// will probably not work since the matrix will not always be positive definite
//[SkippableFact]
private static void TestRowAdditionReverse()
{
Skip.IfNot(TestSettings.TestSuiteSparse, TestSettings.MessageWhenSkippingSuiteSparse);
Matrix original = Matrix.CreateFromArray(SparsePosDef10by10.Matrix);
Vector rhs = Vector.CreateFromArray(SparsePosDef10by10.Rhs);
// Start the matrix as diagonal
var matrixExpected = Matrix.CreateIdentity(original.NumColumns);
var dok = DokSymmetric.CreateIdentity(SparsePosDef10by10.Order);
var factor = CholeskySuiteSparse.Factorize(dok.BuildSymmetricCscMatrix(true), false);
for (int i = 0; i < matrixExpected.NumRows; ++i)
{
// Update matrix
Vector newRowVector = original.GetRow(i);
matrixExpected.SetSubrow(i, newRowVector);
matrixExpected.SetSubcolumn(i, newRowVector);
//Console.WriteLine($"\nOnly dofs [0, {i}]");
factor.AddRow(i, SparseVector.CreateFromDense(newRowVector));
// Solve new linear system
Vector solutionExpected = matrixExpected.FactorCholesky(true).SolveLinearSystem(rhs);
Vector solutionComputed = factor.SolveLinearSystem(rhs);
comparer.AssertEqual(solutionExpected, solutionComputed);
}
}
private static void TestSystemSolution1()
{
Skip.IfNot(TestSettings.TestSuiteSparse, TestSettings.MessageWhenSkippingSuiteSparse);
// Define linear system
var rhs = Vector.CreateFromArray(new double[] { 6.0, 14.0, 11.0, 12.0 });
var solutionExpected = Vector.CreateFromArray(new double[] { 1.0, 1.0, 1.0, 1.0 });
var matrixDOK = DokSymmetric.CreateEmpty(4);
matrixDOK[0, 0] = 4.0; matrixDOK[0, 2] = 2.0;
matrixDOK[1, 1] = 10.0; matrixDOK[1, 2] = 1.0; matrixDOK[1, 3] = 3.0;
matrixDOK[2, 2] = 8.0;
matrixDOK[3, 3] = 9.0;
SymmetricCscMatrix matrixCSC = matrixDOK.BuildSymmetricCscMatrix(true);
//const int n = 4;
//const int nnz = 7;
//int[] colOffsets = new int[n + 1] { 0, 1, 2, 5, nnz };
//int[] rowIndices = new int[nnz] { 0, 1, 0, 1, 2, 1, 3 };
//double[] values = new double[nnz] { 4.0, 10.0, 2.0, 1.0, 8.0, 3.0, 9.0 };
//SymmetricCSC matrixCSC = new SymmetricCSC(values, rowIndices, colOffsets, false);
//Solve it using SuiteSparse
using (var factor = CholeskySuiteSparse.Factorize(matrixCSC, true))
{
Vector solution = factor.SolveLinearSystem(rhs);
comparer.AssertEqual(solutionExpected, solution);
}
}
public static void MemoryConsumptionDebugging()
{
int order = 100000;
int bandwidth = 200;
for (int rep = 0; rep < 10; ++rep)
{
var dok = DokSymmetric.CreateEmpty(order);
for (int i = 0; i < order; ++i)
{
dok[i, i] = 10.0;
if (i >= bandwidth)
{
dok[i - bandwidth, i] = 1.0;
}
else
{
dok[0, i] = 1.0;
}
}
dok[0, 0] = 10.0;
SymmetricCscMatrix matrix = dok.BuildSymmetricCscMatrix(true);
var rhs = Vector.CreateWithValue(order, 2.0);
var solution = Vector.CreateZero(order);
using (var factorization = CholeskySuiteSparse.Factorize(matrix, true))
{
factorization.SolveLinearSystem(rhs, solution);
}
}
}
/// <summary>
/// Solves the linear system with back-forward substitution. If the matrix has been modified, it will be refactorized.
/// </summary>
public override void Solve()
{
var watch = new Stopwatch();
if (linearSystem.SolutionConcrete == null)
{
linearSystem.SolutionConcrete = linearSystem.CreateZeroVectorConcrete();
}
//else linearSystem.Solution.Clear(); // no need to waste computational time on this in a direct solver
// Factorization
if (mustFactorize)
{
watch.Start();
factorization = CholeskySuiteSparse.Factorize(linearSystem.Matrix, useSuperNodalFactorization);
watch.Stop();
Logger.LogTaskDuration("Matrix factorization", watch.ElapsedMilliseconds);
watch.Reset();
mustFactorize = false;
}
// Substitutions
watch.Start();
factorization.SolveLinearSystem(linearSystem.RhsConcrete, linearSystem.SolutionConcrete);
watch.Stop();
Logger.LogTaskDuration("Back/forward substitutions", watch.ElapsedMilliseconds);
Logger.IncrementAnalysisStep();
}
protected override Matrix InverseSystemMatrixTimesOtherMatrix(IMatrixView otherMatrix)
{
var watch = new Stopwatch();
// Factorization
if (mustFactorize)
{
watch.Start();
factorization = CholeskySuiteSparse.Factorize(linearSystem.Matrix, useSuperNodalFactorization);
watch.Stop();
Logger.LogTaskDuration("Matrix factorization", watch.ElapsedMilliseconds);
watch.Reset();
mustFactorize = false;
}
// Substitutions
watch.Start();
Matrix solutionVectors;
if (otherMatrix is Matrix otherDense)
{
return(factorization.SolveLinearSystems(otherDense));
}
else
{
try
{
// If there is enough memory, copy the RHS matrix to a dense one, to speed up computations.
//TODO: must be benchmarked, if it is actually more efficient than solving column by column.
Matrix rhsVectors = otherMatrix.CopyToFullMatrix();
solutionVectors = factorization.SolveLinearSystems(rhsVectors);
}
catch (InsufficientMemoryException) //TODO: what about OutOfMemoryException?
{
// Solution vectors
int systemOrder = linearSystem.Matrix.NumColumns;
int numRhs = otherMatrix.NumColumns;
solutionVectors = Matrix.CreateZero(systemOrder, numRhs);
Vector solutionVector = linearSystem.CreateZeroVectorConcrete();
// Solve each linear system separately, to avoid copying the RHS matrix to a dense one.
for (int j = 0; j < numRhs; ++j)
{
if (j != 0)
{
solutionVector.Clear();
}
Vector rhsVector = otherMatrix.GetColumn(j);
factorization.SolveLinearSystem(rhsVector, solutionVector);
solutionVectors.SetSubcolumn(j, solutionVector);
}
}
}
watch.Stop();
Logger.LogTaskDuration("Back/forward substitutions", watch.ElapsedMilliseconds);
Logger.IncrementAnalysisStep();
return(solutionVectors);
}
private static void CheckSystemSolution2()
{
Skip.IfNot(TestSettings.TestSuiteSparse, TestSettings.MessageWhenSkippingSuiteSparse);
int order = SparsePosDef10by10.Order;
// Build the matrices and right hand sides
var dense = Matrix.CreateFromArray(SparsePosDef10by10.Matrix);
//var skyline = SkylineMatrix.CreateFromArrays(order, SparsePositiveDefinite.skylineValues,
// SparsePositiveDefinite.skylineDiagOffsets, false);
//var dok = DOKSymmetricColMajor.CreateFromSparseMatrix(skyline);
var dok = DokSymmetric.CreateEmpty(order);
for (int j = 0; j < order; ++j)
{
for (int i = 0; i <= j; ++i)
{
if (dense[i, j] != 0)
{
dok[i, j] = dense[i, j];
}
}
}
Vector b = Vector.CreateFromArray(SparsePosDef10by10.Rhs);
Matrix B = Matrix.CreateFromArray(SquareInvertible10by10.Matrix);
// Solve using dense algebra
CholeskyFull chol = dense.FactorCholesky(false);
Matrix U = chol.GetFactorU();
Matrix L = U.Transpose();
Vector xSolveExpect = chol.SolveLinearSystem(b);
Matrix XSolveExpect = dense.Invert() * B;
Vector xBackExpect = U.Invert() * b;
Matrix XBackExpect = U.Invert() * B;
Vector xForwardExpect = L.Invert() * b;
Matrix XForwardExpect = L.Invert() * B;
// Solve using SuiteSparse
var(values, rowIndices, colOffsets) = dok.BuildSymmetricCscArrays(true);
CholeskySuiteSparse factor = CholeskySuiteSparse.Factorize(order, values.Length, values, rowIndices, colOffsets,
true);
Vector xSolveComput = factor.SolveLinearSystem(b);
Matrix XSolveComput = factor.SolveLinearSystems(B);
Vector xBackComput = factor.BackSubstitution(b);
Matrix XBackComput = factor.BackSubstitutions(B);
Vector xForwardComput = factor.ForwardSubstitution(b);
Matrix XForwardComput = factor.ForwardSubstitutions(B);
Vector xSolveComput2 = factor.BackSubstitution(factor.ForwardSubstitution(b));
// Check results
comparer.AssertEqual(xSolveExpect, xSolveComput);
comparer.AssertEqual(XSolveExpect, XSolveComput);
comparer.AssertEqual(xBackExpect, xBackComput);
comparer.AssertEqual(XBackExpect, XBackComput);
comparer.AssertEqual(xForwardExpect, xForwardComput);
comparer.AssertEqual(XForwardExpect, XForwardComput);
}
private static void TestRowDeletion()
{
Skip.IfNot(TestSettings.TestSuiteSparse, TestSettings.MessageWhenSkippingSuiteSparse);
Matrix original = Matrix.CreateFromArray(SparsePosDef10by10.Matrix);
Vector rhs = Vector.CreateFromArray(SparsePosDef10by10.Rhs);
// Start the matrix from the original
var matrixExpected = Matrix.CreateFromArray(SparsePosDef10by10.Matrix);
var dok = DokSymmetric.CreateEmpty(SparsePosDef10by10.Order);
for (int j = 0; j < matrixExpected.NumColumns; ++j)
{
for (int i = 0; i <= j; ++i)
{
if (matrixExpected[i, j] != 0)
{
dok[i, j] = matrixExpected[i, j];
}
}
}
var factor = CholeskySuiteSparse.Factorize(dok.BuildSymmetricCscMatrix(true), false);
for (int i = 0; i < matrixExpected.NumRows; ++i)
{
// Update matrix
Vector identityRow = Vector.CreateZero(matrixExpected.NumColumns);
identityRow[i] = 1.0;
matrixExpected.SetSubrow(i, identityRow);
matrixExpected.SetSubcolumn(i, identityRow);
//Console.WriteLine($"\nOnly dofs [{i + 1}, 10)");
factor.DeleteRow(i);
// Solve new linear system
Vector solutionExpected = matrixExpected.FactorCholesky(false).SolveLinearSystem(rhs);
Vector solutionComputed = factor.SolveLinearSystem(rhs);
comparer.AssertEqual(solutionExpected, solutionComputed);
}
}