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 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);
}
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++;
}
}
protected double Vol(int meshSteps = 2500)
{
var _P = m_A;
var _V = m_B.Subtract(m_A);
var _W = m_C.Subtract(m_A);
var _U = m_D.Subtract(m_A);
var span = Matrix<double>.Build.DenseOfColumnArrays(new List<double[]>() { _V, _W, _U});
var detSpan = span.Determinant();
var dt = 1.0 / (double)meshSteps;
var aSixth = 1.0 / 6.0;
var fiveSixth = 5.0 / 6.0;
#if MULTITHREADS
var nbThreads = 4;
var vols = new double[nbThreads];
var partition = VariousHelpers.GetPartition(meshSteps, nbThreads, 1.0 / 3.0);
Parallel.For(0, nbThreads, ell =>
{
#else
var partition = new int[1][]{ new int[2] { 0, meshSteps } };
var vols = new double[1];
var ell = 0;
#endif
var volume = .0;
double weight;
var _Y = new double[3];
for (int _v = partition[ell][0]; _v < partition[ell][1]; _v++)
{
for (int _w = 0; _w < meshSteps - _v; _w++)
{
for (int _u = 0; _u < meshSteps - _w - _v; _u++)
{
weight = 1.0;
if (_u == meshSteps - _w - _v - 1)
weight = aSixth;
else if (_u == meshSteps - _w - _v - 2)
weight = fiveSixth;
for (int ekk = 0; ekk < 3; ekk++)
_Y[ekk] = _P[ekk] + (_v * _V[ekk] + _w * _W[ekk] + _u * _U[ekk]) * dt;
var yNormSq = _Y.Dot(_Y);
volume += weight * (1.0 / ((1.0 - yNormSq) * (1.0 - yNormSq) * (1.0 - yNormSq)));
}
}
}
vols[ell] = volume;
#if MULTITHREADS
});
#endif
return vols.Sum() * Math.Sqrt(detSpan * detSpan) * dt * dt * dt;
}
private static void Execute(Options options)
{
var path = "C:\\Users\\bergerd\\simplices.csv";
var samples = ShearTriangle2D.RandomSamples(50000);
//foreach(var sample in samples)
// VariousHelpers.SampleToFile(path, sample);
Console.WriteLine(MessageAtStart(options));
var randomSimplices = Simplex3D.RandomSamples(options.NumberSamples);
var counter = 0;
var progressBar = new ProgressBar();
var nbThreads = 7;
var vols = new double[nbThreads];
if (File.Exists(path))
{
File.Delete(path);
}
var partition = VariousHelpers.GetPartition(options.NumberSamples, nbThreads);
Parallel.For(0, nbThreads, ell =>
{
for (int i = partition[ell][0]; i < partition[ell][1]; i++)
{
var stopWatch = new Stopwatch();
stopWatch.Start();
randomSimplices[i].Compute(3000);
stopWatch.Stop();
counter += 1;
Debug.WriteLine($"Successfully generated {counter} random samples.");
lock (_simplexLock)
{
progressBar.Report(counter, options.NumberSamples, stopWatch.Elapsed.TotalSeconds);
VariousHelpers.SampleToFile(path, randomSimplices[i]);
}
}
});
/*
* var sampleFactory = new SampleFactory(options.NumberSamples, options.Dimension, options.Integrate,
* options.MeshSteps, options.MaxNorm, options.ZeroAmongEdges, options.ComputeAngles, options.ComputeAnalytical);
*
* var progressBar = new ProgressBar();
* sampleFactory.RaiseSampleCreatorEvent += progressBar.HandleSampleCreationEvent;
*
* Console.WriteLine(_computing);
* (var randomSimplices, var hyperRandomComplexes) = sampleFactory.RandomSamples();
*/
}
public List <double[]> GetMesh(MeshKey meshKey)
{
if (_meshs.ContainsKey(meshKey))
{
return(_meshs[meshKey]);
}
else
{
_meshs[meshKey] = VariousHelpers.CreateMesh(meshKey.MeshSteps, meshKey.Dim);
return(_meshs[meshKey]);
}
}
public static List<Simplex3D> RandomSamples(int nbSamples, double maxNorm = 1.0)
{
var maxHyperbolicNorm = Math.Tanh(maxNorm);
var rndVectors = VariousHelpers.RandomVectors(nbSamples * 4, 3, maxHyperbolicNorm);
var ret = new List<Simplex3D>();
for (int i = 0; i < nbSamples; i++)
{
ret.Add(new Simplex3D(rndVectors[4 * i].ToArray(), rndVectors[4 * i + 1].ToArray(),
rndVectors[4 * i + 2].ToArray(), rndVectors[4 * i + 3].ToArray()));
}
return ret;
}
public void ComputeAngle()
{
var ind1 = Simplex1.Indices;
var ind2 = Simplex2.Indices;
var ind1_ext = ind2.Except(ind1).ToArray()[0];
var vec1 = Simplex2.GetEdgeByIndex(ind1_ext);
var ind2_ext = ind1.Except(ind2).ToArray()[0];
var vec2 = Simplex1.GetEdgeByIndex(ind2_ext);
var normal1 = VariousHelpers.GetNormalVector(Simplex1, vec1 - Simplex1.BasePoint);
var normal2 = VariousHelpers.GetNormalVector(Simplex2, vec2 - Simplex2.BasePoint);
var commonBasePoint = CommonBase.BasePoint;
Angle = Math.PI - CommonBase.AmbiantSpace.Angle(commonBasePoint, normal1, normal2);
}
public void TestTriangles()
{
var randomSamples = ShearTriangle2D.RandomSamples(NUMBER_SAMPLES);
var counter = 0;
var path = "C:\\Users\\bergerd\\simplices.csv";
foreach (var triangle in randomSamples)
{
var trigonometricRelations = TestFastSimplex3D.Relations();
foreach (var trigonometricRelation in trigonometricRelations)
{
var deviation = Math.Abs(trigonometricRelation(triangle) - .0);
if (deviation >= TOLERANCE)
{
throw new Exception($"Deviation too high for triangle number {counter}!");
}
}
VariousHelpers.SampleToFile(path, triangle);
}
}
