/// <summary>
/// Uses a moment-fitting basis of order <paramref name="order"/> for
/// determining optimal weights of a quadrature rule for a sub-region
/// of each cell in the given <paramref name="mask"/>.
/// </summary>
/// <param name="mask">
/// Cells for which rules shall be created
/// </param>
/// <param name="nodes">Integration nodes</param>
/// <param name="quadResults">
/// Integration results for each function in the
/// <see cref="lambdaBasis"/>
/// </param>
/// <param name="order">
/// Desired order of the moment-fitting system. Assuming that
/// <see cref="surfaceRuleFactory"/> integrates the basis
/// polynomials exactly over the zero iso-contour (which it usually
/// doesn't), the resulting quadrature rules will be exact up to this
/// order.
/// </param>
/// <returns>
/// A set of quadrature rules
/// </returns>
private QuadRule[] GetOptimizedRules(CellMask mask, NodeSet nodes, double[,] quadResults, int order)
{
using (var tr = new FuncTrace()) {
int maxLambdaDegree = order + 1;
int noOfLambdas = GetNumberOfLambdas(maxLambdaDegree);
int noOfNodes = nodes.GetLength(0);
QuadRule[] optimizedRules = new QuadRule[mask.NoOfItemsLocally];
if (mask.NoOfItemsLocally == 0)
{
return(optimizedRules);
}
// Leading dimension of B (rhs); required by DGELSY
int LDB = Math.Max(noOfLambdas, noOfNodes);
double[] rhs = new double[LDB * mask.NoOfItemsLocally];
Basis basis = new Basis(LevelSetData.GridDat, order);
MultidimensionalArray basisValues = basis.Evaluate(nodes);
int n = 0;
foreach (Chunk chunk in mask)
{
foreach (int cell in chunk.Elements)
{
int iSubGrid = localCellIndex2SubgridIndex[cell];
for (int k = 0; k < noOfLambdas; k++)
{
rhs[n * LDB + k] += quadResults[iSubGrid, k];
}
n++;
}
}
double[] matrix;
if (basisValues.IsContinious)
{
matrix = basisValues.Storage;
}
else
{
matrix = new double[basisValues.Length];
basisValues.CopyTo(matrix, true, 0);
}
LAPACK.F77_LAPACK.DGELSY(noOfLambdas, noOfNodes, matrix, rhs, mask.NoOfItemsLocally, RCOND);
n = 0;
foreach (Chunk chunk in mask)
{
foreach (int cell in chunk.Elements)
{
optimizedRules[n] = new QuadRule()
{
Nodes = nodes,
Weights = MultidimensionalArray.Create(noOfNodes),
OrderOfPrecision = order
};
for (int j = 0; j < noOfNodes; j++)
{
optimizedRules[n].Weights[j] = rhs[n * LDB + j];
}
double max = optimizedRules[n].Weights.Max(d => d.Abs());
if (max > 2.0 * RefElement.Volume)
{
tr.Info(String.Format(
"Warning: Abnormally large integration weight detected"
+ " for level set volume integral in cell {0}"
+ " (|w| = {1}). This may indicate a loss of"
+ " integration accuracy.",
cell,
max));
}
n++;
}
}
return(optimizedRules);
}
}