/// <summary>
/// Tests that the inputs to the root-finder are not null, and that a root is bracketed by the bounding values.
/// </summary>
/// <param name="function"> The function, not null </param>
/// <param name="x1"> The first bound, not null </param>
/// <param name="x2"> The second bound, not null, must be greater than x1 </param>
/// <exception cref="IllegalArgumentException"> if x1 and x2 do not bracket a root </exception>
protected internal virtual void checkInputs(DoubleFunction1D function, double?x1, double?x2)
{
ArgChecker.notNull(function, "function");
ArgChecker.notNull(x1, "x1");
ArgChecker.notNull(x2, "x2");
ArgChecker.isTrue(x1 <= x2, "x1 must be less or equal to x2");
ArgChecker.isTrue(function.applyAsDouble(x1) * function.applyAsDouble(x2) <= 0, "x1 and x2 do not bracket a root");
}
/// <summary>
/// {@inheritDoc}
/// </summary>
public virtual GaussianQuadratureData generate(int n)
{
ArgChecker.isTrue(n > 0);
Pair <DoubleFunction1D, DoubleFunction1D>[] polynomials = LAGUERRE.getPolynomialsAndFirstDerivative(n, _alpha);
Pair <DoubleFunction1D, DoubleFunction1D> pair = polynomials[n];
DoubleFunction1D p1 = polynomials[n - 1].First;
DoubleFunction1D function = pair.First;
DoubleFunction1D derivative = pair.Second;
double[] x = new double[n];
double[] w = new double[n];
double root = 0;
for (int i = 0; i < n; i++)
{
root = ROOT_FINDER.getRoot(function, derivative, getInitialRootGuess(root, i, n, x)).Value;
x[i] = root;
w[i] = -GAMMA_FUNCTION.applyAsDouble(_alpha + n) / CombinatoricsUtils.factorialDouble(n) / (derivative.applyAsDouble(root) * p1.applyAsDouble(root));
}
return(new GaussianQuadratureData(x, w));
}