From 71dcca73520cc1c76f419eaa23994e259943b6e8 Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Thu, 15 Mar 2012 07:51:03 +0000
Subject: [PATCH] Add test for the derivative of rotations mapped into the
space of orthogonal matrices.
[[Imported from SVN: r8573]]
---
test/cosseratenergytest.cc | 235 +++++++++++++++++++++++++++++++++++--
1 file changed, 225 insertions(+), 10 deletions(-)
diff --git a/test/cosseratenergytest.cc b/test/cosseratenergytest.cc
index 49467608..de698606 100644
--- a/test/cosseratenergytest.cc
+++ b/test/cosseratenergytest.cc
@@ -1,6 +1,7 @@
#include "config.h"
#include <dune/grid/uggrid.hh>
+#include <dune/grid/onedgrid.hh>
#include <dune/geometry/type.hh>
#include <dune/geometry/quadraturerules.hh>
@@ -15,6 +16,10 @@
#include "multiindex.hh"
#include "valuefactory.hh"
+#ifdef COSSERAT_ENERGY_FD_GRADIENT
+#warning Comparing two finite-difference approximations
+#endif
+
const double eps = 1e-4;
typedef RigidBodyMotion<double,3> TargetSpace;
@@ -22,6 +27,19 @@ typedef RigidBodyMotion<double,3> TargetSpace;
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, Rotation<double,3>::distance(v[i].q,v[j].q));
+ return d;
+}
+
+
+
// ////////////////////////////////////////////////////////
// Make a test grid consisting of a single simplex
// ////////////////////////////////////////////////////////
@@ -236,6 +254,195 @@ void testFrameInvariance()
}
+template <int domainDim, class LocalFiniteElement>
+void
+evaluateFD_dDR_WRTCoefficient(const LocalGeodesicFEFunction<domainDim,double,LocalFiniteElement,RigidBodyMotion<double,3> >& f,
+ const Dune::FieldVector<double, domainDim>& local,
+ int coefficient,
+ Dune::array<Tensor3<double,3,3,4>, 3>& result)
+{
+ typedef RigidBodyMotion<double,3> TargetSpace;
+ typedef double ctype;
+
+ double eps = 1e-3;
+
+ for (int j=0; j<4; j++) {
+
+ assert(f.type().isSimplex());
+
+ int ncoeff = domainDim+1;
+ std::vector<TargetSpace> cornersPlus(ncoeff);
+ std::vector<TargetSpace> cornersMinus(ncoeff);
+ for (int k=0; k<ncoeff; k++)
+ cornersMinus[k] = cornersPlus[k] = f.coefficient(k);
+
+ typename TargetSpace::CoordinateType aPlus = f.coefficient(coefficient).globalCoordinates();
+ typename TargetSpace::CoordinateType aMinus = f.coefficient(coefficient).globalCoordinates();
+ aPlus[j+3] += eps;
+ aMinus[j+3] -= eps;
+ cornersPlus[coefficient] = TargetSpace(aPlus);
+ cornersMinus[coefficient] = TargetSpace(aMinus);
+ LocalGeodesicFEFunction<domainDim,double,LocalFiniteElement,TargetSpace> fPlus(f.localFiniteElement_,cornersPlus);
+ LocalGeodesicFEFunction<domainDim,double,LocalFiniteElement,TargetSpace> fMinus(f.localFiniteElement_,cornersMinus);
+
+ TargetSpace qPlus = fPlus.evaluate(local);
+ FieldMatrix<double,7,domainDim> qDerPlus = fPlus.evaluateDerivative(local);
+ TargetSpace qMinus = fMinus.evaluate(local);
+ FieldMatrix<double,7,domainDim> qDerMinus = fMinus.evaluateDerivative(local);
+ Tensor3<double,3,3,3> DRPlus,DRMinus;
+
+ typedef typename SelectType<domainDim==1,OneDGrid,UGGrid<domainDim> >::Type GridType;
+ CosseratEnergyLocalStiffness<typename GridType::LeafGridView,LocalFiniteElement,3>::computeDR(qPlus,qDerPlus,DRPlus);
+ CosseratEnergyLocalStiffness<typename GridType::LeafGridView,LocalFiniteElement,3>::computeDR(qMinus,qDerMinus,DRMinus);
+
+ for (int i=0; i<3; i++)
+ for (int k=0; k<3; k++)
+ for (int l=0; l<3; l++)
+ result[i][k][l][j] = (DRPlus[i][k][l] - DRMinus[i][k][l]) / (2*eps);
+
+ }
+
+ // Project onto the tangent space at M(q)
+ TargetSpace q = f.evaluate(local);
+ Dune::FieldMatrix<double,3,3> Mtmp;
+ q.q.matrix(Mtmp);
+ OrthogonalMatrix<double,3> M(Mtmp);
+
+ for (int k=0; k<domainDim; k++)
+ for (int v_i=0; v_i<4; v_i++) {
+
+ Dune::FieldMatrix<double,3,3> unprojected;
+ for (int i=0; i<3; i++)
+ for (int j=0; j<3; j++)
+ unprojected[i][j] = result[i][j][k][v_i];
+
+ Dune::FieldMatrix<double,3,3> projected = M.projectOntoTangentSpace(unprojected);
+
+ for (int i=0; i<3; i++)
+ for (int j=0; j<3; j++)
+ result[i][j][k][v_i] = projected[i][j];
+ }
+
+}
+
+
+
+template <int domainDim, class GridType, class LocalFiniteElement>
+void testDerivativeOfGradientOfRotationMatrixWRTCoefficient(const LocalGeodesicFEFunction<domainDim,double,LocalFiniteElement,RigidBodyMotion<double,3> >& f,
+ const FieldVector<double,domainDim>& local,
+ unsigned int coeff)
+{
+ RigidBodyMotion<double,3> value = f.evaluate(local);
+ FieldMatrix<double,7,domainDim> derOfValueWRTx = f.evaluateDerivative(local);
+
+ FieldMatrix<double,7,7> derOfValueWRTCoefficient;
+ f.evaluateDerivativeOfValueWRTCoefficient(local, coeff, derOfValueWRTCoefficient);
+
+ Tensor3<double,7,7,domainDim> derOfGradientWRTCoefficient;
+ f.evaluateDerivativeOfGradientWRTCoefficient(local, coeff, derOfGradientWRTCoefficient);
+
+ Tensor3<double,7,7,domainDim> FDderOfGradientWRTCoefficient;
+ f.evaluateFDDerivativeOfGradientWRTCoefficient(local, coeff, FDderOfGradientWRTCoefficient);
+
+ // Evaluate the analytical derivative
+ Dune::array<Tensor3<double,3,3,4>, 3> dDR_dv;
+
+ CosseratEnergyLocalStiffness<typename GridType::LeafGridView,LocalFiniteElement,3>::compute_dDR_dv(value,
+ derOfValueWRTx,
+ derOfValueWRTCoefficient,
+ derOfGradientWRTCoefficient,
+ dDR_dv);
+
+ Dune::array<Tensor3<double,3,3,4>, 3> dDR_dv_FD;
+
+ evaluateFD_dDR_WRTCoefficient<domainDim,LocalFiniteElement>(f,local, coeff, dDR_dv_FD);
+
+ // Check whether the two are the same
+ double maxError = 0;
+ for (size_t j=0; j<3; j++)
+ for (size_t k=0; k<3; k++)
+ for (size_t l=0; l<3; l++)
+ for (size_t m=0; m<4; m++) {
+ double diff = std::fabs(dDR_dv[j][k][l][m] - dDR_dv_FD[j][k][l][m]);
+ maxError = std::max(maxError, diff);
+ }
+
+ if (maxError > 1e-3) {
+
+ std::cout << "Analytical and FD derivatives differ!"
+ << " local: " << local
+ << " coefficient: " << coeff << std::endl;
+
+ std::cout << "dDR_dv" << std::endl;
+ for (size_t i=0; i<dDR_dv.size(); i++)
+ std::cout << dDR_dv[i] << std::endl << std::endl;
+
+ std::cout << "finite differences: dDR_dv" << std::endl;
+ std::cout << dDR_dv_FD << std::endl;
+
+ abort();
+ }
+
+}
+
+template <int domainDim>
+void testDerivativeOfGradientOfRotationMatrixWRTCoefficient()
+{
+ std::cout << " --- test derivative of gradient of rotation matrix wrt coefficient ---" << std::endl;
+
+ // we just need the type
+ typedef typename SelectType<domainDim==1,OneDGrid,UGGrid<domainDim> >::Type GridType;
+
+ std::vector<TargetSpace> testPoints;
+ ValueFactory<TargetSpace>::get(testPoints);
+
+ // Set up elements of SE(3)
+ std::vector<TargetSpace> coefficients(domainDim+1);
+
+ MultiIndex index(domainDim+1, testPoints.size());
+ int numIndices = index.cycle();
+
+ for (int i=0; i<numIndices; i++, ++index) {
+
+ std::cout << "testing der of grad index: " << i << std::endl;
+
+ for (int j=0; j<domainDim+1; j++)
+ coefficients[j] = testPoints[index[j]];
+
+ if (diameter(coefficients) > M_PI-0.1) {
+ std::cout << "skipping, diameter = " << diameter(coefficients) << std::endl;
+ continue;
+ }
+
+ PQkLocalFiniteElementCache<double,double,GridType::dimension,1> feCache;
+ typedef typename PQkLocalFiniteElementCache<double,double,GridType::dimension,1>::FiniteElementType LocalFiniteElement;
+
+ GeometryType simplex;
+ simplex.makeSimplex(domainDim);
+ LocalGeodesicFEFunction<GridType::dimension,double,LocalFiniteElement,RigidBodyMotion<double,3> > f(feCache.get(simplex),coefficients);
+
+ // Loop over the coefficients -- we test derivation with respect to each of them
+ for (size_t j=0; j<coefficients.size(); j++) {
+
+ // A quadrature rule as a set of test points
+ int quadOrder = 3;
+
+ const Dune::QuadratureRule<double, domainDim>& quad
+ = Dune::QuadratureRules<double, domainDim>::rule(GeometryType(GeometryType::simplex,domainDim), quadOrder);
+
+ for (size_t pt=0; pt<quad.size(); pt++) {
+
+ testDerivativeOfGradientOfRotationMatrixWRTCoefficient<domainDim,GridType,LocalFiniteElement>(f, quad[pt].position(), j);
+
+ }
+
+ }
+
+ }
+
+}
+
+
template <int domainDim>
void testEnergyGradient()
@@ -291,9 +498,16 @@ void testEnergyGradient()
for (int i=0; i<numIndices; i++, ++index) {
+ std::cout << "testing index: " << i << std::endl;
+
for (int j=0; j<domainDim+1; j++)
coefficients[j] = testPoints[index[j]];
+ if (diameter(coefficients) > M_PI-0.05) {
+ std::cout << "skipped, diameter: " << diameter(coefficients) << std::endl;
+ continue;
+ }
+
// Compute the analytical gradient
assembler.assembleGradient(*grid->template leafbegin<0>(),
feCache.get(grid->template leafbegin<0>()->type()),
@@ -309,16 +523,14 @@ void testEnergyGradient()
fdGradient);
// Check whether the two are the same
- double diff = 0;
+ double maxError = 0;
for (size_t j=0; j<gradient.size(); j++)
- for (size_t k=0; k<gradient[j].size(); k++)
- diff = std::max(diff, std::fabs(gradient[j][k] - fdGradient[j][k]));
-
- double maxRelError = 0;
- for (size_t j=0; j<gradient.size(); j++)
- maxRelError = std::max(maxRelError, diff/gradient[j].infinity_norm());
+ for (size_t k=0; k<gradient[j].size(); k++) {
+ double diff = std::abs(gradient[j][k] - fdGradient[j][k]);
+ maxError = std::max(maxError, diff);
+ }
- if (maxRelError > 1e-3) {
+ if (maxError > 1e-3) {
std::cout << "Analytical and FD gradients differ!" << std::endl;
@@ -373,8 +585,11 @@ int main(int argc, char** argv) try
//////////////////////////////////////////////////////////////////////////////////////
// Test the gradient of the energy functional
//////////////////////////////////////////////////////////////////////////////////////
-
- testEnergyGradient<domainDim>();
+
+ testDerivativeOfGradientOfRotationMatrixWRTCoefficient<1>();
+ testDerivativeOfGradientOfRotationMatrixWRTCoefficient<2>();
+
+ testEnergyGradient<2>();
} catch (Exception e) {
--
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