public static void Initialize(string name, string path,
Func <AircadiaComponent, string, bool> askUserOverwriteConfirmation = null,
Func <AircadiaComponent, string, bool> askUserConfirmImportantChanges = null,
Func <AircadiaComponent, string, bool> askUserDeleteDependencies = null)
{
Instance = new AircadiaProject(name, path, askUserOverwriteConfirmation, askUserConfirmImportantChanges, askUserDeleteDependencies);
Compiler.ProjectPath = path;
}
public double[] GenSamples_FAST(int Number_of_Sim, int Omiga_i, List <double> s_k)
{
double[] Samples = new double[Number_of_Sim];
for (int i = 0; i < Number_of_Sim; i++)
{
Samples[i] = 0.5 + 1 / Math.PI * Math.Asin(Math.Sin(Omiga_i * s_k[i])); //generate ditermistic sampling points from [0,1]
}
#region store the raw data to .csv for debugging
//should be a uniform distribution (not strictly because FAST sampling strategy)
AircadiaProject Project = AircadiaProject.Instance;
string file_path = Project.ProjectPath + "\\temp_FAST_raw.csv";
var FileStream = new FileStream(file_path, FileMode.Append);
var sw = new StreamWriter(FileStream, System.Text.Encoding.UTF8);
for (int j = 0; j < Number_of_Sim; j++)
{
sw.WriteLine(Samples[j].ToString());
}
sw.Flush();
sw.Close();
FileStream.Close();
#endregion
switch (DisType)
{
case "Uniform":
//in uniform distribution: lower boundary = FirstPara
// upper boundary = SecondPara
for (int i = 0; i < Number_of_Sim; i++)
{
Samples[i] = (SecondPara - FirstPara) * Samples[i] + FirstPara;
}
break;
case "Triangular":
//in triangular distribution: mean = FirstPara
double a = FirstPara - SecondPara; // left point = mean - SecondPara
double b = FirstPara + ThirdPara; // right point = mean + ThirdPara
double c = FirstPara + SecondPara - ThirdPara; // top point = mean + SecondPara - ThirdPara
for (int i = 0; i < Number_of_Sim; i++)
{
if (Samples[i] <= (c - a) / (b - a))
{
Samples[i] = a + Math.Sqrt(Samples[i] * (c - a) * (b - a));
}
else
{
Samples[i] = b - Math.Sqrt((1 - Samples[i]) * (b - a) * (b - c));
}
}
break;
case "Normal":
/*
* Approximation from
* author = {Dongbin Xiu and George E M Karniadakis},
* title = {The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations},
* journal = {SIAM J. SCI. COMPUT},
* year = {2002},
* pages = {619--644}
*/
double c0 = 2.515517;
double c1 = 0.802853;
double c2 = 0.010328;
double d1 = 1.432788;
double d2 = 0.189269;
double d3 = 0.001308;
double t; //temp
double X; //temp
double mu = FirstPara; //mean
double sigma = SecondPara; //std
for (int i = 0; i < Number_of_Sim; i++)
{
t = Math.Sqrt(-Math.Log(Math.Pow(Math.Min(Samples[i], 1 - Samples[i]), 2)));
X = Math.Sign(Samples[i] - 0.5) * (t - (c0 + c1 * t + c2 * Math.Pow(t, 2)) / (1 + d1 * t + d2 * Math.Pow(t, 2) + d3 * Math.Pow(t, 3)));
Samples[i] = mu + X * sigma;
}
break;
case "Rayleigh":
//Equation from lecture notes 3F1 Random Processes Course
//Nick Kingsbury, 2012.
//Also in Book by Peyton Z. Peebles, JR.
//Title Probability Random Variables and Random Signal Principles
a = FirstPara;
b = SecondPara;
for (int i = 0; i < Number_of_Sim; i++)
{
Samples[i] = Math.Sqrt(-b * Math.Log(1.0 - Samples[i])) + a;
}
break;
case "Mixture Gaussian":
c0 = 2.515517;
c1 = 0.802853;
c2 = 0.010328;
d1 = 1.432788;
d2 = 0.189269;
d3 = 0.001308;
double mu1 = FirstPara;
double mu2 = SecondPara;
double sigma1 = ThirdPara;
double sigma2 = ForthPara;
double p1 = FifthPara;
double p2 = SixthPara;
double u;
for (int i = 0; i < Number_of_Sim; i++)
{
if (Samples[i] <= p1)
{
u = Samples[i] / p1;
t = Math.Sqrt(-Math.Log(Math.Pow(Math.Min(u, 1.0 - u), 2)));
X = Math.Sign(u - 0.5) * (t - (c0 + c1 * t + c2 * Math.Pow(t, 2)) / (1 + d1 * t + d2 * Math.Pow(t, 2) + d3 * Math.Pow(t, 3)));
Samples[i] = mu1 + X * sigma1;
}
else
{
u = (Samples[i] - (p1 + 1e-8)) / p2;
t = Math.Sqrt(-Math.Log(Math.Pow(Math.Min(u, 1.0 - u), 2)));
X = Math.Sign(u - 0.5) * (t - (c0 + c1 * t + c2 * Math.Pow(t, 2)) / (1 + d1 * t + d2 * Math.Pow(t, 2) + d3 * Math.Pow(t, 3)));
Samples[i] = mu2 + X * sigma2;
}
}
break;
}
return(Samples);
}
