/// <summary>
/// Evaluates the vector-valued anti-derivatives defining the
/// moment-fitting basis (cf. <see cref="lambdaBasis"/>) in each node
/// of all cells in the given range
/// </summary>
/// <param name="i0">
/// First cell in range
/// </param>
/// <param name="length">
/// Number of cells
/// </param>
/// <returns>
/// The values of <see cref="lambdaBasis"/> in each node
/// <list type="bullet">
/// <item>1st index: Node index</item>
/// <item>2nd index: Basis function index</item>
/// <item>3rd index: Spatial dimension</item>
/// </list>
/// </returns>
/// <remarks>
/// This method does not evaluate a Lambda which is constant since the
/// derivative of such function is zero. As a result, the integral over
/// this function is zero, too, which makes it useless for the
/// construction of a quadrature rule
/// </remarks>
/// <param name="NS">
/// Nodes at which to evaluate.
/// </param>
private MultidimensionalArray EvaluateLambdas(int cell, NodeSet NS)
{
int D = LevelSetData.GridDat.SpatialDimension;
Debug.Assert(
lambdaBasis.Count % D == 0,
"Number of polynomials in basis should be divisible by D = " + D);
int noOfLambdas = lambdaBasis.Count / D;
int noOfNodes = NS.NoOfNodes;
if (RestrictNodes)
{
AffineTrafo trafo = trafos[localCellIndex2SubgridIndex[cell]];
AffineTrafo inverse = trafo.Invert();
NS = new NodeSet(RefElement, inverse.Transform(NS));
NS.LockForever();
MultidimensionalArray lambdaValues = lambdaBasis.Values.GetValues(NS);
lambdaValues = lambdaValues.ResizeShallow(noOfNodes, noOfLambdas, D);
for (int i = 0; i < noOfNodes; i++)
{
for (int j = 0; j < noOfLambdas; j++)
{
for (int d = 0; d < D; d++)
{
// Bounding box transformation is assumed to just a
// stretching, i.e. off-diagonals are zero
lambdaValues[i, j, d] *= trafo.Matrix[d, d];
}
}
}
return(lambdaValues);
}
else
{
MultidimensionalArray lambdaValues = lambdaBasis.Values.GetValues(NS);
return(lambdaValues.ResizeShallow(noOfNodes, noOfLambdas, D));
}
}
/// <summary>
/// Non-vectorized reference implementation of
/// <see cref="GetOptimizedRule(int, AffineTrafo, NodeSet, double[,], int)"/>
/// </summary>
/// <param name="cell"></param>
/// <param name="trafo"></param>
/// <param name="nodes"></param>
/// <param name="quadResults"></param>
/// <param name="order"></param>
/// <returns></returns>
private QuadRule GetOptimizedRule(int cell, AffineTrafo trafo, NodeSet nodes, double[,] quadResults, int order)
{
int maxLambdaDegree = order + 1;
int noOfLambdas = GetNumberOfLambdas(maxLambdaDegree);
int noOfNodes = nodes.GetLength(0);
// Leading dimension of B (rhs); required by DGELSY
int LDB = Math.Max(noOfLambdas, noOfNodes);
double[] rhs = new double[LDB];
AffineTrafo inverseTrafo = trafo.Invert();
NodeSet trafoNodes = new NodeSet(RefElement, inverseTrafo.Transform(nodes));
trafoNodes.LockForever();
Basis basis = new Basis(LevelSetData.GridDat, order);
MultidimensionalArray basisValues = basis.Evaluate(trafoNodes);
int iSubGrid = localCellIndex2SubgridIndex[cell];
for (int k = 0; k < noOfLambdas; k++)
{
rhs[k] += quadResults[iSubGrid, k];
}
LAPACK.F77_LAPACK.DGELSY(noOfLambdas, noOfNodes, basisValues.Storage, rhs, 1, RCOND);
QuadRule optimizedRule = new QuadRule()
{
Nodes = nodes,
Weights = MultidimensionalArray.Create(noOfNodes),
OrderOfPrecision = order
};
for (int j = 0; j < noOfNodes; j++)
{
optimizedRule.Weights[j] = rhs[j];
}
return(optimizedRule);
}