public void SquareRandomMatrixLUDecomposition()
{
for (int d = 1; d <= 256; d += 11)
{
SquareMatrix M = CreateSquareRandomMatrix(d);
// LU decompose the matrix
//Stopwatch sw = Stopwatch.StartNew();
LUDecomposition LU = M.LUDecomposition();
//sw.Stop();
//Console.WriteLine(sw.ElapsedMilliseconds);
Assert.IsTrue(LU.Dimension == d);
// test that the decomposition works
SquareMatrix P = LU.PMatrix();
SquareMatrix L = LU.LMatrix();
SquareMatrix U = LU.UMatrix();
Assert.IsTrue(TestUtilities.IsNearlyEqual(P * M, L * U));
// check that the inverse works
SquareMatrix MI = LU.Inverse();
Assert.IsTrue(TestUtilities.IsNearlyEqual(M * MI, UnitMatrix.OfDimension(d)));
// test that a solution works
ColumnVector t = new ColumnVector(d);
for (int i = 0; i < d; i++)
{
t[i] = i;
}
ColumnVector s = LU.Solve(t);
Assert.IsTrue(TestUtilities.IsNearlyEqual(M * s, t));
}
}
public static void LUDecomposition()
{
SquareMatrix A = new SquareMatrix(new double[, ] {
{ 1, -2, 3 },
{ 2, -5, 12 },
{ 0, 2, -10 }
});
ColumnVector b = new ColumnVector(2, 8, -4);
LUDecomposition lud = A.LUDecomposition();
ColumnVector x = lud.Solve(b);
PrintMatrix("x", x);
PrintMatrix("Ax", A * x);
SquareMatrix L = lud.LMatrix();
SquareMatrix U = lud.UMatrix();
SquareMatrix P = lud.PMatrix();
PrintMatrix("LU", L * U);
PrintMatrix("PA", P * A);
SquareMatrix AI = lud.Inverse();
PrintMatrix("A * AI", A * AI);
Console.WriteLine($"det(a) = {lud.Determinant()}");
}
public void SquareVandermondeMatrixLUDecomposition()
{
// fails now for d = 8 because determinant slightly off
for (int d = 1; d <= 7; d++)
{
Console.WriteLine("d={0}", d);
double[] x = new double[d];
for (int i = 0; i < d; i++)
{
x[i] = i;
}
double det = 1.0;
for (int i = 0; i < d; i++)
{
for (int j = 0; j < i; j++)
{
det = det * (x[i] - x[j]);
}
}
// LU decompose the matrix
SquareMatrix V = CreateVandermondeMatrix(d);
LUDecomposition LU = V.LUDecomposition();
// test that the decomposition works
SquareMatrix P = LU.PMatrix();
SquareMatrix L = LU.LMatrix();
SquareMatrix U = LU.UMatrix();
Assert.IsTrue(TestUtilities.IsNearlyEqual(P * V, L * U));
// check that the determinant agrees with the analytic expression
Console.WriteLine("det {0} {1}", LU.Determinant(), det);
Assert.IsTrue(TestUtilities.IsNearlyEqual(LU.Determinant(), det));
// check that the inverse works
SquareMatrix VI = LU.Inverse();
//PrintMatrix(VI);
//PrintMatrix(V * VI);
SquareMatrix I = TestUtilities.CreateSquareUnitMatrix(d);
Assert.IsTrue(TestUtilities.IsNearlyEqual(V * VI, I));
// test that a solution works
ColumnVector t = new ColumnVector(d);
for (int i = 0; i < d; i++)
{
t[i] = 1.0;
}
ColumnVector s = LU.Solve(t);
Assert.IsTrue(TestUtilities.IsNearlyEqual(V * s, t));
}
}