public void StirlingNumbers1RowSum()
{
foreach (int n in TestUtilities.GenerateIntegerValues(1, 100, 4))
{
double sum = 0.0;
foreach (double s in AdvancedIntegerMath.StirlingNumbers1(n))
{
sum += s;
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(sum, AdvancedIntegerMath.Factorial(n)));
}
}
public void StirlingNumberMatrixInverse()
{
int n = 8;
SquareMatrix S1 = new SquareMatrix(n);
for (int i = 0; i < n; i++)
{
double[] s = AdvancedIntegerMath.StirlingNumbers1(i);
for (int j = 0; j < s.Length; j++)
{
if ((i - j) % 2 == 0)
{
S1[i, j] = s[j];
}
else
{
S1[i, j] = -s[j];
}
}
}
SquareMatrix S2 = new SquareMatrix(n);
for (int i = 0; i < n; i++)
{
double[] s = AdvancedIntegerMath.StirlingNumbers2(i);
for (int j = 0; j < s.Length; j++)
{
S2[i, j] = s[j];
}
}
SquareMatrix S12 = S1 * S2;
SquareMatrix I = new SquareMatrix(n);
for (int i = 0; i < n; i++)
{
I[i, i] = 1.0;
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(S12, I));
}