public static void CellwiseSubSelection(
[Values(SelectionType.all_combined, SelectionType.degrees, SelectionType.species, SelectionType.variables)] SelectionType SType
)
{
Utils.TestInit((int)SType);
Console.WriteLine("SubSelection({0})", SType);
//Arrange --- extracts entries of matrix according to hardcoded selection
int DGdegree = 2;
int GridResolution = 4;
var mgo = Utils.CreateTestMGOperator(XDGusage.all, DGdegree, MatrixShape.full_var_spec, GridResolution);
int sampleCellA = Utils.GetIdxOfFirstBlockWith(mgo.Mapping, false); //1 species
int sampleCellB = Utils.GetIdxOfFirstBlockWith(mgo.Mapping, true); //2 species
BlockMsrMatrix compA = Utils.GetCellCompMatrix(SType, mgo, sampleCellA);
BlockMsrMatrix compB = Utils.GetCellCompMatrix(SType, mgo, sampleCellB);
int iBlock = sampleCellB + mgo.Mapping.AggGrid.CellPartitioning.i0;
int i0 = mgo.Mapping.GetBlockI0(iBlock);
var block = MultidimensionalArray.Create(mgo.Mapping.GetBlockLen(iBlock), mgo.Mapping.GetBlockLen(iBlock));
mgo.OperatorMatrix.ReadBlock(i0, i0, block);
//Arrange --- setup masking, which correspond to hardcoded
SubBlockSelector sbsA = new SubBlockSelector(mgo.Mapping);
sbsA.GetDefaultSelection(SType, sampleCellA); // single spec
BlockMask maskA = new BlockMask(sbsA, null);
SubBlockSelector sbsB = new SubBlockSelector(mgo.Mapping);
sbsB.GetDefaultSelection(SType, sampleCellB); // double spec
BlockMask maskB = new BlockMask(sbsB, null);
//Arrange --- some time measurement
Stopwatch stw = new Stopwatch();
stw.Reset();
//Act --- subblock extraction
stw.Start();
var blocksA = maskA.GetDiagonalBlocks(mgo.OperatorMatrix, false, false);
var blocksB = maskB.GetDiagonalBlocks(mgo.OperatorMatrix, false, false);
stw.Stop();
//Assert ---
Assert.IsTrue(blocksA.Length == 1);
Assert.IsTrue(blocksB.Length == 1);
Assert.IsTrue(compA.RowPartitioning.LocalLength == blocksA[0].GetLength(0));
Assert.IsTrue(compB.RowPartitioning.LocalLength == blocksB[0].GetLength(0));
//Assert --- compare masking of single spec cell
Debug.Assert(compA.InfNorm() != 0.0);
compA.AccBlock(0, 0, -1.0, blocksA[0]);
Assert.IsTrue(compA.InfNorm() == 0.0);
//Assert --- compare masking of double spec cell
Debug.Assert(compB.InfNorm() != 0.0);
compB.AccBlock(0, 0, -1.0, blocksB[0]);
Assert.IsTrue(compB.InfNorm() == 0.0, String.Format("proc{0}: not fulfilled at block {1}", mgo.Mapping.MpiRank, sampleCellB));
}
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 DefaultCellSplit(this SubBlockSelector sbs, bool upper, bool islocal = true)
{
List <int> odds = new List <int>();
List <int> even = new List <int>();
int i0, iE;
if (islocal)
{
i0 = 0;
iE = sbs.GetMapping.LocalNoOfBlocks;
}
else
{
i0 = sbs.GetMapping.LocalNoOfBlocks;
iE = sbs.GetMapping.AggGrid.iLogicalCells.NoOfExternalCells + sbs.GetMapping.LocalNoOfBlocks;
}
for (int i = i0; i < iE; i++)
{
if (i % 2 != 0)
{
odds.Add(i);
}
else
{
even.Add(i);
}
}
sbs.CellSelector(upper ? odds : even, false);
}
public static void GetDefaultSelection(this SubBlockSelector sbs, SelectionType SType, int iCell)
{
SpeciesId A = ((XdgAggregationBasis)sbs.GetMapping.AggBasis[0]).UsedSpecies[0];
SpeciesId B = ((XdgAggregationBasis)sbs.GetMapping.AggBasis[0]).UsedSpecies[1];
sbs.CellSelector(iCell, false);
//do not change this, selection corresponds to hardcoded masking
//see GetSubIndices
switch (SType)
{
case SelectionType.degrees:
sbs.ModeSelector(p => p == 1);
break;
case SelectionType.species:
sbs.SpeciesSelector(A);
break;
case SelectionType.variables:
sbs.VariableSelector(1);
break;
case SelectionType.all_combined:
sbs.ModeSelector(p => p == 1);
sbs.SpeciesSelector(A);
sbs.VariableSelector(1);
break;
}
}
public static int[] AllExternalCellsSelection(this SubBlockSelector sbs)
{
var map = sbs.GetMapping;
var extcells = GetAllExternalCells(map);
sbs.CellSelector(extcells, false);
return(extcells);
}
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);
}
/// <summary>
/// returns the condition number of the full matrix
/// </summary>
public double CondNumMatlab()
{
int[] DepVars = this.VarGroup;
var grd = m_map.GridDat;
int NoOfCells = grd.Grid.NumberOfCells;
int NoOfBdryCells = grd.GetBoundaryCells().NoOfItemsLocally_WithExternal;
var Mtx = m_MultigridOp.OperatorMatrix;
// Blocks and selectors
// ====================
var InnerCellsMask = grd.GetBoundaryCells().Complement();
var FullSel = new SubBlockSelector(m_MultigridOp.Mapping);
FullSel.VariableSelector(this.VarGroup);
// Matlab
// ======
double[] Full_0Vars = (new BlockMask(FullSel)).GlobalIndices.Select(i => i + 1.0).ToArray();
MultidimensionalArray output = MultidimensionalArray.Create(2, 1);
string[] names = new string[] { "Full_0Vars", "Inner_0Vars" };
using (BatchmodeConnector bmc = new BatchmodeConnector()) {
// if Octave should be used instead of Matlab....
// BatchmodeConnector.Flav = BatchmodeConnector.Flavor.Octave;
bmc.PutSparseMatrix(Mtx, "FullMatrix");
bmc.PutVector(Full_0Vars, "Full_0Vars");
bmc.Cmd("output = ones(2,1);");
bmc.Cmd("output(1) = condest(FullMatrix(Full_0Vars,Full_0Vars));");
bmc.GetMatrix(output, "output");
bmc.Execute(false);
double condestFull = output[0, 0];
Debug.Assert(condestFull.MPIEquals(), "value does not match on procs");
Console.WriteLine($"MATLAB condition number: {condestFull:0.###e-00}");
return(condestFull);
}
}
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);
}
public static void SplitVectorOperations(
XDGusage UseXdg,
int DGOrder,
MatrixShape MShape
)
{
Utils.TestInit((int)UseXdg, DGOrder, (int)MShape);
Console.WriteLine("SplitVectorOperations({0},{1},{2})", UseXdg, DGOrder, MShape);
//matrix Erzeugung wie in ExtractDiagonalCellBlocks...
//Auf der HierarchieEbene, auf der Kopplung ausgesetzt wird kann Auswahl vorgenommen werden
//bei var: 0 / 1, bei DG: <=1 / >1, bei spec: A / B, bei Cells: odd / even
//accumulierte Teilergebnisse sind dann == fullM*fullX
var mop = Utils.CreateTestMGOperator(UseXdg, DGOrder, MShape);
var map = mop.Mapping;
double[] Vec = Utils.GetRandomVector(mop.Mapping.LocalLength);
//Arrange --- setup masking
SubBlockSelector sbsA = new SubBlockSelector(map);
sbsA.SetDefaultSplitSelection(MShape, true);
BlockMask maskA = new BlockMask(sbsA, null);
SubBlockSelector sbsB = new SubBlockSelector(map);
sbsB.SetDefaultSplitSelection(MShape, false);
BlockMask maskB = new BlockMask(sbsB, null);
double[] VecAB = new double[Vec.Length];
//Arrange --- some time measurement
Stopwatch stw = new Stopwatch();
stw.Reset();
//Act ---
stw.Start();
var VecA = maskA.GetSubVec(Vec);
var VecB = maskB.GetSubVec(Vec);
maskA.AccSubVec(VecA, VecAB);
maskB.AccSubVec(VecB, VecAB);
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!"));
}
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 static void DefaultVarSplit(this SubBlockSelector sbs, bool upper)
{
sbs.VariableSelector(upper ? 0 : 1);
int NoOfVar = sbs.GetMapping.NoOfVariables;
int[] OtherVars = (NoOfVar - 1).ForLoop(i => i + 1);
if (upper)
{
sbs.VariableSelector(0);
}
else
{
sbs.VariableSelector(OtherVars);
}
}
public static void SubSelection(
[Values(SelectionType.all_combined, SelectionType.degrees, SelectionType.species, SelectionType.variables)] SelectionType SType
)
{
Utils.TestInit((int)SType);
Console.WriteLine("SubSelection({0})", SType);
//Arrange --- extracts entries of matrix according to hardcoded selection
int DGdegree = 2;
int GridResolution = 4;
var mgo = Utils.CreateTestMGOperator(XDGusage.all, DGdegree, MatrixShape.full_var_spec, GridResolution);
int sampleCellA = Utils.GetIdxOfFirstBlockWith(mgo.Mapping, false); //1 species
int sampleCellB = Utils.GetIdxOfFirstBlockWith(mgo.Mapping, true); //2 species
BlockMsrMatrix compA = Utils.GetCellCompMatrix(SType, mgo, sampleCellA);
BlockMsrMatrix compB = Utils.GetCellCompMatrix(SType, mgo, sampleCellB);
//Arrange --- setup masking, which correspond to hardcoded
SubBlockSelector sbsA = new SubBlockSelector(mgo.Mapping);
sbsA.GetDefaultSelection(SType, sampleCellA); // single spec
BlockMask maskA = new BlockMask(sbsA, null);
SubBlockSelector sbsB = new SubBlockSelector(mgo.Mapping);
sbsB.GetDefaultSelection(SType, sampleCellB); // double spec
BlockMask maskB = new BlockMask(sbsB, null);
//Arrange --- stop the watch
Stopwatch stw = new Stopwatch();
stw.Reset();
//Act --- get subblocks
stw.Start();
BlockMsrMatrix subA = maskA.GetSubBlockMatrix(mgo.OperatorMatrix);
BlockMsrMatrix subB = maskB.GetSubBlockMatrix(mgo.OperatorMatrix);
stw.Stop();
//Assert --- compare masking of single spec cell
Debug.Assert(compA.InfNorm() != 0.0);
subA.Acc(-1.0, compA);
Assert.IsTrue(subA.InfNorm() == 0.0);
//Assert --- compare masking of double spec cell
Debug.Assert(compB.InfNorm() != 0.0);
subB.Acc(-1.0, compB);
Assert.IsTrue(subB.InfNorm() == 0.0);
}
public static void CellBlockVectorOperations(
[Values(XDGusage.none, XDGusage.all)] XDGusage UseXdg,
[Values(2)] int DGOrder,
[Values(MatrixShape.diagonal, MatrixShape.diagonal_var, MatrixShape.diagonal_spec, MatrixShape.diagonal_var_spec)] MatrixShape MShape
)
{
//matrix Erzeugung wie in ExtractDiagonalCellBlocks...
//Auf der HierarchieEbene, auf der Kopplung ausgesetzt wird kann Auswahl vorgenommen werden
//bei var: 0 / 1, bei DG: <=1 / >1, bei spec: A / B, bei Cells: odd / even
//accumulierte Teilergebnisse sind dann == fullM*fullX
Utils.TestInit((int)UseXdg, DGOrder, (int)MShape);
Console.WriteLine("CellBlockVectorOperations({0},{1},{2})", UseXdg, DGOrder, MShape);
var mop = Utils.CreateTestMGOperator(UseXdg, DGOrder, MShape);
var map = mop.Mapping;
double[] Vec = Utils.GetRandomVector(mop.Mapping.LocalLength);
//Arrange --- setup masking
SubBlockSelector SBS = new SubBlockSelector(map);
BlockMask mask = new BlockMask(SBS, null);
//Arrange --- some time measurement
Stopwatch stw = new Stopwatch();
stw.Reset();
//Assert --- all diagonal blocks are extracted
//Assert.IsTrue(blocks.Length == map.LocalNoOfBlocks);
double[] Vec_col = new double[map.LocalLength];
for (int i = 0; i < map.LocalNoOfBlocks; i++)
{
stw.Start();
double[] Vec_i = mask.GetSubVecOfCell(Vec, i);
mask.AccSubVecOfCell(Vec_i, i, Vec_col);
stw.Stop();
}
Vec_col.AccV(-1.0, Vec);
//Assert --- are extracted blocks and
Assert.IsTrue(Vec_col.L2Norm() == 0.0, String.Format("L2Norm neq 0!"));
}
private static void DefaultSpeciesSplit(this SubBlockSelector sbs, bool upper)
{
if (sbs.GetMapping.AggBasis[0] is XdgAggregationBasis)
{
SpeciesId[] SIdc = ((XdgAggregationBasis)sbs.GetMapping.AggBasis[0]).UsedSpecies;
SpeciesId[] OtherSpec = (SIdc.Length - 1).ForLoop(i => SIdc[i + 1]);
if (upper)
{
sbs.SpeciesSelector(SIdc[0]);
}
else
{
sbs.SpeciesSelector(OtherSpec);
}
}
else
{
throw new NotSupportedException();
}
}
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);
}
/// <summary>
/// Local condition number formed by the block of each cell and its neighbors.
/// </summary>
/// <returns>
/// one value per cell:
/// - index: local cell index
/// - content: condition number (one norm) of the local stencil
/// </returns>
public double[] StencilCondNumbers()
{
using (new FuncTrace()) {
int J = m_map.LocalNoOfBlocks;
Debug.Assert(J == m_map.GridDat.iLogicalCells.NoOfLocalUpdatedCells);
var Mtx = m_MultigridOp.OperatorMatrix;
Debug.Assert(Mtx._ColPartitioning.LocalNoOfBlocks == J);
Debug.Assert(Mtx._RowPartitioning.LocalNoOfBlocks == J);
var grd = m_MultigridOp.Mapping.AggGrid;
double[] BCN = new double[J];
for (int j = 0; j < J; j++)
{
var LocBlk = grd.GetCellNeighboursViaEdges(j).Select(t => t.Item1).ToList();
LocBlk.Add(j);
for (int i = 0; i < LocBlk.Count; i++)
{
if (LocBlk[i] >= J)
{
LocBlk.RemoveAt(i);
i--;
}
}
var Sel = new SubBlockSelector(m_MultigridOp.Mapping);
Sel.VariableSelector(this.VarGroup);
Sel.CellSelector(LocBlk, global: false);
var Mask = new BlockMask(Sel);
MultidimensionalArray[,] Blocks = Mask.GetFullSubBlocks(Mtx, ignoreSpecCoupling: false, ignoreVarCoupling: false);
MultidimensionalArray FullBlock = Blocks.Cat();
BCN[j] = FullBlock.Cond('I');
}
return(BCN);
}
}
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]);
}
}
/// <summary>
/// Local condition number for the block formed by each cell.
/// </summary>
/// <returns>
/// one value per cell:
/// - index: local cell index
/// - content: condition number (one norm) of the local stencil
/// </returns>
public double[] BlockCondNumbers()
{
int J = m_map.LocalNoOfBlocks;
Debug.Assert(J == m_map.GridDat.iLogicalCells.NoOfLocalUpdatedCells);
var Mtx = m_MultigridOp.OperatorMatrix;
Debug.Assert(Mtx._ColPartitioning.LocalNoOfBlocks == J);
Debug.Assert(Mtx._RowPartitioning.LocalNoOfBlocks == J);
var Sel = new SubBlockSelector(m_MultigridOp.Mapping);
Sel.VariableSelector(this.VarGroup);
var Mask = new BlockMask(Sel);
MultidimensionalArray[] Blocks = Mask.GetDiagonalBlocks(Mtx, ignoreSpecCoupling: false, ignoreVarCoupling: false);
Debug.Assert(Blocks.Length == J);
double[] BCN = new double[J];
for (int j = 0; j < J; j++)
{
#if DEBUG
int N = this.VarGroup.Sum(iVar => m_MultigridOp.Mapping.AggBasis[iVar].GetLength(j, m_MultigridOp.Degrees[iVar]));
Debug.Assert(Blocks[j].NoOfCols == N);
Debug.Assert(Blocks[j].NoOfRows == N);
int i0 = m_MultigridOp.Mapping.GlobalUniqueIndex(this.VarGroup.Min(), j, 0);
Debug.Assert(Mtx[i0, i0] == Blocks[j][0, 0]);
#endif
BCN[j] = Blocks[j].Cond();
}
return(BCN);
}
/// <summary>
/// returns the condition number of the full matrix using MUMPS;
/// Note:
/// </summary>
public double CondNumMUMPS()
{
using (new FuncTrace()) {
int[] DepVars = this.VarGroup;
var grd = m_map.GridDat;
int NoOfCells = grd.Grid.NumberOfCells;
int NoOfBdryCells = grd.GetBoundaryCells().NoOfItemsLocally_WithExternal;
var Mtx = m_MultigridOp.OperatorMatrix;
// Blocks and selectors
// ====================
var InnerCellsMask = grd.GetBoundaryCells().Complement();
var FullSel = new SubBlockSelector(m_MultigridOp.Mapping);
FullSel.VariableSelector(this.VarGroup);
var InnerSel = new SubBlockSelector(m_MultigridOp.Mapping);
InnerSel.VariableSelector(this.VarGroup);
InnerSel.CellSelector(InnerCellsMask);
// MUMPS condition number
// ======================
double condestFullMUMPS = (new BlockMask(FullSel)).GetSubBlockMatrix(Mtx).Condest_MUMPS();
//double condestInnerMUMPS = 1.0;
//if(InnerCellsMask.NoOfItemsLocally.MPISum() > 0) {
// condestInnerMUMPS = (new BlockMask(InnerSel)).GetSubBlockMatrix(Mtx).Condest_MUMPS();
//}
//return new[] { condestFullMUMPS, condestInnerMUMPS };
return(condestFullMUMPS);
}
}
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 static void SetDefaultSplitSelection(this SubBlockSelector sbs, MatrixShape shape, bool upper, bool islocal = true)
{
switch (shape)
{
case MatrixShape.diagonal:
case MatrixShape.full:
sbs.DefaultCellSplit(upper, islocal);
break;
case MatrixShape.diagonal_var:
case MatrixShape.full_var:
sbs.DefaultSpeciesSplit(upper);
if (!islocal)
{
sbs.AllExternalCellsSelection();
}
break;
case MatrixShape.diagonal_spec:
case MatrixShape.full_spec:
sbs.DefaultVarSplit(upper);
if (!islocal)
{
sbs.AllExternalCellsSelection();
}
break;
case MatrixShape.diagonal_var_spec:
case MatrixShape.full_var_spec:
sbs.DefaultCellSplit(upper, islocal);
break;
default:
throw new NotSupportedException(String.Format("{0} is not supported by this test", shape));
}
}
public static void SubBlockExtraction(
[Values(XDGusage.none, XDGusage.all)] XDGusage UseXdg,
[Values(2)] int DGOrder,
[Values(MatrixShape.diagonal_var_spec, MatrixShape.diagonal_spec, MatrixShape.diagonal_var, MatrixShape.diagonal)] MatrixShape MShape,
[Values(4)] int Res
)
{
Utils.TestInit((int)UseXdg, DGOrder, (int)MShape);
Console.WriteLine("SubMatrixIgnoreCoupling({0},{1},{2})", UseXdg, DGOrder, MShape);
//Arrange --- create test matrix and MG mapping
MultigridOperator mgo = Utils.CreateTestMGOperator(UseXdg, DGOrder, MShape, Res);
MultigridMapping map = mgo.Mapping;
BlockMsrMatrix M = mgo.OperatorMatrix;
//Arrange --- masking of all external cells
var sbs = new SubBlockSelector(map);
sbs.AllExternalCellsSelection();
var M_ext = BlockMask.GetAllExternalRows(map, M);
var mask = new BlockMask(sbs, M_ext);
//bool[] coup = Utils.SetCoupling(MShape);
//Arrange --- get index dictonary of all external cell indices
Dictionary <int, int[]> Didc = Utils.GetDictOfAllExtCellIdc(map);
//Arrange --- stopwatch
var stw = new Stopwatch();
stw.Reset();
//Act --- Extract subblocks
stw.Start();
//var eblocks = mask.GetSubBlocks(M,coup[0],coup[1],coup[2]);
var eblocks = mask.GetDiagonalBlocks(M, false, false);
stw.Stop();
//Assert --- same number of blocks?
Assert.IsTrue(eblocks.Length == M_ext._RowPartitioning.LocalNoOfBlocks);
bool test = eblocks.Length.MPIEquals();
Debug.Assert(test);
for (int iBlock = 0; iBlock < eblocks.Length; iBlock++)
{
var infNorm = MultidimensionalArray.Create(4, 1);
int rank = map.MpiRank;
int ExtBlockIdx = iBlock + map.AggGrid.iLogicalCells.NoOfLocalUpdatedCells;
Didc.TryGetValue(ExtBlockIdx, out int[] idc);
using (BatchmodeConnector matlab = new BatchmodeConnector()) {
double[] GlobIdx = idc.Count().ForLoop(i => (double)idc[i] + 1.0);
Assert.IsTrue(GlobIdx.Length == eblocks[iBlock].Lengths[0]);
MsrMatrix M_sub = eblocks[iBlock].ConvertToMsr();
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); //
}
}
public static void VectorCellwiseOperation(
[Values(XDGusage.none, XDGusage.all)] XDGusage UseXdg,
[Values(2)] int DGOrder,
[Values(MatrixShape.diagonal_var_spec, MatrixShape.diagonal_spec, MatrixShape.diagonal_var, MatrixShape.diagonal)] MatrixShape MShape,
[Values(4)] int Res
)
{
Utils.TestInit((int)UseXdg, DGOrder, (int)MShape);
Console.WriteLine("SubMatrixIgnoreCoupling({0},{1},{2})", UseXdg, DGOrder, MShape);
//Arrange --- create test matrix, MG mapping
MultigridOperator mgo = Utils.CreateTestMGOperator(UseXdg, DGOrder, MShape, Res);
MultigridMapping map = mgo.Mapping;
BlockMsrMatrix M = mgo.OperatorMatrix;
//Arrange --- masking and subblock extraction of external cells
var sbs = new SubBlockSelector(map);
sbs.AllExternalCellsSelection();
var M_ext = BlockMask.GetAllExternalRows(map, M);
var mask = new BlockMask(sbs, M_ext);
var eblocks = mask.GetDiagonalBlocks(M, false, false);
//Dictionary<int, int[]> Didc = Utils.GetDictOfAllExtCellIdc(map);
//Arrange --- generate rnd vector and distribute it
double[] vec = new double[map.LocalLength];
vec = Utils.GetRandomVector(map.LocalLength);
var vec_ex = new MPIexchange <double[]>(map, vec);
vec_ex.TransceiveStartImReturn();
vec_ex.TransceiveFinish(0.0);
Debug.Assert(vec_ex.Vector_Ext.L2Norm() != 0);
//Arrange --- stopwatch
var stw = new Stopwatch();
stw.Reset();
//Arrange --- get extended (loc+external cells) vector
double[] Vec_ext = new double[vec.Length + vec_ex.Vector_Ext.Length];
mask.AccSubVec(vec_ex.Vector_Ext, Vec_ext);
bool test = eblocks.Length.MPIEquals();
Debug.Assert(test);
//Act --- calculate blockwise result: M_i*vec_i=Res_i
double[] Res_ext = new double[Vec_ext.Length];
stw.Start();
for (int i = 0; i < eblocks.Length; i++)
{
//int iBlock = i + map.AggGrid.iLogicalCells.NoOfLocalUpdatedCells;
double[] vec_i = mask.GetSubVecOfCell(Vec_ext, i);
double[] Res_i = new double[vec_i.Length];
eblocks[i].MatVecMul(1.0, vec_i, 0.0, Res_i);
mask.AccSubVecOfCell(Res_i, i, Res_ext);
if (map.MpiRank == 0)
{
eblocks[i].ConvertToMsr().SaveToTextFileSparseDebug(String.Format("block_{0}_{1}", i, map.MpiRank));
vec_i.SaveToTextFileDebug(String.Format("vec_{0}_{1}", i, map.MpiRank));
Res_i.SaveToTextFileDebug(String.Format("Res_{0}_{1}", i, map.MpiRank));
}
}
stw.Stop();
//Act --- project Res_i onto Res_g and Res_g=M_ext*vec_ext-Res_g
double[] Res_g = mask.GetSubVec(Res_ext);
var qM_ext = M_ext.ConvertToQuadraticBMsr(mask.GlobalIList_External.ToArray(), false);
qM_ext.SpMV(1.0, vec_ex.Vector_Ext, -1.0, Res_g);
if (map.MpiRank == 0)
{
vec_ex.Vector_Ext.SaveToTextFileDebug("vec_g");
Res_g.SaveToTextFileDebug("Res_g");
M_ext.SaveToTextFileSparseDebug("M_ext");
qM_ext.SaveToTextFileSparseDebug("qM_ext");
}
//Assert --- |Res_g| should be at least near to zero
Assert.IsTrue(Res_g.L2Norm() == 0.0);
}
public static void FastSubMatrixExtraction(
[Values(XDGusage.none, XDGusage.all)] XDGusage UseXdg,
[Values(2)] int DGOrder,
[Values(MatrixShape.laplace)] MatrixShape MShape,
[Values(4)] int Res
)
{
Utils.TestInit((int)UseXdg, DGOrder, (int)MShape);
Console.WriteLine("FastSubMatrixExtraction({0},{1},{2})", UseXdg, DGOrder, MShape);
//Arrange ---
MultigridOperator mgo = Utils.CreateTestMGOperator(UseXdg, DGOrder, MShape, Res);
MultigridMapping map = mgo.Mapping;
BlockMsrMatrix M = mgo.OperatorMatrix;
var sbs = new SubBlockSelector(map);
int[] extcells = sbs.AllExternalCellsSelection();
var M_ext = BlockMask.GetAllExternalRows(map, M);
var mask = new BlockMask(sbs, M_ext);
//Arrange --- get index list of all external cells
int[] idc = Utils.GetAllExtCellIdc(map);
double[] GlobIdx = idc.Count().ForLoop(i => (double)idc[i] + 1.0);
//Arrange --- stopwatch
var stw = new Stopwatch();
stw.Reset();
//Act --- Extract SubMatrix
stw.Start();
BlockMsrMatrix subM = mask.GetSubBlockMatrix(M);
stw.Stop();
//Arrange --- Extract Blocks in Matlab and substract
var infNorm = MultidimensionalArray.Create(4, 1);
int rank = map.MpiRank;
using (BatchmodeConnector matlab = new BatchmodeConnector()) {
matlab.PutSparseMatrix(M, "M");
// note: M_sub lives on Comm_Self, therefore we have to distinguish between procs ...
matlab.PutSparseMatrixRankExclusive(subM, "M_sub");
matlab.PutVectorRankExclusive(GlobIdx, "Idx");
matlab.Cmd("M_0 = M(Idx_0, Idx_0);");
matlab.Cmd("M_1 = M(Idx_1, Idx_1);");
matlab.Cmd("M_2 = M(Idx_2, Idx_2);");
matlab.Cmd("M_3 = 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 --- mask blocks and extracted blocks are the same
Assert.IsTrue(infNorm[rank, 0] == 0.0);
}
public static void SubBlockExtractionWithCoupling(
[Values(XDGusage.none, XDGusage.all)] XDGusage UseXdg,
[Values(2)] int DGOrder,
[Values(MatrixShape.diagonal, MatrixShape.diagonal_var, MatrixShape.diagonal_spec, MatrixShape.diagonal_var_spec)] MatrixShape MShape
)
{
Utils.TestInit((int)UseXdg, DGOrder, (int)MShape);
Console.WriteLine("ExtractDiagonalBlocks({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[] coupling = Utils.SetCoupling(MShape);
//Arrange --- some time measurement
Stopwatch stw = new Stopwatch();
stw.Reset();
//Arrange --- setup auxiliary matrix
//this will show us if more is extracted, than it should ...
var Mprep = new BlockMsrMatrix(map);
Mprep.Acc(1.0, M);
//Act --- diagonal subblock extraction
stw.Start();
var blocks = mask.GetDiagonalBlocks(Mprep, coupling[0], coupling[1]);
stw.Stop();
//Assert --- all diagonal blocks are extracted
Assert.IsTrue(blocks.Length == map.LocalNoOfBlocks);
for (int i = 0; i < map.LocalNoOfBlocks; i++)
{
//Arrange --- get ith diagonal block of M: M_i
int iBlock = i + map.AggGrid.CellPartitioning.i0;
int L = map.GetBlockLen(iBlock);
int i0 = map.GetBlockI0(iBlock);
var Mblock = MultidimensionalArray.Create(L, L);
M.ReadBlock(i0, i0, Mblock);
//Act --- M_i-Mones_i
Mblock.Acc(-1.0, blocks[i]);
//Assert --- are extracted blocks and
Assert.IsTrue(Mblock.InfNorm() == 0.0, String.Format("infNorm of block {0} neq 0!", i));
}
//BlockMsrMatrix all1;
//all1.SetAll(1);
//Generate broken diagonal matrix, die zur Maske passt: M
//M+all1=M_prep
//Wende Extraction auf M_prep an, Man sollte nun M bekommen
//Test: M_prep-extract(M_prep)=all1
//Test-crit: Result.SumEntries=DOF^2 oder Result.Max()==Result.Min()==1
//oder (besser)
//Test: M-extract(M_prep)=zeros
//Test-crit: Result.InfNorm()==0
//Der Test kann für ExtractSubMatrix mit ignore coupling wiederholt werden
//eventuell: Testmatrix finden mit brauchbaren Nebendiagonalen für einen Fall
//Was wird getestet: funktioniert ignorecoupling richtig?
}
public TestMask(SubBlockSelector SBS, BlockMsrMatrix ExtRows) : base(SBS, ExtRows)
{
Global_IList_LocalCells = base.GlobalIList_Internal.ToArray();
Global_IList_ExternalCells = base.GlobalIList_External.ToArray();
}
