Package index • fdars

Functional Data Objects

fdata(): Create a functional data object
fdata.cen(): Center functional data
deriv(): Compute functional derivative
mean(<fdata>): Compute functional mean
median(): Compute Functional Median
trimmed(): Compute Functional Trimmed Mean
trimvar(): Compute Functional Trimmed Variance
var(): Functional Variance
sd(): Functional Standard Deviation
normalize(): Normalize functional data
standardize(): Standardize functional data (z-score normalization)
scale_minmax(): Min-Max scaling for functional data
gmed(): Geometric Median of Functional Data
inprod.fdata(): Inner Product of Functional Data
int.simpson(): Utility Functions for Functional Data Analysis
localavg.fdata(): Local Averages Feature Extraction
fdata.bootstrap(): Bootstrap Functional Data
fdata.bootstrap.ci(): Bootstrap Confidence Intervals for Functional Statistics
df_to_fdata2d(): Convert DataFrame to 2D functional data

Basis Representation

fdata2basis(): Convert Functional Data to Basis Coefficients
fdata2basis_2d(): Convert 2D Functional Data to Tensor Product Basis Coefficients
fdata2basis_cv(): Cross-Validation for Basis Function Number Selection
basis2fdata(): Basis Representation Functions for Functional Data
basis2fdata_2d(): Reconstruct 2D Functional Data from Tensor Product Basis Coefficients
fdata2fd(): Convert Functional Data to fd class
fdata2pc(): Convert Functional Data to Principal Component Scores
fdata2pls(): Convert Functional Data to PLS Scores
basis.aic(): AIC for Basis Representation
basis.bic(): BIC for Basis Representation
basis.gcv(): GCV Score for Basis Representation
select.basis.auto(): Automatic Per-Curve Basis Type and Number Selection
pspline(): P-spline Smoothing for Functional Data
pspline.2d(): P-spline Smoothing for 2D Functional Data

Elastic Alignment

srsf.transform(): Elastic Alignment for Functional Data
srsf.inverse(): Inverse SRSF Transform
elastic.align(): Elastic Curve Alignment
elastic.distance(): Elastic Distance Matrix
metric.elastic(): Elastic Distance (Metric Dispatcher Alias)
karcher.mean(): Karcher Mean in Elastic Metric
periodic.rotate(): Periodic Rotation for Functional Data
alignment.quality(): Alignment Quality Diagnostics
elastic.decomposition(): Elastic Phase-Amplitude Decomposition
amplitude.distance(): Amplitude Distance Matrix
phase.distance(): Phase Distance Matrix
elastic.align.constrained(): Landmark-Constrained Elastic Alignment
alignment.pairwise.consistency(): Pairwise Alignment Consistency
plot(<elastic.align>): Plot Elastic Alignment Results
plot(<karcher.mean>): Plot Karcher Mean Results
plot(<alignment.quality>): Plot Alignment Quality Diagnostics

Landmark Registration

detect.landmarks(): Landmark Registration for Functional Data
landmark.register(): Landmark Registration
plot(<landmark.register>): Plot Landmark Registration Results

TSRVF

tsrvf.transform(): TSRVF: Transported Square-Root Velocity Function
tsrvf.from.alignment(): TSRVF from Pre-computed Alignment
tsrvf.inverse(): Inverse TSRVF Transform
plot(<tsrvf>): Plot TSRVF Results

Tolerance Bands

tolerance.band(): Tolerance Bands for Functional Data
plot(<tolerance.band>): Plot Tolerance Band

Depth Functions

depth(): Depth Functions for Functional Data
depth.BD(): Band Depth
depth.FM(): Fraiman-Muniz Depth
depth.FSD(): Functional Spatial Depth
depth.KFSD(): Kernel Functional Spatial Depth
depth.MBD(): Modified Band Depth
depth.MEI(): Modified Epigraph Index
depth.mode(): Modal Depth
depth.RP(): Random Projection Depth
depth.RPD(): Random Projection Depth with Derivatives
depth.RT(): Random Tukey Depth
streaming.depth(): Streaming Depth for Functional Data
depth.streaming(): Streaming Depth (Alias)

Distance & Metrics

metric(): Distance Metrics for Functional Data
metric.DTW(): Dynamic Time Warping for Functional Data
metric.hausdorff(): Hausdorff Metric for Functional Data
metric.kl(): Kullback-Leibler Divergence Metric for Functional Data
metric.lp(): Lp Metric for Functional Data
metric.softDTW(): Soft Dynamic Time Warping Distance
softdtw.barycenter(): Soft-DTW Barycenter
norm(): Compute Lp Norm of Functional Data
semimetric.basis(): Semi-metric based on Basis Expansion
semimetric.deriv(): Semi-metric based on Derivatives
semimetric.fourier(): Semi-metric based on Fourier Coefficients (FFT)
semimetric.hshift(): Semi-metric based on Horizontal Shift (Time Warping)
semimetric.pca(): Semi-metric based on Principal Components
group.distance(): Compute Distance/Similarity Between Groups of Functional Data

Clustering

cluster.fcm(): Fuzzy C-Means Clustering for Functional Data
cluster.init(): K-Means++ Center Initialization
cluster.kmeans(): Clustering Functions for Functional Data
cluster.optim(): Optimal Number of Clusters for Functional K-Means

Outlier Detection

outliergram(): Outliergram for Functional Data
outliers.boxplot(): Outlier Detection using Functional Boxplot
outliers.depth.pond(): Outlier Detection for Functional Data
outliers.depth.trim(): Outlier Detection using Trimmed Depth
outliers.lrt(): LRT-based Outlier Detection for Functional Data
outliers.thres.lrt(): LRT Outlier Detection Threshold
magnitudeshape(): Magnitude-Shape Outlier Detection for Functional Data

Regression

fregre.basis(): Functional Basis Regression
fregre.basis.cv(): Cross-Validation for Functional Basis Regression
fregre.np(): Nonparametric Functional Regression
fregre.np.cv(): Cross-Validation for Nonparametric Functional Regression
fregre.np.multi(): Nonparametric Regression with Multiple Functional Predictors
fregre.pc(): Functional Regression
fregre.pc.cv(): Cross-Validation for Functional PC Regression
optim.np(): Optimize Bandwidth Using Cross-Validation
flm.test(): Statistical Tests for Functional Data
pred.MAE(): Mean Absolute Error
pred.MSE(): Mean Squared Error
pred.R2(): R-Squared (Coefficient of Determination)
pred.RMSE(): Root Mean Squared Error

Seasonal Analysis

estimate.period(): Estimate Seasonal Period using FFT
detect.period(): Seasonal Analysis Functions for Functional Data
detect.periods(): Detect Multiple Concurrent Periods
detect.peaks(): Detect Peaks in Functional Data
autoperiod(): Autoperiod: Hybrid FFT + ACF Period Detection
cfd.autoperiod(): CFDAutoperiod: Clustered Filtered Detrended Autoperiod
sazed(): SAZED: Spectral-ACF Zero-crossing Ensemble Detection
lomb.scargle(): Lomb-Scargle Periodogram
matrix.profile(): Matrix Profile for Motif Discovery and Period Detection
stl.fd(): STL Decomposition: Seasonal and Trend decomposition using LOESS
ssa.fd(): Singular Spectrum Analysis (SSA) for Time Series Decomposition
seasonal.strength(): Measure Seasonal Strength
seasonal.strength.curve(): Time-Varying Seasonal Strength
detect.seasonality.changes(): Detect Changes in Seasonality
detect.seasonality.changes.auto(): Detect Seasonality Changes with Automatic Threshold
detect_amplitude_modulation(): Detect Amplitude Modulation in Seasonal Time Series
instantaneous.period(): Estimate Instantaneous Period
analyze.peak.timing(): Analyze Peak Timing Variability
classify.seasonality(): Classify Seasonality Type
detrend(): Remove Trend from Functional Data
decompose(): Seasonal-Trend Decomposition

Smoothing

S.KNN(): K-Nearest Neighbors Smoother Matrix
S.LCR(): Local Cubic Regression Smoother Matrix
S.LLR(): Local Linear Regression Smoother Matrix
S.LPR(): Local Polynomial Regression Smoother Matrix
S.NW(): Smoothing Functions for Functional Data
CV.S(): Cross-Validation for Smoother Selection
GCV.S(): Generalized Cross-Validation for Smoother Selection
h.default(): Default Bandwidth
register.fd(): Curve Registration (Alignment)

Kernels (Smoothing)

Kernel(): Unified Symmetric Kernel Interface
Kernel.asymmetric(): Unified Asymmetric Kernel Interface
Kernel.integrate(): Unified Integrated Kernel Interface
Ker.cos(): Cosine Kernel
Ker.epa(): Epanechnikov Kernel
Ker.norm(): Kernel Functions
Ker.quar(): Quartic (Biweight) Kernel
Ker.tri(): Triweight Kernel
Ker.unif(): Uniform (Rectangular) Kernel
AKer.cos(): Asymmetric Cosine Kernel
AKer.epa(): Asymmetric Epanechnikov Kernel
AKer.norm(): Asymmetric Normal Kernel
AKer.quar(): Asymmetric Quartic Kernel
AKer.tri(): Asymmetric Triweight Kernel
AKer.unif(): Asymmetric Uniform Kernel
IKer.cos(): Integrated Cosine Kernel
IKer.epa(): Integrated Epanechnikov Kernel
IKer.norm(): Integrated Normal Kernel
IKer.quar(): Integrated Quartic Kernel
IKer.tri(): Integrated Triweight Kernel
IKer.unif(): Integrated Uniform Kernel

Covariance Functions (GP)

kernel.add(): Add Covariance Functions
kernel.brownian(): Brownian Motion Covariance Function
kernel.exponential(): Exponential Covariance Function
kernel.gaussian(): Gaussian (Squared Exponential) Covariance Function
kernel.linear(): Linear Covariance Function
kernel.matern(): Matern Covariance Function
kernel.mult(): Multiply Covariance Functions
kernel.periodic(): Periodic Covariance Function
kernel.polynomial(): Polynomial Covariance Function
kernel.whitenoise(): White Noise Covariance Function
make.gaussian.process(): Generate Gaussian Process Samples
cov(): Functional Covariance Function

Simulation

eFun(): Generate Eigenfunction Basis
eVal(): Generate Eigenvalue Sequence
simFunData(): Simulate Functional Data via Karhunen-Loeve Expansion
simMultiFunData(): Simulate Multivariate Functional Data
addError(): Add Measurement Error to Functional Data

Irregular Functional Data

irregFdata(): Create an Irregular Functional Data Object
is.irregular(): Check if an Object is Irregular Functional Data
sparsify(): Convert Regular Functional Data to Irregular by Subsampling
as.fdata(): Convert Irregular Functional Data to Regular Grid
mean(<irregFdata>): Estimate Mean Function for Irregular Data
summary(<irregFdata>): Summary method for irregFdata objects
print(<irregFdata>): Print method for irregFdata objects
autoplot(<irregFdata>): Autoplot method for irregFdata objects
plot(<irregFdata>): Plot method for irregFdata objects
`[`(<irregFdata>): Subset method for irregFdata objects

Random Processes

r.bridge(): Generate Brownian Bridge
r.brownian(): Generate Brownian Motion
r.ou(): Generate Ornstein-Uhlenbeck Process

Statistical Tests

fmean.test.fdata(): Test for Equality of Functional Means
fequiv.test(): Functional Equivalence Test (TOST)
group.test(): Permutation Test for Group Differences

Plotting

autoplot(<fdata>): Create a ggplot for fdata objects
plot(<fdata>): Plot method for fdata objects
boxplot(<fdata>): Functional Boxplot
plot(<fdata2pc>): Plot FPCA Results
plot(<basis.auto>): Plot method for basis.auto objects
plot(<basis.cv>): Plot method for basis.cv objects
plot(<cluster.fcm>): Plot Method for cluster.fcm Objects
plot(<cluster.kmeans>): Plot Method for cluster.kmeans Objects
plot(<cluster.optim>): Plot Method for cluster.optim Objects
plot(<fequiv.test>): Plot method for fequiv.test
plot(<group.distance>): Plot method for group.distance
plot(<outliergram>): Plot Method for Outliergram Objects
plot(<outliers.fdata>): Plot method for outliers.fdata objects
plot(<pspline>): Plot method for pspline objects
plot(<pspline.2d>): Plot method for pspline.2d objects
plot(<register.fd>): Plot Method for register.fd Objects
plot(<magnitudeshape>): Plot Method for magnitudeshape Objects
plot(<amplitude_modulation>): Plot method for amplitude_modulation objects
plot(<lomb_scargle_result>): Plot method for lomb_scargle_result objects
plot(<matrix_profile_result>): Plot method for matrix_profile_result objects
plot(<ssa_result>): Plot method for ssa_result objects
plot(<stl_result>): Plot method for stl_result objects

Prediction

predict(<fregre.fd>): Predict Method for Functional Regression (fregre.fd)
predict(<fregre.np>): Predict Method for Nonparametric Functional Regression (fregre.np)
predict(<fregre.np.multi>): Predict method for fregre.np.multi

Print & Summary

print(<fdata>): Print method for fdata objects
print(<fdata2pc>): Print Method for FPCA Results
print(<fdata.bootstrap.ci>): Print method for bootstrap CI
print(<basis.auto>): Print method for basis.auto objects
print(<basis.cv>): Print method for basis.cv objects
print(<cluster.fcm>): Print Method for cluster.fcm Objects
print(<cluster.kmeans>): Print Method for cluster.kmeans Objects
print(<cluster.optim>): Print Method for cluster.optim Objects
print(<fbplot>): Print Method for fbplot Objects
print(<fregre.fd>): Print method for fregre objects
print(<fregre.np>): Print method for fregre.np objects
print(<fregre.np.multi>): Print method for fregre.np.multi
print(<group.distance>): Print method for group.distance
print(<fequiv.test>): Print method for fequiv.test
print(<group.test>): Print method for group.test
print(<kernel>): Print Method for Covariance Functions
print(<magnitudeshape>): Print Method for magnitudeshape Objects
print(<outliergram>): Print Method for Outliergram Objects
print(<outliers.fdata>): Print method for outliers.fdata objects
print(<pspline>): Print method for pspline objects
print(<pspline.2d>): Print method for pspline.2d objects
print(<register.fd>): Print Method for register.fd Objects
summary(<basis.auto>): Summary method for basis.auto objects
summary(<fdata>): Summary method for fdata objects
print(<amplitude_modulation>): Print method for amplitude_modulation objects
print(<autoperiod_result>): Print method for autoperiod_result objects
print(<cfd_autoperiod_result>): Print method for cfd_autoperiod_result objects
print(<decomposition>): Print method for decomposition objects
print(<lomb_scargle_result>): Print method for lomb_scargle_result objects
print(<matrix_profile_result>): Print method for matrix_profile_result objects
print(<multiFunData>): Print method for multiFunData objects
print(<multiple_periods>): Print method for multiple_periods objects
print(<peak_detection>): Print method for peak_detection objects
print(<peak_timing>): Print method for peak_timing objects
print(<period_estimate>): Print method for period_estimate objects
print(<sazed_result>): Print method for sazed_result objects
print(<seasonality_changes>): Print method for seasonality_changes objects
print(<seasonality_changes_auto>): Print method for seasonality_changes_auto objects
print(<seasonality_classification>): Print method for seasonality_classification objects
print(<ssa_result>): Print method for ssa_result objects
print(<stl_result>): Print method for stl_result objects

Other

`[`(<fdata>): Subset method for fdata objects
Ops(<fdata>): Arithmetic Operations for Functional Data
kernels: Covariance Kernel Functions for Gaussian Processes
fdars fdars-package: fdars: Functional Data Analysis in 'Rust'

Internal (Rust Bindings)

Low-level Rust function wrappers. Use the R-level functions instead.

alignment_align_to_target(): Align all curves to a target curve
alignment_amplitude_dist(): Amplitude self-distance matrix
alignment_compose_warps(): Compose two warping functions
alignment_constrained(): Elastic alignment with landmark constraints
alignment_cross_dist(): Elastic cross-distance matrix
alignment_decomposition(): Elastic phase-amplitude decomposition
alignment_elastic_distance(): Elastic (Fisher-Rao) distance between two curves
alignment_elastic_pair(): Elastic alignment of one curve to another
alignment_karcher_mean(): Karcher (Fréchet) mean in elastic metric
alignment_pairwise_consistency(): Pairwise alignment consistency
alignment_phase_dist(): Phase self-distance matrix
alignment_quality_compute(): Compute alignment quality metrics
alignment_reparameterize(): Apply warping function to reparameterize a curve
alignment_self_dist(): Elastic self-distance matrix
alignment_srsf_inverse(): Inverse SRSF: reconstruct curve from SRSF representation
alignment_srsf_transform(): SRSF transform of functional data
alignment_tsrvf_from_karcher(): Compute TSRVF from a pre-computed Karcher mean
alignment_tsrvf_inverse(): Inverse TSRVF: reconstruct curves from tangent vectors
alignment_tsrvf_transform(): Full TSRVF transform
alignment_warp_complexity(): Compute warp complexity
alignment_warp_smoothness(): Compute warp smoothness
alignment_with_landmarks(): Elastic alignment with automatic landmark detection
landmark_detect(): Detect landmarks in a single curve
landmark_register_curves(): Detect landmarks and register curves
tolerance_conformal(): Conformal prediction band
tolerance_elastic(): Elastic tolerance band (alignment + FPCA)
tolerance_exponential(): Exponential family tolerance band
tolerance_fpca(): FPCA-based tolerance band
tolerance_scb_degras(): SCB mean confidence band (Degras method)
streaming_depth_batch(): Streaming depth: batch self-depth computation
streaming_depth_one(): Streaming depth: single curve against reference
streaming_depth_vs_ref(): Streaming depth: new data against reference
depth_bd_1d(): Band Depth (BD) for 1D functional data BD(x) = proportion of pairs (i,j) where x lies within the band formed by curves i and j A curve lies in the band if at every time point t, min(X_i(t), X_j(t)) <= x(t) <= max(X_i(t), X_j(t))
depth_fm_1d(): Compute Fraiman-Muniz depth
depth_fm_2d(): Fraiman-Muniz depth for 2D functional data (surfaces) Integrates univariate depth over (s,t) grid
depth_fsd_1d(): Compute Functional Spatial Depth
depth_fsd_2d(): Functional Spatial Depth for 2D functional data
depth_kfsd_1d(): Kernel Functional Spatial Depth (KFSD) for 1D functional data Implements the RKHS-based formulation matching fda.usc h is treated as the actual bandwidth, matching how fda.usc uses hq2 argvals is used for trapezoidal integration to compute L2 norms
depth_kfsd_2d(): Kernel Functional Spatial Depth (KFSD) for 2D functional data Implements the RKHS-based formulation matching fda.usc
depth_mbd_1d(): Modified Band Depth (MBD) for 1D functional data MBD(x) = average over pairs (i,j) of the proportion of the domain where x is inside the band This is more robust than BD as it doesn't require complete containment
depth_mei_1d(): Modified Epigraph Index (MEI) for 1D functional data MEI measures the proportion of time a curve is below other curves MEI(x_i) = (1/n) * sum_j (1/m) * sum_t I(x_i(t) < x_j(t)) + 0.5*I(x_i(t) = x_j(t))
depth_mode_1d(): Compute modal depth
depth_mode_2d(): Modal depth for 2D functional data (surfaces) Uses L2 distance in the flattened surface space
depth_rp_1d(): Compute random projection depth
depth_rp_2d(): Random projection depth for 2D functional data (surfaces) Projects surfaces to scalars using random projections
depth_rt_1d(): Compute random Tukey depth
depth_rt_2d(): Random Tukey depth for 2D functional data (surfaces)
metric_dtw_cross_1d(): Compute DTW distance matrix for cross-distances (n1 x n2)
metric_dtw_self_1d(): Compute DTW distance matrix for self-distances (symmetric)
metric_hausdorff_1d(): Compute Hausdorff distance matrix for self-distances (symmetric)
metric_hausdorff_2d(): Compute Hausdorff distance for 2D functional data (surfaces)
metric_hausdorff_cross_1d(): Compute Hausdorff distance matrix for cross-distances (n1 x n2)
metric_hausdorff_cross_2d(): Compute Hausdorff cross-distances for 2D functional data
metric_kl_cross_1d(): Compute symmetric KL divergence matrix for cross-distances (1D)
metric_kl_self_1d(): Compute symmetric KL divergence matrix for self-distances (1D) Curves are first normalized to be valid probability distributions
metric_lp_1d(): Compute Lp distance matrix between two sets of functional data
metric_lp_2d(): Compute Lp distance between two 2D functional data objects (surfaces)
metric_lp_self_1d(): Compute Lp distance matrix for self-distances (symmetric)
metric_lp_self_2d(): Compute Lp self-distance matrix for 2D functional data (symmetric)
metric_soft_dtw_barycenter(): Soft-DTW barycenter computation
metric_soft_dtw_cross_1d(): Soft-DTW cross-distance matrix
metric_soft_dtw_div_cross_1d(): Soft-DTW divergence cross-distance matrix
metric_soft_dtw_div_self_1d(): Soft-DTW divergence self-distance matrix
metric_soft_dtw_self_1d(): Soft-DTW self-distance matrix
fdata_center_1d(): Center functional data by subtracting the mean function
fdata_deriv_1d(): Compute numerical derivative of functional data (parallelized over rows)
fdata_deriv_2d(): Compute 2D partial derivatives for surface data
fdata_mean_1d(): Compute the mean function across all samples (1D)
fdata_mean_2d(): Compute the mean function across all samples (2D surfaces) Data is stored as n x (m1*m2) matrix where each row is a flattened surface
fdata_norm_lp_1d(): Compute Lp norm for each sample
fdata2basis(): Convert Functional Data to Basis Coefficients
fdata2basis_1d(): Convert functional data to basis coefficients type: 0 = bspline, 1 = fourier
fdata2basis_2d(): Convert 2D Functional Data to Tensor Product Basis Coefficients
fdata2basis_2d_raw(): Project 2D functional data to tensor product basis coefficients (raw binding)
fdata2basis_cv(): Cross-Validation for Basis Function Number Selection
fdata2fd(): Convert Functional Data to fd class
fdata2pc(): Convert Functional Data to Principal Component Scores
fdata2pc_1d(): Perform functional PCA via SVD on centered data Returns: singular values, rotation matrix (loadings), scores, mean
fdata2pls(): Convert Functional Data to PLS Scores
fdata2pls_1d(): Perform PLS via NIPALS algorithm Returns: weights, scores, loadings
basis.aic(): AIC for Basis Representation
basis.bic(): BIC for Basis Representation
basis.gcv(): GCV Score for Basis Representation
basis2fdata(): Basis Representation Functions for Functional Data
basis2fdata_1d(): Reconstruct functional data from basis coefficients Returns data matrix (n x m)
basis2fdata_2d(): Reconstruct 2D Functional Data from Tensor Product Basis Coefficients
basis2fdata_2d_raw(): Reconstruct 2D functional data from tensor product basis coefficients (raw binding)
basis_aic_1d(): Compute AIC for basis fit AIC = n * log(RSS/n) + 2 * total_edf Where total_edf = n_curves * edf (each curve has edf parameters) When pooled=true: compute single AIC across all curves When pooled=false: compute per-curve AIC and return mean
basis_bic_1d(): Compute BIC for basis fit BIC = n * log(RSS/n) + log(n) * total_edf Where total_edf = n_curves * edf (each curve has edf parameters) When pooled=true: compute single BIC across all curves When pooled=false: compute per-curve BIC and return mean
basis_gcv_1d(): Compute GCV score for basis fit GCV = RSS/n / (1 - edf/n)^2 When pooled=true: compute single GCV across all curves When pooled=false: compute per-curve GCV and return mean
semimetric_fourier_cross_1d(): Compute semimetric based on Fourier coefficients for cross-distances
semimetric_fourier_self_1d(): Compute semimetric based on Fourier coefficients for self-distances (symmetric) Uses FFT to compute Fourier coefficients and then L2 distance on coefficients
semimetric_hshift_cross_1d(): Compute semimetric based on horizontal shift for cross-distances
semimetric_hshift_self_1d(): Compute semimetric based on horizontal shift for self-distances (symmetric) This finds the minimum L2 distance after optimally shifting one curve horizontally
compute_adot(): Compute the Adot matrix (parallelized)
pcvm_statistic(): Compute the PCvM statistic
rp_stat(): Compute random projection statistics (parallelized over projections)
outliers_lrt(): LRT-based outlier detection Returns indices of detected outliers
outliers_thres_lrt(): Compute bootstrap threshold for LRT outlier detection Highly parallelized across bootstrap iterations
s_knn(): K-Nearest Neighbors smoother matrix
s_llr(): Local Linear Regression smoother matrix Uses weighted least squares with degree-1 polynomial
s_lpr(): Local Polynomial Regression smoother matrix Solves (p+1)×(p+1) weighted least squares system for each point
s_nw(): Nadaraya-Watson smoother matrix S_ij = K((t_i - t_j)/h) * w_j / sum_k(K((t_i - t_k)/h) * w_k)
kmeans_fd(): Functional k-means clustering
fuzzycmeans_fd(): Fuzzy C-Means clustering for functional data m_fuzz is the fuzziness parameter (typically 2)
register_shift_1d(): Shift registration: find optimal horizontal shift for each curve to align with a target (usually the mean)
int_simpson(): Simpson's rule integration for functional data Integrates each curve over the domain
inprod_fdata(): Inner product of two functional data objects <f, g> = integral(f(t) * g(t) dt)
knn_gcv(): k-NN with Global Cross-Validation Finds a single optimal k for all observations
knn_lcv(): k-NN with Local Cross-Validation Finds an optimal k for each observation
knn_predict(): Kernel prediction with fixed bandwidth for prediction on new data
silhouette_score(): Compute silhouette score for clustering Returns the mean silhouette coefficient across all samples
calinski_harabasz(): Compute Calinski-Harabasz index (variance ratio criterion) Higher values indicate better defined clusters
seasonal_analyze_peak_timing(): Analyze peak timing variability across cycles (uses Fourier smoothing)
seasonal_autoperiod(): Autoperiod: Hybrid FFT + ACF period detection with gradient ascent refinement Returns period, confidence, FFT power, ACF validation score, and candidates
seasonal_cfd_autoperiod(): CFDAutoperiod: Clustered Filtered Detrended Autoperiod Uses differencing for detrending and clustering for robust period detection
seasonal_classify_seasonality(): Classify seasonality type
seasonal_decompose(): Decompose functional data into trend, seasonal, and remainder components
seasonal_detect_amplitude_modulation(): Detect amplitude modulation in seasonal time series using Hilbert transform
seasonal_detect_amplitude_modulation_wavelet(): Detect amplitude modulation using wavelet transform (Morlet wavelet)
seasonal_detect_changes(): Detect seasonality changes (onset/cessation)
seasonal_detect_changes_auto(): Detect seasonality changes with automatic threshold
seasonal_detect_multiple_periods(): Detect multiple concurrent periodicities using iterative residual subtraction
seasonal_detect_peaks(): Detect peaks in functional data using Fourier basis smoothing
seasonal_detrend(): Detrend functional data using specified method Returns trend, detrended data, method used, RSS per curve, and number of parameters
seasonal_estimate_period_acf(): Estimate period using autocorrelation
seasonal_estimate_period_fft(): Estimate period using FFT periodogram
seasonal_instantaneous_period(): Estimate instantaneous period using Hilbert transform
seasonal_lomb_scargle(): Lomb-Scargle periodogram for irregularly sampled data Computes the power spectrum and significance for period detection
seasonal_matrix_profile(): Matrix Profile for motif discovery and period detection Uses STOMP algorithm for efficient computation
seasonal_sazed(): SAZED: Spectral-ACF Zero-crossing Ensemble Detection A parameter-free ensemble method for robust period detection Returns period, confidence, component periods, and agreeing component count
seasonal_ssa(): Singular Spectrum Analysis for time series decomposition Extracts trend, seasonal, and noise components via SVD
seasonal_stl(): STL (Seasonal and Trend decomposition using LOESS) Implements Cleveland et al. 1990 algorithm
seasonal_strength_spectral(): Measure seasonal strength using spectral method
seasonal_strength_variance(): Measure seasonal strength using variance decomposition
seasonal_strength_wavelet(): Measure seasonal strength using wavelet (Morlet) method
seasonal_strength_windowed(): Time-varying seasonal strength using sliding windows
eigenfunctions_1d(): Compute eigenfunction basis values efun_type: 0 = Fourier, 1 = Poly, 2 = PolyHigh, 3 = Wiener
eigenvalues_1d(): Generate eigenvalue sequence eval_type: 0 = linear, 1 = exponential, 2 = wiener
sim_kl_1d(): Simulate functional data via Karhunen-Loève expansion
add_error_curve_1d(): Add curve-level Gaussian noise to functional data
add_error_pointwise_1d(): Add pointwise Gaussian noise to functional data
irreg_fdata2basis(): Fit basis functions to irregular functional data Each curve is individually fitted via least squares at its own observation points basis_type: 0 = bspline, 1 = fourier
irreg_integrate(): Compute integral for each curve in irregular functional data
irreg_mean_kernel(): Estimate mean function for irregular data using kernel smoothing
irreg_metric_lp(): Compute pairwise Lp distances for irregular functional data
irreg_norm_lp(): Compute Lp norm for each curve in irregular functional data
irreg_to_regular(): Convert irregular data to regular grid via interpolation
select_basis_auto(): Automatic basis selection for each curve individually.
pspline_fit_1d(): P-spline fitting: returns coefficients, fitted values, and diagnostics
pspline_fit_2d(): 2D P-spline fitting with anisotropic penalties
geometric_median_1d(): Compute the geometric median (L1 median) of functional data using Weiszfeld's algorithm The geometric median minimizes sum of L2 distances to all curves
geometric_median_2d(): Compute the geometric median (L1 median) of 2D functional data using Weiszfeld's algorithm Data is stored as n x (m1*m2) matrix where each row is a flattened surface