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>
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 # every case, into figures/
python plot_mu_trajectories.py x_trajectories_mu_2 # a single case
pytest
Cases (A, x0, and optionally b and c) are listed in CASES at the top of
plot_mu_trajectories.py; each one produces <name>.png and <name>.pdf.
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
plot_mu_trajectories.py: the figure. The quadric,x(mu),f,f',mu*and the degenerate points come from quadproj; the script only addsmu**, the asymptotes and the ellipse boundary.test_plot_mu_trajectories.py: checks these helpers against brute-force sampling of the ellipse and againstquadproj.project.