public Simplex(Tuple <int, Vector <double> >[] edges, RiemannianSpace ambiantSpace) : base(edges)
{
var directionalVectors = new List <Vector <double> >();
foreach (var item in edges.Skip(1))
{
directionalVectors.Add(item.Item2 - BasePoint);
}
DirectionalVectors = directionalVectors.ToArray();
DimAmbiantSpace = BasePoint.Count();
Parametrization chart = x => {
var dir = Matrix <double> .Build.DenseOfColumnVectors(DirectionalVectors);
return(dir * x + BasePoint);
};
PushForward pushForward = x => {
return(Matrix <double> .Build.DenseOfColumnVectors(DirectionalVectors));
};
AmbiantSpace = ambiantSpace;
Trivialization = new LocalTrivialization(chart, pushForward, ambiantSpace);
}
public static List <Simplex> RandomSamples(int nbSamples, int dim, RiemannianSpace ambiantSpace, bool zeroAmongEdges = true, double maxNorm = double.NaN)
{
var ret = new List <Simplex>();
var hyperbolicNorm = Math.Tanh(maxNorm);
var nbEdgesPerSimplex = zeroAmongEdges ? dim : dim + 1;;
var rndVectors = VariousHelpers.RandomVectors(nbSamples * nbEdgesPerSimplex, dim, hyperbolicNorm);
for (int i = 0; i < nbSamples; i++)
{
var edges = new Tuple <int, Vector <double> > [dim + 1];
if (zeroAmongEdges)
{
edges[0] = new Tuple <int, Vector <double> >(1, Vector <double> .Build.Dense(new double[dim]));
for (int j = 1; j <= dim; j++)
{
edges[j] = new Tuple <int, Vector <double> >(j + 1, rndVectors[i * (dim - 1) + j]);
}
}
else
{
for (int j = 0; j <= dim; j++)
{
edges[j] = new Tuple <int, Vector <double> >(j + 1, rndVectors[i * dim + j]);
}
}
ret.Add(new Simplex(edges, ambiantSpace));
}
return(ret);
}
