could I check the symbolic derivative equation of my residual function?

[dong-won-shin]

Hello, thanks for this great nonlinear optimization library.

I want to check the result of derivated equation of my residual function to debug it step by step. Is it possible to see the results from symengine?

in case of the rotation parameters, does symengine derive by angle-axis paramterization?

my jacobian values by angle-axis parameterization and the jacobian values by symengine look quite different.

[dong-won-shin]

does jacobian_helpers.py related to the equation? https://github.com/symforce-org/symforce/blob/main/symforce/jacobian_helpers.py

[aaron-skydio]

Yeah you can look at the symbolic expressions for the jacobians - assuming you're getting jacobians using Codegen.with_linearization or Codegen.with_jacobians, yes those call jacobian_helpers.tangent_jacobians internally. You should be able to get the equivalent expression by calling tangent_jacobians on your expression yourself. You could also look at the outputs field on the Codegen object returned from with_linearization or with_jacobians, which should include the symbolic expressions for any jacobians added by those methods.

The jacobians are computed with respect to the SO(3) tangent space (technically the coordinate space) at the input element - depending on what exactly you mean by the angle-axis parameterization, what you may be seeing is the difference between what we're computing: $$\left. \frac{\partial}{\partial v} \left[ r(R.\mathrm{retract}(v)) \right] \right|_{v=0}$$

and this: $$\left. \frac{\partial}{\partial v} \left[ r(\mathrm{from\_tangent}(\mathrm{to\_tangent}(R) + v)) \right] \right|_{v=0}$$

[dong-won-shin]

great! thanks for your answer! I'll look into the details of jacobian_helpers.tangent_jacobians function. thanks!