commons-commits mailing list archives

Site index · List index
Message view « Date » · « Thread »
Top « Date » · « Thread »
From celes...@apache.org
Subject svn commit: r1378450 - in /commons/proper/math/trunk/src: main/java/org/apache/commons/math3/special/Gamma.java test/java/org/apache/commons/math3/special/GammaTest.java
Date Wed, 29 Aug 2012 06:20:21 GMT
Author: celestin
Date: Wed Aug 29 06:20:21 2012
New Revision: 1378450

URL: http://svn.apache.org/viewvc?rev=1378450&view=rev
Log:
MATH-849: new implementation of double Gamma.logGamma(double x) for x < 8.0.
This greatly improves the accurarcy, from more than 130 ulps down to 3 ulps.
Unit tests updated accordingly.


Modified:
    commons/proper/math/trunk/src/main/java/org/apache/commons/math3/special/Gamma.java
    commons/proper/math/trunk/src/test/java/org/apache/commons/math3/special/GammaTest.java

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/special/Gamma.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/special/Gamma.java?rev=1378450&r1=1378449&r2=1378450&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/special/Gamma.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/special/Gamma.java Wed
Aug 29 06:20:21 2012
@@ -17,12 +17,37 @@
 package org.apache.commons.math3.special;
 
 import org.apache.commons.math3.exception.MaxCountExceededException;
+import org.apache.commons.math3.exception.NumberIsTooLargeException;
+import org.apache.commons.math3.exception.NumberIsTooSmallException;
 import org.apache.commons.math3.util.ContinuedFraction;
 import org.apache.commons.math3.util.FastMath;
 
 /**
+ * <p>
  * This is a utility class that provides computation methods related to the
- * Gamma family of functions.
+ * &Gamma; (Gamma) family of functions.
+ * </p>
+ * <p>
+ * Implementation of {@link #invGamma1pm1(double)} and
+ * {@link #logGamma1p(double)} is based on the algorithms described in
+ * <ul>
+ * <li><a href="http://dx.doi.org/10.1145/22721.23109">Didonato and Morris
+ * (1986)</a>, <em>Computation of the Incomplete Gamma Function Ratios and
+ *     their Inverse</em>, TOMS 12(4), 377-393,</li>
+ * <li><a href="http://dx.doi.org/10.1145/131766.131776">Didonato and Morris
+ * (1992)</a>, <em>Algorithm 708: Significant Digit Computation of the
+ *     Incomplete Beta Function Ratios</em>, TOMS 18(3), 360-373,</li>
+ * </ul>
+ * and implemented in the
+ * <a href="http://www.dtic.mil/docs/citations/ADA476840">NSWC Library of Mathematical
Functions</a>,
+ * available
+ * <a href="http://www.ualberta.ca/CNS/RESEARCH/Software/NumericalNSWC/site.html">here</a>.
+ * This library is "approved for public release", and the
+ * <a href="http://www.dtic.mil/dtic/pdf/announcements/CopyrightGuidance.pdf">Copyright
guidance</a>
+ * indicates that unless otherwise stated in the code, all FORTRAN functions in
+ * this library are license free. Since no such notice appears in the code these
+ * functions can safely be ported to Commons-Math.
+ * </p>
  *
  * @version $Id$
  */
@@ -67,33 +92,163 @@ public class Gamma {
     /** S limit. */
     private static final double S_LIMIT = 1e-5;
 
+    /*
+     * Constants for the computation of double invGamma1pm1(double).
+     * Copied from DGAM1 in the NSWC library.
+     */
+
+    /** The constant {@code A0} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_A0 = .611609510448141581788E-08;
+
+    /** The constant {@code A1} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_A1 = .624730830116465516210E-08;
+
+    /** The constant {@code B1} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_B1 = .203610414066806987300E+00;
+
+    /** The constant {@code B2} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_B2 = .266205348428949217746E-01;
+
+    /** The constant {@code B3} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_B3 = .493944979382446875238E-03;
+
+    /** The constant {@code B4} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_B4 = -.851419432440314906588E-05;
+
+    /** The constant {@code B5} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_B5 = -.643045481779353022248E-05;
+
+    /** The constant {@code B6} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_B6 = .992641840672773722196E-06;
+
+    /** The constant {@code B7} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_B7 = -.607761895722825260739E-07;
+
+    /** The constant {@code B8} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_B8 = .195755836614639731882E-09;
+
+    /** The constant {@code P0} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_P0 = .6116095104481415817861E-08;
+
+    /** The constant {@code P1} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_P1 = .6871674113067198736152E-08;
+
+    /** The constant {@code P2} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_P2 = .6820161668496170657918E-09;
+
+    /** The constant {@code P3} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_P3 = .4686843322948848031080E-10;
+
+    /** The constant {@code P4} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_P4 = .1572833027710446286995E-11;
+
+    /** The constant {@code P5} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_P5 = -.1249441572276366213222E-12;
+
+    /** The constant {@code P6} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_P6 = .4343529937408594255178E-14;
+
+    /** The constant {@code Q1} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_Q1 = .3056961078365221025009E+00;
+
+    /** The constant {@code Q2} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_Q2 = .5464213086042296536016E-01;
+
+    /** The constant {@code Q3} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_Q3 = .4956830093825887312020E-02;
+
+    /** The constant {@code Q4} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_Q4 = .2692369466186361192876E-03;
+
+    /** The constant {@code C} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C = -.422784335098467139393487909917598E+00;
+
+    /** The constant {@code C0} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C0 = .577215664901532860606512090082402E+00;
+
+    /** The constant {@code C1} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C1 = -.655878071520253881077019515145390E+00;
+
+    /** The constant {@code C2} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C2 = -.420026350340952355290039348754298E-01;
+
+    /** The constant {@code C3} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C3 = .166538611382291489501700795102105E+00;
+
+    /** The constant {@code C4} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C4 = -.421977345555443367482083012891874E-01;
+
+    /** The constant {@code C5} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C5 = -.962197152787697356211492167234820E-02;
+
+    /** The constant {@code C6} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C6 = .721894324666309954239501034044657E-02;
+
+    /** The constant {@code C7} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C7 = -.116516759185906511211397108401839E-02;
+
+    /** The constant {@code C8} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C8 = -.215241674114950972815729963053648E-03;
+
+    /** The constant {@code C9} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C9 = .128050282388116186153198626328164E-03;
+
+    /** The constant {@code C10} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C10 = -.201348547807882386556893914210218E-04;
+
+    /** The constant {@code C11} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C11 = -.125049348214267065734535947383309E-05;
+
+    /** The constant {@code C12} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C12 = .113302723198169588237412962033074E-05;
+
+    /** The constant {@code C13} defined in {@code DGAM1}. */
+    private static final double INV_GAMMA1P_M1_C13 = -.205633841697760710345015413002057E-06;
+
     /**
      * Default constructor.  Prohibit instantiation.
      */
     private Gamma() {}
 
     /**
-     * Returns the natural logarithm of the gamma function &#915;(x).
-     *
-     * The implementation of this method is based on:
+     * <p>
+     * Returns the value of log&nbsp;&Gamma;(x) for x&nbsp;&gt;&nbsp;0.
+     * </p>
+     * <p>
+     * For x &lt; 8, the implementation is based on the double precision
+     * implementation in the <em>NSWC Library of Mathematics Subroutines</em>,
+     * {@code DGAMLN}. For x &ge; 8, the implementation is based on
+     * </p>
      * <ul>
-     * <li><a href="http://mathworld.wolfram.com/GammaFunction.html">
-     * Gamma Function</a>, equation (28).</li>
+     * <li><a href="http://mathworld.wolfram.com/GammaFunction.html">Gamma
+     *     Function</a>, equation (28).</li>
      * <li><a href="http://mathworld.wolfram.com/LanczosApproximation.html">
-     * Lanczos Approximation</a>, equations (1) through (5).</li>
+     *     Lanczos Approximation</a>, equations (1) through (5).</li>
      * <li><a href="http://my.fit.edu/~gabdo/gamma.txt">Paul Godfrey, A note
on
-     * the computation of the convergent Lanczos complex Gamma approximation
-     * </a></li>
+     *     the computation of the convergent Lanczos complex Gamma
+     *     approximation</a></li>
      * </ul>
      *
-     * @param x Value.
-     * @return log(&#915;(x))
+     * @param x argument.
+     * @return the value of {@code log(Gamma(x))}, {@code Double.NaN} if
+     * {@code x <= 0.0}.
      */
     public static double logGamma(double x) {
         double ret;
 
         if (Double.isNaN(x) || (x <= 0.0)) {
             ret = Double.NaN;
+        } else if (x < 0.5) {
+            return logGamma1p(x) - FastMath.log(x);
+        } else if (x <= 2.5) {
+            return logGamma1p((x - 0.5) - 0.5);
+        } else if (x < 8.0) {
+            final int n = (int) FastMath.floor(x - 1.5);
+            double prod = 1.0;
+            for (int i = 1; i <= n; i++) {
+                prod *= x - i;
+            }
+            return logGamma1p(x - (n + 1)) + FastMath.log(prod);
         } else {
             double sum = lanczos(x);
             double tmp = x + LANCZOS_G + .5;
@@ -352,4 +507,119 @@ public class Gamma {
         }
         return sum + LANCZOS[0];
     }
+
+    /**
+     * Returns the value of 1 / &Gamma;(1 + x) - 1 for -0&#46;5 &le; x &le;
+     * 1&#46;5. This implementation is based on the double precision
+     * implementation in the <em>NSWC Library of Mathematics Subroutines</em>,
+     * {@code DGAM1}.
+     *
+     * @param x the argument
+     * @return the value of {@code 1.0 / Gamma(1.0 + x) - 1.0}
+     * @throws NumberIsTooSmallException if {@code x < -0.5}
+     * @throws NumberIsTooLargeException if {@code x > 1.5}
+     */
+    public static double invGamma1pm1(final double x) {
+
+        if (x < -0.5) {
+            throw new NumberIsTooSmallException(x, -0.5, true);
+        }
+        if (x > 1.5) {
+            throw new NumberIsTooLargeException(x, 1.5, true);
+        }
+
+        final double ret;
+        final double t = x <= 0.5 ? x : (x - 0.5) - 0.5;
+        if (t < 0.0) {
+            final double a = INV_GAMMA1P_M1_A0 + t * INV_GAMMA1P_M1_A1;
+            double b = INV_GAMMA1P_M1_B8;
+            b = INV_GAMMA1P_M1_B7 + t * b;
+            b = INV_GAMMA1P_M1_B6 + t * b;
+            b = INV_GAMMA1P_M1_B5 + t * b;
+            b = INV_GAMMA1P_M1_B4 + t * b;
+            b = INV_GAMMA1P_M1_B3 + t * b;
+            b = INV_GAMMA1P_M1_B2 + t * b;
+            b = INV_GAMMA1P_M1_B1 + t * b;
+            b = 1.0 + t * b;
+
+            double c = INV_GAMMA1P_M1_C13 + t * (a / b);
+            c = INV_GAMMA1P_M1_C12 + t * c;
+            c = INV_GAMMA1P_M1_C11 + t * c;
+            c = INV_GAMMA1P_M1_C10 + t * c;
+            c = INV_GAMMA1P_M1_C9 + t * c;
+            c = INV_GAMMA1P_M1_C8 + t * c;
+            c = INV_GAMMA1P_M1_C7 + t * c;
+            c = INV_GAMMA1P_M1_C6 + t * c;
+            c = INV_GAMMA1P_M1_C5 + t * c;
+            c = INV_GAMMA1P_M1_C4 + t * c;
+            c = INV_GAMMA1P_M1_C3 + t * c;
+            c = INV_GAMMA1P_M1_C2 + t * c;
+            c = INV_GAMMA1P_M1_C1 + t * c;
+            c = INV_GAMMA1P_M1_C + t * c;
+            if (x > 0.5) {
+                ret = t * c / x;
+            } else {
+                ret = x * ((c + 0.5) + 0.5);
+            }
+        } else {
+            double p = INV_GAMMA1P_M1_P6;
+            p = INV_GAMMA1P_M1_P5 + t * p;
+            p = INV_GAMMA1P_M1_P4 + t * p;
+            p = INV_GAMMA1P_M1_P3 + t * p;
+            p = INV_GAMMA1P_M1_P2 + t * p;
+            p = INV_GAMMA1P_M1_P1 + t * p;
+            p = INV_GAMMA1P_M1_P0 + t * p;
+
+            double q = INV_GAMMA1P_M1_Q4;
+            q = INV_GAMMA1P_M1_Q3 + t * q;
+            q = INV_GAMMA1P_M1_Q2 + t * q;
+            q = INV_GAMMA1P_M1_Q1 + t * q;
+            q = 1.0 + t * q;
+
+            double c = INV_GAMMA1P_M1_C13 + (p / q) * t;
+            c = INV_GAMMA1P_M1_C12 + t * c;
+            c = INV_GAMMA1P_M1_C11 + t * c;
+            c = INV_GAMMA1P_M1_C10 + t * c;
+            c = INV_GAMMA1P_M1_C9 + t * c;
+            c = INV_GAMMA1P_M1_C8 + t * c;
+            c = INV_GAMMA1P_M1_C7 + t * c;
+            c = INV_GAMMA1P_M1_C6 + t * c;
+            c = INV_GAMMA1P_M1_C5 + t * c;
+            c = INV_GAMMA1P_M1_C4 + t * c;
+            c = INV_GAMMA1P_M1_C3 + t * c;
+            c = INV_GAMMA1P_M1_C2 + t * c;
+            c = INV_GAMMA1P_M1_C1 + t * c;
+            c = INV_GAMMA1P_M1_C0 + t * c;
+
+            if (x > 0.5) {
+                ret = (t / x) * ((c - 0.5) - 0.5);
+            } else {
+                ret = x * c;
+            }
+        }
+
+        return ret;
+    }
+
+    /**
+     * Returns the value of log &Gamma;(1 + x) for -0&#46;5 &le; x &le; 1&#46;5.
+     * This implementation is based on the double precision implementation in
+     * the <em>NSWC Library of Mathematics Subroutines</em>, {@code DGMLN1}.
+     *
+     * @param x the argument
+     * @return the value of {@code log(Gamma(1 + x))}
+     * @throws NumberIsTooSmallException if {@code x < -0.5}
+     * @throws NumberIsTooLargeException if {@code x > 1.5}
+     */
+    public static double logGamma1p(final double x) {
+
+        if (x < -0.5) {
+            throw new NumberIsTooSmallException(x, -0.5, true);
+        }
+        if (x > 1.5) {
+            throw new NumberIsTooLargeException(x, 1.5, true);
+        }
+
+        return -FastMath.log1p(invGamma1pm1(x));
+    }
 }

Modified: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/special/GammaTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/special/GammaTest.java?rev=1378450&r1=1378449&r2=1378450&view=diff
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/special/GammaTest.java
(original)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/special/GammaTest.java
Wed Aug 29 06:20:21 2012
@@ -262,7 +262,7 @@ public class GammaTest {
 
     @Test
     public void testLogGamma() {
-        final int ulps = 130;
+        final int ulps = 3;
         for (int i = 0; i < LOG_GAMMA_REF.length; i++) {
             final double[] data = LOG_GAMMA_REF[i];
             final double x = data[0];



Mime
View raw message