loicvhandClaude Opus 5
b2b782394a
Cleaned-up extraction of test_mu_ellipse from proj_ellipsoid: - quadric.py: minimal Ellipsoid class (standardization, KKT trajectory, extreme roots by exact bracketing, degenerate points, asymptotes). - plot_mu_trajectories.py: the 4-panel figure, typeset with LaTeX. - test_quadric.py: checks against brute-force sampling of the ellipse. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
29 lines
1.1 KiB
Markdown
29 lines
1.1 KiB
Markdown
# mu-trajectories
|
|
|
|
Visualize the KKT trajectory of the Euclidean projection of a point `x0` onto an ellipse
|
|
`x'Ax + b'x + c = 0`:
|
|
|
|
x(mu) = (I + mu A)^{-1} (x0 - mu b / 2)
|
|
|
|
The figure shows the trajectory in the plane, `f(mu) = psi(x(mu))`, the distance
|
|
`||x0 - x(mu)||` and `f'(mu)`, together with the nearest/farthest KKT points `x(mu*)`,
|
|
`x(mu**)` and, when `x0` has a zero standardized coordinate, the degenerate point `x^d`.
|
|
|
|
## Usage
|
|
|
|
pip install -r requirements.txt
|
|
python plot_mu_trajectories.py # degenerate case x0 = (0, -0.1)
|
|
python plot_mu_trajectories.py --x0 0.3 0.2 --output figures/generic
|
|
pytest
|
|
|
|
The ellipse is set by `A`, `B`, `C` at the top of `plot_mu_trajectories.py`.
|
|
|
|
Text is typeset with LaTeX (`text.usetex`) when `latex` is on the `PATH`, with the `cm-super` and
|
|
`type1cm` packages; otherwise matplotlib's Computer Modern math font is used.
|
|
|
|
## Files
|
|
|
|
- `quadric.py`: the `Ellipsoid` class (standardization, trajectory, extreme roots, degenerate points).
|
|
- `plot_mu_trajectories.py`: the figure.
|
|
- `test_quadric.py`: checks against brute-force sampling of the ellipse.
|