Fix complex-valued t_span for complex-valued ODEs in odeint

[gautierronan]

Following up on my PR #178 and on this issue #177.

In the current state of odeint, the time values t are complex-valued if x is initially complex-valued when calling f(t, x) at every time step. Instead, they should be float like. Otherwise, this could be problematic if f(t, x) requires real-valued times (e.g. if f(t, x) = torch.erf(t) * x).

This PR fixes this by making changes to the solver.tableau definitions. The c constants in the tableaus are initialized with a float dtype of the same precision as the (complex or float) dtype of x. This is done by calling t_dtype = getattr(torch, torch.finfo(x.dtype).dtype). If x is float-valued, then t_dtype = x.dtype and things work as usual. Changes in sync_device_dtype were also required to differentiate between the t.dtype and the x.dtype.

Sorry for having missed this in the initial PR !

[codecov-commenter]

Codecov Report

Base: 62.53% // Head: 62.63% // Increases project coverage by +0.09% 🎉

Coverage data is based on head (c068b2b) compared to base (201026a).
Patch coverage: 90.00% of modified lines in pull request are covered.

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Additional details and impacted files

@@            Coverage Diff             @@
##           master     #179      +/-   ##
==========================================
+ Coverage   62.53%   62.63%   +0.09%     
==========================================
  Files          27       27              
  Lines        1879     1884       +5     
==========================================
+ Hits         1175     1180       +5     
  Misses        704      704              

Impacted Files	Coverage Δ
torchdyn/numerics/solvers/ode.py	53.12% <50.00%> (+0.21%)	⬆️
torchdyn/numerics/sensitivity.py	97.95% <100.00%> (ø)
torchdyn/numerics/solvers/_constants.py	100.00% <100.00%> (ø)
torchdyn/numerics/solvers/templates.py	75.00% <100.00%> (+0.58%)	⬆️

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[gautierronan]

Actually, thinking more on this, I'm not sure what's the best practice. Should tspan stay complex-valued to keep every object in the model of the same type? Or should it be real-valued for consistency?

I'm unsure of what's best... I'll let the maintainers decide!

[Zymrael]

Thanks for contributing! It makes sense to keep t real-valued. We don't really have any particular use case at the moment where it becomes convenient to keep x and t of the same dtype.