public IMatrix GetSecondSpaceDerivatives(ISubdomain subdomain, IVectorView vector)
{
var ndofs = model.Subdomains[subdomain.ID].Nodes.Count;
var v1 = new double[] { 1, 0, 0 };
var v2 = new double[] { 0, 1, 0 };
var v3 = new double[] { 0, 0, 1 };
var i1 = Vector.CreateFromArray(v1);
var i2 = Vector.CreateFromArray(v2);
var i3 = Vector.CreateFromArray(v3);
var secondSpaceDerivatives = Matrix.CreateZero(ndofs, 1);
var ddX = (Vector)SecondDerivativeXMatrix[subdomain.ID].Multiply(vector);
var ddY = (Vector)SecondDerivativeYMatrix[subdomain.ID].Multiply(vector);
var ddZ = (Vector)SecondDerivativeZMatrix[subdomain.ID].Multiply(vector);
var ddMX = ddX.TensorProduct(i1);
var ddMY = ddY.TensorProduct(i2);
var ddMZ = ddZ.TensorProduct(i3);
ddMX.AddIntoThis(ddMY);
ddMX.AddIntoThis(ddMZ);
return(ddMX);
}
internal static void CsrTransTimesVector(int numCsrRows, double[] csrValues, int[] csrRowOffsets, int[] csrColIndices,
IVectorView lhs, IVector rhs)
{
var temp = new double[rhs.Length];
CsrTransTimesVector(numCsrRows, csrValues, csrRowOffsets, csrColIndices, lhs, temp);
rhs.CopyFrom(Vector.CreateFromArray(temp));
// The following requires a lot of indexing into the rhs vector.
//// A^T * x = linear combination of columns of A^T = rows of A, with the entries of x as coefficients
//for (int i = 0; i < numCsrRows; ++i)
//{
// double scalar = lhs[i];
// int rowStart = csrRowOffsets[i]; //inclusive
// int rowEnd = csrRowOffsets[i + 1]; //exclusive
// for (int k = rowStart; k < rowEnd; ++k)
// {
// rhs.Set(csrColIndices[k], rhs[csrColIndices[k]] + scalar * csrValues[k]);
// }
//}
}
/// <summary>
/// See <see cref="IVectorView.LinearCombination(double, IVectorView, double)"/>.
/// </summary>
public IVector LinearCombination(double thisCoefficient, IVectorView otherVector, double otherCoefficient)
{
if (otherVector is Vector3 casted)
{
return(LinearCombination(thisCoefficient, casted, otherCoefficient));
}
else if (thisCoefficient == 1.0)
{
return(Axpy(otherVector, otherCoefficient));
}
else
{
Preconditions.CheckVectorDimensions(this, otherVector);
return(new Vector3(new double[]
{
thisCoefficient *data[0] + otherCoefficient * otherVector[0],
thisCoefficient *data[1] + otherCoefficient * otherVector[1],
thisCoefficient *data[2] + otherCoefficient * otherVector[2]
}));
}
}
private static bool CompareResults(IVectorView solution)
{
var comparer = new ValueComparer(1E-5);
// dofs: 1, 2, 4, 5, 7, 8
var expectedSolution = Vector.CreateFromArray(new double[] { 150, 200, 150, 200, 150, 200 });
int numFreeDofs = 6;
if (solution.Length != 6)
{
return(false);
}
for (int i = 0; i < numFreeDofs; ++i)
{
if (!comparer.AreEqual(expectedSolution[i], solution[i]))
{
return(false);
}
}
return(true);
}
private static bool CompareResults(IVectorView solution)
{
var comparer = new ValueComparer(1E-3);
// dofs: 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 18, 22, 23, 24, 25, 26, 27
var expectedSolution = Vector.CreateFromArray(new double[] { 135.054, 158.824, 135.054, 469.004, 147.059, 159.327, 178.178, 147.299, 139.469, 147.059, 191.717, 147.059, 135.054, 158.824, 135.054, 469.004, 147.059, 159.327 });
int numFreeDofs = 18;
if (solution.Length != 18)
{
return(false);
}
for (int i = 0; i < numFreeDofs; ++i)
{
if (!comparer.AreEqual(expectedSolution[i], solution[i]))
{
return(false);
}
}
return(true);
}
internal T Indexer_Get <T>(int index)
{
if (index < 0)
{
throw new ArgumentOutOfRangeException("index");
}
IVectorView <T> vectorView = JitHelpers.UnsafeCast <IVectorView <T> >((object)this);
try
{
return(vectorView.GetAt((uint)index));
}
catch (Exception ex)
{
if (-2147483637 == ex._HResult)
{
throw new ArgumentOutOfRangeException("index");
}
throw;
}
}
/// <summary>
/// See <see cref="IVectorView.DotProduct(IVectorView)"/>.
/// </summary>
public double DotProduct(IVectorView vector)
{
Preconditions.CheckVectorDimensions(this, vector);
if (vector is Vector dense)
{
return(SparseBlas.Ddoti(values.Length, values, indices, 0, dense.RawData, 0));
}
else if ((vector is SparseVector sparse) && HasSameIndexer(sparse))
{
return(Blas.Ddot(values.Length, this.values, 0, 1, sparse.values, 0, 1));
}
double sum = 0;
for (int i = 0; i < values.Length; ++i)
{
sum += values[i] * vector[indices[i]];
}
return(sum);
}
/// <summary>
/// See <see cref="IVector.AxpySubvectorIntoThis(int, IVectorView, double, int, int)"/>
/// </summary>
public void AxpySubvectorIntoThis(int destinationIndex, IVectorView sourceVector, double sourceCoefficient,
int sourceIndex, int length)
{
Preconditions.CheckSubvectorDimensions(this, destinationIndex, length);
Preconditions.CheckSubvectorDimensions(sourceVector, sourceIndex, length);
if (sourceVector is Vector2 casted)
{
for (int i = 0; i < length; ++i)
{
data[i + destinationIndex] += sourceCoefficient * casted.data[i + sourceIndex];
}
}
else
{
for (int i = 0; i < length; ++i)
{
data[i + destinationIndex] += sourceCoefficient * sourceVector[i + sourceIndex];
}
}
}
public IVector GetRhsFromSolution(IVectorView solution, IVectorView dSolution)
{
var forces = Vector.CreateZero(FreeDofOrdering.NumFreeDofs); //TODO: use Vector
foreach (Element element in Elements)
{
//var localSolution = GetLocalVectorFromGlobal(element, solution);//TODOMaria: This is where the element displacements are calculated //removeMaria
//var localdSolution = GetLocalVectorFromGlobal(element, dSolution);//removeMaria
//TODO: ElementType should operate with Vector instead of double[]. Then the ToRawArray() calls can be removed
double[] localSolution = CalculateElementDisplacements(element, solution);
double[] localdSolution = CalculateElementDisplacements(element, dSolution);
element.ElementType.CalculateStresses(element, localSolution, localdSolution);
if (element.ElementType.MaterialModified)
{
element.Subdomain.StiffnessModified = true;
}
var f = element.ElementType.CalculateForces(element, localSolution, localdSolution);
FreeDofOrdering.AddVectorElementToSubdomain(element, f, forces);
}
return(forces);
}
/// <summary>
/// See <see cref="IVector.AxpySubvectorIntoThis(int, IVectorView, double, int, int)"/>.
/// </summary>
public void AxpySubvectorIntoThis(int destinationIndex, IVectorView sourceVector, double sourceCoefficient,
int sourceIndex, int length)
{
//TODO: needs testing for off-by-1 bugs and extension to cases where source and destination indices are different.
Preconditions.CheckSubvectorDimensions(this, destinationIndex, length);
Preconditions.CheckSubvectorDimensions(sourceVector, sourceIndex, length);
if ((sourceVector is SparseVector otherSparse) && HasSameIndexer(otherSparse))
{
if (destinationIndex != sourceIndex)
{
throw new NotImplementedException();
}
int start = Array.FindIndex(this.indices, x => x >= destinationIndex);
int end = Array.FindIndex(this.indices, x => x >= destinationIndex + length);
int sparseLength = end - start;
Blas.Daxpy(sparseLength, sourceCoefficient, otherSparse.values, start, 1, this.values, start, 1);
}
throw new SparsityPatternModifiedException(
"This operation is legal only if the other vector has the same sparsity pattern");
}
/// <summary>
/// See <see cref="IVector.AddIntoThisNonContiguouslyFrom(int[], IVectorView)"/>
/// </summary>
public void AddIntoThisNonContiguouslyFrom(int[] thisIndices, IVectorView otherVector)
{
if (thisIndices.Length != otherVector.Length)
{
throw new NonMatchingDimensionsException(
"thisIndices and otherVector must have the same length.");
}
if (otherVector is Vector casted)
{
for (int i = 0; i < casted.Length; ++i)
{
this.data[thisIndices[i]] += casted.data[i];
}
}
else
{
for (int i = 0; i < otherVector.Length; ++i)
{
data[thisIndices[i]] += otherVector[i];
}
}
}
//ADDED1
public IVector GetRHSFromSolutionWithInitialDisplacementsEffect(IVectorView solution, IVectorView dSolution, Dictionary <int, INode> boundaryNodes,
Dictionary <int, Dictionary <IDofType, double> > initialConvergedBoundaryDisplacements, Dictionary <int, Dictionary <IDofType, double> > totalBoundaryDisplacements,
int nIncrement, int totalIncrements)
{
var forces = Vector.CreateZero(FreeDofOrdering.NumFreeDofs); //TODO: use Vector
foreach (Element element in Elements)
{
var localSolution = GetLocalVectorFromGlobalWithoutPrescribedDisplacements(element, solution);
ImposePrescribedDisplacementsWithInitialConditionSEffect(element, localSolution, boundaryNodes, initialConvergedBoundaryDisplacements, totalBoundaryDisplacements, nIncrement, totalIncrements);
var localdSolution = GetLocalVectorFromGlobalWithoutPrescribedDisplacements(element, dSolution);
ImposePrescribed_d_DisplacementsWithInitialConditionSEffect(element, localdSolution, boundaryNodes, initialConvergedBoundaryDisplacements, totalBoundaryDisplacements, nIncrement, totalIncrements);
element.ElementType.CalculateStresses(element, localSolution, localdSolution);
if (element.ElementType.MaterialModified)
{
element.Subdomain.StiffnessModified = true;
}
var f = element.ElementType.CalculateForces(element, localSolution, localdSolution);
FreeDofOrdering.AddVectorElementToSubdomain(element, f, forces);
}
return(forces);
}
/// <summary>
/// See <see cref="IVector.CopyNonContiguouslyFrom(IVectorView, int[])"/>
/// </summary>
public void CopyNonContiguouslyFrom(IVectorView otherVector, int[] otherIndices)
{
if (otherIndices.Length != this.Length)
{
throw new NonMatchingDimensionsException(
"otherIndices and this vector must have the same length.");
}
if (otherVector is Vector casted)
{
for (int i = 0; i < this.Length; ++i)
{
this.data[i] = casted.data[otherIndices[i]];
}
}
else
{
for (int i = 0; i < this.Length; ++i)
{
data[i] = otherVector[otherIndices[i]];
}
}
}
public Vector GatherGlobalForces(Dictionary <int, IVectorView> subdomainForces)
{
var globalForces = Vector.CreateZero(model.GlobalDofOrdering.NumGlobalFreeDofs);
foreach (ISubdomain subdomain in model.Subdomains)
{
int id = subdomain.ID;
int[] subdomainFreeToGlobalDofs = model.GlobalDofOrdering.MapFreeDofsSubdomainToGlobal(subdomain);
IVectorView forces = subdomainForces[id]; //TODO: benchmark the performance if this was concrete Vector
for (int i = 0; i < forces.Length; ++i)
{
// Internal forces will be copied (which is identical to adding 0 + single value).
// Boundary remainder forces will be summed. Previously we had distributed them depending on
// homogeneity / heterogeneity (e.g. Ftot = 0.4 * Ftot + 0.6 * Ftot) and now we sum them.
// Boundary corner forces are also summed. Previously we had also distributed them equally irregardless of
// homogeneity / heterogeneity (e.g. Ftot = 0.5 * Ftot + 0.5 * Ftot) and now we sum them.
globalForces[subdomainFreeToGlobalDofs[i]] += forces[i];
}
}
return(globalForces);
}
public Vector GatherGlobalDisplacements(Dictionary <int, IVectorView> subdomainRemainderDisplacements,
IVectorView globalCornerDisplacements)
{
var globalDisplacements = Vector.CreateZero(model.GlobalDofOrdering.NumGlobalFreeDofs);
// Remainder dofs
foreach (ISubdomain subdomain in model.Subdomains)
{
int id = subdomain.ID;
int[] freeToGlobalDofs = model.GlobalDofOrdering.MapFreeDofsSubdomainToGlobal(subdomain);
int[] remainderToFreeDofs = dofSeparator.RemainderDofIndices[id];
IVectorView remainderDisplacements = subdomainRemainderDisplacements[id]; //TODO: benchmark the performance if this was concrete Vector
// Internal dofs are copied without averaging.
foreach (int remainderDofIdx in dofSeparator.InternalDofIndices[id])
{
int globalDofIdx = freeToGlobalDofs[remainderToFreeDofs[remainderDofIdx]];
globalDisplacements[globalDofIdx] = remainderDisplacements[remainderDofIdx];
}
// For boundary dofs we take average across subdomains with respect to multiplicity or stiffness.
double[] boundaryDofCoeffs = distribution.CalcBoundaryDofCoefficients(subdomain);
for (int i = 0; i < dofSeparator.BoundaryDofIndices[id].Length; ++i)
{
int remainderDofIdx = dofSeparator.BoundaryDofIndices[id][i];
int globalDofIdx = freeToGlobalDofs[remainderToFreeDofs[remainderDofIdx]];
globalDisplacements[globalDofIdx] += remainderDisplacements[remainderDofIdx] * boundaryDofCoeffs[i];
}
}
// Corner dofs are copied without averaging.
for (int i = 0; i < dofSeparator.NumGlobalCornerDofs; ++i)
{
int globalDofIdx = dofSeparator.GlobalCornerToFreeDofMap[i];
globalDisplacements[globalDofIdx] = globalCornerDisplacements[i];
}
return(globalDisplacements);
}
/// <summary>
/// See <see cref="IMatrixView.Multiply(IVectorView, bool)"/>.
/// </summary>
public IVector Multiply(IVectorView vector, bool transposeThis = false)
{
if (vector is Vector dense)
{
return(Multiply(dense, transposeThis));
}
if (transposeThis)
{
var result = new double[NumColumns];
Preconditions.CheckMultiplicationDimensions(NumRows, vector.Length);
CsrMultiplications.CsrTimesVector(NumColumns, values, colOffsets, rowIndices, vector, result);
return(Vector.CreateFromArray(result, false));
}
else
{
var result = new double[NumRows];
Preconditions.CheckMultiplicationDimensions(NumColumns, vector.Length);
CsrMultiplications.CsrTransTimesVector(NumColumns, values, colOffsets, rowIndices, vector, result);
return(Vector.CreateFromArray(result, false));
}
}
internal double CalculateForceAt(Node node, IDofType dofType, IVectorView totalDisplacements)
{
double totalForce = 0.0;
foreach (Element element in node.ElementsDictionary.Values)
{
// It is possible that one of the elements at this node does not engage this dof type, in which case -1 will be returned.
// We will not have any contribution from them. If none of the elements engage this dof type, the total force will always be 0.
int monitorDofIdx = FindLocalDofIndex(element, node, dofType);
if (monitorDofIdx == -1)
{
continue;
}
//TODO: if an element has embedded elements, then we must also take into account their forces.
double[] totalElementDisplacements = subdomain.CalculateElementDisplacements(element, totalDisplacements);
double[] elementForces = element.ElementType.CalculateForcesForLogging(element, totalElementDisplacements);
totalForce += elementForces[monitorDofIdx];
}
return(totalForce);
}
/// <summary>
/// Solves the linear system A * x = b, where A = <paramref name="matrix"/> and b = <paramref name="rhs"/>.
/// Initially x = <paramref name="initialGuess"/> and then it converges to the solution.
/// </summary>
/// <param name="matrix">
/// Represents the matrix A of the linear system A * x = b, which must be symmetric positive definite.
/// </param>
/// <param name="rhs">
/// The right hand side vector b of the linear system A * x = b. Constraints:
/// <paramref name="rhs"/>.<see cref="IIndexable1D.Length"/>
/// == <paramref name="matrix"/>.<see cref="IIndexable2D.NumRows"/>.
/// </param>
/// <param name="solution">
/// The vector from which to start refining the solution vector x. Constraints:
/// <paramref name="solution"/>.<see cref="IIndexable1D.Length"/>
/// == <paramref name="matrix"/>.<see cref="IIndexable2D.NumColumns"/>.
/// </param>
/// <param name="initialGuessIsZero">
/// If <paramref name="solution"/> is 0, then set <paramref name="initialGuessIsZero"/> to true to avoid performing the
/// operation b-A*0 before starting.
/// </param>
/// <exception cref="NonMatchingDimensionsException">
/// Thrown if <paramref name="rhs"/> or <paramref name="solution"/> violate the described constraints.
/// </exception>
public IterativeStatistics Solve(ILinearTransformation matrix, IVectorView rhs, IVector solution,
bool initialGuessIsZero) //TODO: find a better way to handle the case x0=0
{
//TODO: these will also be checked by the matrix vector multiplication.
Preconditions.CheckMultiplicationDimensions(matrix.NumColumns, solution.Length);
Preconditions.CheckSystemSolutionDimensions(matrix.NumRows, rhs.Length);
this.Matrix = matrix;
this.Rhs = rhs;
this.solution = solution;
// r = b - A * x
if (initialGuessIsZero)
{
residual = rhs.Copy();
}
else
{
residual = ExactResidual.Calculate(matrix, rhs, solution);
}
return(SolveInternal(maxIterationsProvider.GetMaxIterations(matrix.NumColumns)));
}
/// <summary>
/// See <see cref="IVectorView.Axpy(IVectorView, double)"/>.
/// </summary>
public IVector Axpy(IVectorView otherVector, double otherCoefficient)
{
Preconditions.CheckVectorDimensions(this, otherVector);
if (otherVector is SparseVector otherSparse) // In case both matrices have the exact same index arrays
{
if (HasSameIndexer(otherSparse))
{
// Do not copy the index arrays, since they are already spread around. TODO: is this a good idea?
double[] result = new double[this.values.Length];
Array.Copy(this.values, result, this.values.Length);
Blas.Daxpy(values.Length, otherCoefficient, otherSparse.values, 0, 1, result, 0, 1);
return(new SparseVector(Length, result, indices));
}
}
else if (otherVector is Vector otherDense)
{
double[] result = otherDense.Scale(otherCoefficient).RawData;
SparseBlas.Daxpyi(this.indices.Length, 1.0, this.values, this.indices, 0, result, 0);
return(Vector.CreateFromArray(result, false));
}
// All entries must be processed. TODO: optimizations may be possible (e.g. only access the nnz in this vector)
return(DenseStrategies.LinearCombination(this, 1.0, otherVector, otherCoefficient));
}
public void UpdateModelAndAnalyze(IVectorView youngModuli)
{
this.youngModuli = youngModuli;
// Global stiffness matrix assembly
int numAllDofs = 2 * (numElementsX + 1) * (numElementsY + 1);
var K = DokSymmetric.CreateEmpty(numAllDofs);
for (int e = 0; e < NumElements; ++e)
{
int[] elementDofsGlobal = GetElementDofs(e);
K.AddSubmatrixSymmetric(unitStiffness.Scale(youngModuli[e]), elementDofsLocal, elementDofsGlobal);
}
// Apply boundary conditions
(int[] freeDofs, Vector[] Fs) = ApplyBoundaryConditions();
int numLoadCases = Fs.Length;
globalDisplacements = new Vector[numLoadCases];
// Solve linear system
DokSymmetric Kf = K.GetSubmatrix(freeDofs);
var factor = CholeskyCSparseNet.Factorize(Kf.BuildSymmetricCscMatrix(true));
for (int c = 0; c < numLoadCases; ++c)
{
Vector Ff = Fs[c].GetSubvector(freeDofs);
Vector Uf = factor.SolveLinearSystem(Ff);
var U = Vector.CreateZero(numAllDofs);
for (int i = 0; i < freeDofs.Length; ++i)
{
U[freeDofs[i]] = Uf[i];
}
globalDisplacements[c] = U;
//U.CopyNonContiguouslyFrom(freeDofs, Uf, Enumerable.Range(0, freeDofs.Length).ToArray()); // alternative way, but probably slower.
}
}
/// <summary>
/// Solves the linear system A * x = b by solving the preconditioned system inv(P) * A * inv(P)^T * y = inv(P) * b,
/// where A = <paramref name="matrix"/>, b = <paramref name="rhsVector"/>, x is the solution, y = P^T * x,
/// P*P^T = <paramref name="preconditioner"/>.
/// Initially x = <paramref name="initialGuess"/> and then it converges to the solution.
/// </summary>
/// <param name="matrix">
/// Represents the matrix A of the linear system A * x = b, which must be symmetric positive definite.
/// </param>
/// <param name="rhs">
/// The right hand side vector b of the linear system A * x = b. Constraints:
/// <paramref name="rhs"/>.<see cref="IIndexable1D.Length"/>
/// == <paramref name="matrix"/>.<see cref="IIndexable2D.NumRows"/>.
/// </param>
/// <param name="preconditioner">
/// A preconditioner matrix that is also symmetric positive definite and has the same dimensions as A.
/// </param>
/// <param name="solution">
/// The vector from which to start refining the solution vector x. Constraints:
/// <paramref name="solution"/>.<see cref="IIndexable1D.Length"/>
/// == <paramref name="matrix"/>.<see cref="IIndexable2D.NumColumns"/>.
/// </param>
/// <param name="initialGuessIsZero">
/// If <paramref name="solution"/> is 0, then set <paramref name="initialGuessIsZero"/> to true to avoid performing the
/// operation b-A*0 before starting.
/// </param>
/// <exception cref="NonMatchingDimensionsException">
/// Thrown if <paramref name="rhs"/> or <paramref name="solution"/> violate the described constraints.
/// </exception>
public virtual IterativeStatistics Solve(ILinearTransformation matrix, IPreconditioner preconditioner, IVectorView rhs,
IVector solution, bool initialGuessIsZero, Func <IVector> zeroVectorInitializer)
{
//TODO: find a better way to handle optimizations for the case x0=0, than using an initialGuessIsZero flag
Preconditions.CheckMultiplicationDimensions(matrix.NumColumns, solution.Length);
Preconditions.CheckSystemSolutionDimensions(matrix.NumRows, rhs.Length);
this.Matrix = matrix;
this.Preconditioner = preconditioner;
this.Rhs = rhs;
this.solution = solution;
// r = b - A * x
if (initialGuessIsZero)
{
residual = rhs.Copy();
}
else
{
residual = ExactResidual.Calculate(matrix, rhs, solution);
}
return(SolveInternal(MaxIterationsProvider.GetMaxIterations(matrix.NumColumns), zeroVectorInitializer));
}
public void ExtractVectorElementFromSubdomain(IElement element, IVectorView subdomainVector, IVector elementVector)
{
IReadOnlyList <INode> elementNodes = element.ElementType.DofEnumerator.GetNodesForMatrixAssembly(element);
IReadOnlyList <IReadOnlyList <IDofType> > elementDofs = element.ElementType.DofEnumerator.GetDofTypesForMatrixAssembly(element);
//int numElementDofs = 0;
//for (int nodeIdx = 0; nodeIdx < elementDofs.Count; ++nodeIdx) numElementDofs += elementDofs[nodeIdx].Count;
int elementDofIdx = 0;
for (int nodeIdx = 0; nodeIdx < elementNodes.Count; ++nodeIdx)
{
for (int dofIdx = 0; dofIdx < elementDofs[nodeIdx].Count; ++dofIdx)
{
bool isFree = FreeDofs.TryGetValue(elementNodes[nodeIdx], elementDofs[nodeIdx][dofIdx],
out int subdomainDofIdx);
if (isFree)
{
elementVector.Set(elementDofIdx, subdomainVector[subdomainDofIdx]);
}
// Else, the quantity of interest is 0.0 at all constrained dofs.
++elementDofIdx; // This must be incremented for constrained dofs as well
}
}
}
// Stiffness ratio = 1E-6
//[InlineData(1E-6, InterfaceSolver.Method1, Precond.Dirichlet, MatrixQ.Identity, Residual.Exact, 40)] // converges, stagnates almost before the tolerance and then diverges
//[InlineData(1E-6, InterfaceSolver.Method2, Precond.Dirichlet, MatrixQ.Precond, Residual.Exact, 9)] // converges, stagnates almost before the tolerance and then diverges
//[InlineData(1E-6, InterfaceSolver.Method3, Precond.Dirichlet, MatrixQ.Precond, Residual.Exact, 23)] //3
//[InlineData(1E-6, InterfaceSolver.Method4, Precond.Dirichlet, MatrixQ.Precond, Residual.Exact, 9)] // converges, stagnates almost before the tolerance and then diverges
//[InlineData(1E-6, InterfaceSolver.Default, Precond.Dirichlet, MatrixQ.Precond, Residual.Approximate, 9)]
public static void Run(double stiffnessRatio, InterfaceSolver interfaceSolver, Precond precond, MatrixQ q,
Residual convergence, int iterExpected)
{
//InterfaceSolver interfaceSolver = 0;
double factorizationTol = 1E-3, pcpgConvergenceTol = 1E-5;
IVectorView directDisplacements = SolveModelWithoutSubdomains(stiffnessRatio);
(IVectorView ddDisplacements, SolverLogger logger, int numUniqueGlobalDofs, int numExtenedDomainDofs) =
SolveModelWithSubdomains(stiffnessRatio, interfaceSolver, precond, q, convergence,
factorizationTol, pcpgConvergenceTol);
double normalizedError = directDisplacements.Subtract(ddDisplacements).Norm2() / directDisplacements.Norm2();
int analysisStep = 0;
Assert.Equal(882, numUniqueGlobalDofs); // 882 includes constrained and free dofs
Assert.Equal(1056, numExtenedDomainDofs); // 1056 includes constrained and free dofs
Assert.Equal(190, logger.GetNumDofs(analysisStep, "Lagrange multipliers"));
// The error is provided in the reference solution the, but it is almost impossible for two different codes run on
// different machines to achieve the exact same accuracy.
Assert.Equal(0.0, normalizedError, 5);
// Allow a tolerance: It is ok if my solver is better or off by 1 iteration
int pcgIterations = logger.GetNumIterationsOfIterativeAlgorithm(analysisStep);
Assert.InRange(pcgIterations, 1, iterExpected + 1); // the upper bound is inclusive!
}
public static void Run(double stiffnessRatio, Precond precond, Residual convergence, int iterExpected)
{
double pcgConvergenceTol = 1E-5;
IVectorView directDisplacements = SolveModelWithoutSubdomains(stiffnessRatio);
(IVectorView ddDisplacements, SolverLogger logger) =
SolveModelWithSubdomains(stiffnessRatio, precond, convergence, pcgConvergenceTol);
double normalizedError = directDisplacements.Subtract(ddDisplacements).Norm2() / directDisplacements.Norm2();
int analysisStep = 0;
Assert.Equal(140, logger.GetNumDofs(analysisStep, "Lagrange multipliers"));
Assert.Equal(20, logger.GetNumDofs(analysisStep, "Corner dofs"));
// The error is provided in the reference solution the, but it is almost impossible for two different codes run on
// different machines to achieve the exact same accuracy.
Assert.Equal(0.0, normalizedError, 6);
// Allow some tolerance for the iterations:
int maxIterationsForApproximateResidual = (int)Math.Ceiling(1.0 * iterExpected);
int pcgIterations = logger.GetNumIterationsOfIterativeAlgorithm(analysisStep);
Assert.InRange(pcgIterations, 1, maxIterationsForApproximateResidual); // the upper bound is inclusive!
}
/// <summary>
/// See <see cref="IVector.AxpyIntoThis(IVectorView, double)"/>.
/// </summary>
public void AxpyIntoThis(IVectorView otherVector, double otherCoefficient)
{
if (otherVector is Vector dense)
{
AxpyIntoThis(dense, otherCoefficient);
}
else
{
Preconditions.CheckVectorDimensions(this, otherVector);
if (otherVector is SparseVector sparse)
{
//TODO: should I check whether the sparse vector is all 0, in order to avoid the BLAS call?
SparseBlas.Daxpyi(sparse.RawIndices.Length, otherCoefficient, sparse.RawValues,
sparse.RawIndices, 0, data, 0);
}
else
{
for (int i = 0; i < Length; ++i)
{
this.data[i] += otherCoefficient * otherVector[i];
}
}
}
}
private static void WinRT_IReadOnlyList <T>(IVectorViewToIReadOnlyListAdapter vectorToListAdapter, IReadOnlyListToIVectorViewAdapter listToVectorAdapter, IVectorView <T> vectorView)
{
Internal.WinRT_IEnumerable <T>(null, null, null);
Internal.WinRT_IReadOnlyCollection <T>(null);
vectorToListAdapter.Indexer_Get <T>(0);
listToVectorAdapter.GetAt <T>(0U);
listToVectorAdapter.Size <T>();
}
public static double[] CalculateFppReactionsVector(Subdomain subdomain, IElementMatrixProvider elementProvider,
IScaleTransitions scaleTransitions, Dictionary <int, INode> boundaryNodes, IVectorView solution, IVectorView dSolution,
Dictionary <int, Dictionary <IDofType, double> > initialConvergedBoundaryDisplacements, Dictionary <int, Dictionary <IDofType, double> > totalBoundaryDisplacements,
int nIncrement, int totalIncrements)
{
//TODOGerasimos: 1) Subdomain2 einai h upo kataskevh subdomain.cs ths Marias gia na mporoume na anaferthoume sthn methodo ths CalculateElementNodalDisplacements(..,..).
// Otan parei telikh morfh tha taftizetai me thn Subdomain.cs
// 2)IVector solution, IVector dSolution EINAI AFTA ME TA OPOIA kaloume thn GetRHSFromSolution sthn 213 tou NRNLAnalyzer
double[] FppReactionVector;
Dictionary <int, int> boundaryNodesOrder = GetNodesOrderInDictionary(boundaryNodes);
FppReactionVector = new double[boundaryNodesOrder.Count * scaleTransitions.PrescribedDofsPerNode()]; // h allliws subdomain.Forces.GetLength(0)
var times = new Dictionary <string, TimeSpan>();
var totalStart = DateTime.Now;
times.Add("rowIndexCalculation", DateTime.Now - totalStart);
times.Add("element", TimeSpan.Zero);
times.Add("addition", TimeSpan.Zero);
foreach (Element element in subdomain.Elements)
{
var isEmbeddedElement = element.ElementType is IEmbeddedElement;
var elStart = DateTime.Now;
//IMatrix2D ElementK = elementProvider.Matrix(element);
var localSolution = subdomain.GetLocalVectorFromGlobalWithoutPrescribedDisplacements(element, solution);
subdomain.ImposePrescribedDisplacementsWithInitialConditionSEffect(element, localSolution, boundaryNodes, initialConvergedBoundaryDisplacements, totalBoundaryDisplacements, nIncrement, totalIncrements);
double[] localdSolution = subdomain.GetLocalVectorFromGlobalWithoutPrescribedDisplacements(element, dSolution);
double[] f = element.ElementType.CalculateForces(element, localSolution, localdSolution);
times["element"] += DateTime.Now - elStart;
elStart = DateTime.Now;
var elementDOFTypes = element.ElementType.DofEnumerator.GetDofTypesForMatrixAssembly(element);
var matrixAssemblyNodes = element.ElementType.DofEnumerator.GetNodesForMatrixAssembly(element);
int iElementMatrixRow = 0;
for (int i = 0; i < elementDOFTypes.Count; i++)
{
INode nodeRow = matrixAssemblyNodes[i];
if (boundaryNodes.ContainsKey(nodeRow.ID))
{
for (int i1 = 0; i1 < scaleTransitions.PrescribedDofsPerNode(); i1++)
{
int dofrow_p = scaleTransitions.PrescribedDofsPerNode() * (boundaryNodesOrder[nodeRow.ID] - 1) + i1;
FppReactionVector[dofrow_p] += f[iElementMatrixRow + i1];
}
}
iElementMatrixRow += elementDOFTypes[i].Count;
}
times["addition"] += DateTime.Now - elStart;
}
var totalTime = DateTime.Now - totalStart;
return(FppReactionVector);
}
/// <summary>
/// Solves the linear system A * x = b by solving the preconditioned system inv(P) * A * inv(P)^T * y = inv(P) * b,
/// where A = <paramref name="matrix"/>, b = <paramref name="rhsVector"/>, x is the solution, y = P^T * x,
/// P*P^T = <paramref name="preconditioner"/>.
/// Initially x = <paramref name="initialGuess"/> and then it converges to the solution.
/// </summary>
/// <param name="matrix">The matrix A of the linear system A * x = b. It must be symmetric positive definite.</param>
/// <param name="rhs">
/// The right hand side vector b of the linear system A * x = b. Constraints:
/// <paramref name="rhs"/>.<see cref="IIndexable1D.Length"/>
/// == <paramref name="matrix"/>.<see cref="IIndexable2D.NumRows"/>.
/// </param>
/// <param name="preconditioner">
/// A preconditioner matrix that is also symmetric positive definite and has the same dimensions as A.
/// </param>
/// <param name="solution">
/// The vector from which to start refining the solution vector x. Constraints:
/// <paramref name="solution"/>.<see cref="IIndexable1D.Length"/>
/// == <paramref name="matrix"/>.<see cref="IIndexable2D.NumColumns"/>.
/// </param>
/// <param name="initialGuessIsZero">
/// If <paramref name="solution"/> is 0, then set <paramref name="initialGuessIsZero"/> to true to avoid performing the
/// operation b-A*0 before starting.
/// </param>
/// <exception cref="NonMatchingDimensionsException">
/// Thrown if <paramref name="rhs"/> or <paramref name="solution"/> violate the described constraints.
/// </exception>
public IterativeStatistics Solve(IMatrixView matrix, IPreconditioner preconditioner, IVectorView rhs, IVector solution,
bool initialGuessIsZero, Func <IVector> zeroVectorInitializer) //TODO: find a better way to handle the case x0=0
{
return(Solve(new ExplicitMatrixTransformation(matrix), preconditioner, rhs, solution, initialGuessIsZero,
zeroVectorInitializer));
}
public IVectorViewToIBindableVectorViewAdapter(IVectorView <T> vectorView)
{
_vectorView = vectorView;
}
public IVector GetRhsFromSolution(IVectorView solution, IVectorView dSolution)
{
throw new NotImplementedException();
}