/// <summary>
/// The main method that uses the Ilutp preconditioner.
/// </summary>
public void UseSolver()
{
// Create a sparse matrix. For now the size will be 10 x 10 elements
Matrix matrix = CreateMatrix(10);
// Create the right hand side vector. The size is the same as the matrix
// and all values will be 2.0.
Vector rightHandSideVector = new DenseVector(10, 2.0);
// Create the Ilutp preconditioner
Ilutp preconditioner = new Ilutp();
// Set the drop tolerance. All entries with absolute values smaller than this value will be
// removed from the preconditioner matrices.
preconditioner.DropTolerance = 1e-5;
// Set the relative fill level. This indicates how much additional fill we allow. In this case
// about 200%
preconditioner.FillLevel = 200;
// Set the pivot tolerance. This indicates when pivoting is used. In this case we pivot if
// the largest off-diagonal entry is twice as big as the diagonal entry.
preconditioner.PivotTolerance = 0.5;
// Create the actual preconditioner
preconditioner.Initialize(matrix);
// Now that all is set we can solve the matrix equation.
Vector solutionVector = preconditioner.Approximate(rightHandSideVector);
// Another way to get the values is by using the overloaded solve method
// In this case the solution vector needs to be of the correct size.
preconditioner.Approximate(rightHandSideVector, solutionVector);
}
public void CompareWithOriginalDenseMatrixWithoutPivoting()
{
var sparseMatrix = new SparseMatrix(3);
sparseMatrix[0, 0] = -1;
sparseMatrix[0, 1] = 5;
sparseMatrix[0, 2] = 6;
sparseMatrix[1, 0] = 3;
sparseMatrix[1, 1] = -6;
sparseMatrix[1, 2] = 1;
sparseMatrix[2, 0] = 6;
sparseMatrix[2, 1] = 8;
sparseMatrix[2, 2] = 9;
var ilu = new Ilutp
{
PivotTolerance = 0.0,
DropTolerance = 0,
FillLevel = 10
};
ilu.Initialize(sparseMatrix);
var l = GetLowerTriangle(ilu);
// Assert l is lower triagonal
for (var i = 0; i < l.RowCount; i++)
{
for (var j = i + 1; j < l.RowCount; j++)
{
Assert.IsTrue(0.0.AlmostEqual(l[i, j].Magnitude, -Epsilon.Magnitude()), "#01-" + i + "-" + j);
}
}
var u = GetUpperTriangle(ilu);
// Assert u is upper triagonal
for (var i = 0; i < u.RowCount; i++)
{
for (var j = 0; j < i; j++)
{
Assert.IsTrue(0.0.AlmostEqual(u[i, j].Magnitude, -Epsilon.Magnitude()), "#02-" + i + "-" + j);
}
}
var original = l.Multiply(u);
for (var i = 0; i < sparseMatrix.RowCount; i++)
{
for (var j = 0; j < sparseMatrix.ColumnCount; j++)
{
Assert.IsTrue(sparseMatrix[i, j].Real.AlmostEqual(original[i, j].Real, -Epsilon.Magnitude()), "#03-" + i + "-" + j);
Assert.IsTrue(sparseMatrix[i, j].Imaginary.AlmostEqual(original[i, j].Imaginary, -Epsilon.Magnitude()), "#04-" + i + "-" + j);
}
}
}
public void SolveWithPivoting()
{
const int Size = 10;
var newMatrix = CreateReverseUnitMatrix(Size);
var vector = CreateStandardBcVector(Size);
var preconditioner = new Ilutp
{
PivotTolerance = 1.0,
DropTolerance = 0,
FillLevel = 10
};
preconditioner.Initialize(newMatrix);
Vector result = new DenseVector(vector.Count);
preconditioner.Approximate(vector, result);
CheckResult(preconditioner, newMatrix, vector, result);
}
public void CompareWithOriginalDenseMatrixWithPivoting()
{
var sparseMatrix = new SparseMatrix(3);
sparseMatrix[0, 0] = -1;
sparseMatrix[0, 1] = 5;
sparseMatrix[0, 2] = 6;
sparseMatrix[1, 0] = 3;
sparseMatrix[1, 1] = -6;
sparseMatrix[1, 2] = 1;
sparseMatrix[2, 0] = 6;
sparseMatrix[2, 1] = 8;
sparseMatrix[2, 2] = 9;
var ilu = new Ilutp
{
PivotTolerance = 1.0,
DropTolerance = 0,
FillLevel = 10
};
ilu.Initialize(sparseMatrix);
var l = GetLowerTriangle(ilu);
var u = GetUpperTriangle(ilu);
var pivots = GetPivots(ilu);
var p = new SparseMatrix(l.RowCount);
for (var i = 0; i < p.RowCount; i++)
{
p[i, pivots[i]] = 1.0;
}
var temp = l.Multiply(u);
var original = temp.Multiply(p);
for (var i = 0; i < sparseMatrix.RowCount; i++)
{
for (var j = 0; j < sparseMatrix.ColumnCount; j++)
{
Assert.IsTrue(sparseMatrix[i, j].Real.AlmostEqual(original[i, j].Real, -Epsilon.Magnitude()), "#01-" + i + "-" + j);
Assert.IsTrue(sparseMatrix[i, j].Imaginary.AlmostEqual(original[i, j].Imaginary, -Epsilon.Magnitude()), "#02-" + i + "-" + j);
}
}
}