/// <summary>
/// LU Det example
/// </summary>
public static void LUDetExample()
{
double[,] m = {{2, 3, 3, 5},
{6, 6, 8, 9},
{10, 11, 12, 13},
{14, 15, 17, 17}};
PZMath_matrix matrix = new PZMath_matrix(m);
double det = matrix.LUDet();
// correct answer:
// det(m) = -12
System.Console.WriteLine(det);
}
/// <summary>
/// A-R example
/// S Chib and E Greenberg, Understanding the Metropolis-Hastings Algorithm, The American Statistician, Vol. 49, No. 4. (Nov., 1995), pp. 327-335
/// samples are tesitfied by SigmaPlot
/// </summary>
public static void Example()
{
int N = 6000;
int n0 = 0;
string filename1 = "v1.txt";
FileStream fs1 = new FileStream(filename1, FileMode.Create, FileAccess.Write);
StreamWriter w1 = new StreamWriter(fs1);
// target distribution
//double[,] S = {{1, 0.9},{0.9, 1}};
double[,] S = { { 2, 0 }, { 0, 1 } };
double[] m = { 1, 2 };
PZMath_matrix targetSigma = new PZMath_matrix(S);
PZMath_vector targetMu = new PZMath_vector(m);
// instrumental distribution
double[,] D = {{2, 0},{0, 1}};
PZMath_matrix instrumentalSigma = new PZMath_matrix(D);
PZMath_vector instrumentalMu = new PZMath_vector(m);
double c = System.Math.Sqrt(System.Math.Abs(instrumentalSigma.LUDet()) / System.Math.Abs(targetSigma.LUDet()));
// prepare workspace
AcceptRejectionSampler ARSample = new AcceptRejectionSampler(c, N);
// prepare instrumental distribution
InstrumentalDistribution instrumentalDistribution = new InstrumentalDistribution(instrumentalMu, instrumentalSigma);
// prepare target distribution
TargetDistribution targetDistribution = new TargetDistribution();
targetDistribution.TargetDistributionFunction = new targetDistribution(AcceptRejectionSampler.ExampleTargetDistributionFunction);
// assign target distribution and instrumental distribution to the work space
ARSample.ARSInstrumentalDistribution = instrumentalDistribution;
ARSample.ARSTargetDistribution = targetDistribution;
// A-R sample
List<double[]> samples = ARSample.Sample();
for (int i = 0; i < N - n0; i++)
{
w1.Write(samples[i][0]);
w1.Write(" ");
w1.WriteLine(samples[i][1]);
}
w1.Close();
fs1.Close();
}