Worked examples¶

The examples are grouped by the scientific analysis problem, not by the module that implements it. Each example is intended to connect executable code to diagnostics, interpretation limits, and the corresponding method contract.

Foundations & representation¶

Examples for native trajectories, irregular sampling, sparse data, multilevel structure, AOI compositions, phase, and native functional simulation with exact retained truth for recovery studies.

FPCA & uncertainty¶

Examples for component stability, retention, simultaneous bands, score/basis uncertainty, mean inference, outlier review, and conformal anomaly evidence.

Functional regression & prediction¶

Examples for scalar-on-function and function-on-scalar workflows, generalized functional outcomes, FPCR bootstrap uncertainty, simultaneous inference, and future prediction.

Repeated-trial mixed effects¶

Examples for participant functional random effects, nested trial effects, residual covariance, covariance sensitivity, simultaneous bands, residual diagnostics, and full-refit bootstrap.

Geometry & trajectory comparison¶

Examples for continuous path geometry, discrete Fréchet distance, dynamic time warping, and sensitivity to defensible distance definitions.

Nonlinear, recurrence & information flow¶

Examples for recurrence/RQA, recurrence networks, Lyapunov estimation, parameter sensitivity, transfer entropy, multivariate surrogates, and return maps.

Audit utilities¶

Use the function → equation registry to trace public functions to mathematical contracts, and failure cases to see how the package behaves when assumptions are violated.