public void TestHalton()
{
for (var m = 1; m <= 3; m++)
{
int i;
for (i = 0; i <= 10; i++)
{
var r = HaltonSequence.Halton(i, m);
int j;
for (j = 0; j < m; j++)
{
Debug.Print(r[j].ToString(CultureInfo.InvariantCulture));
}
}
}
}
public void TestHalton2()
{
//("Testing Halton sequences...");
double[] point;
double tolerance = 1.0e-15;
// testing "high" dimensionality
int dimensionality = 2;
int points = 100, i;
for (i = 0; i < points; i++)
{
point = HaltonSequence.Halton(i, dimensionality);
Assert.AreEqual(point.Length, dimensionality);
}
// testing first and second dimension (van der Corput sequence)
double[] vanderCorputSequenceModuloTwo =
{
// first cycle (zero excluded)
0.50000,
// second cycle
0.25000, 0.75000,
// third cycle
0.12500, 0.62500, 0.37500, 0.87500,
// fourth cycle
0.06250, 0.56250, 0.31250, 0.81250, 0.18750, 0.68750, 0.43750,
0.93750,
// fifth cycle
0.03125, 0.53125, 0.28125, 0.78125, 0.15625, 0.65625, 0.40625,
0.90625,
0.09375, 0.59375, 0.34375, 0.84375, 0.21875, 0.71875, 0.46875,
0.96875,
};
dimensionality = 1;
points = (int)Math.Pow(2.0, 5) - 1; // five cycles
for (i = 0; i < points; i++)
{
point = HaltonSequence.Halton(i, dimensionality);
double error = Math.Abs(point[0] - vanderCorputSequenceModuloTwo[i]);
if (error > tolerance)
{
Debug.Print(i + 1 + " draw ("
+ +point[0]
+ ") in 1-D Halton sequence is not in the "
+ "van der Corput sequence modulo two: "
+ "it should have been "
+ vanderCorputSequenceModuloTwo[i]
+ " (error = " + error + ")");
}
}
double[] vanderCorputSequenceModuloThree =
{
// first cycle (zero excluded)
1.0 / 3, 2.0 / 3,
// second cycle
1.0 / 9, 4.0 / 9, 7.0 / 9, 2.0 / 9, 5.0 / 9, 8.0 / 9,
// third cycle
1.0 / 27, 10.0 / 27, 19.0 / 27, 4.0 / 27, 13.0 / 27, 22.0 / 27,
7.0 / 27, 16.0 / 27, 25.0 / 27, 2.0 / 27, 11.0 / 27, 20.0 / 27,
5.0 / 27, 14.0 / 27, 23.0 / 27, 8.0 / 27, 17.0 / 27, 26.0 / 27
};
dimensionality = 2;
points = (int)Math.Pow(3.0, 3) - 1; // three cycles of the higher dimension
for (i = 0; i < points; i++)
{
point = HaltonSequence.Halton(i, dimensionality);
double error = Math.Abs(point[0] - vanderCorputSequenceModuloTwo[i]);
if (error > tolerance)
{
Debug.Print("First component of " + i + 1
+ " draw (" + +point[0]
+ ") in 2-D Halton sequence is not in the "
+ "van der Corput sequence modulo two: "
+ "it should have been "
+ vanderCorputSequenceModuloTwo[i]
+ " (error = " + error + ")");
}
error = Math.Abs(point[1] - vanderCorputSequenceModuloThree[i]);
if (error > tolerance)
{
Debug.Print("Second component of " + i + 1
+ " draw (" + +point[1]
+ ") in 2-D Halton sequence is not in the "
+ "van der Corput sequence modulo three: "
+ "it should have been "
+ vanderCorputSequenceModuloThree[i]
+ " (error = " + error + ")");
}
}
}