public static void PreconditioningPosDefSparse()
{
Console.WriteLine("Assessing correctness and efficiency of preconditioned MINRES:\n");
var A = Matrix.CreateFromArray(SparsePosDef10by10.Matrix);
var b = Vector.CreateFromArray(SparsePosDef10by10.Rhs);
var xExpected = Vector.CreateFromArray(SparsePosDef10by10.Lhs);
var M = new JacobiPreconditioner(A.GetDiagonalAsArray());
var minres = new MinRes(A.NumRows, 1e-10, 0, true, false);
// Without preconditioning
Console.WriteLine("Sparse pos-def system WITHOUT preconditioning:");
(IVector xSimple, MinresStatistics statsSimple) = minres.Solve(A, b);
Console.Write(statsSimple);
if (xSimple != null)
{
CheckSolution(xExpected, xSimple);
}
Console.WriteLine();
// With preconditioning
Console.WriteLine("Sparse pos-def system WITH preconditioning:");
(IVector xPrec, MinresStatistics statsPrec) = minres.Solve(A, b, M);
Console.Write(statsPrec);
if (xPrec != null)
{
CheckSolution(xExpected, xPrec);
}
Console.WriteLine();
}
private static void TestIndefiniteSystem(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
var comparer = new MatrixComparer(1E-4);
double residualTolerance = 1e-8;
(Matrix A, Vector b, Vector xExpected, IPreconditioner M) = DiagonalIndefinite.BuildIndefiniteSystem(20);
var minres = new MinRes(A.NumRows, residualTolerance, 0, false, false);
(IVector xComputed, MinresStatistics stats) = minres.Solve(A, b);
comparer.AssertEqual(xExpected, xComputed);
});
}
private static void TestPosDefSparseSystem(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
var comparer = new MatrixComparer(1E-6);
int n = SparsePosDef10by10.Order;
var A = Matrix.CreateFromArray(SparsePosDef10by10.Matrix);
var b = Vector.CreateFromArray(SparsePosDef10by10.Rhs);
var xExpected = Vector.CreateFromArray(SparsePosDef10by10.Lhs);
var minres = new MinRes(n, 1e-10, 0, false, false);
(IVector xComputed, MinresStatistics stats) = minres.Solve(A, b);
comparer.AssertEqual(xExpected, xComputed);
});
}
public static void PreconditioningIndefinite()
{
Console.WriteLine("Dense pos-def system WITHOUT preconditioning:");
(Matrix A, Vector b, Vector xExpected, IPreconditioner M) = DiagonalIndefinite.BuildIndefiniteSystem(2000);
var minres = new MinRes(A.NumRows, 1e-10, 0, true, false);
// Without preconditioning
(IVector xSimple, MinresStatistics statsSimple) = minres.Solve(A, b);
Console.Write(statsSimple);
if (xSimple != null)
{
CheckSolution(xExpected, xSimple);
}
Console.WriteLine();
// With preconditioning
(IVector xPrec, MinresStatistics statsPrec) = minres.Solve(A, b, M);
Console.Write(statsPrec);
if (xPrec != null)
{
CheckSolution(xExpected, xPrec);
}
Console.WriteLine();
}
