diff --git a/test/rotationtest.cc b/test/rotationtest.cc
index 055be5e76fd373edcd4a12524641069dda3671e5..2ecbb3d8ca449fd5e8e1010197480c7fc5f2b9d7 100644
--- a/test/rotationtest.cc
+++ b/test/rotationtest.cc
@@ -35,14 +35,17 @@ void testDDExp()
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);
+
+ SkewMatrix<double,3> forward(v[i]);
+ forward.axial()[j] += eps;
+ Rotation<double,3> forwardQ = Rotation<double,3>::exp(forward);
+
+ SkewMatrix<double,3> center(v[i]);
+ Rotation<double,3> centerQ = Rotation<double,3>::exp(center);
+
+ SkewMatrix<double,3> backward(v[i]);
+ backward.axial()[j] -= eps;
+ Rotation<double,3> backwardQ = Rotation<double,3>::exp(backward);
for (int l=0; l<4; l++)
fdDDExp[l][j][j] = (forwardQ[l] - 2*centerQ[l] + backwardQ[l]) / (eps*eps);
@@ -55,10 +58,10 @@ void testDDExp()
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);
+ Rotation<double,3> forwardForwardQ = Rotation<double,3>::exp(ffV);
+ Rotation<double,3> forwardBackwardQ = Rotation<double,3>::exp(fbV);
+ Rotation<double,3> backwardForwardQ = Rotation<double,3>::exp(bfV);
+ Rotation<double,3> backwardBackwardQ = Rotation<double,3>::exp(bbV);
for (int l=0; l<4; l++)
fdDDExp[l][j][k] = (forwardForwardQ[l] + backwardBackwardQ[l]
@@ -88,18 +91,18 @@ void testDDExp()
void testDerivativeOfInterpolatedPosition()
{
- array<Quaternion<double>, 6> q;
+ array<Rotation<double,3>, 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);
+ q[0] = Rotation<double,3>(xAxis, 0);
+ q[1] = Rotation<double,3>(xAxis, M_PI/2);
+ q[2] = Rotation<double,3>(yAxis, 0);
+ q[3] = Rotation<double,3>(yAxis, M_PI/2);
+ q[4] = Rotation<double,3>(zAxis, 0);
+ q[5] = Rotation<double,3>(zAxis, M_PI/2);
double eps = 1e-7;
@@ -111,41 +114,31 @@ void testDerivativeOfInterpolatedPosition()
double s = k/6.0;
- array<Quaternion<double>,6> fdGrad;
+ array<Rotation<double,3>,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;
+ for (int l=0; l<3; l++) {
+ SkewMatrix<double,3> forward(FieldVector<double,3>(0));
+ SkewMatrix<double,3> backward(FieldVector<double,3>(0));
+ forward.axial()[l] += eps;
+ backward.axial()[l] -= eps;
+ fdGrad[l] = Rotation<double,3>::interpolate(q[i].mult(Rotation<double,3>::exp(forward)), q[j], s);
+ fdGrad[l] -= Rotation<double,3>::interpolate(q[i].mult(Rotation<double,3>::exp(backward)), q[j], s);
+ fdGrad[l] /= 2*eps;
+
+ fdGrad[3+l] = Rotation<double,3>::interpolate(q[i], q[j].mult(Rotation<double,3>::exp(forward)), s);
+ fdGrad[3+l] -= Rotation<double,3>::interpolate(q[i], q[j].mult(Rotation<double,3>::exp(backward)), s);
+ fdGrad[3+l] /= 2*eps;
+ }
// Compute analytical gradient
- array<Quaternion<double>,6> grad;
+ array<Rotation<double,3>,6> grad;
RodLocalStiffness<OneDGrid,double>::interpolationDerivative(q[i], q[j], s, grad);
for (int l=0; l<6; l++) {
- Quaternion<double> diff = fdGrad[l];
+ Rotation<double,3> diff = fdGrad[l];
diff -= grad[l];
if (diff.two_norm() > 1e-6) {
std::cout << "Error in position " << l << ": fd: " << fdGrad[l]
@@ -162,41 +155,41 @@ void testDerivativeOfInterpolatedPosition()
double intervalLength = l/(double(3));
- fdGrad[0] = Rotation<double,3>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(eps,0,0)),
+ fdGrad[0] = Rotation<double,3>::interpolateDerivative(q[i].mult(Rotation<double,3>::exp(eps,0,0)),
q[j], s, intervalLength);
- fdGrad[0] -= Rotation<double,3>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(-eps,0,0)),
+ fdGrad[0] -= Rotation<double,3>::interpolateDerivative(q[i].mult(Rotation<double,3>::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)),
+ fdGrad[1] = Rotation<double,3>::interpolateDerivative(q[i].mult(Rotation<double,3>::exp(0,eps,0)),
q[j], s, intervalLength);
- fdGrad[1] -= Rotation<double,3>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(0,-eps,0)),
+ fdGrad[1] -= Rotation<double,3>::interpolateDerivative(q[i].mult(Rotation<double,3>::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)),
+ fdGrad[2] = Rotation<double,3>::interpolateDerivative(q[i].mult(Rotation<double,3>::exp(0,0,eps)),
q[j], s, intervalLength);
- fdGrad[2] -= Rotation<double,3>::interpolateDerivative(q[i].mult(Quaternion<double>::exp(0,0,-eps)),
+ fdGrad[2] -= Rotation<double,3>::interpolateDerivative(q[i].mult(Rotation<double,3>::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] = Rotation<double,3>::interpolateDerivative(q[i], q[j].mult(Rotation<double,3>::exp(eps,0,0)), s, intervalLength);
+ fdGrad[3] -= Rotation<double,3>::interpolateDerivative(q[i], q[j].mult(Rotation<double,3>::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] = Rotation<double,3>::interpolateDerivative(q[i], q[j].mult(Rotation<double,3>::exp(0,eps,0)), s, intervalLength);
+ fdGrad[4] -= Rotation<double,3>::interpolateDerivative(q[i], q[j].mult(Rotation<double,3>::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] = Rotation<double,3>::interpolateDerivative(q[i], q[j].mult(Rotation<double,3>::exp(0,0,eps)), s, intervalLength);
+ fdGrad[5] -= Rotation<double,3>::interpolateDerivative(q[i], q[j].mult(Rotation<double,3>::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];
+ Rotation<double,3> diff = fdGrad[m];
diff -= grad[m];
if (diff.two_norm() > 1e-6) {
std::cout << "Error in velocity " << m
@@ -243,10 +236,10 @@ void testRotation(Rotation<double,3> q)
Rotation<double,3> newQ;
newQ.set(matrix);
- Quaternion<double> diff = newQ;
+ Rotation<double,3> diff = newQ;
diff -= q;
- Quaternion<double> sum = newQ;
+ Rotation<double,3> sum = newQ;
sum += q;
if (diff.infinity_norm() > 1e-12 && sum.infinity_norm() > 1e-12)
@@ -270,7 +263,7 @@ void testRotation(Rotation<double,3> q)
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));
+ Rotation<double,3> q2(Rotation<double,3>(i,j,k,l));
q2.normalize();
// set up corresponding rotation matrix
@@ -296,7 +289,7 @@ void testRotation(Rotation<double,3> q)
// Check the operators 'B' that create an orthonormal basis of H
// ////////////////////////////////////////////////////////////////
- Quaternion<double> Bq[4];
+ Rotation<double,3> Bq[4];
Bq[0] = q;
Bq[1] = q.B(0);
Bq[2] = q.B(1);