/// <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);
}
}
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>
///
/// </summary>
/// <param name="CellPairs">
/// 1st index: list of cells <br/>
/// 2nd index: in {0, 1}
/// </param>
/// <param name="M">
/// 1st index: corresponds with 1st index of <paramref name="CellPairs"/><br/>
/// 2nd index: matrix row index <br/>
/// 3rd index: matrix column index
/// </param>
/// <param name="Minv">the inverse of <paramref name="M"/></param>
/// <remarks>
/// Let \f$ K_j \f$ and \f$ K_i \f$ be two different cells with a linear-affine
/// transformation to the reference element.
/// Here, \f$ j \f$=<paramref name="CellPairs"/>[a,0] and \f$ i \f$=<paramref name="CellPairs"/>[a,1].
/// The DG-basis in these cells can uniquely be represented as
/// \f[
/// \phi_{j n} (\vec{x}) = p_n (\vec{x}) \vec{1}_{K_j} (\vec{x})
/// \textrm{ and }
/// \phi_{i m} (\vec{x}) = q_m (\vec{x}) \vec{1}_{K_i} (\vec{x})
/// \f]
/// where \f$ \vec{1}_X \f$ denotes the characteristic function for set \f$ X \f$
/// and \f$ p_n\f$ and \f$ p_m\f$ are polynomials.
/// Then, for the output \f$ M \f$ =<paramref name="M"/>[a,-,-] fulfills
/// \f[
/// \phi_{j n} + \sum_{m} M_{m n} \phi_{i m}
/// =
/// p_n \vec{1}_{K_j \cup K_i}
/// \f]
/// </remarks>
public void GetExtrapolationMatrices(int[,] CellPairs, MultidimensionalArray M, MultidimensionalArray Minv = null)
{
var m_Context = this.GridDat;
int N = this.Length;
int Esub = CellPairs.GetLength(0);
int JE = this.GridDat.iLogicalCells.Count;
int J = this.GridDat.iLogicalCells.NoOfLocalUpdatedCells;
if (CellPairs.GetLength(1) != 2)
{
throw new ArgumentOutOfRangeException("second dimension is expected to be 2!");
}
if (M.Dimension != 3)
{
throw new ArgumentException();
}
if (M.GetLength(0) != Esub)
{
throw new ArgumentException();
}
if (M.GetLength(1) != N || M.GetLength(2) != N)
{
throw new ArgumentException();
}
if (Minv != null)
{
if (Minv.GetLength(0) != Esub)
{
throw new ArgumentException();
}
if (Minv.GetLength(1) != N || Minv.GetLength(2) != N)
{
throw new ArgumentException();
}
}
MultidimensionalArray NodesGlobal = new MultidimensionalArray(3);
MultidimensionalArray Minv_tmp = MultidimensionalArray.Create(N, N);
MultidimensionalArray M_tmp = MultidimensionalArray.Create(N, N);
for (int esub = 0; esub < Esub; esub++) // loop over the cell pairs...
{
int jCell0 = CellPairs[esub, 0];
int jCell1 = CellPairs[esub, 1];
if (jCell0 < 0 || jCell0 >= JE)
{
throw new ArgumentOutOfRangeException("Cell index out of range.");
}
if (jCell1 < 0 || jCell1 >= JE)
{
throw new ArgumentOutOfRangeException("Cell index out of range.");
}
bool swap;
if (jCell0 >= J)
{
//if(true) {
swap = true;
int a = jCell0;
jCell0 = jCell1;
jCell1 = a;
}
else
{
swap = false;
}
if (!m_Context.iGeomCells.IsCellAffineLinear(jCell0))
{
throw new NotSupportedException("Currently not supported for curved cells.");
}
if (!m_Context.iGeomCells.IsCellAffineLinear(jCell1))
{
throw new NotSupportedException("Currently not supported for curved cells.");
}
Debug.Assert(jCell0 < J);
var cellMask = new CellMask(m_Context, new[] { new Chunk()
{
i0 = jCell0, Len = 1
} }, MaskType.Geometrical);
// we project the basis function from 'jCell1' onto 'jCell0'
CellQuadrature.GetQuadrature(new int[2] {
N, N
}, m_Context,
(new CellQuadratureScheme(true, cellMask)).Compile(m_Context, this.Degree * 2), // integrate over target cell
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray _EvalResult) {
NodeSet nodes_Cell0 = QR.Nodes;
Debug.Assert(Length == 1);
NodesGlobal.Allocate(1, nodes_Cell0.GetLength(0), nodes_Cell0.GetLength(1));
m_Context.TransformLocal2Global(nodes_Cell0, jCell0, 1, NodesGlobal, 0);
var nodes_Cell1 = new NodeSet(GridDat.iGeomCells.GetRefElement(jCell1), nodes_Cell0.GetLength(0), nodes_Cell0.GetLength(1));
m_Context.TransformGlobal2Local(NodesGlobal.ExtractSubArrayShallow(0, -1, -1), nodes_Cell1, jCell1, null);
nodes_Cell1.LockForever();
var phi_0 = this.CellEval(nodes_Cell0, jCell0, 1).ExtractSubArrayShallow(0, -1, -1);
var phi_1 = this.CellEval(nodes_Cell1, jCell1, 1).ExtractSubArrayShallow(0, -1, -1);
var EvalResult = _EvalResult.ExtractSubArrayShallow(0, -1, -1, -1);
EvalResult.Multiply(1.0, phi_1, phi_0, 0.0, "kmn", "kn", "km");
},
/*_SaveIntegrationResults:*/ delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
Debug.Assert(Length == 1);
var res = ResultsOfIntegration.ExtractSubArrayShallow(0, -1, -1);
Minv_tmp.Clear();
Minv_tmp.Acc(1.0, res);
}).Execute();
// compute the inverse
Minv_tmp.InvertTo(M_tmp);
// store
if (!swap)
{
M.ExtractSubArrayShallow(esub, -1, -1).AccMatrix(1.0, M_tmp);
if (Minv != null)
{
Minv.ExtractSubArrayShallow(esub, -1, -1).AccMatrix(1.0, Minv_tmp);
}
}
else
{
M.ExtractSubArrayShallow(esub, -1, -1).AccMatrix(1.0, Minv_tmp);
if (Minv != null)
{
Minv.ExtractSubArrayShallow(esub, -1, -1).AccMatrix(1.0, M_tmp);
}
}
}
}
/// <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);
}
}
/// <summary>
/// Integrand evaluation.
/// </summary>
protected override void Evaluate(int i0, int Length, QuadRule rule, MultidimensionalArray EvalResult)
{
NodeSet NodesUntransformed = rule.Nodes;
int M = NodesUntransformed.GetLength(0);
int D = NodesUntransformed.GetLength(1);
// evaluate scalar function ans store result in 'EvalResult'
// =========================================================
Debug.Assert(!((m_func != null) && (m_funcEx != null)));
if (m_func != null || m_Map != null)
{
GridDat.TransformLocal2Global(NodesUntransformed, i0, Length, m_NodesTransformed, 0);
}
if (m_func != null)
{
MultidimensionalArray inp = m_NodesTransformed.ResizeShallow(new int[] { Length *M, D });
MultidimensionalArray outp = EvalResult.ResizeShallow(new int[] { Length *M });
m_func(inp, outp);
Debug.Assert(m_funcEx == null);
}
if (m_funcEx != null)
{
m_funcEx(i0, Length, NodesUntransformed, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
Debug.Assert(m_func == null);
}
if (m_Map == null)
{
// L2 error branch
// +++++++++++++++
MultidimensionalArray fieldvals = EvalResult.ResizeShallow(new int[] { Length, NodesUntransformed.GetLength(0) });
m_Owner.Evaluate(i0, Length, NodesUntransformed, fieldvals, -1.0);
for (int j = 0; j < Length; j++)
{
for (int m = 0; m < M; m++)
{
double e;
e = EvalResult[j, m, 0];
EvalResult[j, m, 0] = e * e;
}
}
}
else
{
// arbitrary mapping branch
// ++++++++++++++++++++++++
MultidimensionalArray fieldvals = MultidimensionalArray.Create(new int[] { Length, NodesUntransformed.GetLength(0) });
m_Owner.Evaluate(i0, Length, NodesUntransformed, fieldvals, -1.0);
double[] X = new double[D];
for (int j = 0; j < Length; j++)
{
for (int m = 0; m < M; m++)
{
double e;
e = EvalResult[j, m, 0];
for (int d = 0; d < D; d++)
{
X[d] = m_NodesTransformed[j, m, d];
}
EvalResult[j, m, 0] = this.m_Map(X, fieldvals[j, m], e);
}
}
}
}
/// <summary>
/// Returns the minimum and the maximum value of <paramref name="mod"/>(this DG field), for each cell;
/// </summary>
/// <param name="max">
/// Vector, with the same number of entries as the cell mask <paramref name="cm"/>;
/// On exit, the approximate local maximum within the cell.
/// </param>
/// <param name="min">
/// Vector, with the same number of entries as the cell mask <paramref name="cm"/>;
/// On exit, the approximate local minimum within the cell.
/// </param>
/// <param name="cm">
/// optional domain restriction
/// </param>
/// <param name="mod">
/// optimal modifier, which e.g. may select the absolute value; if null, the identity function;
/// </param>
public void GetCellwiseExtremalValues <T1, T2>(T1 min, T2 max, CellMask cm = null, Func <double, double> mod = null)
where T1 : IList <double>
where T2 : IList <double> //
{
using (new FuncTrace()) {
int J = Basis.GridDat.iLogicalCells.NoOfLocalUpdatedCells;
int Jcm = cm == null ? J : cm.NoOfItemsLocally;
if (min.Count != Jcm)
{
throw new ArgumentException("wrong length of output vector", "min");
}
if (max.Count != Jcm)
{
throw new ArgumentException("wrong length of output vector", "max");
}
min.SetAll(double.MaxValue);
max.SetAll(double.MinValue);
if (mod == null)
{
mod = (x => x);
}
//int N = m_context.Grid.GridSimplex.NoOfVertices + 1;
// find maximum on this processor
// ------------------------------
// create node set
if (m_ExtremalProbeNS == null)
{
// nodes for the evaluation of the velocity vector
// (all vertices an 0)
int D = Basis.GridDat.SpatialDimension;
var KrefS = Basis.GridDat.iGeomCells.RefElements;
m_ExtremalProbeNS = new NodeSet[KrefS.Length];
for (int i = 0; i < KrefS.Length; i++)
{
m_ExtremalProbeNS[i] = new NodeSet(KrefS[i], KrefS[i].Vertices);
}
}
// vectorisation of this method
int VectorSize = -1;
int N0 = m_ExtremalProbeNS[0].NoOfNodes; // number of nodes
MultidimensionalArray fieldValues = new MultidimensionalArray(2);
IEnumerable <Chunk> all_chunks;
if (cm == null)
{
var _ch = new Chunk[1];
_ch[0].i0 = 0;
_ch[0].Len = J;
all_chunks = _ch;
}
else
{
all_chunks = cm;
}
int jSub = 0;
foreach (Chunk chk in all_chunks)
{
VectorSize = this.GridDat.iGeomCells.GetNoOfSimilarConsecutiveCells(CellInfo.RefElementIndex_Mask, chk.i0, Math.Min(100, chk.Len)); // try to be a little vectorized;
int _J = chk.Len + chk.i0;
for (int j0 = chk.i0; j0 < _J; j0 += VectorSize)
{
if (j0 + VectorSize > _J)
{
VectorSize = _J - j0;
}
int iKref = Basis.GridDat.iGeomCells.GetRefElementIndex(j0);
int N = m_ExtremalProbeNS[iKref].NoOfNodes;
if (fieldValues.GetLength(0) != VectorSize || fieldValues.GetLength(1) != N)
{
fieldValues = MultidimensionalArray.Create(VectorSize, N);
}
this.Evaluate(j0, VectorSize, m_ExtremalProbeNS[iKref], fieldValues, 0.0);
// loop over cells ...
for (int jCell = j0; jCell < j0 + VectorSize; jCell++)
{
// loop over nodes ...
for (int n = 0; n < N; n++)
{
double vel = 0;
vel = mod(fieldValues[jCell - j0, n]);
min[jSub] = Math.Min(min[jSub], vel);
max[jSub] = Math.Max(max[jSub], vel);
}
jSub++;
}
}
}
}
}
/// <summary>
/// Evaluates all 2nd derivatives (by cell-local analytic derivation of
/// the basis polynomials) of this field;
/// </summary>
/// <param name="j0"></param>
/// <param name="Len"></param>
/// <param name="NS"></param>
/// <param name="result">
/// <list type="bullet">
/// <item>1st index: cell index <em>j</em></item>
/// <item>2nd index: node index <em>m</em> into nodeset #<paramref name="NodeSetIndex"/></item>
/// <item>3rd index: spatial direction of 1st derivation, <em>k</em></item>
/// <item>4th index: spatial direction of 2nd derivation, <em>l</em></item>
/// </list>
/// So, the entry [j,m,k,l] = \f$ \frac{\partial}{\partial x_k} \frac{\partial}{\partial x_l} \varphi (\vec{\xi}_m)\f$
/// where \f$ \vec{xi}_m\f$ is the <em>m</em>-th
/// vector in the node set #<paramref name="NodeSetIndex"/>, in the
/// <em>j</em>-th cell.
/// </param>
/// <remarks>
/// Because of 2 derivatives taken, this field needs to be at least of
/// DG degree 2 to get a non-zero result from this method.
/// </remarks>
public void EvaluateHessian(int j0, int Len, NodeSet NS, MultidimensionalArray result)
{
int D = this.GridDat.SpatialDimension; // spatial dimension
int N = m_Basis.GetLength(j0); // number of coordinates per cell
if (result.Dimension != 4)
{
throw new ArgumentException("dimension must be 4", "result");
}
if (Len > result.GetLength(0))
{
throw new ArgumentOutOfRangeException("mismatch between Len and 0-th length of result");
}
if (result.GetLength(2) != D || result.GetLength(3) != D)
{
throw new ArgumentOutOfRangeException("3rd and 4th length of result must be " + D + "x" + D + ";");
}
// not very optimized....
MultidimensionalArray BasisHessian = this.Basis.CellEval2ndDeriv(NS, j0, Len);
result.Multiply(1.0, this.m_Mda_Coordinates.ExtractSubArrayShallow(new int[] { j0, 0 }, new int[] { j0 + Len - 1, N - 1 }), BasisHessian, 0.0, "jkde", "jn", "jknde");
/*
* var scales = this.GridDat.ChefBasis.Scaling;
* var Tinv = this.GridDat.Cells.InverseTransformation;
*
* MultidimensionalArray gbv = Basis.Evaluate2ndDeriv(NS);
* int M = gbv.GetLength(0); // number of nodes per cell
* if (result.GetLength(1) != M)
* throw new ArgumentException("length of dimension 1 must be " + M, "result");
*
* var Coordinates = (MultidimensionalArray)this.Coordinates;
*
* double[,] acc = new double[D, D];
* double[,] Tinv_j = new double[D, D];
*
* // loop over cells...
* for (int j = 0; j < Len; j++) {
* double sc = scales[j0 + j];
*
* if (this.GridDat.Cells.IsCellAffineLinear(j0 + j)) {
*
* // load transformation matrix for easier access
* for (int d1 = 0; d1 < D; d1++)
* for (int d2 = 0; d2 < D; d2++)
* Tinv_j[d1, d2] = Tinv[j + j0, d1, d2];
*
* // loop over nodes ...
* for (int m = 0; m < M; m++) {
*
* Array.Clear(acc, 0, D * D);
*
* // sum up...
* for (int n = 0; n < N; n++) { // loop over basis functions
*
* double coord = Coordinates[j + j0, n];
* for (int d1 = 0; d1 < D; d1++) { // 1st loop over spatial dimension
* for (int d2 = 0; d2 < D; d2++) { // 1st loop over spatial dimension
* acc[d1, d2] += gbv[m, n, d1, d2] * coord;
* }
* }
* }
*
* // transform...
* for (int d1 = 0; d1 < D; d1++) {
* for (int d2 = 0; d2 < D; d2++) {
* double r = 0.0;
* for (int k1 = 0; k1 < D; k1++) {
* double rr = 0;
* for (int k2 = 0; k2 < D; k2++) {
* rr += acc[k1, k2] * Tinv_j[k2, d1];
* }
* r += rr * Tinv_j[k1, d2];
* }
* result[j, m, d1, d2] = r * sc;
* }
* }
* }
* } else {
* throw new NotImplementedException("nonlinear cell: todo");
* }
*/
/*
*
* //Test code;
*
* var HessBasis = this.Basis.CellEval2ndDeriv(NodeSetIndex, j0, Len);
* var CheckResult = result.CloneAs();
*
*
* for (int j = 0; j < Len; j++) {
*
* // loop over nodes ...
* for (int m = 0; m < M; m++) {
*
* for (int d1 = 0; d1 < D; d1++) {
* for (int d2 = 0; d2 < D; d2++) {
* double accu = 0;
*
* for (int n = 0; n < N; n++) {
* accu += HessBasis[j, m, n, d1, d2]*Coordinates[j + j0, n];
* }
*
* CheckResult[j, m, d1, d2] = accu;
* }
* }
*
* }
* }
*
* CheckResult.Acc(-1.0, result);
* if (CheckResult.L2Norm() > 1.0e-8)
* throw new Exception();
*/
}
/// <summary>
/// Evaluates the field along edges.
/// </summary>
/// <param name="ResultIndexOffset">
/// An offset for the first index of <paramref name="ValueIN"/> resp. <paramref name="ValueOT"/>,
/// i.e. the first result will be written to
/// <paramref name="ValueIN"/>[<paramref name="ResultIndexOffset"/>,*].
/// </param>
/// <param name="e0">Index of the first edge to evaluate.</param>
/// <param name="Len">Number of edges to evaluate</param>
/// <param name="NS">
/// nodes to evaluate at
/// </param>
/// <param name="ValueIN">
/// If not null, contains the following output:
/// On exit, the value of the DG field at the given nodes are
/// <em>accumulated</em> (!) there. Before the values are added,
/// the original content is scaled by <paramref name="ResultPreScale"/>.<br/>
/// The array is 2-dimensional:
/// <list type="bullet">
/// <item>
/// 1st index: edge index <i>j</i> - <paramref name="e0"/>;
/// </item>
/// <item>
/// 2nd index: node index <i>k</i>, corresponds with 1st index of
/// the node set <paramref name="NS"/>;
/// </item>
/// </list>
/// </param>
/// <param name="ValueOUT">
/// Same as <paramref name="ValueIN"/>.
/// </param>
/// <param name="MeanValueIN">
/// If not null, contains the following output:
/// On exit, the mean values of the DG field at the given edges are
/// <em>accumulated</em> (!) there. Before the values are added,
/// the original content is scaled by <paramref name="ResultPreScale"/>.<br/>
/// The array is 2-dimensional:
/// <list type="bullet">
/// <item>
/// 1st index: edge index <i>j</i> - <paramref name="e0"/>;
/// </item>
/// <item>
/// 2nd index: node index <i>k</i>, corresponds with 1st index of
/// the node set <paramref name="NS"/>;
/// </item>
/// </list>
/// </param>
/// <param name="MeanValueOT">
/// Same as <paramref name="MeanValueIN"/>.
/// </param>
/// <param name="GradientIN">
/// If not null, contains the following output:
/// On exit, the value of the gradient of DG field at the given nodes
/// are <em>accumulated</em> (!) there. Before the values are added,
/// the original content is scaled by <paramref name="ResultPreScale"/>.<br/>
/// The array is 3-dimensional:
/// <list type="bullet">
/// <item>
/// 1st index: edge index <i>j</i> - <paramref name="e0"/>;
/// </item>
/// <item>
/// 2nd index: node index <i>k</i>, corresponds with 1st index of
/// the node set <paramref name="NS"/>;
/// </item>
/// <item>
/// 2rd index: spatial dimension;
/// </item>
/// </list>
/// </param>
/// <param name="GradientOT">
/// Same as <paramref name="GradientIN"/>.
/// </param>
/// <param name="ResultPreScale">
/// Scaling that is applied to <paramref name="ValueIN"/> and <paramref name="ValueOUT"/> before
/// the field evaluation is added
/// </param>
public override void EvaluateEdge(int e0, int Len, NodeSet NS,
MultidimensionalArray ValueIN, MultidimensionalArray ValueOT,
MultidimensionalArray MeanValueIN = null, MultidimensionalArray MeanValueOT = null,
MultidimensionalArray GradientIN = null, MultidimensionalArray GradientOT = null,
int ResultIndexOffset = 0, double ResultPreScale = 0.0) //
{
int D = GridDat.SpatialDimension; // spatial dimension
int N = m_Basis.Length; // number of coordinates per cell
int K = NS.NoOfNodes; // number of nodes
if ((ValueIN != null) != (ValueOT != null))
{
throw new ArgumentException();
}
if ((MeanValueIN != null) != (MeanValueOT != null))
{
throw new ArgumentException();
}
if ((GradientIN != null) != (GradientOT != null))
{
throw new ArgumentException();
}
if (ValueIN != null)
{
if (ValueIN.Dimension != 2)
{
throw new ArgumentException("result", "dimension of result array must be 2");
}
if (Len > ValueIN.GetLength(0) + ResultIndexOffset)
{
throw new ArgumentException("mismatch between Len and 0-th length of result");
}
if (ValueIN.GetLength(1) != K)
{
throw new ArgumentException();
}
if (ValueOT.Dimension != 2)
{
throw new ArgumentException("result", "dimension of result array must be 2");
}
if (Len > ValueOT.GetLength(0) + ResultIndexOffset)
{
throw new ArgumentException("mismatch between Len and 0-th length of result");
}
if (ValueOT.GetLength(1) != K)
{
throw new ArgumentException();
}
if (!(ResultIndexOffset == 0 && Len == ValueIN.GetLength(0)))
{
ValueIN = ValueIN.ExtractSubArrayShallow(new int[] { ResultIndexOffset, 0 }, new int[] { ResultIndexOffset + Len - 1, K - 1 });
}
if (!(ResultIndexOffset == 0 && Len == ValueOT.GetLength(0)))
{
ValueOT = ValueOT.ExtractSubArrayShallow(new int[] { ResultIndexOffset, 0 }, new int[] { ResultIndexOffset + Len - 1, K - 1 });
}
}
if (MeanValueIN != null)
{
if (MeanValueIN.Dimension != 1)
{
throw new ArgumentException("Dimension of mean-value result array must be 1.");
}
if (Len > MeanValueIN.GetLength(0) + ResultIndexOffset)
{
throw new ArgumentException("mismatch between Len and 0-th length of result");
}
if (MeanValueOT.Dimension != 1)
{
throw new ArgumentException("Dimension of mean-value result array must be 1.");
}
if (Len > MeanValueOT.GetLength(0) + ResultIndexOffset)
{
throw new ArgumentException("mismatch between Len and 0-th length of result");
}
if (!(ResultIndexOffset == 0 && Len == MeanValueIN.GetLength(0)))
{
MeanValueIN = MeanValueIN.ExtractSubArrayShallow(new int[] { ResultIndexOffset }, new int[] { ResultIndexOffset + Len - 1 });
}
if (!(ResultIndexOffset == 0 && Len == MeanValueOT.GetLength(0)))
{
MeanValueOT = MeanValueOT.ExtractSubArrayShallow(new int[] { ResultIndexOffset }, new int[] { ResultIndexOffset + Len - 1 });
}
}
if (GradientIN != null)
{
if (GradientIN.Dimension != 3)
{
throw new ArgumentException("Dimension of gradient result array must be 3.");
}
if (Len > GradientIN.GetLength(0) + ResultIndexOffset)
{
throw new ArgumentException("mismatch between Len and 0-th length of result");
}
if (GradientIN.GetLength(1) != K)
{
throw new ArgumentException();
}
if (GradientIN.GetLength(2) != D)
{
throw new ArgumentException();
}
if (GradientOT.Dimension != 3)
{
throw new ArgumentException("Dimension of gradient result array must be 3.");
}
if (Len > GradientOT.GetLength(0) + ResultIndexOffset)
{
throw new ArgumentException("mismatch between Len and 0-th length of result");
}
if (GradientOT.GetLength(1) != K)
{
throw new ArgumentException();
}
if (GradientOT.GetLength(2) != D)
{
throw new ArgumentException();
}
if (!(ResultIndexOffset == 0 && Len == GradientIN.GetLength(0)))
{
GradientIN = GradientIN.ExtractSubArrayShallow(new int[] { ResultIndexOffset, 0, 0 }, new int[] { ResultIndexOffset + Len - 1, K - 1, D - 1 });
}
if (!(ResultIndexOffset == 0 && Len == GradientOT.GetLength(0)))
{
GradientOT = GradientOT.ExtractSubArrayShallow(new int[] { ResultIndexOffset, 0, 0 }, new int[] { ResultIndexOffset + Len - 1, K - 1, D - 1 });
}
}
var coöSys = NS.GetNodeCoordinateSystem(this.GridDat);
if (coöSys != NodeCoordinateSystem.EdgeCoord)
{
throw new ArgumentOutOfRangeException();
}
DGField.EvaluateEdgeInternal(e0, Len, NS, this.m_Basis, this.m_Mda_Coordinates,
ValueIN, ValueOT,
MeanValueIN, MeanValueOT,
GradientIN, GradientOT,
ResultPreScale);
}
/// <summary>
/// Evaluates the gradient of all polynomials in this basis (see <see cref="Polynomials"/>) at specified edges.
/// </summary>
/// <param name="NS"></param>
/// <param name="j0">index of first edge to evaluate</param>
/// <param name="Len">number of cells to evaluate</param>
/// <returns>
/// For each 'in'- and 'out'-cell, arrays;<br/>
/// <list type="bullet">
/// <item>1st index: cell index</item>
/// <item>2nd index: node index</item>
/// <item>3rd index: polynomial index</item>
/// <item>4th index: spatial dimension</item>
/// </list>
/// </returns>
public virtual Tuple <MultidimensionalArray, MultidimensionalArray> EdgeEvalGradient(NodeSet NS, int j0, int Len)
{
var ret = this.GridDat.ChefBasis.CellBasisGradientValues.GetValue_EdgeDV(NS, j0, Len, this.Degree);
if (ret.Item1.GetLength(0) != Len)
{
int M = ret.Item1.GetLength(1);
int N = ret.Item1.GetLength(2);
int D = ret.Item1.GetLength(3);
ret = new Tuple <MultidimensionalArray, MultidimensionalArray>(
ret.Item1.ExtractSubArrayShallow(new int[] { 0, 0, 0, 0 }, new int[] { Len - 1, M - 1, N - 1, D - 1 }),
ret.Item2.ExtractSubArrayShallow(new int[] { 0, 0, 0, 0 }, new int[] { Len - 1, M - 1, N - 1, D - 1 }));
}
return(ret);
}