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
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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
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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
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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
5652719642
Require triangle sides to be planar
2024-07-09 14:10:23 -07:00
Aaron Fenyes
f84d475580
Visualize neighborhoods of global minima
2024-07-09 14:01:30 -07:00
Aaron Fenyes
77bc124170
Change loss function to match gradient
2024-07-09 14:00:24 -07:00
Aaron Fenyes
023759a267
Start "circles in triangle" from a very close guess
2024-07-08 14:21:10 -07:00
Aaron Fenyes
610fc451f0
Track slope in gradient descent history
2024-07-08 14:19:25 -07:00
Aaron Fenyes
93dd05c317
Add required package to "sphere in tetrahedron" example
2024-07-08 14:19:05 -07:00
Aaron Fenyes
9efa99e8be
Test gradient descent for circles in triangle
2024-07-08 12:56:28 -07:00
Aaron Fenyes
828498b3de
Add sphere and plane utilities to engine
2024-07-08 12:56:14 -07:00
Aaron Fenyes
736ac50b07
Test gradient descent for sphere in tetrahedron
2024-07-07 17:58:55 -07:00
Aaron Fenyes
ea354b6c2b
Randomize guess in gradient descent test
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Randomly perturb the pre-solved part of the guess, and randomly choose
the unsolved part.
2024-07-07 17:56:12 -07:00
Aaron Fenyes
d39244d308
Host Ganja.js locally
2024-07-06 21:35:09 -07:00
Aaron Fenyes
7e94fef19e
Improve random vector generator
2024-07-06 21:32:43 -07:00
Aaron Fenyes
abc53b4705
Sketch random vector generator
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This needs to be rewritten: it can fail at generating spacelike vectors.
2024-07-02 17:16:31 -07:00
Aaron Fenyes
17fefff61e
Name gradient descent test more specifically
2024-07-02 17:16:19 -07:00
Aaron Fenyes
133519cacb
Encapsulate gradient descent code
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The completed gram matrix from this commit matches the one from commit
e7dde58
2024-07-02 15:02:59 -07:00
Aaron Fenyes
e7dde5800c
Do gradient descent entirely in BigFloat
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The previos version accidentally returned steps in Float64.
2024-07-02 12:35:12 -07:00
Aaron Fenyes
c933e07312
Switch to Ganja.js basis ordering
2024-06-26 11:39:34 -07:00
Aaron Fenyes
2b6c4f4720
Avoid naming conflict with identity transformation
2024-06-26 11:28:47 -07:00
Aaron Fenyes
4a28a47520
Update namespace of AbstractAlgebra.Rationals
2024-06-26 01:06:27 -07:00
Aaron Fenyes
58a5c38e62
Try numerical low-rank factorization
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The best technique I've found so far is the homemade gradient descent
routine in `descent-test.jl`.
2024-05-30 00:36:03 -07:00
Aaron Fenyes
ef33b8ee10
Correct signature
2024-03-01 13:26:20 -05:00
Aaron Fenyes
717e5a6200
Extend Gram matrix automatically
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The signature of the Minkowski form on the subspace spanned by the Gram
matrix should tell us what the big Gram matrix has to look like
2024-02-21 03:00:06 -05:00
Aaron Fenyes
16826cf07c
Try out the Gram matrix approach
2024-02-20 22:35:24 -05:00
