The code provides the demonstration of intrinsic sparse Gaussian process regression on three examples such as U shape domain, Bitten Torus and Aral sea. In order to run the code, just go to the folder with example names and following DEMO_'example name'_Steps.r, you can generate the figures as shown in the paper (Intrinsic Gaussian processes on complex constrained domains, JRSSB)

There is a folder 'BM_Paths' under each example folders. It is used to store the BM sample paths which are generated by Brownian motion simulation. It is empty because the sample path files are too big to upload to github. Users can download the code and generate paths by running 'example name'_BM_sim.r from their local machine.

The folder 'inference' stores R6 class codes for computing Gaussian process regression prediction and intrinsic Gaussian process regression likelihoods and hyper parameters optimisatin.

For demonstration purpose, user can just run DEMO_'example name'_Steps.r. If user want to reproduce the whole process as stated in the paper, user can go to the example folders and follow the steps below:
1) Generate BM sample paths by running 'example name'_BM_sim.r. parallel computing are recommended.

2) Generate estimated rows of Covariances matrices by running 'example name'_BM_TrDensity.r

3) run DEMO_'example name'_Steps.r to produce GP and in-GP regression results.