//Algorithm 2
//page: A1005
private void SurfaceIntegrand(MultidimensionalArray X, double X_weight, T arg, bool isNew)
{
Debug.Assert(arg.n == 1);
//Calculate the roots of phi in the interval R = ... (line 1)
S phi = arg.PsiAndS[0].Item1;
int heightDirection = arg.HeightDirection;
double[] bounds = GetBoundaries(arg, heightDirection);
ISortedBoundedList <double> roots = new SayeSortedList(3, 1.0e-14);
roots.SetBounds(bounds[0], bounds[1]);
double[] newRoots = FindRoots(phi, X, heightDirection, bounds, this.cell);
roots.Add(newRoots);
//if there is a root, insert node
Debug.Assert(roots.Count() <= 3);
if (roots.Count() > 2)
{
X[0, heightDirection] = roots[1];
SayeQuadRule surfaceQuadNode = BuildSurfaceQuadRule(X, X_weight, heightDirection, this.cell);
arg.NodesAndWeights.AddRule(surfaceQuadNode, true);
}
//else remove node
else
{
arg.NodesAndWeights.RemoveActiveNode();
}
}
//Algorithm 1
//page: A1005
private void VolumeIntegrand(MultidimensionalArray X, double X_weight, T arg, bool isNew)
{
//Calculate the set of roots and union with the interval endpoints ( line 1)
int heightDirection = arg.HeightDirection;
//Sort R into ascending order such that ... (line 2) : Implemented with a sortedList
ISortedBoundedList <double> roots = new SayeSortedList(2 + arg.n, 1.0e-14);
double[] bounds = GetBoundaries(arg, heightDirection);
roots.SetBounds(bounds[0], bounds[1]);
RestrictToBound(X, bounds[0], arg.HeightDirection);
for (int i = 0; i < arg.n; ++i)
{
S psi_i = arg.PsiAndS[i].Item1;
double[] rootsInPsi = FindRoots(psi_i, X, heightDirection, bounds, this.cell);
roots.Add(rootsInPsi);
}
//For j = 1 to l - 1 do (line 4)
bool xIsUnchanged = true;
for (int j = 0; j < roots.Count() - 1; ++j)
{
//Define L and x_c(line 5)
double L = roots[j + 1] - roots[j];
NodeSet x_c = NodeOnRay(X, heightDirection, roots[j] - roots[0] + L / 2.0);
//If s_i * psi_i >= 0 for all i (line 6)
bool updateIntegrand = true;
foreach (Tuple <S, int> psiAndS in arg.PsiAndS)
{
S psi_i = psiAndS.Item1;
int s_i = psiAndS.Item2;
updateIntegrand &= s_i * EvaluateAt(psi_i, x_c) >= 0;
}
//Update I = ...(line 7)
if (updateIntegrand)
{
SayeQuadRule newRule = BuildQuadRule(x_c, X_weight, heightDirection, L);
bool deriveFromExistingNode = !isNew && xIsUnchanged;
arg.NodesAndWeights.AddRule(newRule, deriveFromExistingNode);
xIsUnchanged = false;
}
}
if (xIsUnchanged && !isNew)
{
arg.NodesAndWeights.RemoveActiveNode();
}
}