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], -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], -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(((double)sparseMatrix[i, j]).AlmostEqualInDecimalPlaces(original[i, j], 5), "#03-" + i + "-" + j);
}
}
}
/// <summary>
/// Check the result.
/// </summary>
/// <param name="preconditioner">Specific preconditioner.</param>
/// <param name="matrix">Source matrix.</param>
/// <param name="vector">Initial vector.</param>
/// <param name="result">Result vector.</param>
protected override void CheckResult(IPreConditioner preconditioner, SparseMatrix matrix, Vector <double> vector, Vector <double> result)
{
Assert.AreEqual(typeof(Diagonal), preconditioner.GetType(), "#01");
// Compute M * result = product
// compare vector and product. Should be equal
var product = new DenseVector(result.Count);
matrix.Multiply(result, product);
for (var i = 0; i < product.Count; i++)
{
Assert.IsTrue(vector[i].AlmostEqual(product[i], -Epsilon.Magnitude()), "#02-" + i);
}
}
protected override void CheckResult(IPreConditioner <Complex> preconditioner, SparseMatrix matrix, Vector <Complex> vector, Vector <Complex> result)
{
Assert.AreEqual(typeof(Ilutp), preconditioner.GetType(), "#01");
// Compute M * result = product
// compare vector and product. Should be equal
Vector <Complex> product = new DenseVector(result.Count);
matrix.Multiply(result, product);
for (var i = 0; i < product.Count; i++)
{
Assert.IsTrue(vector[i].Real.AlmostEqual(product[i].Real, -Epsilon.Magnitude()), "#02-" + i);
Assert.IsTrue(vector[i].Imaginary.AlmostEqual(product[i].Imaginary, -Epsilon.Magnitude()), "#03-" + i);
}
}
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].AlmostEqual(original[i, j], -Epsilon.Magnitude()), "#01-" + i + "-" + j);
}
}
}
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 ILUTPPreconditioner
{
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.AlmostEqualNumbersBetween(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.AlmostEqualNumbersBetween(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.AlmostEqualNumbersBetween(original[i, j].Real, -Epsilon.Magnitude()), "#03-" + i + "-" + j);
Assert.IsTrue(sparseMatrix[i, j].Imaginary.AlmostEqualNumbersBetween(original[i, j].Imaginary, -Epsilon.Magnitude()), "#04-" + i + "-" + j);
}
}
}
public void CompareWithOriginalSparseMatrix()
{
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 IncompleteLU();
ilu.Initialize(sparseMatrix);
var original = GetLowerTriangle(ilu).Multiply(GetUpperTriangle(ilu));
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);
}
}
}
public void CompareWithOriginalSparseMatrix()
{
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 ILU0Preconditioner();
ilu.Initialize(sparseMatrix);
var original = GetLowerTriangle(ilu).Multiply(GetUpperTriangle(ilu));
for (var i = 0; i < sparseMatrix.RowCount; i++)
{
for (var j = 0; j < sparseMatrix.ColumnCount; j++)
{
Assert.IsTrue(sparseMatrix[i, j].AlmostEqualNumbersBetween(original[i, j], -Epsilon.Magnitude()), "#01-" + i + "-" + j);
}
}
}