Class Gamma

java.lang.Object
smile.math.special.Gamma
public class Gamma extends Object
The gamma, digamma, and incomplete gamma functions.

  • Method Details

    • gamma

      public static double gamma(double x)
      Gamma function. Lanczos approximation (6 terms).
      Parameters:
      x - a real number.
      Returns:
      the function value.

    • lgamma

      public static double lgamma(double x)
      The log of the Gamma function. Lanczos approximation (6 terms). For negative non-integer x the log-gamma is computed via the reflection formula; if the resulting value would be negative (i.e. Γ(x) < 0) an IllegalArgumentException is thrown. Returns Double.POSITIVE_INFINITY for x = 0, -1, -2, …
      Parameters:
      x - a real number.
      Returns:
      the function value.

    • regularizedIncompleteGamma

      public static double regularizedIncompleteGamma(double s, double x)
      Regularized Incomplete Gamma Function P(s,x) = ∫0x e-t t(s-1) dt
      Parameters:
      s - s >= 0
      x - x >= 0
      Returns:
      the function value.

    • regularizedUpperIncompleteGamma

      public static double regularizedUpperIncompleteGamma(double s, double x)
      Regularized Upper/Complementary Incomplete Gamma Function Q(s,x) = 1 - P(s,x) = 1 - ∫0x e-t t(s-1) dt

      Returns 0 when x = 0, and Double.NaN when x is NaN.

      Parameters:
      s - s >= 0
      x - x >= 0
      Returns:
      the function value.

    • digamma

      public static double digamma(double x)
      The digamma function is defined as the logarithmic derivative of the gamma function. The digamma function has poles at zero and the negative integers.
      Parameters:
      x - a real number, not a non-positive integer.
      Returns:
      the function value.

    • inverseRegularizedIncompleteGamma

      public static double inverseRegularizedIncompleteGamma(double a, double p)
      The inverse of regularized incomplete gamma function.
      Parameters:
      a - a > 0
      p - a real number.
      Returns:
      the function value.