/// <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.");
// }
//}
}
}
}