public void testOperatorConsistency()
{
//("Testing differential operators...");
NormalDistribution normal = new NormalDistribution(average, sigma);
CumulativeNormalDistribution cum = new CumulativeNormalDistribution(average, sigma);
double xMin = average - 4 * sigma,
xMax = average + 4 * sigma;
int N = 10001;
double h = (xMax - xMin) / (N - 1);
Vector x = new Vector(N),
y = new Vector(N),
yi = new Vector(N),
yd = new Vector(N),
temp = new Vector(N),
diff = new Vector(N);
for (int i = 0; i < N; i++)
x[i] = xMin + h * i;
for (int i = 0; i < x.Count; i++)
y[i] = normal.value(x[i]);
for (int i = 0; i < x.Count; i++)
yi[i] = cum.value(x[i]);
for (int i = 0; i < x.size(); i++)
yd[i] = normal.derivative(x[i]);
// define the differential operators
DZero D = new DZero(N, h);
DPlusDMinus D2 = new DPlusDMinus(N, h);
// check that the derivative of cum is Gaussian
temp = D.applyTo(yi);
for (int i = 0; i < y.Count; i++)
diff[i] = y[i] - temp[i];
double e = Utilities.norm(diff, diff.size(), h);
if (e > 1.0e-6)
{
Assert.Fail("norm of 1st derivative of cum minus Gaussian: " + e + "\ntolerance exceeded");
}
// check that the second derivative of cum is normal.derivative
temp = D2.applyTo(yi);
for (int i = 0; i < yd.Count; i++)
diff[i] = yd[i] - temp[i];
e = Utilities.norm(diff, diff.size(), h);
if (e > 1.0e-4)
{
Assert.Fail("norm of 2nd derivative of cum minus Gaussian derivative: " + e + "\ntolerance exceeded");
}
}
