PrimitiveElasticGraphEmbedment: Function fitting a primitive elastic graph to the data
In Albluca/ElPiGraph.R: Elastic principal graph construction

Function fitting a primitive elastic graph to the data

PrimitiveElasticGraphEmbedment(X, NodePositions, ElasticMatrix,
  MaxNumberOfIterations, TrimmingRadius, eps, Mode = 1,
  FinalEnergy = "Base", SquaredX = NULL, verbose = FALSE,
  FastSolve = FALSE, DisplayWarnings = FALSE, alpha = 0, beta = 0,
  gamma = 0, prob = 1)

`X`	is n-by-m matrix containing the positions of the n points in the m-dimensional space
`NodePositions`	is k-by-m matrix of positions of the graph nodes in the same space as X
`ElasticMatrix`	is a k-by-k symmetric matrix describing the connectivity and the elastic properties of the graph. Star elasticities (mu coefficients) are along the main diagonal (non-zero entries only for star centers), and the edge elasticity moduli are at non-diagonal elements.
`MaxNumberOfIterations`	is an integer number indicating the maximum number of iterations for the EM algorithm
`TrimmingRadius`	is a real value indicating the trimming radius, a parameter required for robust principal graphs (see https://github.com/auranic/Elastic-principal-graphs/wiki/Robust-principal-graphs)
`eps`	a real number indicating the minimal relative change in the nodenpositions to be considered the graph embedded (convergence criteria)
`Mode`	integer, the energy mode. It can be 1 (difference is computed using the position of the nodes) and 2 (difference is computed using the changes in elestic energy of the configuraztions)
`FinalEnergy`	string indicating the final elastic emergy associated with the configuration. Currently it can be "Base" or "Penalized"
`SquaredX`	the sum (by node) of X squared. It not specified, it will be calculated by the fucntion
`verbose`	is a boolean indicating whether diagnostig informations should be plotted
`FastSolve`	boolean, shuold the Fastsolve of Armadillo by enabled?
`DisplayWarnings`	boolean, should warning about convergence be displayed?
`alpha`	positive numeric, the value of the alpha parameter of the penalized elastic energy
`beta`	positive numeric, the value of the beta parameter of the penalized elastic energy
`prob`	numeric between 0 and 1. If less than 1 point will be sampled at each iteration. Prob indicate the probability of using each points. This is an experimental feature, which may helps speeding up the computation if a large number of points is present.