public static void Bench()
{
int n = 100;
foreach (var iteration in Benchmark.Iterations)
{
double a = 0;
using (iteration.StartMeasurement())
{
for (int i = 0; i < Iterations; i++)
{
SpectralNorm s = new SpectralNorm();
a += s.Approximate(n);
}
}
double norm = a / Iterations;
double expected = 1.274219991;
bool valid = Math.Abs(norm - expected) < 1e-4;
if (!valid)
{
throw new Exception("Benchmark failed to validate");
}
}
}
public static void Bench()
{
int n = 100;
foreach (var iteration in Benchmark.Iterations)
{
double a = 0;
using (iteration.StartMeasurement())
{
for (int i = 0; i < Iterations; i++)
{
SpectralNorm s = new SpectralNorm();
a += s.Approximate(n);
}
}
double norm = a / Iterations;
double expected = 1.274219991;
bool valid = Math.Abs(norm - expected) < 1e-4;
if (!valid)
{
throw new Exception("Benchmark failed to validate");
}
}
}
public static int Main(String[] args)
{
int n = 100;
if (args.Length > 0) n = Int32.Parse(args[0]);
double norm = new SpectralNorm().Approximate(n);
Console.WriteLine("Norm={0:f9}", norm);
double expected = 1.274219991;
bool result = Math.Abs(norm - expected) < 1e-4;
return (result ? 100 : -1);
}
public static int Main(String[] args)
{
int n = 100;
if (args.Length > 0)
{
n = Int32.Parse(args[0]);
}
double norm = new SpectralNorm().Approximate(n);
Console.WriteLine("Norm={0:f9}", norm);
double expected = 1.274219991;
bool result = Math.Abs(norm - expected) < 1e-4;
return(result ? 100 : -1);
}
public static void Main(string[] args)
{
var target = "C#";
if (args.Length > 0)
{
target = args[0];
}
Console.WriteLine($"============ {target} ============");
{
Console.WriteLine("##### N-Body #####");
NBodySystem dummy = new NBodySystem();
dummy.Advance(0.01);
Func <Int32, TimeSpan> test = (ti) =>
{
NBodySystem bodies = new NBodySystem();
var e = new Elapsed("11");
for (int i = 0; i < 50000000; i++)
{
bodies.Advance(0.01);
}
var d = e.Done();
Console.WriteLine($"Try #{ti} : {d}, {bodies.Energy()}");
return(d);
};
var times0 = new List <TimeSpan>(10);
for (var i = 0; i < 10; i++)
{
times0.Add(test(i));
}
var times = times0.Where(x => x != times0.Min() && x != times0.Max()).ToList();
var average = new TimeSpan((long)times.Select(ts => ts.Ticks).Average());
//Console.WriteLine($"{target} [N-Body] : {average}\n");
using (StreamWriter sw = File.AppendText("averages.txt"))
{
sw.WriteLine($"{target} [N-Body] : {average}");
}
}
{
Console.WriteLine("##### Spectral-Norm #####");
SpectralNorm.RunGame(0);
Func <Int32, TimeSpan> test = (ti) =>
{
var e = new Elapsed("11");
var r = SpectralNorm.RunGame(5500);
var d = e.Done();
//Console.WriteLine("{0:f9}", r);
Console.WriteLine($"Try #{ti} : {d}, {r}");
return(d);
};
var times0 = new List <TimeSpan>(10);
for (var i = 0; i < 10; i++)
{
times0.Add(test(i));
}
var times = times0.Where(x => x != times0.Min() && x != times0.Max()).ToList();
var average = new TimeSpan((long)times.Select(ts => ts.Ticks).Average());
//Console.WriteLine($"{target} [Spectral-Norm] : {average}");
using (StreamWriter sw = File.AppendText("averages.txt"))
{
sw.WriteLine($"{target} [S-Norm] : {average}");
}
}
{
Console.WriteLine("##### Quicksort #####");
Quicksort.DoSort(new Int32[3] {
0, 1, 2
}, 0, 2);
Func <Int32, TimeSpan> test = (ti) =>
{
var n = 50000000;
var r = new Random();
var array = new Int32[n];
for (var i = 0; i < n; i++)
{
array[i] = r.Next(0, n);
}
var e = new Elapsed("");
Quicksort.DoSort(array, 0, n - 1);
var d = e.Done();
Console.WriteLine($"Try #{ti} : {d}, {array[1000]}");
return(d);
};
var times0 = new List <TimeSpan>(10);
for (var i = 0; i < 10; i++)
{
times0.Add(test(i));
}
var times = times0.Where(x => x != times0.Min() && x != times0.Max()).ToList();
var average = new TimeSpan((long)times.Select(ts => ts.Ticks).Average());
//Console.WriteLine($"{target} [Spectral-Norm] : {average}");
using (StreamWriter sw = File.AppendText("averages.txt"))
{
sw.WriteLine($"{target} [Q-Sort] : {average}");
}
}
}
public static List <Cluster> SpectralClustering(List <Column> cols, int Nc, SpectralNorm norm, double sigma = 1e3)
{
// data
List <ClusterLoad> dataN = cols.SelectMany(c => c.Loads.Select(l => new ClusterLoad(new MWPoint3D(l.MEdx, l.MEdy, l.P), c, l.Name))).ToList();
int N = dataN.Count;
// Similarity matrix construction
Matrix <double> S = Matrix <double> .Build.Dense(N, N);
for (int i = 0; i < N; i++)
{
for (int j = i; j < N; j++)
{
double dist = Points.Distance3D(dataN[i].Load, dataN[j].Load);
S[i, j] = Math.Exp(-Math.Pow(dist, 2) / (2 * Math.Pow(sigma, 2)));
//S[i, j] = dist;
S[j, i] = S[i, j];
}
}
// Diagonal matrix of degrees D
Matrix <double> D = Matrix <double> .Build.Dense(N, N);
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
D[i, i] += S[i, j];
}
}
// Laplacian matrix
Matrix <double> L = Matrix <double> .Build.Dense(N, N);
Matrix <double> I = Matrix <double> .Build.DenseIdentity(N);
switch (norm)
{
case (SpectralNorm.None):
L = D.Subtract(S);
break;
case (SpectralNorm.Division):
Matrix <double> Dinv = Matrix <double> .Build.Dense(N, N, (i, j) => i == j? 1 / D[i, j] : 0);
L = I.Subtract(Dinv.Multiply(S));
break;
case (SpectralNorm.SymmetricDivision):
Matrix <double> Dhalfinv = Matrix <double> .Build.Dense(N, N, (i, j) => i == j? 1 / Math.Sqrt(D[i, i]) : 0);
L = I.Subtract(Dhalfinv.Multiply(S.Multiply(Dhalfinv)));
break;
case (SpectralNorm.Additive):
double dmax = D.Enumerate().Max();
L = I.Subtract(S.Add(I.Multiply(dmax).Subtract(D)).Divide(dmax));
break;
}
//L = D.Subtract(S);
// Diagonalisation of L
Evd <double> eigen = L.Evd(Symmetricity.Symmetric);
Matrix <double> eigenVectors = eigen.EigenVectors;
Vector <double> eigenValues = eigen.EigenValues.Real();
// Construction of matrix X
Matrix <double> X = eigenVectors.SubMatrix(0, N, 0, Nc);
// K means applied to the lines of X
List <List <Vector <double> > > clusters = KMeans(X);
// Assignment of column loads to their cluster
List <Cluster> res = new List <Cluster>();
List <Vector <double> > rows = X.EnumerateRows().ToList();
if (norm == SpectralNorm.SymmetricDivision)
{
X = X.NormalizeRows(2);
}
for (int i = 0; i < Nc; i++)
{
res.Add(new Cluster());
List <Vector <double> > cluster = clusters[i];
for (int j = 0; j < clusters[i].Count; j++)
{
int ind = rows.IndexOf(cluster[j]);
res[i].Loads.Add(dataN[ind]);
}
}
return(res);
}
