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 FibonacciSpecialCases()
{
Assert.IsTrue(AdvancedIntegerMath.FibonacciNumber(0) == 0.0);
Assert.IsTrue(AdvancedIntegerMath.FibonacciNumber(1) == 1.0);
Assert.IsTrue(AdvancedIntegerMath.FibonacciNumber(2) == 1.0);
Assert.IsTrue(AdvancedIntegerMath.FibonacciNumber(3) == 2.0);
}
public void FibonacciRecurrence()
{
foreach (int n in TestUtilities.GenerateIntegerValues(2, 1000, 8))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedIntegerMath.FibonacciNumber(n),
AdvancedIntegerMath.FibonacciNumber(n - 1) + AdvancedIntegerMath.FibonacciNumber(n - 2)
));
}
}