Software    : PLoM: Probabilisting Learning on Manifolds (PLoM)
Version     : 21 February 2021
Copyright   : Christian SOIZE, 21 February 2021
Affiliation : Christian SOIZE, MSME UMR 8208, Universite Gustave Eiffel
              christian.soize@univ-eiffel.fr
              https://pagespro.univ-gustave-eiffel.fr/christian-soize
              https://scholar.google.fr/citations?user=XktTSHMAAAAJ\&hl=fr
              http://msme.u-pem.fr/equipe-mecanique/les-publications-hal/halbib/soize    

--- Software written with Matlab 2020b ---
    
              This code is a novel version of the PLoM algorithm for which the first version of the algorithm was published in ref. [1]
              and for which the mathematics foundations can be found in ref. [2]
              The present version of this PLoM software includes three novel capabilities:
                 - parallel computing
                 - automatic indentification of the smoothing parameter of the DMAP kernel as explained in Ref. [3].
                 - possibility to introduce constraints for keeping the normalization of the PCA coordinates during the probabilistic learning
                   process as explained in Ref. [3], based on Ref. [4].

              The input data parameters entered for each STEP correpond to those for Application 1 for which the results are
              in the file: "listing_RESULTS.txt"

              Publications: [1] C. Soize, R. Ghanem, Data-driven probability concentration and sampling on manifold, 
                                Journal of Computational Physics,  doi:10.1016/j.jcp.2016.05.044, 321, 242-258 (2016).
                            
                            [2] C. Soize, R. Ghanem, Probabilistic learning on manifolds, Foundations of Data Science, 
                                American  Institute of Mathematical Sciences (AIMS), doi: 10.3934/fods.2020013, 
                                2(3), 279-307 (2020).
                                Also in arXiv:2002.12653  [math.ST], 28 Feb 2020, https://arxiv.org/abs/2002.12653.

                            [3] C. Soize, R. Ghanem, Probabilistic learning on manifolds with partition, 
                                in arXiv:2010.14324 [stat.ML], 21 Feb 2021, https://arxiv.org/abs/2102.10894 
                                Also submitted in SIAM-ASA Journal on Uncertainty Quantification}, 2021.

[                           [4] C. Soize, R. Ghanem, Physics-constrained non-Gaussian probabilistic learning on manifolds, 
                                International Journal for Numerical Methods in Engineering, doi: 10.1002/nme.6202, 121 (1), 110-145 (2020).

-------- EXEC THE SOFTWARE

1. "run.m" is the main program in which all the parameters 
   are defined for each STEP of the Job.

2. For running the software, exec "run.m".
