public (List <Simplex>, List <SimplexComplex>) RandomSamples()
{
var riemannianSpace = Geometries.GetSpace(CurvatureType, Dim);
var randomSimplices = Simplex.RandomSamples(NbSamples, Dim, riemannianSpace, ZeroAmongEdges, MaxNorm);
var randomComplexes = new List <SimplexComplex>();
var counter = 0;
foreach (var randomSimplex in randomSimplices)
{
var stopWatch = new Stopwatch();
stopWatch.Start();
var simplexComplex = new SimplexComplex(randomSimplex);
simplexComplex.Propagate();
if (Integrate)
{
simplexComplex.Integrate(MeshSteps, null, ComputeAnalytical);
}
if (ComputeAngles)
{
simplexComplex.ComputeAngles();
}
counter++;
stopWatch.Stop();
var sampleCreationEventArgs = new SampleCreationEventArgs(counter, NbSamples, stopWatch.Elapsed.TotalSeconds);
OnSampleCreationEvent(sampleCreationEventArgs);
randomComplexes.Add(simplexComplex);
}
return(randomSimplices, randomComplexes);
}
public void TestDefect2Dim()
{
var ambiantSpace = Geometries.GetSpace(CurvatureType.NEGATIVE, 2);
var randomSamples = Simplex.RandomSamples(NUMBER_SAMPLES, 2, ambiantSpace, true, MAX_NORM);
var counter = 0;
foreach (var simplex in randomSamples)
{
foreach (var face in simplex.Faces)
{
var normalVector = VariousHelpers.GetNormalVector(face);
foreach (var dirVector in face.DirectionalVectors)
{
var scalarProduct = dirVector.DotProduct(normalVector);
if (Math.Abs(scalarProduct) >= TOLERANCE)
{
throw new Exception($"Deviation to high for simplex number {counter}");
}
}
counter++;
}
}
}
public void TestAngleComputation2Dim()
{
var ambiantSpace = Geometries.GetSpace(CurvatureType.FLAT, 2);
var randomSamples = Simplex.RandomSamples(NUMBER_SAMPLES, 2, ambiantSpace, true, MAX_NORM);
var counter = 0;
foreach (var simplex in randomSamples)
{
var faceA = simplex.Faces[0];
var faceB = simplex.Faces[1];
var faceC = simplex.Faces[2];
var normVectorA = VariousHelpers.GetNormalVector(faceA);
var normVectorB = VariousHelpers.GetNormalVector(faceB);
var normVectorC = VariousHelpers.GetNormalVector(faceC);
var alpha = Math.PI - VariousHelpers.Angle(normVectorB, normVectorC);
var beta = Math.PI - VariousHelpers.Angle(normVectorA, normVectorC);
var gamma = Math.PI - VariousHelpers.Angle(normVectorA, normVectorB);
if (Math.Abs(alpha + beta + gamma - Math.PI) >= TOLERANCE)
{
throw new Exception($"Deviation to high for simplex number {counter}");
}
counter++;
}
}
public void TestNormVectorComputation()
{
for (int iDim = 2; iDim < 10; iDim++)
{
var ambiantSpace = Geometries.GetSpace(CurvatureType.FLAT, iDim);
var randomSamples = Simplex.RandomSamples(NUMBER_SAMPLES, iDim, ambiantSpace, true, MAX_NORM);
var counter = 0;
foreach (var simplex in randomSamples)
{
var normalVectorSum = Vector <double> .Build.DenseOfArray(new double[iDim]);
foreach (var face in simplex.Faces)
{
var normalVector = VariousHelpers.GetNormalVector(face);
face.Integrate(0, true);
var volumeFace = face.Volume;
var normNormalVector = normalVector.L2Norm();
normalVectorSum += volumeFace * normalVector;
}
if (Math.Abs(normalVectorSum.L2Norm()) >= TOLERANCE)
{
throw new Exception($"Deviation to high for simplex number {counter}");
}
counter++;
}
}
}
public void TestRelations(string relation)
{
var ambiantSpace = Geometries.GetSpace(CurvatureType.FLAT, 2);
var randomSamples = Simplex.RandomSamples(NUMBER_SAMPLES, 2, ambiantSpace, true, MAX_NORM);
var counter = 0;
var anlgeRelations = GetAnlgeRelations();
foreach (var simplex in randomSamples)
{
foreach (var angleRelation in anlgeRelations)
{
var faceA = simplex.Faces[0];
var faceB = simplex.Faces[1];
var faceC = simplex.Faces[2];
var normVectorA = VariousHelpers.GetNormalVector(faceA);
var normVectorB = VariousHelpers.GetNormalVector(faceB);
var normVectorC = VariousHelpers.GetNormalVector(faceC);
var alpha = Math.PI - VariousHelpers.Angle(normVectorB, normVectorC);
var beta = Math.PI - VariousHelpers.Angle(normVectorA, normVectorC);
var gamma = Math.PI - VariousHelpers.Angle(normVectorA, normVectorB);
var value = angleRelation.Value(alpha, beta, gamma);
if (Math.Abs(value) >= TOLERANCE)
{
throw new Exception($"Deviation to high for simplex number {counter}");
}
}
counter++;
}
}
public void TestRelations()
{
var ambiantSpace = Geometries.GetSpace(CurvatureType.FLAT, 2);
var randomSamples = Simplex.RandomSamples(NUMBER_SAMPLES, 2, ambiantSpace, true, MAX_NORM);
var counter = 0;
foreach (var simplex in randomSamples)
{
var faceSum = Vector <double> .Build.DenseOfArray(new double[2]);
foreach (var face in simplex.Faces)
{
faceSum += face.DirectionalVectors[0];
}
if (Math.Abs(faceSum.L2Norm()) >= TOLERANCE)
{
throw new Exception($"Deviation to high for simplex number {counter}");
}
counter++;
}
}
public void TestLength(CurvatureType curvatureType)
{
var ambiantSpace = Geometries.GetSpace(CurvatureType.NEGATIVE, 2);
var randomSamples = Simplex.RandomSamples(NUMBER_SAMPLES, 2, ambiantSpace, true, MAX_NORM);
var counter = 0;
foreach (var simplex in randomSamples)
{
foreach (var face in simplex.Faces)
{
face.Integrate(MESH_STEPS, true);
var volumeAnalytical = face.Volume;
face.Integrate(MESH_STEPS, false);
var volume = face.Volume;
if (Math.Abs(volumeAnalytical - volume) >= TOLERANCE)
{
throw new Exception($"Deviation to high for simplex number {counter}");
}
}
counter++;
}
}