Crate fdars_core 

fdars-core

Core algorithms for Functional Data Analysis in Rust.

This crate provides pure Rust implementations of various FDA methods including:

• Functional data operations (mean, derivatives, norms)
• Depth measures (Fraiman-Muniz, modal, band, random projection, etc.)
• Distance metrics (Lp, Hausdorff, DTW, Fourier, etc.)
• Basis representations (B-splines, P-splines, Fourier)
• Clustering (k-means, fuzzy c-means)
• Smoothing (Nadaraya-Watson, local linear/polynomial regression)
• Outlier detection
• Regression (PCA, PLS, ridge)
• Seasonal analysis (period estimation, peak detection, seasonal strength)
• Detrending and decomposition for non-stationary data

Data Layout

Functional data is represented using the FdMatrix type, a column-major matrix wrapping a flat Vec<f64> with safe (i, j) indexing and dimension tracking:

• For n observations with m evaluation points: data[(i, j)] gives observation i at point j
• 2D surfaces (n observations, m1 x m2 grid): stored as n x (m1*m2) matrices
• Zero-copy column access via data.column(j), row gather via data.row(i)
• nalgebra interop via to_dmatrix() / from_dmatrix() for SVD operations

Re-exports

pub use matrix::FdCurveSet;

pub use matrix::FdMatrix;

pub use alignment::align_to_target;

pub use alignment::alignment_quality;

pub use alignment::amplitude_distance;

pub use alignment::amplitude_self_distance_matrix;

pub use alignment::compose_warps;

pub use alignment::elastic_align_pair;

pub use alignment::elastic_align_pair_constrained;

pub use alignment::elastic_align_pair_nd;

pub use alignment::elastic_align_pair_with_landmarks;

pub use alignment::elastic_cross_distance_matrix;

pub use alignment::elastic_decomposition;

pub use alignment::elastic_distance;

pub use alignment::elastic_distance_nd;

pub use alignment::elastic_self_distance_matrix;

pub use alignment::karcher_mean;

pub use alignment::pairwise_consistency;

pub use alignment::phase_distance_pair;

pub use alignment::phase_self_distance_matrix;

pub use alignment::reparameterize_curve;

pub use alignment::srsf_inverse;

pub use alignment::srsf_inverse_nd;

pub use alignment::srsf_transform;

pub use alignment::srsf_transform_nd;

pub use alignment::tsrvf_from_alignment;

pub use alignment::tsrvf_from_alignment_with_method;

pub use alignment::tsrvf_inverse;

pub use alignment::tsrvf_transform;

pub use alignment::tsrvf_transform_with_method;

pub use alignment::warp_complexity;

pub use alignment::warp_smoothness;

pub use alignment::AlignmentQuality;

pub use alignment::AlignmentResult;

pub use alignment::AlignmentResultNd;

pub use alignment::AlignmentSetResult;

pub use alignment::ConstrainedAlignmentResult;

pub use alignment::DecompositionResult;

pub use alignment::KarcherMeanResult;

pub use alignment::TransportMethod;

pub use alignment::TsrvfResult;

pub use helpers::cumulative_trapz;

pub use helpers::extract_curves;

pub use helpers::gradient;

pub use helpers::gradient_nonuniform;

pub use helpers::gradient_uniform;

pub use helpers::l2_distance;

pub use helpers::linear_interp;

pub use helpers::simpsons_weights;

pub use helpers::simpsons_weights_2d;

pub use helpers::trapz;

pub use helpers::DEFAULT_CONVERGENCE_TOL;

pub use helpers::NUMERICAL_EPS;

pub use warping::exp_map_sphere;

pub use warping::gam_to_psi;

pub use warping::gam_to_psi_smooth;

pub use warping::inner_product_l2;

pub use warping::inv_exp_map_sphere;

pub use warping::invert_gamma;

pub use warping::l2_norm_l2;

pub use warping::normalize_warp;

pub use warping::phase_distance;

pub use warping::psi_to_gam;

pub use seasonal::autoperiod;

pub use seasonal::autoperiod_fdata;

pub use seasonal::cfd_autoperiod;

pub use seasonal::cfd_autoperiod_fdata;

pub use seasonal::hilbert_transform;

pub use seasonal::sazed;

pub use seasonal::sazed_fdata;

pub use seasonal::AutoperiodCandidate;

pub use seasonal::AutoperiodResult;

pub use seasonal::CfdAutoperiodResult;

pub use seasonal::ChangeDetectionResult;

pub use seasonal::ChangePoint;

pub use seasonal::ChangeType;

pub use seasonal::DetectedPeriod;

pub use seasonal::InstantaneousPeriod;

pub use seasonal::Peak;

pub use seasonal::PeakDetectionResult;

pub use seasonal::PeriodEstimate;

pub use seasonal::SazedComponents;

pub use seasonal::SazedResult;

pub use seasonal::StrengthMethod;

pub use landmark::detect_and_register;

pub use landmark::detect_landmarks;

pub use landmark::landmark_register;

pub use landmark::Landmark;

pub use landmark::LandmarkKind;

pub use landmark::LandmarkResult;

pub use detrend::DecomposeResult;

pub use detrend::TrendResult;

pub use simulation::EFunType;

pub use simulation::EValType;

pub use irreg_fdata::IrregFdata;

pub use irreg_fdata::KernelType;

pub use tolerance::conformal_prediction_band;

pub use tolerance::elastic_tolerance_band;

pub use tolerance::equivalence_test;

pub use tolerance::equivalence_test_one_sample;

pub use tolerance::exponential_family_tolerance_band;

pub use tolerance::fpca_tolerance_band;

pub use tolerance::scb_mean_degras;

pub use tolerance::BandType;

pub use tolerance::EquivalenceBootstrap;

pub use tolerance::EquivalenceTestResult;

pub use tolerance::ExponentialFamily;

pub use tolerance::MultiplierDistribution;

pub use tolerance::NonConformityScore;

pub use tolerance::ToleranceBand;

pub use famm::fmm;

pub use famm::fmm_predict;

pub use famm::fmm_test_fixed;

pub use famm::FmmResult;

pub use famm::FmmTestResult;

pub use function_on_scalar::fanova;

pub use function_on_scalar::fosr;

pub use function_on_scalar::fosr_fpc;

pub use function_on_scalar::predict_fosr;

pub use function_on_scalar::FanovaResult;

pub use function_on_scalar::FosrFpcResult;

pub use function_on_scalar::FosrResult;

pub use scalar_on_function::bootstrap_ci_fregre_lm;

pub use scalar_on_function::bootstrap_ci_functional_logistic;

pub use scalar_on_function::fregre_basis_cv;

pub use scalar_on_function::fregre_cv;

pub use scalar_on_function::fregre_lm;

pub use scalar_on_function::fregre_np_cv;

pub use scalar_on_function::fregre_np_mixed;

pub use scalar_on_function::functional_logistic;

pub use scalar_on_function::model_selection_ncomp;

pub use scalar_on_function::predict_fregre_lm;

pub use scalar_on_function::predict_fregre_np;

pub use scalar_on_function::predict_functional_logistic;

pub use scalar_on_function::BootstrapCiResult;

pub use scalar_on_function::FregreBasisCvResult;

pub use scalar_on_function::FregreCvResult;

pub use scalar_on_function::FregreLmResult;

pub use scalar_on_function::FregreNpCvResult;

pub use scalar_on_function::FregreNpResult;

pub use scalar_on_function::FunctionalLogisticResult;

pub use scalar_on_function::ModelSelectionResult;

pub use scalar_on_function::SelectionCriterion;

pub use explain_generic::generic_ale;

pub use explain_generic::generic_anchor;

pub use explain_generic::generic_conditional_permutation_importance;

pub use explain_generic::generic_counterfactual;

pub use explain_generic::generic_domain_selection;

pub use explain_generic::generic_friedman_h;

pub use explain_generic::generic_lime;

pub use explain_generic::generic_pdp;

pub use explain_generic::generic_permutation_importance;

pub use explain_generic::generic_prototype_criticism;

pub use explain_generic::generic_saliency;

pub use explain_generic::generic_shap_values;

pub use explain_generic::generic_sobol_indices;

pub use explain_generic::generic_stability;

pub use explain_generic::generic_vif;

pub use explain_generic::FpcPredictor;

pub use explain_generic::TaskType;

pub use elastic_explain::elastic_pcr_attribution;

pub use elastic_explain::ElasticAttributionResult;

pub use explain::anchor_explanation;

pub use explain::anchor_explanation_logistic;

pub use explain::beta_decomposition;

pub use explain::beta_decomposition_logistic;

pub use explain::calibration_diagnostics;

pub use explain::conditional_permutation_importance;

pub use explain::conditional_permutation_importance_logistic;

pub use explain::conformal_prediction_residuals;

pub use explain::counterfactual_logistic;

pub use explain::counterfactual_regression;

pub use explain::dfbetas_dffits;

pub use explain::domain_selection;

pub use explain::domain_selection_logistic;

pub use explain::expected_calibration_error;

pub use explain::explanation_stability;

pub use explain::explanation_stability_logistic;

pub use explain::fpc_ale;

pub use explain::fpc_ale_logistic;

pub use explain::fpc_permutation_importance;

pub use explain::fpc_permutation_importance_logistic;

pub use explain::fpc_shap_values;

pub use explain::fpc_shap_values_logistic;

pub use explain::fpc_vif;

pub use explain::fpc_vif_logistic;

pub use explain::friedman_h_statistic;

pub use explain::friedman_h_statistic_logistic;

pub use explain::functional_pdp;

pub use explain::functional_pdp_logistic;

pub use explain::functional_saliency;

pub use explain::functional_saliency_logistic;

pub use explain::influence_diagnostics;

pub use explain::lime_explanation;

pub use explain::lime_explanation_logistic;

pub use explain::loo_cv_press;

pub use explain::pointwise_importance;

pub use explain::pointwise_importance_logistic;

pub use explain::prediction_intervals;

pub use explain::prototype_criticism;

pub use explain::regression_depth;

pub use explain::regression_depth_logistic;

pub use explain::significant_regions;

pub use explain::significant_regions_from_se;

pub use explain::sobol_indices;

pub use explain::sobol_indices_logistic;

pub use explain::AleResult;

pub use explain::AnchorCondition;

pub use explain::AnchorResult;

pub use explain::AnchorRule;

pub use explain::BetaDecomposition;

pub use explain::CalibrationDiagnosticsResult;

pub use explain::ConditionalPermutationImportanceResult;

pub use explain::ConformalPredictionResult;

pub use explain::CounterfactualResult;

pub use explain::DepthType;

pub use explain::DfbetasDffitsResult;

pub use explain::DomainSelectionResult;

pub use explain::EceResult;

pub use explain::FpcPermutationImportance;

pub use explain::FpcShapValues;

pub use explain::FriedmanHResult;

pub use explain::FunctionalPdpResult;

pub use explain::FunctionalSaliencyResult;

pub use explain::ImportantInterval;

pub use explain::InfluenceDiagnostics;

pub use explain::LimeResult;

pub use explain::LooCvResult;

pub use explain::PointwiseImportanceResult;

pub use explain::PredictionIntervalResult;

pub use explain::PrototypeCriticismResult;

pub use explain::RegressionDepthResult;

pub use explain::SignificanceDirection;

pub use explain::SignificantRegion;

pub use explain::SobolIndicesResult;

pub use explain::StabilityAnalysisResult;

pub use explain::VifResult;

pub use classification::fclassif_cv;

pub use classification::fclassif_dd;

pub use classification::fclassif_kernel;

pub use classification::fclassif_knn;

pub use classification::fclassif_knn_fit;

pub use classification::fclassif_lda;

pub use classification::fclassif_lda_fit;

pub use classification::fclassif_qda;

pub use classification::fclassif_qda_fit;

pub use classification::ClassifCvResult;

pub use classification::ClassifFit;

pub use classification::ClassifMethod;

pub use classification::ClassifResult;

pub use conformal::conformal_classif;

pub use conformal::conformal_elastic_logistic;

pub use conformal::conformal_elastic_pcr;

pub use conformal::conformal_elastic_regression;

pub use conformal::conformal_fregre_lm;

pub use conformal::conformal_fregre_np;

pub use conformal::conformal_generic_classification;

pub use conformal::conformal_generic_regression;

pub use conformal::conformal_logistic;

pub use conformal::cv_conformal_classification;

pub use conformal::cv_conformal_regression;

pub use conformal::jackknife_plus_regression;

pub use conformal::ClassificationScore;

pub use conformal::ConformalClassificationResult;

pub use conformal::ConformalMethod;

pub use conformal::ConformalRegressionResult;

pub use gmm::gmm_cluster;

pub use gmm::gmm_em;

pub use gmm::predict_gmm;

pub use gmm::CovType;

pub use gmm::GmmClusterResult;

pub use gmm::GmmResult;

pub use streaming_depth::FullReferenceState;

pub use streaming_depth::RollingReference;

pub use streaming_depth::SortedReferenceState;

pub use streaming_depth::StreamingBd;

pub use streaming_depth::StreamingDepth;

pub use streaming_depth::StreamingFraimanMuniz;

pub use streaming_depth::StreamingMbd;

pub use smooth_basis::basis_nbasis_cv;

pub use smooth_basis::bspline_penalty_matrix;

pub use smooth_basis::fourier_penalty_matrix;

pub use smooth_basis::smooth_basis;

pub use smooth_basis::smooth_basis_gcv;

pub use smooth_basis::BasisCriterion;

pub use smooth_basis::BasisNbasisCvResult;

pub use smooth_basis::BasisType;

pub use smooth_basis::FdPar;

pub use smooth_basis::SmoothBasisResult;

pub use elastic_fpca::horiz_fpca;

pub use elastic_fpca::joint_fpca;

pub use elastic_fpca::vert_fpca;

pub use elastic_fpca::HorizFpcaResult;

pub use elastic_fpca::JointFpcaResult;

pub use elastic_fpca::VertFpcaResult;

pub use elastic_regression::elastic_logistic;

pub use elastic_regression::elastic_pcr;

pub use elastic_regression::elastic_regression;

pub use elastic_regression::predict_elastic_logistic;

pub use elastic_regression::predict_elastic_regression;

pub use elastic_regression::ElasticLogisticResult;

pub use elastic_regression::ElasticPcrResult;

pub use elastic_regression::ElasticRegressionResult;

pub use elastic_regression::PcaMethod;

pub use elastic_changepoint::elastic_amp_changepoint;

pub use elastic_changepoint::elastic_fpca_changepoint;

pub use elastic_changepoint::elastic_ph_changepoint;

pub use elastic_changepoint::ChangepointResult;

pub use elastic_changepoint::ChangepointType;

pub use elastic_changepoint::CovKernel;

pub use elastic_changepoint::FpcaChangepointMethod;

pub use cv::create_folds;

pub use cv::create_stratified_folds;

pub use cv::cv_fdata;

pub use cv::fold_indices;

pub use cv::subset_rows;

pub use cv::subset_vec;

pub use cv::CvFdataResult;

pub use cv::CvMetrics;

pub use cv::CvType;

pub use smoothing::cv_smoother;

pub use smoothing::gcv_smoother;

pub use smoothing::knn_gcv;

pub use smoothing::knn_lcv;

pub use smoothing::optim_bandwidth;

pub use smoothing::CvCriterion;

pub use smoothing::KnnCvResult;

pub use smoothing::OptimBandwidthResult;

Modules

alignment

Elastic alignment and SRSF (Square-Root Slope Function) transforms.

basis

Basis representation functions for functional data.

classification

Functional classification with mixed scalar/functional predictors.

clustering

Clustering algorithms for functional data.

conformal

Conformal prediction intervals and prediction sets.

cv

Cross-validation utilities and unified CV framework.

depth

Depth measures for functional data.

detrend

Detrending and decomposition functions for non-stationary functional data.

elastic_changepoint

Elastic changepoint detection for functional data streams.

elastic_explain

Elastic shape explainability: amplitude vs phase attribution.

elastic_fpca

Vertical, horizontal, and joint FPCA for elastic functional data.

elastic_regression

Elastic regression models (alignment-integrated regression).

explain

Explainability toolkit for FPC-based scalar-on-function models.

explain_generic

Generic explainability for any FPC-based model.

famm

Functional Additive Mixed Models (FAMM).

fdata

Functional data operations: mean, center, derivatives, norms, and geometric median.

function_on_scalar

Function-on-scalar regression and functional ANOVA.

gmm

Model-based functional clustering via Gaussian mixture models.

helpers

Helper functions for numerical integration and common operations.

irreg_fdata

Irregular functional data operations.

landmark

Landmark-based registration for functional data.

matrix

Column-major matrix type for functional data analysis.

metric

Distance metrics and semimetrics for functional data.

outliers

Outlier detection for functional data.

parallel

Parallel iteration abstraction for WASM compatibility.

regression

Regression functions for functional data.

scalar_on_function

Scalar-on-function regression with mixed scalar/functional covariates.

seasonal

Seasonal time series analysis for functional data.

simulation

Simulation functions for functional data.

smooth_basis

Basis-penalized smoothing with continuous derivative penalties.

smoothing

Smoothing functions for functional data.

streaming_depth

Streaming / online depth computation for functional data.

tolerance

Tolerance bands for functional data.

utility

Utility functions for functional data analysis.

warping

Warping function utilities and Hilbert sphere geometry.

Macros

iter_maybe_parallel

Macro for conditionally parallel iteration over ranges.

maybe_par_chunks_mut

Macro for parallel/sequential chunks iteration on mutable slices.

maybe_par_chunks_mut_enumerate

Macro for enumerated parallel/sequential chunks iteration.

slice_maybe_parallel

Macro for conditionally parallel reference iteration over slices.

slice_maybe_parallel_mut

Macro for conditionally parallel mutable iteration over slices.