Examples

Examples are included in the documentation to illustrate the usage of the package. The examples are divided into different categories, each corresponding to a specific functionality of the package.

Representation

These examples illustrate the use of the FDApy.representation module. It contains various functionalities to represent functional data in different formats.

Representation of univariate and dense functional data

Representation of univariate and dense functional data

Representation of univariate and irregular functional data

Representation of univariate and irregular functional data

Representation of functional data using a basis

Representation of functional data using a basis

Representation of multivariate functional data

Representation of multivariate functional data

Basis

These examples illustrate the use of the FDApy.basis module. It contains examples of the different basis functions available in the package.

One-dimensional Basis

One-dimensional Basis

Two-dimensional Basis

Two-dimensional Basis

Multivariate Basis

Multivariate Basis

Smoothing

These examples illustrate the use of the FDApy.preprocessing.smoothing module. It contains various functionalities to smooth functional data.

Smoothing of dense one-dimensional functional data

Smoothing of dense one-dimensional functional data

Smoothing of dense two-dimensional functional data

Smoothing of dense two-dimensional functional data

Dimension Reduction

These examples illustrate the use of the FDApy.preprocessing.dim_reduction module. It contains various functionalities to reduce the dimension of functional data.

FPCA of 1-dimensional data

FPCA of 1-dimensional data

FPCA of 1-dimensional sparse data

FPCA of 1-dimensional sparse data

FPCA of 2-dimensional data

FPCA of 2-dimensional data

MFPCA of 1-dimensional data

MFPCA of 1-dimensional data

MFPCA of 2-dimensional data

MFPCA of 2-dimensional data

MFPCA of 1- and 2-dimensional data

MFPCA of 1- and 2-dimensional data

MFPCA of 1-dimensional sparse data

MFPCA of 1-dimensional sparse data

Real data analysis

These examples illustrate the use of the package using real datasets.

Canadian weather dataset

Canadian weather dataset

CD4 dataset

CD4 dataset

Simulation

These examples illustrate the use of the FDApy.simulation module. It contains various functionalities to simulate functional data.

Simulation using Karhunen-Loève decomposition

Simulation using Karhunen-Loève decomposition

Simulation using multivariate Karhunen-Loève decomposition

Simulation using multivariate Karhunen-Loève decomposition

Simulation of Brownian motion

Simulation of Brownian motion

Simulation of functional data

Simulation of functional data

Simulation of clusters of univariate functional data

Simulation of clusters of univariate functional data

Simulation of clusters of multivariate functional data

Simulation of clusters of multivariate functional data

Miscellaneous

These examples illustrate diverse functionalities of the package that are not directly related to the main modules and to functional data analysis. They could be useful for the user to understand how to use the package in a more general context.

Smoothing of 1D data using local polynomial regression

Smoothing of 1D data using local polynomial regression

Smoothing of 2D data using local polynomial regression

Smoothing of 2D data using local polynomial regression

Smoothing of 1D data using P-Splines

Smoothing of 1D data using P-Splines

Smoothing of 2D data using P-Splines

Smoothing of 2D data using P-Splines