[UNOPTIMIZED] Sims-Flanagan High-Fidelity Leg Feature

[sbcow]

Contents

• This PR adds the capability of a user to model a Sims-Flanagan leg with a higher fidelity model; specifically, the thrust is now represented by a continuous and constant thrust per segment. The integration is done using a Taylor-adaptive integrator from Heyoka.
• This PR includes testing, the Python API, documentation, plotting functionality, and benchmarks.
• The functionality is unoptimized; the benchmark of the lower and higher fidelity model shows:

Lower fidelity model

Computes the same analytical and numerical gradients and tests for speed:
5 nseg - timing: analytical 0.041078 - numerical 0.09194
10 nseg - timing: analytical 0.078556 - numerical 0.282018
15 nseg - timing: analytical 0.12666399999999997 - numerical 0.5756969999999999
20 nseg - timing: analytical 0.17625000000000005 - numerical 0.957421
70 nseg - timing: analytical 1.0853019999999995 - numerical 10.098478

Higher fidelity model

Computes the same analytical and numerical gradients and tests for speed:
5 nseg - timing: analytical 4.063857 - numerical 117.57327499999998
10 nseg - timing: analytical 4.674794000000002 - numerical 242.16195299999998
JIT session error: Cannot allocate memory
terminate called after throwing an instance of 'std::invalid_argument'
  what():  Could not find the symbol 'd_out_f' in the compiled module

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.20%. Comparing base (285a825) to head (4870cdd).
Report is 25 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #38      +/-   ##
==========================================
+ Coverage   98.10%   98.20%   +0.09%     
==========================================
  Files          30       33       +3     
  Lines        1798     2116     +318     
==========================================
+ Hits         1764     2078     +314     
- Misses         34       38       +4     

Files with missing lines	Coverage Δ
include/kep3/leg/sims_flanagan.hpp	100.00% <100.00%> (ø)
include/kep3/leg/sims_flanagan_hf.hpp	100.00% <100.00%> (ø)
src/core_astro/propagate_lagrangian.cpp	97.69% <100.00%> (-0.76%)	⬇️
src/leg/sf_checks.cpp	100.00% <100.00%> (ø)
src/leg/sims_flanagan.cpp	98.14% <100.00%> (-0.37%)	⬇️
src/leg/sims_flanagan_hf.cpp	100.00% <100.00%> (ø)
src/ta/stark.cpp	100.00% <ø> (ø)

... and 15 files with indirect coverage changes

[sbcow]

With the latest commit, I hope that this PR can be merged or at least reviewed in its entirety; the benchmark now performs more in line with expectations. The HF method is still slower by a factor of almost 20 for 5 segment legs with the analytical gradient, however, this improves for more legs to only a factor of 5. The numerical gradient is slower by a factor of 5 and improves to a factor of 2 for more legs. Below is the updated output of the benchmarks:

Lower fidelity method

Computes the same analytical and numerical gradients and tests for speed:
5 nseg - timing: analytical 0.079302 - numerical 0.37446699999999994
10 nseg - timing: analytical 0.11105100000000001 - numerical 0.8789960000000002
20 nseg - timing: analytical 0.19491599999999992 - numerical 2.4924320000000013
40 nseg - timing: analytical 0.4830399999999998 - numerical 9.198903

Solves the same optimization problems with and without analytical gradients:
xx........xx.....^[.......................xxxx................xx..xx................xx....xx....xx......................xx....xx................xxxxxxxx............................xx..........xx..xx....
5 nseg - success rates: analytical 82/100 - numerical 82/100
..........xx............................xxxx....................xx................xx..........xx......................xx....xx................xxxxxxxx............................xx..........xx..xx....
10 nseg - success rates: analytical 85/100 - numerical 85/100
..........xx..............x.....x.......xxxx....................xx................xx..........xx......................xx....xx................xxxxxxxx............................xx..........xx..xx....
15 nseg - success rates: analytical 83/100 - numerical 85/100

Higher fidelity method

Computes the same analytical and numerical gradients and tests for speed:
5 nseg - timing: analytical 1.419368 - numerical 1.5734220000000003
10 nseg - timing: analytical 1.5456520000000007 - numerical 3.0710530000000005
20 nseg - timing: analytical 1.7754720000000004 - numerical 6.831982999999997
40 nseg - timing: analytical 2.3899 - numerical 18.493235999999992

Solves the same optimization problems with and without analytical gradients:
..........xx............................xxxx................xx..xx................xx..........xx......................xx....xx........xx......xxxxxxxx............................xx..........xx..xx....
5 nseg - success rates: analytical 83/100 - numerical 83/100
..........xx............................xxxx....................xx................xx..........xx......................xx....xx................xxxxxxxx............................xx..........xx..xx....
10 nseg - success rates: analytical 85/100 - numerical 85/100
..........xx................x...........xxxx....................xx................xx..........xx......................xx....xx................xxxxxxxx............................xx..........xx..xx....
15 nseg - success rates: analytical 84/100 - numerical 85/100