Eigenmode Analysis

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Track eigenmode candidates without losing their identity or hiding missing samples. Array-based path and directed-graph tracking exposes assignment costs, coverage, rejected candidates and graph diagnostics.

Computed synthetic demonstration. Both panels contain the same 265 observations; eight missing slots remain missing. Colors denote numerical tracks, not unique physical mode identities. Source · Provenance.

Capabilities

Capability	Public interface	Application
Ordered scans	CandidateSet, TrackingConfig, track_path	Reordered candidates, crossing branches and missing observations
Parameter graphs	TraversalEdge, rectilinear_traversal, track_graph	Explicit traversal, incoming-edge diagnostics and empty sites
Field and mode analysis	symmetry, polarization, topology, propagation	Reusable numerical operations on arrays
Sampling and characterization	grid_sampling, lineshapes, peak_tracking, field_regimes	Analysis independent of readers and rendering

Runtime dependencies are NumPy and SciPy. The numerical package does not import plotting backends, DataFrames, simulator APIs or consumers. Callers own readers, physical selection, output paths and interpretation.

flowchart LR
    A[Arrays and candidate IDs] --> B[Explicit path or graph]
    B --> C[Configured assignment]
    C --> D[Tracked IDs and arrays]
    C --> E[Missing slots, costs, diagnostics]
    D --> F[Caller analysis or plotting]

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Release lines and installation

Public branch	Version	Compatibility
Default: public-release	0.2.10	Stable path/graph API; compatible with Plot Workflows 0.1.7
feature/band-tracking-v2	0.3.1	Adds opt-in band_grouping; outside Workflows 0.1.7's <0.3 requirement

This is the default stable-release documentation. The gallery runs against the 0.2.10 wheel, and does not validate the separate grouping algorithm. Python 3.10+ and Git are required for this pinned public-source install; no package-index release or version tag is assumed.

python -m venv .venv
# Activate .venv for your shell, then:
python -m pip install "eigenmode-analysis @ git+https://github.com/Patr1ck2005/eigenmode-analysis.git@e172495aa0c561cf0edf251ae9828dd5e54d2d64"
python -m pip check

A verified local eigenmode_analysis-0.2.10-py3-none-any.whl is also suitable. Stable consumers should install wheels rather than inject sibling-source paths.

Complete small example

import numpy as np
from eigenmode_analysis.tracking import CandidateSet, TrackingConfig, track_path

t = np.linspace(-1, 1, 21)
points = []
for i, value in enumerate(t):
    order = [1, 0] if i % 2 else [0, 1]
    values = np.array([1 + 0.2 * value, 1 - 0.2 * value])
    points.append(CandidateSet(order, values[order, None]))
result = track_path(points, coordinates=t,
                    config=TrackingConfig(n_tracks=2, derivative_weights=2))
assert result.coverage == 1.0
print(result.features.shape)  # (21, 2, 1)

Candidate IDs are opaque and local to each site. Feature scaling and continuity assumptions affect assignment; cost is not probability. Missing or rejected assignments remain None/NaN rather than silently becoming another mode.

Computed examples

Crossing and missing samples	Directed-graph diagnostics

Path-cost diagnostic · Offline PNG/SVG gallery.

From this repository, install the example's rendering dependency and run:

python -m pip install "plot-foundation @ git+https://github.com/Patr1ck2005/plot-foundation.git@c3d3cc23b2bb4da7ade7e5edf553d4a36d19db7f"
python examples/synthetic_tracking.py --out docs/assets/showcase

The fixed-seed example uses public APIs and independently defined mathematics. Assertions check observation preservation, the expected crossing, eight missing slots, an empty graph site and input-order invariance. PNG/SVG exports, the HTML gallery and manifest record source hashes, versions, dimensions and checks.

Separate advanced grouping line

Version 0.3.1 is available on the separate public feature branch. Read its grouping contract before adopting it; do not implicitly upgrade a workflow environment requiring a version below 0.3.

Documentation and development

Public API · Architecture · Changelog · Agent rules · Four-library example.

For package development, use an isolated environment, install .[dev], and run python -m pytest -q. Example assertions cover less than the complete package suite.

MIT licensed; these examples make no experimental, full-wave or unpublished-research claim.