/// <summary>
/// Computes four correlated deviates for Monte Carlo simulation.
/// </summary>
/// <param name="R">Correlation matrix (which is always symmetric).</param>
/// <param name="dt">Time step.</param>
/// <param name="z">Array to store correlated deviates.</param>
/// <returns></returns>
public double[] GenerateCorrelatedDeviates(SymmetricMatrix R, double dt, double[] z)
{
double sum = 0.0;
// standard normal deviate
double deviate = 0.0;
// number of rows in correlation matrix.
int m = R.GetNumberOfRows();
// list of correlated deviates
//List<double> dz;
// list of eigenvalues
List<double> eigenValues = new List<double>();
// array of eigenvectors
List<double>[] eigenVectors = new List<double>[4];
// stores eigenvalues of correlation matrix R
double[] lambda = new double[] { 0.0, 0.0, 0.0, 0.0 };
// stores correlated deviates
double[] dw = new double[] { 0.0, 0.0, 0.0, 0.0 };
DiagonalMatrix D = R.GetEigenValues();
Matrix V = GenerateEigenVectors(R);
// store eigen values
for (int i = 0; i < m; i++)
{
eigenValues.Add(D.GetElement(i, i));
lambda[i] = D.GetElement(i, i);
}
// stores rows of eigenvectors so that we can compute
// dz[i] = v[i][1]*sqrt(eigenvalue[1])*dw1 + v[i][2]*sqrt(eigenvalue[2])*dw2 + ...
for (int i = 0; i < m; i++)
{
for (int j = 0; j < m; j++)
{
eigenVectors[i].Add(V.GetElement(i, j));
}
}
Random randomNumberGenerator = new Random();
long seed = randomNumberGenerator.Next() % 100;
// generate uncorrelated deviates
for (int i = 0; i < m; i++)
{
deviate = NormalDeviate(ref seed);
dw[i] = deviate * Math.Sqrt(dt);
}
// generate correlated deviates
for (int i = 0; i < m; i++)
{
for (int j = 0; j < m; j++)
{
sum += eigenVectors[i][j] * Math.Sqrt(eigenValues[j]) * dw[j];
}
z[i] = sum;
}
return z;
}
private Matrix GenerateEigenVectors(SymmetricMatrix symmetricMatrix)
{
// OkashTODO: why do we need the diagonal matrix here??
DiagonalMatrix D = new DiagonalMatrix(symmetricMatrix.GetNumberOfRows());
Matrix eigenVectors = symmetricMatrix.GetEigenValues(D);
return eigenVectors;
}
/// <summary>
/// Computes correlated deviates from Cholesky decomposition.
/// </summary>
/// <param name="R">correlation matrix</param>
/// <param name="dt">step size</param>
/// <param name="z">correlated deviates array to be returned.</param>
/// <returns>array of correlated normal deviates</returns>
/// <remarks>
/// OkashTODO: do we need the parameter double[] z?? Dont think so.
/// Same question goes to the method GenerateCorrelatedDeviates above.
/// </remarks>
public double[] GenerateCorrelatedDeviatesCholesky(SymmetricMatrix R, double dt, double[] z)
{
int m = R.GetNumberOfRows();
int n = R.GetNumberOfColumns();
StatUtility util = new StatUtility();
// standard normal deviate
double deviate = 0.0;
// stores deviate * sqrt(dt)
double[] dw = new double[4] { 0.0, 0.0, 0.0, 0.0 };
double sum = 0.0;
// lower-banded (lb) matrix
Matrix lb = R.Cholesky();
Random randomNumberGenerator = new Random();
long seed = randomNumberGenerator.Next() % 100;
// generate uncorrelated deviates
for (int i = 0; i < m; i++)
{
deviate = util.gasdev(ref seed);
dw[i] = deviate * Math.Sqrt(dt);
}
// generate correlated deviates
for (int i = 0; i < m; i++)
{
sum = 0;
for (int j = 0; j < n; j++)
{
sum += lb.GetElement(i, j) * dw[j];
}
z[i] = sum;
}
return z;
}