fdars AI Capability Map¶

This page is the human-readable companion to the machine-readable llms.txt digest. It lists every public callable in the fdars library, grouped by submodule.

30 submodules · 409 public callables — all generated offline from the committed capability map. AI agents: use fdars_list_capabilities() (MCP tool) or llms.txt for the machine-readable form.

Module Index¶

Module	Purpose	Functions
`fdars.alignment`	Elastic alignment, SRSF registration, Karcher mean, elastic FPCA	68
`fdars.basis`	Basis representations — B-spline, Fourier, functional PCA	16
`fdars.classification`	Functional classifiers — k-nearest neighbours, SVM, centroid-based	9
`fdars.clustering`	Functional k-means, fuzzy, GMM, and elastic clustering	11
`fdars.conformal`	Conformal prediction and classification bands	7
`fdars.covariance`	Kernel covariance functions for Gaussian processes over functions	14
`fdars.datasets`	Built-in datasets — Canadian weather, Tecator, phoneme, growth, and more	7
`fdars.density_fda`	Density-based functional data analysis and Wasserstein distances	5
`fdars.depth`	Functional depth measures — Fraiman-Muniz, band, modal, random-projection	18
`fdars.explain`	Functional explainability — SHAP, FCI, GRAD-CAM, and attribution maps	46
`fdars.famm`	Functional additive mixed models (FAMM) for longitudinal data	3
`fdars.fdata`	Core functional data operations — mean, deriv, norm, integrate, reconstruct	15
`fdars.frechet`	Fréchet regression for metric-space responses	4
`fdars.fts`	Functional time series — forecasting, correlation, spectral analysis	13
`fdars.inference`	Functional inference — two-sample tests, interval-wise testing	11
`fdars.metric`	Functional distance and similarity metrics — L2, L1, Mahalanobis, DTW	26
`fdars.metrics`	Regression and classification scoring metrics for functional outputs	5
`fdars.multi_fdata`	Multi-domain functional data — paired domains, joint analysis	2
`fdars.outliers`	Functional outlier detection — depth-based, magnitude, shape outliers	8
`fdars.pace_fpca`	PACE: Principal Analysis by Conditional Expectation for sparse data	3
`fdars.regression`	Functional regression — scalar-on-function, function-on-scalar, GLM	29
`fdars.represent`	Dimensionality reduction and functional representation tools	4
`fdars.scalar_on_function`	Scalar-on-function regression with regularisation	5
`fdars.scoring`	Functional scoring — penalised, tolerance-band, and integrated scores	5
`fdars.seasonal`	Seasonal functional decomposition and periodic pattern analysis	18
`fdars.shapelet`	Functional shapelets — pattern-based classification and feature learning	7
`fdars.simulation`	Simulation of functional data — GPs, Brownian motion, Ornstein-Uhlenbeck	8
`fdars.smoothing`	Functional smoothing — kernel, basis, and roughness-penalised methods	10
`fdars.spm`	Statistical process monitoring — T2, SPE, control charts	23
`fdars.tolerance`	Functional tolerance bands — simultaneous and pointwise coverage	9

Module Details¶

`fdars.alignment`¶

Elastic alignment, SRSF registration, Karcher mean, elastic FPCA.

Function	Signature	Purpose
`align_to_target`	`(data, target, argvals, lambda_=0.0)`	Align all curves to a single target curve.
`alignment_quality`	`(data, argvals, lambda_=0.0, max_iter=20, tol=0.0001)`	Comprehensive alignment quality metrics.
`amplitude_distance`	`(curve1, curve2, argvals, lambda_=0.0)`	Amplitude distance between two curves.
`amplitude_self_distance_matrix`	`(data, argvals, lambda_=0.0)`	Amplitude self distance matrix (same as elastic self distance matrix).
`bayesian_align_pair`	`(f1, f2, argvals, n_samples=1000, burn_in=200, step_size=0.1, proposal_variance=1.0, seed=42)`	Bayesian pairwise alignment via pCN MCMC on the Hilbert sphere.
`compose_warps`	`(warp1, warp2, argvals)`	Compose two warping functions.
`curve_geodesic`	`(f1, f2, argvals, n_points=10, lambda_=0.0)`	Compute the geodesic path between two 1-D curves in the elastic metric.
`detect_landmarks`	`(curve, argvals, kind='peak', min_prominence=0.0)`	Detect landmarks (peaks, valleys, zero-crossings, inflections) in a curve.
`diagnose_alignment`	`(data, argvals, lambda_=0.0, max_iter=20, tol=0.0001, over_alignment_threshold=1.0, under_alignment_threshold=1e-06, max_bending_energy=100.0, min_improvement_ratio=0.5)`	Diagnose alignment quality for every curve after Karcher mean computation.
`elastic_align_pair`	`(curve1, curve2, argvals, lambda_=0.0)`	Pairwise elastic alignment of two curves.
`elastic_align_pair_closed`	`(f1, f2, argvals, lambda_=0.0)`	Align closed (periodic) curve f2 to f1 with rotation search.
`elastic_align_pair_constrained`	`(f1, f2, argvals, landmark_targets, landmark_sources, lambda_=0.0)`	Landmark-constrained elastic alignment.
`elastic_align_pair_multires`	`(f1, f2, argvals, coarsen_factor=4, n_refine_steps=10, step_size=0.01, lambda_=0.0)`	Multi-resolution elastic alignment (coarse DP + gradient refinement).
`elastic_align_pair_penalized`	`(curve1, curve2, argvals, lambda_=0.0, penalty_type='first_order', second_order_weight=0.1)`	Elastic alignment with configurable penalty type.
`elastic_changepoint`	`(data, argvals, kind='amplitude', lam=0.0, max_iter=30, n_mc=200, seed=42, ncomp=5, pca_method='joint')`	Detect a distributional changepoint in a sequence of curves (elastic).
`elastic_cross_distance_matrix`	`(data1, data2, argvals, lambda_=0.0)`	Elastic cross distance matrix.
`elastic_cross_distance_matrix_with_band`	`(data1, data2, argvals, lambda_=0.0, band_frac=None)`	Elastic cross-distance matrix with optional Sakoe–Chiba band.
`elastic_decomposition`	`(f1, f2, argvals, lambda_=0.0)`	Elastic phase-amplitude decomposition of two curves.
`elastic_depth`	`(data, argvals, lambda_=0.0)`	Elastic depth (depth under elastic metric).
`elastic_distance`	`(curve1, curve2, argvals, lambda_=0.0)`	Elastic (Fisher-Rao) distance between two curves.
`elastic_distance_closed`	`(f1, f2, argvals, lambda_=0.0)`	Elastic distance between two closed curves.
`elastic_logistic`	`(data, argvals, labels, ncomp_beta=10, lambda_=0.0, max_iter=20, tol=0.0001)`	Elastic logistic regression.
`elastic_outlier_detection`	`(data, argvals, lambda_=0.0, alpha=0.05, use_median=True)`	Elastic outlier detection using distances and Tukey fence.
`elastic_partial_match`	`(template, target, argvals_template, argvals_target, lambda_=0.0, min_span=0.5)`	Elastic partial matching: find best-aligned subcurve of a longer curve.
`elastic_regression`	`(data, argvals, response, ncomp_beta=10, lambda_=0.0, max_iter=20, tol=0.0001)`	Elastic scalar-on-function regression.
`elastic_self_distance_matrix`	`(data, argvals, lambda_=0.0)`	Elastic self distance matrix.
`elastic_self_distance_matrix_with_band`	`(data, argvals, lambda_=0.0, band_frac=None)`	Elastic self-distance matrix with optional Sakoe–Chiba band.
`gauss_model`	`(data, argvals, ncomp=3, n_samples=100, lambda_=0.0, max_iter=20, tol=0.0001, seed=42)`	Generate random curves from a fitted Gaussian model on aligned data.
`hierarchical_cut`	`(dist_mat, k=2, linkage='single')`	Hierarchical clustering then cut to produce k clusters (convenience function).
`hierarchical_from_distances`	`(dist_mat, linkage='single')`	Hierarchical agglomerative clustering from a precomputed distance matrix.
`horiz_fpca`	`(data, argvals, n_comp=3, lambda_=0.0, max_iter=20, tol=0.0001)`	Horizontal (phase) FPCA.
`horiz_fpns`	`(data, argvals, ncomp=3, lambda_=0.0, max_iter=20, tol=0.0001)`	Horizontal Functional Principal Nested Spheres (FPNS) analysis.
`invert_warp`	`(warp, argvals)`	Invert a warping function.
`joint_fpca`	`(data, argvals, n_comp=3, lambda_=0.0, max_iter=20, tol=0.0001)`	Joint (amplitude + phase) FPCA.
`joint_gauss_model`	`(data, argvals, ncomp=3, n_samples=100, balance_c=1.0, lambda_=0.0, max_iter=20, tol=0.0001, seed=42)`	Generate random curves from a joint Gaussian model preserving amplitude-phase correlation.
`karcher_mean`	`(data, argvals, lambda_=0.0, max_iter=20, tol=0.0001)`	Karcher (Frechet) mean under the elastic metric.
`karcher_mean_closed`	`(data, argvals, max_iter=20, tol=0.0001, lambda_=0.0)`	Karcher mean for closed (periodic) curves.
`karcher_mean_with_band`	`(data, argvals, lambda_=0.0, max_iter=20, tol=0.0001, band_frac=None)`	Karcher (Fréchet) mean under the elastic metric with optional Sakoe–Chiba band.
`karcher_median`	`(data, argvals, lambda_=0.0, max_iter=20, tol=0.001)`	Karcher median under the elastic metric.
`kmedoids_from_distances`	`(dist_mat, k=2, max_iter=100, seed=42)`	K-medoids clustering from a precomputed distance matrix.
`lambda_cv`	`(data, argvals, lambdas=None, n_folds=5, max_iter=15, tol=0.001, seed=42)`	Cross-validation for the elastic alignment regularisation parameter lambda.
`landmark_detect_and_register`	`(data, argvals, kind='peak', min_prominence=0.0, expected_count=0)`	Detect landmarks and register in one call.
`landmark_register`	`(data, argvals, landmarks, target=None)`	Register curves to common landmark positions.
`least_squares_score`	`(registered, argvals)`	Least-squares registration score: mean Simpson-weighted L2 spread of the
`least_squares_shift_registration`	`(data, argvals, max_shift)`	Register curves by a per-curve rigid horizontal shift (least-squares).
`pairwise_consistency`	`(data, argvals, lambda_=0.0, max_triplets=0)`	Pairwise alignment consistency via triplet checks.
`pairwise_correlation_score`	`(registered, argvals)`	Pairwise correlation registration score: mean functional Pearson correlation
`peak_persistence`	`(data, argvals, lambdas, max_iter=10, tol=0.001)`	Peak persistence diagram for choosing the alignment regularisation parameter.
`phase_boxplot`	`(gammas, argvals, factor=1.5)`	Phase (warping) box plot for functional data.
`phase_distance`	`(curve1, curve2, argvals, lambda_=0.0)`	Phase distance between two curves.
`phase_self_distance_matrix`	`(data, argvals, lambda_=0.0)`	Phase self distance matrix.
`reparameterize_curve`	`(curve, argvals, gamma)`	Apply a warping function to a curve (reparameterize).
`robust_karcher_mean`	`(data, argvals, lambda_=0.0, max_iter=20, tol=0.001, trim_fraction=0.1)`	Robust Karcher mean (trimmed).
`shape_confidence_interval`	`(data, argvals, n_bootstrap=200, confidence_level=0.95, lambda_=0.0, max_iter=15, tol=0.001, seed=42)`	Bootstrap confidence intervals for the elastic Karcher mean.
`shape_distance`	`(curve1, curve2, argvals, lambda_=0.0)`	Shape distance (quotient space distance).
`shape_mean`	`(data, argvals, quotient='reparameterization', lambda_=0.0, max_iter=20, tol=0.0001)`	Shape mean of a set of curves.
`shape_self_distance_matrix`	`(data, argvals, quotient='reparameterization', lambda_=0.0)`	Pairwise shape distance matrix.
`sobolev_least_squares_score`	`(registered, argvals, lambda_=0.0)`	Sobolev least-squares registration score: LS spread plus a derivative-penalty
`srsf_inverse`	`(srsf, argvals, initial_value=0.0)`	Inverse SRSF transform.
`srsf_transform`	`(curve, argvals)`	SRSF (Square Root Slope Function) transform.
`transfer_alignment`	`(source_data, target_data, argvals, lambda_=0.0, max_iter=15, tol=0.001)`	Align curves from a target population to a source population's coordinate system.
`tsrvf_transform`	`(data, argvals, max_iter=20, tol=0.0001, lambda_=0.0)`	TSRVF (Transported SRSF) transform.
`tsrvf_transform_with_method`	`(data, argvals, max_iter=20, tol=0.0001, lambda_=0.0, method='log_map')`	TSRVF transform with configurable transport method.
`vert_fpca`	`(data, argvals, n_comp=3, lambda_=0.0, max_iter=20, tol=0.0001)`	Vertical (amplitude) FPCA on aligned data.
`warp_complexity`	`(warp, argvals)`	Warp complexity (geodesic distance from identity).
`warp_inverse_error`	`(warp, argvals)`	Compute the L2 error of a warp inverse: \|\|gamma(gamma_inv(t)) - t\|\|.
`warp_smoothness`	`(warp, argvals)`	Warp smoothness (bending energy).
`warp_statistics`	`(gammas, argvals, confidence_level=0.95)`	Warp statistics: mean, variance, confidence bands, Karcher mean warp.

Function	Signature	Purpose
`basis_nbasis_cv`	`(data, argvals, nbasis_min=4, nbasis_max=20, basis_type='bspline', criterion='gcv', n_folds=5, lambda_=0.0)`	Cross-validated selection of number of basis functions.
`basis_to_fdata_1d`	`(coefficients, argvals, n_basis, basis_type='bspline')`	Reconstruct functional data from basis coefficients.
`bspline_basis`	`(argvals, nknots, order=4)`	Evaluate a B-spline basis at given points.
`bspline_basis_from_knots`	`(argvals, knots, order=4)`	Evaluate a B-spline basis from a given knot vector.
`constant_basis`	`(argvals)`	Evaluate the constant (intercept) basis on a grid of evaluation points.
`construct_bspline_knots`	`(t_min, t_max, nknots, order=4)`	Construct B-spline knot vector.
`fdata_to_basis_1d`	`(data, argvals, n_basis, basis_type='bspline')`	Project functional data onto a B-spline or Fourier basis.
`fourier_basis`	`(argvals, n_basis)`	Evaluate a Fourier basis at given points.
`fourier_basis_with_period`	`(argvals, n_basis, period)`	Evaluate a Fourier basis with specified period at given points.
`fourier_fit_1d`	`(data, argvals, nbasis)`	Fit Fourier basis to functional data using least squares.
`pspline_fit_1d`	`(data, argvals, n_basis, lambda_, order=2)`	Fit P-splines to 1D functional data.
`pspline_fit_gcv`	`(data, argvals, n_basis, order=2)`	P-spline fit with GCV-selected smoothing parameter.
`select_basis_auto_1d`	`(data, argvals, criterion='gcv', nbasis_min=0, nbasis_max=0, lambda_pspline=Ellipsis, use_seasonal_hint=True)`	Automatic basis selection (GCV/AIC/BIC) for 1D data.
`select_fourier_nbasis_gcv`	`(data, argvals, min_nbasis, max_nbasis)`	Select optimal number of Fourier basis functions via GCV.
`smooth_basis_aic`	`(data, argvals, n_basis, basis_type='bspline', lfd_order=2, log_lambda_min=Ellipsis, log_lambda_max=4.0, n_grid=25)`	Smooth functional data using basis expansion with AIC-optimal lambda.
`smooth_basis_gcv`	`(data, argvals, n_basis, basis_type='bspline', lfd_order=2, log_lambda_min=Ellipsis, log_lambda_max=4.0, n_grid=25)`	Smooth functional data using basis expansion with GCV.

Function	Signature	Purpose
`elastic_multinomial`	`(data, labels, argvals, ncomp_beta=10, lambda_=0.1, max_iter=100, tol=0.0001)`	K-class elastic multinomial classifier for functional data (one-vs-rest).
`fclassif_cv`	`(data, argvals, labels, method='lda', ncomp=3, nfold=5)`	Cross-validated classification.
`fclassif_dd`	`(data, labels)`	Depth-based DD-classifier for functional data.
`fclassif_kernel`	`(data, argvals, labels, h_func=1.0, h_scalar=1.0)`	Kernel classification for functional data.
`fclassif_knn`	`(data, labels, ncomp=3, k=5)`	k-NN classification for functional data.
`fclassif_lda`	`(data, labels, ncomp=3)`	LDA classification for functional data via FPC scores.
`fclassif_qda`	`(data, labels, ncomp=3)`	QDA classification for functional data.
`kernel_classify_from_distances`	`(func_dists, labels, h_func=1.0, h_scalar=1.0)`	Kernel classification from a precomputed functional distance matrix.
`knn_classify_from_distances`	`(dist_matrix, labels, k=5)`	k-NN classification from a precomputed distance matrix.

Function	Signature	Purpose
`align_cluster_fd`	`(data, argvals, k=2, max_iter=20, seed=42, use_amplitude_only=True, elastic_lambda=0.0, karcher_max_iter=15, karcher_tol=0.0001)`	Elastic-alignment functional clustering.
`calinski_harabasz`	`(dist_matrix, labels)`	Calinski-Harabasz index for cluster quality (from distance matrix).
`calinski_harabasz_data`	`(data, argvals, labels)`	Calinski-Harabasz index for cluster quality (from data and argvals).
`dbscan_fd`	`(data, argvals, eps=0.5, min_points=3)`	Density-based spatial clustering of functional data (DBSCAN).
`funfem_cluster`	`(data, argvals, k=2, ncomp=10, p_disc=0, max_iter=50, tol=1e-06, seed=42)`	Fisher-EM discriminative functional clustering (FunFEM).
`fuzzy_cmeans_fd`	`(data, argvals, k, fuzziness=2.0, max_iter=100, tol=1e-06, seed=42)`	Fuzzy C-means clustering for functional data.
`gmm_cluster`	`(data, argvals, k_range, nbasis=5, max_iter=200, tol=1e-06, seed=42)`	GMM clustering for functional data (via basis projection).
`kcfc_cluster`	`(data, argvals, k=2, ncomp=3, max_iter=50, seed=42)`	K-means with per-cluster FPCA (KCFC) clustering for functional data.
`kmeans_fd`	`(data, argvals, k, max_iter=100, tol=1e-06, seed=42)`	K-means clustering for functional data.
`silhouette_score`	`(dist_matrix, labels)`	Silhouette score for cluster quality assessment (from distance matrix).
`silhouette_score_data`	`(data, argvals, labels)`	Silhouette score for cluster quality assessment (from data and argvals).

Function	Signature	Purpose
`conformal_classif`	`(data, labels, test_data, ncomp=3, classifier='lda', cal_fraction=0.25, alpha=0.1, seed=42)`	Conformal classification prediction sets.
`conformal_elastic_logistic`	`(data, labels, test_data, argvals, lambda=0.0, cal_fraction=0.25, alpha=0.1, seed=42)`	Conformal elastic logistic regression prediction sets.
`conformal_elastic_pcr`	`(data, response, test_data, argvals, ncomp=3, pca_method="vertical", lambda=0.0, cal_fraction=0.25, alpha=0.1, seed=42)`	Conformal elastic PCR prediction intervals.
`conformal_elastic_regression`	`(data, response, test_data, argvals, ncomp_beta=3, lambda=0.0, cal_fraction=0.25, alpha=0.1, seed=42)`	Conformal elastic regression prediction intervals.
`conformal_fregre_lm`	`(data, response, test_data, ncomp=3, cal_fraction=0.25, alpha=0.1, seed=42)`	Conformal regression prediction intervals.
`conformal_fregre_np`	`(data, response, test_data, argvals, cal_fraction=0.25, alpha=0.1, h_func=1.0, h_scalar=1.0, seed=42)`	Conformal nonparametric regression.
`conformal_logistic`	`(data, response, test_data, ncomp=3, max_iter=100, tol=1e-06, cal_fraction=0.25, alpha=0.1, seed=42)`	Conformal logistic regression prediction sets.

Function	Signature	Purpose
`kernel_add`	`(k1, k2)`	Sum of two kernels.
`kernel_brownian`	`(variance: 'float' = 1.0)`	Brownian-motion (Wiener) kernel: `variance * min(s, t)`.
`kernel_exponential`	`(lengthscale: 'float' = 1.0, variance: 'float' = 1.0)`	Exponential kernel (Matern nu=1/2): `variance * exp(-\|s-t\| / l)`.
`kernel_gaussian`	`(lengthscale: 'float' = 1.0, variance: 'float' = 1.0)`	Squared-exponential (RBF) kernel: `variance * exp(-(s-t)^2 / (2 l^2))`.
`kernel_linear`	`(variance: 'float' = 1.0, center: 'float' = 0.0)`	Linear kernel: `variance * (s-c) * (t-c)`.
`kernel_matern`	`(lengthscale: 'float' = 1.0, nu: 'float' = 1.5, variance: 'float' = 1.0)`	Matern kernel for `nu` in {0.5, 1.5, 2.5} (closed forms).
`kernel_mult`	`(k1, k2)`	Product of two kernels.
`kernel_periodic`	`(lengthscale: 'float' = 1.0, period: 'float' = 1.0, variance: 'float' = 1.0)`	Periodic kernel: `variance * exp(-2 sin^2(pi\|s-t\|/p) / l^2)`.
`kernel_polynomial`	`(degree: 'int' = 2, variance: 'float' = 1.0, offset: 'float' = 1.0)`	Polynomial kernel: `variance * (s*t + offset)^degree`.
`kernel_whitenoise`	`(variance: 'float' = 1.0)`	White-noise kernel: `variance` on the diagonal (s == t), else 0.
`make_gaussian_process`	`(argvals, kernel, n: 'int' = 1, mean=0.0, jitter: 'float' = 1e-08, seed: 'int \| None' = None)`	Sample `n` Gaussian-process curves from `kernel` on `argvals`.
`r_bridge`	`(n: 'int' = 1, argvals=None, n_points: 'int \| None' = None, sigma: 'float' = 1.0, seed: 'int \| None' = None)`	Sample `n` Brownian-bridge paths B(t) - (t/T) B(T) (R `r.bridge`).
`r_brownian`	`(n: 'int' = 1, argvals=None, n_points: 'int \| None' = None, sigma: 'float' = 1.0, seed: 'int \| None' = None)`	Sample `n` standard Brownian-motion paths (R `r.brownian`).
`r_ou`	`(n: 'int' = 1, argvals=None, n_points: 'int \| None' = None, theta: 'float' = 1.0, mu: 'float' = 0.0, sigma: 'float' = 1.0, x0: 'float \| None' = None, seed: 'int \| None' = None)`	Sample `n` Ornstein-Uhlenbeck paths (R `r.ou`).

Function	Signature	Purpose
`Dataset`	`(data: 'Fdata', argvals: 'Any', y: 'Optional[np.ndarray]', meta: 'Any', name: 'str' = '', description: 'str' = '', _extras: 'Dict[str, Any]' = <factory>) -> None`	Container for a loaded example dataset.
`load_canadian_weather`	`(variable: 'str' = 'temperature', return_fdata: 'bool' = True)`	Canadian Weather: daily curves for 35 stations over a 365-day year.
`load_growth`	`(return_fdata: 'bool' = True)`	Berkeley Growth Study: heights (cm) of 39 boys & 54 girls at 31 ages.
`load_phoneme`	`(return_fdata: 'bool' = True)`	Phoneme: log-periodograms (256 freqs) for 5 phoneme classes.
`load_sonar`	`(return_fdata: 'bool' = True)`	Sonar (UCI): 60-band sonar return energies for 208 objects.
`load_tecator`	`(return_fdata: 'bool' = True)`	Tecator: 100-channel NIR absorbance spectra of 240 meat samples.
`load_wine`	`(return_fdata: 'bool' = True)`	Wine (UCI): 13 chemical measurements for 178 wines of 3 cultivars.

Function	Signature	Purpose
`inverse_lqd`	`(psi, t_grid, target_argvals)`	Compute the inverse LQD transform: reconstruct a density from its LQD representation.
`lqd_fpca`	`(density_matrix, argvals, ncomp=3, n_quantile_pts=None)`	Functional PCA of densities via the LQD transform.
`lqd_transform`	`(density, argvals, n_quantile_pts=None)`	Compute the log-quantile density (LQD) transform of a density function.
`normalize_density`	`(vals, argvals)`	Normalize a density function to integrate to 1.
`wasserstein_barycenter`	`(density_matrix, argvals, weights=None)`	Compute the Wasserstein Fréchet mean (barycenter) of a collection of densities.

Function	Signature	Purpose
`band_1d`	`(data, ref_data)`	Band depth for 1D functional data.
`fraiman_muniz_1d`	`(data, ref_data, scale=True)`	Fraiman-Muniz depth for 1D functional data.
`fraiman_muniz_2d`	`(data, ref_data, scale=True)`	Fraiman-Muniz depth for 2D functional data.
`functional_boxplot`	`(data, method='modified_band', factor=1.5, scale=True, nproj=50, seed=None)`	Canonical López-Pintado–Romo depth-fence functional boxplot (numeric only).
`functional_depth`	`(data, method='fraiman_muniz', scale=True, nproj=50, seed=None)`	Unified self-depth dispatcher for functional data.
`functional_spatial_1d`	`(data, ref_data, argvals=None)`	Functional spatial depth for 1D data.
`functional_spatial_2d`	`(data, ref_data)`	Functional spatial depth for 2D data.
`kernel_functional_spatial_1d`	`(data, ref_data, argvals, h=1.0)`	Kernel functional spatial depth for 1D data.
`kernel_functional_spatial_2d`	`(data, ref_data, h=1.0)`	Kernel functional spatial depth for 2D data.
`modal_1d`	`(data, ref_data, h=1.0)`	Modal depth for 1D functional data.
`modal_2d`	`(data, ref_data, h=1.0)`	Modal depth for 2D functional data.
`modified_band_1d`	`(data, ref_data)`	Modified band depth for 1D functional data.
`modified_epigraph_index_1d`	`(data, ref_data)`	Modified epigraph index for 1D functional data.
`random_projection_1d`	`(data, ref_data, n_proj=50)`	Random projection depth for 1D functional data.
`random_projection_2d`	`(data, ref_data, n_proj=50)`	Random projection depth for 2D functional data.
`random_projection_deriv_1d`	`(data, ref_data, argvals=None, n_proj=50, n_deriv=1, seed=None)`	Random-projection depth using curves and their derivatives (RPD).
`random_tukey_1d`	`(data, ref_data, n_proj=50)`	Random Tukey depth for 1D functional data.
`random_tukey_2d`	`(data, ref_data, n_proj=50)`	Random Tukey depth for 2D functional data.

Function	Signature	Purpose
`anchor_explanation`	`(data, response, ncomp=3, observation=0, precision_threshold=0.95, n_bins=4)`	Anchor explanation (linear model).
`anchor_explanation_logistic`	`(data, labels, ncomp=3, observation=0, precision_threshold=0.95, n_bins=4)`	Anchor explanation (logistic model).
`andrews_loadings`	`(rotation, n_grid=100)`	Andrews-curve loadings for a rotation/loading matrix.
`andrews_transform`	`(data, n_grid=100)`	Andrews-curve transform of functional/multivariate data.
`beta_decomposition`	`(data, response, ncomp=3)`	Beta function decomposition.
`beta_decomposition_logistic`	`(data, labels, ncomp=3)`	Beta decomposition for a logistic regression model.
`calibration_diagnostics`	`(data, labels, ncomp=3, n_groups=10)`	Calibration diagnostics for a logistic model.
`conditional_permutation_importance`	`(data, response, ncomp=3, n_bins=5, n_perm=10, seed=42)`	Conditional permutation importance for a linear regression model.
`conditional_permutation_importance_logistic`	`(data, labels, ncomp=3, n_bins=5, n_perm=10, seed=42)`	Conditional permutation importance for a logistic regression model.
`conformal_prediction_residuals`	`(data, response, test_data, ncomp=3, cal_fraction=0.25, alpha=0.1, seed=42)`	Split-conformal prediction intervals.
`counterfactual_logistic`	`(data, labels, ncomp=3, observation=0, max_iter=100, step_size=0.1)`	Counterfactual explanation (logistic model, gradient descent).
`counterfactual_regression`	`(data, response, ncomp=3, observation=0, target_value=0.0)`	Counterfactual explanation (linear regression).
`dfbetas_dffits`	`(data, response, ncomp=3)`	DFBETAS and DFFITS diagnostics.
`domain_selection`	`(data, response, ncomp=3, window_width=5, threshold=0.0)`	Domain selection / interval importance (linear model).
`domain_selection_logistic`	`(data, labels, ncomp=3, window_width=5, threshold=0.0)`	Domain selection / interval importance (logistic model).
`expected_calibration_error`	`(data, labels, ncomp=3, n_bins=10)`	Expected calibration error (ECE, MCE, ACE).
`explanation_stability`	`(data, response, ncomp=3, n_boot=100, seed=42)`	Bootstrap stability analysis (linear model).
`explanation_stability_logistic`	`(data, labels, ncomp=3, n_boot=100, seed=42)`	Bootstrap stability analysis (logistic model).
`fpc_ale`	`(data, response, ncomp=3, component=0, n_bins=10)`	ALE plot for an FPC component (linear model).
`fpc_ale_logistic`	`(data, labels, ncomp=3, component=0, n_bins=10)`	ALE plot for an FPC component (logistic model).
`fpc_permutation_importance`	`(data, response, ncomp=3, n_perm=10, seed=42)`	FPC-based permutation importance.
`fpc_permutation_importance_logistic`	`(data, labels, ncomp=3, n_perm=10, seed=42)`	FPC permutation importance for a logistic model.
`fpc_shap_values`	`(data, response, ncomp=3)`	FPC SHAP values.
`fpc_shap_values_logistic`	`(data, labels, ncomp=3, n_samples=100, seed=42)`	Kernel SHAP values for a logistic model.
`fpc_vif`	`(data, response, ncomp=3)`	Variance inflation factors for FPC scores.
`fpc_vif_logistic`	`(data, labels, ncomp=3)`	Variance inflation factors for a logistic model.
`friedman_h_statistic`	`(data, response, ncomp=3, component_j=0, component_k=1, n_grid=20)`	Friedman H-statistic for interaction between two FPC components (linear model).
`friedman_h_statistic_logistic`	`(data, labels, ncomp=3, component_j=0, component_k=1, n_grid=20)`	Friedman H-statistic for a logistic model.
`functional_pdp`	`(data, response, ncomp=3, component=0, n_grid=50)`	Functional partial dependence plot.
`functional_pdp_logistic`	`(data, labels, ncomp=3, component=0, n_grid=50)`	Functional PDP/ICE for a logistic regression model.
`functional_saliency`	`(data, response, ncomp=3)`	Functional saliency maps (linear model).
`functional_saliency_logistic`	`(data, labels, ncomp=3)`	Functional saliency maps (logistic model, gradient-based).
`influence_diagnostics`	`(data, response, ncomp=3)`	Influence diagnostics (Cook's distance, leverage).
`lime_explanation`	`(data, response, ncomp=3, observation=0, n_samples=100, kernel_width=1.0, seed=42)`	LIME explanation for a linear regression model.
`lime_explanation_logistic`	`(data, labels, ncomp=3, observation=0, n_samples=100, kernel_width=1.0, seed=42)`	LIME explanation for a logistic regression model.
`loo_cv_press`	`(data, response, ncomp=3)`	LOO-CV / PRESS diagnostics.
`pointwise_importance`	`(data, response, ncomp=3)`	Pointwise variable importance for a linear regression model.
`pointwise_importance_logistic`	`(data, labels, ncomp=3)`	Pointwise variable importance for a logistic regression model.
`prediction_intervals`	`(data, response, new_data, ncomp=3, confidence_level=0.95)`	Prediction intervals for new observations.
`prototype_criticism`	`(data, ncomp=3, n_prototypes=5, n_criticisms=5)`	Prototype/criticism selection (MMD-based).
`regression_depth`	`(data, response, ncomp=3, n_boot=100, depth_type='fraiman_muniz', seed=42)`	Regression depth diagnostics (linear model).
`regression_depth_logistic`	`(data, labels, ncomp=3, n_boot=100, depth_type='fraiman_muniz', seed=42)`	Regression depth diagnostics (logistic model).
`significant_regions`	`(lower, upper)`	Significant regions of the beta function.
`significant_regions_from_se`	`(beta_t, beta_se, z_alpha=1.96)`	Significant regions from beta(t) and its standard error.
`sobol_indices`	`(data, response, ncomp=3)`	Sobol sensitivity indices (linear model).
`sobol_indices_logistic`	`(data, labels, ncomp=3, n_samples=1000, seed=42)`	Sobol sensitivity indices (logistic model, Saltelli MC).

Function	Signature	Purpose
`dense_flmm`	`(data, subject_ids, covariates=None, ncomp=3, max_iter=50, tol=1e-10)`	Fit a Functional Linear Mixed Model (FLMM) via REML-EM.
`fast_fmm`	`(data, subject_ids, covariates=None, smooth_window=3, max_iter=30, tol=1e-08, compute_inference=True)`	Fit a fast Functional Mixed Model (FMM) with optional Wald inference.
`multi_famm`	`(data_list, subject_ids, covariates=None, ncomp=3, max_iter=50, tol=1e-10)`	Fit a multi-variable Functional Additive Mixed Model (multiFAMM).

Function	Signature	Purpose
`frechet_anova`	`(responses, argvals, group_labels, n_perm=999, seed=42)`	Fréchet ANOVA: test equality of Fréchet means across groups.
`frechet_global_reg`	`(predictors, responses, argvals, xout)`	Global Fréchet linear regression for density-response functional data.
`frechet_local_reg`	`(predictors, responses, argvals, xout, bandwidth)`	Local Fréchet regression for density-response functional data.
`frechet_mean`	`(objects, space, d, weights=None)`	Fréchet mean over a metric space, dispatched by space name.

Function	Signature	Purpose
`pred_mae`	`(y_true, y_pred) -> 'float'`	Mean absolute error (R `pred.MAE`).
`pred_mse`	`(y_true, y_pred) -> 'float'`	Mean squared error (R `pred.MSE`).
`pred_r2`	`(y_true, y_pred) -> 'float'`	Coefficient of determination R^2 (R `pred.R2`).
`pred_rmse`	`(y_true, y_pred) -> 'float'`	Root mean squared error (R `pred.RMSE`).
`prediction_metrics`	`(y_true, y_pred) -> 'dict'`	All four `pred.*` metrics as a dict (`mae`, `mse`, `rmse`, `r2`).

Function	Signature	Purpose
`PyMultiFunData`	`(...)`	Opaque handle wrapping fdars-core MultiFunData for multi-domain functional data.
`multi_fdata_from_components`	`(data_list, argvals_list)`	Build a PyMultiFunData handle from lists of 2-D data arrays and 1-D argvals vectors.

Function	Signature	Purpose
`center_1d`	`(data)`	Center functional data by subtracting the pointwise mean.
`depth_based_median`	`(data)`	Return the depth-based median curve of 1D functional data.
`deriv_1d`	`(data, argvals, nderiv=1)`	Compute numerical derivatives of 1D functional data.
`deriv_2d`	`(data, argvals_s, argvals_t)`	Compute numerical derivatives of 2D functional data.
`functional_covariance`	`(data)`	Compute the Bessel-corrected m×m covariance surface of 1D functional data.
`functional_std`	`(data)`	Compute the Bessel-corrected pointwise standard deviation of 1D functional data.
`functional_variance`	`(data)`	Compute the Bessel-corrected pointwise variance of 1D functional data.
`geometric_median_1d`	`(data, argvals, max_iter=100, tol=1e-08)`	Compute the geometric (L1) median of 1D functional data.
`geometric_median_2d`	`(data, argvals_s, argvals_t, max_iter=100, tol=1e-08)`	Compute the geometric (L1) median of 2D functional data.
`mean_1d`	`(data)`	Compute the pointwise mean of 1D functional data.
`mean_2d`	`(data)`	Compute the pointwise mean of 2D functional data.
`norm_lp_1d`	`(data, argvals, p=2.0)`	Compute Lp norms of 1D functional data.
`normalize`	`(data, method='center')`	Normalize functional data.
`normalize_with_argvals`	`(data, argvals, method='center', p=2.0)`	Normalize functional data (with argvals for Lp normalization).
`trim_mean`	`(data, alpha=0.0)`	Compute the depth-trimmed mean of 1D functional data.

Function	Signature	Purpose
`dpca`	`(data, argvals, ncomp=3, bandwidth=None, filter_lag=None)`	Fit Dynamic Functional Principal Components Analysis (DPCA).
`dpca_reconstruct`	`(data, argvals, ncomp=3, bandwidth=None, filter_lag=None)`	Fit DPCA and reconstruct the functional time series from dynamic components.
`fplsr`	`(data, argvals, ncomp=3)`	Functional Partial Least Squares Regression (fPLSR) one-step-ahead forecast.
`ftsm`	`(data, argvals, ncomp=3)`	Fit a Functional Time Series Model (FTSM) via FPCA + Yule-Walker AR fitting.
`ftsm_forecast`	`(data, argvals, h=1, ncomp=3)`	Fit an FTSM and produce a single- or multi-horizon forecast (single-step variant).
`ftsm_forecast_multistep`	`(data, argvals, h=5, ncomp=3)`	Fit an FTSM and produce a multi-step forecast (iterative multi-step variant).
`ftsm_update`	`(data, new_curve, argvals, ncomp=3)`	Online update of an FTSM with one or more new curves.
`functional_acf`	`(data, argvals, max_lag=None, n_sim=999, ci=0.95, seed=42)`	Compute the functional autocorrelation function (ACF) with Monte Carlo bands.
`functional_difference`	`(data)`	Compute the first-order functional difference (lag-1 differencing).
`functional_pacf`	`(data, argvals, max_lag=None, n_sim=999, ci=0.95, seed=42)`	Compute the functional partial autocorrelation function (PACF) with Monte Carlo bands.
`long_run_covariance`	`(data, argvals, bandwidth=None)`	Estimate the long-run covariance operator of a functional time series.
`spectral_density`	`(data, argvals, bandwidth=None)`	Estimate the spectral density operator of a functional time series.
`stationarity_test`	`(data, argvals, n_perm=999, seed=42)`	Test stationarity of functional time series via permutation test.

Function	Signature	Purpose
`f_perm_test`	`(data_a, data_b, argvals, n_perm=999, seed=None)`	Functional two-sample permutation F-test.
`flm_f_test`	`(data, response, n_comp=5)`	Functional linear model overall-significance F-test.
`flm_gof_test`	`(data, response, n_comp=5)`	Functional linear model goodness-of-fit test (Ramsey-RESET style).
`itp_flm`	`(data, response, argvals, basis_type='bspline', nbasis=5, n_perm=999, seed=None)`	Interval-wise testing procedure for the functional linear model.
`itp_one_pop`	`(data, argvals, mu0=None, basis_type='bspline', nbasis=5, n_perm=999, seed=None)`	Interval-wise testing procedure for a single functional population.
`itp_two_pop`	`(data_a, data_b, argvals, basis_type='bspline', nbasis=5, n_perm=999, seed=None)`	Interval-wise testing procedure for two functional populations.
`mean_scb`	`(data, argvals, bandwidth, nb=200, confidence=0.95, multiplier='gaussian')`	Simultaneous confidence band for the mean function (Degras).
`oneway_anova_vstat`	`(data, groups, argvals)`	One-way functional ANOVA V-statistic (asymptotic scaled-χ² test).
`scb_two_sample_test`	`(data_a, data_b, argvals, bandwidth, nb=200, confidence=0.95, multiplier='gaussian')`	Two-sample mean-equality test via a simultaneous confidence band for the
`t_perm_test`	`(data_a, data_b, argvals, n_perm=999, seed=None)`	Functional two-sample permutation t-test.
`two_sample_mean_test`	`(data_a, data_b, argvals, ncomp=5)`	Functional two-sample mean-equality test via Hotelling-T² on a shared FPC

Function	Signature	Purpose
`PyGakGramTrain`	`(...)`	Opaque handle wrapping fdars-core GakGramTrain for incremental GAK Gram computation.
`dtw_cross_1d`	`(data1, data2, p=2.0, w=0)`	DTW cross distance for 1D data.
`dtw_self_1d`	`(data, p=2.0, w=0)`	DTW distance matrix (self) for 1D data.
`fourier_cross_1d`	`(data1, data2, n_basis=5)`	Fourier coefficient distance (cross).
`fourier_self_1d`	`(data, n_basis=5)`	Fourier coefficient distance (self) for 1D data.
`gak`	`(x, y, sigma)`	Global Alignment Kernel between two 1-D time series.
`gak_gram_matrix`	`(data, sigma=None)`	Global Alignment Kernel Gram matrix (one-shot, symmetric).
`gak_gram_predict`	`(train, new_data)`	Compute the GAK Gram matrix between new data and the training set.
`gak_gram_train`	`(data, sigma=None)`	Fit a GAK Gram handle for incremental train/predict computation.
`hausdorff_cross_1d`	`(data1, data2, argvals)`	Hausdorff cross distance for 1D data.
`hausdorff_cross_2d`	`(data1, data2, argvals_s, argvals_t)`	Hausdorff cross distance for 2D data.
`hausdorff_self_1d`	`(data, argvals)`	Hausdorff distance matrix (self) for 1D data.
`hausdorff_self_2d`	`(data, argvals_s, argvals_t)`	Hausdorff self distance for 2D data.
`hshift_cross_1d`	`(data1, data2, argvals, max_shift=0)`	Horizontal shift distance (cross).
`hshift_self_1d`	`(data, argvals, max_shift=0)`	Horizontal shift distance (self) for 1D data.
`inprod`	`(data1, data2, argvals=None)`	Inner product between two functional data sets (Simpson-integrated).
`int_simpson`	`(data, argvals=None)`	Simpson's-rule integral of each curve.
`lp_cross_1d`	`(data1, data2, argvals, p=2.0)`	Lp distance matrix (cross) between two 1D functional datasets.
`lp_cross_2d`	`(data1, data2, argvals_s, argvals_t, p=2.0)`	Lp cross distance for 2D data.
`lp_self_1d`	`(data, argvals, p=2.0)`	Lp distance matrix (self) for 1D functional data.
`lp_self_2d`	`(data, argvals_s, argvals_t, p=2.0)`	Lp distance matrix (self) for 2D functional data.
`sigma_gak`	`(data)`	Heuristic GAK bandwidth: median pairwise Euclidean distance, floored at 1e-8.
`soft_dtw_cross_1d`	`(data1, data2, gamma=1.0)`	Soft-DTW cross distance for 1D data.
`soft_dtw_div_cross_1d`	`(data1, data2, gamma=1.0)`	Soft-DTW divergence cross distance.
`soft_dtw_div_self_1d`	`(data, gamma=1.0)`	Soft-DTW divergence distance matrix (self) for 1D data.
`soft_dtw_self_1d`	`(data, gamma=1.0)`	Soft-DTW distance matrix (self) for 1D data.

Function	Signature	Purpose
`depthgram`	`(data, outliergram_factor=1.5, boxplot_factor=1.5)`	Depthgram functional outlier detection.
`detect_outliers_lrt`	`(data, alpha=0.05, n_bootstrap=200, trim=0.1, smo=0.02)`	LRT-based outlier detection with bootstrap.
`detect_outliers_lrt_with_dist`	`(data, alpha=0.05, n_bootstrap=200, trim=0.1, smo=0.02, seed=42)`	LRT-based outlier detection with bootstrap (returns threshold and null distribution).
`magnitude_shape`	`(data)`	Magnitude-shape outlyingness.
`muod`	`(data, factor=1.5)`	MUOD (Massive Unsupervised Outlier Detection) for functional data.
`outliergram`	`(data, factor=1.5)`	Outliergram (MEI vs MBD plot).
`sequential_transform_outliers`	`(data, transforms, depth_method='modified_band', emp_factor=1.5)`	Sequential transform outlier detection.
`tvdmss`	`(data, emp_factor_mss=1.5, emp_factor_tvd=1.5, central_region_tvd=0.5)`	TVD-MSS functional outlier detection.

Function	Signature	Purpose
`PyIrregFdata`	`(...)`	Opaque handle wrapping fdars-core IrregFdata for irregular/sparse functional data.
`irreg_fdata_from_lists`	`(argvals_list, values_list)`	Build an IrregFdata handle from two Python lists of ragged 1-D arrays.
`pace_fpca`	`(data, ncomp=3, bandwidth=0.1, sigma2=0.01, work_grid=None, alpha=0.05)`	Run PACE FPCA on irregular/sparse functional data.

Function	Signature	Purpose
`bootstrap_ci_fregre_lm`	`(data, response, n_comp=3, n_boot=200, alpha=0.05, seed=42)`	Bootstrap confidence intervals for beta(t) from a functional linear model.
`bootstrap_ci_functional_logistic`	`(data, labels, n_comp=3, n_boot=200, alpha=0.05, seed=42, max_iter=25, tol=1e-06)`	Bootstrap confidence intervals for beta(t) from a functional logistic model.
`concurrent_regression`	`(predictors, response, argvals=None, bandwidth=0.2, kernel='gaussian')`	Concurrent (varying-coefficient) functional regression.
`fanova`	`(data, groups, n_perm=999)`	Functional ANOVA.
`fof_cv`	`(x_data, y_data, x_argvals, y_argvals, ncomp_x_max=5, ncomp_y_max=5, n_folds=5, seed=42)`	Cross-validated selection of FPC component counts for function-on-function regression.
`fof_re_regression`	`(x_data, y_data, subject_ids, x_argvals, y_argvals, ncomp_x=3, ncomp_y=3, max_iter=50, tol=1e-10)`	Function-on-function random-effects regression (mixed model).
`fof_regression`	`(x_data, y_data, x_argvals, y_argvals, ncomp_x=3, ncomp_y=3)`	Function-on-function linear regression via FPC basis decomposition.
`fosr`	`(response, predictors, lambda_=0.0)`	Function-on-scalar regression (FOSR).
`fosr_fpc`	`(data, predictors, n_comp=3)`	Function-on-scalar regression via FPCs (FOSR-FPC).
`fpca`	`(data, argvals, n_comp=3)`	Functional principal component analysis (FPCA).
`fpls`	`(data, argvals, response, n_comp=3)`	Functional PLS (Partial Least Squares).
`fregre_cv`	`(data, response, k_min=1, k_max=10, n_folds=5)`	Cross-validated selection of number of FPC components using K-fold CV.
`fregre_huber`	`(data, response, n_comp=3, huber_k=1.345)`	Huber M-estimation regression for functional data.
`fregre_l1`	`(data, response, n_comp=3)`	L1 robust regression for functional data.
`fregre_lm`	`(data, response, n_comp=3)`	Scalar-on-function linear regression via FPCs.
`fregre_np`	`(dist_matrix, response, h=0.0)`	Nonparametric kernel regression for functional data (from distance matrix).
`fregre_np_cv`	`(data, response, argvals, n_folds=5, h_range=None, scalar_covariates=None)`	Cross-validated bandwidth selection for nonparametric functional regression.
`fregre_np_mixed`	`(data, response, argvals, h_func, h_scalar=1.0, scalar_covariates=None)`	Nonparametric functional regression mixing functional and scalar predictors.
`fregre_pls`	`(data, argvals, response, n_comp=3)`	Scalar-on-function PLS regression.
`functional_glm`	`(data, response, family='gaussian', n_comp=3, scalar_covariates=None, max_iter=25, tol=1e-06)`	Functional generalised linear model (GLM) via FPC scores.
`functional_logistic`	`(data, labels, n_comp=3, max_iter=25, tol=1e-06)`	Functional logistic regression.
`model_selection_ncomp`	`(data, response, max_comp=10, criterion='gcv')`	Cross-validated selection of number of FPC components.
`predict_fof`	`(x_data, y_data, new_x, x_argvals, y_argvals, ncomp_x=3, ncomp_y=3)`	Predict functional responses for new predictor curves using a function-on-function model.
`predict_fof_re`	`(x_data, y_data, subject_ids, new_x, x_argvals, y_argvals, ncomp_x=3, ncomp_y=3, max_iter=50, tol=1e-10)`	Predict functional responses using a function-on-function random-effects model.
`predict_fosr`	`(response, predictors, new_predictors, lambda_=0.0)`	Predict new functional responses from a fitted FOSR model.
`predict_fregre_lm`	`(data_fit, response, new_data, n_comp=3)`	Predict new responses using a fitted functional linear model.
`predict_fregre_pls`	`(data, argvals, response, new_data, n_comp=3)`	Predict new responses using a fitted PLS regression.
`predict_fregre_robust`	`(data, response, new_data, n_comp=3, method='l1', huber_k=1.345)`	Predict new responses using a fitted robust regression (L1 or Huber).
`predict_functional_logistic`	`(data, labels, new_data, n_comp=3, max_iter=25, tol=1e-06)`	Predict probabilities for new data using a fitted functional logistic model.

Function	Signature	Purpose
`fdata_interpolate_with_policy`	`(data, argvals, query_points, policy='exception', fill_value=0.0, method='linear')`	Interpolate functional data with explicit extrapolation control (linear/cubic variant).
`impute_missing_values`	`(data, argvals, method='linear', constant_value=0.0)`	Impute NaN values in a functional data matrix.
`spline_interpolate`	`(data, argvals, query_points, order=4)`	Interpolate functional data onto a new set of query points using B-splines.
`spline_interpolate_with_policy`	`(data, argvals, query_points, policy='exception', fill_value=0.0, order=4)`	Interpolate functional data with explicit extrapolation control (spline variant).

Function	Signature	Purpose
`fam`	`(data, y, argvals, scalar_covariates=None, ncomp=0, bandwidth=0.0, kernel='gaussian', n_grid_bandwidth=20)`	Fit a Functional Additive Model (FAM) with a single functional predictor.
`fregre_gkam`	`(predictors, y, argvals_list, scalar_covariates=None, bandwidth=0.0, kernel='gaussian', max_iter=50, epsilon=1e-06)`	Fit a Generalised Kernel Additive Model (GKAM) with multiple functional predictors.
`fregre_gsam`	`(data, y, argvals, scalar_covariates=None, ncomp=0, bandwidth=0.0, kernel='gaussian', n_grid_bandwidth=20)`	Fit a Generalised Structured Additive Model (GSAM) with a single functional predictor.
`model_selection_ncomp`	`(data, response, max_comp=10, criterion='gcv')`	Select the optimal number of FPC components for scalar-on-function regression.
`variable_selection`	`(predictors, y, argvals_list, scalar_covariates=None, ncomp=3, penalty='group_lasso', lambda_=0.0, max_iter=100, epsilon=1e-05, lambda_n_grid=20)`	Functional variable selection via group-lasso penalised regression.

Function	Signature	Purpose
`functional_explained_variance`	`(y_true, y_pred, argvals)`	Functional Explained Variance Score integrated over `argvals`.
`functional_mae`	`(y_true, y_pred, argvals)`	Functional Mean Absolute Error integrated over `argvals`.
`functional_mape`	`(y_true, y_pred, argvals)`	Functional Mean Absolute Percentage Error integrated over `argvals`.
`functional_mse`	`(y_true, y_pred, argvals)`	Functional Mean Squared Error integrated over `argvals`.
`functional_msle`	`(y_true, y_pred, argvals)`	Functional Mean Squared Logarithmic Error integrated over `argvals`.

fdars AI Capability Map¶

Module Index¶

Module Details¶

fdars.alignment¶

fdars.basis¶

fdars.classification¶

fdars.clustering¶

fdars.conformal¶

fdars.covariance¶

fdars.datasets¶

fdars.density_fda¶

fdars.depth¶

fdars.explain¶

fdars.famm¶

fdars.fdata¶

fdars.frechet¶

fdars.fts¶

fdars.inference¶

fdars.metric¶

fdars.metrics¶

fdars.multi_fdata¶

fdars.outliers¶

fdars.pace_fpca¶

fdars.regression¶

fdars.represent¶

fdars.scalar_on_function¶

fdars.scoring¶

fdars.seasonal¶

fdars.shapelet¶

fdars.simulation¶

fdars.smoothing¶

fdars.spm¶

fdars.tolerance¶

`fdars.alignment`¶

`fdars.basis`¶

`fdars.classification`¶

`fdars.clustering`¶

`fdars.conformal`¶

`fdars.covariance`¶

`fdars.datasets`¶

`fdars.density_fda`¶

`fdars.depth`¶

`fdars.explain`¶

`fdars.famm`¶

`fdars.fdata`¶

`fdars.frechet`¶

`fdars.fts`¶

`fdars.inference`¶

`fdars.metric`¶

`fdars.metrics`¶

`fdars.multi_fdata`¶

`fdars.outliers`¶

`fdars.pace_fpca`¶

`fdars.regression`¶

`fdars.represent`¶

`fdars.scalar_on_function`¶

`fdars.scoring`¶

`fdars.seasonal`¶

`fdars.shapelet`¶

`fdars.simulation`¶

`fdars.smoothing`¶

`fdars.spm`¶

`fdars.tolerance`¶

Function	Signature	Purpose
`analyze_peak_timing`	`(data, argvals, period, smooth_nbasis=None)`	Analyze peak timing variability.
`autoperiod`	`(data, argvals, n_candidates=None, gradient_steps=None)`	Autoperiod algorithm for period detection.
`cfd_autoperiod`	`(data, argvals, cluster_tolerance=None, min_cluster_size=None)`	CFD autoperiod for period detection.
`classify_seasonality`	`(data, argvals, period, strength_threshold=None, timing_threshold=None)`	Classify seasonality type.
`detect_multiple_periods`	`(data, argvals, max_periods=3, min_confidence=1.5, min_strength=0.1)`	Detect multiple seasonal periods by iterative residual peeling.
`detect_peaks`	`(data, argvals, min_distance=None, min_prominence=None, smooth_first=False, smooth_nbasis=None)`	Detect peaks in functional data.
`detect_seasonality_changes`	`(data, argvals, period, threshold, window_size, min_duration)`	Detect seasonality change points.
`estimate_period_acf`	`(data, argvals, max_lag=None)`	Estimate the dominant seasonal period via autocorrelation (ACF).
`estimate_period_fft`	`(data, argvals)`	Estimate period using FFT periodogram.
`instantaneous_period`	`(data, argvals)`	Instantaneous period estimation via Hilbert transform.
`lomb_scargle_fdata`	`(data, argvals, oversampling=None, nyquist_factor=None)`	Lomb-Scargle periodogram for functional data.
`matrix_profile_fdata`	`(data, subsequence_length=None, exclusion_zone=None)`	Matrix Profile analysis for functional data.
`sazed`	`(data, argvals, tolerance=None)`	SAZED period detection algorithm.
`seasonal_strength`	`(data, argvals, period, method='variance')`	Seasonal strength measure (variance method).
`seasonal_strength_wavelet`	`(data, argvals, period)`	Seasonal strength using wavelet method.
`seasonal_strength_windowed`	`(data, argvals, period, window_size, method='variance')`	Time-varying seasonal strength using windowed estimation.
`ssa_fdata`	`(data, window_length=None, n_components=None)`	Singular Spectrum Analysis for functional data.
`stl_decompose`	`(data, period, s_window=None, t_window=None, robust=False)`	STL decomposition of functional data.

Function	Signature	Purpose
`PyShapeletClassifierFit`	`(...)`	Opaque handle wrapping fdars-core ShapeletClassifierFit.
`PyShapeletFit`	`(...)`	Opaque handle wrapping fdars-core ShapeletTransformFit.
`discover_shapelets`	`(data, labels, min_length=3, max_length=0, max_candidates=10000, max_shapelets=0, quality='info_gain', seed=0)`	Discover shapelets in labeled functional data and return a summary dict.
`shapelet_classifier_fit`	`(data, labels, min_length=3, max_length=0, max_candidates=10000, max_shapelets=0, quality='info_gain', seed=0, classifier='knn', k=1, ncomp=None)`	Fit a shapelet-based classifier on labeled functional data.
`shapelet_distance`	`(shapelet_z, series, best_so_far=Ellipsis)`	Compute the shapelet distance between a z-normalized shapelet and a series.
`shapelet_transform`	`(fit, data)`	Apply a fitted shapelet transform to new functional data.
`shapelet_transform_fit`	`(data, labels, min_length=3, max_length=0, max_candidates=10000, max_shapelets=0, quality='info_gain', seed=0)`	Fit a shapelet transform on labeled functional data.

Function	Signature	Purpose
`add_error_curve`	`(data, sd, seed=None)`	Add curve-level Gaussian noise to functional data.
`add_error_pointwise`	`(data, sd, seed=None)`	Add pointwise Gaussian noise to functional data.
`covariance_matrix`	`(argvals, kernel='gaussian', length_scale=0.2, variance=1.0)`	Compute covariance matrix from a kernel.
`eigenfunctions`	`(argvals, n_basis, efun_type='fourier')`	Compute eigenfunctions.
`eigenvalues`	`(n_basis, eval_type='linear')`	Compute eigenvalues.
`gaussian_process`	`(n, argvals, kernel='gaussian', length_scale=0.2, variance=1.0, seed=None)`	Generate Gaussian process samples.
`sim_kl`	`(n, phi, big_m, lambda_, seed=None)`	Simulate functional data via Karhunen-Loeve expansion (low-level).
`simulate`	`(n, argvals, n_basis=5, efun_type='fourier', eval_type='linear', seed=None)`	Simulate functional data via Karhunen-Loeve expansion.

Function	Signature	Purpose
`cv_smoother`	`(x, y, bandwidth, kernel='gaussian')`	LOO-CV score for a kernel smoother.
`gcv_smoother`	`(x, y, bandwidth, kernel='gaussian')`	GCV score for a kernel smoother.
`knn_gcv`	`(x, y, max_k)`	Global LOO-CV for kNN k selection.
`knn_lcv`	`(x, y, max_k)`	Local (per-observation) LOO-CV for kNN k selection.
`knn_smoother`	`(x, y, x_new, k)`	K-nearest neighbors smoother.
`local_linear`	`(x, y, x_new, bandwidth, kernel='gaussian')`	Local linear regression smoother.
`local_polynomial`	`(x, y, x_new, bandwidth, degree=1, kernel='gaussian')`	Local polynomial regression smoother.
`nadaraya_watson`	`(x, y, x_new, bandwidth, kernel='gaussian')`	Nadaraya-Watson kernel smoother.
`optim_bandwidth`	`(x, y, criterion='gcv', kernel='gaussian', n_grid=50, h_min=None, h_max=None)`	Optimal bandwidth selection via cross-validation.
`smoothing_matrix_nw`	`(x, bandwidth, kernel='gaussian')`	Smoothing matrix for Nadaraya-Watson.

Function	Signature	Purpose
`arl0_ewma_t2`	`(eigenvalues, ucl, lambda_, n_simulations=10000, max_run_length=5000, seed=42)`	In-control ARL for EWMA T-squared chart.
`arl0_spe`	`(spe_df, spe_scale, ucl, n_simulations=10000, max_run_length=5000, seed=42)`	In-control ARL for SPE chart.
`arl0_t2`	`(eigenvalues, ucl, n_simulations=10000, max_run_length=5000, seed=42)`	In-control ARL for T-squared chart (ARL0).
`arl1_t2`	`(eigenvalues, ucl, shift, n_simulations=10000, max_run_length=5000, seed=42)`	Out-of-control ARL for T-squared chart (ARL1).
`ewma_scores`	`(scores, lambda_)`	EWMA smoothing of FPC scores.
`hotelling_t2`	`(scores, eigenvalues)`	Hotelling T^2 statistic.
`hotelling_t2_regularized`	`(scores, eigenvalues, epsilon)`	Hotelling T^2 with eigenvalue regularization.
`mfpca`	`(variables, ncomp=5, weighted=True)`	Multivariate Functional Principal Component Analysis (MFPCA).
`nelson_rules`	`(values, center, sigma)`	Apply Nelson rules to monitoring data.
`select_ncomp`	`(eigenvalues, method='cumulative_variance', threshold=0.95)`	Select the number of principal components.
`spe_control_limit`	`(spe_values, alpha)`	Compute SPE control limit using moment-matched chi-squared approximation.
`spe_limit_robust`	`(spe_values, alpha=0.05, method='empirical')`	Robust SPE (squared prediction error) control limit.
`spe_moment_match_diagnostic`	`(spe_values)`	Diagnostic for SPE moment-match chi-squared approximation.
`spe_multivariate`	`(standardized_vars, reconstructed_vars, argvals_list)`	Multivariate Squared Prediction Error (SPE) monitoring statistic.
`spm_cusum`	`(train_data, sequential_data, argvals, ncomp=5, alpha=0.05, k=0.5, h=5.0, multivariate=False)`	Functional CUSUM control chart (fit Phase I + monitor).
`spm_ewma`	`(train_data, sequential_data, argvals, ncomp=5, alpha=0.05, lam=0.2)`	Functional EWMA control chart (fit Phase I + monitor).
`spm_monitor`	`(mean, loadings, weights, eigenvalues, t2_limit, spe_limit, new_data, argvals)`	SPM Phase II monitoring.
`spm_phase1`	`(data, argvals, ncomp=3, alpha=0.05)`	SPM Phase I estimation.
`t2_control_limit`	`(ncomp, alpha)`	Compute T-squared control limit from chi-squared distribution.
`t2_limit_robust`	`(t2_values, ncomp, alpha=0.05, method='empirical')`	Robust Hotelling T^2 control limit.
`t2_pc_contributions`	`(scores, eigenvalues)`	Per-PC T-squared contributions.
`t2_pc_significance`	`(contributions, alpha)`	Test per-PC T-squared contributions for Bonferroni-adjusted significance.
`western_electric_rules`	`(values, center, sigma)`	Apply Western Electric rules to monitoring data.

Function	Signature	Purpose
`conformal_prediction_band`	`(data, coverage=0.95, cal_fraction=0.25, seed=42)`	Conformal prediction band.
`elastic_tolerance_band`	`(data, argvals, ncomp=3, nb=200, coverage=0.95, band_type='simultaneous', max_iter=20, seed=42)`	Elastic tolerance band (amplitude only, after alignment).
`elastic_tolerance_band_with_config`	`(data, argvals, ncomp_amplitude=3, ncomp_phase=3, nb=200, coverage=0.95, band_type='pointwise', max_iter=20, tol=0.0001, seed=42)`	Joint amplitude and phase elastic tolerance bands.
`equivalence_test`	`(data1, data2, delta, alpha=0.05, nb=1000, seed=42)`	Functional equivalence test (TOST).
`equivalence_test_one_sample`	`(data, mu0, delta, alpha=0.05, nb=1000, seed=42)`	One-sample equivalence test.
`exponential_family_tolerance_band`	`(data, family='gaussian', ncomp=3, nb=200, coverage=0.95, seed=42)`	Exponential family tolerance band.
`fpca_tolerance_band`	`(data, ncomp=3, nb=1000, coverage=0.95, seed=42)`	FPCA-based tolerance band.
`phase_tolerance_band`	`(data, argvals, ncomp=3, nb=200, coverage=0.95, band_type='simultaneous', max_iter=20, seed=42)`	Phase tolerance band on warping functions.
`scb_mean_degras`	`(data, argvals, bandwidth=0.0, nb=1000, confidence=0.95)`	Simultaneous confidence band (Degras method).