Physics-Informed Spatial and Functional Data Analysis

An implementation of regression models with partial differential regularizations, making use of the Finite Element Method. The models efficiently handle data distributed over irregularly shaped domains and can comply with various conditions at the boundaries of the domain. A priori information about the spatial structure of the phenomenon under study can be incorporated in the model via the differential regularization. See Sangalli, L. M. (2021) "Spatial Regression With Partial Differential Equation Regularisation" for an overview. The release 1.1-9 requires R (>= 4.2.0) to be installed on windows machines.

fdaPDE

This repository contains the development version of fdaPDE package.

New features wrt CRAN: Wald inference on the nonparametric term for space-time models.

Compiled in Ubuntu using g++ compiler and in macOS: for the precise versions tested, see the report. If using a Linux machine, it is advisable to install rgl, geometry, plot3D and plot3Drgl before fdaPDE.

Image.FEM has been restored. Bugs in fPCA, boundary conditions and space-varying regression have been fixed. Issues of point location in 2.5D have been fixed. Compiled in Win RStudio, Ubuntu using g++ compiler and in macOS: for the precise versions tested, see the report. If using a Linux machine, it is advisable to install rgl, geometry, plot3D and before fdaPDE. If using Windows, it is advisable to install Rtools and then rgl, plot3D, geometry and RcppEigen libraries.

Subfolder structure:

/src contains all C++ code and a special file named Makevars necessary to build and install the R package. The code is now organized in subfolders and divided into source files and header files. See the report for the precise new orgaization. We suggest to use a base-8 scale as spacing scale for visualization, in order to preserve the code style.

/R contains the R functions that wrap the C++ calls,

/data contains the data to run the tests in the examples,

/man contains the manual for the package.

Installation:

Two different methods are proposed in order to install the package in the R environment.
Download the .zip file from the repository, unzip it, and for the installation choose one of the two following methods:

• R console: install.packages("/path/to/fdaPDE", type='source', repos=NULL)

• From the Terminal: $ R CMD build <path to folder to be installed>
$ R CMD INSTALL -l <path name of the R library tree> <path to folder to be installed>

see the installation section in the report for more information.

Remarks:

1. the shift of indexes from R to C++ is done within the R functions smooth.FEM and FPCA.FEM Do not use C++ scripts directly on the R mesh objects, unless you take care of shifing indexes by yourself.