private static void LowDiscrepancySequenceApproach()
{
do
{
int length = UI.AcceptValidInt("Enter how many points to generate: (0 to quit, max 2147483637) \n>", 0, int.MaxValue - 10);
if (length == 0)
{
break;
}
int eachstep = UI.AcceptValidInt("Enter how many points per step to print (Put bigger steps >10000000 to avoid screen flash): (0 to quit) \n>", 0, int.MaxValue - 50);
if (eachstep == 0)
{
break;
}
int inside = 0;
int total = 0;
Stopwatch stopwatch = new Stopwatch();
stopwatch.Start();
foreach (var v in QuasiRandom.SobolSequence(2, length))
{
if (hypotenuseSquare(new XYCoord(v[0], v[1])) < 1)
{
inside++;
}
total++;
if (total % eachstep == 0)
{
Console.WriteLine($"{inside}, {total}, {(double)inside / total * 4} Elasped time:{stopwatch.Elapsed.TotalSeconds} Seconds");
}
}
decimal estimatePi = (decimal)inside / total * 4;
Console.WriteLine($"================================================================\n" +
$"Estimated Pi Value: {estimatePi:f14}\n" +
$"Actual Pi Value: {Math.PI}\n" +
$"Difference: {Math.Abs(estimatePi - (decimal)Math.PI):f14}\n" +
$"Elasped time: {stopwatch.Elapsed.TotalSeconds} Seconds\n" +
$"Inside Pts Generated:{inside}\n" +
$"Total Pts Generated:{total}\n" +
$"================================================================\n");
} while (true);
}
public static void Initialise(int numberOfPaths)
{
_nPaths = numberOfPaths;
#if USE_THIRD_PARTY_RANDOM_GENERATORS
if (UseQuasiRandom)
{
if (UseExtreme)
{
_enumerator = QuasiRandom.HaltonSequence(Dimension, numberOfPaths).GetEnumerator();
}
else
{
var generator = new SobolQuasiRandomGenerator(Dimension);
_generatedRandoms = generator.Next(new DoubleRandomUniformDistribution(), numberOfPaths);
}
return;
}
#endif
var random = new Random();
var useAntithetic = UseAntithetic && _nPaths % 2 == 0;
var nPaths = useAntithetic ? _nPaths / 2 : _nPaths;
var defaultRandoms = new List <List <double> >();
for (var i = 0; i < nPaths; ++i)
{
var list = new List <double>();
for (var j = 0; j < Dimension; ++j)
{
list.Add(random.NextDouble());
}
defaultRandoms.Add(list);
if (useAntithetic)
{
defaultRandoms.Add(list.Select(x => 1.0 - x).ToList());
}
}
_defaultEnumerator = defaultRandoms.GetEnumerator();
}
