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Visual gallery

These figures are regenerated from deterministic synthetic data during the documentation workflow. The gallery is therefore part of the tested documentation build rather than a collection of manually exported screenshots.

  • Continuous planar trajectories

    Synthetic planar gaze trajectories

    Whole-path inspection before dimensional reduction.

    API: simulate_planar_trajectories(), plot_planar_trajectories()

    Worked example · Mathematics

  • FPC interpretation curve

    First functional principal component

    Mean and score-SD perturbations for one functional dimension.

    API: fit_mfpca(), plot_fpca_component()

    FPCA guide · Mathematics

  • Cumulative FPCA variance

    Cumulative functional principal component variance

    Retained functional variance across the fitted component sequence.

    API: plot_fpca_variance()

    FPCA guide · Function → equation index

  • Registration displacement

    Landmark registration warping displacement

    The retained phase displacement (h_i(t)-t), rather than a hidden registration side effect.

    API: register_to_landmarks(), plot_warping_functions()

    Registration guide · Mathematics

  • Simultaneous functional mean band

    Functional mean simultaneous band

    Observed-grid Gaussian multiplier calibration.

    API: multiplier_functional_mean_band(), plot_functional_mean_band()

    Worked example · Mathematics

  • Experimental condition coefficient over trial time

    Function-on-scalar condition coefficient with simultaneous band

    Observed-grid function-on-scalar condition coefficient with a fixed-design wild-bootstrap simultaneous band.

    API: fit_function_on_scalar_regression(), function_on_scalar_simultaneous_bands(), plot_function_on_scalar_coefficients()

    Worked example · Guide · Mathematics

  • Repeated-measures condition coefficient

    Functional mixed-effects condition coefficient

    One joint repeated-measures Gaussian functional mixed model with a participant functional random intercept and a participant-cluster observed-grid simultaneous band for the condition coefficient.

    API: fit_functional_mixed_effects_regression(), bootstrap_functional_mixed_effects_coefficients(), functional_mixed_effects_simultaneous_bands(), plot_functional_mixed_effects_coefficient()

    Worked simultaneous example · Guide · Mathematics

  • Participant-specific condition-response heterogeneity

    Participant random functional slope functions

    Participant BLUP random-slope functions from one guarded random functional slope for the declared condition predictor. The full intercept/slope covariance, eigenvalues, condition diagnostics, and covariance dimensionality remain part of the fitted result rather than being hidden behind the plot.

    API: fit_functional_mixed_effects_regression(), functional_random_effect_frame(), plot_functional_random_effects()

    Worked example · Method guide · Mathematics

  • Multivariate IAAFT preservation diagnostics

    Per-surrogate power-spectrum and cross-spectrum mismatch diagnostics

    Cross-spectrum-aware x/y surrogate generation with exact marginal rank restoration and explicit retained Fourier mismatch diagnostics.

    API: generate_multivariate_iaaft_surrogates(), plot_multivariate_iaaft_diagnostics()

    Worked example · Method guide · Mathematics

  • Heteroscedastic FPCR target intervals

    Wild bootstrap fixed target intervals

    Studentized fixed-regressor wild-bootstrap intervals for centered target projections.

    API: wild_bootstrap_fpca_projection(), plot_fpca_wild_bootstrap_projection()

    Worked example · Mathematics

  • Fixed-family wild-bootstrap tests

    Target-wise and maxT adjusted wild-bootstrap p-values

    Target-wise and single-step max-(|t|) probabilities for one declared family.

    API: fpca_wild_bootstrap_projection_family_test(), plot_fpca_wild_bootstrap_family_test()

    Worked example · Mathematics

  • Finite-bootstrap precision

    Monte Carlo precision diagnostics

    Exact binomial intervals around retained bootstrap exceedance probabilities.

    API: fpca_wild_bootstrap_family_test_monte_carlo_diagnostics(), plot_fpca_wild_bootstrap_monte_carlo_diagnostics()

    Worked example · Mathematics

  • Continuous signed curvature

    Signed curvature over time for a smooth planar trajectory

    Continuous local path curvature computed from the observed planar trajectory without hidden smoothing, interpolation, or denominator stabilization.

    API: signed_curvature_function(), plot_trajectory_overlay()

    Worked example · Method guide · Mathematics

  • Audited dynamic time warping alignment

    Dynamic time warping alignment path

    A normalizable symmetric2 alignment with an explicit Sakoe-Chiba sample-index band, shown against the same-index diagonal.

    API: dynamic_time_warping_distance(), plot_dynamic_time_warping_alignment()

    Worked example · Method guide · Mathematics

  • Trajectory-distance robustness

    Spearman rank agreement across L2, Frechet, and DTW specifications

    Native-scale distance matrices are compared through pair-distance rank agreement without constructing a consensus metric or choosing a winner.

    API: trajectory_distance_sensitivity(), plot_trajectory_distance_rank_correlations()

    Worked example · Method guide · Mathematics

  • Sparse recurrence structure

    Sparse recurrence plot

    Recurrent reconstructed states under an explicit target recurrence rate and Theiler exclusion.

    API: delay_embed_trajectory(), recurrence_matrix(), plot_recurrence()

    Worked example · Mathematics

  • Synchronized joint recurrence

    Joint recurrence plot for two synchronized component systems

    Sparse logical intersection of separately declared auto-recurrence matrices on one exact time grid and shared Theiler exclusion.

    API: joint_recurrence_matrix(), joint_rqa_metrics(), plot_joint_recurrence()

    Worked example · Method guide · Mathematics

  • Sparse recurrence-network degree

    Normalized recurrence-network degree across state indices

    Node degree from the sparse auto-recurrence adjacency, retaining the declared recurrence threshold and Theiler exclusion.

    API: recurrence_network(), plot_recurrence_network_degree()

    Worked example · Method guide · Mathematics

  • Recurrence threshold profile

    Recurrence rate over an analyst-declared radius grid

    Exact RR(radius) diagnostics and pair-distance threshold sensitivity without automatic radius selection.

    API: recurrence_radius_profile(), plot_recurrence_rate_curve()

    Worked example · Method guide · Mathematics

  • Population uncertainty for RQA summaries

    Participant-level bootstrap intervals for population-average RQA metrics

    Percentile-bootstrap uncertainty for fixed-specification curve-level RQA metrics using equal-weight participant inference units.

    API: bootstrap_rqa_metric_means(), plot_rqa_metric_mean_bootstrap()

    Worked example · Method guide · Mathematics

  • Time-varying RQA

    Windowed recurrence quantification

    Full-window recurrence rate, determinism, and laminarity retained over trial time.

    API: windowed_rqa(), plot_windowed_rqa()

    Nonlinear guide · Mathematics

  • RQA-derived functional trajectories

    Windowed RQA recurrence-rate trajectories across source curves

    Sliding-window recurrence summaries promoted to a native functional representation while retaining overlap, edge/tail, and radius-policy provenance.

    API: windowed_rqa_trajectory_set(), plot_windowed_rqa_trajectories()

    Worked example · Mathematics - Local divergence / Rosenstein LLE

    Local divergence with declared Lyapunov fit interval

    Mean nearest-neighbor log divergence and the explicitly declared linear fit interval.

    API: local_divergence_curve(), estimate_largest_lyapunov_rosenstein(), plot_local_divergence()

    Worked example · Mathematics

  • Kantz neighborhood divergence

    Kantz fixed-radius neighborhood divergence with declared LLE fit

    Fixed-radius local-neighborhood divergence with explicit minimum-neighbor support and analyst-declared fit interval.

    API: kantz_divergence_curve(), estimate_largest_lyapunov_kantz(), plot_local_divergence()

    Worked comparison · Method guide · Mathematics

  • Kantz radius sensitivity

    Kantz largest-Lyapunov estimate over a declared radius grid

    Exponent sensitivity over a predeclared fixed-radius grid with reconstruction, minimum-neighbor, Theiler, and fit settings held explicit.

    API: kantz_parameter_sensitivity(), plot_kantz_sensitivity()

    Worked example · Sensitivity guide · Mathematics

  • Experimental empirical return map

    Empirical Poincare return map

    Successive section crossings and a local affine return map for a deterministic synthetic contracting cycle.

    API: poincare_crossings(), fit_local_return_map(), return_map_stability(), plot_poincare_return_map()

    Worked example · Mathematics

Run:

python scripts/generate_docs_gallery.py

The generator uses the package itself, fixed random seeds, the non-interactive Matplotlib backend, deterministic SVG hashing, and timestamp-free SVG metadata.

Plot → method → equation

plot_fpca_component() visualizes

\[ \widehat{\boldsymbol\mu}(t) +a\sqrt{\widehat\lambda_k}\widehat{\boldsymbol\phi}_k(t). \]

plot_function_on_scalar_coefficients() visualizes an observed-grid coefficient function and, when a simultaneous-band result is supplied, the calibrated lower/upper band for the declared coefficient or coefficient family.

plot_functional_mean_band() visualizes

\[ \overline X_d(t_m) \pm c_{1-\alpha}\widehat{\mathrm{SE}}_d(t_m). \]

plot_fpca_wild_bootstrap_projection() visualizes

\[ \widehat\theta_{0,h} \pm c_{0,1-\alpha}\widehat{\mathrm{SE}}_0. \]

plot_dynamic_time_warping_alignment() visualizes the selected monotone index path. For symmetric2, the raw path cost uses step weights 2 for diagonal moves and 1 for horizontal/vertical moves; the optional normalized distance divides the complete global cost by \(N+M\).

plot_recurrence() visualizes sparse entries satisfying

$ R_{ij}=\mathbb I{|\mathbf z_i-\mathbf z_j|_p\le\varepsilon}. $

plot_local_divergence() visualizes

$ D(k)=\frac{1}{N_k}\sum_i\log d_i(k), $

with the analyst-declared LLE fit interval when an estimate is supplied.

plot_poincare_return_map() visualizes successive crossings under

$ \mathbf z_{n+1}\approx \mathbf a+\mathbf J(\mathbf z_n-\mathbf z_0). $

plot_fpca_wild_bootstrap_monte_carlo_diagnostics() visualizes the raw retained tail estimate and exact binomial precision limits, where

\[ \widehat q=\frac{r}{B}. \]

The docs workflow regenerates all twenty-five assets before the strict MkDocs build and runs scripts/validate_docs_contracts.py. A missing image, stale generated equation index, broken nav target, undefined mathematical deep link, missing mathematical API contract, stale MathJax hook, or unresolved documented public symbol fails the documentation job.