Example usage for org.apache.commons.math3.special Gamma Gamma

Introduction

In this page you can find the example usage for org.apache.commons.math3.special Gamma Gamma.

Prototype

private Gamma() 

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Document

Default constructor.

Usage

From source file:org.magicdgs.popgenlib.diversity.NucleotideDiversity.java

/**
 * Gets the denominator of Watterson's θ
 * (formula 3 in <a href="http://www.genetics.org/content/123/3/585">Tajima (1989)</a>), which
 * is the {@code numberOfSamples}<SUP>th</SUP> -1 Harmonic Number.
 *
 * This method returns the exact value for up to 49 samples. Otherwise, it uses the
 * EulerMascheroni constant (&gamma;) and an approximation for the digamma distribution
 * (&psi;) for computing the n<SUP>th</SUP> Harmonic Number:
 *
 * <p>&gamma; + &psi;({@code numberOfSamples})
 *
 * @param numberOfSamples number of samples to compute the denominator.
 *
 * @throws IllegalArgumentException if the number of samples is lower than 2.
 * @see Gamma#digamma(double)//from w  w  w . j a va  2 s. c  o m
 */
public static double wattersonsDenominatorApproximation(final int numberOfSamples) {
    // Defined as sum(1/j) for j=1 to j=n-1; where n is the number of samples
    // This is actually the (n-1)th Harmonic number (https://en.wikipedia.org/wiki/Harmonic_number)
    // This could be more efficiently computed using the formula implying the digamma distribution,
    // which is implemented in an approximated way in commons-math3 (good enough for our purposes).
    // In common-math3 they only use the fast algorithm if n is >= 49
    // thus, here the limit for switching to the fast algorithm is 49 too,
    // because it will use the same number of iterations if not
    if (numberOfSamples < 49) {
        return IntStream.range(1, numberOfSamples).mapToDouble(i -> 1d / i).sum();
    }
    // The formula of the nth Harmonic number using the digamma function is defined as:
    // gamma + psi(n + 1); where gamma is the Euler-Mascheroni constant and psi the digamma function
    // because here we want the number numberOfSamples-1 Harmonic number, we can use directly
    // gamma + psi(numberOfSamples) if 49 or more samples were provided (efficient computation)
    return Gamma.GAMMA + Gamma.digamma(numberOfSamples);
}

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From source file:reflex.module.ReflexGamma.java

public ReflexValue gamma(List<ReflexValue> params) {
    if (params.size() == 0) {
        return new ReflexValue(Gamma.GAMMA);
    } else {/*  w  w  w . j a v  a  2  s .  c o m*/
        throw new ReflexException(-1, "Where is gamma?");
    }
}

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