/// <summary>
/// Test if the matrix is symmetric positive definite
/// </summary>
/// <returns>bool array res=[symmetry, positive definit]</returns>
public bool[] Symmetry()
{
bool[] res = new bool[2];
//extract submatrix for selected dependent variables
int[] DepVars = this.VarGroup;
double[] DepVars_subvec = this.m_map.GetSubvectorIndices(true, DepVars).Select(i => i + 1.0).ToArray();
//MsrMatrix OpMtxMSR = m_OpMtx.ToMsrMatrix();
int[] SubMatrixIdx_Row = m_map.GetSubvectorIndices(false, DepVars);
int[] SubMatrixIdx_Cols = m_map.GetSubvectorIndices(false, DepVars);
int L = SubMatrixIdx_Row.Length;
MsrMatrix SubOpMtx = new MsrMatrix(L, L, 1, 1);
m_OpMtx.WriteSubMatrixTo(SubOpMtx, SubMatrixIdx_Row, default(int[]), SubMatrixIdx_Cols, default(int[]));
// symmetry test by calculation of symmetry deviation
bool sym = false;
double SymmDev = m_OpMtx.SymmetryDeviation();
if (SymmDev < 1e-5)
{
sym = true;
}
res[0] = sym;
// positive definite test by Cholesky decomposition
var FullyPopulatedMatrix = m_OpMtx.ToFullMatrixOnProc0();
bool posDef = true;
// only proc 0 gets info so the following is executed exclusively on rank 0
if (ilPSP.Environment.MPIEnv.MPI_Rank == 0)
{
try
{
FullyPopulatedMatrix.Cholesky();
}
catch (ArithmeticException)
{
posDef = false;
}
}
res[1] = MPIEnviroment.Broadcast <bool>(posDef, 0, ilPSP.Environment.MPIEnv.Mpi_comm);
Debug.Assert(res[0].MPIEquals(), "value does not match on procs");
Debug.Assert(res[1].MPIEquals(), "value does not match on procs");
return(res);
}
/// <summary>
/// Test code for debugging.
/// </summary>
/// <param name="OperatorsFlowField"></param>
/// <param name="VelocityMapping"></param>
/// <param name="VelocityVectorMapping"></param>
private void SaveMatricesToTextFile(OperatorFactoryFlowFieldVariableDensity OperatorsFlowField,
UnsetteledCoordinateMapping VelocityMapping, UnsetteledCoordinateMapping VelocityVectorMapping)
{
OperatorsFlowField.Swip2[0].OperatorMatrix.SaveToTextFileSparse("C:\\tmp\\Swip20.txt");
OperatorsFlowField.Swip2[1].OperatorMatrix.SaveToTextFileSparse("C:\\tmp\\Swip21.txt");
OperatorsFlowField.Swip3[0].OperatorMatrix.SaveToTextFileSparse("C:\\tmp\\Swip30.txt");
OperatorsFlowField.Swip3[1].OperatorMatrix.SaveToTextFileSparse("C:\\tmp\\Swip31.txt");
ViscSplit[0, 0].AssemblyMatrix.SaveToTextFileSparse("C:\\tmp\\ViscSplit00.txt");
ViscSplit[0, 1].AssemblyMatrix.SaveToTextFileSparse("C:\\tmp\\ViscSplit01.txt");
ViscSplit[1, 0].AssemblyMatrix.SaveToTextFileSparse("C:\\tmp\\ViscSplit10.txt");
ViscSplit[1, 1].AssemblyMatrix.SaveToTextFileSparse("C:\\tmp\\ViscSplit11.txt");
int[] IndicesVelocity = VelocityMapping.GetSubvectorIndices(true, 0);
int[] IndicesVelocityVector0 = VelocityVectorMapping.GetSubvectorIndices(true, 0);
int[] IndicesVelocityVector1 = VelocityVectorMapping.GetSubvectorIndices(true, 1);
MsrMatrix Swip2Mtx = new MsrMatrix(VelocityVectorMapping);
OperatorsFlowField.Swip2[0].OperatorMatrix.WriteSubMatrixTo <IList <int>, IList <int>, IList <int>, IList <int> >(Swip2Mtx,
IndicesVelocity,
IndicesVelocityVector0,
IndicesVelocityVector0,
IndicesVelocityVector0);
OperatorsFlowField.Swip2[0].OperatorMatrix.AccSubMatrixTo <IList <int>, IList <int>, IList <int>, IList <int> >(1.0,
Swip2Mtx,
IndicesVelocity,
IndicesVelocityVector0,
IndicesVelocityVector1,
IndicesVelocityVector1);
OperatorsFlowField.Swip2[1].OperatorMatrix.AccSubMatrixTo <IList <int>, IList <int>, IList <int>, IList <int> >(1.0,
Swip2Mtx,
IndicesVelocity,
IndicesVelocityVector1,
IndicesVelocityVector0,
IndicesVelocityVector0);
OperatorsFlowField.Swip2[1].OperatorMatrix.AccSubMatrixTo <IList <int>, IList <int>, IList <int>, IList <int> >(1.0,
Swip2Mtx,
IndicesVelocity,
IndicesVelocityVector1,
IndicesVelocityVector1,
IndicesVelocityVector1);
Swip2Mtx.SaveToTextFileSparse("C:\\tmp\\Swip2.txt");
}
/// <summary>
/// Ctor.
/// </summary>
/// <param name="Swip2"></param>
/// <param name="Swip3">Can be null for multiphase flows.</param>
/// <param name="Component">Component of velocity vector.</param>
/// <param name="VelocityMapping"></param>
/// <param name="VelocityVectorMapping"></param>
public MatrixAssemblyViscSplit(SIMPLEOperator Swip2, SIMPLEOperator Swip3, int Component,
UnsetteledCoordinateMapping VelocityMapping, UnsetteledCoordinateMapping VelocityVectorMapping)
: base(false, false)
{
this.Swip2 = Swip2;
this.Swip3 = Swip3;
RowIndicesSource = new int[Swip2.LocalLength];
int i0 = Swip2.RowPartition.i0;
for (int i = 0; i < Swip2.LocalLength; i++)
{
RowIndicesSource[i] = i + i0;
}
ColumnIndicesSource = VelocityVectorMapping.GetSubvectorIndices(true, Component);
ColumnIndicesTarget = VelocityMapping.GetSubvectorIndices(true, 0);
base.Initialize();
}
public void ImplicitEuler(double dt, SubGrid S, SinglePhaseField inout_Levset)
{
var VolMsk = S.VolumeMask;
var EdgMsk = S.InnerEdgesMask;
UnsetteledCoordinateMapping Map = inout_Levset.Mapping;
if (dt <= 0.0)
{
throw new ArgumentOutOfRangeException("Timestep size must be greater than 0.");
}
MsrMatrix Pmtx = PenaltyMatrix(EdgMsk, inout_Levset.Basis, inout_Levset.Basis);
Pmtx.Scale(-1.0);
int[] SubVecIdx = Map.GetSubvectorIndices(S, true, new int[] { 0 });
int L = SubVecIdx.Length;
MsrMatrix SubMtx = new MsrMatrix(L, L);
Pmtx.AccSubMatrixTo(1.0, SubMtx, SubVecIdx, default(int[]), SubVecIdx, default(int[]));
SubMtx.AccEyeSp(1.0 / dt);
double[] RHS = new double[L];
double[] SOL = new double[L];
RHS.AccV(1.0 / dt, inout_Levset.CoordinateVector, default(int[]), SubVecIdx);
using (var solver = new PARDISOSolver()) {
solver.DefineMatrix(SubMtx);
solver.Solve(SOL, RHS);
}
inout_Levset.CoordinateVector.ClearEntries(SubVecIdx);
inout_Levset.CoordinateVector.AccV(1.0, SOL, SubVecIdx, default(int[]));
}
/// <summary>
/// Tests if a matrix (associated with some operator) depends only on values in this sub-grid,
/// or not.
/// </summary>
/// <param name="_Mtx">some operator matrix</param>
/// <param name="RowMap">row-/co-domain mapping for matrix <paramref name="_Mtx"/></param>
/// <param name="ColMap">column/domain mapping for matrix <paramref name="_Mtx"/></param>
/// <param name="NoOfTests"></param>
/// <returns>
/// 0.0 if there is no dependency of the matrix <paramref name="_Mtx"/>
/// on values outside of this subgrid.
/// </returns>
public double TestMatrixDependency(MsrMatrix _Mtx, UnsetteledCoordinateMapping RowMap, UnsetteledCoordinateMapping ColMap, int NoOfTests = 10)
{
Random RND = new Random();
if (!_Mtx.RowPartitioning.Equals(RowMap))
{
throw new ArgumentException();
}
if (!_Mtx.ColPartition.Equals(ColMap))
{
throw new ArgumentException();
}
var Mtx = new ilPSP.LinSolvers.monkey.CPU.RefMatrix(_Mtx);
int[] IR = RowMap.BasisS.Count.ForLoop(i => i);
int[] IC = ColMap.BasisS.Count.ForLoop(i => i);
var SgrdRow = RowMap.GetSubvectorIndices(this, true, IR);
var SgrdCol = SgrdRow; // ColMap.GetSubvectorIndices(this, true, true, IC);
double[] X0 = new double[ColMap.LocalLength];
double[] Y0 = new double[RowMap.LocalLength];
for (int i = 0; i < X0.Length; i++)
{
X0[i] = RND.NextDouble();
}
Mtx.SpMV(1.0, X0, 0.0, Y0);
int i0Row = RowMap.i0;
int i0Col = ColMap.i0;
int iECol = ColMap.iE;
double err = 0;
for (int iTest = 0; iTest < NoOfTests; iTest++)
{
double[] X1 = new double[ColMap.LocalLength];
double[] Y1 = new double[RowMap.LocalLength];
for (int i = 0; i < X0.Length; i++)
{
X1[i] = RND.NextDouble();
}
foreach (int i in SgrdCol)
{
if (i >= i0Col && i < iECol)
{
X1[i - i0Col] = X0[i - i0Col];
}
}
Mtx.SpMV(1.0, X1, 0.0, Y1);
foreach (int k in SgrdRow)
{
double Y1k = Y1[k - i0Row];
double Y0k = Y0[k - i0Row];
//Debug.Assert((Y0k - Y1k).Pow2() < 1.0e-8);
err += (Y0k - Y1k).Pow2();
}
}
return(err.MPISum());
}