Commit Graph

22 Commits

Author SHA1 Message Date
Aaron Fenyes
b24dcc9af8 Report success correctly when step limit is reached 2024-07-18 01:04:40 -07:00
Aaron Fenyes
74c7f64b0c Correct sign of normal in plane utility
Clarify the relevant notes too.
2024-07-18 00:03:12 -07:00
Aaron Fenyes
d0340c0b65 Correct point utility again
The balance between the light cone basis vectors was wrong, throwing the
point's coordinates off by a factor of two.
2024-07-17 23:37:28 -07:00
Aaron Fenyes
69a704d414 Use notes' sign convention for light cone basis 2024-07-17 23:07:34 -07:00
Aaron Fenyes
d51d43f481 Correct point utility 2024-07-17 18:27:22 -07:00
Aaron Fenyes
2038103d80 Write examples directly in light cone basis 2024-07-17 15:37:14 -07:00
Aaron Fenyes
bde42ebac0 Switch engine to light cone basis 2024-07-17 14:30:43 -07:00
Aaron Fenyes
1ce609836b Implement frozen variables 2024-07-15 22:11:54 -07:00
Aaron Fenyes
b185fd4b83 Switch to backtracking Newton's method in Optim
This performs much better than the trust region Newton's method for the
actual `circles-in-triangle` problem. (The trust region method performs
better for the simplified problem produced by the conversion bug.)
2024-07-15 15:52:38 -07:00
Aaron Fenyes
94e0d321d5 Switch back to BigFloat precision in examples 2024-07-15 14:31:30 -07:00
Aaron Fenyes
53d8c38047 Preserve explicit zeros in Gram matrix conversion
In previous commits, the `circles-in-triangle` example converged much
more slowly in BigFloat precision than in Float64 precision. This
turned out to be a sign of a bug in the Float64 computation: converting
the Gram matrix using `Float64.()` dropped the explicit zeros, removing
many constraints and making the problem much easier to solve. This
commit corrects the Gram matrix conversion. The Float64 search now
solves the same problem as the BigFloat search, with comparable
performance.
2024-07-15 14:08:57 -07:00
Aaron Fenyes
7b3efbc385 Clean up backtracking gradient descent code
Drop experimental singularity handling strategies. Reduce the default
tolerance to within 64-bit floating point precision. Report success.
2024-07-15 13:15:15 -07:00
Aaron Fenyes
25b09ebf92 Sketch backtracking Newton's method
This code is a mess, but I'm committing it to record a working state
before I start trying to clean up.
2024-07-15 11:32:04 -07:00
Aaron Fenyes
3910b9f740 Use Newton's method for polishing 2024-07-11 13:43:52 -07:00
Aaron Fenyes
d538cbf716 Correct improvement threshold by using unit step
Our formula for the improvement theshold works when the step size is
an absolute distance. However, in commit `4d5ea06`, the step size was
measured relative to the current gradient instead. This commit scales
the base step to unit length, so now the step size really is an absolute
distance.
2024-07-10 23:31:44 -07:00
Aaron Fenyes
4d5ea062a3 Record gradient and last line search in history 2024-07-09 15:00:13 -07:00
Aaron Fenyes
77bc124170 Change loss function to match gradient 2024-07-09 14:00:24 -07:00
Aaron Fenyes
610fc451f0 Track slope in gradient descent history 2024-07-08 14:19:25 -07:00
Aaron Fenyes
828498b3de Add sphere and plane utilities to engine 2024-07-08 12:56:14 -07:00
Aaron Fenyes
7e94fef19e Improve random vector generator 2024-07-06 21:32:43 -07:00
Aaron Fenyes
abc53b4705 Sketch random vector generator
This needs to be rewritten: it can fail at generating spacelike vectors.
2024-07-02 17:16:31 -07:00
Aaron Fenyes
133519cacb Encapsulate gradient descent code
The completed gram matrix from this commit matches the one from commit
e7dde58 to six decimal places.
2024-07-02 15:02:59 -07:00