/// <summary>
/// Constructor for XDG solvers
/// </summary>
public OpAnalysisBase(LevelSetTracker LsTrk, BlockMsrMatrix Mtx, double[] RHS, UnsetteledCoordinateMapping Mapping, MultiphaseCellAgglomerator CurrentAgglomeration, BlockMsrMatrix _mass, IEnumerable <MultigridOperator.ChangeOfBasisConfig[]> OpConfig, ISpatialOperator abstractOperator)
{
int RHSlen = Mapping.TotalLength;
m_map = Mapping; // mapping
VarGroup = Mapping.BasisS.Count.ForLoop(i => i); //default: all dependent variables are included in operator matrix
m_LsTrk = LsTrk;
m_OpMtx = Mtx.CloneAs();
localRHS = RHS.CloneAs();
// create the Dummy XDG aggregation basis
var baseGrid = Mapping.GridDat;
var mgSeq = Foundation.Grid.Aggregation.CoarseningAlgorithms.CreateSequence(baseGrid, 1);
AggregationGridBasis[][] XAggB = AggregationGridBasis.CreateSequence(mgSeq, Mapping.BasisS);
//
XAggB.UpdateXdgAggregationBasis(CurrentAgglomeration);
// create multigrid operator
m_MultigridOp = new MultigridOperator(XAggB, Mapping,
m_OpMtx,
_mass,
OpConfig,
abstractOperator.DomainVar.Select(varName => abstractOperator.FreeMeanValue[varName]).ToArray());
}
public static void MapConsistencyTest(
[Values(XDGusage.none, XDGusage.all)] XDGusage UseXdg,
[Values(2)] int DGOrder
)
{
//if no selection is chosen mapping should be the same as of origin
//assume: indexing is right 'cause of other tests
Utils.TestInit((int)UseXdg, DGOrder);
Console.WriteLine("MapConsistencyTest({0},{1})", UseXdg, DGOrder);
//Arrange
MultigridOperator MGOp = Utils.CreateTestMGOperator(UseXdg, DGOrder);
var sbs = new SubBlockSelector(MGOp.Mapping);
var mask = new BlockMask(sbs);
var stw = new Stopwatch();
stw.Restart();
//Act --- Create Mapping from mask
stw.Start();
var submatrix = mask.GetSubBlockMatrix(MGOp.OperatorMatrix);
stw.Stop();
var rowpart = submatrix._RowPartitioning;
var colpart = submatrix._ColPartitioning;
//Assert --- Equal Partition of mask and origin
Assert.AreEqual(rowpart, colpart);
Assert.IsTrue(rowpart.IsLocallyEqual(MGOp.Mapping));
}
private static void MgConsistencyTestRec(MultigridOperator mgOp, double[] mgSolVec, double[] mgRhsVec)
{
double[] mgResidual = mgRhsVec.CloneAs();
mgOp.OperatorMatrix.SpMV(1.0, mgSolVec, -1.0, mgResidual);
double scale = 1.0 / (mgRhsVec.L2Norm() + mgSolVec.L2Norm());
int DOFs = mgOp.Mapping.TotalLength;
Debug.Assert(DOFs == mgOp.OperatorMatrix.NoOfRows);
Debug.Assert(DOFs == mgOp.OperatorMatrix.NoOfCols);
double mgResidual_l2Norm = mgResidual.L2Norm();
Console.WriteLine("Multigrid Residual norm, level {0}: {1} ({2} DOFs)", mgOp.LevelIndex, mgResidual_l2Norm, DOFs);
Assert.LessOrEqual(scale * mgResidual_l2Norm, 1.0e-8);
if (mgOp.CoarserLevel != null)
{
double[] mgCoarseSolVec = new double[mgOp.CoarserLevel.Mapping.LocalLength];
double[] mgCoarseRhsVec = new double[mgOp.CoarserLevel.Mapping.LocalLength];
mgOp.CoarserLevel.Restrict(mgSolVec, mgCoarseSolVec);
mgOp.CoarserLevel.Restrict(mgRhsVec, mgCoarseRhsVec);
MgConsistencyTestRec(mgOp.CoarserLevel, mgCoarseSolVec, mgCoarseRhsVec);
}
}
/// <summary>
/// Restricts some solution vector down to a certain multigrid level and prolongates it back.
/// </summary>
/// <param name="i">
/// Multigrid level index; usually 0 at start of recursion.
/// </param>
/// <param name="iEnd">
/// End level index.
/// </param>
/// <param name="mgOp"></param>
/// <param name="FineIn">
/// Input; solution vector which will be restricted down to level <paramref name="iEnd"/>.
/// </param>
/// <param name="FineOut">
/// Output; vector <paramref name="FineIn"/> restricted to level <paramref name="iEnd"/>, and prolongated back to level <paramref name="i"/>.
/// </param>
static void XDG_Recursive(int i, int iEnd, MultigridOperator mgOp, double[] FineIn, double[] FineOut)
{
MultigridMapping mgMap = mgOp.Mapping;
int Lfin = mgMap.LocalLength;
int Lcrs = mgOp.CoarserLevel.Mapping.LocalLength;
Assert.IsTrue(FineIn.Length == Lfin);
Assert.IsTrue(FineOut.Length == Lfin);
double[] Coarse1 = new double[Lcrs];
double[] Coarse2 = new double[Lcrs];
mgOp.CoarserLevel.Restrict(FineIn, Coarse1);
if (i == iEnd)
{
Coarse2.SetV(Coarse1);
}
else
{
XDG_Recursive(i + 1, iEnd, mgOp.CoarserLevel, Coarse1, Coarse2);
}
mgOp.CoarserLevel.Prolongate(1.0, FineOut, 0.0, Coarse2);
}
public static void GetExternalRowsTest(
[Values(XDGusage.none, XDGusage.all)] XDGusage UseXdg,
[Values(2)] int DGOrder,
[Values(4)] int Res)
{
//Matlabaufruf --> gesamte Matrix nach Matlab schreiben
//Teilmatritzen gemäß Globalid extrahieren
//Mit ExternalRows vergleichen
//Die große Frage: funktioniert der batchmode connector parallel? Beim rausschreiben beachten
Utils.TestInit((int)UseXdg, DGOrder);
Console.WriteLine("GetExternalRowsTest({0},{1})", UseXdg, DGOrder);
//Arrange --- setup mgo and mask
MultigridOperator mgo = Utils.CreateTestMGOperator(UseXdg, DGOrder, MatrixShape.laplace, Res);
MultigridMapping map = mgo.Mapping;
BlockMsrMatrix M = mgo.OperatorMatrix;
//Delete this plz ...
//M.SaveToTextFileSparse("M");
//int[] A = Utils.GimmeAllBlocksWithSpec(map, 9);
//int[] B = Utils.GimmeAllBlocksWithSpec(map, 18);
//if (map.MpiRank == 0) {
// A.SaveToTextFileDebug("ACells");
// B.SaveToTextFileDebug("BCells");
//}
var selector = new SubBlockSelector(map);
var dummy = new BlockMsrMatrix(map); // we are only interested in getting indices, so a dummy is sufficient
var mask = new BlockMask(selector, dummy);
//Arrange --- get stuff to put into matlab
int[] GlobalIdx_ext = Utils.GetAllExtCellIdc(map);
double[] GlobIdx = GlobalIdx_ext.Length.ForLoop(i => (double)GlobalIdx_ext[i] + 1.0);
//Arrange --- get external rows by mask
BlockMsrMatrix extrows = BlockMask.GetAllExternalRows(mgo.Mapping, mgo.OperatorMatrix);
//Assert --- idc and rows of extrows have to be the same
Assert.IsTrue(GlobIdx.Length == extrows._RowPartitioning.LocalLength);
//Arrange --- get external rows by matlab
var infNorm = MultidimensionalArray.Create(1, 1);
using (BatchmodeConnector matlab = new BatchmodeConnector()) {
//note: BatchmodeCon maybe working on proc0 but savetotxt file, etc. (I/O) is full mpi parallel
//so concider this as full mpi-parallel
matlab.PutSparseMatrix(M, "M");
matlab.PutSparseMatrix(extrows, "M_test");
matlab.PutVector(GlobIdx, "Idx");
matlab.Cmd(String.Format("M_ext = M(Idx, :);"));
matlab.Cmd("n=norm(M_test-M_ext,inf)");
matlab.GetMatrix(infNorm, "n");
matlab.Execute();
}
//Assert --- test if we actually got the right Matrix corresponding to Index
Assert.IsTrue(infNorm[0, 0] == 0.0);
}
public static void SubSelection(
[Values(XDGusage.none, XDGusage.all)] XDGusage UseXdg,
[Values(2)] int DGOrder,
[Values(MatrixShape.full_var_spec, MatrixShape.full_spec, MatrixShape.full_var, MatrixShape.full)] MatrixShape MShape,
[Values(4)] int Res)
{
Utils.TestInit((int)UseXdg, DGOrder, (int)MShape, Res);
Console.WriteLine("SubSelection({0},{1},{2},{3})", UseXdg, DGOrder, MShape, Res);
//Arrange --- create test matrix, MG mapping
MultigridOperator mgo = Utils.CreateTestMGOperator(UseXdg, DGOrder, MShape, Res);
MultigridMapping map = mgo.Mapping;
BlockMsrMatrix M = mgo.OperatorMatrix;
//Arrange --- get mask
int[] cells = Utils.GetCellsOfOverlappingTestBlock(map);
Array.Sort(cells);
var sbs = new SubBlockSelector(map);
sbs.CellSelector(cells, false);
BlockMsrMatrix M_ext = BlockMask.GetAllExternalRows(map, M);
var mask = new BlockMask(sbs, M_ext);
//Arrange --- get GlobalIdxList
int[] idc = Utils.GetIdcOfSubBlock(map, cells);
bool[] coup = Utils.SetCoupling(MShape);
var M_sub = mask.GetSubBlockMatrix(M, false, coup[0], coup[1]);
var infNorm = MultidimensionalArray.Create(4, 1);
int rank = map.MpiRank;
using (BatchmodeConnector matlab = new BatchmodeConnector()) {
double[] GlobIdx = idc.Count().ForLoop(i => (double)idc[i] + 1.0);
Assert.IsTrue(GlobIdx.Length == M_sub.NoOfRows);
matlab.PutSparseMatrix(M, "M");
// note: M_sub lives on Comm_Self, therefore we have to distinguish between procs ...
matlab.PutSparseMatrixRankExclusive(M_sub, "M_sub");
matlab.PutVectorRankExclusive(GlobIdx, "Idx");
matlab.Cmd("M_0 = full(M(Idx_0, Idx_0));");
matlab.Cmd("M_1 = full(M(Idx_1, Idx_1));");
matlab.Cmd("M_2 = full(M(Idx_2, Idx_2));");
matlab.Cmd("M_3 = full(M(Idx_3, Idx_3));");
matlab.Cmd("n=[0; 0; 0; 0];");
matlab.Cmd("n(1,1)=norm(M_0-M_sub_0,inf);");
matlab.Cmd("n(2,1)=norm(M_1-M_sub_1,inf);");
matlab.Cmd("n(3,1)=norm(M_2-M_sub_2,inf);");
matlab.Cmd("n(4,1)=norm(M_3-M_sub_3,inf);");
matlab.GetMatrix(infNorm, "n");
matlab.Execute();
}
Assert.IsTrue(infNorm[rank, 0] == 0.0);
}
private static List <ChangeOfBasisConfig[]> MgDescend(MultigridOperator mgo, List <ChangeOfBasisConfig[]> cobc)
{
cobc.Add(mgo.Config);
if (mgo.CoarserLevel != null)
{
return(MgDescend(mgo.CoarserLevel, cobc));
}
else
{
return(cobc);
}
}
public void Init(MultigridOperator op)
{
this.m_MgOp = op;
int D = this.LsTrk.GridDat.SpatialDimension;
int[] VelVarIdx = D.ForLoop(d => d);
this.USubMatrixIdx_Row = this.m_MgOp.Mapping.GetSubvectorIndices(VelVarIdx);
this.PSubMatrixIdx_Row = this.m_MgOp.Mapping.GetSubvectorIndices(new int[] { D });
this.ExtractMatrices();
}
private static List <AggregationGridBasis[]> MgDescend(MultigridOperator mgo, List <AggregationGridBasis[]> agggb)
{
agggb.Add(mgo.Mapping.AggBasis);
if (mgo.CoarserLevel != null)
{
return(MgDescend(mgo.CoarserLevel, agggb));
}
else
{
return(agggb);
}
}
public static void VectorSplitOperation(
[Values(XDGusage.none, XDGusage.all)] XDGusage UseXdg,
[Values(2)] int DGOrder,
[Values(MatrixShape.full_var_spec, MatrixShape.full_spec, MatrixShape.full)] MatrixShape MShape,
[Values(4)] int Res)
{
Utils.TestInit((int)UseXdg, DGOrder, (int)MShape, Res);
Console.WriteLine("VectorSplitOperation({0},{1},{2},{3})", UseXdg, DGOrder, MShape, Res);
//Arrange --- create test matrix, MG mapping
MultigridOperator mgo = Utils.CreateTestMGOperator(UseXdg, DGOrder, MShape, Res);
MultigridMapping map = mgo.Mapping;
BlockMsrMatrix M = mgo.OperatorMatrix;
BlockMsrMatrix M_ext = BlockMask.GetAllExternalRows(map, M);
double[] Vec = Utils.GetRandomVector(M_ext.RowPartitioning.LocalLength);
//Arrange --- setup masking
SubBlockSelector sbsA = new SubBlockSelector(map);
sbsA.SetDefaultSplitSelection(MShape, true, false);
BlockMask maskA = new BlockMask(sbsA, M_ext);
SubBlockSelector sbsB = new SubBlockSelector(map);
sbsB.SetDefaultSplitSelection(MShape, false, false);
BlockMask maskB = new BlockMask(sbsB, M_ext);
double[] VecAB = new double[Vec.Length];
//Arrange --- some time measurement
Stopwatch stw = new Stopwatch();
stw.Reset();
//Act ---
stw.Start();
var VecA = maskA.GetSubVec(Vec, new double[0]);
var VecB = maskB.GetSubVec(Vec, new double[0]);
maskA.AccSubVec(VecA, VecAB, new double[0]);
maskB.AccSubVec(VecB, VecAB, new double[0]);
stw.Stop();
Debug.Assert(Vec.L2Norm() != 0);
double fac = ((MShape == MatrixShape.full_var || MShape == MatrixShape.diagonal_var) && UseXdg == XDGusage.none) ? -2.0 : -1.0;
VecAB.AccV(fac, Vec);
//Assert --- are extracted blocks and
Assert.IsTrue(VecAB.L2Norm() == 0.0, String.Format("L2Norm neq 0!"));
}
private ConvergenceObserver ActivateCObserver(MultigridOperator mop, BlockMsrMatrix Massmatrix, SolverFactory SF, List <Action <int, double[], double[], MultigridOperator> > Callback)
{
Console.WriteLine("===Convergence Observer activated===");
//string AnalyseOutputpath = String.Join(@"\",this.Control.DbPath, this.CurrentSessionInfo.ID);
string AnalyseOutputpath = System.IO.Directory.GetCurrentDirectory();
var CO = new ConvergenceObserver(mop, Massmatrix, uEx.CoordinateVector.ToArray(), SF);
//CO.TecplotOut = String.Concat(AnalyseOutputpath, @"\Xdg_conv");
Callback.Add(CO.IterationCallback);
Console.WriteLine("Analysis output will be written to: {0}", AnalyseOutputpath);
Console.WriteLine("====================");
return(CO);
}
private void OperatorAnalysis()
{
AggregationGridBasis[][] XAggB = AggregationGridBasis.CreateSequence(base.MultigridSequence, u.Mapping.BasisS);
XAggB.UpdateXdgAggregationBasis(this.Op_Agglomeration);
var MultigridOp = new MultigridOperator(XAggB, this.u.Mapping,
this.Op_Matrix,
this.Op_mass.GetMassMatrix(new UnsetteledCoordinateMapping(this.u.Basis), false),
OpConfig);
var PcOpMatrix = MultigridOp.OperatorMatrix;
//PcOpMatrix.SaveToTextFileSparse("C:\\temp\\Xpoisson.txt");
MultidimensionalArray ret = MultidimensionalArray.Create(1, 4);
using (BatchmodeConnector bmc = new BatchmodeConnector()) {
bmc.PutSparseMatrix(PcOpMatrix, "OpMtx");
bmc.Cmd("OpMtxSym = 0.5*(OpMtx + OpMtx');");
bmc.Cmd("condNo = condest(OpMtxSym);");
bmc.Cmd("eigMaxi = eigs(OpMtxSym,1,'lm')");
bmc.Cmd("eigMini = eigs(OpMtxSym,1,'sm')");
bmc.Cmd("lasterr");
bmc.Cmd("[V,r]=chol(OpMtxSym);");
bmc.Cmd("ret = [condNo, eigMaxi, eigMini, r]");
bmc.GetMatrix(ret, "ret");
bmc.Execute(false);
}
double condNo = ret[0, 0];
double eigMaxi = ret[0, 1];
double eigMini = ret[0, 2];
double posDef = ret[0, 3] == 0 ? 1 : 0;
Console.WriteLine("Condition number: {0:0.####E-00}", condNo);
if (posDef == 0.0)
{
Console.WriteLine("WARNING: Operator matrix is not positive definite.");
}
base.QueryHandler.ValueQuery("condNo", condNo, false);
base.QueryHandler.ValueQuery("eigMaxi", eigMaxi, false);
base.QueryHandler.ValueQuery("eigMini", eigMini, false);
base.QueryHandler.ValueQuery("posDef", posDef, false);
}
public static void SubMatrixExtractionWithCoupling(
[Values(XDGusage.none, XDGusage.all)] XDGusage UseXdg,
[Values(2)] int DGOrder,
[Values(MatrixShape.diagonal, MatrixShape.diagonal_var, MatrixShape.full_spec, MatrixShape.full_var_spec)] MatrixShape MShape
)
{
Utils.TestInit((int)UseXdg, DGOrder, (int)MShape);
Console.WriteLine("ExtractSubMatrixAndIgnoreCoupling({0},{1},{2})", UseXdg, DGOrder, MShape);
//Arrange --- get multigridoperator
MultigridOperator MGOp = Utils.CreateTestMGOperator(UseXdg, DGOrder, MShape);
BlockMsrMatrix M = MGOp.OperatorMatrix;
MultigridMapping map = MGOp.Mapping;
//Arrange --- setup masking
SubBlockSelector SBS = new SubBlockSelector(map);
BlockMask mask = new BlockMask(SBS, null);
bool[] coup = Utils.SetCoupling(MShape);
//Arrange --- some time measurement
Stopwatch stw = new Stopwatch();
stw.Reset();
//Act --- establish submatrix
stw.Start();
//var Ones = M.CloneAs();
//Ones.Clear();
//Ones.SetAll(1);
//var extractOnes = mask.GetSubBlockMatrix(Ones, false, coup[0], coup[1]);
var Mext = mask.GetSubBlockMatrix(M, false, coup[0], coup[1]);
stw.Stop();
var Mquad = M.ConvertToQuadraticBMsr(mask.GlobalIList_Internal.ToArray(), true);
Mext.Acc(-1.0, Mquad);
//Assert --- Mext conains only diagonal blocks of M
Assert.IsTrue(Mext.InfNorm() == 0);
}
public void Init(MultigridOperator op)
{
this.m_MgOp = op;
int D = this.LsTrk.GridDat.SpatialDimension;
int[] VelVarIdx = D.ForLoop(d => d);
this.USubMatrixIdx_Row = this.m_MgOp.Mapping.GetSubvectorIndices(VelVarIdx);
this.PSubMatrixIdx_Row = this.m_MgOp.Mapping.GetSubvectorIndices(new int[] { D });
this.USpcSubMatrix_Row = new int[this.LsTrk.SpeciesIdS.Count][];
this.PSpcSubMatrix_Row = new int[this.LsTrk.SpeciesIdS.Count][];
for (int iSpc = 0; iSpc < this.LsTrk.SpeciesIdS.Count; iSpc++)
{
this.USpcSubMatrix_Row[iSpc] = this.m_MgOp.Mapping.GetSubvectorIndices(this.LsTrk.SpeciesIdS[iSpc], VelVarIdx);
this.PSpcSubMatrix_Row[iSpc] = this.m_MgOp.Mapping.GetSubvectorIndices(this.LsTrk.SpeciesIdS[iSpc], D);
}
this.ExtractMatrices();
this.ApproximationMatrix();
}
public static void ExternalIndexTest(
[Values(XDGusage.none, XDGusage.all)] XDGusage UseXdg,
[Values(2)] int DGOrder,
[Values(4)] int Res
)
{
Utils.TestInit((int)UseXdg, DGOrder);
Console.WriteLine("ExternalIndexTest({0},{1})", UseXdg, DGOrder);
//Arrange --- Get global index by mapping
MultigridOperator MGOp = Utils.CreateTestMGOperator(UseXdg, DGOrder, MatrixShape.laplace, Res);
var map = MGOp.Mapping;
int[] GlobalIdxMap_ext = Utils.GetAllExtCellIdc(map);
//Arrange --- Prepare stuff for mask
var selector = new SubBlockSelector(map);
var dummy = new BlockMsrMatrix(map); // we are only interested in getting indices, so a dummy is sufficient
var stw = new Stopwatch();
stw.Reset();
//Act --- do the masking to get index lists
stw.Start();
var mask = new BlockMask(selector, dummy);
stw.Stop();
int[] GlobalIdxMask_ext = mask.GlobalIList_External.ToArray();
//Assert --- Idx lists are of same length
Assert.IsTrue(GlobalIdxMap_ext.Length == GlobalIdxMask_ext.Length);
//Assert --- Compare map and mask indices
for (int iLoc = 0; iLoc < GlobalIdxMask_ext.Length; iLoc++)
{
Assert.IsTrue(GlobalIdxMask_ext[iLoc] == GlobalIdxMap_ext[iLoc]);
}
}
public static BlockMsrMatrix GetCellCompMatrix(SelectionType SType, MultigridOperator mop, int iB)
{
int rank = mop.Mapping.MpiRank;
int iBlock = mop.Mapping.AggGrid.CellPartitioning.i0 + iB;
int i0 = mop.Mapping.GetBlockI0(iBlock);
//int jBlock = i0 + jB;
int R = mop.Mapping.GetBlockLen(iBlock);
//int C = mop.Mapping.GetBlockLen(jBlock);
bool ZwoSpecR = Math.Max(mop.Mapping.GetSubblkLen(0)[0], mop.Mapping.GetSubblkLen(1)[0]) == R;
//bool ZwoSpecC = (mop.Mapping.AggBasis[0].GetMaximalLength(DGdegree) + mop.Mapping.AggBasis[0].GetMaximalLength(DGdegree - 1)) == C;
SpeciesId A = ((XdgAggregationBasis)mop.Mapping.AggBasis[0]).UsedSpecies[0];
int Specpos = ((XdgAggregationBasis)mop.Mapping.AggBasis[0]).GetSpeciesIndex(iB, A);
int[] SubIdcR = GetSubIndices(SType, ZwoSpecR, Specpos);
//int[] SubIdcC = GetSubIndices(SType, ZwoSpecC);
for (int i = 0; i < SubIdcR.Length; i++)
{
Debug.Assert(SubIdcR[i] < R);
SubIdcR[i] += i0;
}
//for (int i = 0; i < SubIdcC.Length; i++) {
// Debug.Assert(SubIdcC[i] < C);
// SubIdcC[i] += i0;
//}
//return mop.OperatorMatrix.GetSubMatrix(SubIdcR, SubIdcC);
var part = new BlockPartitioning(SubIdcR.Length, new int[] { 0 }, new int[] { SubIdcR.Length }, csMPI.Raw._COMM.SELF);
BlockMsrMatrix sub = new BlockMsrMatrix(part);
mop.OperatorMatrix.WriteSubMatrixTo(sub, SubIdcR, default(int[]), SubIdcR, default(int[]));
return(sub);
//return mop.OperatorMatrix.GetSubMatrix(SubIdcR, SubIdcR);
}
public static void LocalIndexTest(
[Values(XDGusage.none, XDGusage.all)] XDGusage UseXdg,
[Values(2)] int DGOrder)
{
Utils.TestInit((int)UseXdg, DGOrder);
Console.WriteLine("LocalLIndexTest({0},{1})", UseXdg, DGOrder);
//Arrange --- Get global index by mapping
MultigridOperator MGOp = Utils.CreateTestMGOperator(UseXdg, DGOrder);
var map = MGOp.Mapping;
int[] fields = map.NoOfVariables.ForLoop(i => i);
int[] GlobalIdxMap_loc = map.GetSubvectorIndices(fields);
//Arrange --- Prepare stuff for mask
var selector = new SubBlockSelector(map);
var stw = new Stopwatch();
stw.Reset();
//Act --- do the masking to get index lists
stw.Start();
var mask = new BlockMask(selector, null);
stw.Stop();
int[] GlobalIdxMask_loc = mask.GlobalIList_Internal.ToArray();
//Assert --- Idx lists are of same length
Assert.IsTrue(GlobalIdxMap_loc.Length == GlobalIdxMask_loc.Length);
//Assert --- Compare map and mask indices
for (int iLoc = 0; iLoc < GlobalIdxMask_loc.Length; iLoc++)
{
Assert.True(GlobalIdxMap_loc[iLoc] == GlobalIdxMask_loc[iLoc]);
}
}
public XDGTestSetup(
int p,
double AggregationThreshold,
int TrackerWidth,
MultigridOperator.Mode mumo,
XQuadFactoryHelper.MomentFittingVariants momentFittingVariant,
ScalarFunction LevSetFunc = null)
{
// Level set, tracker and XDG basis
// ================================
if (LevSetFunc == null)
{
LevSetFunc = ((_2D)((x, y) => 0.8 * 0.8 - x * x - y * y)).Vectorize();
}
LevSet = new LevelSet(new Basis(grid, 2), "LevelSet");
LevSet.Clear();
LevSet.ProjectField(LevSetFunc);
LsTrk = new LevelSetTracker(grid, XQuadFactoryHelper.MomentFittingVariants.Classic, TrackerWidth, new string[] { "A", "B" }, LevSet);
LsTrk.UpdateTracker();
XB = new XDGBasis(LsTrk, p);
XSpatialOperator Dummy = new XSpatialOperator(1, 0, 1, QuadOrderFunc.SumOfMaxDegrees(RoundUp: true), "C1", "u");
//Dummy.EquationComponents["c1"].Add(new
Dummy.Commit();
//Tecplot.PlotFields(new DGField[] { LevSet }, "agglo", 0.0, 3);
// operator
// ========
Debug.Assert(p <= 4);
XDGBasis opXB = new XDGBasis(LsTrk, 4); // we want to have a very precise quad rule
var map = new UnsetteledCoordinateMapping(opXB);
int quadOrder = Dummy.QuadOrderFunction(map.BasisS.Select(bs => bs.Degree).ToArray(), new int[0], map.BasisS.Select(bs => bs.Degree).ToArray());
//agg = new MultiphaseCellAgglomerator(new CutCellMetrics(momentFittingVariant, quadOrder, LsTrk, LsTrk.SpeciesIdS.ToArray()), AggregationThreshold, false);
agg = LsTrk.GetAgglomerator(LsTrk.SpeciesIdS.ToArray(), quadOrder, __AgglomerationTreshold: AggregationThreshold);
foreach (var S in LsTrk.SpeciesIdS)
{
Console.WriteLine("Species {0}, no. of agglomerated cells {1} ",
LsTrk.GetSpeciesName(S),
agg.GetAgglomerator(S).AggInfo.SourceCells.Count());
}
// mass matrix factory
// ===================
// Basis maxB = map.BasisS.ElementAtMax(b => b.Degree);
//MassFact = new MassMatrixFactory(maxB, agg);
MassFact = LsTrk.GetXDGSpaceMetrics(LsTrk.SpeciesIdS.ToArray(), quadOrder, 1).MassMatrixFactory;
// Test field
// ==========
// set the test field: this is a polynomial function,
// but different for each species; On this field, restriction followed by prolongation should be the identity
this.Xdg_uTest = new XDGField(this.XB, "uTest");
Dictionary <SpeciesId, double> dumia = new Dictionary <SpeciesId, double>();
int i = 2;
foreach (var Spc in LsTrk.SpeciesIdS)
{
dumia.Add(Spc, i);
i -= 1;
}
SetTestValue(Xdg_uTest, dumia);
// dummy operator matrix which fits polynomial degree p
// ====================================================
Xdg_opMtx = new BlockMsrMatrix(Xdg_uTest.Mapping, Xdg_uTest.Mapping);
Xdg_opMtx.AccEyeSp(120.0);
// XDG Aggregation BasiseS
// =======================
//XAggB = MgSeq.Select(agGrd => new XdgAggregationBasis[] { new XdgAggregationBasis(uTest.Basis, agGrd) }).ToArray();
XAggB = new XdgAggregationBasis[MgSeq.Length][];
var _XAggB = AggregationGridBasis.CreateSequence(MgSeq, Xdg_uTest.Mapping.BasisS);
for (int iLevel = 0; iLevel < XAggB.Length; iLevel++)
{
XAggB[iLevel] = new[] { (XdgAggregationBasis)(_XAggB[iLevel][0]) };
XAggB[iLevel][0].Update(agg);
}
// Multigrid Operator
// ==================
Xdg_opMtx = new BlockMsrMatrix(Xdg_uTest.Mapping, Xdg_uTest.Mapping);
Xdg_opMtx.AccEyeSp(120.0);
XdgMultigridOp = new MultigridOperator(XAggB, Xdg_uTest.Mapping,
Xdg_opMtx,
MassFact.GetMassMatrix(Xdg_uTest.Mapping, false),
new MultigridOperator.ChangeOfBasisConfig[][] {
new MultigridOperator.ChangeOfBasisConfig[] {
new MultigridOperator.ChangeOfBasisConfig()
{
VarIndex = new int[] { 0 }, mode = mumo, Degree = p
}
}
});
}
/// <summary>
/// Spatial operator matrix analysis method
/// </summary>
public void SpatialOperatorMatrixAnalysis(bool CheckAssertions, int AnalysisLevel)
{
using (var solver = new Rheology()) {
int D = solver.Grid.SpatialDimension;
if (AnalysisLevel < 0 || AnalysisLevel > 2)
{
throw new ArgumentException();
}
BlockMsrMatrix OpMatrix;
double[] OpAffine;
solver.AssembleMatrix(out OpMatrix, out OpAffine, solver.CurrentSolution.Mapping.ToArray(), true);
// =============================
// AnalysisLevel 0
// =============================
{
var OpMatrixT = OpMatrix.Transpose();
CoordinateVector TestVec = new CoordinateVector(solver.CurrentSolution.Mapping.Fields.Select(f => f.CloneAs()).ToArray());
double testsumPos = 0.0;
double testsumNeg = 0.0;
for (int rnd_seed = 0; rnd_seed < 20; rnd_seed++)
{
// fill the pressure components of the test vector
TestVec.Clear();
Random rnd = new Random(rnd_seed);
DGField Pressack = TestVec.Mapping.Fields[D] as DGField;
int J = solver.GridData.iLogicalCells.NoOfLocalUpdatedCells;
for (int j = 0; j < J; j++)
{
int N = Pressack.Basis.GetLength(j);
for (int n = 0; n < N; n++)
{
Pressack.Coordinates[j, n] = rnd.NextDouble();
}
}
// Gradient times P:
double[] R1 = new double[TestVec.Count];
OpMatrix.SpMV(1.0, TestVec, 0.0, R1); // R1 = Grad * P
//Console.WriteLine("L2 of 'Grad * P': " + R1.L2Norm());
// transpose of Divergence times P:
double[] R2 = new double[TestVec.Count];
OpMatrix.SpMV(1.0, TestVec, 0.0, R2); // R2 = divT * P
//Console.WriteLine("L2 of 'divT * P': " + R2.L2Norm());
TestVec.Clear();
TestVec.Acc(1.0, R1);
TestVec.Acc(1.0, R2);
// analyze!
testsumNeg += GenericBlas.L2Dist(R1, R2);
R2.ScaleV(-1.0);
testsumPos += GenericBlas.L2Dist(R1, R2);
}
Console.WriteLine("Pressure/Divergence Symmetry error in all tests (+): " + testsumPos);
Console.WriteLine("Pressure/Divergence Symmetry error in all tests (-): " + testsumNeg);
if (CheckAssertions)
{
Assert.LessOrEqual(Math.Abs(testsumNeg), testsumPos * 1.0e-13);
}
}
// =============================
// AnalysisLevel 1 and 2
// =============================
if (AnalysisLevel > 0)
{
AggregationGridBasis[][] MgBasis = AggregationGridBasis.CreateSequence(solver.MultigridSequence, solver.CurrentSolution.Mapping.BasisS);
MultigridOperator mgOp = new MultigridOperator(MgBasis, solver.CurrentSolution.Mapping, OpMatrix, null, solver.MultigridOperatorConfig);
// extract
////////////
MsrMatrix FullMatrix = mgOp.OperatorMatrix.ToMsrMatrix();
MsrMatrix DiffMatrix;
{
int[] VelVarIdx = D.ForLoop(d => d);
int[] USubMatrixIdx_Row = mgOp.Mapping.GetSubvectorIndices(VelVarIdx);
int[] USubMatrixIdx_Col = mgOp.Mapping.GetSubvectorIndices(VelVarIdx);
int L = USubMatrixIdx_Row.Length;
DiffMatrix = new MsrMatrix(L, L, 1, 1);
FullMatrix.WriteSubMatrixTo(DiffMatrix, USubMatrixIdx_Row, default(int[]), USubMatrixIdx_Col, default(int[]));
double DiffMatrix_sd = DiffMatrix.SymmetryDeviation();
Console.WriteLine("Diffusion assymetry:" + DiffMatrix_sd);
}
MsrMatrix SaddlePointMatrix;
{
int[] VelPVarIdx = new int[] { 0, 1, 2 };
int[] VelPSubMatrixIdx_Row = mgOp.Mapping.GetSubvectorIndices(VelPVarIdx);
int[] VelPSubMatrixIdx_Col = mgOp.Mapping.GetSubvectorIndices(VelPVarIdx);
int L = VelPSubMatrixIdx_Row.Length;
SaddlePointMatrix = new MsrMatrix(L, L, 1, 1);
FullMatrix.WriteSubMatrixTo(SaddlePointMatrix, VelPSubMatrixIdx_Row, default(int[]), VelPSubMatrixIdx_Col, default(int[]));
}
//SaddlePointMatrix.SaveToTextFileSparse("C:\\Users\\kikker\\Documents\\MATLAB\\spm.txt");
MsrMatrix ConstitutiveMatrix;
{
int[] StressVarIdx = new int[] { 3, 4, 5 };
int[] StressSubMatrixIdx_Row = mgOp.Mapping.GetSubvectorIndices(StressVarIdx);
int[] StressSubMatrixIdx_Col = mgOp.Mapping.GetSubvectorIndices(StressVarIdx);
int L = StressSubMatrixIdx_Row.Length;
ConstitutiveMatrix = new MsrMatrix(L, L, 1, 1);
FullMatrix.WriteSubMatrixTo(ConstitutiveMatrix, StressSubMatrixIdx_Row, default(int[]), StressSubMatrixIdx_Col, default(int[]));
}
// operator analysis
//////////////////////
bool posDef;
if (AnalysisLevel > 1)
{
// +++++++++++++++++++++++++++++++
// check condition number, etc
// +++++++++++++++++++++++++++++++
MultidimensionalArray ret = MultidimensionalArray.Create(1, 5);
Console.WriteLine("Calling MATLAB/Octave...");
using (BatchmodeConnector bmc = new BatchmodeConnector()) {
bmc.PutSparseMatrix(FullMatrix, "FullMatrix");
bmc.PutSparseMatrix(SaddlePointMatrix, "SaddlePointMatrix");
bmc.PutSparseMatrix(ConstitutiveMatrix, "ConstitutiveMatrix");
bmc.PutSparseMatrix(DiffMatrix, "DiffMatrix");
bmc.Cmd("DiffMatrix = 0.5*(DiffMatrix + DiffMatrix');");
bmc.Cmd("condNoFullMatrix = condest(FullMatrix);");
bmc.Cmd("condNoSaddlePointMatrix = condest(SaddlePointMatrix);");
bmc.Cmd("condNoConstitutiveMatrix = condest(ConstitutiveMatrix);");
bmc.Cmd("condNoDiffMatrix = condest(DiffMatrix);");
//bmc.Cmd("eigiMaxiSaddle = 1.0; % eigs(SaddlePointMatrix,1,'lm')");
//bmc.Cmd("eigiMiniSaddle = 1.0; % eigs(SaddlePointMatrix,1,'sm')");
//bmc.Cmd("eigiMaxiConst = 1.0; % eigs(ConstitutiveMatrix,1,'lm')");
//bmc.Cmd("eigiMiniConst = 1.0; % eigs(ConstitutiveMatrix,1,'sm')");
//bmc.Cmd("eigiMaxiDiff = 1.0; % eigs(DiffMatrix,1,'lm')");
//bmc.Cmd("eigiMiniDiff = 1.0; % eigs(DiffMatrix,1,'sm')");
bmc.Cmd("lasterr");
bmc.Cmd("[V,r]=chol(SaddlePointMatrix);");
bmc.Cmd("[V,r]=chol(ConstitutiveMatrix);");
bmc.Cmd("ret = [condNoFullMatrix, condNoSaddlePointMatrix, condNoConstitutiveMatrix, condNoDiffMatrix, r]"); //eigiMaxiSaddle, eigiMiniSaddle, eigiMaxiConst, eigiMiniConst, eigiMaxiDiff, eigiMiniDiff,
bmc.GetMatrix(ret, "ret");
bmc.Execute(false);
}
double condNoFullMatrix = ret[0, 0];
double condNoSaddlePMatrix = ret[0, 1];
double condNoConstitutiveMatrix = ret[0, 2];
double condNoDiffMatrix = ret[0, 3];
//double eigiMaxiSaddle = ret[0, 4];
//double eigiMiniSaddle = ret[0, 5];
//double eigiMaxiConst = ret[0, 6];
//double eigiMiniConst = ret[0, 7];
//double eigiMaxiDiff = ret[0, 8];
//double eigiMiniDiff = ret[0, 9];
posDef = ret[0, 4] == 0;
//Console.WriteLine("Eigenvalue range of saddle point matrix: {0} to {1}", eigiMiniSaddle, eigiMaxiSaddle);
//Console.WriteLine("Eigenvalue range of constitutive matrix: {0} to {1}", eigiMiniConst, eigiMaxiConst);
//Console.WriteLine("Eigenvalue range of diffusion matrix: {0} to {1}", eigiMiniDiff, eigiMaxiDiff);
Console.WriteLine("Condition number full operator: {0:0.####E-00}", condNoFullMatrix);
Console.WriteLine("Condition number saddle point operator: {0:0.####E-00}", condNoSaddlePMatrix);
Console.WriteLine("Condition number constitutive operator: {0:0.####E-00}", condNoConstitutiveMatrix);
Console.WriteLine("Condition number diffusion operator: {0:0.####E-00}", condNoDiffMatrix);
//base.QueryHandler.ValueQuery("ConditionNumber", condNoFullMatrix);
}
else
{
// +++++++++++++++++++++++++++++++++++++++
// test only for positive definiteness
// +++++++++++++++++++++++++++++++++++++++
var SaddlePMatrixFull = SaddlePointMatrix.ToFullMatrixOnProc0();
var ConstMatrixFull = ConstitutiveMatrix.ToFullMatrixOnProc0();
posDef = true;
try {
SaddlePMatrixFull.Cholesky();
} catch (ArithmeticException) {
posDef = false;
}
posDef = true;
try {
ConstMatrixFull.Cholesky();
} catch (ArithmeticException) {
posDef = false;
}
}
double SaddlePSymm = SaddlePointMatrix.SymmetryDeviation();
Console.WriteLine("Symmetry deviation of saddle point matrix: " + SaddlePSymm);
if (posDef)
{
Console.WriteLine("Good news: Saddle point operator matrix seems to be positive definite.");
}
else
{
Console.WriteLine("WARNING: Saddle point operator matrix is not positive definite.");
}
double ConstSymm = ConstitutiveMatrix.SymmetryDeviation();
Console.WriteLine("Symmetry deviation of constitutive matrix: " + ConstSymm);
if (posDef)
{
Console.WriteLine("Good news: constitutive operator matrix seems to be positive definite.");
}
else
{
Console.WriteLine("WARNING: constitutive operator matrix is not positive definite.");
}
//if (CheckAssertions) {
// if (Control.AdvancedDiscretizationOptions.ViscosityMode == ViscosityMode.FullySymmetric && Control.PhysicalParameters.IncludeConvection == false) {
// Assert.IsTrue(posDef, "Positive definiteness test failed.");
// double compVal = DiffMatrix.InfNorm() * 1e-13;
// Assert.LessOrEqual(DiffSymm, compVal, "Diffusion matrix seems to be non-symmetric.");
// }
//}
}
}
}
/// <summary>
/// Logging of residuals (provisional).
/// </summary>
virtual protected void LogResis(int iterIndex, double[] currentSol, double[] currentRes, MultigridOperator Mgop)
{
if (m_ResLogger != null)
{
int NF = this.CurrentStateMapping.Fields.Count;
m_ResLogger.IterationCounter = iterIndex;
if (m_TransformedResi)
{
// +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// transform current solution and residual back to the DG domain
// +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
var R = this.Residuals;
R.Clear();
Mgop.TransformRhsFrom(R, currentRes);
//Mgop.TransformSolFrom(X, currentSol);
//this.m_Agglomerator.Extrapolate(X, X.Mapping);
this.m_CurrentAgglomeration.Extrapolate(R.Mapping);
/*
* CoordinateVector Solution = new CoordinateVector(this.Residuals.Fields.Select(delegate (DGField f) {
* DGField r = f.CloneAs();
* r.Identification = "Sol_" + r.Identification;
* return r;
* }));
* Mgop.TransformSolFrom(Solution, currentSol);
* Tecplot.Tecplot.PlotFields(Solution.Fields.Cat(this.Residuals.Fields), "DuringNewton-" + iterIndex, iterIndex, 3);
*/
for (int i = 0; i < NF; i++)
{
double L2Res = R.Mapping.Fields[i].L2Norm();
m_ResLogger.CustomValue(L2Res, m_ResidualNames[i]);
}
}
else
{
// +++++++++++++++++++++++
// un-transformed residual
// +++++++++++++++++++++++
var VarIdx = NF.ForLoop(i => Mgop.Mapping.GetSubvectorIndices(i));
for (int i = 0; i < VarIdx.Length; i++)
{
double L2Res = 0.0;
foreach (int idx in VarIdx[i])
{
L2Res += currentRes[idx - Mgop.Mapping.i0].Pow2();
}
L2Res = L2Res.MPISum().Sqrt(); // would be better to do the MPISum for all L2Res together,
// but this implementation is anyway inefficient....
m_ResLogger.CustomValue(L2Res, m_ResidualNames[i]);
}
}
if (Config_LevelSetHandling == LevelSetHandling.Coupled_Iterative)
{
m_ResLogger.CustomValue(m_LastLevelSetResidual, "LevelSet");
}
m_ResLogger.NextIteration(true);
}
}
private void RKstageImplicit(double PhysTime, double dt, double[][] k, int s, BlockMsrMatrix[] Mass, CoordinateVector u0, double ActualLevSetRelTime, double[] RK_as, double RelTime)
{
Debug.Assert(s < m_RKscheme.Stages);
Debug.Assert(m_RKscheme.c[s] > 0);
Debug.Assert(RK_as[s] != 0);
int Ndof = m_CurrentState.Count;
// =========
// RHS setup
// =========
m_ImplStParams = new ImplicitStage_AssiParams()
{
m_CurrentDt = dt,
m_CurrentPhystime = PhysTime,
m_IterationCounter = 0,
m_ActualLevSetRelTime = ActualLevSetRelTime,
m_RelTime = RelTime,
m_k = k,
m_u0 = u0,
m_Mass = Mass,
m_RK_as = RK_as,
m_s = s
};
// ================
// solve the system
// ================
NonlinearSolver nonlinSolver;
ISolverSmootherTemplate linearSolver;
GetSolver(out nonlinSolver, out linearSolver);
if (RequiresNonlinearSolver)
{
// Nonlinear Solver (Navier-Stokes)
// --------------------------------
nonlinSolver.SolverDriver(m_CurrentState, default(double[])); // Note: the RHS is passed as the affine part via 'this.SolverCallback'
}
else
{
// Linear Solver (Stokes)
// ----------------------
// build the saddle-point matrix
BlockMsrMatrix System, MaMa;
double[] RHS;
this.AssembleMatrixCallback(out System, out RHS, out MaMa, CurrentStateMapping.Fields.ToArray(), true);
RHS.ScaleV(-1);
// update the multigrid operator
MultigridOperator mgOperator = new MultigridOperator(this.MultigridBasis, CurrentStateMapping,
System, MaMa,
this.Config_MultigridOperator);
// init linear solver
linearSolver.Init(mgOperator);
// try to solve the saddle-point system.
mgOperator.UseSolver(linearSolver, m_CurrentState, RHS);
// 'revert' agglomeration
m_CurrentAgglomeration.Extrapolate(CurrentStateMapping);
}
// ================
// reset
// ================
m_ImplStParams = null;
}
private void ConsistencyTest()
{
// consistency test on the original matrix
// -----------------------------------------------------
this.residual.Clear();
double[] RHSvec = this.GetRHS();
this.residual.CoordinateVector.SetV(RHSvec, 1.0);
this.Op_Matrix.SpMV(-1.0, this.u.CoordinateVector, 1.0, residual.CoordinateVector);
double residual_L2Norm = this.residual.L2Norm();
Console.WriteLine("Residual norm: " + residual_L2Norm);
Assert.LessOrEqual(residual_L2Norm, 1.0e-8);
// consistency test on the multigrid
// --------------------------------------------------------------------
AggregationGridBasis[][] XAggB = AggregationGridBasis.CreateSequence(base.MultigridSequence, u.Mapping.BasisS);
XAggB.UpdateXdgAggregationBasis(this.Op_Agglomeration);
int p = this.u.Basis.Degree;
var MultigridOp = new MultigridOperator(XAggB, this.u.Mapping,
this.Op_Matrix,
this.Op_mass.GetMassMatrix(new UnsetteledCoordinateMapping(this.u.Basis), false),
new MultigridOperator.ChangeOfBasisConfig[][] {
new MultigridOperator.ChangeOfBasisConfig[] {
new MultigridOperator.ChangeOfBasisConfig()
{
VarIndex = new int[] { 0 }, mode = MultigridOperator.Mode.Eye, Degree = u.Basis.Degree
}
}
});
double[] mgSolVec = new double[MultigridOp.Mapping.LocalLength];
double[] mgRhsVec = new double[MultigridOp.Mapping.LocalLength];
MultigridOp.TransformSolInto(this.u.CoordinateVector, mgSolVec);
MultigridOp.TransformRhsInto(RHSvec, mgRhsVec);
MgConsistencyTestRec(MultigridOp, mgSolVec, mgRhsVec);
//
/*
* {
* int Jagg1 = MgSeq[1].NoOfAggregateCells;
* MultigridOperator MgOp0 = MultigridOp;
* MultigridOperator MgOp1 = MultigridOp.CoarserLevel;
* MultigridMapping Map0 = MgOp0.Mapping;
* MultigridMapping Map1 = MgOp1.Mapping;
*
*
* double[] V0 = new double[MgOp0.Mapping.LocalLength];
* double[] V1 = new double[MgOp1.Mapping.LocalLength];
*
* for(int j = 0; j < Jagg1; j++) {
* int idx = Map1.LocalUniqueIndex(0, j, 0);
* V1[idx] = j;
* }
*
* MgOp1.Prolongate(1.0, V0, 0.0, V1);
*
* XDGField Marker = new XDGField(this.u.Basis, "Tracker");
*
* MgOp0.TransformSolFrom(Marker.CoordinatesAsVector, V0);
* this.Op_Agglomeration.Extrapolate(Marker.CoordinatesAsVector, Marker.Mapping);
*
* Tecplot.PlotFields(new DGField[] { Marker }, "Tracker", "Tracker", 0.0, 5);
*
* }
*/
}
protected void CustomItCallback(int iterIndex, double[] currentSol, double[] currentRes, MultigridOperator Mgop)
{
//currentSol.SaveToTextFile("X_"+ iterIndex);
//currentRes.SaveToTextFile("Res_" + iterIndex);
MaxMlevel = Mgop.LevelIndex;
}
protected void CustomItCallback(int iterIndex, double[] currentSol, double[] currentRes, MultigridOperator Mgop)
{
//noch nix ...
MaxMlevel = Mgop.LevelIndex;
}
private void ExperimentalSolver(out double mintime, out double maxtime, out bool Converged, out int NoOfIter, out int DOFs)
{
using (var tr = new FuncTrace()) {
mintime = double.MaxValue;
maxtime = 0;
Converged = false;
NoOfIter = int.MaxValue;
DOFs = 0;
AggregationGridBasis[][] XAggB;
using (new BlockTrace("Aggregation_basis_init", tr)) {
XAggB = AggregationGridBasis.CreateSequence(base.MultigridSequence, u.Mapping.BasisS);
}
XAggB.UpdateXdgAggregationBasis(this.Op_Agglomeration);
var MassMatrix = this.Op_mass.GetMassMatrix(this.u.Mapping, new double[] { 1.0 }, false, this.LsTrk.SpeciesIdS.ToArray());
double[] _RHSvec = this.GetRHS();
Stopwatch stw = new Stopwatch();
stw.Reset();
stw.Start();
Console.WriteLine("Setting up multigrid operator...");
int p = this.u.Basis.Degree;
var MultigridOp = new MultigridOperator(XAggB, this.u.Mapping,
this.Op_Matrix,
this.Op_mass.GetMassMatrix(new UnsetteledCoordinateMapping(this.u.Basis), false),
OpConfig);
Assert.True(MultigridOp != null);
int L = MultigridOp.Mapping.LocalLength;
DOFs = MultigridOp.Mapping.TotalLength;
double[] RHSvec = new double[L];
MultigridOp.TransformRhsInto(_RHSvec, RHSvec);
ISolverSmootherTemplate exsolver;
SolverFactory SF = new SolverFactory(this.Control.NonLinearSolver, this.Control.LinearSolver);
List <Action <int, double[], double[], MultigridOperator> > Callbacks = new List <Action <int, double[], double[], MultigridOperator> >();
Callbacks.Add(CustomItCallback);
SF.GenerateLinear(out exsolver, MultigridSequence, OpConfig, Callbacks);
using (new BlockTrace("Solver_Init", tr)) {
exsolver.Init(MultigridOp);
}
/*
* string filename = "XdgPoisson" + this.Grid.SpatialDimension + "p" + this.u.Basis.Degree + "R" + this.Grid.CellPartitioning.TotalLength;
* MultigridOp.OperatorMatrix.SaveToTextFileSparse(filename + ".txt");
* RHSvec.SaveToTextFile(filename + "_rhs.txt");
*
* var uEx = this.u.CloneAs();
* Op_Agglomeration.ClearAgglomerated(uEx.Mapping);
* var CO = new ConvergenceObserver(MultigridOp, MassMatrix, uEx.CoordinateVector.ToArray());
* uEx = null;
* CO.TecplotOut = "PoissonConvergence";
* //CO.PlotDecomposition(this.u.CoordinateVector.ToArray());
*
* if (exsolver is ISolverWithCallback) {
* ((ISolverWithCallback)exsolver).IterationCallback = CO.IterationCallback;
* }
* //*/
XDGField u2 = u.CloneAs();
using (new BlockTrace("Solver_Run", tr)) {
// use solver (on XDG-field 'u2').
u2.Clear();
MultigridOp.UseSolver(exsolver, u2.CoordinateVector, _RHSvec);
Console.WriteLine("Solver: {0}, converged? {1}, {2} iterations.", exsolver.GetType().Name, exsolver.Converged, exsolver.ThisLevelIterations);
this.Op_Agglomeration.Extrapolate(u2.Mapping);
Assert.IsTrue(exsolver.Converged, "Iterative solver did not converge.");
}
stw.Stop();
mintime = Math.Min(stw.Elapsed.TotalSeconds, mintime);
maxtime = Math.Max(stw.Elapsed.TotalSeconds, maxtime);
Converged = exsolver.Converged;
NoOfIter = exsolver.ThisLevelIterations;
// compute error between reference solution and multigrid solver
XDGField ErrField = u2.CloneAs();
ErrField.Acc(-1.0, u);
double ERR = ErrField.L2Norm();
double RelERR = ERR / u.L2Norm();
Assert.LessOrEqual(RelERR, 1.0e-6, "Result from iterative solver above threshold.");
}
}
/// <summary>
/// Solution of the system
/// <see cref="LaplaceMtx"/>*<see cref="T"/> + <see cref="LaplaceAffine"/> = <see cref="RHS"/>
/// using the modular solver framework.
/// </summary>
private void ExperimentalSolve(out double mintime, out double maxtime, out bool Converged, out int NoOfIter) {
using (var tr = new FuncTrace()) {
int p = this.T.Basis.Degree;
var MgSeq = this.MultigridSequence;
mintime = double.MaxValue;
maxtime = 0;
Converged = false;
NoOfIter = int.MaxValue;
Console.WriteLine("Construction of Multigrid basis...");
Stopwatch mgBasis = new Stopwatch();
mgBasis.Start();
AggregationGridBasis[][] AggBasis;
using (new BlockTrace("Aggregation_basis_init", tr)) {
AggBasis = AggregationGridBasis.CreateSequence(MgSeq, new Basis[] { this.T.Basis });
}
mgBasis.Stop();
Console.WriteLine("done. (" + mgBasis.Elapsed.TotalSeconds + " sec)");
//foreach (int sz in new int[] { 1000, 2000, 5000, 10000, 20000 }) {
// base.Control.TargetBlockSize = sz;
for (int irun = 0; irun < base.Control.NoOfSolverRuns; irun++) {
Stopwatch stw = new Stopwatch();
stw.Reset();
stw.Start();
Console.WriteLine("Setting up multigrid operator...");
var mgsetup = new Stopwatch();
mgsetup.Start();
var MultigridOp = new MultigridOperator(AggBasis, this.T.Mapping, this.LaplaceMtx, null, MgConfig);
mgsetup.Stop();
Console.WriteLine("done. (" + mgsetup.Elapsed.TotalSeconds + " sec)");
Console.WriteLine("Setting up solver...");
var solverSetup = new Stopwatch();
solverSetup.Start();
ISolverSmootherTemplate solver;
switch (base.Control.solver_name) {
case SolverCodes.exp_direct:
solver = new DirectSolver() {
WhichSolver = DirectSolver._whichSolver.PARDISO
};
break;
case SolverCodes.exp_direct_lapack:
solver = new DirectSolver() {
WhichSolver = DirectSolver._whichSolver.Lapack
};
break;
case SolverCodes.exp_softpcg_schwarz_directcoarse: {
double LL = this.LaplaceMtx._RowPartitioning.LocalLength;
int NoOfBlocks = (int)Math.Max(1, Math.Round(LL / (double)this.Control.TargetBlockSize));
Console.WriteLine("Additive Schwarz w. direct coarse, No of blocks: " + NoOfBlocks.MPISum());
solver = new SoftPCG() {
m_MaxIterations = 50000,
m_Tolerance = 1.0e-10,
Precond = new Schwarz() {
m_MaxIterations = 1,
//CoarseSolver = new GenericRestriction() {
// CoarserLevelSolver = new GenericRestriction() {
CoarseSolver = new DirectSolver() {
WhichSolver = DirectSolver._whichSolver.PARDISO
// }
//}
},
m_BlockingStrategy = new Schwarz.METISBlockingStrategy() {
NoOfPartsPerProcess = NoOfBlocks
},
Overlap = 1,
}
};
break;
}
case SolverCodes.exp_softpcg_schwarz: {
double LL = this.LaplaceMtx._RowPartitioning.LocalLength;
int NoOfBlocks = (int)Math.Max(1, Math.Round(LL / (double)this.Control.TargetBlockSize));
Console.WriteLine("Additive Schwarz, No of blocks: " + NoOfBlocks.MPISum());
solver = new SoftPCG() {
m_MaxIterations = 50000,
m_Tolerance = 1.0e-10,
Precond = new Schwarz() {
m_MaxIterations = 1,
CoarseSolver = null,
m_BlockingStrategy = new Schwarz.METISBlockingStrategy {
NoOfPartsPerProcess = NoOfBlocks
},
Overlap = 1
}
};
break;
}
case SolverCodes.exp_softpcg_mg:
solver = MultilevelSchwarz(MultigridOp);
break;
case SolverCodes.exp_Kcycle_schwarz:
solver = KcycleMultiSchwarz(MultigridOp);
break;
default:
throw new ApplicationException("unknown solver: " + this.Control.solver_name);
}
T.Clear();
T.AccLaidBack(1.0, Tex);
ConvergenceObserver CO = null;
//CO = new ConvergenceObserver(MultigridOp, null, T.CoordinateVector.ToArray());
//CO.TecplotOut = "oasch";
if (solver is ISolverWithCallback) {
if (CO == null) {
((ISolverWithCallback)solver).IterationCallback = delegate (int iter, double[] xI, double[] rI, MultigridOperator mgOp) {
double l2_RES = rI.L2NormPow2().MPISum().Sqrt();
double[] xRef = new double[xI.Length];
MultigridOp.TransformSolInto(T.CoordinateVector, xRef);
double l2_ERR = GenericBlas.L2DistPow2(xI, xRef).MPISum().Sqrt();
Console.WriteLine("Iter: {0}\tRes: {1:0.##E-00}\tErr: {2:0.##E-00}\tRunt: {3:0.##E-00}", iter, l2_RES, l2_ERR, stw.Elapsed.TotalSeconds);
//Tjac.CoordinatesAsVector.SetV(xI);
//Residual.CoordinatesAsVector.SetV(rI);
//PlotCurrentState(iter, new TimestepNumber(iter), 3);
};
} else {
((ISolverWithCallback)solver).IterationCallback = CO.IterationCallback;
}
}
using (new BlockTrace("Solver_Init", tr)) {
solver.Init(MultigridOp);
}
solverSetup.Stop();
Console.WriteLine("done. (" + solverSetup.Elapsed.TotalSeconds + " sec)");
Console.WriteLine("Running solver...");
var solverIteration = new Stopwatch();
solverIteration.Start();
double[] T2 = this.T.CoordinateVector.ToArray();
using (new BlockTrace("Solver_Run", tr)) {
solver.ResetStat();
T2.Clear();
var RHSvec = RHS.CoordinateVector.ToArray();
BLAS.daxpy(RHSvec.Length, -1.0, this.LaplaceAffine, 1, RHSvec, 1);
MultigridOp.UseSolver(solver, T2, RHSvec);
T.CoordinateVector.SetV(T2);
}
solverIteration.Stop();
Console.WriteLine("done. (" + solverIteration.Elapsed.TotalSeconds + " sec)");
Console.WriteLine("Pardiso phase 11: " + ilPSP.LinSolvers.PARDISO.PARDISOSolver.Phase_11.Elapsed.TotalSeconds);
Console.WriteLine("Pardiso phase 22: " + ilPSP.LinSolvers.PARDISO.PARDISOSolver.Phase_22.Elapsed.TotalSeconds);
Console.WriteLine("Pardiso phase 33: " + ilPSP.LinSolvers.PARDISO.PARDISOSolver.Phase_33.Elapsed.TotalSeconds);
// time measurement, statistics
stw.Stop();
mintime = Math.Min(stw.Elapsed.TotalSeconds, mintime);
maxtime = Math.Max(stw.Elapsed.TotalSeconds, maxtime);
Converged = solver.Converged;
NoOfIter = solver.ThisLevelIterations;
if (CO != null)
CO.PlotTrend(true, true, true);
}
}
}
/// <summary>
///
/// </summary>
ISolverSmootherTemplate KcycleMultiSchwarz(MultigridOperator op) {
var solver = new OrthonormalizationScheme() {
MaxIter = 500,
Tolerance = 1.0e-10,
};
// my tests show that the ideal block size may be around 10'000
int DirectKickIn = base.Control.TargetBlockSize;
MultigridOperator Current = op;
var PrecondChain = new List<ISolverSmootherTemplate>();
for (int iLevel = 0; iLevel < base.MultigridSequence.Length; iLevel++) {
int SysSize = Current.Mapping.TotalLength;
int NoOfBlocks = (int)Math.Ceiling(((double)SysSize) / ((double)DirectKickIn));
bool useDirect = false;
useDirect |= (SysSize < DirectKickIn);
useDirect |= iLevel == base.MultigridSequence.Length - 1;
useDirect |= NoOfBlocks.MPISum() <= 1;
ISolverSmootherTemplate levelSolver;
if (useDirect) {
levelSolver = new DirectSolver() {
WhichSolver = DirectSolver._whichSolver.PARDISO,
TestSolution = false
};
} else {
Schwarz swz1 = new Schwarz() {
m_MaxIterations = 1,
CoarseSolver = null,
m_BlockingStrategy = new Schwarz.METISBlockingStrategy() {
NoOfPartsPerProcess = NoOfBlocks
},
Overlap = 2 // overlap seems to help
};
SoftPCG pcg1 = new SoftPCG() {
m_MinIterations = 5,
m_MaxIterations = 5
};
//*/
var pre = new SolverSquence() {
SolverChain = new ISolverSmootherTemplate[] { swz1, pcg1 }
};
levelSolver = swz1;
}
if (iLevel > 0) {
GenericRestriction[] R = new GenericRestriction[iLevel];
for (int ir = 0; ir < R.Length; ir++) {
R[ir] = new GenericRestriction();
if (ir >= 1)
R[ir - 1].CoarserLevelSolver = R[ir];
}
R[iLevel - 1].CoarserLevelSolver = levelSolver;
PrecondChain.Add(R[0]);
} else {
PrecondChain.Add(levelSolver);
}
if (useDirect) {
Console.WriteLine("Kswz: using {0} levels, lowest level DOF is {1}, target size is {2}.", iLevel + 1, SysSize, DirectKickIn);
break;
}
Current = Current.CoarserLevel;
}
if (PrecondChain.Count > 1) {
/*
// construct a V-cycle
for (int i = PrecondChain.Count - 2; i>= 0; i--) {
PrecondChain.Add(PrecondChain[i]);
}
*/
var tmp = PrecondChain.ToArray();
for (int i = 0; i < PrecondChain.Count; i++) {
PrecondChain[i] = tmp[PrecondChain.Count - 1 - i];
}
}
solver.PrecondS = PrecondChain.ToArray();
solver.MaxKrylovDim = solver.PrecondS.Length * 4;
return solver;
}
protected void CustomItCallback(int iterIndex, double[] currentSol, double[] currentRes, MultigridOperator Mgop)
{
MaxMlevel = Mgop.LevelIndex;
//currentRes.SaveToTextFileDebug(String.Format("Res_{0}_proc",iterIndex));
//currentSol.SaveToTextFileDebug(String.Format("Sol_{0}_proc",iterIndex));
//Console.WriteLine("Callback executed {0} times",iterIndex);
}
/// <summary>
/// Ganz ok.
/// </summary>
ISolverSmootherTemplate MultilevelSchwarz(MultigridOperator op) {
var solver = new SoftPCG() {
m_MaxIterations = 500,
m_Tolerance = 1.0e-12
};
//var solver = new OrthonormalizationScheme() {
// MaxIter = 500,
// Tolerance = 1.0e-10,
//};
//var solver = new SoftGMRES() {
// m_MaxIterations = 500,
// m_Tolerance = 1.0e-10,
//};
// my tests show that the ideal block size may be around 10'000
int DirectKickIn = base.Control.TargetBlockSize;
MultigridOperator Current = op;
ISolverSmootherTemplate[] MultigridChain = new ISolverSmootherTemplate[base.MultigridSequence.Length];
for (int iLevel = 0; iLevel < base.MultigridSequence.Length; iLevel++) {
int SysSize = Current.Mapping.TotalLength;
int NoOfBlocks = (int)Math.Ceiling(((double)SysSize) / ((double)DirectKickIn));
bool useDirect = false;
useDirect |= (SysSize < DirectKickIn);
useDirect |= iLevel == base.MultigridSequence.Length - 1;
useDirect |= NoOfBlocks.MPISum() <= 1;
if (useDirect) {
MultigridChain[iLevel] = new DirectSolver() {
WhichSolver = DirectSolver._whichSolver.PARDISO,
TestSolution = false
};
} else {
ClassicMultigrid MgLevel = new ClassicMultigrid() {
m_MaxIterations = 1,
m_Tolerance = 0.0 // termination controlled by top level PCG
};
MultigridChain[iLevel] = MgLevel;
ISolverSmootherTemplate pre, pst;
if (iLevel > 0) {
Schwarz swz1 = new Schwarz() {
m_MaxIterations = 1,
CoarseSolver = null,
m_BlockingStrategy = new Schwarz.METISBlockingStrategy() {
NoOfPartsPerProcess = NoOfBlocks
},
Overlap = 0 // overlap does **NOT** seem to help
};
SoftPCG pcg1 = new SoftPCG() {
m_MinIterations = 5,
m_MaxIterations = 5
};
SoftPCG pcg2 = new SoftPCG() {
m_MinIterations = 5,
m_MaxIterations = 5
};
var preChain = new ISolverSmootherTemplate[] { swz1, pcg1 };
var pstChain = new ISolverSmootherTemplate[] { swz1, pcg2 };
pre = new SolverSquence() { SolverChain = preChain };
pst = new SolverSquence() { SolverChain = pstChain };
} else {
// +++++++++++++++++++++++++++++++++++++++++++++++++++
// top level - use only iterative (non-direct) solvers
// +++++++++++++++++++++++++++++++++++++++++++++++++++
pre = new BlockJacobi() {
NoOfIterations = 3,
omega = 0.5
};
pst = new BlockJacobi() {
NoOfIterations = 3,
omega = 0.5
};
//preChain = new ISolverSmootherTemplate[] { pcg1 };
//pstChain = new ISolverSmootherTemplate[] { pcg2 };
}
//if (iLevel > 0) {
// MgLevel.PreSmoother = pre;
// MgLevel.PostSmoother = pst;
//} else {
// //MgLevel.PreSmoother = pcg1; // ganz schlechte Idee, konvergiert gegen FALSCHE lösung
// //MgLevel.PostSmoother = pcg2; // ganz schlechte Idee, konvergiert gegen FALSCHE lösung
// MgLevel.PreSmoother = pre;
// MgLevel.PostSmoother = pst;
//}
MgLevel.PreSmoother = pre;
MgLevel.PostSmoother = pst;
}
if (iLevel > 0) {
((ClassicMultigrid)(MultigridChain[iLevel - 1])).CoarserLevelSolver = MultigridChain[iLevel];
}
if (useDirect) {
Console.WriteLine("MG: using {0} levels, lowest level DOF is {1}, target size is {2}.", iLevel + 1, SysSize, DirectKickIn);
break;
}
Current = Current.CoarserLevel;
} // end of level loop
solver.Precond = MultigridChain[0];
//solver.PrecondS = new[] { MultigridChain[0] };
return solver;
}
protected override double RunSolverOneStep(int TimestepNo, double phystime, double dt)
{
LsUpdate(phystime);
// operator-matrix assemblieren
OperatorMatrix = new BlockMsrMatrix(MG_Mapping.ProblemMapping);
AltOperatorMatrix = new MsrMatrix(MG_Mapping.ProblemMapping);
double[] Affine = new double[OperatorMatrix.RowPartitioning.LocalLength];
MultiphaseCellAgglomerator Agg;
Agg = LsTrk.GetAgglomerator(this.LsTrk.SpeciesIdS.ToArray(), m_quadOrder, __AgglomerationTreshold: this.THRESHOLD);
XSpatialOperatorMk2.XEvaluatorLinear mtxBuilder = Op.GetMatrixBuilder(base.LsTrk, MG_Mapping.ProblemMapping, null, MG_Mapping.ProblemMapping);
mtxBuilder.time = 0.0;
mtxBuilder.ComputeMatrix(OperatorMatrix, Affine);
Agg.ManipulateMatrixAndRHS(OperatorMatrix, Affine, MG_Mapping.ProblemMapping, MG_Mapping.ProblemMapping);
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);
}
MGOp = new MultigridOperator(XAggB, map,
OperatorMatrix,
this.massFact.GetMassMatrix(map, false),
OpConfig, null);
Debug.Assert(MGOp.OperatorMatrix != null);
Debug.Assert(MGOp.Mapping != null);
someVec = GetRHS(Affine, OperatorMatrix);
mtxBuilder.ComputeMatrix(AltOperatorMatrix, Affine);
Agg.ManipulateMatrixAndRHS(AltOperatorMatrix, Affine, MG_Mapping.ProblemMapping, MG_Mapping.ProblemMapping);
//LsTrk.GetSpeciesName(((XdgAggregationBasis)MGOp.Mapping.AggBasis[0]).UsedSpecies[1]);
//LsTrk.GetSpeciesName(((XdgAggregationBasis)MGOp.Mapping.AggBasis[0]).UsedSpecies[0]);
int nnz = this.OperatorMatrix.GetTotalNoOfNonZeros();
Console.WriteLine("Number of non-zeros in matrix: " + nnz);
int nnz2 = this.AltOperatorMatrix.GetTotalNoOfNonZeros();
Assert.IsTrue(nnz == nnz2, "Number of non-zeros in matrix different for " + OperatorMatrix.GetType() + " and " + AltOperatorMatrix.GetType());
Console.WriteLine("Number of non-zeros in matrix (reference): " + nnz2);
MsrMatrix Comp = AltOperatorMatrix.CloneAs();
Comp.Acc(-1.0, OperatorMatrix);
double CompErr = Comp.InfNorm();
double Denom = Math.Max(AltOperatorMatrix.InfNorm(), OperatorMatrix.InfNorm());
double CompErrRel = Denom > Math.Sqrt(double.Epsilon) ? CompErr / Denom : CompErr;
Console.WriteLine("Comparison: " + CompErrRel);
Assert.LessOrEqual(CompErrRel, 1.0e-7, "Huge difference between MsrMatrix and BlockMsrMatrix.");
base.TerminationKey = true;
return(0.0);
}