fdaPDE

Physics-Informed Spatial and Functional Data Analysis

fdaPDE is a C++ library for the analysis of spatial and functional data observed over complex multidimensional domains, featuring a Partial Differential Equation regularization.

It is built on top of the fdaPDE Core Library.

Documentation

Documentation can be found on our documentation site

Functional regression models

Include <fdaPDE/models.h> to use fPLS or fPCR. Both take centered functional predictors through a single GeoFrame layer and centered responses with subjects in rows; scalar and multivariate responses retain every response column.

fPLS saves direction and loading GCV curves, their actual EDF estimates, candidate tuples and zero-based selected candidate indices during calibration. The public direction_gcv_edfs(), loading_gcv_edfs(), direction_lambda_grid(), loading_lambda_grid(), direction_selected_indices() and loading_selected_indices() accessors perform no solves or EDF estimates. Fixed fits clear the calibration snapshots and record the fixed penalties; each repeated fit replaces the previous snapshot.

fPCR("X", Y, data, penalty) reuses native power-iteration fPCA. Its fit takes a component count, fixed penalty tuple or GCV candidate tuples, calibration/SVD flags, iteration limit, tolerance, EDF probe count and seed. X_latent_scores() projects final loadings sequentially; score_coefficients(h) refits OLS for every prefix. fitted(h), predict(Xnew, h), reconstructed(h) and Beta(h) expose prefix results. Beta maps the original centered predictors through the functional basis, including all preceding deflations: X * Psi * Beta(h) == fitted(h). Prefix zero selects all fitted components. gcv_values(), gcv_edf(), lambda_grid() and selected_indices() expose the evaluations used by its fPCA calibration. The supported bindings are single-parameter elliptic FEM and spline smoothers.

Power-solver GCV now uses floating-point residual degrees of freedom (m - edf) rather than truncating them to an integer. Explicit seeds and probe counts are honored on repeated elliptic fits. These corrections can change GCV selections relative to callers that previously used default random probes. Explicit EDF controls are supported by the fPCA power policy; other policies reject nondefault controls; the missing-data path also rejects nondefault EDF controls rather than ignoring them. This branch's pinned core still provides the legacy one-argument assertion macro, so new permanent public validation uses exceptions pending the core assertion API migration.