/**
* Computes x + y without losing precision using ln(x) and ln(y).
*
* @param lna Value.
* @param lnc Value.
* @return Result.
*/
public static double LogSum(float lna, float lnc) {
if (lna == Float.NEGATIVE_INFINITY) return lnc;
if (lnc == Float.NEGATIVE_INFINITY) return lna;
if (lna > lnc) return lna + Special.Log1p(Math.exp(lnc - lna));
return lnc + Special.Log1p(Math.exp(lna - lnc));
}
/** Computes the Basic Spline of order <c>n</c>. */
public static double BSpline(int n, double x) {
// ftp://ftp.esat.kuleuven.ac.be/pub/SISTA/hamers/PhD_bhamers.pdf
// http://sepwww.stanford.edu/public/docs/sep105/sergey2/paper_html/node5.html
if (n == Integer.MAX_VALUE) throw new IllegalArgumentException("n");
double a = 1.0 / Special.Factorial(n);
double c;
boolean positive = true;
for (int k = 0; k <= n + 1; k++) {
c = Binomial(n + 1, k) * Tools.TruncatedPower(x + (n + 1.0) / 2.0 - k, n);
a += positive ? c : -c;
positive = !positive;
}
return a;
}