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>
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: theEllipsoidclass (standardization, trajectory, extreme roots, degenerate points).plot_mu_trajectories.py: the figure.test_quadric.py: checks against brute-force sampling of the ellipse.