/// <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;
}