loicvhandClaude Opus 5
f1d5a73cc6
The quadric, x(mu), f, f', mu* and the degenerate points now come from quadproj; the script keeps small helpers for what quadproj does not provide: mu**, the asymptotes and the ellipse boundary. The tests check these helpers against brute-force sampling and quadproj.project. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
32 lines
1.3 KiB
Markdown
32 lines
1.3 KiB
Markdown
# mu-trajectories
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Visualize the KKT trajectory of the Euclidean projection of a point `x0` onto an ellipse
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`x'Ax + b'x + c = 0`:
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x(mu) = (I + mu A)^{-1} (x0 - mu b / 2)
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The figure shows the trajectory in the plane, `f(mu) = psi(x(mu))`, the distance
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`||x0 - x(mu)||` and `f'(mu)`, together with the nearest/farthest KKT points `x(mu*)`,
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`x(mu**)` and, when `x0` has a zero standardized coordinate, the degenerate point `x^d`.
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## Usage
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pip install -r requirements.txt
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python plot_mu_trajectories.py # every case, into figures/
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python plot_mu_trajectories.py x_trajectories_mu_2 # a single case
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pytest
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Cases (`A`, `x0`, and optionally `b` and `c`) are listed in `CASES` at the top of
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`plot_mu_trajectories.py`; each one produces `<name>.png` and `<name>.pdf`.
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Text is typeset with LaTeX (`text.usetex`) when `latex` is on the `PATH`, with the `cm-super` and
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`type1cm` packages; otherwise matplotlib's Computer Modern math font is used.
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## Files
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- `plot_mu_trajectories.py`: the figure. The quadric, `x(mu)`, `f`, `f'`, `mu*` and the degenerate
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points come from [quadproj](https://loicvh.gitlab.io/quadproj); the script only adds `mu**`,
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the asymptotes and the ellipse boundary.
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- `test_plot_mu_trajectories.py`: checks these helpers against brute-force sampling of the ellipse
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and against `quadproj.project`.
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