public void TridiagonalMatrixFibinacciDeterminant()
{
// The n X n tri-diagonal matrix with 1s on the diagonal,
// 1s on the super-diagonal, and -1s on the sub-diagonal
// has determinant equal to the (n+1)th Fibonacci number.
foreach (int n in TestUtilities.GenerateIntegerValues(2, 128, 4))
{
TridiagonalMatrix T = new TridiagonalMatrix(n);
for (int i = 0; i < n; i++)
{
T[i, i] = 1.0;
}
for (int i = 1; i < n; i++)
{
T[i - 1, i] = 1.0;
T[i, i - 1] = -1.0;
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(
T.Determinant(),
AdvancedIntegerMath.FibonacciNumber(n + 1)
));
}
}
public void TridiagonalMatrixLUDecompositionTest()
{
for (int d = 3; d < 100; d = 2 * d)
{
Console.WriteLine("d={0}", d);
TridiagonalMatrix T = CreateRandomTridiagonalMatrix(d);
Assert.IsTrue(T.Dimension == d);
TridiagonalLUDecomposition LU = T.LUDecomposition();
Assert.IsTrue(LU.Dimension == d);
// check determinant
Assert.IsTrue(TestUtilities.IsNearlyEqual(LU.Determinant(), T.Determinant()));
//SquareMatrix P = LU.PMatrix();
//SquareMatrix L = LU.LMatrix();
//SquareMatrix U = LU.UMatrix();
//SquareMatrixTest.PrintMatrix(T);
//SquareMatrixTest.PrintMatrix(L);
//SquareMatrixTest.PrintMatrix(U);
//SquareMatrixTest.PrintMatrix(L * U);
// check solution to decomposition
ColumnVector b = new ColumnVector(d);
for (int i = 0; i < d; i++)
{
b[i] = i;
}
ColumnVector x = LU.Solve(b);
Assert.IsTrue(TestUtilities.IsNearlyEqual(T * x, b));
// test inverse
SquareMatrix TI = LU.Inverse();
SquareMatrix I = new SquareMatrix(d);
for (int i = 0; i < d; i++)
{
I[i, i] = 1.0;
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(TI * T, I));
}
}