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#include <config.h>
#include <dune/common/bitfield.hh>
#include <dune/common/configparser.hh>
#include <dune/grid/onedgrid.hh>
#include <dune/istl/io.hh>
#include "../common/iterativesolver.hh"
#include "src/configuration.hh"
#include "src/quaternion.hh"
#include "src/rodassembler.hh"
#include "fdcheck.hh"
// Number of degrees of freedom:
// 7 (x, y, z, q_1, q_2, q_3, q_4) for a spatial rod
const int blocksize = 6;
using namespace Dune;
void testDDExp()
{
std::tr1::array<FieldVector<double,3>, 125> v;
int ct = 0;
double eps = 1e-4;
for (int i=-2; i<3; i++)
for (int j=-2; j<3; j++)
for (int k=-2; k<3; k++) {
v[ct][0] = i;
v[ct][1] = j;
v[ct][2] = k;
ct++;
}
for (size_t i=0; i<v.size(); i++) {
// Compute FD approximation of second derivative of exp
Dune::array<Dune::FieldMatrix<double,3,3>, 4> fdDDExp;
for (int j=0; j<3; j++) {
for (int k=0; k<3; k++) {
if (j==k) {
Quaternion<double> forwardQ = Quaternion<double>::exp(v[i][0] + (j==0)*eps,
v[i][1] + (j==1)*eps,
v[i][2] + (j==2)*eps);
Quaternion<double> centerQ = Quaternion<double>::exp(v[i][0],v[i][1],v[i][2]);
Quaternion<double> backwardQ = Quaternion<double>::exp(v[i][0] - (j==0)*eps,
v[i][1] - (j==1)*eps,
v[i][2] - (j==2)*eps);
for (int l=0; l<4; l++)
fdDDExp[l][j][j] = (forwardQ[l] - 2*centerQ[l] + backwardQ[l]) / (eps*eps);
} else {
FieldVector<double,3> ffV = v[i]; ffV[j] += eps; ffV[k] += eps;
FieldVector<double,3> fbV = v[i]; fbV[j] += eps; fbV[k] -= eps;
FieldVector<double,3> bfV = v[i]; bfV[j] -= eps; bfV[k] += eps;
FieldVector<double,3> bbV = v[i]; bbV[j] -= eps; bbV[k] -= eps;
Quaternion<double> forwardForwardQ = Quaternion<double>::exp(ffV);
Quaternion<double> forwardBackwardQ = Quaternion<double>::exp(fbV);
Quaternion<double> backwardForwardQ = Quaternion<double>::exp(bfV);
Quaternion<double> backwardBackwardQ = Quaternion<double>::exp(bbV);
for (int l=0; l<4; l++)
fdDDExp[l][j][k] = (forwardForwardQ[l] + backwardBackwardQ[l]
- forwardBackwardQ[l] - backwardForwardQ[l]) / (4*eps*eps);
}
}
}
// Compute analytical second derivative of exp
Dune::array<Dune::FieldMatrix<double,3,3>, 4> ddExp;
Quaternion<double>::DDexp(v[i], ddExp);
for (int m=0; m<4; m++)
for (int j=0; j<3; j++)
for (int k=0; k<3; k++)
if ( std::abs(fdDDExp[m][j][k] - ddExp[m][j][k]) > eps) {
std::cout << "Error at v = " << v[i]
<< "[" << m << ", " << j << ", " << k << "] "
<< " fd: " << fdDDExp[m][j][k]
<< " analytical: " << ddExp[m][j][k] << std::endl;
}
}
}
void testDerivativeOfInterpolatedPosition()
{
std::tr1::array<Quaternion<double>, 6> q;
FieldVector<double,3> xAxis(0); xAxis[0] = 1;
FieldVector<double,3> yAxis(0); yAxis[1] = 1;
FieldVector<double,3> zAxis(0); zAxis[2] = 1;
q[0] = Quaternion<double>(xAxis, 0);
q[1] = Quaternion<double>(xAxis, M_PI/2);
q[2] = Quaternion<double>(yAxis, 0);
q[3] = Quaternion<double>(yAxis, M_PI/2);
q[4] = Quaternion<double>(zAxis, 0);
q[5] = Quaternion<double>(zAxis, M_PI/2);
double eps = 1e-7;
for (int i=0; i<6; i++) {
for (int j=0; j<6; j++) {
for (int k=0; k<7; k++) {
double s = k/6.0;
std::tr1::array<Quaternion<double>,6> fdGrad;
// ///////////////////////////////////////////////////////////
// First: test the interpolated position
// ///////////////////////////////////////////////////////////
fdGrad[0] = Quaternion<double>::interpolate(q[i].mult(Quaternion<double>::exp(eps,0,0)), q[j], s);
fdGrad[0] -= Quaternion<double>::interpolate(q[i].mult(Quaternion<double>::exp(-eps,0,0)), q[j], s);
fdGrad[0] /= 2*eps;
fdGrad[1] = Quaternion<double>::interpolate(q[i].mult(Quaternion<double>::exp(0,eps,0)), q[j], s);
fdGrad[1] -= Quaternion<double>::interpolate(q[i].mult(Quaternion<double>::exp(0,-eps,0)), q[j], s);
fdGrad[1] /= 2*eps;
fdGrad[2] = Quaternion<double>::interpolate(q[i].mult(Quaternion<double>::exp(0,0,eps)), q[j], s);
fdGrad[2] -= Quaternion<double>::interpolate(q[i].mult(Quaternion<double>::exp(0,0,-eps)), q[j], s);
fdGrad[2] /= 2*eps;
fdGrad[3] = Quaternion<double>::interpolate(q[i], q[j].mult(Quaternion<double>::exp(eps,0,0)), s);
fdGrad[3] -= Quaternion<double>::interpolate(q[i], q[j].mult(Quaternion<double>::exp(-eps,0,0)), s);
fdGrad[3] /= 2*eps;
fdGrad[4] = Quaternion<double>::interpolate(q[i], q[j].mult(Quaternion<double>::exp(0,eps,0)), s);
fdGrad[4] -= Quaternion<double>::interpolate(q[i], q[j].mult(Quaternion<double>::exp(0,-eps,0)), s);
fdGrad[4] /= 2*eps;
fdGrad[5] = Quaternion<double>::interpolate(q[i], q[j].mult(Quaternion<double>::exp(0,0,eps)), s);
fdGrad[5] -= Quaternion<double>::interpolate(q[i], q[j].mult(Quaternion<double>::exp(0,0,-eps)), s);
fdGrad[5] /= 2*eps;
// Compute analytical gradient
std::tr1::array<Quaternion<double>,6> grad;
RodLocalStiffness<OneDGrid,double>::interpolationDerivative(q[i], q[j], s, grad);
for (int l=0; l<6; l++) {
Quaternion<double> diff = fdGrad[l];
diff -= grad[l];
if (diff.two_norm() > 1e-6) {
std::cout << "Error in position " << l << ": fd: " << fdGrad[l]
<< " analytical: " << grad[l] << std::endl;
}
}
// ///////////////////////////////////////////////////////////
// Second: test the interpolated velocity vector
// ///////////////////////////////////////////////////////////
for (int l=1; l<7; l++) {
double intervalLength = l/(double(3));
fdGrad[0] = Quaternion<double>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(eps,0,0)),
q[j], s, intervalLength);
fdGrad[0] -= Quaternion<double>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(-eps,0,0)),
q[j], s, intervalLength);
fdGrad[0] /= 2*eps;
fdGrad[1] = Quaternion<double>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(0,eps,0)),
q[j], s, intervalLength);
fdGrad[1] -= Quaternion<double>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(0,-eps,0)),
q[j], s, intervalLength);
fdGrad[1] /= 2*eps;
fdGrad[2] = Quaternion<double>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(0,0,eps)),
q[j], s, intervalLength);
fdGrad[2] -= Quaternion<double>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(0,0,-eps)),
q[j], s, intervalLength);
fdGrad[2] /= 2*eps;
fdGrad[3] = Quaternion<double>::interpolateDerivative(q[i], q[j].mult(Quaternion<double>::exp(eps,0,0)), s, intervalLength);
fdGrad[3] -= Quaternion<double>::interpolateDerivative(q[i], q[j].mult(Quaternion<double>::exp(-eps,0,0)), s, intervalLength);
fdGrad[3] /= 2*eps;
fdGrad[4] = Quaternion<double>::interpolateDerivative(q[i], q[j].mult(Quaternion<double>::exp(0,eps,0)), s, intervalLength);
fdGrad[4] -= Quaternion<double>::interpolateDerivative(q[i], q[j].mult(Quaternion<double>::exp(0,-eps,0)), s, intervalLength);
fdGrad[4] /= 2*eps;
fdGrad[5] = Quaternion<double>::interpolateDerivative(q[i], q[j].mult(Quaternion<double>::exp(0,0,eps)), s, intervalLength);
fdGrad[5] -= Quaternion<double>::interpolateDerivative(q[i], q[j].mult(Quaternion<double>::exp(0,0,-eps)), s, intervalLength);
fdGrad[5] /= 2*eps;
// Compute analytical velocity vector gradient
RodLocalStiffness<OneDGrid,double>::interpolationVelocityDerivative(q[i], q[j], s, intervalLength, grad);
for (int m=0; m<6; m++) {
Quaternion<double> diff = fdGrad[m];
diff -= grad[m];
if (diff.two_norm() > 1e-6) {
std::cout << "Error in velocity " << m
<< ": s = " << s << " of (" << intervalLength << ")"
<< " fd: " << fdGrad[m] << " analytical: " << grad[m] << std::endl;
}
}
}
}
}
}
}
int main (int argc, char *argv[]) try
{
// //////////////////////////////////////////////
// Test second derivative of exp
// //////////////////////////////////////////////
testDDExp();
// //////////////////////////////////////////////
// Test derivative of interpolated position
// //////////////////////////////////////////////
testDerivativeOfInterpolatedPosition();
exit(0);
typedef std::vector<Configuration> SolutionType;
// ///////////////////////////////////////
// Create the grid
// ///////////////////////////////////////
typedef OneDGrid GridType;
GridType grid(1, 0, 1);
SolutionType x(grid.size(1));
// //////////////////////////
// Initial solution
// //////////////////////////
FieldVector<double,3> xAxis(0);
xAxis[0] = 1;
FieldVector<double,3> zAxis(0);
zAxis[2] = 1;
for (size_t i=0; i<x.size(); i++) {
x[i].r[0] = 0; // x
x[i].r[1] = 0; // y
x[i].r[2] = double(i)/(x.size()-1); // z
//x[i].r[2] = i+5;
x[i].q = Quaternion<double>::identity();
//x[i].q = Quaternion<double>(zAxis, M_PI/2 * double(i)/(x.size()-1));
}
//x.back().r[1] = 0.1;
//x.back().r[2] = 2;
//x.back().q = Quaternion<double>(zAxis, M_PI/4);
std::cout << "Left boundary orientation:" << std::endl;
std::cout << "director 0: " << x[0].q.director(0) << std::endl;
std::cout << "director 1: " << x[0].q.director(1) << std::endl;
std::cout << "director 2: " << x[0].q.director(2) << std::endl;
std::cout << std::endl;
std::cout << "Right boundary orientation:" << std::endl;
std::cout << "director 0: " << x[x.size()-1].q.director(0) << std::endl;
std::cout << "director 1: " << x[x.size()-1].q.director(1) << std::endl;
std::cout << "director 2: " << x[x.size()-1].q.director(2) << std::endl;
// exit(0);
//x[0].r[2] = -1;
// ///////////////////////////////////////////
// Create a solver for the rod problem
// ///////////////////////////////////////////
RodAssembler<GridType> rodAssembler(grid);
//rodAssembler.setShapeAndMaterial(0.01, 0.0001, 0.0001, 2.5e5, 0.3);
//rodAssembler.setParameters(0,0,0,0,1,0);
rodAssembler.setParameters(0,0,100,0,0,0);
std::cout << "Energy: " << rodAssembler.computeEnergy(x) << std::endl;
double pos = (argc==2) ? atof(argv[1]) : 0.5;
FieldVector<double,1> shapeGrad[2];
shapeGrad[0] = -1;
shapeGrad[1] = 1;
FieldVector<double,1> shapeFunction[2];
shapeFunction[0] = 1-pos;
shapeFunction[1] = pos;
exit(0);
BlockVector<FieldVector<double,6> > rhs(x.size());
BCRSMatrix<FieldMatrix<double,6,6> > hessianMatrix;
MatrixIndexSet indices(grid.size(1), grid.size(1));
rodAssembler.getNeighborsPerVertex(indices);
indices.exportIdx(hessianMatrix);
rodAssembler.assembleGradient(x, rhs);
rodAssembler.assembleMatrix(x, hessianMatrix);
gradientFDCheck(x, rhs, rodAssembler);
hessianFDCheck(x, hessianMatrix, rodAssembler);
// //////////////////////////////
} catch (Exception e) {
std::cout << e << std::endl;
}