public static (double, double) plainmc(Func <vector, double> F, vector a, vector b, int N, bool print_points = false, bool Lattice = false, bool Halton = false, bool Quasi = false, Random RND = null)
{
double volume = 1;
int dim = a.size;
lattice RNDL = new lattice(dim);
halton RNDH = new halton(dim);
if (RND == null)
{
RND = new Random();
}
vector x = new vector(dim);
vector y = new vector(dim);
for (int i = 0; i < dim; i++)
{
volume *= b[i] - a[i];
}
double sum = 0, sum2 = 0, sumy = 0;
for (int i = 0; i < N; i++)
{
if (Quasi)
{
randomx(x, a, b, RND, RNDL, RNDH, print_points, Lattice: true);
randomx(y, a, b, RND, RNDL, RNDH, print_points, Halton: true);
}
else
{
randomx(x, a, b, RND, RNDL, RNDH, print_points, Lattice: Lattice, Halton: Halton);
}
double fx = F(x);
sum += fx;
sum2 += fx * fx;
if (Quasi)
{
double fy = F(y);
sumy += fy;
}
}
if (Quasi)
{
double meanL = sum / N;
double meanH = sumy / N;
return(meanL * volume, Abs(meanL * volume - meanH * volume));
}
else
{
double mean = sum / N; // <f_i>
double sigma = Sqrt(sum2 / N - mean * mean); // sigma² = <(f_i)²> - <f_i>²
double SIGMA = sigma / Sqrt(N); // SIGMA² = <Q²> - <Q>²
return(mean * volume, SIGMA *volume);
}
}
public static void randomx(vector x, vector a, vector b, Random RND, lattice RNDL, halton RNDH, bool print_points, bool Lattice = false, bool Halton = false)
{
int dim = a.size;
if (Lattice)
{
vector y = x.copy();
RNDL.next(y);
for (int i = 0; i < dim; i++)
{
x[i] = a[i] + y[i] * (b[i] - a[i]);
}
}
if (Halton)
{
vector y = x.copy();
RNDH.next(y);
for (int i = 0; i < dim; i++)
{
x[i] = a[i] + y[i] * (b[i] - a[i]);
}
}
if (!Lattice && !Halton)
{
for (int i = 0; i < dim; i++)
{
x[i] = a[i] + RND.NextDouble() * (b[i] - a[i]);
}
}
if (print_points)
{
StreamWriter pointWriter = new StreamWriter("sample_points.txt", true);
for (int i = 0; i < x.size; i++)
{
pointWriter.Write($"{x[i]} ");
}
pointWriter.Write("\n");
pointWriter.Close();
}
}