public CsrMatrix BuildGlobalMatrix(ISubdomainFreeDofOrdering dofOrdering, IEnumerable <IElement> elements,
IElementMatrixProvider matrixProvider)
{
int numFreeDofs = dofOrdering.NumFreeDofs;
var subdomainMatrix = DokRowMajor.CreateEmpty(numFreeDofs, numFreeDofs);
foreach (IElement element in elements)
{
(int[] elementDofIndices, int[] subdomainDofIndices) = dofOrdering.MapFreeDofsElementToSubdomain(element);
IMatrix elementMatrix = matrixProvider.Matrix(element);
subdomainMatrix.AddSubmatrixSymmetric(elementMatrix, elementDofIndices, subdomainDofIndices);
}
(double[] values, int[] colIndices, int[] rowOffsets) = subdomainMatrix.BuildCsrArrays(sortColsOfEachRow);
if (!isIndexerCached)
{
cachedColIndices = colIndices;
cachedRowOffsets = rowOffsets;
isIndexerCached = true;
}
else
{
Debug.Assert(Utilities.AreEqual(cachedColIndices, colIndices));
Debug.Assert(Utilities.AreEqual(cachedRowOffsets, rowOffsets));
}
return(CsrMatrix.CreateFromArrays(numFreeDofs, numFreeDofs, values, cachedColIndices, cachedRowOffsets, false));
}
private static void TestIndexer()
{
Matrix dense = Matrix.CreateFromArray(SparseRectangular10by5.Matrix);
DokRowMajor dok = CreateDok(SparseRectangular10by5.Matrix);
comparer.AssertEqual(dense, dok);
}
private void CreateCoarseSpaceInterpolation()
{
var degreKsi = _ksiDecomposition.Degree;
var knotValueVectorKsi = _ksiDecomposition.KnotValueVector;
var coarsePointsKsi = _ksiDecomposition.GetAxisCoarsePoints();
var degreeHeta = _hetaDecomposition.Degree;
var knotValueVectorHeta = _hetaDecomposition.KnotValueVector;
var coarsePointsHeta = _hetaDecomposition.GetAxisCoarsePoints();
var coarsePoints2D =
(from ksi in coarsePointsKsi from heta in coarsePointsHeta select new NaturalPoint(ksi, heta)).ToList();
var R0 = DokRowMajor.CreateEmpty(_patchControlPoints.Count * 2, coarsePoints2D.Count * 2);
for (int i = 0; i < coarsePoints2D.Count; i++)
{
var NurbsValues = CalculateNURBS2D(degreKsi, degreeHeta, knotValueVectorKsi,
knotValueVectorHeta, coarsePoints2D[i], _patchControlPoints);
for (int j = 0; j < NurbsValues.NumRows; j++)
{
if (Math.Abs(NurbsValues[j, 0]) < 10e-9)
{
continue;
}
R0[2 * j, 2 * i] = NurbsValues[j, 0];
R0[2 * j + 1, 2 * i + 1] = NurbsValues[j, 0];
}
}
_coarseSpaceInterpolation = R0.BuildCsrMatrix(true).GetSubmatrix(freeSubdomainDofs.ToArray(), _coarseSpaceNodeSelection.GetFreeCoarseSpaceDofs());
}
public static void CompareDokCsrMultiplication()
{
int numRows = 100000;
int numCols = 10000;
DokRowMajor dok = RandomUtilities.CreateRandomSparseMatrix(numRows, numCols, 0.15);
Vector lhs = RandomUtilities.CreateRandomVector(numCols);
var watch = new Stopwatch();
watch.Start();
Vector dokTimesLhs = dok.MultiplyRight(lhs);
watch.Stop();
long dokTime = watch.ElapsedMilliseconds;
LibrarySettings.LinearAlgebraProviders = LinearAlgebraProviderChoice.Managed;
watch.Restart();
Vector csrUnsortedTimesLhs = dok.BuildCsrMatrix(false).Multiply(lhs, false);
watch.Stop();
long csrUnsortedTime = watch.ElapsedMilliseconds;
watch.Restart();
Vector csrSortedTimesLhs = dok.BuildCsrMatrix(true).Multiply(lhs, false);
watch.Stop();
long csrSortedTime = watch.ElapsedMilliseconds;
LibrarySettings.LinearAlgebraProviders = LinearAlgebraProviderChoice.MKL;
watch.Restart();
Vector csrUnsortedMklTimesLhs = dok.BuildCsrMatrix(false).Multiply(lhs, false);
watch.Stop();
long csrUnsortedMklTime = watch.ElapsedMilliseconds;
watch.Restart();
Vector csrSortedMklTimesLhs = dok.BuildCsrMatrix(true).Multiply(lhs, false);
watch.Stop();
long csrSortedMklTime = watch.ElapsedMilliseconds;
Console.WriteLine("Checking correctness and performance of DOK, sorted and unsorted CSR * vector:");
Console.WriteLine($"DOK * vector: time = {dokTime} ms");
Console.WriteLine($"Unsorted CSR * vector (C#): time = {csrUnsortedTime} ms");
Console.WriteLine($"Sorted CSR * vector (C#): time = {csrSortedTime} ms");
Console.WriteLine($"Unsorted CSR * vector (MKL): time = {csrUnsortedMklTime} ms");
Console.WriteLine($"Sorted CSR * vector (MKL): time = {csrSortedMklTime} ms");
var comparer = new ValueComparer(1e-12);
double errorUnsorted = (csrUnsortedTimesLhs - dokTimesLhs).Norm2() / dokTimesLhs.Norm2();
double errorSorted = (csrSortedTimesLhs - dokTimesLhs).Norm2() / dokTimesLhs.Norm2();
double errorUnsortedMkl = (csrUnsortedMklTimesLhs - dokTimesLhs).Norm2() / dokTimesLhs.Norm2();
double errorSortedMkl = (csrSortedMklTimesLhs - dokTimesLhs).Norm2() / dokTimesLhs.Norm2();
Console.WriteLine("Multiplication DOK - unsorted CSR (C#): normalized error = " + errorUnsorted);
Console.WriteLine("Multiplication DOK - sorted CSR (C#): normalized error = " + errorSorted);
Console.WriteLine("Multiplication DOK - unsorted CSR (MKL): normalized error = " + errorUnsortedMkl);
Console.WriteLine("Multiplication DOK - sorted CSR (MKL): normalized error = " + errorSortedMkl);
}
/// <summary>
/// Reads a general sparse matrix from the file specified by <paramref name="path"/>. Even if the matrix is symmetric,
/// the file must contain both the upper and lower triangle.
/// </summary>
/// <param name="path">The absolute path of the array.</param>
/// <exception cref="IOException">Thrown if there is no such file or if the dimensions of the matrix specified in the
/// first line are invalid.</exception>
public DokRowMajor ReadFileAsDokRowMajor(string path)
{
using (var reader = new StreamReader(path))
{
(int numRows, int numCols, int nnz) = ReadMatrixDimensions(reader);
var builder = DokRowMajor.CreateEmpty(numRows, numCols);
ReadMatrixEntries(reader, nnz, builder);
return(builder);
}
}
matrixConstrConstr) BuildGlobalSubmatrices(ISubdomainFreeDofOrdering freeDofRowOrdering,
ISubdomainFreeDofOrdering freeDofColOrdering,
ISubdomainConstrainedDofOrdering constrainedDofRowOrdering,
ISubdomainConstrainedDofOrdering constrainedDofColOrdering, IEnumerable <IElement> elements,
IElementMatrixProvider matrixProvider)
{
int numFreeRowDofs = freeDofRowOrdering.NumFreeDofs;
int numFreeColDofs = freeDofColOrdering.NumFreeDofs;
var subdomainMatrix = DokRowMajor.CreateEmpty(numFreeRowDofs, numFreeColDofs);
constrainedAssembler.InitializeNewMatrices(freeDofRowOrdering.NumFreeDofs,
constrainedDofRowOrdering.NumConstrainedDofs);
foreach (var element in elements)
{
(int[] elementRowDofsFree, int[] subdomainRowDofsFree) =
freeDofRowOrdering.MapFreeDofsElementToSubdomain(element);
(int[] elementColDofsFree, int[] subdomainColDofsFree) =
freeDofColOrdering.MapFreeDofsElementToSubdomain(element);
(int[] elementRowDofsConstrained, int[] subdomainRowDofsConstrained) =
constrainedDofRowOrdering.MapConstrainedDofsElementToSubdomain(element);
(int[] elementColDofsConstrained, int[] subdomainColDofsConstrained) =
constrainedDofColOrdering.MapConstrainedDofsElementToSubdomain(element);
IMatrix elementMatrix = matrixProvider.Matrix(element);
subdomainMatrix.AddSubmatrix(elementMatrix, elementRowDofsFree, subdomainRowDofsFree,
elementColDofsFree, subdomainColDofsFree);
constrainedAssembler.AddElementMatrix(elementMatrix, elementRowDofsFree, subdomainRowDofsFree,
elementRowDofsConstrained, subdomainRowDofsConstrained); //TODO: check validity
}
(double[] values, int[] colIndices, int[] rowOffsets) = subdomainMatrix.BuildCsrArrays(sortColsOfEachRow);
if (!isIndexerCached)
{
cachedColIndices = colIndices;
cachedRowOffsets = rowOffsets;
isIndexerCached = true;
}
else
{
Debug.Assert(Utilities.AreEqual(cachedColIndices, colIndices));
Debug.Assert(Utilities.AreEqual(cachedRowOffsets, rowOffsets));
}
subdomainMatrix = null;
var matrixFreeFree =
CsrMatrix.CreateFromArrays(numFreeRowDofs, numFreeColDofs, values, cachedColIndices, cachedRowOffsets,
false);
(CsrMatrix matrixConstrFree, CsrMatrix matrixConstrConstr) =
constrainedAssembler.BuildMatrices(); // TODO: see if this work
return(matrixFreeFree, matrixConstrFree, matrixConstrFree.TransposeToCSC(false), matrixConstrConstr);
}
internal (CsrMatrix matrixConstrFree, CsrMatrix matrixConstrConstr) BuildMatrices()
{
// Also free the memory used by each builders, as soon as it is no longer used.
CsrMatrix matrixConstrFree = dokConstrFree.BuildCsrMatrix(true);
dokConstrFree = null;
CsrMatrix matrixConstrConstr = dokConstrConstr.BuildCsrMatrix(true);
dokConstrConstr = null;
return(matrixConstrFree, matrixConstrConstr);
}
//TODO: this should be done by an assembler class
//TODO: make sure this is called whenever the ordering changes
private CsrMatrix BuildQFromSubdomain(Subdomain subdomain)
{
int numFreeDofs = subdomain.FreeDofOrdering.NumFreeDofs;
var qSubdomain = DokRowMajor.CreateEmpty(numFreeDofs, numFreeDofs);
DofTable allDofs = subdomain.FreeDofOrdering.FreeDofs;
foreach (Element element in subdomain.Elements)
{
if (!(element.ElementType is IPorousFiniteElement))
{
continue;
}
var e = (IPorousFiniteElement)element.ElementType;
IMatrix q = e.CouplingMatrix(element);
int iElementMatrixRow = 0;
for (int i = 0; i < element.ElementType.DofEnumerator.GetDofTypesForMatrixAssembly(element).Count; i++)
{
Node nodeRow = element.Nodes[i];
foreach (IDofType dofTypeRow in element.ElementType.DofEnumerator.GetDofTypesForMatrixAssembly(element)[i])
{
if (dofTypeRow != PorousMediaDof.Pressure)
{
continue;
}
int dofRow = allDofs[nodeRow, dofTypeRow];
int iElementMatrixColumn = 0;
for (int j = 0; j < element.ElementType.DofEnumerator.GetDofTypesForMatrixAssembly(element).Count; j++)
{
Node nodeColumn = element.Nodes[j];
foreach (IDofType dofTypeColumn in element.ElementType.DofEnumerator.GetDofTypesForMatrixAssembly(element)[j])
{
if (dofTypeColumn == PorousMediaDof.Pressure)
{
continue;
}
int dofColumn = allDofs[nodeColumn, dofTypeColumn];
qSubdomain.AddToEntry(dofColumn, dofRow, q[iElementMatrixRow, iElementMatrixColumn]);
iElementMatrixColumn++;
}
}
iElementMatrixRow++;
}
}
}
return(qSubdomain.BuildCsrMatrix(true));
}
private static void TestBuildCSR()
{
var dense = Matrix.CreateFromArray(SparseRectangular10by5.Matrix);
DokRowMajor dok = CreateDok(SparseRectangular10by5.Matrix);
// CSR with sorted col indices of each row
CsrMatrix csrSorted = dok.BuildCsrMatrix(true);
comparer.AssertEqual(dense, csrSorted);
// CSR without sorting
CsrMatrix csrUnsorted = dok.BuildCsrMatrix(false);
comparer.AssertEqual(dense, csrUnsorted);
}
internal static DokRowMajor CreateRandomSparseMatrix(int numRows, int numCols, double nonZeroChance)
{
var rand = new Random();
var dok = DokRowMajor.CreateEmpty(numRows, numCols);
for (int i = 0; i < numRows; ++i)
{
for (int j = 0; j < numCols; ++j)
{
if (rand.NextDouble() <= nonZeroChance)
{
dok[i, j] = rand.NextDouble();
}
}
}
return(dok);
}
IMatrixView matrixConstrConstr) BuildGlobalSubmatrices(
ISubdomainFreeDofOrdering freeDofOrdering, ISubdomainConstrainedDofOrdering constrainedDofOrdering,
IEnumerable <IElement> elements, IElementMatrixProvider matrixProvider)
{
int numFreeDofs = freeDofOrdering.NumFreeDofs;
var subdomainMatrix = DokRowMajor.CreateEmpty(numFreeDofs, numFreeDofs);
//TODO: also reuse the indexers of the constrained matrices.
constrainedAssembler.InitializeNewMatrices(freeDofOrdering.NumFreeDofs, constrainedDofOrdering.NumConstrainedDofs);
// Process the stiffness of each element
foreach (IElement element in elements)
{
(int[] elementDofsFree, int[] subdomainDofsFree) = freeDofOrdering.MapFreeDofsElementToSubdomain(element);
(int[] elementDofsConstrained, int[] subdomainDofsConstrained) =
constrainedDofOrdering.MapConstrainedDofsElementToSubdomain(element);
IMatrix elementMatrix = matrixProvider.Matrix(element);
subdomainMatrix.AddSubmatrixSymmetric(elementMatrix, elementDofsFree, subdomainDofsFree);
constrainedAssembler.AddElementMatrix(elementMatrix, elementDofsFree, subdomainDofsFree,
elementDofsConstrained, subdomainDofsConstrained);
}
// Create and cache the CSR arrays for the free dofs.
(double[] values, int[] colIndices, int[] rowOffsets) = subdomainMatrix.BuildCsrArrays(sortColsOfEachRow);
if (!isIndexerCached)
{
cachedColIndices = colIndices;
cachedRowOffsets = rowOffsets;
isIndexerCached = true;
}
else
{
Debug.Assert(Utilities.AreEqual(cachedColIndices, colIndices));
Debug.Assert(Utilities.AreEqual(cachedRowOffsets, rowOffsets));
}
// Create the free and constrained matrices.
subdomainMatrix = null; // Let the DOK be garbaged collected early, in case there isn't sufficient memory.
var matrixFreeFree =
CsrMatrix.CreateFromArrays(numFreeDofs, numFreeDofs, values, cachedColIndices, cachedRowOffsets, false);
(CsrMatrix matrixConstrFree, CsrMatrix matrixConstrConstr) = constrainedAssembler.BuildMatrices();
return(matrixFreeFree, matrixConstrFree, matrixConstrFree.TransposeToCSC(false), matrixConstrConstr);
}
private static DokRowMajor CreateDok(double[,] matrix)
{
int m = matrix.GetLength(0);
int n = matrix.GetLength(1);
var dok = DokRowMajor.CreateEmpty(m, n);
for (int i = 0; i < m; ++i)
{
for (int j = 0; j < n; ++j)
{
if (matrix[i, j] != 0.0)
{
dok[i, j] = matrix[i, j];
}
}
}
return(dok);
}
internal void InitializeNewMatrices(int numFreeDofs, int numConstrainedDofs)
{
dokConstrFree = DokRowMajor.CreateEmpty(numConstrainedDofs, numFreeDofs);
dokConstrConstr = DokRowMajor.CreateEmpty(numConstrainedDofs, numConstrainedDofs);
}