/// <summary>
/// The index of a descendant of node (i,j).
/// The three descendants of one node in x[i,j] are: x[i, Descendant(i+1, j, BranchDirection.Up)], x[i, Descendant(i+1, j, BranchDirection.Middle)] and x[i+1, Descendant(i, j, BranchDirection.Down)]
/// </summary>
/// <param name="i">The i^{th} point on time grid.</param>
/// <param name="j">The j^{th} node at i^{th} time, starting from the bottom as 0.</param>
/// <param name="branchDirection">The b direction.</param>
/// <returns></returns>
public int Descendant(int i, int j, BranchDirection branchDirection)
{
var branching = Branchings[i];
switch (branchDirection)
{
case BranchDirection.Down:
return(branching.K[j] - branching.JMin - 1);
case BranchDirection.Up:
return(branching.K[j] - branching.JMin + 1);
case BranchDirection.Middle:
return(branching.K[j] - branching.JMin);
default:
throw new ArgumentOutOfRangeException("branchDirection");
}
}
public static Vector3 GetVector(int level, BranchDirection branch)
{
Vector3 position = new Vector3();
LevelModifiers(level);
//if (level == 0) return MiddleBase;
switch (branch)
{
case BranchDirection.LEFT:
position = LeftBase;
break;
case BranchDirection.RIGHT:
position = RightBase;
break;
case BranchDirection.MIDDLE:
position = MiddleBase;
break;
}
position *= level;
position += GetLevelPosition();
return(position);
}
/// <summary>
/// The branching probability from node (i, j).
/// </summary>
/// <param name="i">The i^{th} point on time grid.</param>
/// <param name="j">The j^{th} node at i^{th} time, starting from the bottom as 0.</param>
/// <param name="bDirection">The b direction.</param>
/// <returns></returns>
public double Probability(int i, int j, BranchDirection bDirection)
{
return(Branchings[i].Probability[Convert.ToInt32(bDirection)][j]);
}
public abstract double Probability(int i, int j, BranchDirection branch);
/// <summary>
/// Returns the descendant of node [i,j].
/// The three descendants of one node in x[i,j] are: x[i+1, Descendant(i, j, BranchDirection.Up)], and x[i+1, Descendant(i, j, BranchDirection.Down)]
/// </summary>
/// <param name="i">The i^{th} time step, starts from 0.</param>
/// <param name="j">The j^{th} state.</param>
/// <param name="branch">The branching direction, <see cref="BranchDirection"/>. In binomial tree case, it takes value as either Up or Down.</param>
/// <returns></returns>
public int Descendant(int i, int j, BranchDirection branch)
{
return(branch == BranchDirection.Down ? j : j + 1);
}
public override double Probability(int i, int j, BranchDirection branch)
{
return(branch == BranchDirection.Up ? PUp : PDown);
}
