From 747476596eb9721297f2e3682dac012d81bd323a Mon Sep 17 00:00:00 2001 From: Luc Maisonobe Date: Fri, 15 Mar 2013 11:37:35 +0000 Subject: [PATCH] Inverse error function and inverse complementary error function. JIRA: MATH-948 git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1456905 13f79535-47bb-0310-9956-ffa450edef68 --- NOTICE.txt | 5 + src/changes/changes.xml | 4 + .../org/apache/commons/math3/special/Erf.java | 114 ++++++++++++++++++ .../apache/commons/math3/special/ErfTest.java | 46 +++++++ 4 files changed, 169 insertions(+) diff --git a/NOTICE.txt b/NOTICE.txt index 7ea0cf881..12232535f 100644 --- a/NOTICE.txt +++ b/NOTICE.txt @@ -6,6 +6,11 @@ The Apache Software Foundation (http://www.apache.org/). =============================================================================== +The inverse error function implementation in the Erf class is based on CUDA +code developed by Mike Giles, Oxford-Man Institute of Quantitative Finance, +and published in GPU Computing Gems, volume 2, 2010. +=============================================================================== + The BracketFinder (package org.apache.commons.math3.optimization.univariate) and PowellOptimizer (package org.apache.commons.math3.optimization.general) classes are based on the Python code in module "optimize.py" (version 0.5) diff --git a/src/changes/changes.xml b/src/changes/changes.xml index 6ff9d75fe..67aa62b6c 100644 --- a/src/changes/changes.xml +++ b/src/changes/changes.xml @@ -55,6 +55,10 @@ This is a minor release: It combines bug fixes and new features. Changes to existing features were made in a backwards-compatible way such as to allow drop-in replacement of the v3.1[.1] JAR file. "> + + Implementations for inverse error function and inverse complementary + error functions have been added. + Extended ranges for FastMath performance tests. diff --git a/src/main/java/org/apache/commons/math3/special/Erf.java b/src/main/java/org/apache/commons/math3/special/Erf.java index 25341af28..c40f6c2dc 100644 --- a/src/main/java/org/apache/commons/math3/special/Erf.java +++ b/src/main/java/org/apache/commons/math3/special/Erf.java @@ -126,5 +126,119 @@ public class Erf { erfc(x1) - erfc(x2) : erf(x2) - erf(x1); } + + /** + * Returns the inverse erf. + *

+ * This implementation is described in the paper: + * Approximating + * the erfinv function by Mike Giles, Oxford-Man Institute of Quantitative Finance, + * which was published in GPU Computing Gems, volume 2, 2010. + * The source code is available here. + *

+ * @param x the value + * @return t such that x = erf(t) + * @since 3.2 + */ + public static double erfInv(final double x) { + + // beware that the logarithm argument must be + // commputed as (1.0 - x) * (1.0 + x), + // it must NOT be simplified as 1.0 - x * x as this + // would induce rounding errors near the boundaries +/-1 + double w = - FastMath.log((1.0 - x) * (1.0 + x)); + double p; + + if (w < 6.25) { + w = w - 3.125; + p = -3.6444120640178196996e-21; + p = -1.685059138182016589e-19 + p * w; + p = 1.2858480715256400167e-18 + p * w; + p = 1.115787767802518096e-17 + p * w; + p = -1.333171662854620906e-16 + p * w; + p = 2.0972767875968561637e-17 + p * w; + p = 6.6376381343583238325e-15 + p * w; + p = -4.0545662729752068639e-14 + p * w; + p = -8.1519341976054721522e-14 + p * w; + p = 2.6335093153082322977e-12 + p * w; + p = -1.2975133253453532498e-11 + p * w; + p = -5.4154120542946279317e-11 + p * w; + p = 1.051212273321532285e-09 + p * w; + p = -4.1126339803469836976e-09 + p * w; + p = -2.9070369957882005086e-08 + p * w; + p = 4.2347877827932403518e-07 + p * w; + p = -1.3654692000834678645e-06 + p * w; + p = -1.3882523362786468719e-05 + p * w; + p = 0.0001867342080340571352 + p * w; + p = -0.00074070253416626697512 + p * w; + p = -0.0060336708714301490533 + p * w; + p = 0.24015818242558961693 + p * w; + p = 1.6536545626831027356 + p * w; + } else if (w < 16.0) { + w = FastMath.sqrt(w) - 3.25; + p = 2.2137376921775787049e-09; + p = 9.0756561938885390979e-08 + p * w; + p = -2.7517406297064545428e-07 + p * w; + p = 1.8239629214389227755e-08 + p * w; + p = 1.5027403968909827627e-06 + p * w; + p = -4.013867526981545969e-06 + p * w; + p = 2.9234449089955446044e-06 + p * w; + p = 1.2475304481671778723e-05 + p * w; + p = -4.7318229009055733981e-05 + p * w; + p = 6.8284851459573175448e-05 + p * w; + p = 2.4031110387097893999e-05 + p * w; + p = -0.0003550375203628474796 + p * w; + p = 0.00095328937973738049703 + p * w; + p = -0.0016882755560235047313 + p * w; + p = 0.0024914420961078508066 + p * w; + p = -0.0037512085075692412107 + p * w; + p = 0.005370914553590063617 + p * w; + p = 1.0052589676941592334 + p * w; + p = 3.0838856104922207635 + p * w; + } else if (!Double.isInfinite(w)) { + w = FastMath.sqrt(w) - 5.0; + p = -2.7109920616438573243e-11; + p = -2.5556418169965252055e-10 + p * w; + p = 1.5076572693500548083e-09 + p * w; + p = -3.7894654401267369937e-09 + p * w; + p = 7.6157012080783393804e-09 + p * w; + p = -1.4960026627149240478e-08 + p * w; + p = 2.9147953450901080826e-08 + p * w; + p = -6.7711997758452339498e-08 + p * w; + p = 2.2900482228026654717e-07 + p * w; + p = -9.9298272942317002539e-07 + p * w; + p = 4.5260625972231537039e-06 + p * w; + p = -1.9681778105531670567e-05 + p * w; + p = 7.5995277030017761139e-05 + p * w; + p = -0.00021503011930044477347 + p * w; + p = -0.00013871931833623122026 + p * w; + p = 1.0103004648645343977 + p * w; + p = 4.8499064014085844221 + p * w; + } else { + // this branch does not appears in the original code, it + // was added because the previous branch does not handle + // x = +/-1 correctly. In this case, w is positive infinity + // and as the first coefficient (-2.71e-11) is negative. + // Once the first multiplication is done, p becomes negative + // infinity and remains so throughout the polynomial evaluation. + // So the branch above incorrectly returns negative infinity + // instead of the correct positive infinity. + p = Double.POSITIVE_INFINITY; + } + + return p * x; + + } + + /** + * Returns the inverse erfc. + * @param x the value + * @return t such that x = erfc(t) + * @since 3.2 + */ + public static double erfcInv(final double x) { + return erfInv(1 - x); + } + } diff --git a/src/test/java/org/apache/commons/math3/special/ErfTest.java b/src/test/java/org/apache/commons/math3/special/ErfTest.java index 4227125f7..e5553d844 100644 --- a/src/test/java/org/apache/commons/math3/special/ErfTest.java +++ b/src/test/java/org/apache/commons/math3/special/ErfTest.java @@ -213,4 +213,50 @@ public class ErfTest { } } } + + @Test + public void testErfInvNaN() { + Assert.assertTrue(Double.isNaN(Erf.erfInv(-1.001))); + Assert.assertTrue(Double.isNaN(Erf.erfInv(+1.001))); + } + + @Test + public void testErfInvInfinite() { + Assert.assertTrue(Double.isInfinite(Erf.erfInv(-1))); + Assert.assertTrue(Erf.erfInv(-1) < 0); + Assert.assertTrue(Double.isInfinite(Erf.erfInv(+1))); + Assert.assertTrue(Erf.erfInv(+1) > 0); + } + + @Test + public void testErfInv() { + for (double x = -5.9; x < 5.9; x += 0.01) { + final double y = Erf.erf(x); + final double dydx = 2 * FastMath.exp(-x * x) / FastMath.sqrt(FastMath.PI); + Assert.assertEquals(x, Erf.erfInv(y), 1.0e-15 / dydx); + } + } + + @Test + public void testErfcInvNaN() { + Assert.assertTrue(Double.isNaN(Erf.erfcInv(-0.001))); + Assert.assertTrue(Double.isNaN(Erf.erfcInv(+2.001))); + } + + @Test + public void testErfcInvInfinite() { + Assert.assertTrue(Double.isInfinite(Erf.erfcInv(-0))); + Assert.assertTrue(Erf.erfcInv( 0) > 0); + Assert.assertTrue(Double.isInfinite(Erf.erfcInv(+2))); + Assert.assertTrue(Erf.erfcInv(+2) < 0); + } + + @Test + public void testErfcInv() { + for (double x = -5.85; x < 5.9; x += 0.01) { + final double y = Erf.erfc(x); + final double dydxAbs = 2 * FastMath.exp(-x * x) / FastMath.sqrt(FastMath.PI); + Assert.assertEquals(x, Erf.erfcInv(y), 1.0e-15 / dydxAbs); + } + } }