Author: celestin
Date: Wed Nov 28 05:27:27 2012
New Revision: 1414527
URL: http://svn.apache.org/viewvc?rev=1414527&view=rev
Log:
In class Gamma, removed auxiliary functions logGammaSum and
logGammaMinusLogGammaSum, as they are not ready to be included in version 3.1
of Commons-Math.
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=1414527&r1=1414526&r2=1414527&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 Nov 28 05:27:27 2012
@@ -19,7 +19,6 @@ 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.exception.OutOfRangeException;
import org.apache.commons.math3.util.ContinuedFraction;
import org.apache.commons.math3.util.FastMath;
@@ -29,9 +28,8 @@ import org.apache.commons.math3.util.Fas
* Γ (Gamma) family of functions.
* </p>
* <p>
- * Implementation of {@link #invGamma1pm1(double)},
- * {@link #logGamma1p(double)} and {@link #logGammaSum(double, double)} is
- * based on the algorithms described in
+ * 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
@@ -215,68 +213,6 @@ public class Gamma {
private static final double INV_GAMMA1P_M1_C13 =
-.205633841697760710345015413002057E-06;
/**
- * <p>
- * The d<sub>0</sub> coefficient of the minimax approximation of the Î
- * function. This function is defined as follows
- * </p>
- * <center>Î(x) = log Î(x) - (x - 0.5) log a + a - 0.5 log 2Ï,</center>
- * <p>
- * The minimax approximation is defined by the following sum
- * </p>
- * <pre>
- * 5
- * ====
- * \ - 2 n - 1
- * Î(x) = > d x
- * / n
- * ====
- * n = 0
- * <pre>
- * <p>
- * see equations (23) and (25) in Didonato and Morris (1992).
- * </p>
- */
- private static final double D0 = .833333333333333E-01;
-
- /**
- * The d<sub>1</sub> coefficent of the minimax approximation of the Î
- * function (see {@link #D0}).
- */
- private static final double D1 = -.277777777760991E-02;
-
- /**
- * The d<sub>2</sub> coefficent of the minimax approximation of the Î
- * function (see {@link #D0}).
- */
- private static final double D2 = .793650666825390E-03;
-
- /**
- * The d<sub>3</sub> coefficent of the minimax approximation of the Î
- * function (see {@link #D0}).
- */
- private static final double D3 = -.595202931351870E-03;
-
- /**
- * The d<sub>4</sub> coefficent of the minimax approximation of the Î
- * function (see {@link #D0}).
- */
- private static final double D4 = .837308034031215E-03;
-
- /**
- * The d<sub>5</sub> coefficent of the minimax approximation of the Î
- * function (see {@link #D0}).
- */
- private static final double D5 = -.165322962780713E-02;
- /*
- * NOTA: the value of d0 published in Didonato and Morris (1992), eq. (25)
- * and the value implemented in the NSWC library are NOT EQUAL
- * - in Didonato and Morris (1992) D5 = -.125322962780713E-02,
- * - while in the NSWC library D5 = -.165322962780713E-02.
- * Checking the value of algdiv(1.0, 8.0)}, it seems that the second value
- * leads to the smallest error. This is the one which is implemented here.
- */
-
- /**
* Default constructor. Prohibit instantiation.
*/
private Gamma() {}
@@ -767,101 +703,4 @@ public class Gamma {
}
return ret;
}
-
- /**
- * Returns the value of log Î(a + b) for 1 ⤠a, b ⤠2. The present
- * implementation is based on the double precision implementation in the
- * <em>NSWC Library of Mathematics Subroutines</em>, {@code GSUMLN}.
- *
- * @param a First argument.
- * @param b Second argument.
- * @return the value of {@code log(Gamma(a + b))}.
- * @throws OutOfRangeException if {@code a} or {@code b} is lower than
- * {@code 1.0} or greater than {@code 2.0}.
- */
- static double logGammaSum(final double a, final double b)
- throws OutOfRangeException {
-
- if ((a < 1.0) || (a > 2.0)) {
- throw new OutOfRangeException(a, 1.0, 2.0);
- }
- if ((b < 1.0) || (b > 2.0)) {
- throw new OutOfRangeException(b, 1.0, 2.0);
- }
-
- final double x = a + b - 2.0;
- if (x <= 0.25) {
- return Gamma.logGamma1p(1.0 + x);
- } else if (x <= 1.25) {
- return Gamma.logGamma1p(x) + FastMath.log1p(x);
- } else {
- return Gamma.logGamma1p(x - 1.0) + FastMath.log(x * (1.0 + x));
- }
- }
-
- /**
- * Returns the value of log[Î(b) / Î(a + b)] for a ⥠0 and b ⥠8. The
- * present implementation is based on the double precision implementation
in
- * the <em>NSWC Library of Mathematics Subroutines</em>, {@code ALGDIV}.
- *
- * @param a First argument.
- * @param b Second argument.
- * @return the value of {@code log(Gamma(b) / Gamma(a + b))}.
- * @throws NumberIsTooSmallException if {@code a < 0.0} or {@code b < 8.0}.
- */
- static final double logGammaMinusLogGammaSum(final double a,
- final double b)
- throws NumberIsTooSmallException {
-
- if (a < 0.0) {
- throw new NumberIsTooSmallException(a, 0.0, true);
- }
- if (b < 8.0) {
- throw new NumberIsTooSmallException(b, 8.0, true);
- }
-
- /*
- * p = a / (a + b), q = b / (a + b), d = a + b - 0.5
- */
- final double p;
- final double q;
- final double d;
- if (a <= b) {
- final double h = a / b;
- p = h / (1.0 + h);
- q = 1.0 / (1.0 + h);
- d = b + (a - 0.5);
- } else {
- final double h = b / a;
- p = 1.0 / (1.0 + h);
- q = h / (1.0 + h);
- d = a + (b - 0.5);
- }
- /*
- * s_n = 1 + q + ... + q^(n - 1)
- */
- final double q2 = q * q;
- final double s3 = 1.0 + (q + q2);
- final double s5 = 1.0 + (q + q2 * s3);
- final double s7 = 1.0 + (q + q2 * s5);
- final double s9 = 1.0 + (q + q2 * s7);
- final double s11 = 1.0 + (q + q2 * s9);
- /*
- * w = Î(b) - Î(a + b)
- */
- final double tmp = 1.0 / b;
- final double t = tmp * tmp;
- double w = D5 * s11;
- w = D4 * s9 + t * w;
- w = D3 * s7 + t * w;
- w = D2 * s5 + t * w;
- w = D1 * s3 + t * w;
- w = D0 + t * w;
- w *= p / b;
-
- final double u = d * FastMath.log1p(a / b);
- final double v = a * (FastMath.log(b) - 1.0);
-
- return u <= v ? (w - u) - v : (w - v) - u;
- }
}
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=1414527&r1=1414526&r2=1414527&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 Nov 28 05:27:27 2012
@@ -961,303 +961,4 @@ public class GammaTest {
Assert.assertTrue(Integer.toString(i),
Double.isNaN(Gamma.gamma(i)));
}
}
-
- /**
- * Reference data for the {@link Gamma#logGammaSum(double, double)}
- * function. This data was generated with the following
- * <a href="http://maxima.sourceforge.net/";>Maxima</a> script.
- *
- * <pre>
- * kill(all);
- *
- * fpprec : 64;
- * gsumln(a, b) := log(gamma(a + b));
- *
- * x : [1.0b0, 1.125b0, 1.25b0, 1.375b0, 1.5b0, 1.625b0, 1.75b0, 1.875b0,
2.0b0];
- *
- * for i : 1 while i <= length(x) do
- * for j : 1 while j <= length(x) do block(
- * a : x[i],
- * b : x[j],
- * print("{", float(a), ",", float(b), ",", float(gsumln(a, b)), "},")
- * );
- * </pre>
- */
- private static final double[][] LOG_GAMMA_SUM_REF = {
- { 1.0 , 1.0 , 0.0 },
- { 1.0 , 1.125 , .05775985153034387 },
- { 1.0 , 1.25 , .1248717148923966 },
- { 1.0 , 1.375 , .2006984603774558 },
- { 1.0 , 1.5 , .2846828704729192 },
- { 1.0 , 1.625 , .3763336820249054 },
- { 1.0 , 1.75 , .4752146669149371 },
- { 1.0 , 1.875 , .5809359740231859 },
- { 1.0 , 2.0 , .6931471805599453 },
- { 1.125 , 1.0 , .05775985153034387 },
- { 1.125 , 1.125 , .1248717148923966 },
- { 1.125 , 1.25 , .2006984603774558 },
- { 1.125 , 1.375 , .2846828704729192 },
- { 1.125 , 1.5 , .3763336820249054 },
- { 1.125 , 1.625 , .4752146669149371 },
- { 1.125 , 1.75 , .5809359740231859 },
- { 1.125 , 1.875 , .6931471805599453 },
- { 1.125 , 2.0 , 0.811531653906724 },
- { 1.25 , 1.0 , .1248717148923966 },
- { 1.25 , 1.125 , .2006984603774558 },
- { 1.25 , 1.25 , .2846828704729192 },
- { 1.25 , 1.375 , .3763336820249054 },
- { 1.25 , 1.5 , .4752146669149371 },
- { 1.25 , 1.625 , .5809359740231859 },
- { 1.25 , 1.75 , .6931471805599453 },
- { 1.25 , 1.875 , 0.811531653906724 },
- { 1.25 , 2.0 , .9358019311087253 },
- { 1.375 , 1.0 , .2006984603774558 },
- { 1.375 , 1.125 , .2846828704729192 },
- { 1.375 , 1.25 , .3763336820249054 },
- { 1.375 , 1.375 , .4752146669149371 },
- { 1.375 , 1.5 , .5809359740231859 },
- { 1.375 , 1.625 , .6931471805599453 },
- { 1.375 , 1.75 , 0.811531653906724 },
- { 1.375 , 1.875 , .9358019311087253 },
- { 1.375 , 2.0 , 1.06569589786406 },
- { 1.5 , 1.0 , .2846828704729192 },
- { 1.5 , 1.125 , .3763336820249054 },
- { 1.5 , 1.25 , .4752146669149371 },
- { 1.5 , 1.375 , .5809359740231859 },
- { 1.5 , 1.5 , .6931471805599453 },
- { 1.5 , 1.625 , 0.811531653906724 },
- { 1.5 , 1.75 , .9358019311087253 },
- { 1.5 , 1.875 , 1.06569589786406 },
- { 1.5 , 2.0 , 1.200973602347074 },
- { 1.625 , 1.0 , .3763336820249054 },
- { 1.625 , 1.125 , .4752146669149371 },
- { 1.625 , 1.25 , .5809359740231859 },
- { 1.625 , 1.375 , .6931471805599453 },
- { 1.625 , 1.5 , 0.811531653906724 },
- { 1.625 , 1.625 , .9358019311087253 },
- { 1.625 , 1.75 , 1.06569589786406 },
- { 1.625 , 1.875 , 1.200973602347074 },
- { 1.625 , 2.0 , 1.341414578068493 },
- { 1.75 , 1.0 , .4752146669149371 },
- { 1.75 , 1.125 , .5809359740231859 },
- { 1.75 , 1.25 , .6931471805599453 },
- { 1.75 , 1.375 , 0.811531653906724 },
- { 1.75 , 1.5 , .9358019311087253 },
- { 1.75 , 1.625 , 1.06569589786406 },
- { 1.75 , 1.75 , 1.200973602347074 },
- { 1.75 , 1.875 , 1.341414578068493 },
- { 1.75 , 2.0 , 1.486815578593417 },
- { 1.875 , 1.0 , .5809359740231859 },
- { 1.875 , 1.125 , .6931471805599453 },
- { 1.875 , 1.25 , 0.811531653906724 },
- { 1.875 , 1.375 , .9358019311087253 },
- { 1.875 , 1.5 , 1.06569589786406 },
- { 1.875 , 1.625 , 1.200973602347074 },
- { 1.875 , 1.75 , 1.341414578068493 },
- { 1.875 , 1.875 , 1.486815578593417 },
- { 1.875 , 2.0 , 1.6369886482725 },
- { 2.0 , 1.0 , .6931471805599453 },
- { 2.0 , 1.125 , 0.811531653906724 },
- { 2.0 , 1.25 , .9358019311087253 },
- { 2.0 , 1.375 , 1.06569589786406 },
- { 2.0 , 1.5 , 1.200973602347074 },
- { 2.0 , 1.625 , 1.341414578068493 },
- { 2.0 , 1.75 , 1.486815578593417 },
- { 2.0 , 1.875 , 1.6369886482725 },
- { 2.0 , 2.0 , 1.791759469228055 },
- };
-
- @Test
- public void testLogGammaSum() {
- final int ulps = 5;
- for (int i = 0; i < LOG_GAMMA_SUM_REF.length; i++) {
- final double[] ref = LOG_GAMMA_SUM_REF[i];
- final double a = ref[0];
- final double b = ref[1];
- final double expected = ref[2];
- final double actual = Gamma.logGammaSum(a, b);
- final double tol = ulps * FastMath.ulp(expected);
- final StringBuilder builder = new StringBuilder();
- builder.append(a).append(", ").append(b);
- Assert.assertEquals(builder.toString(), expected, actual, tol);
- }
- }
-
- @Test(expected = OutOfRangeException.class)
- public void testLogGammaSumPrecondition1() {
-
- Gamma.logGammaSum(0.0, 1.0);
- }
-
- @Test(expected = OutOfRangeException.class)
- public void testLogGammaSumPrecondition2() {
-
- Gamma.logGammaSum(3.0, 1.0);
- }
-
- @Test(expected = OutOfRangeException.class)
- public void testLogGammaSumPrecondition3() {
-
- Gamma.logGammaSum(1.0, 0.0);
- }
-
- @Test(expected = OutOfRangeException.class)
- public void testLogGammaSumPrecondition4() {
-
- Gamma.logGammaSum(1.0, 3.0);
- }
-
- private static final double[][] LOG_GAMMA_MINUS_LOG_GAMMA_SUM_REF = {
- { 0.0 , 8.0 , 0.0 },
- { 0.0 , 9.0 , 0.0 },
- { 0.0 , 10.0 , 0.0 },
- { 0.0 , 11.0 , 0.0 },
- { 0.0 , 12.0 , 0.0 },
- { 0.0 , 13.0 , 0.0 },
- { 0.0 , 14.0 , 0.0 },
- { 0.0 , 15.0 , 0.0 },
- { 0.0 , 16.0 , 0.0 },
- { 0.0 , 17.0 , 0.0 },
- { 0.0 , 18.0 , 0.0 },
- { 1.0 , 8.0 , - 2.079441541679836 },
- { 1.0 , 9.0 , - 2.19722457733622 },
- { 1.0 , 10.0 , - 2.302585092994046 },
- { 1.0 , 11.0 , - 2.397895272798371 },
- { 1.0 , 12.0 , - 2.484906649788 },
- { 1.0 , 13.0 , - 2.564949357461537 },
- { 1.0 , 14.0 , - 2.639057329615258 },
- { 1.0 , 15.0 , - 2.70805020110221 },
- { 1.0 , 16.0 , - 2.772588722239781 },
- { 1.0 , 17.0 , - 2.833213344056216 },
- { 1.0 , 18.0 , - 2.890371757896165 },
- { 2.0 , 8.0 , - 4.276666119016055 },
- { 2.0 , 9.0 , - 4.499809670330265 },
- { 2.0 , 10.0 , - 4.700480365792417 },
- { 2.0 , 11.0 , - 4.882801922586371 },
- { 2.0 , 12.0 , - 5.049856007249537 },
- { 2.0 , 13.0 , - 5.204006687076795 },
- { 2.0 , 14.0 , - 5.347107530717468 },
- { 2.0 , 15.0 , - 5.480638923341991 },
- { 2.0 , 16.0 , - 5.605802066295998 },
- { 2.0 , 17.0 , - 5.723585101952381 },
- { 2.0 , 18.0 , - 5.834810737062605 },
- { 3.0 , 8.0 , - 6.579251212010101 },
- { 3.0 , 9.0 , - 6.897704943128636 },
- { 3.0 , 10.0 , - 7.185387015580416 },
- { 3.0 , 11.0 , - 7.447751280047908 },
- { 3.0 , 12.0 , - 7.688913336864796 },
- { 3.0 , 13.0 , - 7.912056888179006 },
- { 3.0 , 14.0 , - 8.11969625295725 },
- { 3.0 , 15.0 , - 8.313852267398207 },
- { 3.0 , 16.0 , - 8.496173824192162 },
- { 3.0 , 17.0 , - 8.668024081118821 },
- { 3.0 , 18.0 , - 8.830543010616596 },
- { 4.0 , 8.0 , - 8.977146484808472 },
- { 4.0 , 9.0 , - 9.382611592916636 },
- { 4.0 , 10.0 , - 9.750336373041954 },
- { 4.0 , 11.0 , - 10.08680860966317 },
- { 4.0 , 12.0 , - 10.39696353796701 },
- { 4.0 , 13.0 , - 10.68464561041879 },
- { 4.0 , 14.0 , - 10.95290959701347 },
- { 4.0 , 15.0 , - 11.20422402529437 },
- { 4.0 , 16.0 , - 11.4406128033586 },
- { 4.0 , 17.0 , - 11.66375635467281 },
- { 4.0 , 18.0 , - 11.87506544834002 },
- { 5.0 , 8.0 , - 11.46205313459647 },
- { 5.0 , 9.0 , - 11.94756095037817 },
- { 5.0 , 10.0 , - 12.38939370265721 },
- { 5.0 , 11.0 , - 12.79485881076538 },
- { 5.0 , 12.0 , - 13.16955226020679 },
- { 5.0 , 13.0 , - 13.517858954475 },
- { 5.0 , 14.0 , - 13.84328135490963 },
- { 5.0 , 15.0 , - 14.14866300446081 },
- { 5.0 , 16.0 , - 14.43634507691259 },
- { 5.0 , 17.0 , - 14.70827879239624 },
- { 5.0 , 18.0 , - 14.96610790169833 },
- { 6.0 , 8.0 , - 14.02700249205801 },
- { 6.0 , 9.0 , - 14.58661827999343 },
- { 6.0 , 10.0 , - 15.09744390375942 },
- { 6.0 , 11.0 , - 15.56744753300516 },
- { 6.0 , 12.0 , - 16.002765604263 },
- { 6.0 , 13.0 , - 16.40823071237117 },
- { 6.0 , 14.0 , - 16.78772033407607 },
- { 6.0 , 15.0 , - 17.14439527801481 },
- { 6.0 , 16.0 , - 17.48086751463602 },
- { 6.0 , 17.0 , - 17.79932124575455 },
- { 6.0 , 18.0 , - 18.10160211762749 },
- { 7.0 , 8.0 , - 16.66605982167327 },
- { 7.0 , 9.0 , - 17.29466848109564 },
- { 7.0 , 10.0 , - 17.8700326259992 },
- { 7.0 , 11.0 , - 18.40066087706137 },
- { 7.0 , 12.0 , - 18.89313736215917 },
- { 7.0 , 13.0 , - 19.35266969153761 },
- { 7.0 , 14.0 , - 19.78345260763006 },
- { 7.0 , 15.0 , - 20.18891771573823 },
- { 7.0 , 16.0 , - 20.57190996799433 },
- { 7.0 , 17.0 , - 20.9348154616837 },
- { 7.0 , 18.0 , - 21.27965594797543 },
- { 8.0 , 8.0 , - 19.37411002277548 },
- { 8.0 , 9.0 , - 20.06725720333542 },
- { 8.0 , 10.0 , - 20.70324597005542 },
- { 8.0 , 11.0 , - 21.29103263495754 },
- { 8.0 , 12.0 , - 21.83757634132561 },
- { 8.0 , 13.0 , - 22.3484019650916 },
- { 8.0 , 14.0 , - 22.82797504535349 },
- { 8.0 , 15.0 , - 23.27996016909654 },
- { 8.0 , 16.0 , - 23.70740418392348 },
- { 8.0 , 17.0 , - 24.11286929203165 },
- { 8.0 , 18.0 , - 24.49853177284363 },
- { 9.0 , 8.0 , - 22.14669874501526 },
- { 9.0 , 9.0 , - 22.90047054739164 },
- { 9.0 , 10.0 , - 23.59361772795159 },
- { 9.0 , 11.0 , - 24.23547161412398 },
- { 9.0 , 12.0 , - 24.8333086148796 },
- { 9.0 , 13.0 , - 25.39292440281502 },
- { 9.0 , 14.0 , - 25.9190174987118 },
- { 9.0 , 15.0 , - 26.41545438502569 },
- { 9.0 , 16.0 , - 26.88545801427143 },
- { 9.0 , 17.0 , - 27.33174511689985 },
- { 9.0 , 18.0 , - 27.75662831086511 },
- { 10.0 , 8.0 , - 24.97991208907148 },
- { 10.0 , 9.0 , - 25.7908423052878 },
- { 10.0 , 10.0 , - 26.53805670711802 },
- { 10.0 , 11.0 , - 27.23120388767797 },
- { 10.0 , 12.0 , - 27.87783105260302 },
- { 10.0 , 13.0 , - 28.48396685617334 },
- { 10.0 , 14.0 , - 29.05451171464095 },
- { 10.0 , 15.0 , - 29.59350821537364 },
- { 10.0 , 16.0 , - 30.10433383913963 },
- { 10.0 , 17.0 , - 30.58984165492133 },
- { 10.0 , 18.0 , - 31.05246517686944 },
- };
-
- @Test
- public void testLogGammaMinusLogGammaSum() {
- final int ulps = 4;
- for (int i = 0; i < LOG_GAMMA_MINUS_LOG_GAMMA_SUM_REF.length; i++) {
- final double[] ref = LOG_GAMMA_MINUS_LOG_GAMMA_SUM_REF[i];
- final double a = ref[0];
- final double b = ref[1];
- final double expected = ref[2];
- final double actual = Gamma.logGammaMinusLogGammaSum(a, b);
- final double tol = ulps * FastMath.ulp(expected);
- final StringBuilder builder = new StringBuilder();
- builder.append(a).append(", ").append(b);
- Assert.assertEquals(builder.toString(), expected, actual, tol);
- }
- }
-
- @Test(expected = NumberIsTooSmallException.class)
- public void testLogGammaMinusLogGammaSumPrecondition1() {
- Gamma.logGammaMinusLogGammaSum(-1.0, 8.0);
- }
-
- @Test(expected = NumberIsTooSmallException.class)
- public void testLogGammaMinusLogGammaSumPrecondition2() {
- Gamma.logGammaMinusLogGammaSum(1.0, 7.0);
- }
-
- private void checkRelativeError(String msg, double expected, double
actual, double tolerance) {
- Assert.assertEquals(msg, expected, actual, FastMath.abs(tolerance *
actual));
- }
}
