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#include <config.h>
#include <fenv.h>
#include <iostream>
#include <iomanip>
#include <dune/common/fvector.hh>
#include <dune/geometry/quadraturerules.hh>
#include <dune/geometry/type.hh>
#include <dune/geometry/referenceelements.hh>
#include <dune/localfunctions/lagrange/pqkfactory.hh>
#include <dune/gfe/rotation.hh>
#include <dune/gfe/realtuple.hh>
#include <dune/gfe/unitvector.hh>
#include <dune/gfe/localprojectedfefunction.hh>
#include "multiindex.hh"
#include "valuefactory.hh"
const double eps = 1e-6;
using namespace Dune;
/** \brief Computes the diameter of a set */
template <class TargetSpace>
double diameter(const std::vector<TargetSpace>& v)
{
double d = 0;
for (size_t i=0; i<v.size(); i++)
for (size_t j=0; j<v.size(); j++)
d = std::max(d, TargetSpace::distance(v[i],v[j]));
return d;
}
template <int dim, class ctype, class LocalFunction>
auto
evaluateDerivativeFD(const LocalFunction& f, const Dune::FieldVector<ctype, dim>& local)
-> decltype(f.evaluateDerivative(local))
{
static const int embeddedDim = LocalFunction::TargetSpace::embeddedDim;
Dune::FieldMatrix<ctype, embeddedDim, dim> result;
for (int i=0; i<dim; i++) {
Dune::FieldVector<ctype, dim> forward = local;
Dune::FieldVector<ctype, dim> backward = local;
forward[i] += eps;
backward[i] -= eps;
auto fdDer = f.evaluate(forward).globalCoordinates() - f.evaluate(backward).globalCoordinates();
fdDer /= 2*eps;
for (int j=0; j<embeddedDim; j++)
result[j][i] = fdDer[j];
}
return result;
}
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template <int domainDim, int dim>
void testDerivativeTangentiality(const RealTuple<double,dim>& x,
const FieldMatrix<double,dim,domainDim>& derivative)
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{
// By construction, derivatives of RealTuples are always tangent
}
// the columns of the derivative must be tangential to the manifold
template <int domainDim, int vectorDim>
void testDerivativeTangentiality(const UnitVector<double,vectorDim>& x,
const FieldMatrix<double,vectorDim,domainDim>& derivative)
{
for (int i=0; i<domainDim; i++) {
// The i-th column is a tangent vector if its scalar product with the global coordinates
// of x vanishes.
double sp = 0;
for (int j=0; j<vectorDim; j++)
sp += x.globalCoordinates()[j] * derivative[j][i];
if (std::fabs(sp) > 1e-8)
DUNE_THROW(Dune::Exception, "Derivative is not tangential: Column: " << i << ", product: " << sp);
}
}
// the columns of the derivative must be tangential to the manifold
template <int domainDim, int vectorDim>
void testDerivativeTangentiality(const Rotation<double,vectorDim-1>& x,
const FieldMatrix<double,vectorDim,domainDim>& derivative)
{
}
// the columns of the derivative must be tangential to the manifold
template <int domainDim, int vectorDim>
void testDerivativeTangentiality(const RigidBodyMotion<double,3>& x,
const FieldMatrix<double,vectorDim,domainDim>& derivative)
{
}
/** \brief Test whether interpolation is invariant under permutation of the simplex vertices
* \todo Implement this for all dimensions
*/
template <int domainDim, class TargetSpace>
void testPermutationInvariance(const std::vector<TargetSpace>& corners)
{
// works only for 2d domains
if (domainDim!=2)
return;
PQkLocalFiniteElementCache<double,double,domainDim,1> feCache;
typedef typename PQkLocalFiniteElementCache<double,double,domainDim,1>::FiniteElementType LocalFiniteElement;
GeometryType simplex = GeometryTypes::simplex(domainDim);
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//
std::vector<TargetSpace> cornersRotated1(domainDim+1);
std::vector<TargetSpace> cornersRotated2(domainDim+1);
cornersRotated1[0] = cornersRotated2[2] = corners[1];
cornersRotated1[1] = cornersRotated2[0] = corners[2];
cornersRotated1[2] = cornersRotated2[1] = corners[0];
GFE::LocalProjectedFEFunction<2,double,LocalFiniteElement,TargetSpace> f0(feCache.get(simplex), corners);
GFE::LocalProjectedFEFunction<2,double,LocalFiniteElement,TargetSpace> f1(feCache.get(simplex), cornersRotated1);
GFE::LocalProjectedFEFunction<2,double,LocalFiniteElement,TargetSpace> f2(feCache.get(simplex), cornersRotated2);
// A quadrature rule as a set of test points
int quadOrder = 3;
const Dune::QuadratureRule<double, domainDim>& quad
= Dune::QuadratureRules<double, domainDim>::rule(simplex, quadOrder);
for (size_t pt=0; pt<quad.size(); pt++) {
const Dune::FieldVector<double,domainDim>& quadPos = quad[pt].position();
Dune::FieldVector<double,domainDim> l0 = quadPos;
Dune::FieldVector<double,domainDim> l1, l2;
l1[0] = quadPos[1];
l1[1] = 1-quadPos[0]-quadPos[1];
l2[0] = 1-quadPos[0]-quadPos[1];
l2[1] = quadPos[0];
// evaluate the three functions
TargetSpace v0 = f0.evaluate(l0);
TargetSpace v1 = f1.evaluate(l1);
TargetSpace v2 = f2.evaluate(l2);
// Check that they are all equal
assert(TargetSpace::distance(v0,v1) < eps);
assert(TargetSpace::distance(v0,v2) < eps);
}
}
template <int domainDim, class TargetSpace>
void testDerivative(const GFE::LocalProjectedFEFunction<domainDim,double,typename PQkLocalFiniteElementCache<double,double,domainDim,1>::FiniteElementType, TargetSpace>& f)
{
static const int embeddedDim = TargetSpace::EmbeddedTangentVector::dimension;
// A quadrature rule as a set of test points
int quadOrder = 3;
const auto& quad = Dune::QuadratureRules<double, domainDim>::rule(f.type(), quadOrder);
for (size_t pt=0; pt<quad.size(); pt++) {
const Dune::FieldVector<double,domainDim>& quadPos = quad[pt].position();
// evaluate actual derivative
Dune::FieldMatrix<double, embeddedDim, domainDim> derivative = f.evaluateDerivative(quadPos);
// evaluate fd approximation of derivative
Dune::FieldMatrix<double, embeddedDim, domainDim> fdDerivative = evaluateDerivativeFD(f,quadPos);
Dune::FieldMatrix<double, embeddedDim, domainDim> diff = derivative;
diff -= fdDerivative;
if ( diff.infinity_norm() > 100*eps ) {
std::cout << className<TargetSpace>() << ": Analytical gradient does not match fd approximation." << std::endl;
std::cout << "Analytical: " << derivative << std::endl;
std::cout << "FD : " << fdDerivative << std::endl;
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assert(false);
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}
testDerivativeTangentiality(f.evaluate(quadPos), derivative);
}
}
template <class TargetSpace, int domainDim>
void test(const GeometryType& element)
{
std::cout << " --- Testing " << className<TargetSpace>() << ", domain dimension: " << element.dim() << " ---" << std::endl;
std::vector<TargetSpace> testPoints;
ValueFactory<TargetSpace>::get(testPoints);
int nTestPoints = testPoints.size();
size_t nVertices = Dune::ReferenceElements<double,domainDim>::general(element).size(domainDim);
// Set up elements of the target space
std::vector<TargetSpace> corners(nVertices);
MultiIndex index(nVertices, nTestPoints);
int numIndices = index.cycle();
for (int i=0; i<numIndices; i++, ++index) {
for (size_t j=0; j<nVertices; j++)
corners[j] = testPoints[index[j]];
if (diameter(corners) > 0.5*M_PI)
continue;
// Make local gfe function to be tested
PQkLocalFiniteElementCache<double,double,domainDim,1> feCache;
typedef typename PQkLocalFiniteElementCache<double,double,domainDim,1>::FiniteElementType LocalFiniteElement;
GFE::LocalProjectedFEFunction<domainDim,double,LocalFiniteElement,TargetSpace> f(feCache.get(element),corners);
//testPermutationInvariance(corners);
testDerivative<domainDim>(f);
}
}
int main()
{
// choke on NaN -- don't enable this by default, as there are
// a few harmless NaN in the loopsolver
//feenableexcept(FE_INVALID);
std::cout << std::setw(15) << std::setprecision(12);
////////////////////////////////////////////////////////////////
// Test functions on 1d elements
////////////////////////////////////////////////////////////////
test<RealTuple<double,1>,1>(GeometryTypes::line);
test<UnitVector<double,2>,1>(GeometryTypes::line);
test<UnitVector<double,3>,1>(GeometryTypes::line);
test<Rotation<double,3>,1>(GeometryTypes::line);
test<RigidBodyMotion<double,3>,1>(GeometryTypes::line);
////////////////////////////////////////////////////////////////
// Test functions on 2d simplex elements
////////////////////////////////////////////////////////////////
test<RealTuple<double,1>,2>(GeometryTypes::triangle);
test<UnitVector<double,2>,2>(GeometryTypes::triangle);
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test<RealTuple<double,3>,2>(GeometryTypes::triangle);
test<UnitVector<double,3>,2>(GeometryTypes::triangle);
test<Rotation<double,3>,2>(GeometryTypes::triangle);
test<RigidBodyMotion<double,3>,2>(GeometryTypes::triangle);
////////////////////////////////////////////////////////////////
// Test functions on 2d quadrilateral elements
////////////////////////////////////////////////////////////////
test<RealTuple<double,1>,2>(GeometryTypes::quadrilateral);
test<UnitVector<double,2>,2>(GeometryTypes::quadrilateral);
test<UnitVector<double,3>,2>(GeometryTypes::quadrilateral);
test<Rotation<double,3>,2>(GeometryTypes::quadrilateral);
test<RigidBodyMotion<double,3>,2>(GeometryTypes::quadrilateral);