public static double rhoDinvA(MsrMatrix A, out MsrMatrix DinvA)
{
double rho;
// extract diagonal matrix
double[] Diag = A.GetDiagVector();
int n = Diag.Length;
// % form (D^-1) A
//Diag = spdiags(1./Diag, 0, n, n);
//DinvA = Diag*A;
DinvA = new MsrMatrix(A.RowPartitioning, A.ColPartition);
int i0 = A.RowPartitioning.i0;
int Lr;
int[] ColumnIdx = null;
double[] Values = null;
for (int i = 0; i < n; i++)
{
Lr = A.GetRow(i + i0, ref ColumnIdx, ref Values);
for (int k = 0; k < Lr; k++)
{
Values[k] *= 1.0 / Diag[i];
}
DinvA.SetRow(i + i0, ColumnIdx, Values, Lr);
}
#if DEBUG
for (int i = 0; i < n; i++)
{
Debug.Assert(Math.Abs(1.0 - DinvA[i + i0, i + i0]) < BLAS.MachineEps * 10);
}
#endif
// estimate the largest eigen value from Arnoldi iteration
int kk = 20;
var rand = new Random(0);
double[] v0 = n.ForLoop(i => rand.NextDouble());
double[][] V; double[,] H; int kact;
arnoldi(out V, out H, out kact, DinvA, v0, kk, false);
kk = Math.Min(H.GetLength(0), H.GetLength(1));
H = H.GetSubMatrix(0, kk, 0, kk);
rho = MaxAbsEigen(H);
return(rho);
}
/// <summary>
/// Create Spatial Operators and build the corresponding Matrices
/// </summary>
public void ComputeMatrices(IList <DGField> InterfaceParams, bool nearfield)
{
OpMatrix = new MsrMatrix(this.Extension.Mapping, this.Extension.Mapping);
OpAffine = new double[OpMatrix.RowPartitioning.LocalLength];
OpMatrix_bulk = new MsrMatrix(this.Extension.Mapping, this.Extension.Mapping);
OpAffine_bulk = new double[OpMatrix.RowPartitioning.LocalLength];
OpMatrix_interface = new MsrMatrix(this.Extension.Mapping, this.Extension.Mapping);
OpAffine_interface = new double[OpMatrix.RowPartitioning.LocalLength];
//LevelSetTracker.GetLevelSetGradients(0,);
// bulk part of the matrix
//Operator_bulk.ComputeMatrix(
// Extension.Mapping,
// LevelSetGradient.ToArray(),
// Extension.Mapping,
// OpMatrix_bulk, OpAffine_bulk,
// OnlyAffine: false, sgrd: null);
switch (Control.FluxVariant)
{
case FluxVariant.GradientBased:
// Flux Direction based on Mean Level Set Gradient
BulkParams = new List <DGField> {
}; // Hack, to make ArrayTools.Cat produce a List of DGFields
// second Hack: Does only work, when InterfaceParams is according to a single component flux,
// else, we will have to change the boundary edge flux
BulkParams = ArrayTools.Cat(BulkParams, LevelSetGradient.ToArray(), Phi, MeanLevelSetGradient.ToArray(), InterfaceParams.ToArray());
MeanLevelSetGradient.Clear();
MeanLevelSetGradient.AccLaidBack(1.0, LevelSetGradient);
break;
case FluxVariant.ValueBased:
// Flux Direction Based on Cell-Averaged Level-Set Value
BulkParams = ArrayTools.Cat(LevelSetGradient.ToArray(), Phi, MeanLevelSet);
MeanLevelSet.Clear();
MeanLevelSet.AccLaidBack(1.0, Phi);
break;
case FluxVariant.SWIP:
BulkParams = LevelSetGradient.ToArray();
break;
default:
throw new Exception();
}
// Build Operator
Operator_bulk.ComputeMatrixEx(Extension.Mapping,
BulkParams,
Extension.Mapping,
OpMatrix_bulk, OpAffine_bulk,
OnlyAffine: false,
time: 0.0,
edgeQuadScheme: new EdgeQuadratureScheme(true, nearfield ? LevelSetTracker.Regions.GetNearFieldSubgrid(1).InnerEdgesMask : null),
volQuadScheme: new CellQuadratureScheme(true, nearfield ? LevelSetTracker.Regions.GetNearFieldSubgrid(1).VolumeMask : null)
);
Operator_interface.ComputeMatrixEx(
LevelSetTracker,
Extension.Mapping,
InterfaceParams,
Extension.Mapping,
OpMatrix_interface,
OpAffine_interface,
OnlyAffine: false,
time: 0,
MPIParameterExchange: false,
whichSpc: LevelSetTracker.GetSpeciesId("A")
);
#if DEBUG
OpMatrix_bulk.CheckForNanOrInfM();
OpAffine_bulk.CheckForNanOrInfV();
OpMatrix_interface.CheckForNanOrInfM();
OpAffine_interface.CheckForNanOrInfV();
#endif
//Only for Debugging purposes
//OpMatrix.SaveToTextFileSparse("C:\\tmp\\EllipticReInit.txt");
Debug.Assert(OpMatrix_interface.GetDiagVector().L2Norm() > 0, "L2-Norm of Diagonal of InterfaceOperator is 0");
Debug.Assert(OpMatrix_bulk.GetDiagVector().L2Norm() > 0, "L2-Norm of Diagonal of BulkOperator is 0");
#if DEBUG
//Console.WriteLine( "L2-Norm of Diagonal of InterfaceOperator is {0}", OpMatrix_interface.GetDiagVector().L2Norm() );
#endif
OpMatrix.Clear();
OpMatrix.Acc(1.0, OpMatrix_bulk);
OpMatrix.Acc(1.0, OpMatrix_interface);
//Console.WriteLine("Op-Matrix Symmetry-Deviation: {0}", OpMatrix.SymmetryDeviation());
OpMatrix.AssumeSymmetric = false;
OpAffine.Clear();
OpAffine.AccV(1.0, OpAffine_bulk);
OpAffine.AccV(1.0, OpAffine_interface);
#if DEBUG
//Console.WriteLine("Condition Number of Extension Operator {0}", OpMatrix.condest());
#endif
}
/// <summary>
/// Create Spatial Operators and build the corresponding Matrices
/// </summary>
public void ComputeMatrices(IList <DGField> InterfaceParams, bool nearfield)
{
OpMatrix = new MsrMatrix(this.Extension.Mapping, this.Extension.Mapping);
OpAffine = new double[OpMatrix.RowPartitioning.LocalLength];
OpMatrix_bulk = new MsrMatrix(this.Extension.Mapping, this.Extension.Mapping);
OpAffine_bulk = new double[OpMatrix.RowPartitioning.LocalLength];
OpMatrix_interface = new MsrMatrix(this.Extension.Mapping, this.Extension.Mapping);
OpAffine_interface = new double[OpMatrix.RowPartitioning.LocalLength];
//LevelSetTracker.GetLevelSetGradients(0,);
// bulk part of the matrix
//Operator_bulk.ComputeMatrix(
// Extension.Mapping,
// LevelSetGradient.ToArray(),
// Extension.Mapping,
// OpMatrix_bulk, OpAffine_bulk,
// OnlyAffine: false, sgrd: null);
switch (Control.FluxVariant)
{
case FluxVariant.GradientBased:
// Flux Direction based on Mean Level Set Gradient
BulkParams = new List <DGField> {
}; // Hack, to make ArrayTools.Cat produce a List of DGFields
// second Hack: Does only work, when InterfaceParams is according to a single component flux,
// else, we will have to change the boundary edge flux
BulkParams = ArrayTools.Cat(BulkParams, LevelSetGradient.ToArray(), Phi, MeanLevelSetGradient.ToArray(), InterfaceParams.ToArray());
MeanLevelSetGradient.Clear();
MeanLevelSetGradient.AccLaidBack(1.0, LevelSetGradient);
break;
case FluxVariant.ValueBased:
// Flux Direction Based on Cell-Averaged Level-Set Value
BulkParams = ArrayTools.Cat(LevelSetGradient.ToArray(), Phi, MeanLevelSet);
MeanLevelSet.Clear();
MeanLevelSet.AccLaidBack(1.0, Phi);
break;
case FluxVariant.SWIP:
BulkParams = LevelSetGradient.ToArray();
break;
default:
throw new Exception();
}
// Build Operator
Operator_bulk.ComputeMatrixEx(Extension.Mapping,
BulkParams,
Extension.Mapping,
OpMatrix_bulk, OpAffine_bulk,
OnlyAffine: false,
time: 0.0,
edgeQuadScheme: new EdgeQuadratureScheme(true, nearfield ? LevelSetTracker.Regions.GetNearFieldSubgrid(1).InnerEdgesMask : null),
volQuadScheme: new CellQuadratureScheme(true, nearfield ? LevelSetTracker.Regions.GetNearFieldSubgrid(1).VolumeMask : null)
);
//Operator_interface.ComputeMatrixEx(
// LevelSetTracker,
// Extension.Mapping,
// InterfaceParams,
// Extension.Mapping,
// OpMatrix_interface,
// OpAffine_interface,
// OnlyAffine: false,
// time: 0,
// MPIParameterExchange: false,
// whichSpc: LevelSetTracker.GetSpeciesId("A")
// );
Operator_interface.OperatorCoefficientsProvider =
delegate(LevelSetTracker lstrk, SpeciesId spc, int quadOrder, int TrackerHistoryIdx, double time) {
var r = new CoefficientSet()
{
};
//throw new NotImplementedException("todo");
return(r);
};
XSpatialOperatorMk2.XEvaluatorLinear mtxBuilder = Operator_interface.GetMatrixBuilder(LevelSetTracker,
Extension.Mapping, InterfaceParams, Extension.Mapping);
MultiphaseCellAgglomerator dummy = LevelSetTracker.GetAgglomerator(LevelSetTracker.SpeciesIdS.ToArray(), 2 * Extension.Basis.Degree + 2, 0.0);
mtxBuilder.CellLengthScales.Add(LevelSetTracker.GetSpeciesId("A"), dummy.CellLengthScales[LevelSetTracker.GetSpeciesId("A")]);
mtxBuilder.time = 0;
mtxBuilder.MPITtransceive = false;
mtxBuilder.ComputeMatrix(OpMatrix_interface, OpAffine_interface);
#if DEBUG
OpMatrix_bulk.CheckForNanOrInfM();
OpAffine_bulk.CheckForNanOrInfV();
OpMatrix_interface.CheckForNanOrInfM();
OpAffine_interface.CheckForNanOrInfV();
#endif
//Only for Debugging purposes
Debug.Assert(OpMatrix_interface.GetDiagVector().L2Norm() > 0, "L2-Norm of Diagonal of InterfaceOperator is 0");
Debug.Assert(OpMatrix_bulk.GetDiagVector().L2Norm() > 0, "L2-Norm of Diagonal of BulkOperator is 0");
#if DEBUG
//Console.WriteLine( "L2-Norm of Diagonal of InterfaceOperator is {0}", OpMatrix_interface.GetDiagVector().L2Norm() );
#endif
OpMatrix.Clear();
OpMatrix.Acc(1.0, OpMatrix_bulk);
OpMatrix.Acc(1.0, OpMatrix_interface);
//Console.WriteLine("Op-Matrix Symmetry-Deviation: {0}", OpMatrix.SymmetryDeviation());
OpMatrix.AssumeSymmetric = false;
OpAffine.Clear();
OpAffine.AccV(1.0, OpAffine_bulk);
OpAffine.AccV(1.0, OpAffine_interface);
#if DEBUG
//Console.WriteLine("Condition Number of Extension Operator {0}", OpMatrix.condest());
#endif
}