public static void Init()
{
//GridCommons grd = Grid2D.Cartesian2DGrid(RandomSpacing(), RandomSpacing());
//grid = new GridData(Grid2D.Cartesian2DGrid(GenericBlas.Linspace(-7, 7, 8), GenericBlas.Linspace(-1, 1, 2)));
//grid = new GridData(Grid2D.Cartesian2DGrid(new double[] { -6, -4, -2, 2, 4, 6 }, GenericBlas.Linspace(-1, 1, 2)));
//if (curved)
//{
// grid = Grid2D.CurvedSquareGrid(GenericBlas.Linspace(1, 2, 5), GenericBlas.Linspace(0, 1, 17), CellType.Square_9, true).GridData;
//}
//else
//{
// grid = (Grid2D.Cartesian2DGrid(GenericBlas.Linspace(-1.5, 1.5, 17), GenericBlas.Linspace(-1.5, 1.5, 17))).GridData;
//}
grid = (Grid2D.Cartesian2DGrid(GenericBlas.Linspace(-1.5, 1.5, 17), GenericBlas.Linspace(-1.5, 1.5, 17))).GridData;
MgSeq = CoarseningAlgorithms.CreateSequence(grid);
for (int p = 0; p <= 3; p++) // loop over polynomial degrees...
{
var uMapping = new UnsetteledCoordinateMapping(new Basis(grid, p));
var MgMapSeq = new MultigridMapping[MgSeq.Length];
var BasisSeq = AggregationGridBasis.CreateSequence(MgSeq, uMapping.BasisS);
for (int iLevel = 0; iLevel < MgSeq.Length; iLevel++)
{
MgMapSeq[iLevel] = new MultigridMapping(uMapping, BasisSeq[iLevel], new int[] { p });
}
MultigrigMap.Add(p, MgMapSeq);
}
}
public static void Init()
{
bool dummy;
ilPSP.Environment.Bootstrap(
new string[0],
BoSSS.Solution.Application.GetBoSSSInstallDir(),
out dummy);
//GridCommons grd = Grid2D.Cartesian2DGrid(RandomSpacing(), RandomSpacing());
//grid = new GridData(Grid2D.Cartesian2DGrid(GenericBlas.Linspace(-7, 7, 8), GenericBlas.Linspace(-1, 1, 2)));
//grid = new GridData(Grid2D.Cartesian2DGrid(new double[] { -6, -4, -2, 2, 4, 6 }, GenericBlas.Linspace(-1, 1, 2)));
grid = new GridData(Grid2D.Cartesian2DGrid(GenericBlas.Linspace(-1.5, 1.5, 17), GenericBlas.Linspace(-1.5, 1.5, 17)));
MgSeq = CoarseningAlgorithms.CreateSequence(grid);
for (int p = 0; p <= 3; p++) // loop over polynomial degrees...
{
var uMapping = new UnsetteledCoordinateMapping(new Basis(grid, p));
var MgMapSeq = new MultigridMapping[MgSeq.Length];
var BasisSeq = AggregationGridBasis.CreateSequence(MgSeq, uMapping.BasisS);
for (int iLevel = 0; iLevel < MgSeq.Length; iLevel++)
{
MgMapSeq[iLevel] = new MultigridMapping(uMapping, BasisSeq[iLevel], new int[] { p });
}
MultigrigMap.Add(p, MgMapSeq);
}
}
/// <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());
}
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);
}
/// <summary>
/// Initialization of the solver/preconditioner.
/// </summary>
protected void InitMultigrid(DGField[] Fields, bool useX)
{
Basis[] bs;
if (useX)
{
bs = new Basis[Fields.Length];
for (int i = 0; i < bs.Length; i++)
{
bs[i] = new XDGBasis(m_LsTrk, Fields[i].Basis.Degree);
}
}
else
{
bs = Fields.Select(f => f.Basis).ToArray();
}
this.MultigridBasis = AggregationGridBasis.CreateSequence(this.MultigridSequence, bs);
}
public static void Init()
{
grid = Grid2D.CurvedSquareGrid(GenericBlas.Linspace(1, 2, 17), GenericBlas.Linspace(0, 1, 17), CellType.Square_9, true).GridData;
MgSeq = CoarseningAlgorithms.CreateSequence(grid);
for (int p = 0; p <= 3; p++)
{ // loop over polynomial degrees...
var uMapping = new UnsetteledCoordinateMapping(new Basis(grid, p));
var MgMapSeq = new MultigridMapping[MgSeq.Length];
var BasisSeq = AggregationGridBasis.CreateSequence(MgSeq, uMapping.BasisS);
for (int iLevel = 0; iLevel < MgSeq.Length; iLevel++)
{
MgMapSeq[iLevel] = new MultigridMapping(uMapping, BasisSeq[iLevel], new int[] { p });
}
MultigrigMap.Add(p, MgMapSeq);
}
}
private void Setup()
{
MgSeq = CoarseningAlgorithms.CreateSequence(m_grid.iGridData);
int p = m_DGorder;
var uMapping = new UnsetteledCoordinateMapping(u1.Basis, u2.Basis);
//var uMapping = new UnsetteledCoordinateMapping(u1.Basis);
//var uMapping = new UnsetteledCoordinateMapping(new Basis(m_grid.iGridData, p));
XAggB = AggregationGridBasis.CreateSequence(MgSeq, uMapping.BasisS);
var bla = LsTrk.SpeciesIdS.ToArray();
var agg = LsTrk.GetAgglomerator(bla, m_quadOrder, THRESHOLD, AgglomerateNewborn: false, AgglomerateDecased: false, ExceptionOnFailedAgglomeration: true);
XAggB.UpdateXdgAggregationBasis(agg);
var VarDegrees = uMapping.BasisS.Count.ForLoop(i => uMapping.BasisS[i].Degree);
MG_Mapping = new MultigridMapping(uMapping, XAggB[0], VarDegrees);
map = uMapping;
}
public static void RestrictionOfSystemOpTest()
{
Basis B1 = new Basis(grid, 0), B2 = new Basis(grid, 2);
var Map = new UnsetteledCoordinateMapping(B1, B2);
AggregationGridBasis[][] aB = AggregationGridBasis.CreateSequence(TestProgram.MgSeq.Take(2), new Basis[] { B1, B2 });
var Lev0 = new MultigridMapping(Map, aB[0], new int[] { B1.Degree, B2.Degree });
var Lev1 = new MultigridMapping(Map, aB[1], new int[] { B1.Degree, B2.Degree });
int[] I0col = Lev0.GetSubvectorIndices(new int[] { 0 });
int[] I1col = Lev0.GetSubvectorIndices(new int[] { 1 });
int[] I0row = Lev1.GetSubvectorIndices(new int[] { 0 });
int[] I1row = Lev1.GetSubvectorIndices(new int[] { 1 });
var RestMtx = Lev1.FromOtherLevelMatrix(Lev0);
MsrMatrix Rest00 = new MsrMatrix(I0row.Length, I0col.Length, 1, 1);
RestMtx.WriteSubMatrixTo(Rest00, I0row, default(int[]), I0col, default(int[]));
MsrMatrix Rest01 = new MsrMatrix(I0row.Length, I1col.Length, 1, 1);
RestMtx.WriteSubMatrixTo(Rest01, I0row, default(int[]), I1col, default(int[]));
MsrMatrix Rest10 = new MsrMatrix(I1row.Length, I0col.Length, 1, 1);
RestMtx.WriteSubMatrixTo(Rest10, I1row, default(int[]), I0col, default(int[]));
MsrMatrix Rest11 = new MsrMatrix(I1row.Length, I1col.Length, 1, 1);
RestMtx.WriteSubMatrixTo(Rest11, I1row, default(int[]), I1col, default(int[]));
Assert.IsTrue(Rest10.InfNorm() == 0.0);
Assert.IsTrue(Rest01.InfNorm() == 0.0);
Assert.IsTrue(Rest00.InfNorm() != 0.0);
Assert.IsTrue(Rest11.InfNorm() != 0.0);
}
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
}
}
});
}
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);
*
* }
*/
}
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>
/// 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>
/// 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);
}
}
}