Failure of rotationtest.cc

On my machine the test for the interpolation of the velocity vector fails. I think it is because the finite difference method is always using interpolateDerivative on the unit interval [0,1], while the analytical linearisation is evaluated on the interval [0,intervalLength]. When I fix intervalLength = 1 the test passes. Am I missing something?

mentioned in merge request !3 (closed)

Hi Jonny, apologies for not looking into this earlier. I think you are correct and the proper scaling of the FD gradient was missing.

Does !3 (closed) look good to you? Then please merge.

Unfortunately, even with !3 (closed) , rotationtest.cc still fails (just a bit later). @jyouett , could you have a look?

Ideally, I'd like to get rid of the interpolation methods in rodlocalstiffness.hh, and use the general code in LocalGeodesicFEFunction instead. But that needs proper testing to not break anything.

I will have a look.

Concerning the second point, I actually encountered some problems when using the general code: Ipopt which is used to solve the small optimisation problems is not always converging. I think it happened when the quaternions representing rotations were not on the same half of the coverage. I can try to reproduce the error and write a test

I am at this very moment hunting a bug in the SO(3)-valued interpolation that sounds very much what you describe. I've already got it cornered in quite closely. Could you rather have a look at why rotationtest.cc stills fails with !3 (closed) ? Thanks!

Is it maybe the one from !1 (merged) ?

No, I tried that.

I also ran into another "error" in the difference method, which is used in the interpolation: When the quaternions are not on the same coverage the fourth entry may become smaller than -1 which should be captured the same way as it is done for the case > 1 I fixed it by extending the test to if (std::fabs(diff[3]) > 1.0)

I think I found out why the test is not running: The method Rotation::interpolateDerivative assumes that the interval is of length 1. Hence the finite difference gradients, which are computed by this interpolation method, are different when checked against the analytic ones on a scaled interval. Further, this dependency is non-linear (I think) which is why one cannot simply re-scale the FD gradients afterwards. I wrote a second method Rotation::interpolateDerivative(intervalLength) which takes into account a general interval length. With this method the test runs (without the changes in !3 (closed)) I attach it hereinterpolateDerivativeWithSteplength.h

Okay I found the bug: The method LocalRodStiffness::interpolationVelocityDerivative expects an input value from the interval [0,IntervalLength]. The test however puts in a value from the unit interval. By changing the input from s to s*intervalLength the test passes again (without using the method I attached)

mentioned in commit 337ee871

mentioned in merge request !5 (merged)

closed via commit 25220fbc

closed via merge request !5 (merged)

closed via commit 337ee871