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Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/d731d164 Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/d731d164 Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/d731d164 Branch: refs/heads/develop Commit: d731d1645ab34c597d66b9195a58b6c66c98ed68 Parents: 2f8ddc3 Author: Gilles <gil...@harfang.homelinux.org> Authored: Mon May 16 19:05:24 2016 +0200 Committer: Gilles <gil...@harfang.homelinux.org> Committed: Mon May 16 19:05:24 2016 +0200 ---------------------------------------------------------------------- .../org/apache/commons/math4/special/Gamma.java | 74 +++++++++++--------- 1 file changed, 39 insertions(+), 35 deletions(-) ---------------------------------------------------------------------- http://git-wip-us.apache.org/repos/asf/commons-math/blob/d731d164/src/main/java/org/apache/commons/math4/special/Gamma.java ---------------------------------------------------------------------- diff --git a/src/main/java/org/apache/commons/math4/special/Gamma.java b/src/main/java/org/apache/commons/math4/special/Gamma.java index e798277..eb13d1b 100644 --- a/src/main/java/org/apache/commons/math4/special/Gamma.java +++ b/src/main/java/org/apache/commons/math4/special/Gamma.java @@ -53,13 +53,14 @@ import org.apache.commons.math4.util.FastMath; public class Gamma { /** * <a href="http://en.wikipedia.org/wiki/Euler-Mascheroni_constant";>Euler-Mascheroni constant</a> + * * @since 2.0 */ public static final double GAMMA = 0.577215664901532860606512090082; /** - * The value of the {@code g} constant in the Lanczos approximation, see - * {@link #lanczos(double)}. + * Constant \( g = \frac{607}{128} \) in the {@link #lanczos(double) Lanczos approximation}. + * * @since 3.1 */ public static final double LANCZOS_G = 607.0 / 128.0; @@ -218,13 +219,12 @@ public class Gamma { private Gamma() {} /** + * Returns the value of \( \log \Gamma(x) \) for \( x > 0 \). + * * <p> - * Returns the value of log Γ(x) for x > 0. - * </p> - * <p> - * For x ≤ 8, the implementation is based on the double precision + * For \( x \leq 8 \), the implementation is based on the double precision * implementation in the <em>NSWC Library of Mathematics Subroutines</em>, - * {@code DGAMLN}. For x > 8, the implementation is based on + * {@code DGAMLN}. For \( x \geq 8 \), the implementation is based on * </p> * <ul> * <li><a href="http://mathworld.wolfram.com/GammaFunction.html";>Gamma @@ -237,8 +237,7 @@ public class Gamma { * </ul> * * @param x Argument. - * @return the value of {@code log(Gamma(x))}, {@code Double.NaN} if - * {@code x <= 0.0}. + * @return the value of {@code log(Gamma(x))} or {@code NaN} if {@code x <= 0}. */ public static double logGamma(double x) { double ret; @@ -267,7 +266,7 @@ public class Gamma { } /** - * Returns the regularized gamma function P(a, x). + * Returns the regularized gamma function \( P(a, x) \). * * @param a Parameter. * @param x Value. @@ -279,7 +278,7 @@ public class Gamma { } /** - * Returns the regularized gamma function P(a, x). + * Returns the regularized gamma function \( P(a, x) \). * * The implementation of this method is based on: * <ul> @@ -360,7 +359,7 @@ public class Gamma { } /** - * Returns the regularized gamma function Q(a, x) = 1 - P(a, x). + * Returns the regularized gamma function \( Q(a, x) = 1 - P(a, x) \). * * The implementation of this method is based on: * <ul> @@ -424,21 +423,24 @@ public class Gamma { /** - * <p>Computes the digamma function of x.</p> + * Computes the digamma function. * * <p>This is an independently written implementation of the algorithm described in * Jose Bernardo, Algorithm AS 103: Psi (Digamma) Function, Applied Statistics, 1976. - * A reflection formula (https://en.wikipedia.org/wiki/Digamma_function#Reflection_formula) - * is incorporated to improve performance on negative values.</p> + * A <a href="https://en.wikipedia.org/wiki/Digamma_function#Reflection_formula";> + * reflection formula</a> is incorporated to improve performance on negative values.</p> * - * <p>Some of the constants have been changed to increase accuracy at the moderate expense - * of run-time. The result should be accurate to within 10^-8 relative tolerance for - * 0 < x < 10^-5 and within 10^-8 absolute tolerance otherwise.</p> + * <p>Some of the constants have been changed to increase accuracy at the moderate + * expense of run-time. The result should be accurate to within \( 10^{-8} \) + * relative tolerance for \( 0 < x < 10^{-5} \) and within \( 10^{-8} \) absolute + * tolerance otherwise.</p> * * @param x Argument. - * @return digamma(x) to within 10^-8 relative or absolute error whichever is larger. + * @return digamma(x) to within \( 10^{-8} \) relative or absolute error whichever is larger. + * * @see <a href="http://en.wikipedia.org/wiki/Digamma_function";>Digamma</a> - * @see <a href="http://www.uv.es/~bernardo/1976AppStatist.pdf";>Bernardo's original article </a> + * @see <a href="http://www.uv.es/~bernardo/1976AppStatist.pdf";>Bernardo's original article</a> + * * @since 2.0 */ public static double digamma(double x) { @@ -475,14 +477,17 @@ public class Gamma { } /** - * Computes the trigamma function of x. + * Computes the trigamma function. * This function is derived by taking the derivative of the implementation * of digamma. * * @param x Argument. - * @return trigamma(x) to within 10^-8 relative or absolute error whichever is smaller + * @return {@code trigamma(x)} to within \( 10^{-8} \) relative or absolute + * error whichever is smaller + * * @see <a href="http://en.wikipedia.org/wiki/Trigamma_function";>Trigamma</a> * @see Gamma#digamma(double) + * * @since 2.0 */ public static double trigamma(double x) { @@ -511,11 +516,11 @@ public class Gamma { * Returns the Lanczos approximation used to compute the gamma function. * The Lanczos approximation is related to the Gamma function by the * following equation - * <center> - * {@code gamma(x) = sqrt(2 * pi) / x * (x + g + 0.5) ^ (x + 0.5) - * * exp(-x - g - 0.5) * lanczos(x)}, - * </center> - * where {@code g} is the Lanczos constant. + * \[ + * \Gamma(x) = \sqrt{2\pi} \, \frac{(x + g + 1/2)^{x + \frac{1}{2}} \, e^{-x - g - \frac{1}{2}} \, \mathrm{lanczos}(x)} + * {x} + * \] + * where \(g\) is the Lanczos constant. * </p> * * @param x Argument. @@ -535,10 +540,9 @@ public class Gamma { } /** - * Returns the value of 1 / Γ(1 + x) - 1 for -0.5 ≤ x ≤ - * 1.5. This implementation is based on the double precision - * implementation in the <em>NSWC Library of Mathematics Subroutines</em>, - * {@code DGAM1}. + * Returns the value of \( 1 / \Gamma(1 + x) - 1 \) for \( -0.5 \leq x \leq 1.5 \). + * This implementation is based on the double precision implementation in + * the <em>NSWC Library of Mathematics Subroutines</em>, {@code DGAM1}. * * @param x Argument. * @return The value of {@code 1.0 / Gamma(1.0 + x) - 1.0}. @@ -629,7 +633,7 @@ public class Gamma { } /** - * Returns the value of log Γ(1 + x) for -0.5 ≤ x ≤ 1.5. + * Returns the value of \( \log \Gamma(1 + x) \) for \( -0.5 \leq x \leq 1.5 \). * This implementation is based on the double precision implementation in * the <em>NSWC Library of Mathematics Subroutines</em>, {@code DGMLN1}. * @@ -654,9 +658,9 @@ public class Gamma { /** - * Returns the value of Î(x). Based on the <em>NSWC Library of - * Mathematics Subroutines</em> double precision implementation, - * {@code DGAMMA}. + * Returns the value of \( \Gamma(x) \). + * Based on the <em>NSWC Library of Mathematics Subroutines</em> double + * precision implementation, {@code DGAMMA}. * * @param x Argument. * @return the value of {@code Gamma(x)}.
