Tests for second derivative of the blending maps
The idea is to create some tests for derivatives of the blending maps, currently I have created some tests here, especially for the AnnulusMap
and IcosahedralMap
.
The first derivatives are tested with Taylor series, we can compare an approximation of the map evalF
at some point with the function value (map) and it's derivative from a nearby point and calculate the error and then check if they are within a certain bound.
Currently the second derivative function evalDFinvDF
calculates the derivative of the inverse transposed Jacobian evalDF
, hence we could directly try to calculate the second derivative with a numerical differentiation scheme and compare the error.
This second derivative test seems to work for the AnnulusMap
but not (yet) for the IcosahedralMap
, here I am not sure if I have messed up or the evalDFinvDF
for IcosahedralMap
has a bug.