/// <summary>
/// Construct an initial simplex, given starting guesses for the constants, and
/// initial step sizes for each dimension
/// </summary>
/// <param name="simplexConstants"></param>
/// <returns></returns>
private static Vector[] _initializeVertices(SimplexConstant[] simplexConstants)
{
int numDimensions = simplexConstants.Length;
Vector[] vertices = new Vector[numDimensions + 1];
GaussianDistribution gaussian;
// define one point of the simplex as the given initial guesses
Vector p0 = new Vector(numDimensions);
for (int i = 0; i < numDimensions; i++)
{
gaussian = new GaussianDistribution(simplexConstants[i].Value, simplexConstants[i].InitialPerturbation);
p0[i] = gaussian.NextGaussian(simplexConstants[i].Value, simplexConstants[i].InitialPerturbation);
}
// now fill in the vertices, creating the additional points as:
// P(i) = P(0) + Scale(i) * UnitVector(i)
vertices[0] = p0;
for (int i = 0; i < numDimensions; i++)
{
gaussian = new GaussianDistribution(simplexConstants[i].InitialPerturbation, simplexConstants[i].InitialPerturbation / 2);
double scale = simplexConstants[i].InitialPerturbation;
Vector unitVector = new Vector(numDimensions);
unitVector[i] = 1;
vertices[i + 1] = p0.Add(unitVector.Multiply(gaussian.NextGaussian(simplexConstants[i].InitialPerturbation, simplexConstants[i].InitialPerturbation / 2)));
}
return(vertices);
}
