NWTC Library: Adjust subroutines for converting between DCM and small angles

[bjonkman]

Feature or improvement description
Adjusted subroutines for computing small angles from DCM and the inverse routines to compute DCMs from small angles. These equations are accurate for larger angles.

Related issue, if one exists

Impacted areas of the software

Additional supporting information

Test results, if applicable

• r-test branch merging required?

[jjonkman]

This matches what I would expect, with one change.

[jjonkman]

Never mind. I see from the plan that the 2's cancel. This implementation looks correct. Thanks!

[bjonkman]

I looped through different angles, converting them to DCMs and then calling this code to get the "small" angles from of the DCM. I then plotted the difference between the starting angle and the calculated angles. As you can see, the error is small (taking into account for all 3 dimensions, the error was no larger than 1.1e-13 degrees).

For reference, this is the plot with the original algorithm that we have now replaced:

[andrew-platt]

I'll look review the regression test changes and update them in the next few days for merging. Thanks @bjonkman!

[deslaughter]

I think this is ready to merge. The ATLAS blas seemed to give clean regression tests without having to rerun any. I say we try it and see.