3, // Multigrid parameters
100, 1e-8 , false); // base solver parameters
// Set Dirichlet values
rod[0] = beginning;
rod.back() = end;
rodSolver.verbosity_ = NumProc::QUIET;
// Trust--Region solver
RiemannianTrustRegionSolver<RodP1Basis, Dune::GFE::ProductManifold<RealTuple<double,spaceDim>,Rotation<double,spaceDim> > > rodSolver;
rodSolver.setup(gridView_.grid(), &assembler, rod,
rodDirichletNodes,
1e-10, 100, // TR tolerance and iterations
20, // init TR radius
200, 1e-00, 1, 3, 3, // Multigrid parameters
100, 1e-8 , false); // base solver parameters
rodSolver.solve();
rodSolver.verbosity_ = NumProc::QUIET;
rod = rodSolver.getSol();
rodSolver.solve();
rod = rodSolver.getSol();
}
}
private:
private:
const GridView gridView_;
};
const GridView gridView_;
};
} // namespace Dune::GFE
#endif
dune/gfe/skewmatrix.hh
View file @ 48b9358e
#ifndef DUNE_SKEW_MATRIX_HH
#define DUNE_SKEW_MATRIX_HH
/** \brief Static dense skew-symmetric matrix */
template <class T, int N>
class SkewMatrix
{};
/** \brief Static dense skew-symmetric 3x3 matrix */
template <class T>
class SkewMatrix<T,3>
namespace Dune::GFE
{
public:
/** \brief Default constructor -- does nothing */
SkewMatrix()
{}
/** \brief Constructor from an axial vector */
explicit SkewMatrix(const Dune::FieldVector<T,3>& v)
: data_(v)
{}
/** \brief Constructor from a general matrix */
explicit SkewMatrix(const Dune::FieldMatrix<T,3,3>& m)
{
data_ = {m[2][1], m[0][2], m[1][0]};
}
SkewMatrix(T v)
: data_(v)
{}
SkewMatrix<T,3>& operator*=(const T& a)
{
data_ *= a;
return *this;
}
Dune::FieldVector<T,3>& axial()
{
return data_;
}
const Dune::FieldVector<T,3>& axial() const
{
return data_;
}
typedef typename Dune::FieldVector<T,3>::Iterator Iterator;
//! begin iterator
Iterator begin ()
{
return Iterator(data_,0);
}
//! end iterator
Iterator end ()
{
return Iterator(data_,3);
}
/** \brief Static dense skew-symmetric matrix */
template <class T, int N>
class SkewMatrix
{};
typedef typename Dune::FieldVector<T,3>::ConstIterator ConstIterator;
//! begin iterator
ConstIterator begin () const
{
return ConstIterator(data_,0);
}
//! end iterator
ConstIterator end () const
{
return ConstIterator(data_,3);
}
/** \brief Embed the skew-symmetric matrix in R^3x3 */
Dune::FieldMatrix<T,3,3> toMatrix() const
/** \brief Static dense skew-symmetric 3x3 matrix */
template <class T>
class SkewMatrix<T,3>
{
Dune::FieldMatrix<T,3,3> mat;
mat = 0;
mat[0][1] = -data_[2];
mat[1][0] = data_[2];
mat[0][2] = data_[1];
mat[2][0] = -data_[1];
mat[1][2] = -data_[0];
mat[2][1] = data_[0];
return mat;
}
private:
// we store the axial vector
Dune::FieldVector<T,3> data_;
};
public:
/** \brief Default constructor -- does nothing */
SkewMatrix()
{}
/** \brief Constructor from an axial vector */
explicit SkewMatrix(const Dune::FieldVector<T,3>& v)
: data_(v)
{}
/** \brief Constructor from a general matrix */
explicit SkewMatrix(const Dune::FieldMatrix<T,3,3>& m)
{
data_ = {m[2][1], m[0][2], m[1][0]};
}
SkewMatrix(T v)
: data_(v)
{}
SkewMatrix<T,3>& operator*=(const T& a)
{
data_ *= a;
return *this;
}
Dune::FieldVector<T,3>& axial()
{
return data_;
}
const Dune::FieldVector<T,3>& axial() const
{
return data_;
}
typedef typename Dune::FieldVector<T,3>::Iterator Iterator;
//! begin iterator
Iterator begin ()
{
return Iterator(data_,0);
}
//! end iterator
Iterator end ()
{
return Iterator(data_,3);
}
typedef typename Dune::FieldVector<T,3>::ConstIterator ConstIterator;
//! begin iterator
ConstIterator begin () const
{
return ConstIterator(data_,0);
}
//! end iterator
ConstIterator end () const
{
return ConstIterator(data_,3);
}
/** \brief Embed the skew-symmetric matrix in R^3x3 */
Dune::FieldMatrix<T,3,3> toMatrix() const
{
Dune::FieldMatrix<T,3,3> mat;
mat = 0;
mat[0][1] = -data_[2];
mat[1][0] = data_[2];
mat[0][2] = data_[1];
mat[2][0] = -data_[1];
mat[1][2] = -data_[0];
mat[2][1] = data_[0];
return mat;
}
private:
// we store the axial vector
Dune::FieldVector<T,3> data_;
};
} // namespace Dune::GFE
#endif
dune/gfe/spaces/hyperbolichalfspacepoint.hh
View file @ 48b9358e
......@@ -9,391 +9,397 @@
#include <dune/gfe/tensor3.hh>
/** \brief A point in the hyperbolic half-space H^N
\tparam N Dimension of the hyperbolic half-space
\tparam T The type used for individual coordinates
*/
template <class T, int N>
class HyperbolicHalfspacePoint
namespace Dune::GFE
{
static_assert(N>=2, "A hyperbolic half-space needs to be at least two-dimensional!");
/** \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;
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
return 2*std::acosh(x) / std::sqrt(x*x-1);
}
/** \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;
if (x < 1+eps) { // regular expression is unstable, use the series expansion instead
return -2.0/3 + 8*(x-1)/15;
} else
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 thirdDerivativeOfArcCosHSquared(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 {
T d = x*x-1;
return -6*x/(d*d) + (4*x*x+2)*std::acosh(x)/(std::pow(d,2.5));
}
}
/** \brief Compute derivative of $F(p,q) = 1 + ||p-q||^2 / 2p_nq_n with respect to p
\param[in] diffNormSquared Expected to be ||p-q||^2, taken from the caller for efficiency reasons
/** \brief A point in the hyperbolic half-space H^N
\tparam N Dimension of the hyperbolic half-space
\tparam T The type used for individual coordinates
*/
static Dune::FieldVector<T,N> computeDFdp(const HyperbolicHalfspacePoint& p, const HyperbolicHalfspacePoint& q, const T& diffNormSquared)
template <class T, int N>
class HyperbolicHalfspacePoint
{
Dune::FieldVector<T,N> result;
static_assert(N>=2, "A hyperbolic half-space needs to be at least two-dimensional!");
/** \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;
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
return 2*std::acosh(x) / std::sqrt(x*x-1);
}
for (size_t i=0; i<N-1; i++)
result[i] = ( p.data_[i] - q.data_[i] ) / (q.data_[N-1] * p.data_[N-1]);
/** \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;
if (x < 1+eps) { // regular expression is unstable, use the series expansion instead
return -2.0/3 + 8*(x-1)/15;
} else
return 2/(x*x-1) - 2*x*std::acosh(x) / std::pow(x*x-1,1.5);
}
result[N-1] = - diffNormSquared / (2*p.data_[N-1]*p.data_[N-1]*q.data_[N-1]) + (p.data_[N-1] - q.data_[N-1]) / (p.data_[N-1]*q.data_[N-1]);
/** \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;
if (x < 1+eps) { // regular expression is unstable, use the series expansion instead
return 8.0/15 - 24*(x-1)/35;
} else {
T d = x*x-1;
return -6*x/(d*d) + (4*x*x+2)*std::acosh(x)/(std::pow(d,2.5));
}
}
return result;
}
/** \brief Compute derivative of $F(p,q) = 1 + ||p-q||^2 / 2p_nq_n with respect to p
\param[in] diffNormSquared Expected to be ||p-q||^2, taken from the caller for efficiency reasons
*/
static Dune::FieldVector<T,N> computeDFdp(const HyperbolicHalfspacePoint& p, const HyperbolicHalfspacePoint& q, const T& diffNormSquared)
{
Dune::FieldVector<T,N> result;
/** \brief Compute 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::FieldVector<T,N> computeDFdq(const HyperbolicHalfspacePoint& p, const HyperbolicHalfspacePoint& q, const T& diffNormSquared)
{
Dune::FieldVector<T,N> result;
for (size_t i=0; i<N-1; i++)
result[i] = ( p.data_[i] - q.data_[i] ) / (q.data_[N-1] * p.data_[N-1]);
for (size_t i=0; i<N-1; i++)
result[i] = ( q.data_[i] - p.data_[i] ) / (q.data_[N-1] * p.data_[N-1]);
result[N-1] = - diffNormSquared / (2*p.data_[N-1]*p.data_[N-1]*q.data_[N-1]) + (p.data_[N-1] - q.data_[N-1]) / (p.data_[N-1]*q.data_[N-1]);
result[N-1] = - diffNormSquared / (2*p.data_[N-1]*q.data_[N-1]*q.data_[N-1]) - (p.data_[N-1] - q.data_[N-1]) / (p.data_[N-1]*q.data_[N-1]);
return result;
}
return result;
}
/** \brief Compute 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::FieldVector<T,N> computeDFdq(const HyperbolicHalfspacePoint& p, const HyperbolicHalfspacePoint& q, const T& diffNormSquared)
{
Dune::FieldVector<T,N> result;
/** \brief Compute second derivative of $F(p,q) = 1 + ||p-q||^2 / 2p_nq_n with respect to p and q
\param[in] diffNormSquared Expected to be ||p-q||^2, taken from the caller for efficiency reasons
*/
static Dune::FieldMatrix<T,N,N> computeDFdpdq(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_;
for (size_t i=0; i<N-1; i++)
result[i] = ( q.data_[i] - p.data_[i] ) / (q.data_[N-1] * p.data_[N-1]);
result[N-1] = - diffNormSquared / (2*p.data_[N-1]*q.data_[N-1]*q.data_[N-1]) - (p.data_[N-1] - q.data_[N-1]) / (p.data_[N-1]*q.data_[N-1]);
Dune::FieldMatrix<T,N,N> dFdpdq;
return result;
}
for (size_t i=0; i<N; i++) {
/** \brief Compute second derivative of $F(p,q) = 1 + ||p-q||^2 / 2p_nq_n with respect to p and q
\param[in] diffNormSquared Expected to be ||p-q||^2, taken from the caller for efficiency reasons
*/
static Dune::FieldMatrix<T,N,N> computeDFdpdq(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_;
for (size_t j=0; j<N; j++) {
Dune::FieldMatrix<T,N,N> dFdpdq;
if (i!=N-1 and j!=N-1) {
for (size_t i=0; i<N; i++) {
dFdpdq[i][j] = -(i==j) / (p[N-1]*q[N-1]);
for (size_t j=0; j<N; j++) {
} else if (i!=N-1 and j==N-1) {
if (i!=N-1 and j!=N-1) {
dFdpdq[i][j] = -(p[i] - q[i]) / (p[N-1]*q[N-1]*q[N-1]);
dFdpdq[i][j] = -(i==j) / (p[N-1]*q[N-1]);
} else if (i==N-1 and j!=N-1) {
} else if (i!=N-1 and j==N-1) {
dFdpdq[i][j] = (p[j] - q[j]) / (p[N-1]*p[N-1]*q[N-1]);
dFdpdq[i][j] = -(p[i] - q[i]) / (p[N-1]*q[N-1]*q[N-1]);
} else if (i==N-1 and j==N-1) {
} else if (i==N-1 and j!=N-1) {
dFdpdq[i][j] = -1/(p[N-1]*q[N-1])
- (p[N-1]-q[N-1]) / (p[N-1]*q[N-1]*q[N-1])
+ (p[N-1]-q[N-1]) / (p[N-1]*p[N-1]*q[N-1]) + diffNormSquared / (2*p[N-1]*p[N-1]*q[N-1]*q[N-1]);
dFdpdq[i][j] = (p[j] - q[j]) / (p[N-1]*p[N-1]*q[N-1]);
} else if (i==N-1 and j==N-1) {
dFdpdq[i][j] = -1/(p[N-1]*q[N-1])
- (p[N-1]-q[N-1]) / (p[N-1]*q[N-1]*q[N-1])
+ (p[N-1]-q[N-1]) / (p[N-1]*p[N-1]*q[N-1]) + diffNormSquared / (2*p[N-1]*p[N-1]*q[N-1]*q[N-1]);
}
}
}
return dFdpdq;
}
return dFdpdq;
}
/** \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_;
/** \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;
Dune::FieldMatrix<T,N,N> dFdqdq;
for (size_t i=0; i<N; i++) {
for (size_t i=0; i<N; i++) {
for (size_t j=0; j<N; j++) {
for (size_t j=0; j<N; j++) {
if (i!=N-1 and j!=N-1) {
if (i!=N-1 and j!=N-1) {
dFdqdq[i][j] = (i==j) / (p[N-1]*q[N-1]);
dFdqdq[i][j] = (i==j) / (p[N-1]*q[N-1]);
} else if (i!=N-1 and j==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]);
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) {
} 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]);
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) {
} 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]);
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;
}
return dFdqdq;
}
public:
public:
/** \brief The type used for coordinates */
typedef T ctype;
/** \brief The type used for coordinates */
typedef T ctype;
/** \brief The type used for global coordinates */
typedef Dune::FieldVector<T,N> CoordinateType;
/** \brief The type used for global coordinates */
typedef Dune::FieldVector<T,N> CoordinateType;
/** \brief Dimension of the manifold */
static const int dim = N;
/** \brief Dimension of the manifold */
static const int dim = N;
/** \brief Dimension of the Euclidean space the manifold is embedded in */
static const int embeddedDim = N;
/** \brief Dimension of the Euclidean space the manifold is embedded in */
static const int embeddedDim = N;
/** \brief Type of a tangent vector in local coordinates */
typedef Dune::FieldVector<T,N> TangentVector;
/** \brief Type of a tangent vector in local coordinates */
typedef Dune::FieldVector<T,N> TangentVector;
/** \brief Type of a tangent vector in the embedding space */
typedef Dune::FieldVector<T,N> EmbeddedTangentVector;
/** \brief Type of a tangent vector in the embedding space */
typedef Dune::FieldVector<T,N> EmbeddedTangentVector;
/** \brief The global convexity radius of the hyberbolic plane */
static constexpr T convexityRadius = std::numeric_limits<T>::infinity();
/** \brief The global convexity radius of the hyberbolic plane */
static constexpr T convexityRadius = std::numeric_limits<T>::infinity();
/** \brief Default constructor */
HyperbolicHalfspacePoint()
{}
/** \brief Default constructor */
HyperbolicHalfspacePoint()
{}
/** \brief Constructor from a vector. The vector gets normalized */
HyperbolicHalfspacePoint(const Dune::FieldVector<T,N>& vector)
: data_(vector)
{
assert(vector[N-1]>0);
}
/** \brief Constructor from a vector. The vector gets normalized */
HyperbolicHalfspacePoint(const Dune::FieldVector<T,N>& vector)
: data_(vector)
{
assert(vector[N-1]>0);
}
/** \brief Constructor from an array. The array gets normalized */
HyperbolicHalfspacePoint(const std::array<T,N>& vector)
{
assert(vector.back()>0);
for (int i=0; i<N; i++)
data_[i] = vector[i];
}
/** \brief Constructor from an array. The array gets normalized */
HyperbolicHalfspacePoint(const std::array<T,N>& vector)
{
assert(vector.back()>0);
for (int i=0; i<N; i++)
data_[i] = vector[i];
}
/** \brief The exponential map */
static HyperbolicHalfspacePoint exp(const HyperbolicHalfspacePoint& p, const TangentVector& v) {
/** \brief The exponential map */
static HyperbolicHalfspacePoint exp(const HyperbolicHalfspacePoint& p, const TangentVector& v) {
assert (N==2);
assert (N==2);
T vNorm = v.two_norm();
T vNorm = v.two_norm();
// we compute geodesics by applying an isometry to a fixed unit-speed geodesic.
// Hence we need a unit velocity vector.
if (vNorm <= 0)
return p;
// we compute geodesics by applying an isometry to a fixed unit-speed geodesic.
// Hence we need a unit velocity vector.
if (vNorm <= 0)
return p;
TangentVector vUnit = v;
vUnit /= vNorm;
TangentVector vUnit = v;
vUnit /= vNorm;
// Compute the coefficients a,b,c,d of the Moebius transform that transforms
// the unit speed upward geodesic to the one through p with direction vUnit.
// We expect the Moebius transform to be an isometry, i.e. ad-bc = 1.
T cc = 1/(2*p.data_[N-1]) - vUnit[N-1] / (2*p.data_[N-1]*p.data_[N-1]);
T dd = 1/(2*p.data_[N-1]) + vUnit[N-1] / (2*p.data_[N-1]*p.data_[N-1]);
T ac = vUnit[0] / (2*p.data_[N-1]) + p.data_[0]*cc;
T bd = p.data_[0] / p.data_[N-1] - ac;
// Compute the coefficients a,b,c,d of the Moebius transform that transforms
// the unit speed upward geodesic to the one through p with direction vUnit.
// We expect the Moebius transform to be an isometry, i.e. ad-bc = 1.
T cc = 1/(2*p.data_[N-1]) - vUnit[N-1] / (2*p.data_[N-1]*p.data_[N-1]);
T dd = 1/(2*p.data_[N-1]) + vUnit[N-1] / (2*p.data_[N-1]*p.data_[N-1]);
T ac = vUnit[0] / (2*p.data_[N-1]) + p.data_[0]*cc;
T bd = p.data_[0] / p.data_[N-1] - ac;
HyperbolicHalfspacePoint result;
HyperbolicHalfspacePoint result;
// vertical part
result.data_[1] = std::exp(vNorm) / (cc*std::exp(2*vNorm) + dd);
// vertical part
result.data_[1] = std::exp(vNorm) / (cc*std::exp(2*vNorm) + dd);
// horizontal part
result.data_[0] = (ac*std::exp(2*vNorm) + bd) / (cc*std::exp(2*vNorm) + dd);
// horizontal part
result.data_[0] = (ac*std::exp(2*vNorm) + bd) / (cc*std::exp(2*vNorm) + dd);
return result;
}
return result;
}
/** \brief Hyperbolic distance between two points
*
* \f dist(a,b) = arccosh ( 1 + ||a-b||^2 / (2a_n b_n) \f
*/
static T distance(const HyperbolicHalfspacePoint& a, const HyperbolicHalfspacePoint& b) {
/** \brief Hyperbolic distance between two points
*
* \f dist(a,b) = arccosh ( 1 + ||a-b||^2 / (2a_n b_n) \f
*/
static T distance(const HyperbolicHalfspacePoint& a, const HyperbolicHalfspacePoint& b) {
T result(0);
T result(0);
for (size_t i=0; i<N; i++)
result += (a.data_[i]-b.data_[i])*(a.data_[i]-b.data_[i]);
for (size_t i=0; i<N; i++)
result += (a.data_[i]-b.data_[i])*(a.data_[i]-b.data_[i]);
return std::acosh(1 + result / (2*a.data_[N-1]*b.data_[N-1]));
}
return std::acosh(1 + result / (2*a.data_[N-1]*b.data_[N-1]));
}
/** \brief Compute the gradient of the squared distance function keeping the first argument fixed
/** \brief Compute the gradient of the squared distance function keeping the first argument fixed
Unlike the distance itself the squared distance is differentiable at zero
*/
static EmbeddedTangentVector derivativeOfDistanceSquaredWRTSecondArgument(const HyperbolicHalfspacePoint& a, const HyperbolicHalfspacePoint& b) {
Unlike the distance itself the squared distance is differentiable at zero
*/
static EmbeddedTangentVector derivativeOfDistanceSquaredWRTSecondArgument(const HyperbolicHalfspacePoint& a, const HyperbolicHalfspacePoint& b) {
T diffNormSquared(0);
T diffNormSquared(0);
for (size_t i=0; i<N; i++)
diffNormSquared += (a.data_[i]-b.data_[i])*(a.data_[i]-b.data_[i]);
for (size_t i=0; i<N; i++)
diffNormSquared += (a.data_[i]-b.data_[i])*(a.data_[i]-b.data_[i]);
TangentVector result = computeDFdq(a,b,diffNormSquared);
TangentVector result = computeDFdq(a,b,diffNormSquared);
T x = 1 + diffNormSquared/ (2*a.data_[N-1]*b.data_[N-1]);
T x = 1 + diffNormSquared/ (2*a.data_[N-1]*b.data_[N-1]);
result *= derivativeOfArcCosHSquared(x);
result *= derivativeOfArcCosHSquared(x);
return result;
}
return result;
}
/** \brief Compute the Hessian of the squared distance function keeping the first argument fixed
/** \brief Compute the Hessian of the squared distance function keeping the first argument fixed
Unlike the distance itself the squared distance is differentiable at zero
*/
static Dune::FieldMatrix<T,N,N> secondDerivativeOfDistanceSquaredWRTSecondArgument(const HyperbolicHalfspacePoint& a, const HyperbolicHalfspacePoint& b) {
Unlike the distance itself the squared distance is differentiable at zero
*/
static Dune::FieldMatrix<T,N,N> secondDerivativeOfDistanceSquaredWRTSecondArgument(const HyperbolicHalfspacePoint& a, const HyperbolicHalfspacePoint& b) {
T diffNormSquared = (a.data_-b.data_).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 first derivative of F
Dune::FieldVector<T,N> dFdq = computeDFdq(a,b,diffNormSquared);
// Compute second derivatives of F
Dune::FieldMatrix<T,N,N> dFdqdq = computeDFdqdq(a,b,diffNormSquared);
// Compute second derivatives of F
Dune::FieldMatrix<T,N,N> dFdqdq = computeDFdqdq(a,b,diffNormSquared);
//
T x = 1 + diffNormSquared/ (2*a.data_[N-1]*b.data_[N-1]);
T alphaPrime = derivativeOfArcCosHSquared(x);
T alphaPrimePrime = secondDerivativeOfArcCosHSquared(x);
//
T x = 1 + diffNormSquared/ (2*a.data_[N-1]*b.data_[N-1]);
T alphaPrime = derivativeOfArcCosHSquared(x);
T alphaPrimePrime = secondDerivativeOfArcCosHSquared(x);
// Sum it all together
Dune::FieldMatrix<T,N,N> result;
for (size_t i=0; i<N; i++)
for (size_t j=0; j<N; j++)
result[i][j] = alphaPrimePrime * dFdq[i] * dFdq[j] + alphaPrime * dFdqdq[i][j];
// Sum it all together
Dune::FieldMatrix<T,N,N> result;
for (size_t i=0; i<N; i++)
for (size_t j=0; j<N; j++)
result[i][j] = alphaPrimePrime * dFdq[i] * dFdq[j] + alphaPrime * dFdqdq[i][j];
return result;
}
return result;
}
/** \brief Compute the mixed second derivative \partial d^2 / \partial da db
/** \brief Compute the mixed second derivative \partial d^2 / \partial da db
*/
static Dune::FieldMatrix<T,N,N> secondDerivativeOfDistanceSquaredWRTFirstAndSecondArgument(const HyperbolicHalfspacePoint& a, const HyperbolicHalfspacePoint& b)
{
// abbreviate notation
const Dune::FieldVector<T,N>& p = a.data_;
const Dune::FieldVector<T,N>& q = b.data_;
*/
static Dune::FieldMatrix<T,N,N> secondDerivativeOfDistanceSquaredWRTFirstAndSecondArgument(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 = (p-q).two_norm2();
// Compute first derivatives of F with respect to p and q
Dune::FieldVector<T,N> dFdp = computeDFdp(a,b,diffNormSquared);
Dune::FieldVector<T,N> dFdq = computeDFdq(a,b,diffNormSquared);
// Compute first derivatives of F with respect to p and q
Dune::FieldVector<T,N> dFdp = computeDFdp(a,b,diffNormSquared);
Dune::FieldVector<T,N> dFdq = computeDFdq(a,b,diffNormSquared);
// Compute second derivatives of F
Dune::FieldMatrix<T,N,N> dFdpdq = computeDFdpdq(a,b,diffNormSquared);
// Compute second derivatives of F
Dune::FieldMatrix<T,N,N> dFdpdq = computeDFdpdq(a,b,diffNormSquared);
//
T x = 1 + diffNormSquared/ (2*p[N-1]*q[N-1]);
T alphaPrime = derivativeOfArcCosHSquared(x);
T alphaPrimePrime = secondDerivativeOfArcCosHSquared(x);
//
T x = 1 + diffNormSquared/ (2*p[N-1]*q[N-1]);
T alphaPrime = derivativeOfArcCosHSquared(x);
T alphaPrimePrime = secondDerivativeOfArcCosHSquared(x);
// Sum it all together
Dune::FieldMatrix<T,N,N> result;
for (size_t i=0; i<N; i++)
for (size_t j=0; j<N; j++)
result[i][j] = alphaPrimePrime * dFdp[i] * dFdq[j] + alphaPrime * dFdpdq[i][j];
// Sum it all together
Dune::FieldMatrix<T,N,N> result;
for (size_t i=0; i<N; i++)
for (size_t j=0; j<N; j++)
result[i][j] = alphaPrimePrime * dFdp[i] * dFdq[j] + alphaPrime * dFdpdq[i][j];
return result;
}
return result;
}
/** \brief Compute the third derivative \partial d^3 / \partial dq^3
/** \brief Compute the third derivative \partial d^3 / \partial dq^3
Unlike the distance itself the squared distance is differentiable at zero
*/
static Tensor3<T,N,N,N> thirdDerivativeOfDistanceSquaredWRTSecondArgument(const HyperbolicHalfspacePoint& a, const HyperbolicHalfspacePoint& b)
{
Tensor3<T,N,N,N> result;
Unlike the distance itself the squared distance is differentiable at zero
*/
static Tensor3<T,N,N,N> thirdDerivativeOfDistanceSquaredWRTSecondArgument(const HyperbolicHalfspacePoint& a, const HyperbolicHalfspacePoint& b)
{
Tensor3<T,N,N,N> result;
// abbreviate notation
const Dune::FieldVector<T,N>& p = a.data_;
const Dune::FieldVector<T,N>& q = b.data_;
// 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 = (p-q).two_norm2();
// Compute first derivative of F
Dune::FieldVector<T,N> dFdq = computeDFdq(a,b,diffNormSquared);
// 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 = computeDFdqdq(a,b,diffNormSquared);
// Compute second derivatives of F
Dune::FieldMatrix<T,N,N> dFdqdq = computeDFdqdq(a,b,diffNormSquared);
// Compute third derivatives of F
Tensor3<T,N,N,N> dFdqdqdq;
// Compute third derivatives of F
Tensor3<T,N,N,N> dFdqdqdq;
for (size_t i=0; i<N; i++) {
for (size_t i=0; i<N; i++) {
for (size_t j=0; j<N; j++) {
for (size_t j=0; j<N; j++) {
for (size_t k=0; k<N; k++) {
for (size_t k=0; k<N; k++) {
if (i!=N-1 and j!=N-1 and k!=N-1) {
if (i!=N-1 and j!=N-1 and k!=N-1) {
dFdqdqdq[i][j][k] = 0;
dFdqdqdq[i][j][k] = 0;
} else if (i!=N-1 and j!=N-1 and k==N-1) {
} else if (i!=N-1 and j!=N-1 and k==N-1) {
dFdqdqdq[i][j][k] = -(i==j) / (p[N-1]*q[N-1]*q[N-1]);
dFdqdqdq[i][j][k] = -(i==j) / (p[N-1]*q[N-1]*q[N-1]);
} else if (i!=N-1 and j==N-1 and k!=N-1) {
} else if (i!=N-1 and j==N-1 and k!=N-1) {
dFdqdqdq[i][j][k] = -(i==k) / (p[N-1]*q[N-1]*q[N-1]);
dFdqdqdq[i][j][k] = -(i==k) / (p[N-1]*q[N-1]*q[N-1]);
} else if (i!=N-1 and j==N-1 and k==N-1) {
} else if (i!=N-1 and j==N-1 and k==N-1) {
dFdqdqdq[i][j][k] = -2*(p[i] - q[i]) / (p[N-1]*Dune::power(q[N-1],3));
dFdqdqdq[i][j][k] = -2*(p[i] - q[i]) / (p[N-1]*Dune::power(q[N-1],3));
} else if (i==N-1 and j!=N-1 and k!=N-1) {
} else if (i==N-1 and j!=N-1 and k!=N-1) {
dFdqdqdq[i][j][k] = - (j==k) / (p[N-1]*q[N-1]*q[N-1]);
dFdqdqdq[i][j][k] = - (j==k) / (p[N-1]*q[N-1]*q[N-1]);
} else if (i==N-1 and j!=N-1 and k==N-1) {
} else if (i==N-1 and j!=N-1 and k==N-1) {
dFdqdqdq[i][j][k] = -2*(p[j] - q[j]) / (p[N-1]*Dune::power(q[N-1],3));
dFdqdqdq[i][j][k] = -2*(p[j] - q[j]) / (p[N-1]*Dune::power(q[N-1],3));
} else if (i==N-1 and j==N-1 and k!=N-1) {
} else if (i==N-1 and j==N-1 and k!=N-1) {
dFdqdqdq[i][j][k] = -2*(p[k] - q[k]) / (p[N-1]*Dune::power(q[N-1],3));
dFdqdqdq[i][j][k] = -2*(p[k] - q[k]) / (p[N-1]*Dune::power(q[N-1],3));
} else if (i==N-1 and j==N-1 and k==N-1) {
} else if (i==N-1 and j==N-1 and k==N-1) {
dFdqdqdq[i][j][k] = -2/Dune::power(q[N-1],3) - 1/(p[N-1]*q[N-1]*q[N-1]) - 4*(p[N-1]-q[N-1])/(p[N-1]*Dune::power(q[N-1],3))
- 3*diffNormSquared / (p[N-1]*Dune::power(q[N-1],4));
dFdqdqdq[i][j][k] = -2/Dune::power(q[N-1],3) - 1/(p[N-1]*q[N-1]*q[N-1]) - 4*(p[N-1]-q[N-1])/(p[N-1]*Dune::power(q[N-1],3))
- 3*diffNormSquared / (p[N-1]*Dune::power(q[N-1],4));
}
}
......@@ -401,89 +407,89 @@ public:
}
//
T x = 1 + diffNormSquared/ (2*p[N-1]*q[N-1]);
T alphaPrime = derivativeOfArcCosHSquared(x);
T alphaPrimePrime = secondDerivativeOfArcCosHSquared(x);
T alphaPrimePrimePrime = thirdDerivativeOfArcCosHSquared(x);
// Sum it all together
for (size_t i=0; i<N; i++)
for (size_t j=0; j<N; j++)
for (size_t k=0; k<N; k++)
result[i][j][k] = alphaPrimePrimePrime * dFdq[i] * dFdq[j] * dFdq[k]
+ alphaPrimePrime * (dFdqdq[i][j] * dFdq[k] + dFdqdq[i][k] * dFdq[j] + dFdqdq[j][k] * dFdq[i])
+ alphaPrime * dFdqdqdq[i][j][k];
return result;
}
//
T x = 1 + diffNormSquared/ (2*p[N-1]*q[N-1]);
T alphaPrime = derivativeOfArcCosHSquared(x);
T alphaPrimePrime = secondDerivativeOfArcCosHSquared(x);
T alphaPrimePrimePrime = thirdDerivativeOfArcCosHSquared(x);
/** \brief Compute the mixed third derivative \partial d^3 / \partial da db^2
*/
static Tensor3<T,N,N,N> thirdDerivativeOfDistanceSquaredWRTFirst1AndSecond2Argument(const HyperbolicHalfspacePoint& a, const HyperbolicHalfspacePoint& b)
{
Tensor3<T,N,N,N> result;
// Sum it all together
for (size_t i=0; i<N; i++)
for (size_t j=0; j<N; j++)
for (size_t k=0; k<N; k++)
result[i][j][k] = alphaPrimePrimePrime * dFdq[i] * dFdq[j] * dFdq[k]
+ alphaPrimePrime * (dFdqdq[i][j] * dFdq[k] + dFdqdq[i][k] * dFdq[j] + dFdqdq[j][k] * dFdq[i])
+ alphaPrime * dFdqdqdq[i][j][k];
// abbreviate notation
const Dune::FieldVector<T,N>& p = a.data_;
const Dune::FieldVector<T,N>& q = b.data_;
return result;
}
T diffNormSquared = (p-q).two_norm2();
/** \brief Compute the mixed third derivative \partial d^3 / \partial da db^2
*/
static Tensor3<T,N,N,N> thirdDerivativeOfDistanceSquaredWRTFirst1AndSecond2Argument(const HyperbolicHalfspacePoint& a, const HyperbolicHalfspacePoint& b)
{
Tensor3<T,N,N,N> result;
// Compute first derivatives of F with respect to p and q
Dune::FieldVector<T,N> dFdp = computeDFdp(a,b,diffNormSquared);
Dune::FieldVector<T,N> dFdq = computeDFdq(a,b,diffNormSquared);
// abbreviate notation
const Dune::FieldVector<T,N>& p = a.data_;
const Dune::FieldVector<T,N>& q = b.data_;
// Compute second derivatives of F
Dune::FieldMatrix<T,N,N> dFdqdq = computeDFdqdq(a,b,diffNormSquared);
T diffNormSquared = (p-q).two_norm2();
Dune::FieldMatrix<T,N,N> dFdpdq = computeDFdpdq(a,b,diffNormSquared);
// Compute first derivatives of F with respect to p and q
Dune::FieldVector<T,N> dFdp = computeDFdp(a,b,diffNormSquared);
Dune::FieldVector<T,N> dFdq = computeDFdq(a,b,diffNormSquared);
// Compute third derivatives of F
Tensor3<T,N,N,N> dFdpdqdq;
// Compute second derivatives of F
Dune::FieldMatrix<T,N,N> dFdqdq = computeDFdqdq(a,b,diffNormSquared);
for (size_t i=0; i<N; i++) {
Dune::FieldMatrix<T,N,N> dFdpdq = computeDFdpdq(a,b,diffNormSquared);
for (size_t j=0; j<N; j++) {
// Compute third derivatives of F
Tensor3<T,N,N,N> dFdpdqdq;
for (size_t k=0; k<N; k++) {
for (size_t i=0; i<N; i++) {
if (i!=N-1 and j!=N-1 and k!=N-1) {
for (size_t j=0; j<N; j++) {
dFdpdqdq[i][j][k] = 0;
for (size_t k=0; k<N; k++) {
} else if (i!=N-1 and j!=N-1 and k==N-1) {
if (i!=N-1 and j!=N-1 and k!=N-1) {
dFdpdqdq[i][j][k] = (i==j) / (p[N-1]*q[N-1]*q[N-1]);
dFdpdqdq[i][j][k] = 0;
} else if (i!=N-1 and j==N-1 and k!=N-1) {
} else if (i!=N-1 and j!=N-1 and k==N-1) {
dFdpdqdq[i][j][k] = (i==k) / (p[N-1]*q[N-1]*q[N-1]);
dFdpdqdq[i][j][k] = (i==j) / (p[N-1]*q[N-1]*q[N-1]);
} else if (i!=N-1 and j==N-1 and k==N-1) {
} else if (i!=N-1 and j==N-1 and k!=N-1) {
dFdpdqdq[i][j][k] = 2*(p[i] - q[i]) / (p[N-1]*Dune::power(q[N-1],3));
dFdpdqdq[i][j][k] = (i==k) / (p[N-1]*q[N-1]*q[N-1]);
} else if (i==N-1 and j!=N-1 and k!=N-1) {
} else if (i!=N-1 and j==N-1 and k==N-1) {
dFdpdqdq[i][j][k] = -(j==k) / (p[N-1]*p[N-1]*q[N-1]);
dFdpdqdq[i][j][k] = 2*(p[i] - q[i]) / (p[N-1]*Dune::power(q[N-1],3));
} else if (i==N-1 and j!=N-1 and k==N-1) {
} else if (i==N-1 and j!=N-1 and k!=N-1) {
dFdpdqdq[i][j][k] = -(p[j] - q[j]) / (p[N-1]*p[N-1]*Dune::power(q[N-1],2));
dFdpdqdq[i][j][k] = -(j==k) / (p[N-1]*p[N-1]*q[N-1]);
} else if (i==N-1 and j==N-1 and k!=N-1) {
} else if (i==N-1 and j!=N-1 and k==N-1) {
dFdpdqdq[i][j][k] = -(p[k] - q[k]) / (p[N-1]*p[N-1]*Dune::power(q[N-1],2));
dFdpdqdq[i][j][k] = -(p[j] - q[j]) / (p[N-1]*p[N-1]*Dune::power(q[N-1],2));
} else if (i==N-1 and j==N-1 and k==N-1) {
} else if (i==N-1 and j==N-1 and k!=N-1) {
dFdpdqdq[i][j][k] = 1.0/(p[N-1]*q[N-1]*q[N-1])
+ 2*(p[N-1]-q[N-1])/(p[N-1]*Dune::power(q[N-1],3))
- (p[N-1]-q[N-1])/(p[N-1]*p[N-1]*q[N-1]*q[N-1])
- diffNormSquared / (p[N-1]*p[N-1]*Dune::power(q[N-1],3));
dFdpdqdq[i][j][k] = -(p[k] - q[k]) / (p[N-1]*p[N-1]*Dune::power(q[N-1],2));
} else if (i==N-1 and j==N-1 and k==N-1) {
dFdpdqdq[i][j][k] = 1.0/(p[N-1]*q[N-1]*q[N-1])
+ 2*(p[N-1]-q[N-1])/(p[N-1]*Dune::power(q[N-1],3))
- (p[N-1]-q[N-1])/(p[N-1]*p[N-1]*q[N-1]*q[N-1])
- diffNormSquared / (p[N-1]*p[N-1]*Dune::power(q[N-1],3));
}
}
......@@ -491,62 +497,62 @@ public:
}
}
//
T x = 1 + diffNormSquared/ (2*p[N-1]*q[N-1]);
T alphaPrime = derivativeOfArcCosHSquared(x);
T alphaPrimePrime = secondDerivativeOfArcCosHSquared(x);
T alphaPrimePrimePrime = thirdDerivativeOfArcCosHSquared(x);
//
T x = 1 + diffNormSquared/ (2*p[N-1]*q[N-1]);
T alphaPrime = derivativeOfArcCosHSquared(x);
T alphaPrimePrime = secondDerivativeOfArcCosHSquared(x);
T alphaPrimePrimePrime = thirdDerivativeOfArcCosHSquared(x);
// Sum it all together
for (size_t i=0; i<N; i++)
for (size_t j=0; j<N; j++)
for (size_t k=0; k<N; k++)
result[i][j][k] = alphaPrimePrimePrime * dFdp[i] * dFdq[j] * dFdq[k]
+ alphaPrimePrime * (dFdpdq[i][j] * dFdq[k] + dFdpdq[i][k] * dFdq[j] + dFdqdq[j][k] * dFdp[i])
+ alphaPrime * dFdpdqdq[i][j][k];
// Sum it all together
for (size_t i=0; i<N; i++)
for (size_t j=0; j<N; j++)
for (size_t k=0; k<N; k++)
result[i][j][k] = alphaPrimePrimePrime * dFdp[i] * dFdq[j] * dFdq[k]
+ alphaPrimePrime * (dFdpdq[i][j] * dFdq[k] + dFdpdq[i][k] * dFdq[j] + dFdqdq[j][k] * dFdp[i])
+ alphaPrime * dFdpdqdq[i][j][k];
return result;
return result;
}
}
/** \brief Project tangent vector of R^n onto the tangent space. For H^m this is the identity */
EmbeddedTangentVector projectOntoTangentSpace(const EmbeddedTangentVector& v) const {
return v;
}
/** \brief Project tangent vector of R^n onto the tangent space. For H^m this is the identity */
EmbeddedTangentVector projectOntoTangentSpace(const EmbeddedTangentVector& v) const {
return v;
}
/** \brief The global coordinates, if you really want them */
const CoordinateType& globalCoordinates() const {
return data_;
}
/** \brief The global coordinates, if you really want them */
const CoordinateType& globalCoordinates() const {
return data_;
}
/** \brief Compute an orthonormal basis of the tangent space of H^N.
*/
Dune::FieldMatrix<T,N,N> orthonormalFrame() const {
/** \brief Compute an orthonormal basis of the tangent space of H^N.
*/
Dune::FieldMatrix<T,N,N> orthonormalFrame() const {
Dune::ScaledIdentityMatrix<T,N> result( data_[N-1] );
Dune::ScaledIdentityMatrix<T,N> result( data_[N-1] );
return Dune::FieldMatrix<T,N,N>(result);
}
return Dune::FieldMatrix<T,N,N>(result);
}
/** \brief Scalar product of two tangent vectors */
T metric(const TangentVector& v, const TangentVector& w) const
{
return v*w/(data_[N-1]*data_[N-1]);
}
/** \brief Scalar product of two tangent vectors */
T metric(const TangentVector& v, const TangentVector& w) const
{
return v*w/(data_[N-1]*data_[N-1]);
}
/** \brief Write unit vector object to output stream */
friend std::ostream& operator<< (std::ostream& s, const HyperbolicHalfspacePoint& p)
{
return s << p.data_;
}
/** \brief Write unit vector object to output stream */
friend std::ostream& operator<< (std::ostream& s, const HyperbolicHalfspacePoint& p)
{
return s << p.data_;
}
private:
private:
Dune::FieldVector<T,N> data_;
};
Dune::FieldVector<T,N> data_;
};
} // namespace Dune::GFE
#endif
dune/gfe/spaces/orthogonalmatrix.hh
View file @ 48b9358e
......@@ -5,176 +5,182 @@
#include <dune/gfe/skewmatrix.hh>
/** \brief An orthogonal \f$ n \times n \f$ matrix
* \tparam T Type of the matrix entries
* \tparam N Space dimension
*/
template <class T, int N>
class OrthogonalMatrix
{
public:
/** \brief The type used for coordinates */
typedef T ctype;
/** \brief Dimension of the manifold formed by the orthogonal matrices */
static const int dim = N*(N-1)/2;
/** \brief Coordinates are embedded into a Euclidean space of N x N - matrices */
static const int embeddedDim = N*N;
/** \brief The type used for global coordinates */
typedef Dune::FieldVector<T,embeddedDim> CoordinateType;
/** \brief Member of the corresponding Lie algebra. This really is a skew-symmetric matrix */
typedef Dune::FieldVector<T,dim> TangentVector;
/** \brief A tangent vector as a vector in the surrounding coordinate space */
typedef Dune::FieldVector<T,embeddedDim> EmbeddedTangentVector;
/** \brief Default constructor -- leaves the matrix uninitialized */
OrthogonalMatrix()
{}
/** \brief Constructor from a general matrix
*
* It is not checked whether the matrix is really orthogonal
*/
explicit OrthogonalMatrix(const Dune::FieldMatrix<T,N,N>& matrix)
: data_(matrix)
{}
namespace Dune::GFE
{
/** \brief Copy constructor
*
* It is not checked whether the matrix is really orthogonal
/** \brief An orthogonal \f$ n \times n \f$ matrix
* \tparam T Type of the matrix entries
* \tparam N Space dimension
*/
explicit OrthogonalMatrix(const CoordinateType& other)
template <class T, int N>
class OrthogonalMatrix
{
DUNE_THROW(Dune::NotImplemented, "constructor");
}
public:
/** \brief The type used for coordinates */
typedef T ctype;
/** \brief Dimension of the manifold formed by the orthogonal matrices */
static const int dim = N*(N-1)/2;
/** \brief Coordinates are embedded into a Euclidean space of N x N - matrices */
static const int embeddedDim = N*N;
/** \brief The type used for global coordinates */
typedef Dune::FieldVector<T,embeddedDim> CoordinateType;
/** \brief Member of the corresponding Lie algebra. This really is a skew-symmetric matrix */
typedef Dune::FieldVector<T,dim> TangentVector;
/** \brief A tangent vector as a vector in the surrounding coordinate space */
typedef Dune::FieldVector<T,embeddedDim> EmbeddedTangentVector;
/** \brief Default constructor -- leaves the matrix uninitialized */
OrthogonalMatrix()
{}
/** \brief Constructor from a general matrix
*
* It is not checked whether the matrix is really orthogonal
*/
explicit OrthogonalMatrix(const Dune::FieldMatrix<T,N,N>& matrix)
: data_(matrix)
{}
/** \brief Copy constructor
*
* It is not checked whether the matrix is really orthogonal
*/
explicit OrthogonalMatrix(const CoordinateType& other)
{
DUNE_THROW(Dune::NotImplemented, "constructor");
}
/** \brief Const access to the matrix entries */
const Dune::FieldMatrix<T,N,N>& data() const
{
return data_;
}
/** \brief Project the input matrix onto the tangent space at "this"
*
* See Absil, Mahoney, Sepulche, Example 5.3.2 for the formula
* \f[ P_X \xi = X \operatorname{skew} (X^T \xi) \f]
*
*/
Dune::FieldMatrix<T,N,N> projectOntoTangentSpace(const Dune::FieldMatrix<T,N,N>& matrix) const
{
// rename to get the same notation as Absil & Co
const Dune::FieldMatrix<T,N,N>& X = data_;
// X^T \xi
Dune::FieldMatrix<T,N,N> XTxi(0);
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
for (int k=0; k<N; k++)
XTxi[i][j] += X[k][i] * matrix[k][j];
// skew (X^T \xi)
Dune::FieldMatrix<T,N,N> skewXTxi(0);
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
skewXTxi[i][j] = 0.5 * ( XTxi[i][j] - XTxi[j][i] );
// X skew (X^T \xi)
Dune::FieldMatrix<T,N,N> result(0);
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
for (int k=0; k<N; k++)
result[i][j] += X[i][k] * skewXTxi[k][j];
return result;
}
/** \brief Rebind the OrthogonalMatrix to another coordinate type */
template<class U>
struct rebind
{
typedef OrthogonalMatrix<U,N> other;
};
OrthogonalMatrix& operator= (const CoordinateType& other)
{
std::size_t idx = 0;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
data_[i][j] = other[idx++];
return *this;
}
/** \brief The exponential map from a given point $p \in SO(n)$.
\param v A tangent vector.
*/
static OrthogonalMatrix<T,3> exp(const OrthogonalMatrix<T,N>& p, const TangentVector& v)
{
DUNE_THROW(Dune::NotImplemented, "exp");
}
/** \brief Return the actual matrix */
void matrix(Dune::FieldMatrix<T,N,N>& m) const
{
m = data_;
}
/** \brief Project tangent vector of R^n onto the normal space space */
EmbeddedTangentVector projectOntoNormalSpace(const EmbeddedTangentVector& v) const
{
DUNE_THROW(Dune::NotImplemented, "projectOntoNormalSpace");
}
/** \brief The Weingarten map */
EmbeddedTangentVector weingarten(const EmbeddedTangentVector& z, const EmbeddedTangentVector& v) const
{
EmbeddedTangentVector result;
DUNE_THROW(Dune::NotImplemented, "weingarten");
return result;
}
static OrthogonalMatrix<T,N> projectOnto(const CoordinateType& p)
{
DUNE_THROW(Dune::NotImplemented, "projectOnto");
}
// TODO return type is wrong
static Dune::FieldMatrix<T,1,1> derivativeOfProjection(const CoordinateType& p)
{
Dune::FieldMatrix<T,1,1> result;
return result;
}
/** \brief The global coordinates, if you really want them */
CoordinateType globalCoordinates() const
{
CoordinateType result;
std::size_t idx = 0;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
result[idx++] = data_[i][j];
return result;
}
/** \brief Compute an orthonormal basis of the tangent space of SO(n). */
Dune::FieldMatrix<T,dim,embeddedDim> orthonormalFrame() const
{
Dune::FieldMatrix<T,dim,embeddedDim> result;
DUNE_THROW(Dune::NotImplemented, "orthonormalFrame");
return result;
}
private:
/** \brief The actual data */
Dune::FieldMatrix<T,N,N> data_;
/** \brief Const access to the matrix entries */
const Dune::FieldMatrix<T,N,N>& data() const
{
return data_;
}
/** \brief Project the input matrix onto the tangent space at "this"
*
* See Absil, Mahoney, Sepulche, Example 5.3.2 for the formula
* \f[ P_X \xi = X \operatorname{skew} (X^T \xi) \f]
*
*/
Dune::FieldMatrix<T,N,N> projectOntoTangentSpace(const Dune::FieldMatrix<T,N,N>& matrix) const
{
// rename to get the same notation as Absil & Co
const Dune::FieldMatrix<T,N,N>& X = data_;
// X^T \xi
Dune::FieldMatrix<T,N,N> XTxi(0);
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
for (int k=0; k<N; k++)
XTxi[i][j] += X[k][i] * matrix[k][j];
// skew (X^T \xi)
Dune::FieldMatrix<T,N,N> skewXTxi(0);
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
skewXTxi[i][j] = 0.5 * ( XTxi[i][j] - XTxi[j][i] );
// X skew (X^T \xi)
Dune::FieldMatrix<T,N,N> result(0);
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
for (int k=0; k<N; k++)
result[i][j] += X[i][k] * skewXTxi[k][j];
return result;
}
/** \brief Rebind the OrthogonalMatrix to another coordinate type */
template<class U>
struct rebind
{
typedef OrthogonalMatrix<U,N> other;
};
OrthogonalMatrix& operator= (const CoordinateType& other)
{
std::size_t idx = 0;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
data_[i][j] = other[idx++];
return *this;
}
/** \brief The exponential map from a given point $p \in SO(n)$.
\param v A tangent vector.
*/
static OrthogonalMatrix<T,3> exp(const OrthogonalMatrix<T,N>& p, const TangentVector& v)
{
DUNE_THROW(Dune::NotImplemented, "exp");
}
/** \brief Return the actual matrix */
void matrix(Dune::FieldMatrix<T,N,N>& m) const
{
m = data_;
}
/** \brief Project tangent vector of R^n onto the normal space space */
EmbeddedTangentVector projectOntoNormalSpace(const EmbeddedTangentVector& v) const
{
DUNE_THROW(Dune::NotImplemented, "projectOntoNormalSpace");
}
/** \brief The Weingarten map */
EmbeddedTangentVector weingarten(const EmbeddedTangentVector& z, const EmbeddedTangentVector& v) const
{
EmbeddedTangentVector result;
DUNE_THROW(Dune::NotImplemented, "weingarten");
return result;
}
static OrthogonalMatrix<T,N> projectOnto(const CoordinateType& p)
{
DUNE_THROW(Dune::NotImplemented, "projectOnto");
}
// TODO return type is wrong
static Dune::FieldMatrix<T,1,1> derivativeOfProjection(const CoordinateType& p)
{
Dune::FieldMatrix<T,1,1> result;
return result;
}
/** \brief The global coordinates, if you really want them */
CoordinateType globalCoordinates() const
{
CoordinateType result;
std::size_t idx = 0;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
result[idx++] = data_[i][j];
return result;
}
/** \brief Compute an orthonormal basis of the tangent space of SO(n). */
Dune::FieldMatrix<T,dim,embeddedDim> orthonormalFrame() const
{
Dune::FieldMatrix<T,dim,embeddedDim> result;
DUNE_THROW(Dune::NotImplemented, "orthonormalFrame");
return result;
}
private:
/** \brief The actual data */
Dune::FieldMatrix<T,N,N> data_;
};
} // namespace Dune::GFE
#endif // DUNE_GFE_SPACES_ORTHOGONALMATRIX_HH
dune/gfe/spaces/productmanifold.hh
View file @ 48b9358e
......@@ -208,7 +208,7 @@ namespace Dune::GFE
static auto secondDerivativeOfDistanceSquaredWRTSecondArgument(const ProductManifold& a,
const ProductManifold& b)
{
Dune::SymmetricMatrix<field_type,embeddedDim> result;
SymmetricMatrix<field_type,embeddedDim> result;
auto secDerivOfDistSqWRTSecArgFunctor = [] (auto& argsTuple, std::array<std::size_t,2>& posHelper, const auto& manifoldInt)
{
auto& deriv = std::get<0>(argsTuple);
......
dune/gfe/spaces/quaternion.hh
View file @ 48b9358e
......@@ -7,165 +7,171 @@
#include <dune/gfe/tensor3.hh>
template <class T>
class Quaternion : public Dune::FieldVector<T,4>
namespace Dune::GFE
{
public:
/** \brief Default constructor */
Quaternion() {}
/** \brief Constructor with the four components */
Quaternion(const T& a, const T& b, const T& c, const T& d) {
(*this)[0] = a;
(*this)[1] = b;
(*this)[2] = c;
(*this)[3] = d;
}
/** \brief Constructor from a single scalar */
Quaternion(const T& a) : Dune::FieldVector<T,4>(a) {}
/** \brief Copy constructor */
Quaternion(const Dune::FieldVector<T,4>& other) : Dune::FieldVector<T,4>(other) {}
/** \brief Assignment from a scalar */
Quaternion<T>& operator=(const T& v) {
for (int i=0; i<4; i++)
(*this)[i] = v;
return (*this);
}
/** \brief Return the identity element */
static Quaternion<T> identity() {
Quaternion<T> id;
id[0] = 0;
id[1] = 0;
id[2] = 0;
id[3] = 1;
return id;
}
/** \brief Right quaternion multiplication */
Quaternion<T> mult(const Quaternion<T>& other) const {
Quaternion<T> q;
q[0] = (*this)[3]*other[0] - (*this)[2]*other[1] + (*this)[1]*other[2] + (*this)[0]*other[3];
q[1] = (*this)[2]*other[0] + (*this)[3]*other[1] - (*this)[0]*other[2] + (*this)[1]*other[3];
q[2] = - (*this)[1]*other[0] + (*this)[0]*other[1] + (*this)[3]*other[2] + (*this)[2]*other[3];
q[3] = - (*this)[0]*other[0] - (*this)[1]*other[1] - (*this)[2]*other[2] + (*this)[3]*other[3];
return q;
}
/** \brief Return the triple of director vectors represented by a unit quaternion
The formulas are taken from Dichmann, Li, Maddocks, (2.6.4), (2.6.5), (2.6.6)
*/
Dune::FieldVector<T,3> director(int i) const {
Dune::FieldVector<T,3> d;
const Dune::FieldVector<T,4>& q = *this; // simpler notation
if (i==0) {
d[0] = q[0]*q[0] - q[1]*q[1] - q[2]*q[2] + q[3]*q[3];
d[1] = 2 * (q[0]*q[1] + q[2]*q[3]);
d[2] = 2 * (q[0]*q[2] - q[1]*q[3]);
} else if (i==1) {
d[0] = 2 * (q[0]*q[1] - q[2]*q[3]);
d[1] = -q[0]*q[0] + q[1]*q[1] - q[2]*q[2] + q[3]*q[3];
d[2] = 2 * (q[1]*q[2] + q[0]*q[3]);
} else if (i==2) {
d[0] = 2 * (q[0]*q[2] + q[1]*q[3]);
d[1] = 2 * (q[1]*q[2] - q[0]*q[3]);
d[2] = -q[0]*q[0] - q[1]*q[1] + q[2]*q[2] + q[3]*q[3];
} else
DUNE_THROW(Dune::Exception, "Nonexisting director " << i << " requested!");
return d;
}
/** \brief Turn quaternion into a unit quaternion by dividing by its Euclidean norm */
void normalize() {
(*this) /= this->two_norm();
}
Dune::FieldVector<double,3> rotate(const Dune::FieldVector<double,3>& v) const {
Dune::FieldVector<double,3> result;
Dune::FieldVector<double,3> d0 = director(0);
Dune::FieldVector<double,3> d1 = director(1);
Dune::FieldVector<double,3> d2 = director(2);
for (int i=0; i<3; i++)
result[i] = v[0]*d0[i] + v[1]*d1[i] + v[2]*d2[i];
return result;
}
/** \brief Conjugate the quaternion */
void conjugate() {
(*this)[0] *= -1;
(*this)[1] *= -1;
(*this)[2] *= -1;
}
/** \brief Invert the quaternion */
void invert() {
conjugate();
(*this) /= this->two_norm2();
}
/** \brief Yield the inverse quaternion */
Quaternion<T> inverse() const {
Quaternion<T> result = *this;
result.invert();
return result;
}
/** \brief Create three vectors which form an orthonormal basis of \mathbb{H} together
with this one.
This is used to compute the strain in rod problems.
See: Dichmann, Li, Maddocks, 'Hamiltonian Formulations and Symmetries in
Rod Mechanics', page 83
*/
Quaternion<T> B(int m) const {
assert(m>=0 && m<3);
Quaternion<T> r;
if (m==0) {
r[0] = (*this)[3];
r[1] = (*this)[2];
r[2] = -(*this)[1];
r[3] = -(*this)[0];
} else if (m==1) {
r[0] = -(*this)[2];
r[1] = (*this)[3];
r[2] = (*this)[0];
r[3] = -(*this)[1];
} else {
r[0] = (*this)[1];
r[1] = -(*this)[0];
r[2] = (*this)[3];
r[3] = -(*this)[2];
template <class T>
class Quaternion : public Dune::FieldVector<T,4>
{
public:
/** \brief Default constructor */
Quaternion() {}
/** \brief Constructor with the four components */
Quaternion(const T& a, const T& b, const T& c, const T& d) {
(*this)[0] = a;
(*this)[1] = b;
(*this)[2] = c;
(*this)[3] = d;
}
/** \brief Constructor from a single scalar */
Quaternion(const T& a) : Dune::FieldVector<T,4>(a) {}
/** \brief Copy constructor */
Quaternion(const Dune::FieldVector<T,4>& other) : Dune::FieldVector<T,4>(other) {}
/** \brief Assignment from a scalar */
Quaternion<T>& operator=(const T& v) {
for (int i=0; i<4; i++)
(*this)[i] = v;
return (*this);
}
/** \brief Return the identity element */
static Quaternion<T> identity() {
Quaternion<T> id;
id[0] = 0;
id[1] = 0;
id[2] = 0;
id[3] = 1;
return id;
}
/** \brief Right quaternion multiplication */
Quaternion<T> mult(const Quaternion<T>& other) const {
Quaternion<T> q;
q[0] = (*this)[3]*other[0] - (*this)[2]*other[1] + (*this)[1]*other[2] + (*this)[0]*other[3];
q[1] = (*this)[2]*other[0] + (*this)[3]*other[1] - (*this)[0]*other[2] + (*this)[1]*other[3];
q[2] = - (*this)[1]*other[0] + (*this)[0]*other[1] + (*this)[3]*other[2] + (*this)[2]*other[3];
q[3] = - (*this)[0]*other[0] - (*this)[1]*other[1] - (*this)[2]*other[2] + (*this)[3]*other[3];
return q;
}
/** \brief Return the triple of director vectors represented by a unit quaternion
The formulas are taken from Dichmann, Li, Maddocks, (2.6.4), (2.6.5), (2.6.6)
*/
Dune::FieldVector<T,3> director(int i) const {
Dune::FieldVector<T,3> d;
const Dune::FieldVector<T,4>& q = *this; // simpler notation
if (i==0) {
d[0] = q[0]*q[0] - q[1]*q[1] - q[2]*q[2] + q[3]*q[3];
d[1] = 2 * (q[0]*q[1] + q[2]*q[3]);
d[2] = 2 * (q[0]*q[2] - q[1]*q[3]);
} else if (i==1) {
d[0] = 2 * (q[0]*q[1] - q[2]*q[3]);
d[1] = -q[0]*q[0] + q[1]*q[1] - q[2]*q[2] + q[3]*q[3];
d[2] = 2 * (q[1]*q[2] + q[0]*q[3]);
} else if (i==2) {
d[0] = 2 * (q[0]*q[2] + q[1]*q[3]);
d[1] = 2 * (q[1]*q[2] - q[0]*q[3]);
d[2] = -q[0]*q[0] - q[1]*q[1] + q[2]*q[2] + q[3]*q[3];
} else
DUNE_THROW(Dune::Exception, "Nonexisting director " << i << " requested!");
return d;
}
/** \brief Turn quaternion into a unit quaternion by dividing by its Euclidean norm */
void normalize() {
(*this) /= this->two_norm();
}
return r;
}
Dune::FieldVector<double,3> rotate(const Dune::FieldVector<double,3>& v) const {
Dune::FieldVector<double,3> result;
Dune::FieldVector<double,3> d0 = director(0);
Dune::FieldVector<double,3> d1 = director(1);
Dune::FieldVector<double,3> d2 = director(2);
for (int i=0; i<3; i++)
result[i] = v[0]*d0[i] + v[1]*d1[i] + v[2]*d2[i];
return result;
}
/** \brief Conjugate the quaternion */
void conjugate() {
(*this)[0] *= -1;
(*this)[1] *= -1;
(*this)[2] *= -1;
}
/** \brief Invert the quaternion */
void invert() {
conjugate();
(*this) /= this->two_norm2();
}
/** \brief Yield the inverse quaternion */
Quaternion<T> inverse() const {
Quaternion<T> result = *this;
result.invert();
return result;
}
/** \brief Create three vectors which form an orthonormal basis of \mathbb{H} together
with this one.
This is used to compute the strain in rod problems.
See: Dichmann, Li, Maddocks, 'Hamiltonian Formulations and Symmetries in
Rod Mechanics', page 83
*/
Quaternion<T> B(int m) const {
assert(m>=0 && m<3);
Quaternion<T> r;
if (m==0) {
r[0] = (*this)[3];
r[1] = (*this)[2];
r[2] = -(*this)[1];
r[3] = -(*this)[0];
} else if (m==1) {
r[0] = -(*this)[2];
r[1] = (*this)[3];
r[2] = (*this)[0];
r[3] = -(*this)[1];
} else {
r[0] = (*this)[1];
r[1] = -(*this)[0];
r[2] = (*this)[3];
r[3] = -(*this)[2];
}
return r;
}
};
};
} // namespace Dune::GFE
namespace Dune
{
/** \brief Specizalization needed to allow certain forms of matrix--quaternion multiplications */
template< class T >
struct FieldTraits< Quaternion<T> >
struct FieldTraits< Dune::GFE::Quaternion<T> >
{
typedef typename FieldTraits<T>::field_type field_type;
typedef typename FieldTraits<T>::real_type real_type;
......
dune/gfe/spaces/realtuple.hh
View file @ 48b9358e
......@@ -9,249 +9,254 @@
#include <dune/gfe/symmetricmatrix.hh>
/** \brief Implement a tuple of real numbers as a Riemannian manifold
Currently this class only exists for testing purposes.
*/
template <class T, int N>
class RealTuple
namespace Dune::GFE
{
public:
typedef T ctype;
typedef T field_type;
/** \brief The type used for global coordinates */
typedef Dune::FieldVector<T,N> CoordinateType;
/** \brief Dimension of the manifold formed by unit vectors */
static const int dim = N;
/** \brief Dimension of the Euclidean space the manifold is embedded in */
static const int embeddedDim = N;
typedef Dune::FieldVector<T,N> EmbeddedTangentVector;
typedef Dune::FieldVector<T,N> TangentVector;
/** \brief The global convexity radius of the Euclidean space */
static constexpr double convexityRadius = std::numeric_limits<double>::infinity();
/** \brief Implement a tuple of real numbers as a Riemannian manifold
/** \brief The return type of the derivativeOfProjection method */
typedef Dune::ScaledIdentityMatrix<T, N> DerivativeOfProjection;
/** \brief Default constructor */
RealTuple()
{}
Currently this class only exists for testing purposes.
*/
/** \brief Construction from a scalar */
RealTuple(T v)
template <class T, int N>
class RealTuple
{
data_ = v;
}
/** \brief Copy constructor */
RealTuple(const RealTuple<T,N>& other)
: data_(other.data_)
{}
/** \brief Constructor from FieldVector*/
RealTuple(const Dune::FieldVector<T,N>& other)
: data_(other)
{}
RealTuple& operator=(const Dune::FieldVector<T,N>& other) {
data_ = other;
return *this;
}
RealTuple& operator-=(const Dune::FieldVector<T,N>& other) {
data_ -= other;
return *this;
}
template <class T2>
RealTuple& operator-=(const RealTuple<T2,N>& other) {
data_ -= other.data_;
return *this;
}
/** \brief Assignment from RealTuple with different type -- used for automatic differentiation with ADOL-C */
template <class T2>
RealTuple& operator <<= (const RealTuple<T2,N>& other) {
for (size_t i=0; i<N; i++)
data_[i] <<= other.data_[i];
return *this;
}
/** \brief Const random-access operator*/
T operator[] (const size_t indexVariable ) const {
return data_[indexVariable];
}
/** \brief Rebind the RealTuple to another coordinate type */
template<class U>
struct rebind
{
typedef RealTuple<U,N> other;
};
/** \brief The exponention map */
static RealTuple exp(const RealTuple& p, const TangentVector& v) {
return RealTuple(p.data_+v);
}
/** \brief Geodesic distance between two points
Simply the Euclidean distance */
static T distance(const RealTuple& a, const RealTuple& b) {
return log(a.data_,b.data_).two_norm();
}
/** \brief The logarithmic map
*
* \result A vector in the tangent space of a, viz: b-a
* */
static auto log(const RealTuple& a, const RealTuple& b) {
return b.data_ - a.data_;
}
public:
typedef T ctype;
typedef T field_type;
/** \brief The type used for global coordinates */
typedef Dune::FieldVector<T,N> CoordinateType;
/** \brief Dimension of the manifold formed by unit vectors */
static const int dim = N;
/** \brief Dimension of the Euclidean space the manifold is embedded in */
static const int embeddedDim = N;
typedef Dune::FieldVector<T,N> EmbeddedTangentVector;
typedef Dune::FieldVector<T,N> TangentVector;
/** \brief The global convexity radius of the Euclidean space */
static constexpr double convexityRadius = std::numeric_limits<double>::infinity();
/** \brief The return type of the derivativeOfProjection method */
typedef Dune::ScaledIdentityMatrix<T, N> DerivativeOfProjection;
/** \brief Default constructor */
RealTuple()
{}
/** \brief Construction from a scalar */
RealTuple(T v)
{
data_ = v;
}
/** \brief Copy constructor */
RealTuple(const RealTuple<T,N>& other)
: data_(other.data_)
{}
/** \brief Constructor from FieldVector*/
RealTuple(const Dune::FieldVector<T,N>& other)
: data_(other)
{}
RealTuple& operator=(const Dune::FieldVector<T,N>& other) {
data_ = other;
return *this;
}
RealTuple& operator-=(const Dune::FieldVector<T,N>& other) {
data_ -= other;
return *this;
}
template <class T2>
RealTuple& operator-=(const RealTuple<T2,N>& other) {
data_ -= other.data_;
return *this;
}
/** \brief Assignment from RealTuple with different type -- used for automatic differentiation with ADOL-C */
template <class T2>
RealTuple& operator <<= (const RealTuple<T2,N>& other) {
for (size_t i=0; i<N; i++)
data_[i] <<= other.data_[i];
return *this;
}
/** \brief Const random-access operator*/
T operator[] (const size_t indexVariable ) const {
return data_[indexVariable];
}
/** \brief Rebind the RealTuple to another coordinate type */
template<class U>
struct rebind
{
typedef RealTuple<U,N> other;
};
/** \brief The exponention map */
static RealTuple exp(const RealTuple& p, const TangentVector& v) {
return RealTuple(p.data_+v);
}
/** \brief Geodesic distance between two points
Simply the Euclidean distance */
static T distance(const RealTuple& a, const RealTuple& b) {
return log(a.data_,b.data_).two_norm();
}
/** \brief The logarithmic map
*
* \result A vector in the tangent space of a, viz: b-a
* */
static auto log(const RealTuple& a, const RealTuple& b) {
return b.data_ - a.data_;
}
#if ADOLC_ADOUBLE_H
/** \brief Geodesic distance squared between two points
Simply the Euclidean distance squared */
static adouble distanceSquared(const RealTuple<double,N>& a, const RealTuple<adouble,N>& b) {
adouble result(0.0);
for (int i=0; i<N; i++)
result += (a.globalCoordinates()[i] - b.globalCoordinates()[i]) * (a.globalCoordinates()[i] - b.globalCoordinates()[i]);
return result;
}
/** \brief Geodesic distance squared between two points
Simply the Euclidean distance squared */
static adouble distanceSquared(const RealTuple<double,N>& a, const RealTuple<adouble,N>& b) {
adouble result(0.0);
for (int i=0; i<N; i++)
result += (a.globalCoordinates()[i] - b.globalCoordinates()[i]) * (a.globalCoordinates()[i] - b.globalCoordinates()[i]);
return result;
}
#endif
/** \brief Compute the gradient of the squared distance function keeping the first argument fixed
/** \brief Compute the gradient of the squared distance function keeping the first argument fixed
Unlike the distance itself the squared distance is differentiable at zero
*/
static EmbeddedTangentVector derivativeOfDistanceSquaredWRTSecondArgument(const RealTuple& a, const RealTuple& b) {
EmbeddedTangentVector result = a.data_;
result -= b.data_;
result *= -2;
return result;
}
/** \brief Compute the Hessian of the squared distance function keeping the first argument fixed
Unlike the distance itself the squared distance is differentiable at zero
*/
static EmbeddedTangentVector derivativeOfDistanceSquaredWRTSecondArgument(const RealTuple& a, const RealTuple& b) {
EmbeddedTangentVector result = a.data_;
result -= b.data_;
result *= -2;
return result;
}
Unlike the distance itself the squared distance is differentiable at zero
*/
static SymmetricMatrix<T,N> secondDerivativeOfDistanceSquaredWRTSecondArgument(const RealTuple& a, const RealTuple& b) {
SymmetricMatrix<T,N> result;
for (int i=0; i<N; i++)
for (int j=0; j<=i; j++)
result(i,j) = 2*(i==j);
/** \brief Compute the Hessian of the squared distance function keeping the first argument fixed
return result;
}
Unlike the distance itself the squared distance is differentiable at zero
*/
static Dune::SymmetricMatrix<T,N> secondDerivativeOfDistanceSquaredWRTSecondArgument(const RealTuple& a, const RealTuple& b) {
/** \brief Compute the mixed second derivate \partial d^2 / \partial da db
Dune::SymmetricMatrix<T,N> result;
for (int i=0; i<N; i++)
for (int j=0; j<=i; j++)
result(i,j) = 2*(i==j);
Unlike the distance itself the squared distance is differentiable at zero
*/
static Dune::FieldMatrix<T,N,N> secondDerivativeOfDistanceSquaredWRTFirstAndSecondArgument(const RealTuple& a, const RealTuple& b) {
return result;
}
Dune::FieldMatrix<T,N,N> result;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
result[i][j] = -2*(i==j);
/** \brief Compute the mixed second derivate \partial d^2 / \partial da db
return result;
}
Unlike the distance itself the squared distance is differentiable at zero
*/
static Dune::FieldMatrix<T,N,N> secondDerivativeOfDistanceSquaredWRTFirstAndSecondArgument(const RealTuple& a, const RealTuple& b) {
/** \brief Compute the mixed third derivative \partial d^3 / \partial db^3
Dune::FieldMatrix<T,N,N> result;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
result[i][j] = -2*(i==j);
The result is the constant zero-tensor.
*/
static Tensor3<T,N,N,N> thirdDerivativeOfDistanceSquaredWRTSecondArgument(const RealTuple& a, const RealTuple& b) {
return Tensor3<T,N,N,N>(0);
}
return result;
}
/** \brief Compute the mixed third derivative \partial d^3 / \partial da db^2
/** \brief Compute the mixed third derivative \partial d^3 / \partial db^3
The result is the constant zero-tensor.
*/
static Tensor3<T,N,N,N> thirdDerivativeOfDistanceSquaredWRTFirst1AndSecond2Argument(const RealTuple& a, const RealTuple& b) {
return Tensor3<T,N,N,N>(0);
}
The result is the constant zero-tensor.
*/
static Tensor3<T,N,N,N> thirdDerivativeOfDistanceSquaredWRTSecondArgument(const RealTuple& a, const RealTuple& b) {
return Tensor3<T,N,N,N>(0);
}
/** \brief Compute the mixed third derivative \partial d^3 / \partial da db^2
/** \brief Project tangent vector of R^n onto the tangent space */
EmbeddedTangentVector projectOntoTangentSpace(const EmbeddedTangentVector& v) const {
return v;
}
The result is the constant zero-tensor.
*/
static Tensor3<T,N,N,N> thirdDerivativeOfDistanceSquaredWRTFirst1AndSecond2Argument(const RealTuple& a, const RealTuple& b) {
return Tensor3<T,N,N,N>(0);
}
/** \brief Project tangent vector of R^n onto the tangent space */
EmbeddedTangentVector projectOntoTangentSpace(const EmbeddedTangentVector& v) const {
return v;
}
/** \brief Project tangent vector of R^n onto the normal space space */
EmbeddedTangentVector projectOntoNormalSpace(const EmbeddedTangentVector& v) const {
return EmbeddedTangentVector(0);
}
/** \brief The Weingarten map */
EmbeddedTangentVector weingarten(const EmbeddedTangentVector& z, const EmbeddedTangentVector& v) const {
return EmbeddedTangentVector(0);
}
/** \brief Projection from the embedding space onto the manifold
*
* For RealTuples this is simply the identity map
*/
static RealTuple<T,N> projectOnto(const CoordinateType& p)
{
return RealTuple<T,N>(p);
}
/** \brief Project tangent vector of R^n onto the normal space space */
EmbeddedTangentVector projectOntoNormalSpace(const EmbeddedTangentVector& v) const {
return EmbeddedTangentVector(0);
}
/** \brief Derivative of the projection from the embedding space onto the manifold
*
* For RealTuples this is simply the identity
*/
static DerivativeOfProjection derivativeOfProjection(const Dune::FieldVector<T,N>& p)
{
return Dune::ScaledIdentityMatrix<T,N>(1.0);
}
/** \brief The Weingarten map */
EmbeddedTangentVector weingarten(const EmbeddedTangentVector& z, const EmbeddedTangentVector& v) const {
return EmbeddedTangentVector(0);
}
/** \brief The global coordinates, if you really want them */
const Dune::FieldVector<T,N>& globalCoordinates() const {
return data_;
}
/** \brief Projection from the embedding space onto the manifold
*
* For RealTuples this is simply the identity map
*/
static RealTuple<T,N> projectOnto(const CoordinateType& p)
{
return RealTuple<T,N>(p);
}
Dune::FieldVector<T,N>& globalCoordinates() {
return data_;
}
/** \brief Derivative of the projection from the embedding space onto the manifold
*
* For RealTuples this is simply the identity
*/
static DerivativeOfProjection derivativeOfProjection(const Dune::FieldVector<T,N>& p)
{
return Dune::ScaledIdentityMatrix<T,N>(1.0);
}
/** \brief The global coordinates, if you really want them */
const Dune::FieldVector<T,N>& globalCoordinates() const {
return data_;
}
/** \brief Compute an orthonormal basis of the tangent space of R^n.
Dune::FieldVector<T,N>& globalCoordinates() {
return data_;
}
In general this frame field, may of course not be continuous, but for RealTuples it is.
*/
Dune::FieldMatrix<T,N,N> orthonormalFrame() const {
Dune::FieldMatrix<T,N,N> result;
/** \brief Compute an orthonormal basis of the tangent space of R^n.
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
result[i][j] = (i==j);
return result;
}
In general this frame field, may of course not be continuous, but for RealTuples it is.
*/
Dune::FieldMatrix<T,N,N> orthonormalFrame() const {
Dune::FieldMatrix<T,N,N> result;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
result[i][j] = (i==j);
return result;
}
/** \brief Write LocalKey object to output stream */
friend std::ostream& operator<< (std::ostream& s, const RealTuple& realTuple)
{
return s << realTuple.data_;
}
/** \brief Write LocalKey object to output stream */
friend std::ostream& operator<< (std::ostream& s, const RealTuple& realTuple)
{
return s << realTuple.data_;
}
private:
private:
Dune::FieldVector<T,N> data_;
Dune::FieldVector<T,N> data_;
};
};
} // namespace Dune::GFE
#endif
dune/gfe/spaces/rotation.hh
View file @ 48b9358e
......@@ -18,454 +18,460 @@
#include <dune/gfe/spaces/quaternion.hh>
#include <dune/gfe/spaces/unitvector.hh>
template <class T, int dim>
class Rotation
{};
/** \brief Specialization for dim==2
\tparam T The type used for coordinates
*/
template <class T>
class Rotation<T,2>
namespace Dune::GFE
{
public:
/** \brief The type used for coordinates */
typedef T ctype;
/** \brief Dimension of the manifold formed by the 2d rotations */
static const int dim = 1;
template <class T, int dim>
class Rotation
{};
/** \brief Coordinates are embedded in the euclidean space */
static const int embeddedDim = 1;
/** \brief Specialization for dim==2
\tparam T The type used for coordinates
*/
template <class T>
class Rotation<T,2>
{
public:
/** \brief The type used for coordinates */
typedef T ctype;
/** \brief Member of the corresponding Lie algebra. This really is a skew-symmetric matrix */
typedef Dune::FieldVector<T,1> TangentVector;
/** \brief Dimension of the manifold formed by the 2d rotations */
static const int dim = 1;
/** \brief Member of the corresponding Lie algebra. This really is a skew-symmetric matrix
/** \brief Coordinates are embedded in the euclidean space */
static const int embeddedDim = 1;
This vector is not really embedded in anything. I have to make my notation more consistent! */
typedef Dune::FieldVector<T,1> EmbeddedTangentVector;
/** \brief Member of the corresponding Lie algebra. This really is a skew-symmetric matrix */
typedef Dune::FieldVector<T,1> TangentVector;
/** \brief The global convexity radius of the rotation group */
static constexpr double convexityRadius = 0.5 * M_PI;
/** \brief Member of the corresponding Lie algebra. This really is a skew-symmetric matrix
/** \brief Default constructor, create the identity rotation */
Rotation()
: angle_(0)
{}
This vector is not really embedded in anything. I have to make my notation more consistent! */
typedef Dune::FieldVector<T,1> EmbeddedTangentVector;
Rotation(const T& angle)
: angle_(angle)
{}
/** \brief The global convexity radius of the rotation group */
static constexpr double convexityRadius = 0.5 * M_PI;
/** \brief Return the identity element */
static Rotation<T,2> identity() {
// Default constructor creates an identity
Rotation<T,2> id;
return id;
}
/** \brief Default constructor, create the identity rotation */
Rotation()
: angle_(0)
{}
static T distance(const Rotation<T,2>& a, const Rotation<T,2>& b) {
T dist = a.angle_ - b.angle_;
while (dist < 0)
dist += 2*M_PI;
while (dist > 2*M_PI)
dist -= 2*M_PI;
Rotation(const T& angle)
: angle_(angle)
{}
return (dist <= M_PI) ? dist : 2*M_PI - dist;
}
/** \brief Return the identity element */
static Rotation<T,2> identity() {
// Default constructor creates an identity
Rotation<T,2> id;
return id;
}
/** \brief The exponential map from a given point $p \in SO(3)$. */
static Rotation<T,2> exp(const Rotation<T,2>& p, const TangentVector& v) {
Rotation<T,2> result = p;
result.angle_ += v;
return result;
}
static T distance(const Rotation<T,2>& a, const Rotation<T,2>& b) {
T dist = a.angle_ - b.angle_;
while (dist < 0)
dist += 2*M_PI;
while (dist > 2*M_PI)
dist -= 2*M_PI;
/** \brief The exponential map from \f$ \mathfrak{so}(2) \f$ to \f$ SO(2) \f$
*/
static Rotation<T,2> exp(const Dune::FieldVector<T,1>& v) {
Rotation<T,2> result;
result.angle_ = v[0];
return result;
}
return (dist <= M_PI) ? dist : 2*M_PI - dist;
}
static TangentVector derivativeOfDistanceSquaredWRTSecondArgument(const Rotation<T,2>& a,
const Rotation<T,2>& b) {
// This assertion is here to remind me of the following laziness:
// The difference has to be computed modulo 2\pi
assert( std::abs(a.angle_ - b.angle_) <= M_PI );
return -2 * (a.angle_ - b.angle_);
}
/** \brief The exponential map from a given point $p \in SO(3)$. */
static Rotation<T,2> exp(const Rotation<T,2>& p, const TangentVector& v) {
Rotation<T,2> result = p;
result.angle_ += v;
return result;
}
static Dune::FieldMatrix<T,1,1> secondDerivativeOfDistanceSquaredWRTSecondArgument(const Rotation<T,2>& a,
const Rotation<T,2>& b) {
return 2;
}
/** \brief The exponential map from \f$ \mathfrak{so}(2) \f$ to \f$ SO(2) \f$
*/
static Rotation<T,2> exp(const Dune::FieldVector<T,1>& v) {
Rotation<T,2> result;
result.angle_ = v[0];
return result;
}
/** \brief Right multiplication */
Rotation<T,2> mult(const Rotation<T,2>& other) const {
Rotation<T,2> q = *this;
q.angle_ += other.angle_;
return q;
}
static TangentVector derivativeOfDistanceSquaredWRTSecondArgument(const Rotation<T,2>& a,
const Rotation<T,2>& b) {
// This assertion is here to remind me of the following laziness:
// The difference has to be computed modulo 2\pi
assert( std::abs(a.angle_ - b.angle_) <= M_PI );
return -2 * (a.angle_ - b.angle_);
}
/** \brief Compute an orthonormal basis of the tangent space of SO(3).
static Dune::FieldMatrix<T,1,1> secondDerivativeOfDistanceSquaredWRTSecondArgument(const Rotation<T,2>& a,
const Rotation<T,2>& b) {
return 2;
}
This basis is of course not globally continuous.
*/
Dune::FieldMatrix<T,1,1> orthonormalFrame() const {
return Dune::FieldMatrix<T,1,1>(1);
}
/** \brief Right multiplication */
Rotation<T,2> mult(const Rotation<T,2>& other) const {
Rotation<T,2> q = *this;
q.angle_ += other.angle_;
return q;
}
//private:
/** \brief Compute an orthonormal basis of the tangent space of SO(3).
// We store the rotation as an angle
T angle_;
};
This basis is of course not globally continuous.
*/
Dune::FieldMatrix<T,1,1> orthonormalFrame() const {
return Dune::FieldMatrix<T,1,1>(1);
}
//! Send configuration to output stream
template <class T>
std::ostream& operator<< (std::ostream& s, const Rotation<T,2>& c)
{
return s << "[" << c.angle_ << " (" << std::sin(c.angle_) << " " << std::cos(c.angle_) << ") ]";
}
//private:
// We store the rotation as an angle
T angle_;
};
/** \brief Specialization for dim==3
//! Send configuration to output stream
template <class T>
std::ostream& operator<< (std::ostream& s, const Rotation<T,2>& c)
{
return s << "[" << c.angle_ << " (" << std::sin(c.angle_) << " " << std::cos(c.angle_) << ") ]";
}
Uses unit quaternion coordinates.
*/
template <class T>
class Rotation<T,3> : public Quaternion<T>
{
/** \brief Computes sin(x/2) / x without getting unstable for small x */
static T sincHalf(const T& x) {
using std::sin;
return (x < 1e-1) ? 0.5 - (x*x/48) + Dune::power(x,4)/3840 - Dune::power(x,6)/645120 : sin(x/2)/x;
}
/** \brief Specialization for dim==3
/** \brief Computes sin(sqrt(x)/2) / sqrt(x) without getting unstable for small x
*
* Using this somewhat exotic series allows to avoid a few calls to std::sqrt near 0,
* which ADOL-C doesn't like.
Uses unit quaternion coordinates.
*/
static T sincHalfOfSquare(const T& x) {
using std::sin;
using std::sqrt;
return (x < 1e-15) ? 0.5 - (x/48) + (x*x)/(120*32) : sin(sqrt(x)/2)/sqrt(x);
}
template <class T>
class Rotation<T,3> : public Quaternion<T>
{
/** \brief Computes sin(sqrt(x)) / sqrt(x) without getting unstable for small x
*
* Using this somewhat exotic series allows to avoid a few calls to std::sqrt near 0,
* which ADOL-C doesn't like.
*/
static T sincOfSquare(const T& x) {
using std::sin;
using std::sqrt;
// we need here lots of terms to be sure that the numerical derivatives are also within maschine precision
return (x < 1e-2) ?
1-x/6
+x*x/120
-Dune::power(x,3)/5040
+Dune::power(x,4)/362880
-Dune::power(x,5)/39916800
+Dune::power(x,6)/6227020800
-Dune::power(x,7)/1307674368000: sin(sqrt(x))/sqrt(x);
}
/** \brief Computes sin(x/2) / x without getting unstable for small x */
static T sincHalf(const T& x) {
using std::sin;
return (x < 1e-1) ? 0.5 - (x*x/48) + Dune::power(x,4)/3840 - Dune::power(x,6)/645120 : sin(x/2)/x;
}
public:
/** \brief Computes sin(sqrt(x)/2) / sqrt(x) without getting unstable for small x
*
* Using this somewhat exotic series allows to avoid a few calls to std::sqrt near 0,
* which ADOL-C doesn't like.
*/
static T sincHalfOfSquare(const T& x) {
using std::sin;
using std::sqrt;
return (x < 1e-15) ? 0.5 - (x/48) + (x*x)/(120*32) : sin(sqrt(x)/2)/sqrt(x);
}
/** \brief The type used for coordinates */
typedef T ctype;
/** \brief Computes sin(sqrt(x)) / sqrt(x) without getting unstable for small x
*
* Using this somewhat exotic series allows to avoid a few calls to std::sqrt near 0,
* which ADOL-C doesn't like.
*/
static T sincOfSquare(const T& x) {
using std::sin;
using std::sqrt;
// we need here lots of terms to be sure that the numerical derivatives are also within maschine precision
return (x < 1e-2) ?
1-x/6
+x*x/120
-Dune::power(x,3)/5040
+Dune::power(x,4)/362880
-Dune::power(x,5)/39916800
+Dune::power(x,6)/6227020800
-Dune::power(x,7)/1307674368000: sin(sqrt(x))/sqrt(x);
}
/** \brief The type used for global coordinates */
typedef Dune::FieldVector<T,4> CoordinateType;
public:
/** \brief Dimension of the manifold formed by the 3d rotations */
static const int dim = 3;
/** \brief The type used for coordinates */
typedef T ctype;
/** \brief Coordinates are embedded into a four-dimension Euclidean space */
static const int embeddedDim = 4;
/** \brief The type used for global coordinates */
typedef Dune::FieldVector<T,4> CoordinateType;
/** \brief Member of the corresponding Lie algebra. This really is a skew-symmetric matrix */
typedef Dune::FieldVector<T,3> TangentVector;
/** \brief Dimension of the manifold formed by the 3d rotations */
static const int dim = 3;
/** \brief A tangent vector as a vector in the surrounding coordinate space */
typedef Quaternion<T> EmbeddedTangentVector;
/** \brief Coordinates are embedded into a four-dimension Euclidean space */
static const int embeddedDim = 4;
/** \brief The global convexity radius of the rotation group */
static constexpr double convexityRadius = 0.5 * M_PI;
/** \brief Member of the corresponding Lie algebra. This really is a skew-symmetric matrix */
typedef Dune::FieldVector<T,3> TangentVector;
/** \brief Default constructor creates the identity element */
Rotation()
: Quaternion<T>(0,0,0,1)
{}
/** \brief A tangent vector as a vector in the surrounding coordinate space */
typedef Quaternion<T> EmbeddedTangentVector;
explicit Rotation(const std::array<T,4>& c)
{
for (int i=0; i<4; i++)
(*this)[i] = c[i];
/** \brief The global convexity radius of the rotation group */
static constexpr double convexityRadius = 0.5 * M_PI;
*this /= this->two_norm();
}
/** \brief Default constructor creates the identity element */
Rotation()
: Quaternion<T>(0,0,0,1)
{}
explicit Rotation(const Dune::FieldVector<T,4>& c)
: Quaternion<T>(c)
{
*this /= this->two_norm();
}
explicit Rotation(const std::array<T,4>& c)
{
for (int i=0; i<4; i++)
(*this)[i] = c[i];
Rotation(Dune::FieldVector<T,3> axis, T angle)
{
axis /= axis.two_norm();
axis *= std::sin(angle/2);
(*this)[0] = axis[0];
(*this)[1] = axis[1];
(*this)[2] = axis[2];
(*this)[3] = std::cos(angle/2);
}
*this /= this->two_norm();
}
/** \brief Rebind the Rotation to another coordinate type */
template<class U>
struct rebind
{
typedef Rotation<U,3> other;
};
explicit Rotation(const Dune::FieldVector<T,4>& c)
: Quaternion<T>(c)
{
*this /= this->two_norm();
}
Rotation& operator= (const Dune::FieldVector<T,4>& other)
{
for (int i=0; i<4; i++)
(*this)[i] = other[i];
*this /= this->two_norm();
return *this;
}
Rotation(Dune::FieldVector<T,3> axis, T angle)
{
axis /= axis.two_norm();
axis *= std::sin(angle/2);
(*this)[0] = axis[0];
(*this)[1] = axis[1];
(*this)[2] = axis[2];
(*this)[3] = std::cos(angle/2);
}
/** \brief Assignment from Rotation with different type -- used for automatic differentiation with ADOL-C */
template <class T2>
Rotation& operator <<= (const Rotation<T2,3>& other) {
for (int i=0; i<4; i++)
(*this)[i] <<= other[i];
return *this;
}
/** \brief Rebind the Rotation to another coordinate type */
template<class U>
struct rebind
{
typedef Rotation<U,3> other;
};
/** \brief Return the identity element */
static Rotation<T,3> identity() {
// Default constructor creates an identity
Rotation<T,3> id;
return id;
}
Rotation& operator= (const Dune::FieldVector<T,4>& other)
{
for (int i=0; i<4; i++)
(*this)[i] = other[i];
*this /= this->two_norm();
return *this;
}
/** \brief Right multiplication */
Rotation<T,3> mult(const Rotation<T,3>& other) const {
Rotation<T,3> q;
q[0] = (*this)[3]*other[0] - (*this)[2]*other[1] + (*this)[1]*other[2] + (*this)[0]*other[3];
q[1] = (*this)[2]*other[0] + (*this)[3]*other[1] - (*this)[0]*other[2] + (*this)[1]*other[3];
q[2] = - (*this)[1]*other[0] + (*this)[0]*other[1] + (*this)[3]*other[2] + (*this)[2]*other[3];
q[3] = - (*this)[0]*other[0] - (*this)[1]*other[1] - (*this)[2]*other[2] + (*this)[3]*other[3];
/** \brief Assignment from Rotation with different type -- used for automatic differentiation with ADOL-C */
template <class T2>
Rotation& operator <<= (const Rotation<T2,3>& other) {
for (int i=0; i<4; i++)
(*this)[i] <<= other[i];
return *this;
}
return q;
}
/** \brief Return the identity element */
static Rotation<T,3> identity() {
// Default constructor creates an identity
Rotation<T,3> id;
return id;
}
/** \brief The exponential map from \f$ \mathfrak{so}(3) \f$ to \f$ SO(3) \f$
*/
static Rotation<T,3> exp(const SkewMatrix<T,3>& v) {
using std::cos;
using std::sqrt;
/** \brief Right multiplication */
Rotation<T,3> mult(const Rotation<T,3>& other) const {
Rotation<T,3> q;
q[0] = (*this)[3]*other[0] - (*this)[2]*other[1] + (*this)[1]*other[2] + (*this)[0]*other[3];
q[1] = (*this)[2]*other[0] + (*this)[3]*other[1] - (*this)[0]*other[2] + (*this)[1]*other[3];
q[2] = - (*this)[1]*other[0] + (*this)[0]*other[1] + (*this)[3]*other[2] + (*this)[2]*other[3];
q[3] = - (*this)[0]*other[0] - (*this)[1]*other[1] - (*this)[2]*other[2] + (*this)[3]*other[3];
return q;
}
Rotation<T,3> q;
/** \brief The exponential map from \f$ \mathfrak{so}(3) \f$ to \f$ SO(3) \f$
*/
static Rotation<T,3> exp(const SkewMatrix<T,3>& v) {
using std::cos;
using std::sqrt;
Dune::FieldVector<T,3> vAxial = v.axial();
T normV2 = vAxial.two_norm2();
Rotation<T,3> q;
// Stabilization for small |v|
T sin = sincHalfOfSquare(normV2);
Dune::FieldVector<T,3> vAxial = v.axial();
T normV2 = vAxial.two_norm2();
assert(!std::isnan(sin));
// Stabilization for small |v|
T sin = sincHalfOfSquare(normV2);
q[0] = sin * vAxial[0];
q[1] = sin * vAxial[1];
q[2] = sin * vAxial[2];
assert(!std::isnan(sin));
// The series expansion of cos(x) at x=0 is
// 1 - x*x/2 + x*x*x*x/24 - ...
// hence the series of cos(x/2) is
// 1 - x*x/8 + x*x*x*x/384 - ...
q[3] = (normV2 < 1e-4)
q[0] = sin * vAxial[0];
q[1] = sin * vAxial[1];
q[2] = sin * vAxial[2];
// The series expansion of cos(x) at x=0 is
// 1 - x*x/2 + x*x*x*x/24 - ...
// hence the series of cos(x/2) is
// 1 - x*x/8 + x*x*x*x/384 - ...
q[3] = (normV2 < 1e-4)
? 1 - normV2/8 + normV2*normV2 / 384-Dune::power(normV2,3)/46080 + Dune::power(normV2,4)/10321920
: cos(sqrt(normV2)/2);
return q;
}
return q;
}
/** \brief The exponential map from a given point $p \in SO(3)$.
/** \brief The exponential map from a given point $p \in SO(3)$.
* \param v A tangent vector *at the identity*!
*/
static Rotation<T,3> exp(const Rotation<T,3>& p, const SkewMatrix<T,3>& v) {
Rotation<T,3> corr = exp(v);
return p.mult(corr);
}
* \param v A tangent vector *at the identity*!
*/
static Rotation<T,3> exp(const Rotation<T,3>& p, const SkewMatrix<T,3>& v) {
Rotation<T,3> corr = exp(v);
return p.mult(corr);
}
/** \brief The exponential map from a given point $p \in SO(3)$.
/** \brief The exponential map from a given point $p \in SO(3)$.
There may be a more direct way to implement this
There may be a more direct way to implement this
\param v A tangent vector in quaternion coordinates
*/
static Rotation<T,3> exp(const Rotation<T,3>& p, const Dune::FieldVector<T,4>& v) {
\param v A tangent vector in quaternion coordinates
*/
static Rotation<T,3> exp(const Rotation<T,3>& p, const Dune::FieldVector<T,4>& v) {
using std::abs;
using std::cos;
using std::sqrt;
assert( abs(p*v) < 1e-8 );
using std::abs;
using std::cos;
using std::sqrt;
assert( abs(p*v) < 1e-8 );
const T norm2 = v.two_norm2();
const T norm2 = v.two_norm2();
Rotation<T,3> result = p;
Rotation<T,3> result = p;
// The series expansion of cos(x) at x=0 is
// 1 - x*x/2 + x*x*x*x/24 - ...
T cosValue = (norm2 < 1e-5)
// The series expansion of cos(x) at x=0 is
// 1 - x*x/2 + x*x*x*x/24 - ...
T cosValue = (norm2 < 1e-5)
? 1 - norm2/2 + norm2*norm2 / 24 - Dune::power(norm2,3)/720+Dune::power(norm2,4)/40320
: cos(sqrt(norm2));
result *= cosValue;
result *= cosValue;
result.axpy(sincOfSquare(norm2), v);
return result;
}
result.axpy(sincOfSquare(norm2), v);
return result;
}
/** \brief The exponential map from a given point $p \in SO(3)$.
/** \brief The exponential map from a given point $p \in SO(3)$.
\param v A tangent vector.
*/
static Rotation<T,3> exp(const Rotation<T,3>& p, const TangentVector& v) {
\param v A tangent vector.
*/
static Rotation<T,3> exp(const Rotation<T,3>& p, const TangentVector& v) {
// embedded tangent vector
Dune::FieldMatrix<T,3,4> basis = p.orthonormalFrame();
Quaternion<T> embeddedTangent;
basis.mtv(v, embeddedTangent);
// embedded tangent vector
Dune::FieldMatrix<T,3,4> basis = p.orthonormalFrame();
Quaternion<T> embeddedTangent;
basis.mtv(v, embeddedTangent);
return exp(p,embeddedTangent);
return exp(p,embeddedTangent);
}
}
/** \brief Compute tangent vector from given basepoint and skew symmetric matrix. */
static TangentVector skewToTangentVector(const Rotation<T,3>& p, const SkewMatrix<T,3>& v ) {
/** \brief Compute tangent vector from given basepoint and skew symmetric matrix. */
static TangentVector skewToTangentVector(const Rotation<T,3>& p, const SkewMatrix<T,3>& v ) {
// embedded tangent vector at identity
Quaternion<T> vAtIdentity(0);
vAtIdentity[0] = 0.5*v.axial()[0];
vAtIdentity[1] = 0.5*v.axial()[1];
vAtIdentity[2] = 0.5*v.axial()[2];
// embedded tangent vector at identity
Quaternion<T> vAtIdentity(0);
vAtIdentity[0] = 0.5*v.axial()[0];
vAtIdentity[1] = 0.5*v.axial()[1];
vAtIdentity[2] = 0.5*v.axial()[2];
// multiply with base point to get real embedded tangent vector
Quaternion<T> vQuat = ((Quaternion<T>)p).mult(vAtIdentity);
// multiply with base point to get real embedded tangent vector
Quaternion<T> vQuat = ((Quaternion<T>)p).mult(vAtIdentity);
//get basis of the tangent space
Dune::FieldMatrix<T,3,4> basis = p.orthonormalFrame();
//get basis of the tangent space
Dune::FieldMatrix<T,3,4> basis = p.orthonormalFrame();
// transform coordinates
TangentVector tang;
basis.mv(vQuat,tang);
// transform coordinates
TangentVector tang;
basis.mv(vQuat,tang);
return tang;
}
return tang;
}
/** \brief Compute skew matrix from given basepoint and tangent vector. */
static SkewMatrix<T,3> tangentToSkew(const Rotation<T,3>& p, const TangentVector& tangent) {
/** \brief Compute skew matrix from given basepoint and tangent vector. */
static SkewMatrix<T,3> tangentToSkew(const Rotation<T,3>& p, const TangentVector& tangent) {
// embedded tangent vector
Dune::FieldMatrix<T,3,4> basis = p.orthonormalFrame();
Quaternion<T> embeddedTangent;
basis.mtv(tangent, embeddedTangent);
// embedded tangent vector
Dune::FieldMatrix<T,3,4> basis = p.orthonormalFrame();
Quaternion<T> embeddedTangent;
basis.mtv(tangent, embeddedTangent);
return tangentToSkew(p,embeddedTangent);
}
return tangentToSkew(p,embeddedTangent);
}
/** \brief Compute skew matrix from given basepoint and an embedded tangent vector. */
static SkewMatrix<T,3> tangentToSkew(const Rotation<T,3>& p, const EmbeddedTangentVector& q) {
/** \brief Compute skew matrix from given basepoint and an embedded tangent vector. */
static SkewMatrix<T,3> tangentToSkew(const Rotation<T,3>& p, const EmbeddedTangentVector& q) {
// left multiplication by the inverse base point yields a tangent vector at the identity
Quaternion<T> vAtIdentity = p.inverse().mult(q);
assert( std::abs(vAtIdentity[3]) < 1e-8 );
// left multiplication by the inverse base point yields a tangent vector at the identity
Quaternion<T> vAtIdentity = p.inverse().mult(q);
assert( std::abs(vAtIdentity[3]) < 1e-8 );
SkewMatrix<T,3> skew;
skew.axial()[0] = 2*vAtIdentity[0];
skew.axial()[1] = 2*vAtIdentity[1];
skew.axial()[2] = 2*vAtIdentity[2];
SkewMatrix<T,3> skew;
skew.axial()[0] = 2*vAtIdentity[0];
skew.axial()[1] = 2*vAtIdentity[1];
skew.axial()[2] = 2*vAtIdentity[2];
return skew;
}
return skew;
}
/** \brief Derivative of the exponential map at the identity
*
* The exponential map at the identity is a map from a neighborhood of zero to the neighborhood of the identity rotation.
*
* \param v Where to evaluate the derivative of the (exponential map at the identity)
*/
static Dune::FieldMatrix<T,4,3> Dexp(const SkewMatrix<T,3>& v) {
/** \brief Derivative of the exponential map at the identity
*
* The exponential map at the identity is a map from a neighborhood of zero to the neighborhood of the identity rotation.
*
* \param v Where to evaluate the derivative of the (exponential map at the identity)
*/
static Dune::FieldMatrix<T,4,3> Dexp(const SkewMatrix<T,3>& v) {
using std::cos;
using std::cos;
Dune::FieldMatrix<T,4,3> result(0);
Dune::FieldVector<T,3> vAxial = v.axial();
T norm = vAxial.two_norm();
Dune::FieldMatrix<T,4,3> result(0);
Dune::FieldVector<T,3> vAxial = v.axial();
T norm = vAxial.two_norm();
for (int i=0; i<3; i++) {
for (int i=0; i<3; i++) {
for (int m=0; m<3; m++) {
for (int m=0; m<3; m++) {
result[m][i] = (norm<1e-10)
/** \todo Isn't there a better way to implement this stably? */
result[m][i] = (norm<1e-10)
/** \todo Isn't there a better way to implement this stably? */
? T(0.5) * (i==m)
: 0.5 * cos(norm/2) * vAxial[i] * vAxial[m] / (norm*norm) + sincHalf(norm) * ( (i==m) - vAxial[i]*vAxial[m]/(norm*norm));
}
}
result[3][i] = - 0.5 * sincHalf(norm) * vAxial[i];
result[3][i] = - 0.5 * sincHalf(norm) * vAxial[i];
}
return result;
}
return result;
}
static void DDexp(const Dune::FieldVector<T,3>& v,
std::array<Dune::FieldMatrix<T,3,3>, 4>& result) {
static void DDexp(const Dune::FieldVector<T,3>& v,
std::array<Dune::FieldMatrix<T,3,3>, 4>& result) {
using std::cos;
using std::sin;
using std::cos;
using std::sin;
T norm = v.two_norm();
if (norm<=1e-10) {
T norm = v.two_norm();
if (norm<=1e-10) {
for (int m=0; m<4; m++)
result[m] = 0;
for (int m=0; m<4; m++)
result[m] = 0;
for (int i=0; i<3; i++)
result[3][i][i] = -0.25;
for (int i=0; i<3; i++)
result[3][i][i] = -0.25;
} else {
} else {
for (int i=0; i<3; i++) {
for (int i=0; i<3; i++) {
for (int j=0; j<3; j++) {
for (int j=0; j<3; j++) {
for (int m=0; m<3; m++) {
for (int m=0; m<3; m++) {
result[m][i][j] = -0.25*sin(norm/2)*v[i]*v[j]*v[m]/(norm*norm*norm)
+ ((i==j)*v[m] + (j==m)*v[i] + (i==m)*v[j] - 3*v[i]*v[j]*v[m]/(norm*norm))
* (0.5*cos(norm/2) - sincHalf(norm)) / (norm*norm);
result[m][i][j] = -0.25*sin(norm/2)*v[i]*v[j]*v[m]/(norm*norm*norm)
+ ((i==j)*v[m] + (j==m)*v[i] + (i==m)*v[j] - 3*v[i]*v[j]*v[m]/(norm*norm))
* (0.5*cos(norm/2) - sincHalf(norm)) / (norm*norm);
}
}
result[3][i][j] = -0.5/(norm*norm)
* ( 0.5*cos(norm/2)*v[i]*v[j] + sin(norm/2) * ((i==j)*norm - v[i]*v[j]/norm));
result[3][i][j] = -0.5/(norm*norm)
* ( 0.5*cos(norm/2)*v[i]*v[j] + sin(norm/2) * ((i==j)*norm - v[i]*v[j]/norm));
}
}
......@@ -473,779 +479,802 @@ public:
}
}
/** \brief The inverse of the exponential map */
static Dune::FieldVector<T,3> expInv(const Rotation<T,3>& q) {
// Compute v = exp^{-1} q
// Due to numerical dirt, q[3] may be larger than 1.
// In that case, use 1 instead of q[3].
Dune::FieldVector<T,3> v;
if (q[3] > 1.0) {
/** \brief The inverse of the exponential map */
static Dune::FieldVector<T,3> expInv(const Rotation<T,3>& q) {
// Compute v = exp^{-1} q
// Due to numerical dirt, q[3] may be larger than 1.
// In that case, use 1 instead of q[3].
Dune::FieldVector<T,3> v;
if (q[3] > 1.0) {
v = 0;
v = 0;
} else {
} else {
using std::acos;
T invSinc = 1/sincHalf(2*acos(q[3]));
using std::acos;
T invSinc = 1/sincHalf(2*acos(q[3]));
v[0] = q[0] * invSinc;
v[1] = q[1] * invSinc;
v[2] = q[2] * invSinc;
v[0] = q[0] * invSinc;
v[1] = q[1] * invSinc;
v[2] = q[2] * invSinc;
}
return v;
}
return v;
}
/** \brief The derivative of the inverse of the exponential map, evaluated at q */
static Dune::FieldMatrix<T,3,4> DexpInv(const Rotation<T,3>& q) {
/** \brief The derivative of the inverse of the exponential map, evaluated at q */
static Dune::FieldMatrix<T,3,4> DexpInv(const Rotation<T,3>& q) {
// Compute v = exp^{-1} q
Dune::FieldVector<T,3> v = expInv(q);
// Compute v = exp^{-1} q
Dune::FieldVector<T,3> v = expInv(q);
// The derivative of exp at v
Dune::FieldMatrix<T,4,3> A = Dexp(SkewMatrix<T,3>(v));
// The derivative of exp at v
Dune::FieldMatrix<T,4,3> A = Dexp(SkewMatrix<T,3>(v));
// Compute the Moore-Penrose pseudo inverse A^+ = (A^T A)^{-1} A^T
Dune::FieldMatrix<T,3,3> ATA;
// Compute the Moore-Penrose pseudo inverse A^+ = (A^T A)^{-1} A^T
Dune::FieldMatrix<T,3,3> ATA;
for (int i=0; i<3; i++)
for (int j=0; j<3; j++) {
ATA[i][j] = 0;
for (int k=0; k<4; k++)
ATA[i][j] += A[k][i] * A[k][j];
}
for (int i=0; i<3; i++)
for (int j=0; j<3; j++) {
ATA[i][j] = 0;
for (int k=0; k<4; k++)
ATA[i][j] += A[k][i] * A[k][j];
}
ATA.invert();
ATA.invert();
Dune::FieldMatrix<T,3,4> APseudoInv;
for (int i=0; i<3; i++)
for (int j=0; j<4; j++) {
APseudoInv[i][j] = 0;
for (int k=0; k<3; k++)
APseudoInv[i][j] += ATA[i][k] * A[j][k];
}
Dune::FieldMatrix<T,3,4> APseudoInv;
for (int i=0; i<3; i++)
for (int j=0; j<4; j++) {
APseudoInv[i][j] = 0;
for (int k=0; k<3; k++)
APseudoInv[i][j] += ATA[i][k] * A[j][k];
}
return APseudoInv;
}
return APseudoInv;
}
/** \brief The cayley mapping from \f$ \mathfrak{so}(3) \f$ to \f$ SO(3) \f$.
*
* The formula is taken from 'J.C.Simo, N.Tarnom, M.Doblare - Non-linear dynamics of
* three-dimensional rods:Exact energy and momentum conserving algorithms'
* (but the corrected version with 0.25 instead of 0.5 in the denominator)
*/
static Rotation<T,3> cayley(const SkewMatrix<T,3>& s) {
Rotation<T,3> q;
/** \brief The cayley mapping from \f$ \mathfrak{so}(3) \f$ to \f$ SO(3) \f$.
*
* The formula is taken from 'J.C.Simo, N.Tarnom, M.Doblare - Non-linear dynamics of
* three-dimensional rods:Exact energy and momentum conserving algorithms'
* (but the corrected version with 0.25 instead of 0.5 in the denominator)
*/
static Rotation<T,3> cayley(const SkewMatrix<T,3>& s) {
Rotation<T,3> q;
Dune::FieldVector<T,3> vAxial = s.axial();
T norm = 0.25*vAxial.two_norm2() + 1;
Dune::FieldMatrix<T,3,3> mat = s.toMatrix();
mat *= 0.5;
Dune::FieldMatrix<T,3,3> skewSquare = mat;
skewSquare.rightmultiply(mat);
mat += skewSquare;
mat *= 2/norm;
Dune::FieldVector<T,3> vAxial = s.axial();
T norm = 0.25*vAxial.two_norm2() + 1;
for (int i=0; i<3; i++)
mat[i][i] += 1;
Dune::FieldMatrix<T,3,3> mat = s.toMatrix();
mat *= 0.5;
Dune::FieldMatrix<T,3,3> skewSquare = mat;
skewSquare.rightmultiply(mat);
mat += skewSquare;
mat *= 2/norm;
q.set(mat);
return q;
}
for (int i=0; i<3; i++)
mat[i][i] += 1;
/** \brief The inverse of the Cayley mapping.
*
* The formula is taken from J.M.Selig - Cayley Maps for SE(3).
*/
static SkewMatrix<T,3> cayleyInv(const Rotation<T,3> q) {
q.set(mat);
return q;
}
Dune::FieldMatrix<T,3,3> mat;
/** \brief The inverse of the Cayley mapping.
*
* The formula is taken from J.M.Selig - Cayley Maps for SE(3).
*/
static SkewMatrix<T,3> cayleyInv(const Rotation<T,3> q) {
// compute the trace of the rotation matrix
T trace = -q[0]*q[0] -q[1]*q[1] -q[2]*q[2]+3*q[3]*q[3];
Dune::FieldMatrix<T,3,3> mat;
if ( (trace+1)>1e-6 || (trace+1)<-1e-6) { // if this term doesn't vanish we can use a direct formula
// compute the trace of the rotation matrix
T trace = -q[0]*q[0] -q[1]*q[1] -q[2]*q[2]+3*q[3]*q[3];
q.matrix(mat);
Dune::FieldMatrix<T,3,3> matT;
Rotation<T,3>(q.inverse()).matrix(matT);
mat -= matT;
mat *= 2/(1+trace);
}
else { // use the formula that involves the computation of an inverse
Dune::FieldMatrix<T,3,3> inv;
q.matrix(inv);
Dune::FieldMatrix<T,3,3> notInv = inv;
for (int i=0; i<3; i++) {
inv[i][i] +=1;
notInv[i][i] -=1;
}
inv.invert();
mat = notInv.leftmultiply(inv);
mat *= 2;
}
if ( (trace+1)>1e-6 || (trace+1)<-1e-6) { // if this term doesn't vanish we can use a direct formula
// result is a skew symmetric matrix
SkewMatrix<T,3> res;
res.axial()[0] = mat[2][1];
res.axial()[1] = mat[0][2];
res.axial()[2] = mat[1][0];
q.matrix(mat);
Dune::FieldMatrix<T,3,3> matT;
Rotation<T,3>(q.inverse()).matrix(matT);
mat -= matT;
mat *= 2/(1+trace);
}
else { // use the formula that involves the computation of an inverse
Dune::FieldMatrix<T,3,3> inv;
q.matrix(inv);
Dune::FieldMatrix<T,3,3> notInv = inv;
return res;
for (int i=0; i<3; i++) {
inv[i][i] +=1;
notInv[i][i] -=1;
}
inv.invert();
mat = notInv.leftmultiply(inv);
mat *= 2;
}
// result is a skew symmetric matrix
SkewMatrix<T,3> res;
res.axial()[0] = mat[2][1];
res.axial()[1] = mat[0][2];
res.axial()[2] = mat[1][0];
static T distance(const Rotation<T,3>& a, const Rotation<T,3>& b) {
return res;
// Distance in the unit quaternions: 2*arccos( ((a^{-1) b)_3 )
// But note that (a^{-1}b)_3 is actually <a,b> (in R^4)
T sp = a.globalCoordinates() * b.globalCoordinates();
}
// Scalar product may be larger than 1.0, due to numerical dirt
using std::acos;
using std::min;
T dist = 2*acos( min(sp,T(1.0)) );
static T distance(const Rotation<T,3>& a, const Rotation<T,3>& b) {
// Make sure we do the right thing if a and b are not in the same sheet
// of the double covering of the unit quaternions over SO(3)
return (dist>=M_PI) ? (2*M_PI - dist) : dist;
}
// Distance in the unit quaternions: 2*arccos( ((a^{-1) b)_3 )
// But note that (a^{-1}b)_3 is actually <a,b> (in R^4)
T sp = a.globalCoordinates() * b.globalCoordinates();
/** \brief Compute the vector in T_aSO(3) that is mapped by the exponential map
to the geodesic from a to b
*/
static EmbeddedTangentVector log(const Rotation<T,3>& a, const Rotation<T,3>& b) {
// Scalar product may be larger than 1.0, due to numerical dirt
using std::acos;
using std::min;
T dist = 2*acos( min(sp,T(1.0)) );
// embedded tangent vector at identity
Quaternion<T> v;
// Make sure we do the right thing if a and b are not in the same sheet
// of the double covering of the unit quaternions over SO(3)
return (dist>=M_PI) ? (2*M_PI - dist) : dist;
}
Quaternion<T> diff = a;
diff.invert();
diff = diff.mult(b);
/** \brief Compute the vector in T_aSO(3) that is mapped by the exponential map
to the geodesic from a to b
*/
static EmbeddedTangentVector log(const Rotation<T,3>& a, const Rotation<T,3>& b) {
// embedded tangent vector at identity
Quaternion<T> v;
// Compute the geodesical distance between a and b on SO(3)
// Due to numerical dirt, diff[3] may be larger than 1.
// In that case, use 1 instead of diff[3].
if (diff[3] > 1.0) {
Quaternion<T> diff = a;
diff.invert();
diff = diff.mult(b);
v = 0;
// Compute the geodesical distance between a and b on SO(3)
// Due to numerical dirt, diff[3] may be larger than 1.
// In that case, use 1 instead of diff[3].
if (diff[3] > 1.0) {
} else {
v = 0;
// TODO: ADOL-C does not like this part of the code,
// because arccos is not differentiable at -1 and 1.
// (Even though the overall 'log' function is differentiable.)
using std::acos;
T dist = 2*acos( diff[3] );
} else {
// Make sure we do the right thing if a and b are not in the same sheet
// of the double covering of the unit quaternions over SO(3)
if (dist>=M_PI) {
dist = 2*M_PI - dist;
diff *= -1;
}
// TODO: ADOL-C does not like this part of the code,
// because arccos is not differentiable at -1 and 1.
// (Even though the overall 'log' function is differentiable.)
using std::acos;
T dist = 2*acos( diff[3] );
T invSinc = 1/sincHalf(dist);
// Make sure we do the right thing if a and b are not in the same sheet
// of the double covering of the unit quaternions over SO(3)
if (dist>=M_PI) {
dist = 2*M_PI - dist;
diff *= -1;
// Compute log on T_a SO(3)
v[0] = 0.5 * diff[0] * invSinc;
v[1] = 0.5 * diff[1] * invSinc;
v[2] = 0.5 * diff[2] * invSinc;
v[3] = 0;
}
T invSinc = 1/sincHalf(dist);
// Compute log on T_a SO(3)
v[0] = 0.5 * diff[0] * invSinc;
v[1] = 0.5 * diff[1] * invSinc;
v[2] = 0.5 * diff[2] * invSinc;
v[3] = 0;
// multiply with base point to get real embedded tangent vector
return ((Quaternion<T>)a).mult(v);
}
// multiply with base point to get real embedded tangent vector
return ((Quaternion<T>)a).mult(v);
}
/** \brief Compute the derivatives of the director vectors with respect to the quaternion coordinates
*
* Let \f$ d_k(q) = (d_{k,1}, d_{k,2}, d_{k,3})\f$ be the k-th director vector at \f$ q \f$.
* Then the return value of this method is
* \f[ A_{ijk} = \frac{\partial d_{i,j}}{\partial q_k} \f]
*/
void getFirstDerivativesOfDirectors(Tensor3<T,3, 3, 4>& dd_dq) const
{
const Quaternion<T>& q = (*this);
dd_dq[0][0] = { 2*q[0], -2*q[1], -2*q[2], 2*q[3]};
dd_dq[0][1] = { 2*q[1], 2*q[0], 2*q[3], 2*q[2]};
dd_dq[0][2] = { 2*q[2], -2*q[3], 2*q[0], -2*q[1]};
/** \brief Compute the derivatives of the director vectors with respect to the quaternion coordinates
*
* Let \f$ d_k(q) = (d_{k,1}, d_{k,2}, d_{k,3})\f$ be the k-th director vector at \f$ q \f$.
* Then the return value of this method is
* \f[ A_{ijk} = \frac{\partial d_{i,j}}{\partial q_k} \f]
*/
void getFirstDerivativesOfDirectors(Tensor3<T,3, 3, 4>& dd_dq) const
{
const Quaternion<T>& q = (*this);
dd_dq[1][0] = { 2*q[1], 2*q[0], -2*q[3], -2*q[2]};
dd_dq[1][1] = {-2*q[0], 2*q[1], -2*q[2], 2*q[3]};
dd_dq[1][2] = { 2*q[3], 2*q[2], 2*q[1], 2*q[0]};
dd_dq[0][0] = { 2*q[0], -2*q[1], -2*q[2], 2*q[3]};
dd_dq[0][1] = { 2*q[1], 2*q[0], 2*q[3], 2*q[2]};
dd_dq[0][2] = { 2*q[2], -2*q[3], 2*q[0], -2*q[1]};
dd_dq[2][0] = { 2*q[2], 2*q[3], 2*q[0], 2*q[1]};
dd_dq[2][1] = {-2*q[3], 2*q[2], 2*q[1], -2*q[0]};
dd_dq[2][2] = {-2*q[0], -2*q[1], 2*q[2], 2*q[3]};
dd_dq[1][0] = { 2*q[1], 2*q[0], -2*q[3], -2*q[2]};
dd_dq[1][1] = {-2*q[0], 2*q[1], -2*q[2], 2*q[3]};
dd_dq[1][2] = { 2*q[3], 2*q[2], 2*q[1], 2*q[0]};
}
dd_dq[2][0] = { 2*q[2], 2*q[3], 2*q[0], 2*q[1]};
dd_dq[2][1] = {-2*q[3], 2*q[2], 2*q[1], -2*q[0]};
dd_dq[2][2] = {-2*q[0], -2*q[1], 2*q[2], 2*q[3]};
/** \brief Compute the second derivatives of the director vectors with respect to the quaternion coordinates
*
* Let \f$ d_k(q) = (d_{k,1}, d_{k,2}, d_{k,3})\f$ be the k-th director vector at \f$ q \f$.
* Then the return value of this method is
* \f[ A_{ijkl} = \frac{\partial^2 d_{i,j}}{\partial q_k \partial q_l} \f]
*/
static void getSecondDerivativesOfDirectors(std::array<Tensor3<T,3, 4, 4>, 3>& dd_dq_dq)
{
for (int i=0; i<3; i++)
dd_dq_dq[i] = T(0);
}
dd_dq_dq[0][0][0][0] = 2; dd_dq_dq[0][0][1][1] = -2; dd_dq_dq[0][0][2][2] = -2; dd_dq_dq[0][0][3][3] = 2;
dd_dq_dq[0][1][0][1] = 2; dd_dq_dq[0][1][1][0] = 2; dd_dq_dq[0][1][2][3] = 2; dd_dq_dq[0][1][3][2] = 2;
dd_dq_dq[0][2][0][2] = 2; dd_dq_dq[0][2][1][3] = -2; dd_dq_dq[0][2][2][0] = 2; dd_dq_dq[0][2][3][1] = -2;
/** \brief Compute the second derivatives of the director vectors with respect to the quaternion coordinates
*
* Let \f$ d_k(q) = (d_{k,1}, d_{k,2}, d_{k,3})\f$ be the k-th director vector at \f$ q \f$.
* Then the return value of this method is
* \f[ A_{ijkl} = \frac{\partial^2 d_{i,j}}{\partial q_k \partial q_l} \f]
*/
static void getSecondDerivativesOfDirectors(std::array<Tensor3<T,3, 4, 4>, 3>& dd_dq_dq)
{
for (int i=0; i<3; i++)
dd_dq_dq[i] = T(0);
dd_dq_dq[1][0][0][1] = 2; dd_dq_dq[1][0][1][0] = 2; dd_dq_dq[1][0][2][3] = -2; dd_dq_dq[1][0][3][2] = -2;
dd_dq_dq[1][1][0][0] = -2; dd_dq_dq[1][1][1][1] = 2; dd_dq_dq[1][1][2][2] = -2; dd_dq_dq[1][1][3][3] = 2;
dd_dq_dq[1][2][0][3] = 2; dd_dq_dq[1][2][1][2] = 2; dd_dq_dq[1][2][2][1] = 2; dd_dq_dq[1][2][3][0] = 2;
dd_dq_dq[0][0][0][0] = 2; dd_dq_dq[0][0][1][1] = -2; dd_dq_dq[0][0][2][2] = -2; dd_dq_dq[0][0][3][3] = 2;
dd_dq_dq[0][1][0][1] = 2; dd_dq_dq[0][1][1][0] = 2; dd_dq_dq[0][1][2][3] = 2; dd_dq_dq[0][1][3][2] = 2;
dd_dq_dq[0][2][0][2] = 2; dd_dq_dq[0][2][1][3] = -2; dd_dq_dq[0][2][2][0] = 2; dd_dq_dq[0][2][3][1] = -2;
dd_dq_dq[2][0][0][2] = 2; dd_dq_dq[2][0][1][3] = 2; dd_dq_dq[2][0][2][0] = 2; dd_dq_dq[2][0][3][1] = 2;
dd_dq_dq[2][1][0][3] = -2; dd_dq_dq[2][1][1][2] = 2; dd_dq_dq[2][1][2][1] = 2; dd_dq_dq[2][1][3][0] = -2;
dd_dq_dq[2][2][0][0] = -2; dd_dq_dq[2][2][1][1] = -2; dd_dq_dq[2][2][2][2] = 2; dd_dq_dq[2][2][3][3] = 2;
dd_dq_dq[1][0][0][1] = 2; dd_dq_dq[1][0][1][0] = 2; dd_dq_dq[1][0][2][3] = -2; dd_dq_dq[1][0][3][2] = -2;
dd_dq_dq[1][1][0][0] = -2; dd_dq_dq[1][1][1][1] = 2; dd_dq_dq[1][1][2][2] = -2; dd_dq_dq[1][1][3][3] = 2;
dd_dq_dq[1][2][0][3] = 2; dd_dq_dq[1][2][1][2] = 2; dd_dq_dq[1][2][2][1] = 2; dd_dq_dq[1][2][3][0] = 2;
}
dd_dq_dq[2][0][0][2] = 2; dd_dq_dq[2][0][1][3] = 2; dd_dq_dq[2][0][2][0] = 2; dd_dq_dq[2][0][3][1] = 2;
dd_dq_dq[2][1][0][3] = -2; dd_dq_dq[2][1][1][2] = 2; dd_dq_dq[2][1][2][1] = 2; dd_dq_dq[2][1][3][0] = -2;
dd_dq_dq[2][2][0][0] = -2; dd_dq_dq[2][2][1][1] = -2; dd_dq_dq[2][2][2][2] = 2; dd_dq_dq[2][2][3][3] = 2;
/** \brief Transform tangent vectors from quaternion representation to matrix representation
*
* This class represents rotations as unit quaternions, and therefore variations of rotations
* (i.e., tangent vector) are represented in quaternion space, too. However, some applications
* require the tangent vectors as matrices. To obtain matrix coordinates we use the
* chain rule, which means that we have to multiply the given derivative with
* the derivative of the embedding of the unit quaternion into the space of 3x3 matrices.
* This second derivative is almost given by the method getFirstDerivativesOfDirectors.
* However, since the directors of a given unit quaternion are the _columns_ of the
* corresponding orthogonal matrix, we need to invert the i and j indices
*
* As a typical GFE assembler will require this for several tangent vectors at once,
* the implementation here is a vector one: It allows to treat several tangent vectors
* together, which have to come as the columns of the `derivative` parameter.
*
* So, if I am not mistaken, result[i][j][k] contains \partial R_ij / \partial k
*
* \param derivative Tangent vector in quaternion coordinates
* \returns DR Tangent vector in matrix coordinates
*/
template <int blocksize>
Tensor3<T,3,3,blocksize> quaternionTangentToMatrixTangent(const Dune::FieldMatrix<T,4,blocksize>& derivative) const
{
Tensor3<T,3,3,blocksize> result = T(0);
Tensor3<T,3 , 3, 4> dd_dq;
getFirstDerivativesOfDirectors(dd_dq);
}
for (int i=0; i<3; i++)
for (int j=0; j<3; j++)
for (int k=0; k<blocksize; k++)
for (int l=0; l<4; l++)
result[i][j][k] += dd_dq[j][i][l] * derivative[l][k];
/** \brief Transform tangent vectors from quaternion representation to matrix representation
*
* This class represents rotations as unit quaternions, and therefore variations of rotations
* (i.e., tangent vector) are represented in quaternion space, too. However, some applications
* require the tangent vectors as matrices. To obtain matrix coordinates we use the
* chain rule, which means that we have to multiply the given derivative with
* the derivative of the embedding of the unit quaternion into the space of 3x3 matrices.
* This second derivative is almost given by the method getFirstDerivativesOfDirectors.
* However, since the directors of a given unit quaternion are the _columns_ of the
* corresponding orthogonal matrix, we need to invert the i and j indices
*
* As a typical GFE assembler will require this for several tangent vectors at once,
* the implementation here is a vector one: It allows to treat several tangent vectors
* together, which have to come as the columns of the `derivative` parameter.
*
* So, if I am not mistaken, result[i][j][k] contains \partial R_ij / \partial k
*
* \param derivative Tangent vector in quaternion coordinates
* \returns DR Tangent vector in matrix coordinates
*/
template <int blocksize>
Tensor3<T,3,3,blocksize> quaternionTangentToMatrixTangent(const Dune::FieldMatrix<T,4,blocksize>& derivative) const
{
Tensor3<T,3,3,blocksize> result = T(0);
return result;
}
Tensor3<T,3 , 3, 4> dd_dq;
getFirstDerivativesOfDirectors(dd_dq);
/** \brief Compute the derivative of the squared distance function with respect to the second argument
*
* The squared distance function is
* \f[ 4 \arccos^2 (|<p,q>|) \f]
* Deriving this with respect to the second coordinate gives
* \f[ 4 (\arccos^2)'(x)|_{x = |<p,q>|} * P_qp \f]
* The whole thing has to be multiplied by -1 if \f$ <p,q> \f$ is negative
*/
static EmbeddedTangentVector derivativeOfDistanceSquaredWRTSecondArgument(const Rotation<T,3>& p,
const Rotation<T,3>& q) {
T sp = p.globalCoordinates() * q.globalCoordinates();
for (int i=0; i<3; i++)
for (int j=0; j<3; j++)
for (int k=0; k<blocksize; k++)
for (int l=0; l<4; l++)
result[i][j][k] += dd_dq[j][i][l] * derivative[l][k];
// Compute the projection of p onto the tangent space of q
EmbeddedTangentVector result = p;
result.axpy(-1*(q*p), q);
return result;
}
// The ternary operator comes from the derivative of the absolute value function
using std::abs;
result *= 4 * UnitVector<T,4>::derivativeOfArcCosSquared(abs(sp)) * ( (sp<0) ? -1 : 1 );
/** \brief Compute the derivative of the squared distance function with respect to the second argument
*
* The squared distance function is
* \f[ 4 \arccos^2 (|<p,q>|) \f]
* Deriving this with respect to the second coordinate gives
* \f[ 4 (\arccos^2)'(x)|_{x = |<p,q>|} * P_qp \f]
* The whole thing has to be multiplied by -1 if \f$ <p,q> \f$ is negative
*/
static EmbeddedTangentVector derivativeOfDistanceSquaredWRTSecondArgument(const Rotation<T,3>& p,
const Rotation<T,3>& q) {
T sp = p.globalCoordinates() * q.globalCoordinates();
// Compute the projection of p onto the tangent space of q
EmbeddedTangentVector result = p;
result.axpy(-1*(q*p), q);
// The ternary operator comes from the derivative of the absolute value function
using std::abs;
result *= 4 * UnitVector<T,4>::derivativeOfArcCosSquared(abs(sp)) * ( (sp<0) ? -1 : 1 );
return result;
}
return result;
}
/** \brief Compute the Hessian of the squared distance function keeping the first argument fixed */
static SymmetricMatrix<T,4> secondDerivativeOfDistanceSquaredWRTSecondArgument(const Rotation<T,3>& p, const Rotation<T,3>& q) {
/** \brief Compute the Hessian of the squared distance function keeping the first argument fixed */
static Dune::SymmetricMatrix<T,4> secondDerivativeOfDistanceSquaredWRTSecondArgument(const Rotation<T,3>& p, const Rotation<T,3>& q) {
T sp = p.globalCoordinates() * q.globalCoordinates();
T sp = p.globalCoordinates() * q.globalCoordinates();
EmbeddedTangentVector pProjected = q.projectOntoTangentSpace(p.globalCoordinates());
EmbeddedTangentVector pProjected = q.projectOntoTangentSpace(p.globalCoordinates());
SymmetricMatrix<T,4> A;
for (int i=0; i<4; i++)
for (int j=0; j<=i; j++)
A(i,j) = pProjected[i]*pProjected[j];
Dune::SymmetricMatrix<T,4> A;
for (int i=0; i<4; i++)
for (int j=0; j<=i; j++)
A(i,j) = pProjected[i]*pProjected[j];
using std::abs;
A *= 4*UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp));
using std::abs;
A *= 4*UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp));
// Compute matrix B (see notes)
SymmetricMatrix<T,4> Pq;
for (int i=0; i<4; i++)
for (int j=0; j<=i; j++)
Pq(i,j) = (i==j) - q.globalCoordinates()[i]*q.globalCoordinates()[j];
// Compute matrix B (see notes)
Dune::SymmetricMatrix<T,4> Pq;
for (int i=0; i<4; i++)
for (int j=0; j<=i; j++)
Pq(i,j) = (i==j) - q.globalCoordinates()[i]*q.globalCoordinates()[j];
// Bring it all together
A.axpy(-4* ((sp<0) ? -1 : 1) * UnitVector<T,4>::derivativeOfArcCosSquared(abs(sp))*sp, Pq);
// Bring it all together
A.axpy(-4* ((sp<0) ? -1 : 1) * UnitVector<T,4>::derivativeOfArcCosSquared(abs(sp))*sp, Pq);
return A;
}
return A;
}
/** \brief Compute the mixed second derivate \partial d^2 / \partial dp dq */
static Dune::FieldMatrix<T,4,4> secondDerivativeOfDistanceSquaredWRTFirstAndSecondArgument(const Rotation<T,3>& p, const Rotation<T,3>& q) {
/** \brief Compute the mixed second derivate \partial d^2 / \partial dp dq */
static Dune::FieldMatrix<T,4,4> secondDerivativeOfDistanceSquaredWRTFirstAndSecondArgument(const Rotation<T,3>& p, const Rotation<T,3>& q) {
T sp = p.globalCoordinates() * q.globalCoordinates();
T sp = p.globalCoordinates() * q.globalCoordinates();
// Compute vector A (see notes)
Dune::FieldMatrix<T,1,4> row;
row[0] = q.projectOntoTangentSpace(p.globalCoordinates());
// Compute vector A (see notes)
Dune::FieldMatrix<T,1,4> row;
row[0] = q.projectOntoTangentSpace(p.globalCoordinates());
EmbeddedTangentVector tmp = p.projectOntoTangentSpace(q.globalCoordinates());
Dune::FieldMatrix<T,4,1> column;
for (int i=0; i<4; i++) // turn row vector into column vector
column[i] = tmp[i];
EmbeddedTangentVector tmp = p.projectOntoTangentSpace(q.globalCoordinates());
Dune::FieldMatrix<T,4,1> column;
for (int i=0; i<4; i++) // turn row vector into column vector
column[i] = tmp[i];
Dune::FieldMatrix<T,4,4> A;
// A = row * column
Dune::FMatrixHelp::multMatrix(column,row,A);
using std::abs;
A *= 4 * UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp));
Dune::FieldMatrix<T,4,4> A;
// A = row * column
Dune::FMatrixHelp::multMatrix(column,row,A);
using std::abs;
A *= 4 * UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp));
// Compute matrix B (see notes)
Dune::FieldMatrix<T,4,4> Pp, Pq;
for (int i=0; i<4; i++)
for (int j=0; j<4; j++) {
Pp[i][j] = (i==j) - p.globalCoordinates()[i]*p.globalCoordinates()[j];
Pq[i][j] = (i==j) - q.globalCoordinates()[i]*q.globalCoordinates()[j];
}
// Compute matrix B (see notes)
Dune::FieldMatrix<T,4,4> Pp, Pq;
for (int i=0; i<4; i++)
for (int j=0; j<4; j++) {
Pp[i][j] = (i==j) - p.globalCoordinates()[i]*p.globalCoordinates()[j];
Pq[i][j] = (i==j) - q.globalCoordinates()[i]*q.globalCoordinates()[j];
}
Dune::FieldMatrix<T,4,4> B;
Dune::FMatrixHelp::multMatrix(Pp,Pq,B);
Dune::FieldMatrix<T,4,4> B;
Dune::FMatrixHelp::multMatrix(Pp,Pq,B);
// Bring it all together
A.axpy(4 * ( (sp<0) ? -1 : 1) * UnitVector<T,4>::derivativeOfArcCosSquared(abs(sp)), B);
// Bring it all together
A.axpy(4 * ( (sp<0) ? -1 : 1) * UnitVector<T,4>::derivativeOfArcCosSquared(abs(sp)), B);
return A;
}
return A;
}
/** \brief Compute the third derivative \partial d^3 / \partial dq^3
/** \brief Compute the third derivative \partial d^3 / \partial dq^3
Unlike the distance itself the squared distance is differentiable at zero
*/
static Tensor3<T,4,4,4> thirdDerivativeOfDistanceSquaredWRTSecondArgument(const Rotation<T,3>& p, const Rotation<T,3>& q) {
Unlike the distance itself the squared distance is differentiable at zero
*/
static Tensor3<T,4,4,4> thirdDerivativeOfDistanceSquaredWRTSecondArgument(const Rotation<T,3>& p, const Rotation<T,3>& q) {
Tensor3<T,4,4,4> result;
Tensor3<T,4,4,4> result;
T sp = p.globalCoordinates() * q.globalCoordinates();
T sp = p.globalCoordinates() * q.globalCoordinates();
// The projection matrix onto the tangent space at p and q
Dune::FieldMatrix<T,4,4> Pq;
for (int i=0; i<4; i++)
for (int j=0; j<4; j++)
Pq[i][j] = (i==j) - q.globalCoordinates()[i]*q.globalCoordinates()[j];
// The projection matrix onto the tangent space at p and q
Dune::FieldMatrix<T,4,4> Pq;
for (int i=0; i<4; i++)
for (int j=0; j<4; j++)
Pq[i][j] = (i==j) - q.globalCoordinates()[i]*q.globalCoordinates()[j];
EmbeddedTangentVector pProjected = q.projectOntoTangentSpace(p.globalCoordinates());
EmbeddedTangentVector pProjected = q.projectOntoTangentSpace(p.globalCoordinates());
double plusMinus = (sp < 0) ? -1 : 1;
double plusMinus = (sp < 0) ? -1 : 1;
using std::abs;
for (int i=0; i<4; i++)
for (int j=0; j<4; j++)
for (int k=0; k<4; k++) {
using std::abs;
for (int i=0; i<4; i++)
for (int j=0; j<4; j++)
for (int k=0; k<4; k++) {
result[i][j][k] = plusMinus * UnitVector<T,4>::thirdDerivativeOfArcCosSquared(abs(sp)) * pProjected[i] * pProjected[j] * pProjected[k]
- UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp)) * ((i==j)*sp + p.globalCoordinates()[i]*q.globalCoordinates()[j])*pProjected[k]
- UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp)) * ((i==k)*sp + p.globalCoordinates()[i]*q.globalCoordinates()[k])*pProjected[j]
- UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp)) * pProjected[i] * Pq[j][k] * sp
+ plusMinus * UnitVector<T,4>::derivativeOfArcCosSquared(abs(sp)) * ((i==j)*q.globalCoordinates()[k] + (i==k)*q.globalCoordinates()[j]) * sp
- plusMinus * UnitVector<T,4>::derivativeOfArcCosSquared(abs(sp)) * p.globalCoordinates()[i] * Pq[j][k];
}
result[i][j][k] = plusMinus * UnitVector<T,4>::thirdDerivativeOfArcCosSquared(abs(sp)) * pProjected[i] * pProjected[j] * pProjected[k]
- UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp)) * ((i==j)*sp + p.globalCoordinates()[i]*q.globalCoordinates()[j])*pProjected[k]
- UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp)) * ((i==k)*sp + p.globalCoordinates()[i]*q.globalCoordinates()[k])*pProjected[j]
- UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp)) * pProjected[i] * Pq[j][k] * sp
+ plusMinus * UnitVector<T,4>::derivativeOfArcCosSquared(abs(sp)) * ((i==j)*q.globalCoordinates()[k] + (i==k)*q.globalCoordinates()[j]) * sp
- plusMinus * UnitVector<T,4>::derivativeOfArcCosSquared(abs(sp)) * p.globalCoordinates()[i] * Pq[j][k];
}
Pq *= 4;
result = Pq * result;
Pq *= 4;
result = Pq * result;
return result;
}
return result;
}
/** \brief Compute the mixed third derivative \partial d^3 / \partial da db^2
/** \brief Compute the mixed third derivative \partial d^3 / \partial da db^2
Unlike the distance itself the squared distance is differentiable at zero
*/
static Tensor3<T,4,4,4> thirdDerivativeOfDistanceSquaredWRTFirst1AndSecond2Argument(const Rotation<T,3>& p, const Rotation<T,3>& q) {
Unlike the distance itself the squared distance is differentiable at zero
*/
static Tensor3<T,4,4,4> thirdDerivativeOfDistanceSquaredWRTFirst1AndSecond2Argument(const Rotation<T,3>& p, const Rotation<T,3>& q) {
Tensor3<T,4,4,4> result;
Tensor3<T,4,4,4> result;
T sp = p.globalCoordinates() * q.globalCoordinates();
T sp = p.globalCoordinates() * q.globalCoordinates();
// The projection matrix onto the tangent space at p and q
Dune::FieldMatrix<T,4,4> Pp, Pq;
for (int i=0; i<4; i++)
for (int j=0; j<4; j++) {
Pp[i][j] = (i==j) - p.globalCoordinates()[i]*p.globalCoordinates()[j];
Pq[i][j] = (i==j) - q.globalCoordinates()[i]*q.globalCoordinates()[j];
}
// The projection matrix onto the tangent space at p and q
Dune::FieldMatrix<T,4,4> Pp, Pq;
for (int i=0; i<4; i++)
for (int j=0; j<4; j++) {
Pp[i][j] = (i==j) - p.globalCoordinates()[i]*p.globalCoordinates()[j];
Pq[i][j] = (i==j) - q.globalCoordinates()[i]*q.globalCoordinates()[j];
}
EmbeddedTangentVector pProjected = q.projectOntoTangentSpace(p.globalCoordinates());
EmbeddedTangentVector qProjected = p.projectOntoTangentSpace(q.globalCoordinates());
EmbeddedTangentVector pProjected = q.projectOntoTangentSpace(p.globalCoordinates());
EmbeddedTangentVector qProjected = p.projectOntoTangentSpace(q.globalCoordinates());
Tensor3<T,4,4,4> derivativeOfPqOTimesPq;
for (int i=0; i<4; i++)
for (int j=0; j<4; j++)
for (int k=0; k<4; k++) {
derivativeOfPqOTimesPq[i][j][k] = 0;
for (int l=0; l<4; l++)
derivativeOfPqOTimesPq[i][j][k] += Pp[i][l] * (Pq[j][l]*pProjected[k] + pProjected[j]*Pq[k][l]);
}
Tensor3<T,4,4,4> derivativeOfPqOTimesPq;
for (int i=0; i<4; i++)
for (int j=0; j<4; j++)
for (int k=0; k<4; k++) {
derivativeOfPqOTimesPq[i][j][k] = 0;
for (int l=0; l<4; l++)
derivativeOfPqOTimesPq[i][j][k] += Pp[i][l] * (Pq[j][l]*pProjected[k] + pProjected[j]*Pq[k][l]);
}
double plusMinus = (sp < 0) ? -1 : 1;
double plusMinus = (sp < 0) ? -1 : 1;
using std::abs;
result = plusMinus * UnitVector<T,4>::thirdDerivativeOfArcCosSquared(abs(sp)) * Tensor3<T,4,4,4>::product(qProjected,pProjected,pProjected)
+ UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp)) * derivativeOfPqOTimesPq
- UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp)) * sp * Tensor3<T,4,4,4>::product(qProjected,Pq)
- plusMinus * UnitVector<T,4>::derivativeOfArcCosSquared(abs(sp)) * Tensor3<T,4,4,4>::product(qProjected,Pq);
using std::abs;
result = plusMinus * UnitVector<T,4>::thirdDerivativeOfArcCosSquared(abs(sp)) * Tensor3<T,4,4,4>::product(qProjected,pProjected,pProjected)
+ UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp)) * derivativeOfPqOTimesPq
- UnitVector<T,4>::secondDerivativeOfArcCosSquared(abs(sp)) * sp * Tensor3<T,4,4,4>::product(qProjected,Pq)
- plusMinus * UnitVector<T,4>::derivativeOfArcCosSquared(abs(sp)) * Tensor3<T,4,4,4>::product(qProjected,Pq);
result *= 4;
result *= 4;
return result;
return result;
}
}
/** \brief Interpolate between two rotations */
static Rotation<T,3> interpolate(const Rotation<T,3>& a, const Rotation<T,3>& b, T omega) {
/** \brief Interpolate between two rotations */
static Rotation<T,3> interpolate(const Rotation<T,3>& a, const Rotation<T,3>& b, T omega) {
// Compute log on T_a SO(3)
EmbeddedTangentVector v = log(a,b);
return exp(a, omega*v);
}
// Compute log on T_a SO(3)
EmbeddedTangentVector v = log(a,b);
return exp(a, omega*v);
}
/** \brief Interpolate between two rotations
\param omega must be between 0 and 1
*/
static Quaternion<T> interpolateDerivative(const Rotation<T,3>& a, const Rotation<T,3>& b,
T omega) {
Quaternion<T> result(0);
/** \brief Interpolate between two rotations
\param omega must be between 0 and 1
*/
static Quaternion<T> interpolateDerivative(const Rotation<T,3>& a, const Rotation<T,3>& b,
T omega) {
Quaternion<T> result(0);
// Compute log on T_a SO(3)
SkewMatrix<T,3> xi = log(a,b);
// Compute log on T_a SO(3)
SkewMatrix<T,3> xi = log(a,b);
SkewMatrix<T,3> v = xi;
v *= omega;
SkewMatrix<T,3> v = xi;
v *= omega;
// //////////////////////////////////////////////////////////////
// v now contains the derivative at 'a'. The derivative at
// the requested site is v pushed forward by Dexp.
// /////////////////////////////////////////////////////////////
// //////////////////////////////////////////////////////////////
// v now contains the derivative at 'a'. The derivative at
// the requested site is v pushed forward by Dexp.
// /////////////////////////////////////////////////////////////
Dune::FieldMatrix<T,4,3> diffExp = Dexp(v);
Dune::FieldMatrix<T,4,3> diffExp = Dexp(v);
diffExp.umv(xi.axial(),result);
diffExp.umv(xi.axial(),result);
return a.Quaternion<T>::mult(result);
}
return a.Quaternion<T>::mult(result);
}
/** \brief Return the corresponding orthogonal matrix */
void matrix(Dune::FieldMatrix<T,3,3>& m) const {
/** \brief Return the corresponding orthogonal matrix */
void matrix(Dune::FieldMatrix<T,3,3>& m) const {
m[0][0] = (*this)[0]*(*this)[0] - (*this)[1]*(*this)[1] - (*this)[2]*(*this)[2] + (*this)[3]*(*this)[3];
m[0][1] = 2 * ( (*this)[0]*(*this)[1] - (*this)[2]*(*this)[3] );
m[0][2] = 2 * ( (*this)[0]*(*this)[2] + (*this)[1]*(*this)[3] );
m[0][0] = (*this)[0]*(*this)[0] - (*this)[1]*(*this)[1] - (*this)[2]*(*this)[2] + (*this)[3]*(*this)[3];
m[0][1] = 2 * ( (*this)[0]*(*this)[1] - (*this)[2]*(*this)[3] );
m[0][2] = 2 * ( (*this)[0]*(*this)[2] + (*this)[1]*(*this)[3] );
m[1][0] = 2 * ( (*this)[0]*(*this)[1] + (*this)[2]*(*this)[3] );
m[1][1] = - (*this)[0]*(*this)[0] + (*this)[1]*(*this)[1] - (*this)[2]*(*this)[2] + (*this)[3]*(*this)[3];
m[1][2] = 2 * ( -(*this)[0]*(*this)[3] + (*this)[1]*(*this)[2] );
m[1][0] = 2 * ( (*this)[0]*(*this)[1] + (*this)[2]*(*this)[3] );
m[1][1] = - (*this)[0]*(*this)[0] + (*this)[1]*(*this)[1] - (*this)[2]*(*this)[2] + (*this)[3]*(*this)[3];
m[1][2] = 2 * ( -(*this)[0]*(*this)[3] + (*this)[1]*(*this)[2] );
m[2][0] = 2 * ( (*this)[0]*(*this)[2] - (*this)[1]*(*this)[3] );
m[2][1] = 2 * ( (*this)[0]*(*this)[3] + (*this)[1]*(*this)[2] );
m[2][2] = - (*this)[0]*(*this)[0] - (*this)[1]*(*this)[1] + (*this)[2]*(*this)[2] + (*this)[3]*(*this)[3];
m[2][0] = 2 * ( (*this)[0]*(*this)[2] - (*this)[1]*(*this)[3] );
m[2][1] = 2 * ( (*this)[0]*(*this)[3] + (*this)[1]*(*this)[2] );
m[2][2] = - (*this)[0]*(*this)[0] - (*this)[1]*(*this)[1] + (*this)[2]*(*this)[2] + (*this)[3]*(*this)[3];
}
}
/** \brief Derivative of the map from unit quaternions to orthogonal matrices
*/
static Tensor3<T,3,3,4> derivativeOfQuaternionToMatrix(const Dune::FieldVector<T,4>& p)
{
Tensor3<T,3,3,4> result;
/** \brief Derivative of the map from unit quaternions to orthogonal matrices
*/
static Tensor3<T,3,3,4> derivativeOfQuaternionToMatrix(const Dune::FieldVector<T,4>& p)
{
Tensor3<T,3,3,4> result;
result[0][0] = { 2*p[0], -2*p[1], -2*p[2], 2*p[3]};
result[0][1] = { 2*p[1], 2*p[0], -2*p[3], -2*p[2]};
result[0][2] = { 2*p[2], 2*p[3], 2*p[0], 2*p[1]};
result[0][0] = { 2*p[0], -2*p[1], -2*p[2], 2*p[3]};
result[0][1] = { 2*p[1], 2*p[0], -2*p[3], -2*p[2]};
result[0][2] = { 2*p[2], 2*p[3], 2*p[0], 2*p[1]};
result[1][0] = { 2*p[1], 2*p[0], 2*p[3], 2*p[2]};
result[1][1] = {-2*p[0], 2*p[1], -2*p[2], 2*p[3]};
result[1][2] = {-2*p[3], 2*p[2], 2*p[1], -2*p[0]};
result[1][0] = { 2*p[1], 2*p[0], 2*p[3], 2*p[2]};
result[1][1] = {-2*p[0], 2*p[1], -2*p[2], 2*p[3]};
result[1][2] = {-2*p[3], 2*p[2], 2*p[1], -2*p[0]};
result[2][0] = { 2*p[2], -2*p[3], 2*p[0], -2*p[1]};
result[2][1] = { 2*p[3], 2*p[2], 2*p[1], 2*p[0]};
result[2][2] = {-2*p[0], -2*p[1], 2*p[2], 2*p[3]};
result[2][0] = { 2*p[2], -2*p[3], 2*p[0], -2*p[1]};
result[2][1] = { 2*p[3], 2*p[2], 2*p[1], 2*p[0]};
result[2][2] = {-2*p[0], -2*p[1], 2*p[2], 2*p[3]};
return result;
}
return result;
}
/** \brief Set rotation from orthogonal matrix
/** \brief Set rotation from orthogonal matrix
We tacitly assume that the matrix really is orthogonal */
void set(const Dune::FieldMatrix<T,3,3>& m) {
We tacitly assume that the matrix really is orthogonal */
void set(const Dune::FieldMatrix<T,3,3>& m) {
using std::sqrt;
using std::sqrt;
// Easier writing
Dune::FieldVector<T,4>& p = (*this);
// The following equations for the derivation of a unit quaternion from a rotation
// matrix comes from 'E. Salamin, Application of Quaternions to Computation with
// Rotations, Technical Report, Stanford, 1974'
// Easier writing
Dune::FieldVector<T,4>& p = (*this);
// The following equations for the derivation of a unit quaternion from a rotation
// matrix comes from 'E. Salamin, Application of Quaternions to Computation with
// Rotations, Technical Report, Stanford, 1974'
p[0] = (1 + m[0][0] - m[1][1] - m[2][2]) / 4;
p[1] = (1 - m[0][0] + m[1][1] - m[2][2]) / 4;
p[2] = (1 - m[0][0] - m[1][1] + m[2][2]) / 4;
p[3] = (1 + m[0][0] + m[1][1] + m[2][2]) / 4;
p[0] = (1 + m[0][0] - m[1][1] - m[2][2]) / 4;
p[1] = (1 - m[0][0] + m[1][1] - m[2][2]) / 4;
p[2] = (1 - m[0][0] - m[1][1] + m[2][2]) / 4;
p[3] = (1 + m[0][0] + m[1][1] + m[2][2]) / 4;
// avoid rounding problems
if (p[0] >= p[1] && p[0] >= p[2] && p[0] >= p[3]) {
// avoid rounding problems
if (p[0] >= p[1] && p[0] >= p[2] && p[0] >= p[3]) {
p[0] = sqrt(p[0]);
p[0] = sqrt(p[0]);
// r_x r_y = (R_12 + R_21) / 4
p[1] = (m[0][1] + m[1][0]) / 4 / p[0];
// r_x r_y = (R_12 + R_21) / 4
p[1] = (m[0][1] + m[1][0]) / 4 / p[0];
// r_x r_z = (R_13 + R_31) / 4
p[2] = (m[0][2] + m[2][0]) / 4 / p[0];
// r_x r_z = (R_13 + R_31) / 4
p[2] = (m[0][2] + m[2][0]) / 4 / p[0];
// r_0 r_x = (R_32 - R_23) / 4
p[3] = (m[2][1] - m[1][2]) / 4 / p[0];
// r_0 r_x = (R_32 - R_23) / 4
p[3] = (m[2][1] - m[1][2]) / 4 / p[0];
} else if (p[1] >= p[0] && p[1] >= p[2] && p[1] >= p[3]) {
} else if (p[1] >= p[0] && p[1] >= p[2] && p[1] >= p[3]) {
p[1] = sqrt(p[1]);
p[1] = sqrt(p[1]);
// r_x r_y = (R_12 + R_21) / 4
p[0] = (m[0][1] + m[1][0]) / 4 / p[1];
// r_x r_y = (R_12 + R_21) / 4
p[0] = (m[0][1] + m[1][0]) / 4 / p[1];
// r_y r_z = (R_23 + R_32) / 4
p[2] = (m[1][2] + m[2][1]) / 4 / p[1];
// r_y r_z = (R_23 + R_32) / 4
p[2] = (m[1][2] + m[2][1]) / 4 / p[1];
// r_0 r_y = (R_13 - R_31) / 4
p[3] = (m[0][2] - m[2][0]) / 4 / p[1];
// r_0 r_y = (R_13 - R_31) / 4
p[3] = (m[0][2] - m[2][0]) / 4 / p[1];
} else if (p[2] >= p[0] && p[2] >= p[1] && p[2] >= p[3]) {
} else if (p[2] >= p[0] && p[2] >= p[1] && p[2] >= p[3]) {
p[2] = sqrt(p[2]);
p[2] = sqrt(p[2]);
// r_x r_z = (R_13 + R_31) / 4
p[0] = (m[0][2] + m[2][0]) / 4 / p[2];
// r_x r_z = (R_13 + R_31) / 4
p[0] = (m[0][2] + m[2][0]) / 4 / p[2];
// r_y r_z = (R_23 + R_32) / 4
p[1] = (m[1][2] + m[2][1]) / 4 / p[2];
// r_y r_z = (R_23 + R_32) / 4
p[1] = (m[1][2] + m[2][1]) / 4 / p[2];
// r_0 r_z = (R_21 - R_12) / 4
p[3] = (m[1][0] - m[0][1]) / 4 / p[2];
// r_0 r_z = (R_21 - R_12) / 4
p[3] = (m[1][0] - m[0][1]) / 4 / p[2];
} else {
} else {
p[3] = sqrt(p[3]);
p[3] = sqrt(p[3]);
// r_0 r_x = (R_32 - R_23) / 4
p[0] = (m[2][1] - m[1][2]) / 4 / p[3];
// r_0 r_x = (R_32 - R_23) / 4
p[0] = (m[2][1] - m[1][2]) / 4 / p[3];
// r_0 r_y = (R_13 - R_31) / 4
p[1] = (m[0][2] - m[2][0]) / 4 / p[3];
// r_0 r_y = (R_13 - R_31) / 4
p[1] = (m[0][2] - m[2][0]) / 4 / p[3];
// r_0 r_z = (R_21 - R_12) / 4
p[2] = (m[1][0] - m[0][1]) / 4 / p[3];
// r_0 r_z = (R_21 - R_12) / 4
p[2] = (m[1][0] - m[0][1]) / 4 / p[3];
}
}
}
/** \brief Derivative of the map from orthogonal matrices to unit quaternions
/** \brief Derivative of the map from orthogonal matrices to unit quaternions
We tacitly assume that the matrix really is orthogonal */
static Tensor3<T,4,3,3> derivativeOfMatrixToQuaternion(const Dune::FieldMatrix<T,3,3>& m)
{
using std::pow;
using std::sqrt;
We tacitly assume that the matrix really is orthogonal */
static Tensor3<T,4,3,3> derivativeOfMatrixToQuaternion(const Dune::FieldMatrix<T,3,3>& m)
{
using std::pow;
using std::sqrt;
Tensor3<T,4,3,3> result;
Tensor3<T,4,3,3> result;
Dune::FieldVector<T,4> p;
Dune::FieldVector<T,4> p;
// The following equations for the derivation of a unit quaternion from a rotation
// matrix comes from 'E. Salamin, Application of Quaternions to Computation with
// Rotations, Technical Report, Stanford, 1974'
// The following equations for the derivation of a unit quaternion from a rotation
// matrix comes from 'E. Salamin, Application of Quaternions to Computation with
// Rotations, Technical Report, Stanford, 1974'
p[0] = (1 + m[0][0] - m[1][1] - m[2][2]) / 4;
p[1] = (1 - m[0][0] + m[1][1] - m[2][2]) / 4;
p[2] = (1 - m[0][0] - m[1][1] + m[2][2]) / 4;
p[3] = (1 + m[0][0] + m[1][1] + m[2][2]) / 4;
p[0] = (1 + m[0][0] - m[1][1] - m[2][2]) / 4;
p[1] = (1 - m[0][0] + m[1][1] - m[2][2]) / 4;
p[2] = (1 - m[0][0] - m[1][1] + m[2][2]) / 4;
p[3] = (1 + m[0][0] + m[1][1] + m[2][2]) / 4;
// avoid rounding problems
if (p[0] >= p[1] && p[0] >= p[2] && p[0] >= p[3])
{
result[0] = {{1,0,0},{0,-1,0},{0,0,-1}};
result[0] *= 1.0/(8.0*sqrt(p[0]));
// avoid rounding problems
if (p[0] >= p[1] && p[0] >= p[2] && p[0] >= p[3])
{
result[0] = {{1,0,0},{0,-1,0},{0,0,-1}};
result[0] *= 1.0/(8.0*sqrt(p[0]));
T denom = 32 * pow(p[0],1.5);
T offDiag = 1.0/(4*sqrt(p[0]));
T denom = 32 * pow(p[0],1.5);
T offDiag = 1.0/(4*sqrt(p[0]));
result[1] = { {-(m[0][1]+m[1][0]) / denom, offDiag, 0},
{offDiag, (m[0][1]+m[1][0]) / denom, 0},
{0, 0, (m[0][1]+m[1][0]) / denom}};
result[1] = { {-(m[0][1]+m[1][0]) / denom, offDiag, 0},
{offDiag, (m[0][1]+m[1][0]) / denom, 0},
{0, 0, (m[0][1]+m[1][0]) / denom}};
result[2] = { {-(m[0][2]+m[2][0]) / denom, 0, offDiag},
{0, (m[0][2]+m[2][0]) / denom, 0},
{offDiag, 0, (m[0][2]+m[2][0]) / denom}};
result[2] = { {-(m[0][2]+m[2][0]) / denom, 0, offDiag},
{0, (m[0][2]+m[2][0]) / denom, 0},
{offDiag, 0, (m[0][2]+m[2][0]) / denom}};
result[3] = { {-(m[2][1]-m[1][2]) / denom, 0, 0},
{0, (m[2][1]-m[1][2]) / denom, -offDiag},
{0, offDiag, (m[2][1]-m[1][2]) / denom}};
}
else if (p[1] >= p[0] && p[1] >= p[2] && p[1] >= p[3])
{
result[1] = {{-1,0,0},{0,1,0},{0,0,-1}};
result[1] *= 1.0/(8.0*sqrt(p[1]));
result[3] = { {-(m[2][1]-m[1][2]) / denom, 0, 0},
{0, (m[2][1]-m[1][2]) / denom, -offDiag},
{0, offDiag, (m[2][1]-m[1][2]) / denom}};
}
else if (p[1] >= p[0] && p[1] >= p[2] && p[1] >= p[3])
{
result[1] = {{-1,0,0},{0,1,0},{0,0,-1}};
result[1] *= 1.0/(8.0*sqrt(p[1]));
T denom = 32 * pow(p[1],1.5);
T offDiag = 1.0/(4*sqrt(p[1]));
T denom = 32 * pow(p[1],1.5);
T offDiag = 1.0/(4*sqrt(p[1]));
result[0] = { {(m[0][1]+m[1][0]) / denom, offDiag, 0},
{offDiag, -(m[0][1]+m[1][0]) / denom, 0},
{0, 0, (m[0][1]+m[1][0]) / denom}};
result[0] = { {(m[0][1]+m[1][0]) / denom, offDiag, 0},
{offDiag, -(m[0][1]+m[1][0]) / denom, 0},
{0, 0, (m[0][1]+m[1][0]) / denom}};
result[2] = { {(m[1][2]+m[2][1]) / denom, 0 , 0},
{0, -(m[1][2]+m[2][1]) / denom, offDiag},
{0, offDiag, (m[1][2]+m[2][1]) / denom}};
result[2] = { {(m[1][2]+m[2][1]) / denom, 0 , 0},
{0, -(m[1][2]+m[2][1]) / denom, offDiag},
{0, offDiag, (m[1][2]+m[2][1]) / denom}};
result[3] = { {(m[0][2]-m[2][0]) / denom, 0, offDiag},
{0, -(m[0][2]-m[2][0]) / denom, 0},
{-offDiag, 0, (m[0][2]-m[2][0]) / denom}};
}
else if (p[2] >= p[0] && p[2] >= p[1] && p[2] >= p[3])
{
result[2] = {{-1,0,0},{0,-1,0},{0,0,1}};
result[2] *= 1.0/(8.0*sqrt(p[2]));
result[3] = { {(m[0][2]-m[2][0]) / denom, 0, offDiag},
{0, -(m[0][2]-m[2][0]) / denom, 0},
{-offDiag, 0, (m[0][2]-m[2][0]) / denom}};
}
else if (p[2] >= p[0] && p[2] >= p[1] && p[2] >= p[3])
{
result[2] = {{-1,0,0},{0,-1,0},{0,0,1}};
result[2] *= 1.0/(8.0*sqrt(p[2]));
T denom = 32 * pow(p[2],1.5);
T offDiag = 1.0/(4*sqrt(p[2]));
T denom = 32 * pow(p[2],1.5);
T offDiag = 1.0/(4*sqrt(p[2]));
result[0] = { {(m[0][2]+m[2][0]) / denom, 0, offDiag},
{0, (m[0][2]+m[2][0]) / denom, 0},
{offDiag, 0, -(m[0][2]+m[2][0]) / denom}};
result[0] = { {(m[0][2]+m[2][0]) / denom, 0, offDiag},
{0, (m[0][2]+m[2][0]) / denom, 0},
{offDiag, 0, -(m[0][2]+m[2][0]) / denom}};
result[1] = { {(m[1][2]+m[2][1]) / denom, 0 , 0},
{0, (m[1][2]+m[2][1]) / denom, offDiag},
{0, offDiag, -(m[1][2]+m[2][1]) / denom}};
result[1] = { {(m[1][2]+m[2][1]) / denom, 0 , 0},
{0, (m[1][2]+m[2][1]) / denom, offDiag},
{0, offDiag, -(m[1][2]+m[2][1]) / denom}};
result[3] = { {(m[1][0]-m[0][1]) / denom, -offDiag, 0},
{offDiag, (m[1][0]-m[0][1]) / denom, 0},
{0, 0, -(m[1][0]-m[0][1]) / denom}};
}
else
{
result[3] = {{1,0,0},{0,1,0},{0,0,1}};
result[3] *= 1.0/(8.0*sqrt(p[3]));
result[3] = { {(m[1][0]-m[0][1]) / denom, -offDiag, 0},
{offDiag, (m[1][0]-m[0][1]) / denom, 0},
{0, 0, -(m[1][0]-m[0][1]) / denom}};
}
else
{
result[3] = {{1,0,0},{0,1,0},{0,0,1}};
result[3] *= 1.0/(8.0*sqrt(p[3]));
T denom = 32 * pow(p[3],1.5);
T offDiag = 1.0/(4*sqrt(p[3]));
T denom = 32 * pow(p[3],1.5);
T offDiag = 1.0/(4*sqrt(p[3]));
result[0] = { {-(m[2][1]-m[1][2]) / denom, 0, 0},
{0, -(m[2][1]-m[1][2]) / denom, -offDiag},
{0, offDiag, -(m[2][1]-m[1][2]) / denom}};
result[0] = { {-(m[2][1]-m[1][2]) / denom, 0, 0},
{0, -(m[2][1]-m[1][2]) / denom, -offDiag},
{0, offDiag, -(m[2][1]-m[1][2]) / denom}};
result[1] = { {-(m[0][2]-m[2][0]) / denom, 0, offDiag},
{0, -(m[0][2]-m[2][0]) / denom, 0},
{-offDiag, 0, -(m[0][2]-m[2][0]) / denom}};
result[1] = { {-(m[0][2]-m[2][0]) / denom, 0, offDiag},
{0, -(m[0][2]-m[2][0]) / denom, 0},
{-offDiag, 0, -(m[0][2]-m[2][0]) / denom}};
result[2] = { {-(m[1][0]-m[0][1]) / denom, -offDiag, 0},
{offDiag, -(m[1][0]-m[0][1]) / denom, 0},
{0, 0, -(m[1][0]-m[0][1]) / denom}};
result[2] = { {-(m[1][0]-m[0][1]) / denom, -offDiag, 0},
{offDiag, -(m[1][0]-m[0][1]) / denom, 0},
{0, 0, -(m[1][0]-m[0][1]) / denom}};
}
return result;
}
return result;
}
/** \brief Project tangent vector of R^n onto the tangent space */
EmbeddedTangentVector projectOntoTangentSpace(const EmbeddedTangentVector& v) const {
EmbeddedTangentVector result = v;
EmbeddedTangentVector data = *this;
result.axpy(-1*(data*result), data);
return result;
}
/** \brief Project tangent vector of R^n onto the normal space space */
EmbeddedTangentVector projectOntoNormalSpace(const EmbeddedTangentVector& v) const {
Dune::FieldVector<T,4> data = *this;
T sp = v*data;
EmbeddedTangentVector result = *this;
result *= sp;
return result;
}
/** \brief Project tangent vector of R^n onto the tangent space */
EmbeddedTangentVector projectOntoTangentSpace(const EmbeddedTangentVector& v) const {
EmbeddedTangentVector result = v;
EmbeddedTangentVector data = *this;
result.axpy(-1*(data*result), data);
return result;
}
/** \brief The Weingarten map */
EmbeddedTangentVector weingarten(const EmbeddedTangentVector& z, const EmbeddedTangentVector& v) const {
/** \brief Project tangent vector of R^n onto the normal space space */
EmbeddedTangentVector projectOntoNormalSpace(const EmbeddedTangentVector& v) const {
Dune::FieldVector<T,4> data = *this;
T sp = v*data;
EmbeddedTangentVector result = *this;
result *= sp;
return result;
}
EmbeddedTangentVector result;
/** \brief The Weingarten map */
EmbeddedTangentVector weingarten(const EmbeddedTangentVector& z, const EmbeddedTangentVector& v) const {
T sp = v*(*this);
EmbeddedTangentVector result;
for (int i=0; i<embeddedDim; i++)
result[i] = -sp * z[i];
T sp = v*(*this);
return result;
}
for (int i=0; i<embeddedDim; i++)
result[i] = -sp * z[i];
/** \brief Project a vector in R^4 onto the unit quaternions
*
* \warning This is NOT the standard projection from R^{3 \times 3} onto SO(3)!
*/
static Rotation<T,3> projectOnto(const CoordinateType& p)
{
Rotation<T,3> result(p);
result /= result.two_norm();
return result;
}
return result;
}
/** \brief Derivative of the projection of a vector in R^4 onto the unit quaternions
*
* \warning This is NOT the standard projection from R^{3 \times 3} onto SO(3)!
*/
static auto derivativeOfProjection(const Dune::FieldVector<T,4>& p)
{
Dune::FieldMatrix<T,4,4> result;
for (int i=0; i<4; i++)
for (int j=0; j<4; j++)
result[i][j] = ( (i==j) - p[i]*p[j] / p.two_norm2() ) / p.two_norm();
return result;
}
/** \brief Project a vector in R^4 onto the unit quaternions
*
* \warning This is NOT the standard projection from R^{3 \times 3} onto SO(3)!
*/
static Rotation<T,3> projectOnto(const CoordinateType& p)
{
Rotation<T,3> result(p);
result /= result.two_norm();
return result;
}
/** \brief The global coordinates, if you really want them */
const CoordinateType& globalCoordinates() const {
return *this;
}
/** \brief Derivative of the projection of a vector in R^4 onto the unit quaternions
*
* \warning This is NOT the standard projection from R^{3 \times 3} onto SO(3)!
*/
static auto derivativeOfProjection(const Dune::FieldVector<T,4>& p)
{
Dune::FieldMatrix<T,4,4> result;
for (int i=0; i<4; i++)
for (int j=0; j<4; j++)
result[i][j] = ( (i==j) - p[i]*p[j] / p.two_norm2() ) / p.two_norm();
return result;
}
/** \brief Compute an orthonormal basis of the tangent space of the unit quaternions
*
* Since the unit quaternions are an odd-dimensional sphere, there exists a globally
* continuous orthonormal frame field. I took the expression here from
* "Dichmann, Li, Maddocks, 'Hamiltonian Formulations and Symmetries in Rod Mechanics', page 83"
*/
Dune::FieldMatrix<T,3,4> orthonormalFrame() const {
return {{ (*this)[3], (*this)[2], -(*this)[1], -(*this)[0]},
{-(*this)[2], (*this)[3], (*this)[0], -(*this)[1]},
{ (*this)[1], -(*this)[0], (*this)[3], -(*this)[2]}};
/** \brief The global coordinates, if you really want them */
const CoordinateType& globalCoordinates() const {
return *this;
}
}
/** \brief Compute an orthonormal basis of the tangent space of the unit quaternions
*
* Since the unit quaternions are an odd-dimensional sphere, there exists a globally
* continuous orthonormal frame field. I took the expression here from
* "Dichmann, Li, Maddocks, 'Hamiltonian Formulations and Symmetries in Rod Mechanics', page 83"
*/
Dune::FieldMatrix<T,3,4> orthonormalFrame() const {
return {{ (*this)[3], (*this)[2], -(*this)[1], -(*this)[0]},
{-(*this)[2], (*this)[3], (*this)[0], -(*this)[1]},
{ (*this)[1], -(*this)[0], (*this)[3], -(*this)[2]}};
};
}
/** \brief Convert a unit quaternion to an orthogonal matrix
*
* This method returns a callable object which does the conversion.
* It can be used together with Functions::makeComposedGridFunction
* to turn a quaternion-valued function into a matrix-valued one.
*/
constexpr static auto quaternionToMatrix = []<typename RT>(Rotation<RT,3> quaternion) -> Dune::FieldMatrix<RT,3,3>
{
Dune::FieldMatrix<RT,3,3> rotationMatrix;
quaternion.matrix(rotationMatrix);
return rotationMatrix;
};
/** \brief Convert an orthogonal matrix to a unit quaternion
*
* This method returns a callable object which does the conversion.
* It can be used together with Functions::makeComposedGridFunction
* to turn a matrix-valued function into a quaternion-valued one.
*/
constexpr static auto matrixToQuaternion = []<typename RT>(const Dune::FieldMatrix<RT,3>& matrix) -> Dune::FieldVector<RT,4>
{
Rotation<RT,3> rotation;
rotation.set(matrix);
return rotation;
};
};
} // namespace Dune::GFE
#endif
dune/gfe/spaces/unitvector.hh
View file @ 48b9358e
......@@ -9,528 +9,534 @@
#include <dune/gfe/tensor3.hh>
#include <dune/gfe/symmetricmatrix.hh>
template <class T, int N>
class Rotation;
/** \brief A unit vector in R^N
\tparam N Dimension of the embedding space
\tparam T The type used for individual coordinates
*/
template <class T, int N>
class UnitVector
namespace Dune::GFE
{
// Rotation<T,3> is friend, because it needs the various derivatives of the arccos
friend class Rotation<T,3>;
/** \brief Computes sin(x) / x without getting unstable for small x */
static T sinc(const T& x) {
using std::sin;
return (x < 1e-2) ? 1.0-x*x/6.0+ Dune::power(x,4)/120.0-Dune::power(x,6)/5040.0+Dune::power(x,8)/362880.0 : sin(x)/x;
}
/** \brief Compute arccos^2 without using the (at 1) nondifferentiable function acos x close to 1 */
static T arcCosSquared(const T& x) {
using std::acos;
const T eps = 1e-2;
if (x > 1-eps) { // acos is not differentiable, use the series expansion instead,
// we need here lots of terms to be sure that the numerical derivatives are also within maschine precision
//return -2 * (x-1) + 1.0/3 * (x-1)*(x-1) - 4.0/45 * (x-1)*(x-1)*(x-1);
return 11665028.0/4729725.0
-141088.0/45045.0*x
+ 413.0/429.0*x*x
- 5344.0/12285.0*Dune::power(x,3)
+ 245.0/1287.0*Dune::power(x,4)
- 1632.0/25025.0*Dune::power(x,5)
+ 56.0/3861.0*Dune::power(x,6)
- 32.0/21021.0*Dune::power(x,7);
} else {
return Dune::power(acos(x),2);
template <class T, int N>
class Rotation;
/** \brief A unit vector in R^N
\tparam N Dimension of the embedding space
\tparam T The type used for individual coordinates
*/
template <class T, int N>
class UnitVector
{
// Rotation<T,3> is friend, because it needs the various derivatives of the arccos
friend class Rotation<T,3>;
/** \brief Computes sin(x) / x without getting unstable for small x */
static T sinc(const T& x) {
using std::sin;
return (x < 1e-2) ? 1.0-x*x/6.0+ Dune::power(x,4)/120.0-Dune::power(x,6)/5040.0+Dune::power(x,8)/362880.0 : sin(x)/x;
}
}
/** \brief Compute the derivative of arccos^2 without getting unstable for x close to 1 */
static T derivativeOfArcCosSquared(const T& x) {
using std::acos;
using std::sqrt;
const T eps = 1e-2;
if (x > 1-eps) { // regular expression is unstable, use the series expansion instead
// we need here lots of terms to be sure that the numerical derivatives are also within maschine precision
//return -2 + 2*(x-1)/3 - 4/15*(x-1)*(x-1);
return -47104.0/15015.0
+12614.0/6435.0*x
-63488.0/45045.0*x*x
+ 1204.0/1287.0*Dune::power(x,3)
- 2048.0/4095.0*Dune::power(x,4)
+ 112.0/585.0*Dune::power(x,5)
-2048.0/45045.0*Dune::power(x,6)
+ 32.0/6435.0*Dune::power(x,7);
} 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*acos(x) / sqrt(1-x*x);
}
/** \brief Compute the second derivative of arccos^2 without getting unstable for x close to 1 */
static T secondDerivativeOfArcCosSquared(const T& x) {
using std::acos;
using std::pow;
const T eps = 1e-2;
if (x > 1-eps) { // regular expression is unstable, use the series expansion instead
// we need here lots of terms to be sure that the numerical derivatives are also within maschine precision
//return 2.0/3 - 8*(x-1)/15;
return 1350030.0/676039.0+5632.0/2028117.0*Dune::power(x,10)
-1039056896.0/334639305.0*x
+150876.0/39767.0*x*x
-445186048.0/111546435.0*Dune::power(x,3)
+ 343728.0/96577.0*Dune::power(x,4)
- 57769984.0/22309287.0*Dune::power(x,5)
+ 710688.0/482885.0*Dune::power(x,6)
- 41615360.0/66927861.0*Dune::power(x,7)
+ 616704.0/3380195.0*Dune::power(x,8)
- 245760.0/7436429.0*Dune::power(x,9);
} 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*acos(x) / pow(1-x*x,1.5);
}
/** \brief Compute the third derivative of arccos^2 without getting unstable for x close to 1 */
static T thirdDerivativeOfArcCosSquared(const T& x) {
using std::acos;
using std::sqrt;
const T eps = 1e-2;
if (x > 1-eps) { // regular expression is unstable, use the series expansion instead
// we need here lots of terms to be sure that the numerical derivatives are also within maschine precision
//return -8.0/15 + 24*(x-1)/35;
return -1039056896.0/334639305.0
+301752.0/39767.0*x
-445186048.0/37182145.0*x*x
+1374912.0/96577.0*Dune::power(x,3)
-288849920.0/22309287.0*Dune::power(x,4)
+4264128.0/482885.0*Dune::power(x,5)
-41615360.0/9561123.0*Dune::power(x,6)
+4933632.0/3380195.0*Dune::power(x,7)
-2211840.0/7436429.0*Dune::power(x,8)
+56320.0/2028117.0*Dune::power(x,9);
} 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*acos(x)/(d*d*sqrt(d)) - 2*acos(x)/(d*sqrt(d));
/** \brief Compute arccos^2 without using the (at 1) nondifferentiable function acos x close to 1 */
static T arcCosSquared(const T& x) {
using std::acos;
const T eps = 1e-2;
if (x > 1-eps) { // acos is not differentiable, use the series expansion instead,
// we need here lots of terms to be sure that the numerical derivatives are also within maschine precision
//return -2 * (x-1) + 1.0/3 * (x-1)*(x-1) - 4.0/45 * (x-1)*(x-1)*(x-1);
return 11665028.0/4729725.0
-141088.0/45045.0*x
+ 413.0/429.0*x*x
- 5344.0/12285.0*Dune::power(x,3)
+ 245.0/1287.0*Dune::power(x,4)
- 1632.0/25025.0*Dune::power(x,5)
+ 56.0/3861.0*Dune::power(x,6)
- 32.0/21021.0*Dune::power(x,7);
} else {
return Dune::power(acos(x),2);
}
}
}
template <class T2, int N2>
friend class UnitVector;
/** \brief Compute the derivative of arccos^2 without getting unstable for x close to 1 */
static T derivativeOfArcCosSquared(const T& x) {
using std::acos;
using std::sqrt;
const T eps = 1e-2;
if (x > 1-eps) { // regular expression is unstable, use the series expansion instead
// we need here lots of terms to be sure that the numerical derivatives are also within maschine precision
//return -2 + 2*(x-1)/3 - 4/15*(x-1)*(x-1);
return -47104.0/15015.0
+12614.0/6435.0*x
-63488.0/45045.0*x*x
+ 1204.0/1287.0*Dune::power(x,3)
- 2048.0/4095.0*Dune::power(x,4)
+ 112.0/585.0*Dune::power(x,5)
-2048.0/45045.0*Dune::power(x,6)
+ 32.0/6435.0*Dune::power(x,7);
} 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*acos(x) / sqrt(1-x*x);
}
public:
/** \brief Compute the second derivative of arccos^2 without getting unstable for x close to 1 */
static T secondDerivativeOfArcCosSquared(const T& x) {
using std::acos;
using std::pow;
const T eps = 1e-2;
if (x > 1-eps) { // regular expression is unstable, use the series expansion instead
// we need here lots of terms to be sure that the numerical derivatives are also within maschine precision
//return 2.0/3 - 8*(x-1)/15;
return 1350030.0/676039.0+5632.0/2028117.0*Dune::power(x,10)
-1039056896.0/334639305.0*x
+150876.0/39767.0*x*x
-445186048.0/111546435.0*Dune::power(x,3)
+ 343728.0/96577.0*Dune::power(x,4)
- 57769984.0/22309287.0*Dune::power(x,5)
+ 710688.0/482885.0*Dune::power(x,6)
- 41615360.0/66927861.0*Dune::power(x,7)
+ 616704.0/3380195.0*Dune::power(x,8)
- 245760.0/7436429.0*Dune::power(x,9);
} 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*acos(x) / pow(1-x*x,1.5);
}
/** \brief The type used for coordinates */
typedef T ctype;
typedef T field_type;
/** \brief Compute the third derivative of arccos^2 without getting unstable for x close to 1 */
static T thirdDerivativeOfArcCosSquared(const T& x) {
using std::acos;
using std::sqrt;
const T eps = 1e-2;
if (x > 1-eps) { // regular expression is unstable, use the series expansion instead
// we need here lots of terms to be sure that the numerical derivatives are also within maschine precision
//return -8.0/15 + 24*(x-1)/35;
return -1039056896.0/334639305.0
+301752.0/39767.0*x
-445186048.0/37182145.0*x*x
+1374912.0/96577.0*Dune::power(x,3)
-288849920.0/22309287.0*Dune::power(x,4)
+4264128.0/482885.0*Dune::power(x,5)
-41615360.0/9561123.0*Dune::power(x,6)
+4933632.0/3380195.0*Dune::power(x,7)
-2211840.0/7436429.0*Dune::power(x,8)
+56320.0/2028117.0*Dune::power(x,9);
} 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*acos(x)/(d*d*sqrt(d)) - 2*acos(x)/(d*sqrt(d));
}
}
/** \brief The type used for global coordinates */
typedef Dune::FieldVector<T,N> CoordinateType;
template <class T2, int N2>
friend class UnitVector;
/** \brief Dimension of the manifold formed by unit vectors */
static const int dim = N-1;
public:
/** \brief Dimension of the Euclidean space the manifold is embedded in */
static const int embeddedDim = N;
/** \brief The type used for coordinates */
typedef T ctype;
typedef T field_type;
typedef Dune::FieldVector<T,N-1> TangentVector;
/** \brief The type used for global coordinates */
typedef Dune::FieldVector<T,N> CoordinateType;
typedef Dune::FieldVector<T,N> EmbeddedTangentVector;
/** \brief Dimension of the manifold formed by unit vectors */
static const int dim = N-1;
/** \brief The global convexity radius of the unit sphere */
static constexpr double convexityRadius = 0.5*M_PI;
/** \brief Dimension of the Euclidean space the manifold is embedded in */
static const int embeddedDim = N;
/** \brief The return type of the derivativeOfProjection method */
typedef Dune::FieldMatrix<T, N, N> DerivativeOfProjection;
typedef Dune::FieldVector<T,N-1> TangentVector;
/** \brief Default constructor */
UnitVector()
{}
typedef Dune::FieldVector<T,N> EmbeddedTangentVector;
/** \brief Constructor from a vector. The vector gets normalized! */
UnitVector(const Dune::FieldVector<T,N>& vector)
: data_(vector)
{
data_ /= data_.two_norm();
}
/** \brief The global convexity radius of the unit sphere */
static constexpr double convexityRadius = 0.5*M_PI;
/** \brief Constructor from an array. The array gets normalized! */
UnitVector(const std::array<T,N>& vector)
{
for (int i=0; i<N; i++)
data_[i] = vector[i];
data_ /= data_.two_norm();
}
/** \brief Assignment from UnitVector with different type -- used for automatic differentiation with ADOL-C */
template <class T2>
UnitVector& operator <<= (const UnitVector<T2,N>& other) {
for (int i=0; i<N; i++)
data_[i] <<= other.data_[i];
return *this;
}
/** \brief Rebind the UnitVector to another coordinate type */
template<class U>
struct rebind
{
typedef UnitVector<U,N> other;
};
/** \brief The return type of the derivativeOfProjection method */
typedef Dune::FieldMatrix<T, N, N> DerivativeOfProjection;
/** \brief Default constructor */
UnitVector()
{}
/** \brief Constructor from a vector. The vector gets normalized! */
UnitVector(const Dune::FieldVector<T,N>& vector)
: data_(vector)
{
data_ /= data_.two_norm();
}
UnitVector<T,N>& operator=(const Dune::FieldVector<T,N>& vector)
{
data_ = vector;
data_ /= data_.two_norm();
return *this;
}
/** \brief Constructor from an array. The array gets normalized! */
UnitVector(const std::array<T,N>& vector)
{
for (int i=0; i<N; i++)
data_[i] = vector[i];
data_ /= data_.two_norm();
}
/** \brief The exponential map */
static UnitVector exp(const UnitVector& p, const TangentVector& v) {
/** \brief Assignment from UnitVector with different type -- used for automatic differentiation with ADOL-C */
template <class T2>
UnitVector& operator <<= (const UnitVector<T2,N>& other) {
for (int i=0; i<N; i++)
data_[i] <<= other.data_[i];
return *this;
}
Dune::FieldMatrix<T,N-1,N> frame = p.orthonormalFrame();
/** \brief Rebind the UnitVector to another coordinate type */
template<class U>
struct rebind
{
typedef UnitVector<U,N> other;
};
EmbeddedTangentVector ev;
frame.mtv(v,ev);
return exp(p,ev);
}
/** \brief The exponential map */
static UnitVector exp(const UnitVector& p, const EmbeddedTangentVector& v) {
UnitVector<T,N>& operator=(const Dune::FieldVector<T,N>& vector)
{
data_ = vector;
data_ /= data_.two_norm();
return *this;
}
using std::abs;
using std::cos;
assert( abs(p.data_*v) < 1e-5 );
/** \brief The exponential map */
static UnitVector exp(const UnitVector& p, const TangentVector& v) {
const T norm = v.two_norm();
UnitVector result = p;
result.data_ *= cos(norm);
result.data_.axpy(sinc(norm), v);
return result;
}
Dune::FieldMatrix<T,N-1,N> frame = p.orthonormalFrame();
/** \brief The inverse of the exponential map
*
* \results A vector in the tangent space of p
*/
static EmbeddedTangentVector log(const UnitVector& p, const UnitVector& q)
{
EmbeddedTangentVector result = p.projectOntoTangentSpace(q.data_-p.data_);
if (result.two_norm() > 1e-10)
result *= distance(p,q) / result.two_norm();
return result;
}
EmbeddedTangentVector ev;
frame.mtv(v,ev);
/** \brief Length of the great arc connecting the two points */
static T distance(const UnitVector& a, const UnitVector& b) {
return exp(p,ev);
}
/** \brief The exponential map */
static UnitVector exp(const UnitVector& p, const EmbeddedTangentVector& v) {
using std::acos;
using std::min;
using std::abs;
using std::cos;
assert( abs(p.data_*v) < 1e-5 );
// Not nice: we are in a class for unit vectors, but the class is actually
// supposed to handle perturbations of unit vectors as well. Therefore
// we normalize here.
T x = a.data_ * b.data_/a.data_.two_norm()/b.data_.two_norm();
const T norm = v.two_norm();
UnitVector result = p;
result.data_ *= cos(norm);
result.data_.axpy(sinc(norm), v);
return result;
}
/** \brief The inverse of the exponential map
*
* \results A vector in the tangent space of p
*/
static EmbeddedTangentVector log(const UnitVector& p, const UnitVector& q)
{
EmbeddedTangentVector result = p.projectOntoTangentSpace(q.data_-p.data_);
if (result.two_norm() > 1e-10)
result *= distance(p,q) / result.two_norm();
return result;
}
// paranoia: if the argument is just eps larger than 1 acos returns NaN
x = min(x,1.0);
/** \brief Length of the great arc connecting the two points */
static T distance(const UnitVector& a, const UnitVector& b) {
return acos(x);
}
using std::acos;
using std::min;
// Not nice: we are in a class for unit vectors, but the class is actually
// supposed to handle perturbations of unit vectors as well. Therefore
// we normalize here.
T x = a.data_ * b.data_/a.data_.two_norm()/b.data_.two_norm();
// paranoia: if the argument is just eps larger than 1 acos returns NaN
x = min(x,1.0);
return acos(x);
}
#if ADOLC_ADOUBLE_H
/** \brief Squared length of the great arc connecting the two points */
static adouble distanceSquared(const UnitVector<double,N>& a, const UnitVector<adouble,N>& b)
{
// Not nice: we are in a class for unit vectors, but the class is actually
// supposed to handle perturbations of unit vectors as well. Therefore
// we normalize here.
adouble x = a.data_ * b.data_ / (a.data_.two_norm()*b.data_.two_norm());
// paranoia: if the argument is just eps larger than 1 acos returns NaN
using std::min;
x = min(x,1.0);
// Special implementation that remains AD-differentiable near x==1
return arcCosSquared(x);
}
/** \brief Squared length of the great arc connecting the two points */
static adouble distanceSquared(const UnitVector<double,N>& a, const UnitVector<adouble,N>& b)
{
// Not nice: we are in a class for unit vectors, but the class is actually
// supposed to handle perturbations of unit vectors as well. Therefore
// we normalize here.
adouble x = a.data_ * b.data_ / (a.data_.two_norm()*b.data_.two_norm());
// paranoia: if the argument is just eps larger than 1 acos returns NaN
using std::fmin;
x = fmin(x,1.0);
// Special implementation that remains AD-differentiable near x==1
return arcCosSquared(x);
}
#endif
/** \brief Compute the gradient of the squared distance function keeping the first argument fixed
/** \brief Compute the gradient of the squared distance function keeping the first argument fixed
Unlike the distance itself the squared distance is differentiable at zero
*/
static EmbeddedTangentVector derivativeOfDistanceSquaredWRTSecondArgument(const UnitVector& a, const UnitVector& b) {
T x = a.data_ * b.data_;
Unlike the distance itself the squared distance is differentiable at zero
*/
static EmbeddedTangentVector derivativeOfDistanceSquaredWRTSecondArgument(const UnitVector& a, const UnitVector& b) {
T x = a.data_ * b.data_;
EmbeddedTangentVector result = a.data_;
EmbeddedTangentVector result = a.data_;
result *= derivativeOfArcCosSquared(x);
result *= derivativeOfArcCosSquared(x);
// Project gradient onto the tangent plane at b in order to obtain the surface gradient
result = b.projectOntoTangentSpace(result);
// Project gradient onto the tangent plane at b in order to obtain the surface gradient
result = b.projectOntoTangentSpace(result);
// Gradient must be a tangent vector at b, in other words, orthogonal to it
using std::abs;
assert(abs(b.data_ * result) < 1e-5);
// Gradient must be a tangent vector at b, in other words, orthogonal to it
using std::abs;
assert(abs(b.data_ * result) < 1e-5);
return result;
}
return result;
}
/** \brief Compute the Hessian of the squared distance function keeping the first argument fixed
/** \brief Compute the Hessian of the squared distance function keeping the first argument fixed
Unlike the distance itself the squared distance is differentiable at zero
*/
static Dune::SymmetricMatrix<T,N> secondDerivativeOfDistanceSquaredWRTSecondArgument(const UnitVector& p, const UnitVector& q) {
Unlike the distance itself the squared distance is differentiable at zero
*/
static SymmetricMatrix<T,N> secondDerivativeOfDistanceSquaredWRTSecondArgument(const UnitVector& p, const UnitVector& q) {
T sp = p.data_ * q.data_;
T sp = p.data_ * q.data_;
Dune::FieldVector<T,N> pProjected = q.projectOntoTangentSpace(p.globalCoordinates());
Dune::FieldVector<T,N> pProjected = q.projectOntoTangentSpace(p.globalCoordinates());
Dune::SymmetricMatrix<T,N> A;
for (int i=0; i<N; i++)
for (int j=0; j<=i; j++)
A(i,j) = pProjected[i]*pProjected[j];
SymmetricMatrix<T,N> A;
for (int i=0; i<N; i++)
for (int j=0; j<=i; j++)
A(i,j) = pProjected[i]*pProjected[j];
A *= secondDerivativeOfArcCosSquared(sp);
A *= secondDerivativeOfArcCosSquared(sp);
// Compute matrix B (see notes)
Dune::SymmetricMatrix<T,N> Pq;
for (int i=0; i<N; i++)
for (int j=0; j<=i; j++)
Pq(i,j) = (i==j) - q.data_[i]*q.data_[j];
// Compute matrix B (see notes)
SymmetricMatrix<T,N> Pq;
for (int i=0; i<N; i++)
for (int j=0; j<=i; j++)
Pq(i,j) = (i==j) - q.data_[i]*q.data_[j];
// Bring it all together
A.axpy(-1*derivativeOfArcCosSquared(sp)*sp, Pq);
// Bring it all together
A.axpy(-1*derivativeOfArcCosSquared(sp)*sp, Pq);
return A;
}
return A;
}
/** \brief Compute the mixed second derivate \partial d^2 / \partial da db
/** \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<T,N,N> secondDerivativeOfDistanceSquaredWRTFirstAndSecondArgument(const UnitVector& a, const UnitVector& b) {
T sp = a.data_ * b.data_;
// Compute vector A (see notes)
Dune::FieldMatrix<T,1,N> row;
row[0] = b.projectOntoTangentSpace(a.globalCoordinates());
Dune::FieldVector<T,N> tmp = a.projectOntoTangentSpace(b.globalCoordinates());
Dune::FieldMatrix<T,N,1> column;
for (int i=0; i<N; i++) // turn row vector into column vector
column[i] = tmp[i];
Dune::FieldMatrix<T,N,N> A;
// A = row * column
Dune::FMatrixHelp::multMatrix(column,row,A);
A *= secondDerivativeOfArcCosSquared(sp);
// Compute matrix B (see notes)
Dune::FieldMatrix<T,N,N> Pp, Pq;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++) {
Pp[i][j] = (i==j) - a.data_[i]*a.data_[j];
Pq[i][j] = (i==j) - b.data_[i]*b.data_[j];
}
Unlike the distance itself the squared distance is differentiable at zero
*/
static Dune::FieldMatrix<T,N,N> secondDerivativeOfDistanceSquaredWRTFirstAndSecondArgument(const UnitVector& a, const UnitVector& b) {
Dune::FieldMatrix<T,N,N> B;
Dune::FMatrixHelp::multMatrix(Pp,Pq,B);
T sp = a.data_ * b.data_;
// Bring it all together
A.axpy(derivativeOfArcCosSquared(sp), B);
// Compute vector A (see notes)
Dune::FieldMatrix<T,1,N> row;
row[0] = b.projectOntoTangentSpace(a.globalCoordinates());
return A;
}
Dune::FieldVector<T,N> tmp = a.projectOntoTangentSpace(b.globalCoordinates());
Dune::FieldMatrix<T,N,1> column;
for (int i=0; i<N; i++) // turn row vector into column vector
column[i] = tmp[i];
Dune::FieldMatrix<T,N,N> A;
// A = row * column
Dune::FMatrixHelp::multMatrix(column,row,A);
A *= secondDerivativeOfArcCosSquared(sp);
/** \brief Compute the third derivative \partial d^3 / \partial dq^3
// Compute matrix B (see notes)
Dune::FieldMatrix<T,N,N> Pp, Pq;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++) {
Pp[i][j] = (i==j) - a.data_[i]*a.data_[j];
Pq[i][j] = (i==j) - b.data_[i]*b.data_[j];
}
Unlike the distance itself the squared distance is differentiable at zero
*/
static Tensor3<T,N,N,N> thirdDerivativeOfDistanceSquaredWRTSecondArgument(const UnitVector& p, const UnitVector& q) {
Dune::FieldMatrix<T,N,N> B;
Dune::FMatrixHelp::multMatrix(Pp,Pq,B);
Tensor3<T,N,N,N> result;
// Bring it all together
A.axpy(derivativeOfArcCosSquared(sp), B);
T sp = p.data_ * q.data_;
return A;
}
// The projection matrix onto the tangent space at p and q
Dune::FieldMatrix<T,N,N> Pq;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
Pq[i][j] = (i==j) - q.globalCoordinates()[i]*q.globalCoordinates()[j];
Dune::FieldVector<T,N> pProjected = q.projectOntoTangentSpace(p.globalCoordinates());
/** \brief Compute the third derivative \partial d^3 / \partial dq^3
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
for (int k=0; k<N; k++) {
Unlike the distance itself the squared distance is differentiable at zero
*/
static Tensor3<T,N,N,N> thirdDerivativeOfDistanceSquaredWRTSecondArgument(const UnitVector& p, const UnitVector& q) {
result[i][j][k] = thirdDerivativeOfArcCosSquared(sp) * pProjected[i] * pProjected[j] * pProjected[k]
- secondDerivativeOfArcCosSquared(sp) * ((i==j)*sp + p.globalCoordinates()[i]*q.globalCoordinates()[j])*pProjected[k]
- secondDerivativeOfArcCosSquared(sp) * ((i==k)*sp + p.globalCoordinates()[i]*q.globalCoordinates()[k])*pProjected[j]
- secondDerivativeOfArcCosSquared(sp) * pProjected[i] * Pq[j][k] * sp
+ derivativeOfArcCosSquared(sp) * ((i==j)*q.globalCoordinates()[k] + (i==k)*q.globalCoordinates()[j]) * sp
- derivativeOfArcCosSquared(sp) * p.globalCoordinates()[i] * Pq[j][k];
}
Tensor3<T,N,N,N> result;
result = Pq * result;
T sp = p.data_ * q.data_;
return result;
}
// The projection matrix onto the tangent space at p and q
Dune::FieldMatrix<T,N,N> Pq;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
Pq[i][j] = (i==j) - q.globalCoordinates()[i]*q.globalCoordinates()[j];
/** \brief Compute the mixed third derivative \partial d^3 / \partial da db^2
Dune::FieldVector<T,N> pProjected = q.projectOntoTangentSpace(p.globalCoordinates());
Unlike the distance itself the squared distance is differentiable at zero
*/
static Tensor3<T,N,N,N> thirdDerivativeOfDistanceSquaredWRTFirst1AndSecond2Argument(const UnitVector& p, const UnitVector& q) {
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
for (int k=0; k<N; k++) {
Tensor3<T,N,N,N> result;
result[i][j][k] = thirdDerivativeOfArcCosSquared(sp) * pProjected[i] * pProjected[j] * pProjected[k]
- secondDerivativeOfArcCosSquared(sp) * ((i==j)*sp + p.globalCoordinates()[i]*q.globalCoordinates()[j])*pProjected[k]
- secondDerivativeOfArcCosSquared(sp) * ((i==k)*sp + p.globalCoordinates()[i]*q.globalCoordinates()[k])*pProjected[j]
- secondDerivativeOfArcCosSquared(sp) * pProjected[i] * Pq[j][k] * sp
+ derivativeOfArcCosSquared(sp) * ((i==j)*q.globalCoordinates()[k] + (i==k)*q.globalCoordinates()[j]) * sp
- derivativeOfArcCosSquared(sp) * p.globalCoordinates()[i] * Pq[j][k];
}
T sp = p.data_ * q.data_;
result = Pq * result;
// The projection matrix onto the tangent space at p and q
Dune::FieldMatrix<T,N,N> Pp, Pq;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++) {
Pp[i][j] = (i==j) - p.globalCoordinates()[i]*p.globalCoordinates()[j];
Pq[i][j] = (i==j) - q.globalCoordinates()[i]*q.globalCoordinates()[j];
}
return result;
}
Dune::FieldVector<T,N> pProjected = q.projectOntoTangentSpace(p.globalCoordinates());
Dune::FieldVector<T,N> qProjected = p.projectOntoTangentSpace(q.globalCoordinates());
/** \brief Compute the mixed third derivative \partial d^3 / \partial da db^2
Tensor3<T,N,N,N> derivativeOfPqOTimesPq;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
for (int k=0; k<N; k++) {
derivativeOfPqOTimesPq[i][j][k] = 0;
for (int l=0; l<N; l++)
derivativeOfPqOTimesPq[i][j][k] += Pp[i][l] * (Pq[j][l]*pProjected[k] + pProjected[j]*Pq[k][l]);
Unlike the distance itself the squared distance is differentiable at zero
*/
static Tensor3<T,N,N,N> thirdDerivativeOfDistanceSquaredWRTFirst1AndSecond2Argument(const UnitVector& p, const UnitVector& q) {
Tensor3<T,N,N,N> result;
T sp = p.data_ * q.data_;
// The projection matrix onto the tangent space at p and q
Dune::FieldMatrix<T,N,N> Pp, Pq;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++) {
Pp[i][j] = (i==j) - p.globalCoordinates()[i]*p.globalCoordinates()[j];
Pq[i][j] = (i==j) - q.globalCoordinates()[i]*q.globalCoordinates()[j];
}
result = thirdDerivativeOfArcCosSquared(sp) * Tensor3<T,N,N,N>::product(qProjected,pProjected,pProjected)
+ secondDerivativeOfArcCosSquared(sp) * derivativeOfPqOTimesPq
- secondDerivativeOfArcCosSquared(sp) * sp * Tensor3<T,N,N,N>::product(qProjected,Pq)
- derivativeOfArcCosSquared(sp) * Tensor3<T,N,N,N>::product(qProjected,Pq);
Dune::FieldVector<T,N> pProjected = q.projectOntoTangentSpace(p.globalCoordinates());
Dune::FieldVector<T,N> qProjected = p.projectOntoTangentSpace(q.globalCoordinates());
return result;
}
Tensor3<T,N,N,N> derivativeOfPqOTimesPq;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
for (int k=0; k<N; k++) {
derivativeOfPqOTimesPq[i][j][k] = 0;
for (int l=0; l<N; l++)
derivativeOfPqOTimesPq[i][j][k] += Pp[i][l] * (Pq[j][l]*pProjected[k] + pProjected[j]*Pq[k][l]);
}
result = thirdDerivativeOfArcCosSquared(sp) * Tensor3<T,N,N,N>::product(qProjected,pProjected,pProjected)
+ secondDerivativeOfArcCosSquared(sp) * derivativeOfPqOTimesPq
- secondDerivativeOfArcCosSquared(sp) * sp * Tensor3<T,N,N,N>::product(qProjected,Pq)
- derivativeOfArcCosSquared(sp) * Tensor3<T,N,N,N>::product(qProjected,Pq);
/** \brief Project tangent vector of R^n onto the tangent space */
EmbeddedTangentVector projectOntoTangentSpace(const EmbeddedTangentVector& v) const {
EmbeddedTangentVector result = v;
result.axpy(-1*(data_*result), data_);
return result;
}
return result;
}
/** \brief Project tangent vector of R^n onto the normal space space */
EmbeddedTangentVector projectOntoNormalSpace(const EmbeddedTangentVector& v) const {
return (v*data_) * data_;
}
/** \brief The Weingarten map
*
* The Weingarten map computes the derivative of a normal vector v with respect to a tangent vector z.
*/
EmbeddedTangentVector weingarten(const EmbeddedTangentVector& z, const EmbeddedTangentVector& v) const {
return -(v*data_) * z;
}
/** \brief Project tangent vector of R^n onto the tangent space */
EmbeddedTangentVector projectOntoTangentSpace(const EmbeddedTangentVector& v) const {
EmbeddedTangentVector result = v;
result.axpy(-1*(data_*result), data_);
return result;
}
static UnitVector<T,N> projectOnto(const CoordinateType& p)
{
UnitVector<T,N> result(p);
result.data_ /= result.data_.two_norm();
return result;
}
/** \brief Project tangent vector of R^n onto the normal space space */
EmbeddedTangentVector projectOntoNormalSpace(const EmbeddedTangentVector& v) const {
return (v*data_) * data_;
}
static DerivativeOfProjection derivativeOfProjection(const Dune::FieldVector<T,N>& p)
{
auto normSquared = p.two_norm2();
auto norm = std::sqrt(normSquared);
/** \brief The Weingarten map
*
* The Weingarten map computes the derivative of a normal vector v with respect to a tangent vector z.
*/
EmbeddedTangentVector weingarten(const EmbeddedTangentVector& z, const EmbeddedTangentVector& v) const {
return -(v*data_) * z;
}
Dune::FieldMatrix<T,N,N> result;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
result[i][j] = ( (i==j) - p[i]*p[j] / normSquared ) / norm;
return result;
}
static UnitVector<T,N> projectOnto(const CoordinateType& p)
{
UnitVector<T,N> result(p);
result.data_ /= result.data_.two_norm();
return result;
}
/** \brief The global coordinates, if you really want them */
const CoordinateType& globalCoordinates() const {
return data_;
}
static DerivativeOfProjection derivativeOfProjection(const Dune::FieldVector<T,N>& p)
{
auto normSquared = p.two_norm2();
auto norm = std::sqrt(normSquared);
/** \brief Compute an orthonormal basis of the tangent space of S^n.
Dune::FieldMatrix<T,N,N> result;
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
result[i][j] = ( (i==j) - p[i]*p[j] / normSquared ) / norm;
return result;
}
This basis is of course not globally continuous.
*/
Dune::FieldMatrix<T,N-1,N> orthonormalFrame() const {
/** \brief The global coordinates, if you really want them */
const CoordinateType& globalCoordinates() const {
return data_;
}
Dune::FieldMatrix<T,N-1,N> result;
/** \brief Compute an orthonormal basis of the tangent space of S^n.
// Coordinates of the stereographic projection
Dune::FieldVector<T,N-1> X;
This basis is of course not globally continuous.
*/
Dune::FieldMatrix<T,N-1,N> orthonormalFrame() const {
if (data_[N-1] <= 0) {
Dune::FieldMatrix<T,N-1,N> result;
// Stereographic projection from the north pole onto R^{N-1}
for (size_t i=0; i<N-1; i++)
X[i] = data_[i] / (1-data_[N-1]);
// Coordinates of the stereographic projection
Dune::FieldVector<T,N-1> X;
} else {
if (data_[N-1] <= 0) {
// Stereographic projection from the south pole onto R^{N-1}
for (size_t i=0; i<N-1; i++)
X[i] = data_[i] / (1+data_[N-1]);
// Stereographic projection from the north pole onto R^{N-1}
for (size_t i=0; i<N-1; i++)
X[i] = data_[i] / (1-data_[N-1]);
}
} else {
T RSquared = X.two_norm2();
// Stereographic projection from the south pole onto R^{N-1}
for (size_t i=0; i<N-1; i++)
X[i] = data_[i] / (1+data_[N-1]);
for (size_t i=0; i<N-1; i++)
for (size_t j=0; j<N-1; j++)
// Note: the matrix is the transpose of the one in the paper
result[j][i] = 2*(i==j)*(1+RSquared) - 4*X[i]*X[j];
}
for (size_t j=0; j<N-1; j++)
result[j][N-1] = 4*X[j];
T RSquared = X.two_norm2();
for (size_t i=0; i<N-1; i++)
for (size_t j=0; j<N-1; j++)
// Note: the matrix is the transpose of the one in the paper
result[j][i] = 2*(i==j)*(1+RSquared) - 4*X[i]*X[j];
// Upper hemisphere: adapt formulas so it is the stereographic projection from the south pole
if (data_[N-1] > 0)
for (size_t j=0; j<N-1; j++)
result[j][N-1] *= -1;
result[j][N-1] = 4*X[j];
// normalize the rows to make the orthogonal basis orthonormal
for (size_t i=0; i<N-1; i++)
result[i] /= result[i].two_norm();
// Upper hemisphere: adapt formulas so it is the stereographic projection from the south pole
if (data_[N-1] > 0)
for (size_t j=0; j<N-1; j++)
result[j][N-1] *= -1;
return result;
}
// normalize the rows to make the orthogonal basis orthonormal
for (size_t i=0; i<N-1; i++)
result[i] /= result[i].two_norm();
/** \brief Write unit vector object to output stream */
friend std::ostream& operator<< (std::ostream& s, const UnitVector& unitVector)
{
return s << unitVector.data_;
}
return result;
}
/** \brief Write unit vector object to output stream */
friend std::ostream& operator<< (std::ostream& s, const UnitVector& unitVector)
{
return s << unitVector.data_;
}
private:
private:
Dune::FieldVector<T,N> data_;
};
Dune::FieldVector<T,N> data_;
};
} // namespace Dune::GFE
#endif
dune/gfe/svd.hh
View file @ 48b9358e
......@@ -12,253 +12,258 @@
// int SIGN(const T& a, const T& b) {return 1;}
#define SIGN(a,b)((b)>=0.0 ? fabs(a) : -fabs(a))
/** Computes (a^2 + b^2 )1/2 without destructive underflow or overflow. */
template <class T>
T pythag(T a, T b)
namespace Dune::GFE
{
T absa=std::fabs(a);
T absb=std::fabs(b);
if (absa > absb)
return absa*std::sqrt(T(1.0)+(absb/absa)*(absb/absa));
else
return (absb == 0.0) ? T(0.0) : absb*sqrt(T(1.0)+(absa/absb)*(absa/absb));
}
/** Computes (a^2 + b^2 )1/2 without destructive underflow or overflow. */
template <class T>
T pythag(T a, T b)
{
T absa=std::fabs(a);
T absb=std::fabs(b);
if (absa > absb)
return absa*std::sqrt(T(1.0)+(absb/absa)*(absb/absa));
else
return (absb == 0.0) ? T(0.0) : absb*sqrt(T(1.0)+(absa/absb)*(absa/absb));
}
/**
Given a matrix a[1..m][1..n], this routine computes its singular value decomposition, A =
U W V^T . The matrix U replaces a on output. The diagonal matrix of singular values W is out-
put as a vector w[1..n]. The matrix V (not the transpose V T ) is output as v[1..n][1..n].
*/
template <class T, int m, int n>
void svdcmp(Dune::FieldMatrix<T,m,n>& a_, Dune::FieldVector<T,n>& w, Dune::FieldMatrix<T,n,n>& v_)
{
Dune::FieldMatrix<T,m+1,n+1> a(0);
Dune::FieldMatrix<T,n+1,n+1> v(0);
for (int i=0; i<m; i++)
for (int j=0; j<n; j++)
a[i+1][j+1] = a_[i][j];
/**
Given a matrix a[1..m][1..n], this routine computes its singular value decomposition, A =
U W V^T . The matrix U replaces a on output. The diagonal matrix of singular values W is out-
put as a vector w[1..n]. The matrix V (not the transpose V T ) is output as v[1..n][1..n].
*/
template <class T, int m, int n>
void svdcmp(Dune::FieldMatrix<T,m,n>& a_, Dune::FieldVector<T,n>& w, Dune::FieldMatrix<T,n,n>& v_)
{
Dune::FieldMatrix<T,m+1,n+1> a(0);
Dune::FieldMatrix<T,n+1,n+1> v(0);
int flag,i,its,j,jj,k,l,nm;
T anorm,c,f,g,h,s,scale,x,y,z;
T rv1[n+1]; // 1 too large to accommodate fortran numbering
for (int i=0; i<m; i++)
for (int j=0; j<n; j++)
a[i+1][j+1] = a_[i][j];
//Householder reduction to bidiagonal form.
g=scale=anorm=0.0;
int flag,i,its,j,jj,k,l,nm;
T anorm,c,f,g,h,s,scale,x,y,z;
T rv1[n+1]; // 1 too large to accommodate fortran numbering
for (i=1; i<=n; i++) {
//Householder reduction to bidiagonal form.
g=scale=anorm=0.0;
l=i+1;
rv1[i]=scale*g;
g=s=scale=0.0;
for (i=1; i<=n; i++) {
if (i <= m) {
for (k=i; k<=m; k++)
scale += std::abs(a[k][i]);
if (scale!=0) {
for (k=i; k<=m; k++) {
a[k][i] /= scale;
s += a[k][i]*a[k][i];
}
f=a[i][i];
g = -SIGN(std::sqrt(s),f);
h=f*g-s;
a[i][i]=f-g;
for (j=l; j<=n; j++) {
for (s=0.0,k=i; k<=m; k++)
s += a[k][i]*a[k][j];
f=s/h;
l=i+1;
rv1[i]=scale*g;
g=s=scale=0.0;
if (i <= m) {
for (k=i; k<=m; k++)
scale += std::abs(a[k][i]);
if (scale!=0) {
for (k=i; k<=m; k++) {
a[k][i] /= scale;
s += a[k][i]*a[k][i];
}
f=a[i][i];
g = -SIGN(std::sqrt(s),f);
h=f*g-s;
a[i][i]=f-g;
for (j=l; j<=n; j++) {
for (s=0.0,k=i; k<=m; k++)
s += a[k][i]*a[k][j];
f=s/h;
for (k=i; k<=m; k++)
a[k][j] += f*a[k][i];
}
for (k=i; k<=m; k++)
a[k][j] += f*a[k][i];
a[k][i] *= scale;
}
for (k=i; k<=m; k++)
a[k][i] *= scale;
}
}
w[i-1]=scale *g;
g=s=scale=0.0;
w[i-1]=scale *g;
g=s=scale=0.0;
if (i <= m && i != n) {
if (i <= m && i != n) {
for (k=l; k<=n; k++) scale += fabs(a[i][k]);
if (scale!=0) {
for (k=l; k<=n; k++) scale += fabs(a[i][k]);
if (scale!=0) {
for (k=l; k<=n; k++) {
a[i][k] /= scale;
s += a[i][k]*a[i][k];
}
f=a[i][l];
g = -SIGN(std::sqrt(s),f);
h=f*g-s;
a[i][l]=f-g;
for (k=l; k<=n; k++) rv1[k]=a[i][k]/h;
for (j=l; j<=m; j++) {
for (s=0.0,k=l; k<=n; k++)
s += a[j][k]*a[i][k];
for (k=l; k<=n; k++) {
a[i][k] /= scale;
s += a[i][k]*a[i][k];
}
f=a[i][l];
g = -SIGN(std::sqrt(s),f);
h=f*g-s;
a[i][l]=f-g;
for (k=l; k<=n; k++) rv1[k]=a[i][k]/h;
for (j=l; j<=m; j++) {
for (s=0.0,k=l; k<=n; k++)
s += a[j][k]*a[i][k];
for (k=l; k<=n; k++)
a[j][k] += s*rv1[k];
}
for (k=l; k<=n; k++)
a[j][k] += s*rv1[k];
a[i][k] *= scale;
}
for (k=l; k<=n; k++)
a[i][k] *= scale;
}
}
anorm = std::max(anorm,(std::abs(w[i-1])+std::abs(rv1[i])));
anorm = std::max(anorm,(std::abs(w[i-1])+std::abs(rv1[i])));
}
}
// Accumulation of right-hand transformations.
for (i=n; i>=1; i--) {
if (i < n) {
if (g!=0) {
// Double division to avoid possible underflow.
for (j=l; j<=n; j++)
v[j][i]=(a[i][j]/a[i][l])/g;
for (j=l; j<=n; j++) {
for (s=0.0,k=l; k<=n; k++) s += a[i][k]*v[k][j];
for (k=l; k<=n; k++) v[k][j] += s*v[k][i];
// Accumulation of right-hand transformations.
for (i=n; i>=1; i--) {
if (i < n) {
if (g!=0) {
// Double division to avoid possible underflow.
for (j=l; j<=n; j++)
v[j][i]=(a[i][j]/a[i][l])/g;
for (j=l; j<=n; j++) {
for (s=0.0,k=l; k<=n; k++) s += a[i][k]*v[k][j];
for (k=l; k<=n; k++) v[k][j] += s*v[k][i];
}
}
for (j=l; j<=n; j++) v[i][j]=v[j][i]=0.0;
}
for (j=l; j<=n; j++) v[i][j]=v[j][i]=0.0;
v[i][i]=1.0;
g=rv1[i];
l=i;
}
v[i][i]=1.0;
g=rv1[i];
l=i;
}
// Accumulation of left-hand transformations.
//for (i=IMIN(m,n);i>=1;i--) {
for (i=std::min(m,n); i>=1; i--) {
l=i+1;
g=w[i-1];
for (j=l; j<=n; j++) a[i][j]=0.0;
if (g!=0) {
g=1.0/g;
for (j=l; j<=n; j++) {
for (s=0.0,k=l; k<=m; k++) s += a[k][i]*a[k][j];
f=(s/a[i][i])*g;
for (k=i; k<=m; k++) a[k][j] += f*a[k][i];
}
for (j=i; j<=m; j++) a[j][i] *= g;
} else for (j=i; j<=m; j++) a[j][i]=0.0;
++a[i][i];
}
// Accumulation of left-hand transformations.
//for (i=IMIN(m,n);i>=1;i--) {
for (i=std::min(m,n); i>=1; i--) {
l=i+1;
g=w[i-1];
for (j=l; j<=n; j++) a[i][j]=0.0;
if (g!=0) {
g=1.0/g;
for (j=l; j<=n; j++) {
for (s=0.0,k=l; k<=m; k++) s += a[k][i]*a[k][j];
f=(s/a[i][i])*g;
for (k=i; k<=m; k++) a[k][j] += f*a[k][i];
}
for (j=i; j<=m; j++) a[j][i] *= g;
} else for (j=i; j<=m; j++) a[j][i]=0.0;
++a[i][i];
}
// Diagonalization of the bidiagonal form: Loop over
//singular values, and over allowed iterations.
for (k=n; k>=1; k--) {
// Diagonalization of the bidiagonal form: Loop over
//singular values, and over allowed iterations.
for (k=n; k>=1; k--) {
for (its=1; its<=30; its++) {
flag=1;
// Test for splitting.
for (l=k; l>=1; l--) {
// Note that rv1[1] is always zero.
nm=l-1;
if ((T)(fabs(rv1[l])+anorm) == anorm) {
flag=0;
break;
for (its=1; its<=30; its++) {
flag=1;
// Test for splitting.
for (l=k; l>=1; l--) {
// Note that rv1[1] is always zero.
nm=l-1;
if ((T)(fabs(rv1[l])+anorm) == anorm) {
flag=0;
break;
}
if ((T)(fabs(w[nm-1])+anorm) == anorm) break;
}
if ((T)(fabs(w[nm-1])+anorm) == anorm) break;
}
if (flag) {
// Cancellation of rv1[l], if l > 1.
c=0.0;
s=1.0;
for (i=l; i<=k; i++) {
if (flag) {
// Cancellation of rv1[l], if l > 1.
c=0.0;
s=1.0;
for (i=l; i<=k; i++) {
f=s*rv1[i];
rv1[i]=c*rv1[i];
if ((T)(fabs(f)+anorm) == anorm) break;
g=w[i-1];
h=pythag(f,g);
w[i-1]=h;
h=1.0/h;
c=g*h;
s = -f*h;
for (j=1; j<=m; j++) {
y=a[j][nm];
z=a[j][i];
a[j][nm]=y*c+z*s;
a[j][i]=z*c-y*s;
f=s*rv1[i];
rv1[i]=c*rv1[i];
if ((T)(fabs(f)+anorm) == anorm) break;
g=w[i-1];
h=pythag(f,g);
w[i-1]=h;
h=1.0/h;
c=g*h;
s = -f*h;
for (j=1; j<=m; j++) {
y=a[j][nm];
z=a[j][i];
a[j][nm]=y*c+z*s;
a[j][i]=z*c-y*s;
}
}
}
}
z=w[k-1];
//Convergence.
if (l == k) {
// Singular value is made nonnegative.
if (z < 0.0) {
w[k-1] = -z;
for (j=1; j<=n; j++) v[j][k] = -v[j][k];
}
break;
}
if (its == 30)
std::cerr << "no convergence in 30 svdcmp iterations" << std::endl;
// Shift from bottom 2-by-2 minor.
x=w[l-1];
nm=k-1;
y=w[nm-1];
g=rv1[nm];
h=rv1[k];
f=((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y);
g=pythag(f,T(1.0));
f=((x-z)*(x+z)+h*((y/(f+SIGN(g,f)))-h))/x;
// Next QR transformation:
c=s=1.0;
for (j=l; j<=nm; j++) {
i=j+1;
g=rv1[i];
y=w[i-1];
h=s*g;
g=c*g;
z=pythag(f,h);
rv1[j]=z;
c=f/z;
s=h/z;
f=x*c+g*s;
g = g*c-x*s;
h=y*s;
y *= c;
for (jj=1; jj<=n; jj++) {
x=v[jj][j];
z=v[jj][i];
v[jj][j]=x*c+z*s;
v[jj][i]=z*c-x*s;
}
z=pythag(f,h);
// Rotation can be arbitrary if z = 0.
w[j-1]=z;
if (z!=0) {
z=1.0/z;
c=f*z;
s=h*z;
z=w[k-1];
//Convergence.
if (l == k) {
// Singular value is made nonnegative.
if (z < 0.0) {
w[k-1] = -z;
for (j=1; j<=n; j++) v[j][k] = -v[j][k];
}
break;
}
f=c*g+s*y;
x=c*y-s*g;
if (its == 30)
std::cerr << "no convergence in 30 svdcmp iterations" << std::endl;
// Shift from bottom 2-by-2 minor.
x=w[l-1];
nm=k-1;
y=w[nm-1];
g=rv1[nm];
h=rv1[k];
f=((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y);
g=pythag(f,T(1.0));
f=((x-z)*(x+z)+h*((y/(f+SIGN(g,f)))-h))/x;
// Next QR transformation:
c=s=1.0;
for (j=l; j<=nm; j++) {
i=j+1;
g=rv1[i];
y=w[i-1];
h=s*g;
g=c*g;
z=pythag(f,h);
rv1[j]=z;
c=f/z;
s=h/z;
f=x*c+g*s;
g = g*c-x*s;
h=y*s;
y *= c;
for (jj=1; jj<=n; jj++) {
x=v[jj][j];
z=v[jj][i];
v[jj][j]=x*c+z*s;
v[jj][i]=z*c-x*s;
}
z=pythag(f,h);
// Rotation can be arbitrary if z = 0.
w[j-1]=z;
if (z!=0) {
z=1.0/z;
c=f*z;
s=h*z;
}
f=c*g+s*y;
x=c*y-s*g;
for (jj=1; jj<=m; jj++) {
y=a[jj][j];
z=a[jj][i];
a[jj][j]=y*c+z*s;
a[jj][i]=z*c-y*s;
for (jj=1; jj<=m; jj++) {
y=a[jj][j];
z=a[jj][i];
a[jj][j]=y*c+z*s;
a[jj][i]=z*c-y*s;
}
}
rv1[l]=0.0;
rv1[k]=f;
w[k-1]=x;
}
rv1[l]=0.0;
rv1[k]=f;
w[k-1]=x;
}
}
for (int i=0; i<m; i++)
for (int j=0; j<n; j++)
a_[i][j] = a[i+1][j+1];
for (int i=0; i<m; i++)
for (int j=0; j<n; j++)
a_[i][j] = a[i+1][j+1];
for (int i=0; i<n; i++)
for (int j=0; j<n; j++)
v_[i][j] = v[i+1][j+1];
}
for (int i=0; i<n; i++)
for (int j=0; j<n; j++)
v_[i][j] = v[i+1][j+1];
}
} // namespace Dune::GFE
#endif
dune/gfe/symmetricmatrix.hh
View file @ 48b9358e
......@@ -4,7 +4,8 @@
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
namespace Dune {
namespace Dune::GFE
{
/** \brief A class implementing a symmetric matrix with compile-time size
*
......@@ -93,5 +94,6 @@ namespace Dune {
Dune::FieldVector<T,N*(N+1)/2> data_;
};
}
} // namespace Dune::GFE
#endif
dune/gfe/targetspacertrsolver.cc
View file @ 48b9358e
......@@ -9,7 +9,7 @@
#include <dune/gfe/gramschmidtsolver.hh>
template <class TargetSpace>
void TargetSpaceRiemannianTRSolver<TargetSpace>::
void Dune::GFE::TargetSpaceRiemannianTRSolver<TargetSpace>::
setup(const AverageDistanceAssembler<TargetSpace>* assembler,
const TargetSpace& x,
double tolerance,
......@@ -25,7 +25,7 @@ setup(const AverageDistanceAssembler<TargetSpace>* assembler,
template <class TargetSpace>
void TargetSpaceRiemannianTRSolver<TargetSpace>::solve()
void Dune::GFE::TargetSpaceRiemannianTRSolver<TargetSpace>::solve()
{
assert(minNumberOfIterations_ > 0);
......
dune/gfe/targetspacertrsolver.hh
View file @ 48b9358e
......@@ -5,62 +5,68 @@
#include <dune/gfe/symmetricmatrix.hh>
/** \brief Riemannian trust-region solver for geodesic finite-element problems
\tparam TargetSpace The manifold that our functions take values in
*/
template <class TargetSpace>
class TargetSpaceRiemannianTRSolver
: public NumProc
namespace Dune::GFE
{
const static int blocksize = TargetSpace::TangentVector::dimension;
const static int embeddedBlocksize = TargetSpace::EmbeddedTangentVector::dimension;
// Centralize the field type here
typedef typename TargetSpace::ctype field_type;
/** \brief Riemannian trust-region solver for geodesic finite-element problems
\tparam TargetSpace The manifold that our functions take values in
*/
template <class TargetSpace>
class TargetSpaceRiemannianTRSolver
: public NumProc
{
const static int blocksize = TargetSpace::TangentVector::dimension;
const static int embeddedBlocksize = TargetSpace::EmbeddedTangentVector::dimension;
typedef Dune::SymmetricMatrix<field_type, embeddedBlocksize> MatrixType;
typedef Dune::FieldVector<field_type, embeddedBlocksize> CorrectionType;
// Centralize the field type here
typedef typename TargetSpace::ctype field_type;
public:
typedef SymmetricMatrix<field_type, embeddedBlocksize> MatrixType;
typedef Dune::FieldVector<field_type, embeddedBlocksize> CorrectionType;
/** \brief Set up the solver using a monotone multigrid method as the inner solver */
void setup(const AverageDistanceAssembler<TargetSpace>* assembler,
const TargetSpace& x,
double tolerance,
int maxNewtonSteps);
public:
void solve();
/** \brief Set up the solver using a monotone multigrid method as the inner solver */
void setup(const AverageDistanceAssembler<TargetSpace>* assembler,
const TargetSpace& x,
double tolerance,
int maxNewtonSteps);
void setInitialSolution(const TargetSpace& x) {
x_ = x;
}
void solve();
TargetSpace getSol() const {return x_;}
void setInitialSolution(const TargetSpace& x) {
x_ = x;
}
protected:
TargetSpace getSol() const {return x_;}
/** \brief The solution vector */
TargetSpace x_;
protected:
/** \brief Tolerance of the solver */
double tolerance_;
/** \brief The solution vector */
TargetSpace x_;
/** \brief Maximum number of Newton steps */
size_t maxNewtonSteps_;
/** \brief Tolerance of the solver */
double tolerance_;
/** \brief The assembler for the average-distance functional */
const AverageDistanceAssembler<TargetSpace>* assembler_;
/** \brief Maximum number of Newton steps */
size_t maxNewtonSteps_;
/** \brief Specify a minimal number of iterations the Newton solver has to do
*
* This is needed when working with automatic differentiation. While a very low
* number of iterations may be enough to precisely compute the value of a
* geodesic finite element function, a higher number may be needed to make an AD
* system compute a derivative with sufficient precision.
*/
size_t minNumberOfIterations_;
/** \brief The assembler for the average-distance functional */
const AverageDistanceAssembler<TargetSpace>* assembler_;
/** \brief Specify a minimal number of iterations the Newton solver has to do
*
* This is needed when working with automatic differentiation. While a very low
* number of iterations may be enough to precisely compute the value of a
* geodesic finite element function, a higher number may be needed to make an AD
* system compute a derivative with sufficient precision.
*/
size_t minNumberOfIterations_;
};
};
} // namespace Dune::GFE
#include "targetspacertrsolver.cc"
......
dune/gfe/tensor3.hh
View file @ 48b9358e
......@@ -8,189 +8,195 @@
#include <array>
#include <dune/common/fmatrix.hh>
/** \brief A third-rank tensor
*/
template <class T, int N1, int N2, int N3>
class Tensor3
: public std::array<Dune::FieldMatrix<T,N2,N3>,N1>
{
public:
/** \brief Default constructor */
Tensor3() {}
/** \brief Constructor from a scalar */
Tensor3(const T& c)
{
for (int i=0; i<N1; i++)
(*this)[i] = c;
}
T infinity_norm() const
{
static_assert(N1>0, "infinity_norm not implemented for empty tensors");
T norm = (*this)[0].infinity_norm();
for (int i=1; i<N1; i++)
norm = std::max(norm, (*this)[i].infinity_norm());
return norm;
}
T frobenius_norm() const
{
T norm = 0;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
norm += (*this)[i][j][k] * (*this)[i][j][k];
return std::sqrt(norm);
}
/** \brief The squared Frobenius norm, i.e., the sum of squared entries */
T frobenius_norm2() const
{
T norm = 0;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
norm += (*this)[i][j][k] * (*this)[i][j][k];
return norm;
}
Tensor3<T,N1,N2,N3>& axpy(const T& alpha, const Tensor3<T,N1,N2,N3>& other)
{
for (int i=0; i<N1; i++)
(*this)[i].axpy(alpha,other[i]);
return *this;
}
static Tensor3<T,N1,N2,N3> product(const Dune::FieldVector<T,N1>& a, const Dune::FieldVector<T,N2>& b, const Dune::FieldVector<T,N3>& c)
{
Tensor3<T,N1,N2,N3> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
result[i][j][k] = a[i]*b[j]*c[k];
return result;
}
static Tensor3<T,N1,N2,N3> product(const Dune::FieldMatrix<T,N1,N2>& ab, const Dune::FieldVector<T,N3>& c)
{
Tensor3<T,N1,N2,N3> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
result[i][j][k] = ab[i][j]*c[k];
return result;
}
static Tensor3<T,N1,N2,N3> product(const Dune::FieldVector<T,N1>& a, const Dune::FieldMatrix<T,N2,N3>& bc)
{
Tensor3<T,N1,N2,N3> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
result[i][j][k] = a[i]*bc[j][k];
return result;
}
template <int N4>
friend Tensor3<T,N1,N2,N4> operator*(const Tensor3<T,N1,N2,N3>& a, const Dune::FieldMatrix<T,N3,N4>& b)
{
Tensor3<T,N1,N2,N4> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N4; k++) {
result[i][j][k] = 0;
for (int l=0; l<N3; l++)
result[i][j][k] += a[i][j][l]*b[l][k];
}
return result;
}
template <int N4>
friend Tensor3<T,N1,N3,N4> operator*(const Dune::FieldMatrix<T,N1,N2>& a, const Tensor3<T,N2,N3,N4>& b)
{
Tensor3<T,N1,N3,N4> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N3; j++)
for (int k=0; k<N4; k++) {
result[i][j][k] = 0;
for (int l=0; l<N2; l++)
result[i][j][k] += a[i][l]*b[l][j][k];
}
return result;
}
friend Tensor3<T,N1,N2,N3> operator+(const Tensor3<T,N1,N2,N3>& a, const Tensor3<T,N1,N2,N3>& b)
{
Tensor3<T,N1,N2,N3> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
result[i][j][k] = a[i][j][k] + b[i][j][k];
return result;
}
friend Tensor3<T,N1,N2,N3> operator-(const Tensor3<T,N1,N2,N3>& a, const Tensor3<T,N1,N2,N3>& b)
{
Tensor3<T,N1,N2,N3> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
result[i][j][k] = a[i][j][k] - b[i][j][k];
return result;
}
namespace Dune::GFE
{
friend Tensor3<T,N1,N2,N3> operator*(const T& scalar, const Tensor3<T,N1,N2,N3>& tensor)
/** \brief A third-rank tensor
*/
template <class T, int N1, int N2, int N3>
class Tensor3
: public std::array<Dune::FieldMatrix<T,N2,N3>,N1>
{
Tensor3<T,N1,N2,N3> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
result[i][j][k] = scalar * tensor[i][j][k];
return result;
}
Tensor3<T,N1,N2,N3>& operator*=(const T& scalar)
public:
/** \brief Default constructor */
Tensor3() {}
/** \brief Constructor from a scalar */
Tensor3(const T& c)
{
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
(*this)[i][j][k] = c;
}
T infinity_norm() const
{
static_assert(N1>0, "infinity_norm not implemented for empty tensors");
T norm = (*this)[0].infinity_norm();
for (int i=1; i<N1; i++)
norm = std::max(norm, (*this)[i].infinity_norm());
return norm;
}
T frobenius_norm() const
{
T norm = 0;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
norm += (*this)[i][j][k] * (*this)[i][j][k];
return std::sqrt(norm);
}
/** \brief The squared Frobenius norm, i.e., the sum of squared entries */
T frobenius_norm2() const
{
T norm = 0;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
norm += (*this)[i][j][k] * (*this)[i][j][k];
return norm;
}
Tensor3<T,N1,N2,N3>& axpy(const T& alpha, const Tensor3<T,N1,N2,N3>& other)
{
for (int i=0; i<N1; i++)
(*this)[i].axpy(alpha,other[i]);
return *this;
}
static Tensor3<T,N1,N2,N3> product(const Dune::FieldVector<T,N1>& a, const Dune::FieldVector<T,N2>& b, const Dune::FieldVector<T,N3>& c)
{
Tensor3<T,N1,N2,N3> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
result[i][j][k] = a[i]*b[j]*c[k];
return result;
}
static Tensor3<T,N1,N2,N3> product(const Dune::FieldMatrix<T,N1,N2>& ab, const Dune::FieldVector<T,N3>& c)
{
Tensor3<T,N1,N2,N3> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
result[i][j][k] = ab[i][j]*c[k];
return result;
}
static Tensor3<T,N1,N2,N3> product(const Dune::FieldVector<T,N1>& a, const Dune::FieldMatrix<T,N2,N3>& bc)
{
Tensor3<T,N1,N2,N3> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
result[i][j][k] = a[i]*bc[j][k];
return result;
}
template <int N4>
friend Tensor3<T,N1,N2,N4> operator*(const Tensor3<T,N1,N2,N3>& a, const Dune::FieldMatrix<T,N3,N4>& b)
{
Tensor3<T,N1,N2,N4> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N4; k++) {
result[i][j][k] = 0;
for (int l=0; l<N3; l++)
result[i][j][k] += a[i][j][l]*b[l][k];
}
return result;
}
template <int N4>
friend Tensor3<T,N1,N3,N4> operator*(const Dune::FieldMatrix<T,N1,N2>& a, const Tensor3<T,N2,N3,N4>& b)
{
Tensor3<T,N1,N3,N4> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N3; j++)
for (int k=0; k<N4; k++) {
result[i][j][k] = 0;
for (int l=0; l<N2; l++)
result[i][j][k] += a[i][l]*b[l][j][k];
}
return result;
}
friend Tensor3<T,N1,N2,N3> operator+(const Tensor3<T,N1,N2,N3>& a, const Tensor3<T,N1,N2,N3>& b)
{
Tensor3<T,N1,N2,N3> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
result[i][j][k] = a[i][j][k] + b[i][j][k];
return result;
}
friend Tensor3<T,N1,N2,N3> operator-(const Tensor3<T,N1,N2,N3>& a, const Tensor3<T,N1,N2,N3>& b)
{
Tensor3<T,N1,N2,N3> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
result[i][j][k] = a[i][j][k] - b[i][j][k];
return result;
}
friend Tensor3<T,N1,N2,N3> operator*(const T& scalar, const Tensor3<T,N1,N2,N3>& tensor)
{
Tensor3<T,N1,N2,N3> result;
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
result[i][j][k] = scalar * tensor[i][j][k];
return result;
}
Tensor3<T,N1,N2,N3>& operator*=(const T& scalar)
{
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
(*this)[i][j][k] *= scalar;
return *this;
}
};
//! Output operator for Tensor3
template <class T, int N1, int N2, int N3>
inline std::ostream& operator<< (std::ostream& s, const Tensor3<T,N1,N2,N3>& tensor)
{
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (int k=0; k<N3; k++)
(*this)[i][j][k] *= scalar;
return *this;
s << tensor[i];
return s;
}
};
//! Output operator for Tensor3
template <class T, int N1, int N2, int N3>
inline std::ostream& operator<< (std::ostream& s, const Tensor3<T,N1,N2,N3>& tensor)
{
for (int i=0; i<N1; i++)
s << tensor[i];
return s;
}
} // namespace Dune::GFE
#endif
dune/gfe/tensorssd.hh
View file @ 48b9358e
......@@ -10,122 +10,127 @@
#include <dune/common/fmatrix.hh>
#include <dune/istl/matrix.hh>
/** \brief A third-rank tensor with two static (SS) and one dynamic (D) dimension
*
* \tparam T Type of the entries
* \tparam N1 Size of the first dimension
* \tparam N2 Size of the second dimension
*/
template <class T, int N1, int N2>
class TensorSSD
namespace Dune::GFE
{
public:
/** \brief Constructor with the third dimension */
explicit TensorSSD(size_t N3)
: N3_(N3)
/** \brief A third-rank tensor with two static (SS) and one dynamic (D) dimension
*
* \tparam T Type of the entries
* \tparam N1 Size of the first dimension
* \tparam N2 Size of the second dimension
*/
template <class T, int N1, int N2>
class TensorSSD
{
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
data_[i][j].resize(N3_);
}
public:
/** \brief Constructor with the third dimension */
explicit TensorSSD(size_t N3)
: N3_(N3)
{
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
data_[i][j].resize(N3_);
}
size_t dim(int index) const
{
switch (index) {
case 0 :
return N1;
case 1 :
return N2;
case 2 :
return N3_;
default :
assert(false);
size_t dim(int index) const
{
switch (index) {
case 0 :
return N1;
case 1 :
return N2;
case 2 :
return N3_;
default :
assert(false);
}
// Make compiler happy even if NDEBUG is set
return 0;
}
// Make compiler happy even if NDEBUG is set
return 0;
}
/** \brief Direct access to individual entries */
T& operator()(size_t i, size_t j, size_t k)
{
assert(i<N1 && j<N2 && k<N3_);
return data_[i][j][k];
}
/** \brief Direct access to individual entries */
T& operator()(size_t i, size_t j, size_t k)
{
assert(i<N1 && j<N2 && k<N3_);
return data_[i][j][k];
}
/** \brief Direct const access to individual entries */
const T& operator()(size_t i, size_t j, size_t k) const
{
assert(i<N1 && j<N2 && k<N3_);
return data_[i][j][k];
}
/** \brief Direct const access to individual entries */
const T& operator()(size_t i, size_t j, size_t k) const
{
assert(i<N1 && j<N2 && k<N3_);
return data_[i][j][k];
}
/** \brief Assignment from scalar */
TensorSSD<T,N1,N2>& operator=(const T& scalar)
{
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (size_t k=0; k<dim(2); k++)
data_[i][j][k] = scalar;
/** \brief Assignment from scalar */
TensorSSD<T,N1,N2>& operator=(const T& scalar)
{
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (size_t k=0; k<dim(2); k++)
data_[i][j][k] = scalar;
return *this;
}
return *this;
}
friend TensorSSD<T,N1,N2> operator*(const TensorSSD<T,N1,N2>& a, const Dune::Matrix<T>& b)
{
TensorSSD<T,N1,N2> result(b.M());
friend TensorSSD<T,N1,N2> operator*(const TensorSSD<T,N1,N2>& a, const Dune::Matrix<T>& b)
{
TensorSSD<T,N1,N2> result(b.M());
assert(a.dim(2)==b.N());
size_t N4 = a.dim(2); // third dimension of a
assert(a.dim(2)==b.N());
size_t N4 = a.dim(2); // third dimension of a
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (size_t k=0; k<b.M(); k++) {
result.data_[i][j][k] = 0;
for (size_t l=0; l<N4; l++)
result.data_[i][j][k] += a.data_[i][j][l]*b[l][k];
}
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (size_t k=0; k<b.M(); k++) {
result.data_[i][j][k] = 0;
for (size_t l=0; l<N4; l++)
result.data_[i][j][k] += a.data_[i][j][l]*b[l][k];
}
return result;
}
return result;
}
friend TensorSSD<T,N1,N2> operator+(const TensorSSD<T,N1,N2>& a, const TensorSSD<T,N1,N2>& b)
{
assert(a.dim(2)==b.dim(2));
size_t N3 = a.dim(2);
TensorSSD<T,N1,N2> result(N3);
friend TensorSSD<T,N1,N2> operator+(const TensorSSD<T,N1,N2>& a, const TensorSSD<T,N1,N2>& b)
{
assert(a.dim(2)==b.dim(2));
size_t N3 = a.dim(2);
TensorSSD<T,N1,N2> result(N3);
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (size_t k=0; k<N3; k++)
result.data_[i][j][k] = a.data_[i][j][k] + b.data_[i][j][k];
for (int i=0; i<N1; i++)
for (int j=0; j<N2; j++)
for (size_t k=0; k<N3; k++)
result.data_[i][j][k] = a.data_[i][j][k] + b.data_[i][j][k];
return result;
}
return result;
}
private:
private:
// having the dynamic data type on the inside is kind of a stupid data layout
std::array<std::array<std::vector<T>, N2>, N1> data_;
// having the dynamic data type on the inside is kind of a stupid data layout
std::array<std::array<std::vector<T>, N2>, N1> data_;
// size of the third dimension
size_t N3_;
};
// size of the third dimension
size_t N3_;
};
//! Output operator for TensorSSD
template <class T, int N1, int N2>
inline std::ostream& operator<< (std::ostream& s, const TensorSSD<T,N1,N2>& tensor)
{
for (int i=0; i<N1; i++) {
for (int j=0; j<N2; j++) {
for (size_t k=0; k<tensor.dim(2); k++)
s << tensor(i,j,k) << " ";
//! Output operator for TensorSSD
template <class T, int N1, int N2>
inline std::ostream& operator<< (std::ostream& s, const TensorSSD<T,N1,N2>& tensor)
{
for (int i=0; i<N1; i++) {
for (int j=0; j<N2; j++) {
for (size_t k=0; k<tensor.dim(2); k++)
s << tensor(i,j,k) << " ";
s << std::endl;
}
s << std::endl;
}
s << std::endl;
return s;
}
return s;
}
} // namespace Dune::GFE
#endif
dune/gfe/trustregionmmgbasesolver.hh
View file @ 48b9358e
......@@ -9,192 +9,196 @@
#include <dune/solvers/solvers/iterativesolver.hh>
#include <dune/solvers/solvers/quadraticipopt.hh>
/** \brief Base solver for a monotone multigrid solver when used as the inner solver in a trust region method
*
* Monotone multigrid methods solve constrained problems even on the coarsest level. Therefore, the choice
* of possible coarse grid solvers is limited. I have tried both Gauss-Seidel and IPOpt, and both of them
* have not satisfied my. Gauss-Seidel is slow when the coarse grid is not coarse enough. The results computed
* by IPOpt appear to be imprecise, and I didn't get good trust-region convergence. I don't really understand
* this -- it may be a bug in our IPOpt wrapper code.
* Ideally, one would use a direct solver, in particular close to the solution. However, a direct solver may
* not produce admissible corrections. Also, it may produce energy increase. Therefore, the TrustRegionMMGBaseSolver
* does a pragmatic approach: a solution is first computed using UMFPack, disregarding the obstacles.
* If the result is admissible and decreases the energy we keep it. Otherwise we fall back to IPOpt.
*/
template <class MatrixType, class VectorType>
class TrustRegionMMGBaseSolver
: public IterativeSolver<VectorType>,
public CanIgnore<Dune::BitSetVector<VectorType::block_type::dimension> >
namespace Dune::GFE
{
typedef typename VectorType::field_type field_type;
// For complex-valued data
typedef typename Dune::FieldTraits<field_type>::real_type real_type;
constexpr static int blocksize = VectorType::value_type::dimension;
typedef Dune::BitSetVector<blocksize> BitVectorType;
public:
/** \brief Constructor taking all relevant data */
TrustRegionMMGBaseSolver(Solver::VerbosityMode verbosity)
: IterativeSolver<VectorType, BitVectorType>(100, // maxIterations
1e-8, // tolerance
nullptr,
verbosity,
false) // false = use absolute error
{}
void setProblem(const MatrixType& matrix,
VectorType& x,
const VectorType& rhs) {
matrix_ = &matrix;
x_ = &x;
rhs_ = &rhs;
}
/** \brief Checks whether all relevant member variables are set
* \exception SolverError if the iteration step is not set up properly
/** \brief Base solver for a monotone multigrid solver when used as the inner solver in a trust region method
*
* Monotone multigrid methods solve constrained problems even on the coarsest level. Therefore, the choice
* of possible coarse grid solvers is limited. I have tried both Gauss-Seidel and IPOpt, and both of them
* have not satisfied my. Gauss-Seidel is slow when the coarse grid is not coarse enough. The results computed
* by IPOpt appear to be imprecise, and I didn't get good trust-region convergence. I don't really understand
* this -- it may be a bug in our IPOpt wrapper code.
* Ideally, one would use a direct solver, in particular close to the solution. However, a direct solver may
* not produce admissible corrections. Also, it may produce energy increase. Therefore, the TrustRegionMMGBaseSolver
* does a pragmatic approach: a solution is first computed using UMFPack, disregarding the obstacles.
* If the result is admissible and decreases the energy we keep it. Otherwise we fall back to IPOpt.
*/
virtual void check() const;
template <class MatrixType, class VectorType>
class TrustRegionMMGBaseSolver
: public IterativeSolver<VectorType>,
public CanIgnore<Dune::BitSetVector<VectorType::block_type::dimension> >
{
typedef typename VectorType::field_type field_type;
// For complex-valued data
typedef typename Dune::FieldTraits<field_type>::real_type real_type;
constexpr static int blocksize = VectorType::value_type::dimension;
typedef Dune::BitSetVector<blocksize> BitVectorType;
public:
/** \brief Constructor taking all relevant data */
TrustRegionMMGBaseSolver(Solver::VerbosityMode verbosity)
: IterativeSolver<VectorType, BitVectorType>(100, // maxIterations
1e-8, // tolerance
nullptr,
verbosity,
false) // false = use absolute error
{}
void setProblem(const MatrixType& matrix,
VectorType& x,
const VectorType& rhs) {
matrix_ = &matrix;
x_ = &x;
rhs_ = &rhs;
}
virtual void preprocess();
/** \brief Checks whether all relevant member variables are set
* \exception SolverError if the iteration step is not set up properly
*/
virtual void check() const;
/** \brief Loop, call the iteration procedure
* and monitor convergence
*/
virtual void solve();
virtual void preprocess();
//! The quadratic term in the quadratic energy, is assumed to be symmetric
const MatrixType* matrix_;
/** \brief Loop, call the iteration procedure
* and monitor convergence
*/
virtual void solve();
//! Vector to store the solution
VectorType* x_;
//! The quadratic term in the quadratic energy, is assumed to be symmetric
const MatrixType* matrix_;
//! The linear term in the quadratic energy
const VectorType* rhs_;
//! Vector to store the solution
VectorType* x_;
std::vector<BoxConstraint<field_type,blocksize> >* obstacles_;
//! The linear term in the quadratic energy
const VectorType* rhs_;
};
std::vector<BoxConstraint<field_type,blocksize> >* obstacles_;
};
template <class MatrixType, class VectorType>
void TrustRegionMMGBaseSolver<MatrixType, VectorType>::check() const
{
// check base class
IterativeSolver<VectorType,BitVectorType>::check();
}
template <class MatrixType, class VectorType>
void TrustRegionMMGBaseSolver<MatrixType, VectorType>::preprocess()
{
//this->iterationStep_->preprocess();
}
template <class MatrixType, class VectorType>
void TrustRegionMMGBaseSolver<MatrixType, VectorType>::check() const
{
// check base class
IterativeSolver<VectorType,BitVectorType>::check();
}
template <class MatrixType, class VectorType>
void TrustRegionMMGBaseSolver<MatrixType, VectorType>::solve()
{
MatrixType modifiedStiffness = *matrix_;
VectorType modifiedRhs = *rhs_;
template <class MatrixType, class VectorType>
void TrustRegionMMGBaseSolver<MatrixType, VectorType>::preprocess()
{
//this->iterationStep_->preprocess();
}
///////////////////////////////////////////
// Modify Dirichlet rows
///////////////////////////////////////////
template <class MatrixType, class VectorType>
void TrustRegionMMGBaseSolver<MatrixType, VectorType>::solve()
{
MatrixType modifiedStiffness = *matrix_;
VectorType modifiedRhs = *rhs_;
for (size_t j=0; j<modifiedStiffness.N(); j++)
for (int k=0; k<blocksize; k++)
modifiedStiffness[j][j][k][k] += 0.0;
///////////////////////////////////////////
// Modify Dirichlet rows
///////////////////////////////////////////
for (size_t j=0; j<modifiedStiffness.N(); j++)
{
auto cIt = modifiedStiffness[j].begin();
auto cEndIt = modifiedStiffness[j].end();
for (size_t j=0; j<modifiedStiffness.N(); j++)
for (int k=0; k<blocksize; k++)
modifiedStiffness[j][j][k][k] += 0.0;
for (; cIt!=cEndIt; ++cIt)
for (size_t j=0; j<modifiedStiffness.N(); j++)
{
auto cIt = modifiedStiffness[j].begin();
auto cEndIt = modifiedStiffness[j].end();
for (; cIt!=cEndIt; ++cIt)
{
for (int k=0; k<blocksize; k++)
if ((*this->ignoreNodes_)[j][k])
{
(*cIt)[k] = 0;
if (cIt.index()==j)
(*cIt)[k][k] = 1.0;
}
}
for (int k=0; k<blocksize; k++)
if ((*this->ignoreNodes_)[j][k])
{
(*cIt)[k] = 0;
if (cIt.index()==j)
(*cIt)[k][k] = 1.0;
}
modifiedRhs[j][k] = 0.0;
}
for (int k=0; k<blocksize; k++)
if ((*this->ignoreNodes_)[j][k])
modifiedRhs[j][k] = 0.0;
}
/////////////////////////////////////////////////////////////////
// Solve the system
/////////////////////////////////////////////////////////////////
Dune::InverseOperatorResult statistics;
Dune::UMFPack<MatrixType> solver(modifiedStiffness);
solver.setOption(UMFPACK_PRL, 0); // no output at all
solver.apply(*x_, modifiedRhs, statistics);
// Model increase? Then the matrix is not positive definite -- fall back to ipopt solver
// The model decrease is $ m(x) - m(x+s) = -<g,s> - 0.5 <s, Hs>
// Note that rhs = -g
VectorType tmp(x_->size());
tmp = 0;
matrix_->umv(*x_, tmp);
double modelDecrease = (modifiedRhs*(*x_)) - 0.5 * ((*x_)*tmp);
if (std::isnan(modelDecrease) or modelDecrease < 0 or true)
{
std::cout << "Model increase: " << -modelDecrease << ", falling back to slower solver" << std::endl;
/////////////////////////////////////////////////////////////////
// Solve the system
/////////////////////////////////////////////////////////////////
Dune::InverseOperatorResult statistics;
Dune::UMFPack<MatrixType> solver(modifiedStiffness);
solver.setOption(UMFPACK_PRL, 0); // no output at all
solver.apply(*x_, modifiedRhs, statistics);
// Model increase? Then the matrix is not positive definite -- fall back to ipopt solver
// The model decrease is $ m(x) - m(x+s) = -<g,s> - 0.5 <s, Hs>
// Note that rhs = -g
VectorType tmp(x_->size());
tmp = 0;
matrix_->umv(*x_, tmp);
double modelDecrease = (modifiedRhs*(*x_)) - 0.5 * ((*x_)*tmp);
if (std::isnan(modelDecrease) or modelDecrease < 0 or true)
{
std::cout << "Model increase: " << -modelDecrease << ", falling back to slower solver" << std::endl;
std::cout << "Total VARIABLES: " << x_->size() << " x " << blocksize << " = " << x_->size()*blocksize << std::endl;
std::cout << "Dirichlet DOFS: " << this->ignoreNodes_->count() << std::endl;
std::cout << "Total VARIABLES: " << x_->size() << " x " << blocksize << " = " << x_->size()*blocksize << std::endl;
std::cout << "Dirichlet DOFS: " << this->ignoreNodes_->count() << std::endl;
QuadraticIPOptSolver<MatrixType, VectorType> baseSolver;
baseSolver.verbosity_ = NumProc::REDUCED;
baseSolver.tolerance_ = 1e-8;
QuadraticIPOptSolver<MatrixType, VectorType> baseSolver;
baseSolver.verbosity_ = NumProc::REDUCED;
baseSolver.tolerance_ = 1e-8;
*x_ = 0;
baseSolver.setProblem(*matrix_, *x_, *rhs_);
baseSolver.obstacles_ = obstacles_;
baseSolver.ignoreNodes_ = this->ignoreNodes_;
*x_ = 0;
baseSolver.setProblem(*matrix_, *x_, *rhs_);
baseSolver.obstacles_ = obstacles_;
baseSolver.ignoreNodes_ = this->ignoreNodes_;
baseSolver.solve();
}
baseSolver.solve();
}
// Check whether the solution is admissible wrt the obstacles
bool admissible = true;
assert (obstacles_->size() == x_->size());
for (size_t i=0; i<obstacles_->size(); i++)
{
for (int j=0; j<blocksize; j++)
if ( (*x_)[i][j] > (*obstacles_)[i].upper(j) or (*x_)[i][j] < (*obstacles_)[i].lower(j) )
{
admissible = false;
// Check whether the solution is admissible wrt the obstacles
bool admissible = true;
assert (obstacles_->size() == x_->size());
for (size_t i=0; i<obstacles_->size(); i++)
{
for (int j=0; j<blocksize; j++)
if ( (*x_)[i][j] > (*obstacles_)[i].upper(j) or (*x_)[i][j] < (*obstacles_)[i].lower(j) )
{
admissible = false;
break;
}
if (not admissible)
break;
}
}
if (not admissible)
break;
}
{
std::cout << "Inadmissible step, falling back to slower solver" << std::endl;
if (not admissible)
{
std::cout << "Inadmissible step, falling back to slower solver" << std::endl;
QuadraticIPOptSolver<MatrixType, VectorType> baseSolver;
baseSolver.verbosity_ = NumProc::REDUCED;
baseSolver.tolerance_ = 1e-8;
QuadraticIPOptSolver<MatrixType, VectorType> baseSolver;
baseSolver.verbosity_ = NumProc::REDUCED;
baseSolver.tolerance_ = 1e-8;
*x_ = 0;
baseSolver.setProblem(*matrix_, *x_, *rhs_);
baseSolver.obstacles_ = obstacles_;
baseSolver.ignoreNodes_ = this->ignoreNodes_;
*x_ = 0;
baseSolver.setProblem(*matrix_, *x_, *rhs_);
baseSolver.obstacles_ = obstacles_;
baseSolver.ignoreNodes_ = this->ignoreNodes_;
baseSolver.solve();
}
baseSolver.solve();
}
}
} // namespace Dune::GFE
#endif
dune/gfe/vtkfile.hh
View file @ 48b9358e
......@@ -17,358 +17,355 @@
// For parallel infrastructure stuff:
#include <dune/grid/io/file/vtk.hh>
namespace Dune {
namespace GFE {
/** \brief A class representing a VTK file, but independent from the Dune grid interface
*
* This file is supposed to represent an abstraction layer in between the pure XML used for VTK files,
* and the VTKWriter from dune-grid, which knows about grids. In theory, the dune-grid VTKWriter
* could use this class to simplify its own code. More importantly, the VTKFile class allows to
* write files containing second-order geometries, which is currently not possible with the dune-grid
* VTKWriter.
*/
class VTKFile
namespace Dune::GFE
{
/** \brief A class representing a VTK file, but independent from the Dune grid interface
*
* This file is supposed to represent an abstraction layer in between the pure XML used for VTK files,
* and the VTKWriter from dune-grid, which knows about grids. In theory, the dune-grid VTKWriter
* could use this class to simplify its own code. More importantly, the VTKFile class allows to
* write files containing second-order geometries, which is currently not possible with the dune-grid
* VTKWriter.
*/
class VTKFile
{
public:
/** \brief Write the file to disk */
void write(const std::string& filename) const
{
int argc = 0;
char** argv = nullptr;
Dune::MPIHelper& mpiHelper = Dune::MPIHelper::instance(argc,argv);
std::string fullfilename = filename + ".vtu";
public:
// Prepend rank and communicator size to the filename, if there are more than one process
if (mpiHelper.size() > 1)
fullfilename = getParallelPieceName(filename, "", mpiHelper.rank(), mpiHelper.size());
/** \brief Write the file to disk */
void write(const std::string& filename) const
// Write the pvtu file that ties together the different parts
if (mpiHelper.size() > 1 && mpiHelper.rank()==0)
{
int argc = 0;
char** argv = nullptr;
Dune::MPIHelper& mpiHelper = Dune::MPIHelper::instance(argc,argv);
std::ofstream pvtuOutFile(getParallelName(filename, "", mpiHelper.size()));
Dune::VTK::PVTUWriter writer(pvtuOutFile, Dune::VTK::unstructuredGrid);
std::string fullfilename = filename + ".vtu";
writer.beginMain();
// Prepend rank and communicator size to the filename, if there are more than one process
if (mpiHelper.size() > 1)
fullfilename = getParallelPieceName(filename, "", mpiHelper.rank(), mpiHelper.size());
writer.beginPointData();
writer.addArray("director0", 3, VTK::Precision::float32);
writer.addArray("director1", 3, VTK::Precision::float32);
writer.addArray("director2", 3, VTK::Precision::float32);
writer.addArray("zCoord", 1, VTK::Precision::float32);
writer.endPointData();
// Write the pvtu file that ties together the different parts
if (mpiHelper.size() > 1 && mpiHelper.rank()==0)
{
std::ofstream pvtuOutFile(getParallelName(filename, "", mpiHelper.size()));
Dune::VTK::PVTUWriter writer(pvtuOutFile, Dune::VTK::unstructuredGrid);
writer.beginCellData();
writer.addArray("mycelldata", 1, VTK::Precision::float32);
writer.endCellData();
writer.beginMain();
// dump point coordinates
writer.beginPoints();
writer.addArray("Coordinates", 3, VTK::Precision::float32);
writer.endPoints();
writer.beginPointData();
writer.addArray("director0", 3, VTK::Precision::float32);
writer.addArray("director1", 3, VTK::Precision::float32);
writer.addArray("director2", 3, VTK::Precision::float32);
writer.addArray("zCoord", 1, VTK::Precision::float32);
writer.endPointData();
for (int i=0; i<mpiHelper.size(); i++)
writer.addPiece(getParallelPieceName(filename, "", i, mpiHelper.size()));
writer.beginCellData();
writer.addArray("mycelldata", 1, VTK::Precision::float32);
writer.endCellData();
// finish main section
writer.endMain();
}
// dump point coordinates
writer.beginPoints();
writer.addArray("Coordinates", 3, VTK::Precision::float32);
writer.endPoints();
std::ofstream outFile(fullfilename);
// Write header
outFile << "<?xml version=\"1.0\"?>" << std::endl;
outFile << "<VTKFile type=\"UnstructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">" << std::endl;
outFile << " <UnstructuredGrid>" << std::endl;
outFile << " <Piece NumberOfCells=\"" << cellOffsets_.size() << "\" NumberOfPoints=\"" << points_.size() << "\">" << std::endl;
// Write vertex coordinates
outFile << " <Points>" << std::endl;
{ // extra parenthesis to control destruction of the pointsWriter object
Dune::VTK::AsciiDataArrayWriter pointsWriter(outFile, "Coordinates", 3, Dune::Indent(4), VTK::Precision::float32);
for (size_t i=0; i<points_.size(); i++)
for (int j=0; j<3; j++)
pointsWriter.write(points_[i][j]);
} // destructor of pointsWriter objects writes trailing </DataArray> to file
outFile << " </Points>" << std::endl;
// Write elements
outFile << " <Cells>" << std::endl;
{ // extra parenthesis to control destruction of the cellConnectivityWriter object
Dune::VTK::AsciiDataArrayWriter cellConnectivityWriter(outFile, "connectivity", 1, Dune::Indent(4), VTK::Precision::int32);
for (size_t i=0; i<cellConnectivity_.size(); i++)
cellConnectivityWriter.write(cellConnectivity_[i]);
}
for (int i=0; i<mpiHelper.size(); i++)
writer.addPiece(getParallelPieceName(filename, "", i, mpiHelper.size()));
{ // extra parenthesis to control destruction of the writer object
Dune::VTK::AsciiDataArrayWriter cellOffsetsWriter(outFile, "offsets", 1, Dune::Indent(4), VTK::Precision::int32);
for (size_t i=0; i<cellOffsets_.size(); i++)
cellOffsetsWriter.write(cellOffsets_[i]);
}
// finish main section
writer.endMain();
}
{ // extra parenthesis to control destruction of the writer object
Dune::VTK::AsciiDataArrayWriter cellTypesWriter(outFile, "types", 1, Dune::Indent(4), VTK::Precision::uint32);
for (size_t i=0; i<cellTypes_.size(); i++)
cellTypesWriter.write(cellTypes_[i]);
}
std::ofstream outFile(fullfilename);
// Write header
outFile << "<?xml version=\"1.0\"?>" << std::endl;
outFile << "<VTKFile type=\"UnstructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">" << std::endl;
outFile << " <UnstructuredGrid>" << std::endl;
outFile << " <Piece NumberOfCells=\"" << cellOffsets_.size() << "\" NumberOfPoints=\"" << points_.size() << "\">" << std::endl;
// Write vertex coordinates
outFile << " <Points>" << std::endl;
{ // extra parenthesis to control destruction of the pointsWriter object
Dune::VTK::AsciiDataArrayWriter pointsWriter(outFile, "Coordinates", 3, Dune::Indent(4), VTK::Precision::float32);
for (size_t i=0; i<points_.size(); i++)
for (int j=0; j<3; j++)
pointsWriter.write(points_[i][j]);
} // destructor of pointsWriter objects writes trailing </DataArray> to file
outFile << " </Points>" << std::endl;
// Write elements
outFile << " <Cells>" << std::endl;
{ // extra parenthesis to control destruction of the cellConnectivityWriter object
Dune::VTK::AsciiDataArrayWriter cellConnectivityWriter(outFile, "connectivity", 1, Dune::Indent(4), VTK::Precision::int32);
for (size_t i=0; i<cellConnectivity_.size(); i++)
cellConnectivityWriter.write(cellConnectivity_[i]);
}
outFile << " </Cells>" << std::endl;
{ // extra parenthesis to control destruction of the writer object
Dune::VTK::AsciiDataArrayWriter cellOffsetsWriter(outFile, "offsets", 1, Dune::Indent(4), VTK::Precision::int32);
for (size_t i=0; i<cellOffsets_.size(); i++)
cellOffsetsWriter.write(cellOffsets_[i]);
}
//////////////////////////////////////////////////
// Point data
//////////////////////////////////////////////////
outFile << " <PointData Scalars=\"zCoord\" Vectors=\"director0\">" << std::endl;
{ // extra parenthesis to control destruction of the writer object
Dune::VTK::AsciiDataArrayWriter cellTypesWriter(outFile, "types", 1, Dune::Indent(4), VTK::Precision::uint32);
for (size_t i=0; i<cellTypes_.size(); i++)
cellTypesWriter.write(cellTypes_[i]);
}
// Z coordinate for better visualization of wrinkles
{ // extra parenthesis to control destruction of the writer object
Dune::VTK::AsciiDataArrayWriter zCoordWriter(outFile, "zCoord", 1, Dune::Indent(4), VTK::Precision::float32);
for (size_t i=0; i<zCoord_.size(); i++)
zCoordWriter.write(zCoord_[i]);
}
outFile << " </Cells>" << std::endl;
// The three director fields
for (size_t i=0; i<3; i++)
{
Dune::VTK::AsciiDataArrayWriter directorWriter(outFile, "director" + std::to_string(i), 3, Dune::Indent(4), VTK::Precision::float32);
for (size_t j=0; j<directors_[i].size(); j++)
for (int k=0; k<3; k++)
directorWriter.write(directors_[i][j][k]);
}
//////////////////////////////////////////////////
// Point data
//////////////////////////////////////////////////
outFile << " <PointData Scalars=\"zCoord\" Vectors=\"director0\">" << std::endl;
outFile << " </PointData>" << std::endl;
// Z coordinate for better visualization of wrinkles
{ // extra parenthesis to control destruction of the writer object
Dune::VTK::AsciiDataArrayWriter zCoordWriter(outFile, "zCoord", 1, Dune::Indent(4), VTK::Precision::float32);
for (size_t i=0; i<zCoord_.size(); i++)
zCoordWriter.write(zCoord_[i]);
}
//////////////////////////////////////////////////
// Cell data
//////////////////////////////////////////////////
// The three director fields
for (size_t i=0; i<3; i++)
{
Dune::VTK::AsciiDataArrayWriter directorWriter(outFile, "director" + std::to_string(i), 3, Dune::Indent(4), VTK::Precision::float32);
for (size_t j=0; j<directors_[i].size(); j++)
for (int k=0; k<3; k++)
directorWriter.write(directors_[i][j][k]);
if (cellData_.size() > 0)
{
outFile << " <CellData>" << std::endl;
{ // extra parenthesis to control destruction of the writer object
Dune::VTK::AsciiDataArrayWriter cellDataWriter(outFile, "mycelldata", 1, Dune::Indent(4), VTK::Precision::float32);
for (size_t i=0; i<cellData_.size(); i++)
cellDataWriter.write(cellData_[i]);
}
outFile << " </CellData>" << std::endl;
}
outFile << " </PointData>" << std::endl;
//////////////////////////////////////////////////
// Write footer
//////////////////////////////////////////////////
outFile << " </Piece>" << std::endl;
outFile << " </UnstructuredGrid>" << std::endl;
outFile << "</VTKFile>" << std::endl;
//////////////////////////////////////////////////
// Cell data
//////////////////////////////////////////////////
if (cellData_.size() > 0)
{
outFile << " <CellData>" << std::endl;
{ // extra parenthesis to control destruction of the writer object
Dune::VTK::AsciiDataArrayWriter cellDataWriter(outFile, "mycelldata", 1, Dune::Indent(4), VTK::Precision::float32);
for (size_t i=0; i<cellData_.size(); i++)
cellDataWriter.write(cellData_[i]);
}
outFile << " </CellData>" << std::endl;
}
}
/** \brief Read a VTKFile object from a file
*
* This method uses TinyXML2. If you do not have TinyXML2 installed the code will simply throw a NotImplemented exception.
*/
void read(const std::string& filename)
{
int argc = 0;
char** argv = nullptr;
Dune::MPIHelper& mpiHelper = Dune::MPIHelper::instance(argc,argv);
//////////////////////////////////////////////////
// Write footer
//////////////////////////////////////////////////
outFile << " </Piece>" << std::endl;
outFile << " </UnstructuredGrid>" << std::endl;
outFile << "</VTKFile>" << std::endl;
std::string fullfilename = filename; // + ".vtu";
// Prepend rank and communicator size to the filename, if there are more than one process
if (mpiHelper.size() > 1)
fullfilename = getParallelPieceName(filename, "", mpiHelper.rank(), mpiHelper.size());
#if ! HAVE_TINYXML2
DUNE_THROW(Dune::NotImplemented, "You need TinyXML2 for vtk file reading!");
#else
tinyxml2::XMLDocument doc;
if (doc.LoadFile(fullfilename.c_str()) != tinyxml2::XML_SUCCESS)
{
DUNE_THROW(Dune::IOError, "Couldn't open the file '" << fullfilename << "'");
}
/** \brief Read a VTKFile object from a file
*
* This method uses TinyXML2. If you do not have TinyXML2 installed the code will simply throw a NotImplemented exception.
*/
void read(const std::string& filename)
// Get number of cells and number of points
int numberOfCells;
int numberOfPoints;
// First try whether this is a vtu file
tinyxml2::XMLElement* pieceElement = doc.FirstChildElement( "VTKFile" )->FirstChildElement( "UnstructuredGrid" )->FirstChildElement( "Piece" );
if (pieceElement)
{
pieceElement->QueryIntAttribute( "NumberOfCells", &numberOfCells );
}
else // No vtu file? So let's try vtp
if ((pieceElement = doc.FirstChildElement( "VTKFile" )->FirstChildElement( "PolyData" )->FirstChildElement( "Piece" )) )
{
int argc = 0;
char** argv = nullptr;
Dune::MPIHelper& mpiHelper = Dune::MPIHelper::instance(argc,argv);
pieceElement->QueryIntAttribute( "NumberOfPolys", &numberOfCells );
}
else
DUNE_THROW(Dune::IOError, "Unsupported file type found");
std::string fullfilename = filename;// + ".vtu";
pieceElement->QueryIntAttribute( "NumberOfPoints", &numberOfPoints );
// Prepend rank and communicator size to the filename, if there are more than one process
if (mpiHelper.size() > 1)
fullfilename = getParallelPieceName(filename, "", mpiHelper.rank(), mpiHelper.size());
//////////////////////////////////
// Read point coordinates
//////////////////////////////////
points_.resize(numberOfPoints);
tinyxml2::XMLElement* pointsElement = pieceElement->FirstChildElement( "Points" )->FirstChildElement( "DataArray" );
#if ! HAVE_TINYXML2
DUNE_THROW(Dune::NotImplemented, "You need TinyXML2 for vtk file reading!");
#else
tinyxml2::XMLDocument doc;
if (doc.LoadFile(fullfilename.c_str()) != tinyxml2::XML_SUCCESS)
std::stringstream coordsStream(pointsElement->GetText());
double inDouble;
size_t i=0;
while (coordsStream >> inDouble)
{
points_[i/3][i%3] = inDouble;
i++;
}
///////////////////////////////////
// Read cells
///////////////////////////////////
tinyxml2::XMLElement* cellsElement = pieceElement->FirstChildElement( "Cells" )->FirstChildElement( "DataArray" );
if (not cellsElement)
cellsElement = pieceElement->FirstChildElement( "Polys" )->FirstChildElement( "DataArray" );
while (cellsElement != nullptr)
{
int inInt;
if (cellsElement->Attribute("Name", "connectivity"))
{
DUNE_THROW(Dune::IOError, "Couldn't open the file '" << fullfilename << "'");
std::stringstream connectivityStream(cellsElement->GetText());
while (connectivityStream >> inInt)
cellConnectivity_.push_back(inInt);
}
// Get number of cells and number of points
int numberOfCells;
int numberOfPoints;
// First try whether this is a vtu file
tinyxml2::XMLElement* pieceElement = doc.FirstChildElement( "VTKFile" )->FirstChildElement( "UnstructuredGrid" )->FirstChildElement( "Piece" );
if (pieceElement)
if (cellsElement->Attribute("Name", "offsets"))
{
pieceElement->QueryIntAttribute( "NumberOfCells", &numberOfCells );
std::stringstream offsetsStream(cellsElement->GetText());
while (offsetsStream >> inInt)
cellOffsets_.push_back(inInt);
}
else // No vtu file? So let's try vtp
if ((pieceElement = doc.FirstChildElement( "VTKFile" )->FirstChildElement( "PolyData" )->FirstChildElement( "Piece" )) )
if (cellsElement->Attribute("Name", "types"))
{
pieceElement->QueryIntAttribute( "NumberOfPolys", &numberOfCells );
std::stringstream typesStream(cellsElement->GetText());
while (typesStream >> inInt)
cellTypes_.push_back(inInt);
}
else
DUNE_THROW(Dune::IOError, "Unsupported file type found");
pieceElement->QueryIntAttribute( "NumberOfPoints", &numberOfPoints );
//////////////////////////////////
// Read point coordinates
//////////////////////////////////
points_.resize(numberOfPoints);
tinyxml2::XMLElement* pointsElement = pieceElement->FirstChildElement( "Points" )->FirstChildElement( "DataArray" );
std::stringstream coordsStream(pointsElement->GetText());
cellsElement = cellsElement->NextSiblingElement();
}
double inDouble;
size_t i=0;
while (coordsStream >> inDouble)
{
points_[i/3][i%3] = inDouble;
i++;
}
/////////////////////////////////////
// Read point data
/////////////////////////////////////
///////////////////////////////////
// Read cells
///////////////////////////////////
tinyxml2::XMLElement* cellsElement = pieceElement->FirstChildElement( "Cells" )->FirstChildElement( "DataArray" );
if (not cellsElement)
cellsElement = pieceElement->FirstChildElement( "Polys" )->FirstChildElement( "DataArray" );
tinyxml2::XMLElement* pointDataElement = pieceElement->FirstChildElement( "PointData" )->FirstChildElement( "DataArray" );
while (cellsElement != nullptr)
while (pointDataElement)
{
size_t j=0;
std::stringstream directorStream(pointDataElement->GetText());
if (pointDataElement->Attribute("Name", "director0"))
{
int inInt;
if (cellsElement->Attribute("Name", "connectivity"))
{
std::stringstream connectivityStream(cellsElement->GetText());
while (connectivityStream >> inInt)
cellConnectivity_.push_back(inInt);
}
if (cellsElement->Attribute("Name", "offsets"))
{
std::stringstream offsetsStream(cellsElement->GetText());
while (offsetsStream >> inInt)
cellOffsets_.push_back(inInt);
}
if (cellsElement->Attribute("Name", "types"))
directors_[0].resize(numberOfPoints);
while (directorStream >> inDouble)
{
std::stringstream typesStream(cellsElement->GetText());
while (typesStream >> inInt)
cellTypes_.push_back(inInt);
directors_[0][j/3][j%3] = inDouble;
j++;
}
cellsElement = cellsElement->NextSiblingElement();
}
/////////////////////////////////////
// Read point data
/////////////////////////////////////
tinyxml2::XMLElement* pointDataElement = pieceElement->FirstChildElement( "PointData" )->FirstChildElement( "DataArray" );
while (pointDataElement)
if (pointDataElement->Attribute("Name", "director1"))
{
size_t j=0;
std::stringstream directorStream(pointDataElement->GetText());
if (pointDataElement->Attribute("Name", "director0"))
directors_[1].resize(numberOfPoints);
while (directorStream >> inDouble)
{
directors_[0].resize(numberOfPoints);
while (directorStream >> inDouble)
{
directors_[0][j/3][j%3] = inDouble;
j++;
}
directors_[1][j/3][j%3] = inDouble;
j++;
}
if (pointDataElement->Attribute("Name", "director1"))
{
directors_[1].resize(numberOfPoints);
while (directorStream >> inDouble)
{
directors_[1][j/3][j%3] = inDouble;
j++;
}
}
if (pointDataElement->Attribute("Name", "director2"))
}
if (pointDataElement->Attribute("Name", "director2"))
{
directors_[2].resize(numberOfPoints);
while (directorStream >> inDouble)
{
directors_[2].resize(numberOfPoints);
while (directorStream >> inDouble)
{
directors_[2][j/3][j%3] = inDouble;
j++;
}
directors_[2][j/3][j%3] = inDouble;
j++;
}
pointDataElement = pointDataElement->NextSiblingElement();
}
#endif
pointDataElement = pointDataElement->NextSiblingElement();
}
#endif
}
std::vector<Dune::FieldVector<double,3> > points_;
std::vector<Dune::FieldVector<double,3> > points_;
std::vector<unsigned int> cellConnectivity_;
std::vector<unsigned int> cellConnectivity_;
std::vector<int> cellOffsets_;
std::vector<int> cellOffsets_;
std::vector<int> cellTypes_;
std::vector<int> cellTypes_;
std::vector<double> zCoord_;
std::vector<double> zCoord_;
std::vector<double> cellData_;
std::vector<double> cellData_;
std::array<std::vector<Dune::FieldVector<double,3> >, 3 > directors_;
std::array<std::vector<Dune::FieldVector<double,3> >, 3 > directors_;
private:
private:
/** \brief Extend filename to contain communicator rank and size
*
* Copied from dune-grid vtkwriter.hh
*/
static std::string getParallelPieceName(const std::string& name,
const std::string& path,
int commRank, int commSize)
{
std::ostringstream s;
if(path.size() > 0) {
s << path;
if(path[path.size()-1] != '/')
s << '/';
}
s << 's' << std::setw(4) << std::setfill('0') << commSize << '-';
s << 'p' << std::setw(4) << std::setfill('0') << commRank << '-';
s << name;
if (true) //(GridType::dimension > 1)
s << ".vtu";
else
s << ".vtp";
return s.str();
/** \brief Extend filename to contain communicator rank and size
*
* Copied from dune-grid vtkwriter.hh
*/
static std::string getParallelPieceName(const std::string& name,
const std::string& path,
int commRank, int commSize)
{
std::ostringstream s;
if(path.size() > 0) {
s << path;
if(path[path.size()-1] != '/')
s << '/';
}
/** \brief Extend filename to contain communicator rank and size
*
* Copied from dune-grid vtkwriter.hh
*/
static std::string getParallelName(const std::string& name,
const std::string& path,
int commSize)
{
std::ostringstream s;
if(path.size() > 0) {
s << path;
if(path[path.size()-1] != '/')
s << '/';
}
s << 's' << std::setw(4) << std::setfill('0') << commSize << '-';
s << name;
if (true) //(GridType::dimension > 1)
s << ".pvtu";
else
s << ".pvtp";
return s.str();
s << 's' << std::setw(4) << std::setfill('0') << commSize << '-';
s << 'p' << std::setw(4) << std::setfill('0') << commRank << '-';
s << name;
if (true) //(GridType::dimension > 1)
s << ".vtu";
else
s << ".vtp";
return s.str();
}
/** \brief Extend filename to contain communicator rank and size
*
* Copied from dune-grid vtkwriter.hh
*/
static std::string getParallelName(const std::string& name,
const std::string& path,
int commSize)
{
std::ostringstream s;
if(path.size() > 0) {
s << path;
if(path[path.size()-1] != '/')
s << '/';
}
};
}
}
s << 's' << std::setw(4) << std::setfill('0') << commSize << '-';
s << name;
if (true) //(GridType::dimension > 1)
s << ".pvtu";
else
s << ".pvtp";
return s.str();
}
};
} // namespace Dune::GFE
#endif
problems/L-clamped-Plate.py 0 → 100644
View file @ 48b9358e
import math
class ParameterSet(dict):
def __init__(self, *args, **kwargs):
super(ParameterSet, self).__init__(*args, **kwargs)
self.__dict__ = self
parameterSet = ParameterSet()
#############################################
# Paths
#############################################
parameterSet.resultPath = '/home/klaus/Desktop/Dune-Hermite/dune-gfe/outputs_L-clamped-Plate'
parameterSet.instrumentedPath = '/home/klaus/Desktop/Dune-Hermite/dune-gfe/outputs_L-clamped-Plate/instrumented'
parameterSet.executablePath = '/home/klaus/Desktop/Dune-Hermite/dune-gfe/build-cmake/src'
parameterSet.baseName= 'L-clamped-Plate'
#############################################
# Grid parameters
#############################################
nX=1
nY=1
parameterSet.structuredGrid = 'simplex'
parameterSet.lower = '0 0'
parameterSet.upper = '4 4'
parameterSet.elements = str(nX)+' '+ str(nY)
parameterSet.macroGridLevel = 3
#############################################
# Solver parameters
#############################################
# Choose solver: "RNHM" (Default:Riemannian Newton with Hessian modification), "RiemannianTR" (Riemannain Trust-region method)
parameterSet.Solver = "RNHM"
# Tolerance of the multigrid solver
parameterSet.tolerance = 1e-12
# Maximum number of multigrid iterations
parameterSet.maxProximalNewtonSteps = 100
# Initial regularization
parameterSet.initialRegularization = 1
# Measure convergence
parameterSet.instrumented = 0
############################
# Problem specifications
############################
# Dimension of the domain (only used for numerical-test python files)
parameterSet.dim = 2
# Dimension of the target space
parameterSet.targetDim = 3
parameterSet.targetSpace = 'BendingIsometry'
#############################################
# Options
#############################################
# Write discrete solution as .vtk-File
parameterSet.writeVTK = 1
# Write Dof-Vector to .txt-file
parameterSet.writeDOFvector = 0
#############################################
# Dirichlet boundary indicator
#############################################
def dirichlet_indicator(x) :
if( (x[0] <= 0.001) or (x[1]<=0.001)):
return True
else:
return False
#############################################
# Initial iterate function
#############################################
def f(x):
return [x[0], x[1], 0]
def df(x):
return ((1,0),
(0,1),
(0,0))
fdf = (f, df)
#############################################
# Force
############################################
def force(x):
return [0, 0, 0.025]