public void Determinant()
{
MatrixD a = new MatrixD(new double[, ] {
{ 1, 2, 3, 4 }, { 5, 6, 7, 8 }, { 0, 1, 2, 0 }, { 1, 0, 1, 0 }
});
LUDecompositionD d = new LUDecompositionD(a);
Assert.AreEqual(false, d.IsNumericallySingular);
Assert.IsTrue(Numeric.AreEqual(-24, d.Determinant()));
MatrixD aPermuted = d.L * d.U;
Assert.IsTrue(MatrixD.AreNumericallyEqual(aPermuted, a.GetSubmatrix(d.PivotPermutationVector, 0, 3)));
}
public void TestRandomRegularA()
{
RandomHelper.Random = new Random(1);
for (int i = 0; i < 100; i++)
{
VectorD column1 = new VectorD(3);
RandomHelper.Random.NextVectorD(column1, 1, 2);
VectorD column2 = new VectorD(3);
RandomHelper.Random.NextVectorD(column2, 1, 2);
// Make linearly independent.
if (column1 / column1[0] == column2 / column2[0])
{
column2[0]++;
}
// Create linearly independent third column.
VectorD column3 = column1 + column2;
column3[1]++;
// Create A.
MatrixD a = new MatrixD(3, 3);
a.SetColumn(0, column1);
a.SetColumn(1, column2);
a.SetColumn(2, column3);
LUDecompositionD d = new LUDecompositionD(a);
MatrixD aPermuted = d.L * d.U;
Assert.IsTrue(MatrixD.AreNumericallyEqual(aPermuted, a.GetSubmatrix(d.PivotPermutationVector, 0, 2)));
aPermuted = d.L * d.U; // Repeat with to test cached values.
Assert.IsTrue(MatrixD.AreNumericallyEqual(aPermuted, a.GetSubmatrix(d.PivotPermutationVector, 0, 2)));
Assert.AreEqual(false, d.IsNumericallySingular);
// Check solving of linear equations.
MatrixD b = new MatrixD(3, 2);
RandomHelper.Random.NextMatrixD(b, 0, 1);
MatrixD x = d.SolveLinearEquations(b);
MatrixD b2 = a * x;
Assert.IsTrue(MatrixD.AreNumericallyEqual(b, b2, 0.01f));
}
}
public void TestRandomRegularA()
{
RandomHelper.Random = new Random(1);
for (int i = 0; i < 100; i++)
{
VectorD column1 = new VectorD(3);
RandomHelper.Random.NextVectorD(column1, 1, 2);
VectorD column2 = new VectorD(3);
RandomHelper.Random.NextVectorD(column2, 1, 2);
// Make linearly independent.
if (column1 / column1[0] == column2 / column2[0])
{
column2[0]++;
}
// Create linearly independent third column.
VectorD column3 = column1 + column2;
column3[1]++;
// Create A.
MatrixD a = new MatrixD(3, 3);
a.SetColumn(0, column1);
a.SetColumn(1, column2);
a.SetColumn(2, column3);
QRDecompositionD d = new QRDecompositionD(a);
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, d.Q * d.R));
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, d.Q * d.R)); // Second time with the cached values.
Assert.AreEqual(true, d.HasNumericallyFullRank);
// Check solving of linear equations.
MatrixD b = new MatrixD(3, 2);
RandomHelper.Random.NextMatrixD(b, 0, 1);
MatrixD x = d.SolveLinearEquations(b);
MatrixD b2 = a * x;
Assert.IsTrue(MatrixD.AreNumericallyEqual(b, b2, 0.01f));
MatrixD h = d.H; // Just call this one to see if it runs through.
h = d.H; // Call it secont time to cover code with internal caching.
}
}
public void TestMatricesWithFullRank()
{
MatrixD a = new MatrixD(new double[, ] {
{ 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, -9 }
});
QRDecompositionD qr = new QRDecompositionD(a);
Assert.AreEqual(true, qr.HasNumericallyFullRank);
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, qr.Q * qr.R));
qr = new QRDecompositionD(a.Transposed);
Assert.AreEqual(true, qr.HasNumericallyFullRank);
Assert.IsTrue(MatrixD.AreNumericallyEqual(a.Transposed, qr.Q * qr.R));
a = new MatrixD(new double[, ] {
{ 1, 2 }, { 4, 5 }, { 4, 5 }
});
qr = new QRDecompositionD(a);
Assert.AreEqual(true, qr.HasNumericallyFullRank);
Assert.IsTrue(MatrixD.AreNumericallyEqual(a, qr.Q * qr.R));
MatrixD h = qr.H; // Just call this one to see if it runs through.
}