Repository navigation
Draw the warm-up start parameters on the scale of the targets - #173
Merged
Merged
Conversation
oameye
force-pushed
the
fix/warmup-start-scale
branch
from
October 19, 2026 08:58
13f4951 to
3e3f56d
Compare
Start parameters of order one tracked towards targets such as ω0 = 41 and F = 20 make the parameter homotopy ill-conditioned: paths end with terminated_step_size_too_small and solutions are lost, depending on the seed and on the order of the parameters. Each start parameter is now a complex normal draw times the largest magnitude that parameter takes. Over 40 seeds of the issue's system, the old draw lost paths for 4 and the scaled draw for none. Closes #170.
oameye
force-pushed
the
fix/warmup-start-scale
branch
from
October 19, 2026 09:21
3e3f56d to
5f6294a
Compare
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Closes #170.
Diagnosis
For the system of #170 the warm-up solve finds all 9 solutions at the random start point for every seed. The loss happens in the parameter homotopy from that point to the targets: for seed 5, 5 of the 9 paths end with
terminated_step_size_too_small. The start parameters were drawn with magnitude of order one, while the targets include ω0 = 41.14 and F = 20, so the straight-line path is a relative change of order 40 in some directions and passes through badly conditioned regions.Fix
random_start_parametersdraws each start parameter as a standard complex normal number times the largest magnitude that parameter takes in the sweep (1 if it is zero throughout). The homotopy to every target is then a relative change of order one. Explicitstart_parametersare used as before.Evidence
Seeds 1 to 40 on the issue's system:
The regression test runs seeds 1 to 12 on that system and requires 9 solutions each (1.3 s in total once warm); before, seed 5 found 4.