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);
}
protected override Matrix InverseSystemMatrixTimesOtherMatrix(IMatrixView otherMatrix)
{
//TODO: Use a reorthogonalizetion approach when solving multiple rhs vectors. It would be even better if the CG
// algorithm exposed a method for solving for multiple rhs vectors.
var watch = new Stopwatch();
// Preconditioning
if (mustUpdatePreconditioner)
{
watch.Start();
preconditioner = preconditionerFactory.CreatePreconditionerFor(linearSystem.Matrix);
watch.Stop();
Logger.LogTaskDuration("Calculating preconditioner", watch.ElapsedMilliseconds);
watch.Reset();
mustUpdatePreconditioner = false;
}
// Iterative algorithm
watch.Start();
int systemOrder = linearSystem.Matrix.NumColumns;
int numRhs = otherMatrix.NumColumns;
var solutionVectors = Matrix.CreateZero(systemOrder, numRhs);
Vector solutionVector = linearSystem.CreateZeroVectorConcrete();
// Solve each linear system
for (int j = 0; j < numRhs; ++j)
{
if (j != 0)
{
solutionVector.Clear();
}
//TODO: we should make sure this is the same type as the vectors used by this solver, otherwise vector operations
// in CG will be slow.
Vector rhsVector = otherMatrix.GetColumn(j);
IterativeStatistics stats = pcgAlgorithm.Solve(linearSystem.Matrix, preconditioner, rhsVector,
solutionVector, true, () => linearSystem.CreateZeroVector());
solutionVectors.SetSubcolumn(j, solutionVector);
}
watch.Stop();
Logger.LogTaskDuration("Iterative algorithm", watch.ElapsedMilliseconds);
Logger.IncrementAnalysisStep();
return(solutionVectors);
}