void values(FieldContainer<double> &values, BasisCachePtr sliceBasisCache)
{
vector<GlobalIndexType> sliceCellIDs = sliceBasisCache->cellIDs();
Teuchos::Array<int> dim;
values.dimensions(dim);
dim[0] = 1; // one cell
std::vector<int> offset(dim.size());
for (int cellOrdinal = 0; cellOrdinal < sliceCellIDs.size(); cellOrdinal++)
{
offset[0] = cellOrdinal;
int enumeration = SerialDenseWrapper::getEnumeration(offset,values);
FieldContainer<double>valuesForCell(dim,&values[enumeration]);
GlobalIndexType sliceCellID = sliceCellIDs[cellOrdinal];
int numPoints = sliceBasisCache->getPhysicalCubaturePoints().dimension(1);
int spaceDim = sliceBasisCache->getPhysicalCubaturePoints().dimension(2);
FieldContainer<double> spaceTimePhysicalPoints(1,numPoints,spaceDim+1);
for (int ptOrdinal=0; ptOrdinal<numPoints; ptOrdinal++)
{
for (int d=0; d<spaceDim; d++)
{
spaceTimePhysicalPoints(0,ptOrdinal,d) = sliceBasisCache->getPhysicalCubaturePoints()(cellOrdinal,ptOrdinal,d);
}
spaceTimePhysicalPoints(0,ptOrdinal,spaceDim) = _t;
}
GlobalIndexType cellID = _cellIDMap[sliceCellID];
BasisCachePtr spaceTimeBasisCache = BasisCache::basisCacheForCell(_spaceTimeMesh, cellID);
FieldContainer<double> spaceTimeRefPoints(1,numPoints,spaceDim+1);
CamelliaCellTools::mapToReferenceFrame(spaceTimeRefPoints, spaceTimePhysicalPoints, _spaceTimeMesh->getTopology(), cellID, spaceTimeBasisCache->cubatureDegree());
spaceTimeRefPoints.resize(numPoints,spaceDim+1);
spaceTimeBasisCache->setRefCellPoints(spaceTimeRefPoints);
_spaceTimeFunction->values(valuesForCell, spaceTimeBasisCache);
}
}
void Projector::projectFunctionOntoBasisInterpolating(FieldContainer<double> &basisCoefficients, FunctionPtr fxn,
BasisPtr basis, BasisCachePtr domainBasisCache) {
basisCoefficients.initialize(0);
CellTopoPtr domainTopo = basis->domainTopology();
unsigned domainDim = domainTopo->getDimension();
IPPtr ip;
bool traceVar = domainBasisCache->isSideCache();
pair<IPPtr, VarPtr> ipVarPair = IP::standardInnerProductForFunctionSpace(basis->functionSpace(), traceVar, domainDim);
ip = ipVarPair.first;
VarPtr v = ipVarPair.second;
IPPtr ip_l2 = Teuchos::rcp( new IP );
ip_l2->addTerm(v);
// for now, make all projections use L^2... (having some issues with gradients and cell Jacobians--I think we need the restriction of the cell Jacobian to the subcell, e.g., and it's not clear how to do that...)
ip = ip_l2;
FieldContainer<double> referenceDomainNodes(domainTopo->getVertexCount(),domainDim);
CamelliaCellTools::refCellNodesForTopology(referenceDomainNodes, domainTopo);
int basisCardinality = basis->getCardinality();
set<int> allDofs;
for (int i=0; i<basisCardinality; i++) {
allDofs.insert(i);
}
for (int d=0; d<=domainDim; d++) {
FunctionPtr projectionThusFar = NewBasisSumFunction::basisSumFunction(basis, basisCoefficients);
FunctionPtr fxnToApproximate = fxn - projectionThusFar;
int subcellCount = domainTopo->getSubcellCount(d);
for (int subcord=0; subcord<subcellCount; subcord++) {
set<int> subcellDofOrdinals = basis->dofOrdinalsForSubcell(d, subcord);
if (subcellDofOrdinals.size() > 0) {
FieldContainer<double> refCellPoints;
FieldContainer<double> cubatureWeightsSubcell; // allows us to integrate over the fine subcell even when domain is higher-dimensioned
if (d == 0) {
refCellPoints.resize(1,domainDim);
for (int d1=0; d1<domainDim; d1++) {
refCellPoints(0,d1) = referenceDomainNodes(subcord,d1);
}
cubatureWeightsSubcell.resize(1);
cubatureWeightsSubcell(0) = 1.0;
} else {
CellTopoPtr subcellTopo = domainTopo->getSubcell(d, subcord);
// Teuchos::RCP<Cubature<double> > subcellCubature = cubFactory.create(subcellTopo, domainBasisCache->cubatureDegree());
BasisCachePtr subcellCache = Teuchos::rcp( new BasisCache(subcellTopo, domainBasisCache->cubatureDegree(), false) );
int numPoints = subcellCache->getRefCellPoints().dimension(0);
refCellPoints.resize(numPoints,domainDim);
cubatureWeightsSubcell = subcellCache->getCubatureWeights();
if (d == domainDim) {
refCellPoints = subcellCache->getRefCellPoints();
} else {
CamelliaCellTools::mapToReferenceSubcell(refCellPoints, subcellCache->getRefCellPoints(), d,
subcord, domainTopo);
}
}
domainBasisCache->setRefCellPoints(refCellPoints, cubatureWeightsSubcell);
IPPtr ipForProjection = (d==0) ? ip_l2 : ip; // just use values at vertices (ignore derivatives)
set<int> dofsToSkip = allDofs;
for (set<int>::iterator dofOrdinalIt=subcellDofOrdinals.begin(); dofOrdinalIt != subcellDofOrdinals.end(); dofOrdinalIt++) {
dofsToSkip.erase(*dofOrdinalIt);
}
FieldContainer<double> newBasisCoefficients;
projectFunctionOntoBasis(newBasisCoefficients, fxnToApproximate, basis, domainBasisCache, ipForProjection, v, dofsToSkip);
for (int cellOrdinal=0; cellOrdinal<newBasisCoefficients.dimension(0); cellOrdinal++) {
for (set<int>::iterator dofOrdinalIt=subcellDofOrdinals.begin(); dofOrdinalIt != subcellDofOrdinals.end(); dofOrdinalIt++) {
basisCoefficients(cellOrdinal,*dofOrdinalIt) = newBasisCoefficients(cellOrdinal,*dofOrdinalIt);
}
}
}
}
}
}
