#include <config.h>
#include <iostream>
#include <dune/common/fmatrix.hh>
#include <dune/gfe/rotation.hh>
#include <dune/gfe/svd.hh>
#include "valuefactory.hh"
using namespace Dune;
void testDDExp()
{
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 {
SkewMatrix<double,3> ffV(v[i]); ffV.axial()[j] += eps; ffV.axial()[k] += eps;
SkewMatrix<double,3> fbV(v[i]); fbV.axial()[j] += eps; fbV.axial()[k] -= eps;
SkewMatrix<double,3> bfV(v[i]); bfV.axial()[j] -= eps; bfV.axial()[k] += eps;
SkewMatrix<double,3> bbV(v[i]); bbV.axial()[j] -= eps; bbV.axial()[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;
Rotation<double,3>::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()
{
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;
array<Quaternion<double>,6> fdGrad;
// ///////////////////////////////////////////////////////////
// First: test the interpolated position
// ///////////////////////////////////////////////////////////
fdGrad[0] = Rotation<double,3>::interpolate(q[i].mult(Quaternion<double>::exp(eps,0,0)), q[j], s);
fdGrad[0] -= Rotation<double,3>::interpolate(q[i].mult(Quaternion<double>::exp(-eps,0,0)), q[j], s);
fdGrad[0] /= 2*eps;
fdGrad[1] = Rotation<double,3>::interpolate(q[i].mult(Quaternion<double>::exp(0,eps,0)), q[j], s);
fdGrad[1] -= Rotation<double,3>::interpolate(q[i].mult(Quaternion<double>::exp(0,-eps,0)), q[j], s);
fdGrad[1] /= 2*eps;
fdGrad[2] = Rotation<double,3>::interpolate(q[i].mult(Quaternion<double>::exp(0,0,eps)), q[j], s);
fdGrad[2] -= Rotation<double,3>::interpolate(q[i].mult(Quaternion<double>::exp(0,0,-eps)), q[j], s);
fdGrad[2] /= 2*eps;
fdGrad[3] = Rotation<double,3>::interpolate(q[i], q[j].mult(Quaternion<double>::exp(eps,0,0)), s);
fdGrad[3] -= Rotation<double,3>::interpolate(q[i], q[j].mult(Quaternion<double>::exp(-eps,0,0)), s);
fdGrad[3] /= 2*eps;
fdGrad[4] = Rotation<double,3>::interpolate(q[i], q[j].mult(Quaternion<double>::exp(0,eps,0)), s);
fdGrad[4] -= Rotation<double,3>::interpolate(q[i], q[j].mult(Quaternion<double>::exp(0,-eps,0)), s);
fdGrad[4] /= 2*eps;
fdGrad[5] = Rotation<double,3>::interpolate(q[i], q[j].mult(Quaternion<double>::exp(0,0,eps)), s);
fdGrad[5] -= Rotation<double,3>::interpolate(q[i], q[j].mult(Quaternion<double>::exp(0,0,-eps)), s);
fdGrad[5] /= 2*eps;
// Compute analytical gradient
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] = Rotation<double,3>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(eps,0,0)),
q[j], s, intervalLength);
fdGrad[0] -= Rotation<double,3>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(-eps,0,0)),
q[j], s, intervalLength);
fdGrad[0] /= 2*eps;
fdGrad[1] = Rotation<double,3>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(0,eps,0)),
q[j], s, intervalLength);
fdGrad[1] -= Rotation<double,3>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(0,-eps,0)),
q[j], s, intervalLength);
fdGrad[1] /= 2*eps;
fdGrad[2] = Rotation<double,3>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(0,0,eps)),
q[j], s, intervalLength);
fdGrad[2] -= Rotation<double,3>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(0,0,-eps)),
q[j], s, intervalLength);
fdGrad[2] /= 2*eps;
fdGrad[3] = Rotation<double,3>::interpolateDerivative(q[i], q[j].mult(Quaternion<double>::exp(eps,0,0)), s, intervalLength);
fdGrad[3] -= Rotation<double,3>::interpolateDerivative(q[i], q[j].mult(Quaternion<double>::exp(-eps,0,0)), s, intervalLength);
fdGrad[3] /= 2*eps;
fdGrad[4] = Rotation<double,3>::interpolateDerivative(q[i], q[j].mult(Quaternion<double>::exp(0,eps,0)), s, intervalLength);
fdGrad[4] -= Rotation<double,3>::interpolateDerivative(q[i], q[j].mult(Quaternion<double>::exp(0,-eps,0)), s, intervalLength);
fdGrad[4] /= 2*eps;
fdGrad[5] = Rotation<double,3>::interpolateDerivative(q[i], q[j].mult(Quaternion<double>::exp(0,0,eps)), s, intervalLength);
fdGrad[5] -= Rotation<double,3>::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;
}
}
}
}
}
}
}
void testRotation(Rotation<double,3> q)
{
// Make sure it really is a unit quaternion
q.normalize();
assert(std::abs(1-q.two_norm()) < 1e-12);
// Turn it into a matrix
FieldMatrix<double,3,3> matrix;
q.matrix(matrix);
// make sure it is an orthogonal matrix
if (std::abs(1-matrix.determinant()) > 1e-12 )
DUNE_THROW(Exception, "Expected determinant 1, but the computed value is " << matrix.determinant());
assert( std::abs( matrix[0]*matrix[1] ) < 1e-12 );
assert( std::abs( matrix[0]*matrix[2] ) < 1e-12 );
assert( std::abs( matrix[1]*matrix[2] ) < 1e-12 );
// Turn the matrix back into a quaternion, and check whether it is the same one
// Since the quaternions form a double covering of SO(3), we may either get q back
// or -q. We have to check both.
Rotation<double,3> newQ;
newQ.set(matrix);
Quaternion<double> diff = newQ;
diff -= q;
Quaternion<double> sum = newQ;
sum += q;
if (diff.infinity_norm() > 1e-12 && sum.infinity_norm() > 1e-12)
DUNE_THROW(Exception, "Backtransformation failed for " << q << ". ");
// //////////////////////////////////////////////////////
// Check the director vectors
// //////////////////////////////////////////////////////
for (int i=0; i<3; i++)
for (int j=0; j<3; j++)
assert( std::abs(matrix[i][j] - q.director(j)[i]) < 1e-12 );
// //////////////////////////////////////////////////////
// Check multiplication with another unit quaternion
// //////////////////////////////////////////////////////
for (int i=-2; i<2; i++)
for (int j=-2; j<2; j++)
for (int k=-2; k<2; k++)
for (int l=-2; l<2; l++)
if (i!=0 || j!=0 || k!=0 || l!=0) {
Rotation<double,3> q2(Quaternion<double>(i,j,k,l));
q2.normalize();
// set up corresponding rotation matrix
FieldMatrix<double,3,3> q2Matrix;
q2.matrix(q2Matrix);
// q2 = q2 * q Quaternion multiplication
q2 = q2.mult(q);
// q2 = q2 * q Matrix multiplication
q2Matrix.rightmultiply(matrix);
FieldMatrix<double,3,3> productMatrix;
q2.matrix(productMatrix);
// Make sure we got identical results
productMatrix -= q2Matrix;
assert(productMatrix.infinity_norm() < 1e-10);
}
// ////////////////////////////////////////////////////////////////
// Check the operators 'B' that create an orthonormal basis of H
// ////////////////////////////////////////////////////////////////
Quaternion<double> Bq[4];
Bq[0] = q;
Bq[1] = q.B(0);
Bq[2] = q.B(1);
Bq[3] = q.B(2);
for (int i=0; i<4; i++) {
for (int j=0; j<4; j++) {
double prod = Bq[i]*Bq[j];
assert( std::abs( prod - (i==j) ) < 1e-6 );
}
}
}
int main (int argc, char *argv[]) try
{
std::vector<Rotation<double,3> > testPoints;
ValueFactory<Rotation<double,3> >::get(testPoints);
int nTestPoints = testPoints.size();
// Test each element in the list
for (int i=0; i<nTestPoints; i++)
testRotation(testPoints[i]);
// //////////////////////////////////////////////
// Test second derivative of exp
// //////////////////////////////////////////////
testDDExp();
// //////////////////////////////////////////////
// Test derivative of interpolated position
// //////////////////////////////////////////////
testDerivativeOfInterpolatedPosition();
} catch (Exception e) {
std::cout << e << std::endl;
}