/// <summary>
/// Jacobi iteration
/// </summary>
public void Solve <U, V>(U xl, V bl)
where U : IList <double>
where V : IList <double>
{
int L = xl.Count;
double[] ql = new double[L];
double iter0_ResNorm = 0;
for (int iIter = 0; true; iIter++)
{
ql.SetV(bl);
Mtx.SpMV(-1.0, xl, 1.0, ql);
double ResNorm = ql.L2NormPow2().MPISum().Sqrt();
if (iIter == 0)
{
iter0_ResNorm = ResNorm;
if (this.IterationCallback != null)
{
double[] _xl = xl.ToArray();
double[] _bl = bl.ToArray();
Mtx.SpMV(-1.0, _xl, 1.0, _bl);
this.IterationCallback(iIter + 1, _xl, _bl, this.m_MultigridOp);
}
}
if (!TerminationCriterion(iIter, iter0_ResNorm, ResNorm))
{
m_Converged = true;
return;
}
Diag.SpMV(1.0, xl, 1.0, ql);
//xl.ScaleV(1.0 - omega);
invDiag.SpMV(omega, ql, 1.0 - omega, xl);
//for(int i = 0; i < L; i++) {
// xl[i] = omega * ((ql[i] + diag[i] * xl[i]) / diag[i])
// + (1.0 - omega) * xl[i];
//}
if (this.IterationCallback != null)
{
double[] _xl = xl.ToArray();
double[] _bl = bl.ToArray();
Mtx.SpMV(-1.0, _xl, 1.0, _bl);
this.IterationCallback(iIter + 1, _xl, _bl, this.m_MultigridOp);
}
}
}
/// <summary>
/// computes the residual on this level.
/// </summary>
public void Residual(double[] Res, double[] X, double[] B)
{
Debug.Assert(Res.Length == m_MgOperator.Mapping.LocalLength);
Debug.Assert(X.Length == m_MgOperator.Mapping.LocalLength);
Debug.Assert(B.Length == m_MgOperator.Mapping.LocalLength);
int L = Res.Length;
Array.Copy(B, Res, L);
OpMatrix.SpMV(-1.0, X, 1.0, Res);
//Res.AccV(1.0, B);
/*
* int L = Res.Count;
*
* var OpMatrix_coarse = m_MgOperator.CoarserLevel.OperatorMatrix;
* int Lc = OpMatrix_coarse._RowPartitioning.LocalLength;
*
* double[] Xc = new double[Lc];
* double[] Bc = new double[Lc];
* m_MgOperator.CoarserLevel.Restrict(X, Xc);
* m_MgOperator.CoarserLevel.Restrict(B, Bc);
*
* double[] Res_coarse = Bc; Bc = null;
* OpMatrix_coarse.SpMV(-1.0, Xc, 1.0, Res_coarse);
*
* m_MgOperator.CoarserLevel.Restrict(Res, Res_coarse);
*
* double[] Res1 = new double[L];// Res.ToArray();
* m_MgOperator.CoarserLevel.Prolongate(-1.0, Res1, 0.0, Res_coarse);
*
* double alpha = ParallelBlas.MPI_ddot(Res, Res1) / Res1.L2NormPow2().MPISum();
*
*
*
* double[] RemRes = Res.ToArray();
* RemRes.AccV(-alpha, Res1);
*
* Res1.ScaleV(alpha);
*
*
* int iLevel = m_MgOperator.LevelIndex;
* Console.Write(" ");
* for(int iLv = 0; iLv <= iLevel; iLv++) {
* Console.Write(" ");
* }
*
* Console.WriteLine(iLevel + " " + Res.L2Norm().ToString("0.####E-00") + " " + RemRes.L2Norm().ToString("0.####E-00") + " " + Res1.L2Norm().ToString("0.####E-00") + " " + GenericBlas.InnerProd(RemRes, Res1));
*
* //viz.PlotVectors(new double[][] { Res.ToArray(), Res1, Res_coarse, RemRes }, new[] { "Residual", "ProloResi", "CarseResi", "RestResi" });
*/
}
/// <summary>
/// computes the residual on this level.
/// </summary>
public void Residual <V1, V2, V3>(V1 rl, V2 xl, V3 bl)
where V1 : IList <double>
where V2 : IList <double>
where V3 : IList <double>
{
OpMatrix.SpMV(-1.0, xl, 0.0, rl);
rl.AccV(1.0, bl);
}
/// <summary>
/// computes the residual on this level.
/// </summary>
public double Residual <V1, V2, V3>(V1 rl, V2 xl, V3 bl)
where V1 : IList <double>
where V2 : IList <double>
where V3 : IList <double>
{
OpMatrix.SpMV(-1.0, xl, 0.0, rl);
rl.AccV(1.0, bl);
return(rl.MPI_L2Norm());
}
protected virtual void UpdateChangeRate(double PhysTime, double[] k)
{
BlockMsrMatrix OpMtx = new BlockMsrMatrix(this.CurrentStateMapping);
double[] OpAff = new double[this.CurrentStateMapping.LocalLength];
base.ComputeOperatorMatrix(OpMtx, OpAff, this.CurrentStateMapping, this.CurrentStateMapping.Fields.ToArray(), base.GetAgglomeratedLengthScales(), PhysTime);
k.SetV(OpAff);
OpMtx.SpMV(1.0, this.m_CurrentState, 1.0, k);
}
static void RestictionMatrixTestRec(int p, IEnumerable <MultigridMapping> MgMapSeq)
{
var currentLevelMap = MgMapSeq.First();
AggregationGridBasis AggBasis = currentLevelMap.AggBasis[0];
var map = new UnsetteledCoordinateMapping(new Basis(grid, p));
Random rnd = new Random();
double[] OrigVec = map.LocalLength.ForLoop(i => rnd.NextDouble());
double[] RestVec = new double[AggBasis.LocalDim];
double[] PrlgVec = new double[OrigVec.Length];
double[] RestVec2 = new double[RestVec.Length];
double[] PrlgVec2 = new double[OrigVec.Length];
AggBasis.RestictFromFullGrid(OrigVec, RestVec);
AggBasis.ProlongateToFullGrid(PrlgVec, RestVec);
BlockMsrMatrix RestOp = new BlockMsrMatrix(MgMapSeq.First(), MgMapSeq.First().ProblemMapping);
AggBasis.GetRestrictionMatrix(RestOp, MgMapSeq.First(), 0);
RestOp.SpMV(1.0, OrigVec, 0.0, RestVec2);
BlockMsrMatrix PrlgOp = RestOp.Transpose();
PrlgOp.SpMV(1.0, RestVec2, 0.0, PrlgVec2);
double RestErrNorm = GenericBlas.L2Dist(RestVec2, RestVec);
double PrlgErrNorm = GenericBlas.L2Dist(PrlgVec2, PrlgVec);
double LostInfNorm = GenericBlas.L2Dist(OrigVec, PrlgVec2);
//Console.WriteLine("Rest. matrix test: {0}, Prolong. matrix test {1}, Lost info {2}", RestErrNorm, PrlgErrNorm, LostInfNorm);
Assert.IsTrue(RestErrNorm < 1.0e-10);
Assert.IsTrue(PrlgErrNorm < 1.0e-10);
// restriction onto level itself
BlockMsrMatrix RestMtx = currentLevelMap.FromOtherLevelMatrix(currentLevelMap);
BlockMsrMatrix ShldBeEye = BlockMsrMatrix.Multiply(RestMtx, RestMtx.Transpose());
ShldBeEye.AccEyeSp(-1.0);
double errNorm = ShldBeEye.InfNorm();
Console.WriteLine("Id norm {0} \t (level {1})", errNorm, currentLevelMap.AggGrid.MgLevel);
Assert.IsTrue(errNorm < 1.0e-8);
// recursion
if (MgMapSeq.Count() > 1)
{
RestictionMatrixTestRec(p, MgMapSeq.Skip(1));
}
}
void DerivativeByFluxLinear(SinglePhaseField fin, SinglePhaseField fres, int d, SinglePhaseField fBnd)
{
var Op = (new LinearDerivFlx(d)).Operator();
BlockMsrMatrix OpMtx = new BlockMsrMatrix(fres.Mapping, fin.Mapping);
double[] OpAff = new double[fres.Mapping.LocalLength];
Op.ComputeMatrixEx(fin.Mapping, new DGField[] { fBnd }, fres.Mapping,
OpMtx, OpAff, OnlyAffine: false);
fres.Clear();
fres.CoordinateVector.Acc(1.0, OpAff);
OpMtx.SpMV(1.0, fin.CoordinateVector, 1.0, fres.CoordinateVector);
}
/// <summary>
/// Jacobi iteration
/// </summary>
/// <param name="l">muligrid level</param>
/// <param name="NoOfIter">number of Jacobi-Iterations</param>
public void Solve <U, V>(U xl, V bl)
where U : IList <double>
where V : IList <double>
{
int L = xl.Count;
double[] ql = new double[L];
for (int iIter = 0; iIter < NoOfIterations; iIter++)
{
this.m_ThisLevelIterations++;
ql.SetV(bl);
Mtx.SpMV(-1.0, xl, 1.0, ql);
if (this.m_Tolerance > 0)
{
double ResNorm = ql.L2NormPow2().MPISum().Sqrt();
if (ResNorm < this.m_Tolerance)
{
m_Converged = true;
return;
}
}
for (int i = 0; i < L; i++)
{
xl[i] = omega * ((ql[i] + diag[i] * xl[i]) / diag[i]) + (1.0 - omega) * xl[i];
}
if (this.IterationCallback != null)
{
double[] _xl = xl.ToArray();
double[] _bl = bl.ToArray();
Mtx.SpMV(-1.0, _xl, 1.0, _bl);
this.IterationCallback(iIter, _xl, _bl, this.m_mgop);
}
}
}
private void RKstage(double dt, double[][] k, int s, BlockMsrMatrix MsInv, BlockMsrMatrix M0, double[] u0, double[] coefficients)
{
// Copy coordinates to temp array since SpMV (below) does not
// support in-place computation
double[] tempCoordinates = CurrentState.ToArray();
M0.SpMV(1.0, u0, 0.0, tempCoordinates); // Non-agglomerated
for (int l = 0; l < s; l++)
{
tempCoordinates.AccV(-coefficients[l] * dt, k[l]); // Non-agglomerated
}
speciesMap.Agglomerator.ManipulateRHS(tempCoordinates, Mapping);
MsInv.SpMV(1.0, tempCoordinates, 0.0, CurrentState);
speciesMap.Agglomerator.Extrapolate(CurrentState.Mapping);
}
static void PolynomialRestAndPrlgTestRec(int p, MultigridMapping[] MgMapSeq)
{
var AggBasis = MgMapSeq.First().AggBasis[0];
//var AggBasis = aggBasisEs[1];
//{
var Orig = new SinglePhaseField(new Basis(grid, p));
SetTestValue(Orig);
var Test = Orig.CloneAs();
double[] OrigVec = Orig.CoordinateVector.ToArray();
double[] RestVec = new double[AggBasis.LocalDim];
double[] PrlgVec = new double[OrigVec.Length];
AggBasis.RestictFromFullGrid(OrigVec, RestVec);
Test.Clear();
AggBasis.ProlongateToFullGrid(PrlgVec, RestVec);
BlockMsrMatrix RestOp = new BlockMsrMatrix(MgMapSeq[0], MgMapSeq[0].ProblemMapping);
AggBasis.GetRestrictionMatrix(RestOp, MgMapSeq[0], 0);
double[] RestVec2 = new double[RestVec.Length];
RestOp.SpMV(1.0, OrigVec, 0.0, RestVec2);
Test.Clear();
Test.CoordinateVector.Acc(1.0, PrlgVec);
Test.Acc(-1.0, Orig);
double ErrNorm = Test.L2Norm();
Console.WriteLine("Polynomial Restriction/Prolongation test (p={1}, level={2}): {0}", ErrNorm, p, -MgMapSeq.Length);
Assert.Less(ErrNorm, 1.0e-8);
if (MgMapSeq.Length > 1)
{
PolynomialRestAndPrlgTestRec(p, MgMapSeq.Skip(1).ToArray());
}
}
static void RestictionMatrixTestRec(int p, IEnumerable <MultigridMapping> MgMapSeq)
{
AggregationGridBasis AggBasis = MgMapSeq.First().AggBasis[0];
var map = new UnsetteledCoordinateMapping(new Basis(grid, p));
Random rnd = new Random();
double[] OrigVec = map.LocalLength.ForLoop(i => rnd.NextDouble());
double[] RestVec = new double[AggBasis.LocalDim];
double[] PrlgVec = new double[OrigVec.Length];
double[] RestVec2 = new double[RestVec.Length];
double[] PrlgVec2 = new double[OrigVec.Length];
AggBasis.RestictFromFullGrid(OrigVec, RestVec);
AggBasis.ProlongateToFullGrid(PrlgVec, RestVec);
BlockMsrMatrix RestOp = new BlockMsrMatrix(MgMapSeq.First(), MgMapSeq.First().ProblemMapping);
AggBasis.GetRestrictionMatrix(RestOp, MgMapSeq.First(), 0);
RestOp.SpMV(1.0, OrigVec, 0.0, RestVec2);
BlockMsrMatrix PrlgOp = RestOp.Transpose();
PrlgOp.SpMV(1.0, RestVec2, 0.0, PrlgVec2);
double RestErrNorm = GenericBlas.L2Dist(RestVec2, RestVec);
double PrlgErrNorm = GenericBlas.L2Dist(PrlgVec2, PrlgVec);
double LostInfNorm = GenericBlas.L2Dist(OrigVec, PrlgVec2);
//Console.WriteLine("Rest. matrix test: {0}, Prolong. matrix test {1}, Lost info {2}", RestErrNorm, PrlgErrNorm, LostInfNorm);
Debug.Assert(RestErrNorm < 1.0e-10);
Debug.Assert(PrlgErrNorm < 1.0e-10);
if (MgMapSeq.Count() > 1)
{
RestictionMatrixTestRec(p, MgMapSeq.Skip(1));
}
}
public static void SpMVTest(
[Values(XDGusage.none, XDGusage.mixed1, XDGusage.mixed2, XDGusage.all)] XDGusage UseXdg,
[Values(1, 3)] int DGOrder,
[Values(false, true)] bool compressL1,
[Values(false, true)] bool compressL2)
{
unsafe
{
int[] Params = new int[8], ParamsGlob = new int[8];
fixed(int *pParams = Params, pParamsGlob = ParamsGlob)
{
pParams[0] = (int)UseXdg;
pParams[1] = DGOrder;
pParams[2] = compressL1 ? 1 : 0;
pParams[3] = compressL2 ? 1 : 0;
pParams[4] = -pParams[0];
pParams[5] = -pParams[1];
pParams[6] = -pParams[2];
pParams[7] = -pParams[3];
csMPI.Raw.Allreduce((IntPtr)pParams, (IntPtr)pParamsGlob, 8, csMPI.Raw._DATATYPE.INT, csMPI.Raw._OP.MIN, csMPI.Raw._COMM.WORLD);
}
int[] ParamsMin = ParamsGlob.GetSubVector(0, 4);
int[] ParamsMax = ParamsGlob.GetSubVector(4, 4);
for (int i = 0; i < 4; i++)
{
if (Params[i] != ParamsMin[i])
{
throw new ApplicationException();
}
if (Params[i] != -ParamsMax[i])
{
throw new ApplicationException();
}
}
Console.WriteLine("SpMVTest({0},{1},{2},{3})", UseXdg, DGOrder, compressL1, compressL2);
}
using (var solver = new Matrix_MPItestMain()
{
m_UseXdg = UseXdg, m_DGorder = DGOrder
}) {
// create the test data
// ====================
BoSSS.Solution.Application.CommandLineOptions opts = null;
//opts = new BoSSS.Solution.Application.CommandLineOptions();
solver.Init(null, opts);
solver.RunSolverMode();
Stopwatch stw = new Stopwatch();
stw.Reset();
BlockMsrMatrix M = solver.OperatorMatrix;
double[] B = new double[M.RowPartitioning.LocalLength];
double[] X = new double[M.ColPartition.LocalLength];
Random R = new Random();
for (int i = 0; i < X.Length; i++)
{
X[i] = R.NextDouble();
}
for (int i = 0; i < B.Length; i++)
{
B[i] = R.NextDouble();
}
double[] Bb4 = B.CloneAs();
double RefNorm = B.L2NormPow2().MPISum().Sqrt() * 1e-10;
stw.Start();
M.SpMV(1.6, X, 0.5, B);
stw.Stop();
//M.SaveToTextFileSparse(@"C:\tmp\M.txt");
//M11.SaveToTextFileSparse(@"C:\tmp\M11.txt");
//M12.SaveToTextFileSparse(@"C:\tmp\M12.txt");
//M21.SaveToTextFileSparse(@"C:\tmp\M21.txt");
//M22.SaveToTextFileSparse(@"C:\tmp\M22.txt");
//M22xM21.SaveToTextFileSparse(@"C:\tmp\M22xM21.txt");
using (var MatlabRef = new BatchmodeConnector()) {
MultidimensionalArray CheckRes = MultidimensionalArray.Create(1, 1);
MatlabRef.PutSparseMatrix(M, "M");
MatlabRef.PutVector(Bb4, "Bref");
MatlabRef.PutVector(B, "B");
MatlabRef.PutVector(X, "X");
MatlabRef.Cmd("Bref = Bref*0.5 + M*X*1.6;");
MatlabRef.Cmd("errB = norm(B - Bref, 2);");
MatlabRef.Cmd("CheckRes = [errB];");
MatlabRef.GetMatrix(CheckRes, "CheckRes");
MatlabRef.Execute();
Console.WriteLine("Matlab check SpMV: " + CheckRes[0, 0]);
Assert.LessOrEqual(CheckRes[0, 0], RefNorm, "Error in SpMV");
}
Console.WriteLine("Time spend in matrix operations: " + stw.Elapsed.TotalSeconds + " sec.");
TotTime_MatrixOp += stw.Elapsed;
}
}
private void AssembleMatrix(double MU_A, double MU_B, out BlockMsrMatrix M, out double[] b, out MultiphaseCellAgglomerator agg, out MassMatrixFactory massFact)
{
using (var tr = new FuncTrace()) {
// create operator
// ===============
if (this.Control.SetDefaultDiriBndCnd)
{
this.Control.xLaplaceBCs.g_Diri = ((CommonParamsBnd inp) => 0.0);
this.Control.xLaplaceBCs.IsDirichlet = (inp => true);
}
double D = this.GridData.SpatialDimension;
int p = u.Basis.Degree;
double penalty_base = (p + 1) * (p + D) / D;
double penalty_multiplyer = base.Control.penalty_multiplyer;
XQuadFactoryHelper.MomentFittingVariants momentFittingVariant;
if (D == 3)
{
momentFittingVariant = XQuadFactoryHelper.MomentFittingVariants.Classic;
}
momentFittingVariant = this.Control.CutCellQuadratureType;
int order = this.u.Basis.Degree * 2;
XSpatialOperator Op = new XSpatialOperator(1, 1, (A, B, C) => order, "u", "c1");
var lengthScales = ((BoSSS.Foundation.Grid.Classic.GridData)GridData).Cells.PenaltyLengthScales;
var lap = new XLaplace_Bulk(this.LsTrk, penalty_multiplyer * penalty_base, "u", this.Control.xLaplaceBCs, 1.0, MU_A, MU_B, lengthScales, this.Control.ViscosityMode);
Op.EquationComponents["c1"].Add(lap); // Bulk form
Op.EquationComponents["c1"].Add(new XLaplace_Interface(this.LsTrk, MU_A, MU_B, penalty_base * 2, this.Control.ViscosityMode)); // coupling form
Op.Commit();
// create agglomeration
// ====================
var map = new UnsetteledCoordinateMapping(u.Basis);
//agg = new MultiphaseCellAgglomerator(
// new CutCellMetrics(momentFittingVariant,
// QuadOrderFunc.SumOfMaxDegrees(RoundUp: true)(map.BasisS.Select(bs => bs.Degree).ToArray(), new int[0], map.BasisS.Select(bs => bs.Degree).ToArray()),
// //this.HMFDegree,
// LsTrk, this.LsTrk.SpeciesIdS.ToArray()),
// this.Control.AgglomerationThreshold, false);
agg = LsTrk.GetAgglomerator(this.LsTrk.SpeciesIdS.ToArray(), order, this.Control.AgglomerationThreshold);
// compute matrix
// =============
using (new BlockTrace("XdgMatrixAssembly", tr)) {
M = new BlockMsrMatrix(map, map);
b = new double[M.RowPartitioning.LocalLength];
Op.ComputeMatrixEx(LsTrk,
map, null, map,
M, b, false, 0.0, true,
agg.CellLengthScales, null, null, //out massFact,
this.LsTrk.SpeciesIdS.ToArray());
}
// compare with linear evaluation
// ==============================
DGField[] testDomainFieldS = map.BasisS.Select(bb => new XDGField(bb as XDGBasis)).ToArray();
CoordinateVector test = new CoordinateVector(testDomainFieldS);
DGField[] errFieldS = map.BasisS.Select(bb => new XDGField(bb as XDGBasis)).ToArray();
CoordinateVector Err = new CoordinateVector(errFieldS);
var eval = Op.GetEvaluatorEx(LsTrk,
testDomainFieldS, null, map);
foreach (var s in this.LsTrk.SpeciesIdS)
{
eval.SpeciesOperatorCoefficients[s].CellLengthScales = agg.CellLengthScales[s];
}
eval.time = 0.0;
int L = test.Count;
Random r = new Random();
for (int i = 0; i < L; i++)
{
test[i] = r.NextDouble();
}
double[] R1 = new double[L];
double[] R2 = new double[L];
eval.Evaluate(1.0, 1.0, R1);
R2.AccV(1.0, b);
M.SpMV(1.0, test, 1.0, R2);
Err.AccV(+1.0, R1);
Err.AccV(-1.0, R2);
double ErrDist = GenericBlas.L2DistPow2(R1, R2).MPISum().Sqrt();
double Ref = test.L2NormPow2().MPISum().Sqrt();
Assert.LessOrEqual(ErrDist, Ref * 1.0e-5, "Mismatch between explicit evaluation of XDG operator and matrix.");
// agglomeration wahnsinn
// ======================
agg.ManipulateMatrixAndRHS(M, b, map, map);
foreach (var S in this.LsTrk.SpeciesNames)
{
Console.WriteLine(" Species {0}: no of agglomerated cells: {1}",
S, agg.GetAgglomerator(this.LsTrk.GetSpeciesId(S)).AggInfo.SourceCells.NoOfItemsLocally);
}
// mass matrix factory
// ===================
Basis maxB = map.BasisS.ElementAtMax(bss => bss.Degree);
//massFact = new MassMatrixFactory(maxB, agg);
massFact = LsTrk.GetXDGSpaceMetrics(this.LsTrk.SpeciesIdS.ToArray(), order).MassMatrixFactory;
}
}
//
//
/// <summary>
/// applies the agglomeration on a general matrix
/// </summary>
/// <param name="Matrix">the matrix that should be manipulated.</param>
/// <param name="Rhs">the right-hand-side that should be manipulated</param>
/// <param name="ColMap"></param>
/// <param name="ColMapAggSw">Turns column agglomeration on/off fore each variable individually; default == null is on. </param>
/// <param name="RowMap"></param>
/// <param name="RowMapAggSw">The same shit as for <paramref name="ColMapAggSw"/>, just for rows.</param>
public void ManipulateMatrixAndRHS<M, T>(M Matrix, T Rhs, UnsetteledCoordinateMapping RowMap, UnsetteledCoordinateMapping ColMap, bool[] RowMapAggSw = null, bool[] ColMapAggSw = null)
where M : IMutableMatrixEx
where T : IList<double>
{
MPICollectiveWatchDog.Watch();
//var mtxS = GetFrameMatrices(Matrix, RowMap, ColMap);
if (Matrix == null && Rhs == null)
// nothing to do
return;
if (TotalNumberOfAgglomerations <= 0)
// nothing to do
return;
if (RowMapAggSw != null)
throw new NotImplementedException();
// generate agglomeration sparse matrices
// ======================================
int RequireRight;
if (Matrix == null) {
// we don't need multiplication-from-the-right at all
RequireRight = 0;
} else {
if (RowMap.EqualsUnsetteled(ColMap) && ArrayTools.ListEquals(ColMapAggSw, RowMapAggSw)) {
// we can use the same matrix for right and left multiplication
RequireRight = 1;
} else {
// separate matrix for the multiplication-from-the-right is required
RequireRight = 2;
}
}
BlockMsrMatrix LeftMul = null, RightMul = null;
{
foreach (var kv in DictAgglomeration) {
var Species = kv.Key;
var m_Agglomerator = kv.Value;
if (m_Agglomerator != null) {
CellMask spcMask = this.Tracker.Regions.GetSpeciesMask(Species);
MiniMapping rowMini = new MiniMapping(RowMap, Species, this.Tracker.Regions);
BlockMsrMatrix LeftMul_Species = m_Agglomerator.GetRowManipulationMatrix(RowMap, rowMini.MaxDeg, rowMini.NoOfVars, rowMini.i0Func, rowMini.NFunc, false, spcMask);
if (LeftMul == null) {
LeftMul = LeftMul_Species;
} else {
LeftMul.Acc(1.0, LeftMul_Species);
}
if (!object.ReferenceEquals(LeftMul, RightMul) && RightMul != null) {
MiniMapping colMini = new MiniMapping(ColMap, Species, this.Tracker.Regions);
BlockMsrMatrix RightMul_Species = m_Agglomerator.GetRowManipulationMatrix(ColMap, colMini.MaxDeg, colMini.NoOfVars, colMini.i0Func, colMini.NFunc, false, spcMask);
if (RightMul == null) {
RightMul = RightMul_Species;
} else {
RightMul.Acc(1.0, RightMul_Species);
}
} else if (RequireRight == 1) {
RightMul = LeftMul;
} else {
RightMul = null;
}
}
}
}
// apply the agglomeration to the matrix
// =====================================
if (Matrix != null) {
BlockMsrMatrix RightMulTr = RightMul.Transpose();
BlockMsrMatrix _Matrix;
if (Matrix is BlockMsrMatrix) {
_Matrix = (BlockMsrMatrix)((object)Matrix);
} else {
_Matrix = Matrix.ToBlockMsrMatrix(RowMap, ColMap);
}
var AggMatrix = BlockMsrMatrix.Multiply(LeftMul, BlockMsrMatrix.Multiply(_Matrix, RightMulTr));
if (object.ReferenceEquals(_Matrix, Matrix)) {
_Matrix.Clear();
_Matrix.Acc(1.0, AggMatrix);
} else {
Matrix.Acc(-1.0, _Matrix); // das ist so
Matrix.Acc(1.0, AggMatrix); // meagaschlecht !!!!!!
}
}
// apply the agglomeration to the Rhs
// ==================================
if (Rhs != null) {
double[] tmp = Rhs.ToArray();
if (object.ReferenceEquals(tmp, Rhs))
throw new ApplicationException("Flache kopie sollte eigentlich ausgeschlossen sein!?");
LeftMul.SpMV(1.0, tmp, 0.0, Rhs);
}
}
/// <summary>
/// computes derivatives in various ways and compares them against known values.
/// </summary>
protected override double RunSolverOneStep(int TimestepNo, double phystime, double dt)
{
base.EndTime = 0.0;
base.NoOfTimesteps = 0;
int D = this.GridData.SpatialDimension;
int J = this.GridData.iLogicalCells.NoOfLocalUpdatedCells;
Console.WriteLine("DerivativeTest.exe, test case #" + GRID_CASE + " ******************************");
//var Fix = this.GridData.iGeomEdges.FaceIndices;
//for(int iEdge = 0; iEdge < Fix.GetLength(0); iEdge++) {
// Debug.Assert(Fix[iEdge, 0] >= 0);
// Debug.Assert(Fix[iEdge, 1] >= 0);
//}
// sealing test
// =================
if (this.GridData is Foundation.Grid.Classic.GridData)
{
TestSealing(this.GridData);
}
// cell volume and edge area check, if possible
// ===============================================
if (this.CellVolume > 0)
{
double err = 0;
double Treshold = 1.0e-10;
for (int j = 0; j < J; j++)
{
err += Math.Abs(this.GridData.iLogicalCells.GetCellVolume(j) - this.CellVolume);
}
bool passed = (err < Treshold);
m_passed = m_passed && passed;
Console.WriteLine("Cell volume error: " + err + " passed? " + passed);
Console.WriteLine("--------------------------------------------");
}
if (this.EdgeArea > 0)
{
double err = 0;
double Treshold = 1.0e-10;
int E = this.GridData.iLogicalEdges.Count;
for (int e = 0; e < E; e++)
{
err += Math.Abs(this.GridData.iLogicalEdges.GetEdgeArea(e) - this.EdgeArea);
}
bool passed = (err < Treshold);
m_passed = m_passed && passed;
Console.WriteLine("Edge area error: " + err + " passed? " + passed);
Console.WriteLine("--------------------------------------------");
}
// Orthonormality of basis in physical coords
// ==========================================
{
Basis Bs = this.f1.Basis;
int N = Bs.Length;
int degQuad = this.GridData.iLogicalCells.GetInterpolationDegree(0) * D + Bs.Degree + 3;
int[] jG2jL = this.GridData.iGeomCells.GeomCell2LogicalCell;
// mass matrix: should be identity!
MultidimensionalArray MassMatrix = MultidimensionalArray.Create(J, N, N);
// compute mass matrix by quadrature.
var quad = CellQuadrature.GetQuadrature(new int[] { N, N }, base.GridData,
(new CellQuadratureScheme()).Compile(base.GridData, degQuad),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
NodeSet QuadNodes = QR.Nodes;
MultidimensionalArray BasisVals = Bs.CellEval(QuadNodes, i0, Length);
EvalResult.Multiply(1.0, BasisVals, BasisVals, 0.0, "jknm", "jkn", "jkm");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
if (jG2jL != null)
{
for (int i = 0; i < Length; i++)
{
int jG = i + i0;
MassMatrix.ExtractSubArrayShallow(jG2jL[jG], -1, -1)
.Acc(1.0, ResultsOfIntegration.ExtractSubArrayShallow(i, -1, -1));
}
}
else
{
MassMatrix.SetSubArray(ResultsOfIntegration, new int[] { i0, 0, 0 }, new int[] { i0 + Length - 1, N - 1, N - 1 });
}
},
cs: CoordinateSystem.Physical);
quad.Execute();
// check that mass matrix is Id.
int MaxErrorCell = -1;
double MaxError = -1;
for (int j = 0; j < J; j++)
{
MultidimensionalArray MassMatrix_j = MassMatrix.ExtractSubArrayShallow(j, -1, -1);
MassMatrix_j.AccEye(-1.0);
double Norm_j = MassMatrix_j.InfNorm();
if (Norm_j > MaxError)
{
MaxError = Norm_j;
MaxErrorCell = j;
}
}
bool passed = (MaxError < 1.0e-8);
m_passed = m_passed && passed;
Console.WriteLine("Mass Matrix, maximum error in Cell #" + MaxErrorCell + ", mass matrix error norm: " + MaxError + " passed? " + passed);
}
// Broken Derivatives
// =================
double totalVolume = (new SubGrid(CellMask.GetFullMask(this.GridData))).Volume;
for (int d = 0; d < D; d++)
{
// compute
f1Gradient_Numerical[d].Clear();
f1Gradient_Numerical[d].Derivative(1.0, f1, d);
f2Gradient_Numerical[d].Clear();
f2Gradient_Numerical[d].Derivative(1.0, f2, d);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Broken Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Flux Derivatives
// =================
for (int d = 0; d < D; d++)
{
// compute
f1Gradient_Numerical[d].Clear();
f1Gradient_Numerical[d].DerivativeByFlux(1.0, f1, d);
f2Gradient_Numerical[d].Clear();
f2Gradient_Numerical[d].DerivativeByFlux(1.0, f2, d);
f1Gradient_Numerical[d].CheckForNanOrInf(true, true, true);
f2Gradient_Numerical[d].CheckForNanOrInf(true, true, true);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Flux Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Linear flux Derivatives
// =======================
for (int d = 0; d < D; d++)
{
double[] korrekto = f1Gradient_Numerical[d].CoordinateVector.ToArray();
// compute
DerivativeByFluxLinear(f1, f1Gradient_Numerical[d], d, f1);
DerivativeByFluxLinear(f2, f2Gradient_Numerical[d], d, f2);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Linear Flux Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Laplacian, nonlinear
// ====================
if (!AltRefSol)
{
var Laplace = (new ipLaplace()).Operator(1);
Laplace.Evaluate(new DGField[] { this.f1 }, new DGField[] { this.Laplace_f1_Numerical });
Laplace.Evaluate(new DGField[] { this.f2 }, new DGField[] { this.Laplace_f2_Numerical });
double Treshold = 1.0e-8;
// subtract analytical
var Errfield1 = Laplace_f1_Numerical.CloneAs();
Errfield1.Acc(-1, Laplace_f1_Analytical);
var Errfield2 = Laplace_f2_Numerical.CloneAs();
Errfield2.Acc(-1, Laplace_f2_Analytical);
double err_Lf1 = Errfield1.L2Norm() / totalVolume;
bool passed = (err_Lf1 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f1 Numerical - /\\f1 Analytical ||_2 = {0} (nonlinear evaluation), passed? {1}", err_Lf1, passed));
double err_Lf2 = Errfield2.L2Norm() / totalVolume;
passed = (err_Lf2 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f2 Numerical - /\\f2 Analytical ||_2 = {0} (nonlinear evaluation), passed? {1}", err_Lf2, passed));
Console.WriteLine("--------------------------------------------");
}
// Laplacian, linear
// ====================
if (!AltRefSol)
{
var Laplace = (new ipLaplace()).Operator(1);
var LaplaceMtx = new BlockMsrMatrix(this.f1.Mapping, this.Laplace_f1_Numerical.Mapping);
var LaplaceAffine = new double[LaplaceMtx.RowPartitioning.LocalLength];
Laplace.ComputeMatrix(this.f1.Mapping, null, this.Laplace_f1_Numerical.Mapping,
LaplaceMtx, LaplaceAffine, false);
this.Laplace_f1_Numerical.CoordinateVector.SetV(LaplaceAffine);
LaplaceMtx.SpMV(1.0, this.f1.CoordinateVector, 1.0, this.Laplace_f1_Numerical.CoordinateVector);
this.Laplace_f2_Numerical.CoordinateVector.SetV(LaplaceAffine);
LaplaceMtx.SpMV(1.0, this.f2.CoordinateVector, 1.0, this.Laplace_f2_Numerical.CoordinateVector);
// subtract analytical
var Errfield1 = Laplace_f1_Numerical.CloneAs();
Errfield1.Acc(-1, Laplace_f1_Analytical);
var Errfield2 = Laplace_f2_Numerical.CloneAs();
Errfield2.Acc(-1, Laplace_f2_Analytical);
double Treshold = 1.0e-8;
double err_Lf1 = Errfield1.L2Norm() / totalVolume;
bool passed = (err_Lf1 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f1 Numerical - /\\f1 Analytical ||_2 = {0} (linear evaluation), passed? {1}", err_Lf1, passed));
double err_Lf2 = Errfield2.L2Norm() / totalVolume;
passed = (err_Lf2 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f2 Numerical - /\\f2 Analytical ||_2 = {0} (linear evaluation), passed? {1}", err_Lf2, passed));
// comparison of finite difference Jacobian and Operator matrix
if (TestFDJacobian)
{
this.f1.Clear();
var FDJbuilder = Laplace.GetFDJacobianBuilder(this.f1.Mapping.Fields, null, this.f1.Mapping,
delegate(IEnumerable <DGField> U0, IEnumerable <DGField> Params) {
return;
});
var CheckMatrix = new BlockMsrMatrix(FDJbuilder.CodomainMapping, FDJbuilder.DomainMapping);
var CheckAffine = new double[FDJbuilder.CodomainMapping.LocalLength];
FDJbuilder.ComputeMatrix(CheckMatrix, CheckAffine);
var ErrMatrix = LaplaceMtx.CloneAs();
var ErrAffine = LaplaceAffine.CloneAs();
ErrMatrix.Acc(-1.0, CheckMatrix);
ErrAffine.AccV(-1.0, CheckAffine);
double LinfMtx = ErrMatrix.InfNorm();
double L2Aff = ErrAffine.L2NormPow2().MPISum().Sqrt();
bool passed1 = (LinfMtx < 1.0e-3);
bool passed2 = (L2Aff < Treshold);
Console.WriteLine("Finite Difference Jacobian: Matrix/Affine delta norm {0} {1}, passed? {2} {3}", LinfMtx, L2Aff, passed1, passed2);
m_passed = m_passed && passed1;
m_passed = m_passed && passed2;
}
Console.WriteLine("--------------------------------------------");
}
// finally...
// =================
if (m_passed)
{
Console.WriteLine("All tests passed. *****************************");
}
else
{
Console.WriteLine("Some error above threshold. *******************");
}
return(0.0); // return some artificial timestep
}
/// <summary>
/// implementation of the CG algorithm
/// </summary>
/// <param name="_x"></param>
/// <param name="_R"></param>
/// <param name="stats"></param>
public void Solve <Vec1, Vec2>(Vec1 _x, Vec2 _R)
where Vec1 : IList <double>
where Vec2 : IList <double>
{
double[] x, R;
if (_x is double[])
{
x = _x as double[];
}
else
{
x = _x.ToArray();
}
if (_R is double[])
{
R = _R as double[];
}
else
{
R = _R.ToArray();
}
int L = x.Length;
double[] P = new double[L];
//double[] R = rhs; // rhs is only needed once, so we can use it to store residuals
double[] V = new double[L];
double[] Z = new double[L];
// compute P0, R0
// ==============
GenericBlas.dswap(L, x, 1, P, 1);
m_OptMatrix.SpMV(-1.0, P, 1.0, R);
if (IterationCallback != null)
{
IterationCallback(NoOfIterations, P.CloneAs(), R.CloneAs(), this.m_MgOp);
}
GenericBlas.dswap(L, x, 1, P, 1);
if (Precond != null)
{
Precond.Solve(Z, R);
P.SetV(Z);
}
else
{
P.SetV(R);
}
double alpha = R.InnerProd(P);
double alpha_0 = alpha;
double ResNorm;
ResNorm = Math.Sqrt(alpha);
// iterate
// =======
NoOfIterations++; // one iteration has allready been performed (P0, R0)
for (int n = 1; n < this.m_MaxIterations; n++)
{
if (ResNorm <= m_Tolerance && NoOfIterations >= m_MinIterations)
{
this.m_Converged = true;
break;
}
NoOfIterations++;
if (Math.Abs(alpha) <= double.Epsilon)
{
// numerical breakdown
break;
}
m_Matrix.SpMV(1.0, P, 0, V);
double VxP = V.InnerProd(P);
//Console.WriteLine("VxP: {0}", VxP);
if (double.IsNaN(VxP) || double.IsInfinity(VxP))
{
throw new ArithmeticException();
}
double lambda = alpha / VxP;
if (double.IsNaN(lambda) || double.IsInfinity(lambda))
{
throw new ArithmeticException();
}
x.AccV(lambda, P);
R.AccV(-lambda, V);
if (IterationCallback != null)
{
IterationCallback(NoOfIterations, x.CloneAs(), R.CloneAs(), this.m_MgOp);
}
if (Precond != null)
{
Z.Clear();
Precond.Solve(Z, R);
}
else
{
Z.SetV(R);
}
double alpha_neu = R.InnerProd(Z).MPISum();
// compute residual norm
ResNorm = R.L2NormPow2().MPISum().Sqrt();
P.ScaleV(alpha_neu / alpha);
P.AccV(1.0, Z);
alpha = alpha_neu;
}
if (!object.ReferenceEquals(_x, x))
{
_x.SetV(x);
}
if (!object.ReferenceEquals(_R, R))
{
_R.SetV(R);
}
return;
}
public void UpdateSensorValues(CNSFieldSet fieldSet, ISpeciesMap speciesMap, CellMask cellMask)
{
DGField fieldToTest = fieldSet.ConservativeVariables.
Concat(fieldSet.DerivedFields.Values).
Where(f => f.Identification == sensorVariable.Name).
Single();
int degree = fieldToTest.Basis.Degree;
int noOfCells = fieldToTest.GridDat.iLogicalCells.NoOfLocalUpdatedCells;
if (sensorValues == null || sensorValues.Length != noOfCells)
{
sensorValues = new double[noOfCells];
}
IMatrix coordinatesTimesMassMatrix;
IMatrix coordinatesTruncatedTimesMassMatrix;
if (speciesMap is ImmersedSpeciesMap ibmMap)
{
// Note: This has to be the _non_-agglomerated mass matrix
// because we still live on the non-agglomerated mesh at this
// point
BlockMsrMatrix massMatrix = ibmMap.GetMassMatrixFactory(fieldToTest.Mapping).NonAgglomeratedMassMatrix;
// Old
DGField temp = fieldToTest.CloneAs();
massMatrix.SpMV(1.0, fieldToTest.CoordinateVector, 0.0, temp.CoordinateVector);
coordinatesTimesMassMatrix = temp.Coordinates;
// Neu
DGField uTruncated = fieldToTest.CloneAs();
// Set all coordinates to zero
for (int cell = 0; cell < uTruncated.Coordinates.NoOfRows; cell++)
{
for (int coordinate = 0; coordinate < uTruncated.Coordinates.NoOfCols; coordinate++)
{
uTruncated.Coordinates[cell, coordinate] = 0;
}
}
// Copy only the coordiantes that belong to the highest modes
foreach (int cell in cellMask.ItemEnum)
{
foreach (int coordinate in fieldToTest.Basis.GetPolynomialIndicesForDegree(cell, degree))
{
uTruncated.Coordinates[cell, coordinate] = fieldToTest.Coordinates[cell, coordinate];
}
}
// Calculate M times u
DGField vecF_Field = fieldToTest.CloneAs();
massMatrix.SpMV(1.0, uTruncated.CoordinateVector, 0.0, vecF_Field.CoordinateVector);
coordinatesTruncatedTimesMassMatrix = vecF_Field.Coordinates;
}
else
{
// Mass matrix is identity
coordinatesTimesMassMatrix = fieldToTest.Coordinates;
coordinatesTruncatedTimesMassMatrix = fieldToTest.Coordinates;
}
//IMatrix coordinatesTimesMassMatrix = fieldToTest.Coordinates;
//cellMask.SaveToTextFile("fluidCells.txt");
// This is equivalent to norm(restrictedField) / norm(originalField)
// Note: THIS WILL FAIL IN CUT CELLS
foreach (int cell in cellMask.ItemEnum)
{
double numerator = 0.0;
foreach (int coordinate in fieldToTest.Basis.GetPolynomialIndicesForDegree(cell, degree))
{
//numerator += fieldToTest.Coordinates[cell, coordinate] * fieldToTest.Coordinates[cell, coordinate];
numerator += fieldToTest.Coordinates[cell, coordinate] * coordinatesTruncatedTimesMassMatrix[cell, coordinate];
}
double denominator = 0.0;
for (int coordinate = 0; coordinate < fieldToTest.Basis.Length; coordinate++)
{
//denominator += fieldToTest.Coordinates[cell, coordinate] * fieldToTest.Coordinates[cell, coordinate];
denominator += fieldToTest.Coordinates[cell, coordinate] * coordinatesTimesMassMatrix[cell, coordinate];
}
double result;
if (denominator == 0.0)
{
result = 0.0;
}
else
{
result = numerator / denominator;
}
//Debug.Assert(denominator != 0, "Persson sensor: Denominator is zero!");
//Debug.Assert(!(numerator / denominator).IsNaN(), "Persson sensor: Sensor value is NaN!");
//Debug.Assert(numerator / denominator >= 0, "Persson sensor: Sensor value is negative!");
sensorValues[cell] = result;
}
}
public void Solve <V1, V2>(V1 _X, V2 _B)
where V1 : IList <double>
where V2 : IList <double>
{
using (var tr = new FuncTrace())
{
double[] X, B;
if (_X is double[])
{
X = _X as double[];
}
else
{
X = _X.ToArray();
}
if (_B is double[])
{
B = _B as double[];
}
else
{
B = _B.ToArray();
}
double bnrm2 = B.L2NormPow2().MPISum().Sqrt();
if (bnrm2 == 0.0)
{
bnrm2 = 1.0;
}
int Nloc = Matrix.RowPartitioning.LocalLength;
int Ntot = Matrix.RowPartitioning.TotalLength;
double[] r = new double[Nloc];
double[] z = new double[Nloc];
//r = M \ ( b-A*x );, where M is the precond
z.SetV(B);
Matrix.SpMV(-1.0, X, 1.0, z);
if (IterationCallback != null)
{
IterationCallback(0, X.CloneAs(), z.CloneAs(), this.m_mgop);
}
if (this.Precond != null)
{
r.Clear();
this.Precond.Solve(r, z);
}
else
{
r.SetV(z);
}
// Inserted for real residual
double error2 = z.L2NormPow2().MPISum().Sqrt();
double error = (r.L2NormPow2().MPISum().Sqrt()) / bnrm2;
if (error < this.m_Tolerance)
{
if (!object.ReferenceEquals(_X, X))
{
_X.SetV(X);
}
B.SetV(z);
this.m_Converged = true;
return;
}
if (MaxKrylovDim <= 0)
{
throw new NotSupportedException("unsupported restart length.");
}
int m = MaxKrylovDim;
double[][] V = (m + 1).ForLoop(i => new double[Nloc]); // V(1:n,1:m+1) = zeros(n,m+1);
MultidimensionalArray H = MultidimensionalArray.Create(m + 1, m); // H(1:m+1,1:m) = zeros(m+1,m);
double[] cs = new double[m];
double[] sn = new double[m];
//double[] s = new double[m+1];
double[] e1 = new double[Nloc];
//if(Matrix.RowPartitioning.Rank == 0)
e1[0] = 1.0;
double[] s = new double[Nloc], w = new double[Nloc], y;
double temp;
int iter;
for (iter = 1; iter <= m_MaxIterations; iter++)
{ // GMRES iterations
// r = M \ ( b-A*x );
z.SetV(B);
Matrix.SpMV(-1.0, X, 1.0, z);
error2 = z.L2NormPow2().MPISum().Sqrt();
if (this.Precond != null)
{
r.Clear();
this.Precond.Solve(r, z);
}
else
{
r.SetV(z);
}
// V(:,1) = r / norm( r );
double norm_r = r.L2NormPow2().MPISum().Sqrt();
V[0].SetV(r, alpha: (1.0 / norm_r));
//s = norm( r )*e1;
s.SetV(e1, alpha: norm_r);
int i;
#region Gram-Schmidt (construct orthonormal basis using Gram-Schmidt)
for (i = 1; i <= m; i++)
{
this.NoOfIterations++;
#region Arnoldi procdure
//w = M \ (A*V(:,i));
Matrix.SpMV(1.0, V[i - 1], 0.0, z);
if (this.Precond != null)
{
w.Clear();
this.Precond.Solve(w, z);
}
else
{
w.SetV(z);
}
for (int k = 1; k <= i; k++)
{
H[k - 1, i - 1] = GenericBlas.InnerProd(w, V[k - 1]).MPISum();
//w = w - H(k,i)*V(:,k);
w.AccV(-H[k - 1, i - 1], V[k - 1]);
}
double norm_w = w.L2NormPow2().MPISum().Sqrt();
H[i + 1 - 1, i - 1] = norm_w; // the +1-1 actually makes me sure I haven't forgotten to subtract -1 when porting the code
//V(:,i+1) = w / H(i+1,i);
V[i + 1 - 1].SetV(w, alpha: (1.0 / norm_w));
#endregion
#region Givens rotation
for (int k = 1; k <= i - 1; k++)
{
// apply Givens rotation, H is Hessenbergmatrix
temp = cs[k - 1] * H[k - 1, i - 1] + sn[k - 1] * H[k + 1 - 1, i - 1];
H[k + 1 - 1, i - 1] = -sn[k - 1] * H[k - 1, i - 1] + cs[k - 1] * H[k + 1 - 1, i - 1];
H[k - 1, i - 1] = temp;
}
// [cs(i),sn(i)] = rotmat( H(i,i), H(i+1,i) ); % form i-th rotation matrix
rotmat(out cs[i - 1], out sn[i - 1], H[i - 1, i - 1], H[i + 1 - 1, i - 1]);
temp = cs[i - 1] * s[i - 1]; // % approximate residual norm
H[i - 1, i - 1] = cs[i - 1] * H[i - 1, i - 1] + sn[i - 1] * H[i + 1 - 1, i - 1];
H[i + 1 - 1, i - 1] = 0.0;
#endregion
// update the residual vector (s == beta in many pseudocodes)
s[i + 1 - 1] = -sn[i - 1] * s[i - 1];
s[i - 1] = temp;
error = Math.Abs(s[i + 1 - 1]) / bnrm2;
//{
// int rootRank = Matrix.RowPartitioning.FindProcess(i + 1 - 1);
// if (Matrix.RowPartitioning.Rank == rootRank) {
// } else {
// error = double.NaN;
// }
// unsafe {
// csMPI.Raw.Bcast((IntPtr)(&error), 1, csMPI.Raw._DATATYPE.DOUBLE, rootRank, Matrix.RowPartitioning.MPI_Comm);
// }
//}
//using (StreamWriter writer = new StreamWriter(m_SessionPath + "//GMRES_Stats.txt", true))
//{
Console.WriteLine(i + " " + error);
//}
if (error <= m_Tolerance)
{
// update approximation and exit
//using (StreamWriter writer = new StreamWriter(m_SessionPath + "//GMRES_Stats.txt", true))
//{
// writer.WriteLine("");
//}
//y = H(1:i,1:i) \ s(1:i);
y = new double[i];
H.ExtractSubArrayShallow(new int[] { 0, 0 }, new int[] { i - 1, i - 1 })
.Solve(y, s.GetSubVector(0, i));
// x = x + V(:,1:i)*y;
for (int ii = 0; ii < i; ii++)
{
X.AccV(y[ii], V[ii]);
}
this.m_Converged = true;
break;
}
}
#endregion
//Debugger.Launch();
if (error <= this.m_Tolerance)
{
this.m_Converged = true;
break;
}
// y = H(1:m,1:m) \ s(1:m);
y = new double[m];
H.ExtractSubArrayShallow(new int[] { 0, 0 }, new int[] { m - 1, m - 1 })
.Solve(y, s.GetSubVector(0, m));
// update approximation: x = x + V(:,1:m)*y;
for (int ii = 0; ii < m; ii++)
{
X.AccV(y[ii], V[ii]);
}
// compute residual: r = M \ ( b-A*x )
z.SetV(B);
Matrix.SpMV(-1.0, X, 1.0, z);
if (IterationCallback != null)
{
error2 = z.L2NormPow2().MPISum().Sqrt();
IterationCallback(iter, X.CloneAs(), z.CloneAs(), this.m_mgop);
//IterationCallback(this.NoOfIterations, X.CloneAs(), z.CloneAs(), this.m_mgop);
}
if (this.Precond != null)
{
r.Clear();
this.Precond.Solve(r, z);
}
else
{
r.SetV(z);
}
norm_r = r.L2NormPow2().MPISum().Sqrt();
s[i + 1 - 1] = norm_r;
error = s[i + 1 - 1] / bnrm2; // % check convergence
// if (error2 <= m_Tolerance) Check for error not error2
//break;
}
if (IterationCallback != null)
{
z.SetV(B);
Matrix.SpMV(-1.0, X, 1.0, z);
IterationCallback(iter, X.CloneAs(), z.CloneAs(), this.m_mgop);
}
if (!object.ReferenceEquals(_X, X))
{
_X.SetV(X);
}
B.SetV(z);
}
}
/// <summary>
/// %
/// </summary>
public void Solve <U, V>(U X, V B)
where U : IList <double>
where V : IList <double> //
{
using (var tr = new FuncTrace()) {
double[] Residual = this.TestSolution ? B.ToArray() : null;
string SolverName = "NotSet";
using (var solver = GetSolver(m_Mtx)) {
SolverName = solver.GetType().FullName;
//Console.Write("Direct solver run {0}, using {1} ... ", IterCnt, solver.GetType().Name);
IterCnt++;
solver.Solve(X, B);
//Console.WriteLine("done.");
}
m_ThisLevelIterations++;
if (Residual != null)
{
//Console.Write("Checking residual (run {0}) ... ", IterCnt - 1);
double RhsNorm = Residual.L2NormPow2().MPISum().Sqrt();
double MatrixInfNorm = m_Mtx.InfNorm();
m_Mtx.SpMV(-1.0, X, 1.0, Residual);
double ResidualNorm = Residual.L2NormPow2().MPISum().Sqrt();
double SolutionNorm = X.L2NormPow2().MPISum().Sqrt();
double Denom = Math.Max(MatrixInfNorm, Math.Max(RhsNorm, Math.Max(SolutionNorm, Math.Sqrt(double.Epsilon))));
double RelResidualNorm = ResidualNorm / Denom;
//Console.WriteLine("done: Abs.: {0}, Rel.: {1}", ResidualNorm, RelResidualNorm);
if (RelResidualNorm > 1.0e-10)
{
//Console.WriteLine("High residual from direct solver: abs {0}, rel {1}", ResidualNorm , ResidualNorm / SolutionNorm);
m_Mtx.SaveToTextFileSparse("Mtx.txt");
X.SaveToTextFile("X.txt");
B.SaveToTextFile("B.txt");
string ErrMsg;
using (var stw = new StringWriter()) {
stw.WriteLine("High residual from direct solver (using {0}).", SolverName);
stw.WriteLine(" L2 Norm of RHS: " + RhsNorm);
stw.WriteLine(" L2 Norm of Solution: " + SolutionNorm);
stw.WriteLine(" L2 Norm of Residual: " + ResidualNorm);
stw.WriteLine(" Relative Residual norm: " + RelResidualNorm);
stw.WriteLine(" Matrix Inf norm: " + MatrixInfNorm);
stw.WriteLine("Dumping text versions of Matrix, Solution and RHS.");
ErrMsg = stw.ToString();
}
Console.WriteLine(ErrMsg);
}
}
if (this.IterationCallback != null)
{
double[] _xl = X.ToArray();
double[] _bl = B.ToArray();
m_Mtx.SpMV(-1.0, _xl, 1.0, _bl);
this.IterationCallback(1, _xl, _bl, this.m_MultigridOp);
}
}
}
public static void XDG_MatrixPolynomialRestAndPrlgTest(
[Values(0, 1, 2, 3)] int p,
[Values(0.0, 0.3)] double AggregationThreshold,
[Values(0, 1)] int TrackerWidth)
{
XQuadFactoryHelper.MomentFittingVariants variant = XQuadFactoryHelper.MomentFittingVariants.OneStepGaussAndStokes;
var xt = new XDGTestSetup(p, AggregationThreshold, TrackerWidth, MultigridOperator.Mode.Eye, variant);
// test matrix version of the restriction operator
// -----------------------------------------------
List <MultigridMapping> MultigridMaps = new List <MultigridMapping>();
for (var mgop = xt.XdgMultigridOp; mgop != null; mgop = mgop.CoarserLevel)
{
MultigridMaps.Add(mgop.Mapping);
}
for (int iLevel = 0; iLevel < MgSeq.Length; iLevel++)
{
MultigridMapping mgMap = MultigridMaps[iLevel];
var XAggBasis = mgMap.AggBasis[0];
// set the test field:
XDGField Test = new XDGField(xt.XB, "Test");
Random rand = new Random();
for (int i = 0; i < Test.CoordinateVector.Count; i++)
{
Test.CoordinateVector[i] = rand.NextDouble();
}
xt.agg.ClearAgglomerated(Test.CoordinateVector, Test.Mapping);
// do restriction/prolongation (Reference)
double[] RestVecRef = new double[XAggBasis.LocalDim];
XAggBasis.RestictFromFullGrid(Test.CoordinateVector, RestVecRef);
// and now with the matrix:
BlockMsrMatrix RestMtx = new BlockMsrMatrix(mgMap, mgMap.ProblemMapping);
XAggBasis.GetRestrictionMatrix(RestMtx, mgMap, 0);
double[] RestVec = new double[mgMap.LocalLength];
RestMtx.SpMV(1.0, Test.CoordinateVector, 0.0, RestVec);
double[] X1 = new double[xt.XdgMultigridOp.Mapping.LocalLength];
XDGField X2 = new XDGField(Test.Basis);
xt.XdgMultigridOp.TransformSolInto(Test.CoordinateVector, X1);
xt.XdgMultigridOp.TransformSolFrom(X2.CoordinateVector, X1);
//xt.agg.Extrapolate(X2.CoordinatesAsVector, X2.Mapping);
var ERR2 = Test.CloneAs();
ERR2.Acc(-1.0, X2);
double ERR2Norm = ERR2.L2Norm();
//Console.WriteLine("MultigridOperator TranformInto/FransformFrom mismatch: " + ERR2Norm);
Assert.LessOrEqual(ERR2Norm, 1.0e-8);
// compare
double ERR = 0.0;
int Nmax = XAggBasis.MaximalLength;
for (int jAgg = 0; jAgg < mgMap.AggGrid.iLogicalCells.NoOfLocalUpdatedCells; jAgg++)
{
int i0Ref = jAgg * Nmax;
int i0Tst = mgMap.LocalUniqueIndex(0, jAgg, 0);
int N = mgMap.GetLength(jAgg);
for (int n = 0; n < N; n++)
{
double dist = RestVecRef[i0Ref + n] - RestVec[i0Tst + n];
ERR += dist.Pow2();
}
}
Console.WriteLine("Restriction matrix test (iLevel = {0}): {1}", iLevel, ERR);
Assert.LessOrEqual(ERR, 1.0e-8);
//
double[] PrlgVecA = new double[XAggBasis.LocalDim];
double[] PrlgVecB = new double[mgMap.LocalLength];
for (int jAgg = 0; jAgg < mgMap.AggGrid.iLogicalCells.NoOfLocalUpdatedCells; jAgg++)
{
int i0Ref = jAgg * Nmax;
int i0Tst = mgMap.LocalUniqueIndex(0, jAgg, 0);
int N = mgMap.GetLength(jAgg);
for (int n = 0; n < N; n++)
{
double rndVal = rand.NextDouble();
PrlgVecA[i0Ref + n] = rndVal;
PrlgVecB[i0Tst + n] = rndVal;
}
}
XDGField QA = new XDGField(Test.Basis);
XDGField QB = new XDGField(Test.Basis);
XAggBasis.ProlongateToFullGrid(QA.CoordinateVector, PrlgVecA);
var PrlgMtx = RestMtx.Transpose();
PrlgMtx.SpMV(1.0, PrlgVecB, 0.0, QB.CoordinateVector);
XDGField ERR5 = QA.CloneAs();
ERR5.Acc(-1.0, QB);
double ERR5_Norm = ERR5.L2Norm();
Console.WriteLine("Prolongation matrix test (iLevel = {0}): {1}", iLevel, ERR5_Norm);
Assert.LessOrEqual(ERR5_Norm, 1.0e-8);
}
}
/// <summary>
///
/// </summary>
public void AssembleMatrix_Timestepper <T>(
int CutCellQuadOrder,
BlockMsrMatrix OpMatrix, double[] OpAffine,
Dictionary <SpeciesId, MultidimensionalArray> AgglomeratedCellLengthScales,
IEnumerable <T> CurrentState,
VectorField <SinglePhaseField> SurfaceForce,
VectorField <SinglePhaseField> LevelSetGradient, SinglePhaseField ExternalyProvidedCurvature,
UnsetteledCoordinateMapping RowMapping, UnsetteledCoordinateMapping ColMapping,
double time, IEnumerable <T> CoupledCurrentState = null, IEnumerable <T> CoupledParams = null) where T : DGField
{
if (ColMapping.BasisS.Count != this.Op.DomainVar.Count)
{
throw new ArgumentException();
}
if (RowMapping.BasisS.Count != this.Op.CodomainVar.Count)
{
throw new ArgumentException();
}
// check:
var Tracker = this.LsTrk;
int D = Tracker.GridDat.SpatialDimension;
if (CurrentState != null && CurrentState.Count() != (D + 1))
{
throw new ArgumentException();
}
if (OpMatrix == null && CurrentState == null)
{
throw new ArgumentException();
}
DGField[] U0;
if (CurrentState != null)
{
U0 = CurrentState.Take(D).ToArray();
}
else
{
U0 = null;
}
LevelSet Phi = (LevelSet)(Tracker.LevelSets[0]);
SpeciesId[] SpcToCompute = AgglomeratedCellLengthScales.Keys.ToArray();
IDictionary <SpeciesId, MultidimensionalArray> InterfaceLengths = this.LsTrk.GetXDGSpaceMetrics(this.LsTrk.SpeciesIdS.ToArray(), CutCellQuadOrder).CutCellMetrics.InterfaceArea;
// advanced settings for the navier slip boundary condition
// ========================================================
CellMask SlipArea;
switch (this.dntParams.GNBC_Localization)
{
case NavierSlip_Localization.Bulk: {
SlipArea = this.LsTrk.GridDat.BoundaryCells.VolumeMask;
break;
}
case NavierSlip_Localization.ContactLine: {
SlipArea = null;
break;
}
case NavierSlip_Localization.Nearband: {
SlipArea = this.LsTrk.GridDat.BoundaryCells.VolumeMask.Intersect(this.LsTrk.Regions.GetNearFieldMask(this.LsTrk.NearRegionWidth));
break;
}
case NavierSlip_Localization.Prescribed: {
throw new NotImplementedException();
}
default:
throw new ArgumentException();
}
MultidimensionalArray SlipLengths;
SlipLengths = this.LsTrk.GridDat.Cells.h_min.CloneAs();
SlipLengths.Clear();
//SlipLengths.AccConstant(-1.0);
if (SlipArea != null)
{
foreach (Chunk cnk in SlipArea)
{
for (int i = cnk.i0; i < cnk.JE; i++)
{
switch (this.dntParams.GNBC_SlipLength)
{
case NavierSlip_SlipLength.hmin_DG: {
int degU = ColMapping.BasisS.ToArray()[0].Degree;
SlipLengths[i] = this.LsTrk.GridDat.Cells.h_min[i] / (degU + 1);
break;
}
case NavierSlip_SlipLength.hmin_Grid: {
SlipLengths[i] = SlipLengths[i] = this.LsTrk.GridDat.Cells.h_min[i];
break;
}
case NavierSlip_SlipLength.Prescribed_SlipLength: {
SlipLengths[i] = this.physParams.sliplength;
break;
}
case NavierSlip_SlipLength.Prescribed_Beta: {
SlipLengths[i] = -1.0;
break;
}
}
}
}
}
// parameter assembly
// ==================
// normals:
SinglePhaseField[] Normals; // Normal vectors: length not normalized - will be normalized at each quad node within the flux functions.
if (this.NormalsRequired)
{
if (LevelSetGradient == null)
{
LevelSetGradient = new VectorField <SinglePhaseField>(D, Phi.Basis, SinglePhaseField.Factory);
LevelSetGradient.Gradient(1.0, Phi);
}
Normals = LevelSetGradient.ToArray();
}
else
{
Normals = new SinglePhaseField[D];
}
// curvature:
SinglePhaseField Curvature;
if (this.CurvatureRequired)
{
Curvature = ExternalyProvidedCurvature;
}
else
{
Curvature = null;
}
// linearization velocity:
DGField[] U0_U0mean;
if (this.U0meanrequired)
{
XDGBasis U0meanBasis = new XDGBasis(Tracker, 0);
VectorField <XDGField> U0mean = new VectorField <XDGField>(D, U0meanBasis, "U0mean_", XDGField.Factory);
U0_U0mean = ArrayTools.Cat <DGField>(U0, U0mean);
}
else
{
U0_U0mean = new DGField[2 * D];
}
// Temperature gradient for evaporation
VectorField <DGField> GradTemp = new VectorField <DGField>(D, new XDGBasis(LsTrk, 0), XDGField.Factory);
if (CoupledCurrentState != null)
{
DGField Temp = CoupledCurrentState.ToArray()[0];
GradTemp = new VectorField <DGField>(D, Temp.Basis, "GradTemp", XDGField.Factory);
XNSEUtils.ComputeGradientForParam(Temp, GradTemp, this.LsTrk);
}
// concatenate everything
var Params = ArrayTools.Cat <DGField>(
U0_U0mean,
Curvature,
((SurfaceForce != null) ? SurfaceForce.ToArray() : new SinglePhaseField[D]),
Normals,
((evaporation) ? GradTemp.ToArray() : new SinglePhaseField[D]),
((evaporation) ? CoupledCurrentState.ToArray <DGField>() : new SinglePhaseField[1]),
((evaporation) ? CoupledParams.ToArray <DGField>() : new SinglePhaseField[1])); //((evaporation) ? GradTemp.ToArray() : new SinglePhaseField[D]));
// linearization velocity:
if (this.U0meanrequired)
{
VectorField <XDGField> U0mean = new VectorField <XDGField>(U0_U0mean.Skip(D).Take(D).Select(f => ((XDGField)f)).ToArray());
U0mean.Clear();
if (this.physParams.IncludeConvection)
{
ComputeAverageU(U0, U0mean, CutCellQuadOrder, LsTrk.GetXDGSpaceMetrics(SpcToCompute, CutCellQuadOrder, 1).XQuadSchemeHelper);
}
}
// assemble the matrix & affine vector
// ===================================
// compute matrix
if (OpMatrix != null)
{
//Op.ComputeMatrixEx(Tracker,
// ColMapping, Params, RowMapping,
// OpMatrix, OpAffine, false, time, true,
// AgglomeratedCellLengthScales,
// InterfaceLengths, SlipLengths,
// SpcToCompute);
XSpatialOperator.XEvaluatorLinear mtxBuilder = Op.GetMatrixBuilder(LsTrk, ColMapping, Params, RowMapping, SpcToCompute);
foreach (var kv in AgglomeratedCellLengthScales)
{
mtxBuilder.SpeciesOperatorCoefficients[kv.Key].CellLengthScales = kv.Value;
mtxBuilder.SpeciesOperatorCoefficients[kv.Key].UserDefinedValues.Add("SlipLengths", SlipLengths);
if (evaporation)
{
BitArray EvapMicroRegion = new BitArray(this.LsTrk.GridDat.Cells.Count);; // this.LsTrk.GridDat.GetBoundaryCells().GetBitMask();
mtxBuilder.SpeciesOperatorCoefficients[kv.Key].UserDefinedValues.Add("EvapMicroRegion", EvapMicroRegion);
}
}
if (Op.SurfaceElementOperator.TotalNoOfComponents > 0)
{
foreach (var kv in InterfaceLengths)
{
mtxBuilder.SpeciesOperatorCoefficients[kv.Key].UserDefinedValues.Add("InterfaceLengths", kv.Value);
}
}
mtxBuilder.time = time;
mtxBuilder.ComputeMatrix(OpMatrix, OpAffine);
#if DEBUG
// remark: remove this piece in a few months from now on (09may18) if no problems occur
{
BlockMsrMatrix checkOpMatrix = new BlockMsrMatrix(RowMapping, ColMapping);
double[] checkAffine = new double[OpAffine.Length];
Op.ComputeMatrixEx(Tracker,
ColMapping, Params, RowMapping,
OpMatrix, OpAffine, false, time, true,
AgglomeratedCellLengthScales,
InterfaceLengths, SlipLengths,
SpcToCompute);
double[] checkResult = checkAffine.CloneAs();
var currentVec = new CoordinateVector(CurrentState.ToArray());
checkOpMatrix.SpMV(1.0, new CoordinateVector(CurrentState.ToArray()), 1.0, checkResult);
double L2_dist = GenericBlas.L2DistPow2(checkResult, OpAffine).MPISum().Sqrt();
double RefNorm = (new double[] { checkResult.L2NormPow2(), OpAffine.L2NormPow2(), currentVec.L2NormPow2() }).MPISum().Max().Sqrt();
Assert.LessOrEqual(L2_dist, RefNorm * 1.0e-6);
Debug.Assert(L2_dist < RefNorm * 1.0e-6);
}
#endif
}
else
{
XSpatialOperator.XEvaluatorNonlin eval = Op.GetEvaluatorEx(Tracker,
CurrentState.ToArray(), Params, RowMapping,
SpcToCompute);
foreach (var kv in AgglomeratedCellLengthScales)
{
eval.SpeciesOperatorCoefficients[kv.Key].CellLengthScales = kv.Value;
eval.SpeciesOperatorCoefficients[kv.Key].UserDefinedValues.Add("SlipLengths", SlipLengths);
if (evaporation)
{
BitArray EvapMicroRegion = new BitArray(this.LsTrk.GridDat.Cells.Count);
eval.SpeciesOperatorCoefficients[kv.Key].UserDefinedValues.Add("EvapMicroRegion", EvapMicroRegion);
}
}
if (Op.SurfaceElementOperator.TotalNoOfComponents > 0)
{
foreach (var kv in InterfaceLengths)
{
eval.SpeciesOperatorCoefficients[kv.Key].UserDefinedValues.Add("InterfaceLengths", kv.Value);
}
}
eval.time = time;
eval.Evaluate(1.0, 1.0, OpAffine);
}
// check
// =====
/*
* {
* DGField[] testDomainFieldS = ColMapping.BasisS.Select(bb => new XDGField(bb as XDGBasis)).ToArray();
* CoordinateVector test = new CoordinateVector(testDomainFieldS);
*
* DGField[] errFieldS = ColMapping.BasisS.Select(bb => new XDGField(bb as XDGBasis)).ToArray();
* CoordinateVector Err = new CoordinateVector(errFieldS);
*
* var eval = Op.GetEvaluatorEx(LsTrk,
* testDomainFieldS, Params, RowMapping);
*
* foreach (var s in this.LsTrk.SpeciesIdS)
* eval.SpeciesOperatorCoefficients[s].CellLengthScales = AgglomeratedCellLengthScales[s];
*
* eval.time = time;
* int L = test.Count;
* Random r = new Random();
* for(int i = 0; i < L; i++) {
* test[i] = r.NextDouble();
* }
*
*
*
* double[] R1 = new double[L];
* double[] R2 = new double[L];
* eval.Evaluate(1.0, 1.0, R1);
*
* R2.AccV(1.0, OpAffine);
* OpMatrix.SpMV(1.0, test, 1.0, R2);
*
* Err.AccV(+1.0, R1);
* Err.AccV(-1.0, R2);
*
* double ErrDist = GenericBlas.L2DistPow2(R1, R2).MPISum().Sqrt();
*
* double Ref = test.L2NormPow2().MPISum().Sqrt();
*
* Debug.Assert(ErrDist <= Ref*1.0e-5, "Mismatch between explicit evaluation of XDG operator and matrix.");
* }
*/
}
