eigenshuffle 0.1.0

Keep consistent order of eigenvalues and eigenvectors of successive eigenvalue/vector problems based on the inital ordering of eigenvalues from low to high by matching closest eigenvectors and eigenvalues.

eigenshuffle

Adapted from code by bmachiel, which in turn was based on matlab eigenshuffle.

Consistently sort eigenvalues and eigenvectors of a series of matrices based on initial ordering from low to high.

Includes eigenshuffle_eig and eigenshuffle_eigh for non-hermitian and hermitian matrices, respectively.

Installation

Install from pypi with:

pip install eigenshuffle

or clone repo and install with pip or directly install from GitHub with:

pip install git+https://github.com/ograsdijk/CeNTREX-trajectories

Example

import numpy as np
import numpy.typing as npt
import matplotlib.pyplot as plt

from eigenshuffle import eigenshuffle_eig

def eigenvalue_function(
    t: float,
) -> npt.NDArray[np.float_]:
    return np.array(
        [
            [1, 2 * t + 1, t**2, t**3],
            [2 * t + 1, 2 - t, t**2, 1 - t**3],
            [t**2, t**2, 3 - 2 * t, t**2],
            [t**3, 1 - t**3, t**2, 4 - 3 * t],
        ]
    )

tseq = np.arange(-1, 1.1, 0.1)
Aseq = np.array([eigenvalue_function(ti) for ti in tseq])

e, v = np.linalg.eig(Aseq)

es, vs = eigenshuffle_eig(Aseq)

# sorting original eig result from low to high
v[np.argsort(e)]
e = np.sort(e)

fig, ax = plt.subplots()
lines = ax.plot(tseq, e)

for i in range(ei.shape[-1]):
    ax.plot(tseq, ei.real[:, i], "--", color=lines[i].get_color())

# for generating the legend
line1 = plt.Line2D([0, 1], [0, 1], linestyle="-", color="black")
line2 = plt.Line2D([0, 1], [0, 1], linestyle="--", color="black")

ax.set_xlabel("t")
ax.set_ylabel("eigenvalue")
ax.legend([line1, line2], ["sorted", "eigenshuffle"])
ax.grid()

Here the eigenvalues are consistently ordered, and are not switching positions after a level crossing (around t=0.3) when using eigenshuffle.