/// <summary>
/// two <see cref="Basis"/>-objects are equal, if their polynomial list
/// (<see cref="Polynomials"/>) is equal (equal Guid for each entry).
/// </summary>
/// <param name="obj"></param>
/// <returns></returns>
public override bool Equals(object obj)
{
if (obj.GetType() != typeof(Basis))
{
return(false);
}
Basis other = (Basis)obj;
if (!object.ReferenceEquals(other.m_GridDat, this.m_GridDat))
{
return(false);
}
int L = m_GridDat.iGeomCells.RefElements.Length;
Debug.Assert(this.Polynomials.Count == L);
Debug.Assert(other.Polynomials.Count == L);
for (int l = 0; l < L; l++)
{
int N = this.Polynomials[l].Count;
if (other.Polynomials[l].Count != N)
{
return(false);
}
for (int i = N - 1; i >= 0; i--)
{
if (!this.Polynomials[l][i].Equals(other.Polynomials[l][i]))
{
return(false);
}
}
}
return(true);
}
private static void CheckArgs(int j0, int L, NodeSet NS, Basis basis, MultidimensionalArray Coördinates, MultidimensionalArray ResultAcc, out int D, out int N, out int M, out bool AffineLinear)
{
D = basis.GridDat.SpatialDimension; // spatial dimension
N = basis.GetLength(j0); // number of coordinates per cell
M = NS.NoOfNodes; // number of nodes
AffineLinear = basis.GridDat.iGeomCells.IsCellAffineLinear(j0);
Debug.Assert(basis.GetType() == typeof(Basis));
Debug.Assert(Coördinates.Dimension == 2);
Debug.Assert(Coördinates.GetLength(0) == L);
Debug.Assert(Coördinates.GetLength(1) == N);
#if DEBUG
for (int i = 1; i < L; i++)
{
int jCell = j0 + i;
Debug.Assert(basis.GridDat.iGeomCells.IsCellAffineLinear(jCell) == AffineLinear);
Debug.Assert(basis.GetLength(jCell) == N);
}
#endif
}
private static void CheckArgs(int j0, int L, NodeSet NS, Basis basis, MultidimensionalArray Coördinates, MultidimensionalArray ResultAcc, out int D, out int N, out int M, out bool AffineLinear)
{
int[] g2l = basis.GridDat.iGeomCells.GeomCell2LogicalCell;
D = basis.GridDat.SpatialDimension; // spatial dimension
if (g2l == null)
{
N = basis.GetLength(j0); // number of coordinates per cell -- standard grid
}
else
{
N = basis.GetLength(g2l[j0]); // number of coordinates per cell -- aggregation grid
}
M = NS.NoOfNodes; // number of nodes
AffineLinear = basis.GridDat.iGeomCells.IsCellAffineLinear(j0);
Debug.Assert(basis.GetType() == typeof(Basis));
Debug.Assert(Coördinates.Dimension == 2);
Debug.Assert(Coördinates.GetLength(1) == N);
#if DEBUG
for (int i = 1; i < L; i++)
{
int jCell = j0 + i;
Debug.Assert(basis.GridDat.iGeomCells.IsCellAffineLinear(jCell) == AffineLinear);
if (g2l == null)
{
Debug.Assert(basis.GetLength(jCell) == N);
}
else
{
Debug.Assert(basis.GetLength(g2l[jCell]) == N);
}
}
#endif
}
public override void GetRestrictionMatrix(BlockMsrMatrix RST, MultigridMapping mgMap, int iF)
{
if (!object.ReferenceEquals(mgMap.AggBasis[iF], this))
{
throw new ArgumentException();
}
//MsrMatrix RST = new MsrMatrix(mgMap.Partitioning, mgMap.ProblemMapping);
int JAGG = this.AggGrid.iLogicalCells.NoOfLocalUpdatedCells;
int[] degrees = mgMap.DgDegree;
int NoFld = degrees.Length;
int N_rest; // = new int[NoFld];
int N_full; // = new int[NoFld];
{
BoSSS.Foundation.Basis b = mgMap.ProblemMapping.BasisS[iF];
BoSSS.Foundation.Basis NxB = (b is BoSSS.Foundation.XDG.XDGBasis) ? ((BoSSS.Foundation.XDG.XDGBasis)b).NonX_Basis : b;
N_rest = NxB.Polynomials[0].Where(poly => poly.AbsoluteDegree <= degrees[iF]).Count();
N_full = NxB.Length;
}
int mgMap_Offset = mgMap.Partitioning.i0;
for (int jAgg = 0; jAgg < JAGG; jAgg++)
{
int[] AgCell = this.AggGrid.iLogicalCells.AggregateCellToParts[jAgg];
int K = AgCell.Length;
int NoSpc_Agg = this.NoOfSpecies[jAgg]; // number of species in aggregate cell
for (int iSpc_Agg = 0; iSpc_Agg < NoSpc_Agg; iSpc_Agg++) // loop over all species in aggregate cell
{
{ // loop over DG fields in the mapping
int NROW = N_rest;
int NCOL = N_full;
Debug.Assert(mgMap.AggBasis[iF].GetLength(jAgg, degrees[iF]) == N_rest * NoSpc_Agg);
int i0Agg_Loc = mgMap.LocalUniqueIndex(iF, jAgg, N_rest * iSpc_Agg);
int i0Agg = i0Agg_Loc + mgMap_Offset;
Debug.Assert(i0Agg >= mgMap.Partitioning.i0);
Debug.Assert(i0Agg < mgMap.Partitioning.iE);
if (this.SpeciesIndexMapping[jAgg] == null)
{
Debug.Assert(NoSpc_Agg == 1);
Debug.Assert(NoSpc_Agg == 1);
// default branch:
// use restriction/prolongation from un-cut basis
// +++++++++++++++++++++++++++++++++++++++++++++
MultidimensionalArray Trf = base.CompositeBasis[jAgg];
for (int k = 0; k < K; k++) // loop over the cells which form the aggregated cell...
{
int jCell = AgCell[k];
int i0Full = mgMap.ProblemMapping.GlobalUniqueCoordinateIndex(iF, jCell, 0);
var Block = Trf.ExtractSubArrayShallow(k, -1, -1);
for (int nRow = 0; nRow < NROW; nRow++)
{
for (int nCol = 0; nCol < NCOL; nCol++)
{
RST[i0Agg + nRow, i0Full + nCol] = Block[nCol, nRow];
}
}
}
}
else
{
int NoSpc = this.NoOfSpecies[jAgg];
int[,] sim = SpeciesIndexMapping[jAgg];
Debug.Assert(sim.GetLength(0) == NoSpc);
Debug.Assert(sim.GetLength(1) == K);
MultidimensionalArray Trf;
if (this.XCompositeBasis[jAgg] == null || this.XCompositeBasis[jAgg][iSpc_Agg] == null)
{
Trf = base.CompositeBasis[jAgg];
}
else
{
Trf = this.XCompositeBasis[jAgg][iSpc_Agg];
}
for (int k = 0; k < K; k++) // loop over the cells which form the aggregated cell...
{
int jCell = AgCell[k];
int iSpcBase = sim[iSpc_Agg, k];
if (iSpcBase < 0)
{
//for(int n = 0; n < N; n++)
// FulCoords[k, n] = 0;
}
else
{
int i0Full = mgMap.ProblemMapping.GlobalUniqueCoordinateIndex(iF, jCell, iSpcBase * N_full);
var Block = Trf.ExtractSubArrayShallow(k, -1, -1);
for (int nRow = 0; nRow < NROW; nRow++)
{
for (int nCol = 0; nCol < NCOL; nCol++)
{
RST[i0Agg + nRow, i0Full + nCol] = Block[nCol, nRow];
}
}
}
}
}
}
}
}
//return RST;
}
/// <summary>
/// Polynomial extrapolation between cells.
/// </summary>
/// <param name="CellPairs">
/// A list of which cells should be extrapolated to which cells. <br/>
/// 1st index: enumeration;<br/>
/// 2nd index, in the range of 0 to 1: 0: cell to extrapolate from (source), i.e. values in this cell remain unchanged.
/// 1: cell to extrapolate to (target), the values in this cell will be the polynomial continuation of the "cell to extrapolate from".
/// </param>
/// <param name="scl">
/// optional scaling for the target cells
/// </param>
/// <param name="beta">
/// optional input scaling scaling for the target cells
/// </param>
virtual public void CellExtrapolation <T, U>(int[,] CellPairs, T scl = default(T), U beta = default(U))
where T : IList <double>
where U : IList <double> //
{
//MPICollectiveWatchDog.Watch();
if (CellPairs.GetLength(1) != 2)
{
throw new ArgumentOutOfRangeException("second dimension is expected to be 2!");
}
//if (!SurpressMPIUpdate)
// this.MPIExchange();
int Esub = CellPairs.GetLength(0);
Basis B = this.Basis;
int N = B.Length;
int JE = this.GridDat.iLogicalCells.Count;
int J = this.GridDat.iLogicalCells.NoOfLocalUpdatedCells;
if (scl != null)
{
if (scl.Count != Esub)
{
throw new ArgumentException();
}
}
var M = MultidimensionalArray.Create(Esub, N, N);
B.GetExtrapolationMatrices(CellPairs, M);
double[] V = null, W = null;
for (int esub = 0; esub < Esub; esub++)
{
var M_tmp = M.ExtractSubArrayShallow(esub, -1, -1);
int jCell0 = CellPairs[esub, 0];
int jCell1 = CellPairs[esub, 1];
if (jCell0 < 0 || jCell0 >= JE)
{
throw new ArgumentOutOfRangeException();
}
if (jCell1 < 0 || jCell1 >= J)
{
throw new ArgumentOutOfRangeException();
}
if (!this.GridDat.iGeomCells.IsCellAffineLinear(jCell0))
{
throw new NotSupportedException("Currently not supported for curved cells.");
}
if (!this.GridDat.iGeomCells.IsCellAffineLinear(jCell1))
{
throw new NotSupportedException("Currently not supported for curved cells.");
}
double _scl = 1.0;
if (scl != null)
{
_scl = scl[esub];
}
double _beta = 0.0;
if (beta != null)
{
_beta = beta[esub];
}
if (esub == 0)
{
V = new double[this.Coordinates.NoOfCols];
W = new double[this.Coordinates.NoOfCols];
}
{
this.Coordinates.GetRow(jCell0, V);
this.Coordinates.GetRow(jCell1, W);
for (int n = 0; n < N; n++)
{
double acc0 = 0;
for (int m = 0; m < N; m++)
{
acc0 += V[m] * M_tmp[n, m];
}
W[n] = W[n] * _beta + acc0 * _scl;
}
this.Coordinates.SetRow(jCell1, W);
}
}
}
protected static void EvaluateEdgeInternal(int e0, int Len, NodeSet NS, Basis _Basis, MultidimensionalArray Coord,
MultidimensionalArray valIN, MultidimensionalArray valOT,
MultidimensionalArray meanValIN, MultidimensionalArray meanValOT,
MultidimensionalArray gradIN, MultidimensionalArray gradOT,
double ResultPreScale)
{
// checks and init
// ===============
var grd = _Basis.GridDat;
int NoOfNodes = NS.NoOfNodes;
bool AffineLinear = grd.iGeomEdges.IsEdgeAffineLinear(e0);
Debug.Assert(NS.GetNodeCoordinateSystem(grd) == NodeCoordinateSystem.EdgeCoord);
Debug.Assert(valIN == null || valIN.Dimension == 2);
Debug.Assert(valOT == null || valOT.Dimension == 2);
Debug.Assert(valIN == null || valIN.GetLength(0) == Len);
Debug.Assert(valOT == null || valOT.GetLength(0) == Len);
Debug.Assert(valIN == null || valIN.GetLength(1) == NoOfNodes);
Debug.Assert(valOT == null || valOT.GetLength(1) == NoOfNodes);
int[,] trfIdx = grd.iGeomEdges.Edge2CellTrafoIndex;
int[,] E2Cl = grd.iGeomEdges.LogicalCellIndices;
int[,] E2Cg = grd.iGeomEdges.CellIndices;
// transform DG coördinates
// ========================
int Nin = _Basis.GetLength(E2Cl[e0, 0]);
int Not = Nin;
#if DEBUG
for (int e = 0; e < Len; e++)
{
int iEdge = e + e0;
int jCellIN = E2Cl[iEdge, 0];
int jCellOT = E2Cl[iEdge, 1];
Debug.Assert(_Basis.GetLength(jCellIN) == Nin);
if (jCellOT >= 0)
{
Debug.Assert(_Basis.GetLength(jCellOT) == Not);
}
}
#endif
int iBufIN, iBufOT = 0;
MultidimensionalArray trfCoördinatesIN = TempBuffer.GetTempMultidimensionalarray(out iBufIN, Len, Nin);
MultidimensionalArray trfCoördinatesOT = Not > 0 ? TempBuffer.GetTempMultidimensionalarray(out iBufOT, Len, Not) : null;
TransformCoördinatesEdge(e0, Len, grd, Coord, Nin, Not, _Basis.Degree, AffineLinear, trfCoördinatesIN, trfCoördinatesOT);
// Evaluate
// ========
unsafe
{
fixed(int *pTrfIndex = trfIdx)
{
MultidimensionalArray BasisValues = null;
Debug.Assert((valIN != null) == (valOT != null));
if (valIN != null)
{
// compute the values
// -------------------
BasisValues = grd.ChefBasis.EdgeEval.GetValues(NS, e0, Len, _Basis.Degree);
Debug.Assert(BasisValues.Dimension == 3);
MultidimensionalArray BasisValuesIN, BasisValuesOT;
if (BasisValues.GetLength(2) > Nin)
{
BasisValuesIN = BasisValues.ExtractSubArrayShallow(new int[] { 0, 0, 0 }, new int[] { BasisValues.GetLength(0) - 1, NoOfNodes - 1, Nin - 1 });
}
else
{
BasisValuesIN = BasisValues;
}
if (BasisValues.GetLength(2) > Not)
{
if (Nin == Not)
{
BasisValuesOT = BasisValuesIN;
}
else
{
BasisValuesOT = BasisValues.ExtractSubArrayShallow(new int[] { 0, 0, 0 }, new int[] { BasisValues.GetLength(0) - 1, NoOfNodes - 1, Nin - 1 });
}
}
else
{
BasisValuesOT = BasisValues;
}
{
valIN.Multiply(1.0, trfCoördinatesIN, BasisValuesIN, ResultPreScale, ref mp_ik_im_Tikm,
pTrfIndex, pTrfIndex,
trfPreOffset_A: 0, trfCycle_A: 0, trfPostOffset_A: 0, trfPreOffset_B: (2 * e0), trfCycle_B: 2, trfPostOffset_B: 0);
}
if (Not > 0)
{
valOT.Multiply(1.0, trfCoördinatesOT, BasisValuesOT, ResultPreScale, ref mp_ik_im_Tikm,
pTrfIndex, pTrfIndex,
trfPreOffset_A: 0, trfCycle_A: 0, trfPostOffset_A: 0, trfPreOffset_B: (2 * e0 + 1), trfCycle_B: 2, trfPostOffset_B: 0);
}
}
Debug.Assert((meanValIN != null) == (meanValOT != null));
if (meanValIN != null)
{
// compute the mean values
// -----------------------
var _Basis0Values = BasisValues;
if (_Basis0Values == null)
{
_Basis0Values = grd.ChefBasis.EdgeEval.GetValues(NS, e0, Len, 0);
}
// assume the 0-th basis polynomial \f$ \phi_0 \f$ is constant!
_Basis0Values = _Basis0Values.ExtractSubArrayShallow(new int[] { 0, 0, 0 }, new int[] { BasisValues.GetLength(0) - 1, -1, -1 });
// DG coördinates for the 0-th mode:
var _trfCoördinatesIN = trfCoördinatesIN.ExtractSubArrayShallow(new int[] { 0, 0 }, new int[] { Len - 1, -1 });
var _trfCoördinatesOT = trfCoördinatesOT.ExtractSubArrayShallow(new int[] { 0, 0 }, new int[] { Len - 1, -1 });
{
meanValIN.Multiply(1.0, _trfCoördinatesIN, _Basis0Values, ResultPreScale, ref mp_i_i_Ti,
pTrfIndex, pTrfIndex,
trfPreOffset_A: 0, trfCycle_A: 0, trfPostOffset_A: 0, trfPreOffset_B: (2 * e0), trfCycle_B: 2, trfPostOffset_B: 0);
}
if (Not > 0)
{
meanValOT.Multiply(1.0, _trfCoördinatesOT, _Basis0Values, ResultPreScale, ref mp_i_i_Ti,
pTrfIndex, pTrfIndex,
trfPreOffset_A: 0, trfCycle_A: 0, trfPostOffset_A: 0, trfPreOffset_B: (2 * e0 + 1), trfCycle_B: 2, trfPostOffset_B: 0);
}
}
Debug.Assert((gradIN != null) == (gradOT != null));
if (gradIN != null)
{
// compute gradient values
// -----------------------
int D = grd.SpatialDimension;
int iBuf2;
MultidimensionalArray GradientRef = TempBuffer.GetTempMultidimensionalarray(out iBuf2, Len, NoOfNodes, D);
MultidimensionalArray BasisGradValues = grd.ChefBasis.EdgeGradientEval.GetValues(NS, e0, Len, _Basis.Degree);
Debug.Assert(BasisGradValues.Dimension == 4);
MultidimensionalArray BasisGradValuesIN, BasisGradValuesOT;
if (BasisGradValues.GetLength(2) > Nin)
{
BasisGradValuesIN = BasisGradValues.ExtractSubArrayShallow(new int[] { 0, 0, 0, 0 }, new int[] { BasisGradValues.GetLength(0) - 1, NoOfNodes - 1, Nin - 1, D - 1 });
}
else
{
BasisGradValuesIN = BasisGradValues;
}
if (BasisGradValues.GetLength(2) > Not)
{
if (Nin == Not)
{
BasisGradValuesOT = BasisGradValuesIN;
}
else
{
BasisGradValuesOT = BasisGradValues.ExtractSubArrayShallow(new int[] { 0, 0, 0, 0 }, new int[] { BasisGradValues.GetLength(0) - 1, NoOfNodes - 1, Nin - 1, D - 1 });
}
}
else
{
BasisGradValuesOT = BasisGradValues;
}
if (AffineLinear)
{
// ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// affine-linear-cell:
// Inverse Jacobian different for each cell, but constant among nodes
// ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
var InvJacobi = grd.iGeomCells.InverseTransformation;
Debug.Assert(grd is Grid.Classic.GridData, "implementation only valid for classic grid");
Debug.Assert(object.ReferenceEquals(E2Cg, E2Cl));
fixed(int *pE2Cl = E2Cl)
{
{
GradientRef.Multiply(1.0, trfCoördinatesIN, BasisGradValuesIN, 0.0, ref mp_ike_im_Tikme,
pTrfIndex, pTrfIndex,
trfPreOffset_A: 0, trfCycle_A: 0, trfPostOffset_A: 0, trfPreOffset_B: (2 * e0), trfCycle_B: 2, trfPostOffset_B: 0); // gradient in reference coördinates
gradIN.Multiply(1.0, InvJacobi, GradientRef, ResultPreScale, ref mp_ikd_Tied_ike,
pE2Cl, pE2Cl,
trfPreOffset_A: (2 * e0), trfCycle_A: 2, trfPostOffset_A: 0, trfPreOffset_B: 0, trfCycle_B: 0, trfPostOffset_B: 0);
}
if (Not > 0)
{
GradientRef.Multiply(1.0, trfCoördinatesOT, BasisGradValuesOT, 0.0, ref mp_ike_im_Tikme,
pTrfIndex, pTrfIndex,
trfPreOffset_A: 0, trfCycle_A: 0, trfPostOffset_A: 0, trfPreOffset_B: (2 * e0 + 1), trfCycle_B: 2, trfPostOffset_B: 0); // gradient in reference coördinates
gradOT.Multiply(1.0, InvJacobi, GradientRef, ResultPreScale, ref mp_ikd_Tied_ike,
pE2Cl, pE2Cl,
trfPreOffset_A: (2 * e0 + 1), trfCycle_A: 2, trfPostOffset_A: 0, trfPreOffset_B: 0, trfCycle_B: 0, trfPostOffset_B: 0);
}
}
}
else
{
// ++++++++++++++++++++++++++++++++++++++++++++++++++++++
// curved-cell:
// Inverse Jacobian different for each node and each cell
// ++++++++++++++++++++++++++++++++++++++++++++++++++++++
MultidimensionalArray invJacobiIN, invJacobiOT;
var TiJ = grd.InverseJacobian.GetValue_EdgeDV(NS, e0, Len);
invJacobiIN = TiJ.Item1;
invJacobiOT = TiJ.Item2;
{
GradientRef.Multiply(1.0, trfCoördinatesIN, BasisGradValuesIN, 0.0, ref mp_ike_im_Tikme,
pTrfIndex, pTrfIndex,
trfPreOffset_A: 0, trfCycle_A: 0, trfPostOffset_A: 0, trfPreOffset_B: (2 * e0), trfCycle_B: 2, trfPostOffset_B: 0); // gradient in reference coördinates, i.e. \f$ \nabla_{\vec{xi}} \f$
gradIN.Multiply(1.0, invJacobiIN, GradientRef, ResultPreScale, ref mp_ikd_iked_ike); // gradient in physical coördinates, i.e. \f$ \nabla_{\vec{x}}n \f$
}
if (Not > 0)
{
GradientRef.Multiply(1.0, trfCoördinatesOT, BasisGradValuesOT, 0.0, ref mp_ike_im_Tikme,
pTrfIndex, pTrfIndex,
trfPreOffset_A: 0, trfCycle_A: 0, trfPostOffset_A: 0, trfPreOffset_B: (2 * e0 + 1), trfCycle_B: 2, trfPostOffset_B: 0); // gradient in reference coördinates, i.e. \f$ \nabla_{\vec{xi}} \f$
gradOT.Multiply(1.0, invJacobiOT, GradientRef, ResultPreScale, ref mp_ikd_iked_ike); // gradient in physical coördinates, i.e. \f$ \nabla_{\vec{x}} \f$
}
}
TempBuffer.FreeTempBuffer(iBuf2);
}
}
}
TempBuffer.FreeTempBuffer(iBufIN);
if (Not > 0)
{
TempBuffer.FreeTempBuffer(iBufOT);
}
/*
* {
* var _BasisValues = grd.ChefBasis.EdgeEval.GetValues(NS, e0, Len, _Basis.Degree);
*
*
* var resultINAccCheck = valIN.CloneAs();
* var resultOTAccCheck = valOT.CloneAs();
*
* for(int e = 0; e < Len; e++) {
* int iEdge = e + e0;
* int jCellIN = E2C[iEdge, 0];
* int jCellOT = E2C[iEdge, 1];
* int iTrfIN = trfIdx[iEdge, 0];
* int iTrfOT = trfIdx[iEdge, 1];
*
* for(int k = 0; k < NoOfNodes; k++) {
* int BN = _Basis.GetLength(jCellIN);
*
* resultINAccCheck[e, k] *= ResultPreScale;
* resultOTAccCheck[e, k] *= ResultPreScale;
*
* for(int n = 0; n < BN; n++) {
* double Cinerr = trfCoördinatesIN[e, n] - Coord[jCellIN, n];
* double Coterr = jCellOT >= 0 ? trfCoördinatesOT[e, n] - Coord[jCellOT, n] : 0.0;
*
* if(Math.Abs(Cinerr) > 1.0e-5)
* Console.WriteLine("44fuckIN" + e);
* if(Math.Abs(Coterr) > 1.0e-5)
* Console.WriteLine("44fuckOT" + e);
*
*
* resultINAccCheck[e, k] += Coord[jCellIN, n] * _BasisValues[iTrfIN, k, n];
* if(jCellOT >= 0)
* resultOTAccCheck[e, k] += Coord[jCellOT, n] * _BasisValues[iTrfOT, k, n];
*
* }
*
* double Vinerr = resultINAccCheck[e, k] - valIN[e, k];
* double Voterr = jCellOT >= 0 ? resultOTAccCheck[e, k] - valOT[e, k] : 0.0;
*
*
*
* if(Math.Abs(Vinerr) > 1.0e-5)
* Console.WriteLine("44fuckIN" + e);
* if(Math.Abs(Voterr) > 1.0e-5)
* Console.WriteLine("44fuckOT" + e);
* }
*
* }
*
* //resultINAcc.Set(resultINAccCheck);
* //resultOTAcc.Set(resultOTAccCheck);
* } */
}
/// <summary>
/// evaluation of DG field; may be used in derived classes to implement <see cref="DGField.Evaluate(int,int,NodeSet,MultidimensionalArray,int,double)"/>.
/// </summary>
protected static void EvaluateInternal(int j0, int L, NodeSet NS, Basis basis, MultidimensionalArray Coördinates, int coördOffset, MultidimensionalArray ResultAcc, double ResultPreScale)
{
int D, N, NumNodes;
bool AffineLinear;
CheckArgs(j0, L, NS, basis, Coördinates, ResultAcc, out D, out N, out NumNodes, out AffineLinear);
Debug.Assert(ResultAcc.Dimension == 2);
Debug.Assert(L == ResultAcc.GetLength(0));
Debug.Assert(NumNodes == ResultAcc.GetLength(1));
/*
* MultidimensionalArray BasisValues;
* BasisValues = basis.CellEval(NS, j0, L);
* Debug.Assert(BasisValues.GetLength(0) == L, "No. of. cells mismatch");
* Debug.Assert(BasisValues.GetLength(1) == M, "No. of. nodes mismatch");
* Debug.Assert(BasisValues.GetLength(2) == N, "No. of. basis elements mismatch");
*
* ResultAcc.Multiply(1.0, Coördinates, BasisValues, ResultPreScale, "jm", "jn", "jmn");
*/
//int[] geom2log = basis.GridDat.iGeomCells.GeomCell2LogicalCell;
MultidimensionalArray BasisValues = basis.Evaluate(NS);
if (L == 1 && AffineLinear)
{
// Special optimization for single-cell evaluation:
// this happens very often for edge quadrature, so it is quite relevant.
double scale0 = basis.GridDat.ChefBasis.Scaling[j0];
Debug.Assert(basis.GridDat.iGeomCells.GeomCell2LogicalCell == null || basis.GridDat.iGeomCells.GeomCell2LogicalCell[j0] == j0);
MultidimensionalArray Coördinates_j;
if (coördOffset == 0 && Coördinates.GetLength(0) == 1)
{
Coördinates_j = Coördinates;
}
else
{
Coördinates_j = Coördinates.ExtractSubArrayShallow(new int[] { coördOffset, 0 }, new int[] { coördOffset, N - 1 });
}
ResultAcc.Multiply(scale0, Coördinates_j, BasisValues, ResultPreScale, ref mp_jk_jm_km); //"jk", "jm", "km");
}
else
{
int iBuf;
MultidimensionalArray trfCoördinates = TempBuffer.GetTempMultidimensionalarray(out iBuf, L, N);
TransformCoördinates(j0, L, basis, Coördinates, coördOffset, N, AffineLinear, trfCoördinates);
if (ResultAcc.IsContinious && trfCoördinates.IsContinious && BasisValues.IsContinious)
{
unsafe
{
fixed(double *_pResultAcc = ResultAcc.Storage, _ptrfCoördinates = trfCoördinates.Storage, _pBasisValues = BasisValues.Storage)
{
double *pResultAcc = _pResultAcc + ResultAcc.Index(0, 0);
double *ptrfCoördinates = _ptrfCoördinates + trfCoördinates.Index(0, 0);
double *pBasisValues = _pBasisValues + BasisValues.Index(0, 0);
//#if DEBUG
// MultidimensionalArray check = ResultAcc.CloneAs();
//#endif
int _M = ResultAcc.GetLength(1); // entspricht k (node index)
int _N = ResultAcc.GetLength(0); // entspricht j (cell index)
int _K = BasisValues.GetLength(1); // entspricht m (DG mode index)
// NOTE: dimensions in FORTRAN order:
// pBasisValues : _K x _M
// ptrfCoördinates : _K x _N
// pResultAcc : _M x _N
//
// => FORTRAN GEMM
// pResultAcc = pBasisValues^T * ptrfCoördinates
int TRANSA = 'T';
int TRANSB = 'N';
BLAS.dgemm(TRANSA, TRANSB, _M, _N, _K,
1.0,
pBasisValues, _K,
ptrfCoördinates, _K,
ResultPreScale,
pResultAcc, _M);
//#if DEBUG
// check.Multiply(1.0, trfCoördinates, BasisValues, ResultPreScale, ref mp_jk_jm_km);
// check.Acc(-1.0, ResultAcc);
// double error = check.L2Norm();
// Console.WriteLine("GEMM error: " + error);
// Debug.Assert(error < 1.0);
//#endif
}
}
}
else
{
ResultAcc.Multiply(1.0, trfCoördinates, BasisValues, ResultPreScale, ref mp_jk_jm_km); //"jk", "jm", "km");
}
TempBuffer.FreeTempBuffer(iBuf);
}
}
/// <summary>
/// evaluation of DG field gradient; may be used in derived classes to implement <see cref="EvaluateGradient"/>.
/// </summary>
protected static void EvaluateGradientInternal(int j0, int L, NodeSet NS, Basis basis, MultidimensionalArray Coördinates, int coördOffset, MultidimensionalArray ResultAcc, double ResultPreScale)
{
int D, N, K;
bool AffineLinear;
CheckArgs(j0, L, NS, basis, Coördinates, ResultAcc, out D, out N, out K, out AffineLinear);
Debug.Assert(ResultAcc.Dimension == 3);
Debug.Assert(L == ResultAcc.GetLength(0));
Debug.Assert(K == ResultAcc.GetLength(1));
Debug.Assert(D == ResultAcc.GetLength(2));
/*
* MultidimensionalArray BasisGradValues;
* BasisGradValues = basis.CellEvalGradient(NS, j0, L);
*
* ResultAcc.Multiply(1.0, Coördinates, BasisGradValues, ResultPreScale, "jmd", "jn", "jmnd");
*/
MultidimensionalArray BasisGradValues = basis.EvaluateGradient(NS);
int iBuf1, iBuf2;
if (AffineLinear)
{
// ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// affine-linear-cell:
// Inverse Jacobian different for each cell, but constant among nodes
// ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
if (L == 1)
{
// Special optimization for single-cell evaluation:
// this happens very often for edge quadrature, so it is quite relevant.
double scale0 = basis.GridDat.ChefBasis.Scaling[j0];
MultidimensionalArray GradientRef = TempBuffer.GetTempMultidimensionalarray(out iBuf2, L, K, D);
MultidimensionalArray InvJacobi = basis.GridDat.iGeomCells.InverseTransformation.ExtractSubArrayShallow(j0, -1, -1);
Debug.Assert(basis.GridDat.iGeomCells.GeomCell2LogicalCell == null || basis.GridDat.iGeomCells.GeomCell2LogicalCell[j0] == j0);
MultidimensionalArray Coördinates_j;
if (coördOffset == 0 && Coördinates.GetLength(0) == 1)
{
Coördinates_j = Coördinates;
}
else
{
Coördinates_j = Coördinates.ExtractSubArrayShallow(new int[] { coördOffset, 0 }, new int[] { coördOffset, N - 1 });
}
GradientRef.Multiply(scale0, Coördinates_j, BasisGradValues, 0.0, ref mp_jke_jm_kme); // gradient in reference coördinates
ResultAcc.Multiply(1.0, InvJacobi, GradientRef, ResultPreScale, ref mp_jkd_ed_jke);
TempBuffer.FreeTempBuffer(iBuf2);
}
else
{
MultidimensionalArray trfCoördinates = TempBuffer.GetTempMultidimensionalarray(out iBuf1, L, N);
MultidimensionalArray GradientRef = TempBuffer.GetTempMultidimensionalarray(out iBuf2, L, K, D);
MultidimensionalArray InvJacobi = basis.GridDat.iGeomCells.InverseTransformation.ExtractSubArrayShallow(new int[] { j0, 0, 0 }, new int[] { j0 + L - 1, D - 1, D - 1 });
TransformCoördinates(j0, L, basis, Coördinates, coördOffset, N, AffineLinear, trfCoördinates);
GradientRef.Multiply(1.0, trfCoördinates, BasisGradValues, 0.0, ref mp_jke_jm_kme); // gradient in reference coördinates
ResultAcc.Multiply(1.0, InvJacobi, GradientRef, ResultPreScale, ref mp_jkd_jed_jke);
TempBuffer.FreeTempBuffer(iBuf1);
TempBuffer.FreeTempBuffer(iBuf2);
}
}
else
{
// ++++++++++++++++++++++++++++++++++++++++++++++++++++++
// curved-cell:
// Inverse Jacobian different for each node and each cell
// ++++++++++++++++++++++++++++++++++++++++++++++++++++++
MultidimensionalArray trfCoördinates = TempBuffer.GetTempMultidimensionalarray(out iBuf1, L, N);
MultidimensionalArray GradientRef = TempBuffer.GetTempMultidimensionalarray(out iBuf2, L, K, D);
MultidimensionalArray InvJacobi = basis.GridDat.InverseJacobian.GetValue_Cell(NS, j0, L);
TransformCoördinates(j0, L, basis, Coördinates, coördOffset, N, AffineLinear, trfCoördinates);
GradientRef.Multiply(1.0, trfCoördinates, BasisGradValues, 0.0, ref mp_jke_jm_kme); // gradient in reference coördinates
ResultAcc.Multiply(1.0, InvJacobi, GradientRef, ResultPreScale, ref mp_jkd_jked_jke);
TempBuffer.FreeTempBuffer(iBuf1);
TempBuffer.FreeTempBuffer(iBuf2);
}
}
private static void TransformCoördinates(int j0, int L,
Basis basis,
MultidimensionalArray Coördinates, int coördOffset,
int N, bool AffineLinear,
MultidimensionalArray trfCoördinates)
{
int[] geom2log = basis.GridDat.iGeomCells.GeomCell2LogicalCell;
if (geom2log != null)
{
// +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// aggregation grid branch -- apply index trafo to coordinates
// (j0..j0+L) are geometical grid indices
// +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// extract trafo
MultidimensionalArray trafo = basis.GridDat.ChefBasis.OrthonormalizationTrafo.GetValue_Cell(j0, L, basis.Degree);
Debug.Assert(trafo.GetLength(0) == L);
if (trafo.GetLength(1) > N)
{
trafo = trafo.ExtractSubArrayShallow(new int[] { 0, 0, 0 }, new int[] { L - 1, N - 1, N - 1 });
}
// apply trafo
unsafe
{
fixed(int *p_geom2log = geom2log)
{
trfCoördinates.Multiply(1.0, trafo, Coördinates, 0.0, ref mp_jm_jmn_Tjn,
p_geom2log, p_geom2log,
trfPreOffset_A: 0, trfCycle_A: 0, trfPostOffset_A: 0,
trfPreOffset_B: coördOffset, trfCycle_B: 1, trfPostOffset_B: 0); // geom cell to logical cell trafo for coördinates
}
}
}
else if (AffineLinear)
{
// +++++++++++++++++++++++++
// affine-linear grid branch
// +++++++++++++++++++++++++
// extract coördinates
MultidimensionalArray _Coördinates;
if (coördOffset > 0 || coördOffset + L < Coördinates.GetLength(0))
{
_Coördinates = Coördinates.ExtractSubArrayShallow(new[] { coördOffset, 0 }, new[] { coördOffset + L - 1, N - 1 });
}
else
{
_Coördinates = Coördinates;
}
// extract trafo
MultidimensionalArray scale = basis.GridDat.ChefBasis.Scaling.ExtractSubArrayShallow(new int[] { j0 }, new int[] { j0 + L - 1 });
// apply trafo
trfCoördinates.Multiply(1.0, scale, _Coördinates, 0.0, ref mp_jn_j_jn);
}
else
{
// ++++++++++++++++++
// curved cell branch
// ++++++++++++++++++
// extract coördinates
MultidimensionalArray _Coördinates;
if (coördOffset > 0 || coördOffset + L < Coördinates.GetLength(0))
{
_Coördinates = Coördinates.ExtractSubArrayShallow(new[] { coördOffset, 0 }, new[] { coördOffset + L - 1, N - 1 });
}
else
{
_Coördinates = Coördinates;
}
// extract trafo
MultidimensionalArray trafo = basis.GridDat.ChefBasis.OrthonormalizationTrafo.GetValue_Cell(j0, L, basis.Degree);
Debug.Assert(trafo.GetLength(0) == L);
if (trafo.GetLength(1) > N)
{
trafo = trafo.ExtractSubArrayShallow(new int[] { 0, 0, 0 }, new int[] { L - 1, N - 1, N - 1 });
}
// apply trafo
trfCoördinates.Multiply(1.0, trafo, _Coördinates, 0.0, ref mp_jm_jmn_jn);
}
}
/// <summary>
///
/// </summary>
/// <param name="ctx"></param>
/// <param name="D"></param>
/// <param name="b"></param>
public Tensor2Field(Context ctx, int D, Basis b)
: this(ctx, D, b, "")
{
}
/// <summary>
///
/// </summary>
/// <param name="ctx"></param>
/// <param name="D"></param>
/// <param name="b"></param>
/// <param name="id"></param>
public Tensor2Field(Context ctx, int D, Basis b, string id)
{
throw new NotImplementedException();
}
/// <summary>
/// constructs a new field with an empty identification string
/// (see <see cref="DGField.Identification"/>); Because of this, this
/// field can't be used for IO;
/// </summary>
public SinglePhaseField(Basis __Basis) :
this(__Basis, null)
{
}
/// <summary>
/// an implementation of <see cref="FieldFactory{T}"/> that creates
/// <see cref="SinglePhaseField"/>-DG-fields.
/// </summary>
/// <param name="__Basis">The basis that is used for this field</param>
/// <param name="__Identification">
/// identification string for this field; This can be null or empty,
/// however, if IO should be performed for this object, the
/// identification must be unique within the given context.
/// </param>
/// <returns>a <see cref="SinglePhaseField"/>-instance</returns>
public static SinglePhaseField Factory(Basis __Basis, String __Identification)
{
return(new SinglePhaseField(__Basis, __Identification));
}
/// <summary>
/// ctor
/// </summary>
/// <param name="D">
/// number of components, i.d. dimension (see <see cref="Dim"/>)
/// </param>
/// <param name="b"></param>
/// <param name="fac">
/// factory for the instantiation of <see cref="DGField"/>-objects; By
/// the factory model, it becomes possible to use this container for
/// different subclasses of <see cref="DGField"/>.
/// </param>
public VectorField(int D, Basis b, Func <Basis, string, T> fac)
: this(D, b, "", fac)
{
}
