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From l..@apache.org
Subject svn commit: r1456905 - in /commons/proper/math/trunk: NOTICE.txt src/changes/changes.xml src/main/java/org/apache/commons/math3/special/Erf.java src/test/java/org/apache/commons/math3/special/ErfTest.java
Date Fri, 15 Mar 2013 11:37:35 GMT
Author: luc
Date: Fri Mar 15 11:37:35 2013
New Revision: 1456905

URL: http://svn.apache.org/r1456905
Log:
Inverse error function and inverse complementary error function.

JIRA: MATH-948

Modified:
    commons/proper/math/trunk/NOTICE.txt
    commons/proper/math/trunk/src/changes/changes.xml
    commons/proper/math/trunk/src/main/java/org/apache/commons/math3/special/Erf.java
    commons/proper/math/trunk/src/test/java/org/apache/commons/math3/special/ErfTest.java

Modified: commons/proper/math/trunk/NOTICE.txt
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/NOTICE.txt?rev=1456905&r1=1456904&r2=1456905&view=diff
==============================================================================
--- commons/proper/math/trunk/NOTICE.txt (original)
+++ commons/proper/math/trunk/NOTICE.txt Fri Mar 15 11:37:35 2013
@@ -6,6 +6,11 @@ The Apache Software Foundation (http://w
 
 ===============================================================================
 
+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)

Modified: commons/proper/math/trunk/src/changes/changes.xml
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/changes/changes.xml?rev=1456905&r1=1456904&r2=1456905&view=diff
==============================================================================
--- commons/proper/math/trunk/src/changes/changes.xml (original)
+++ commons/proper/math/trunk/src/changes/changes.xml Fri Mar 15 11:37:35 2013
@@ -55,6 +55,10 @@ This is a minor release: It combines bug
   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.
 ">
+      <action dev="luc" type="add" issue="MATH-948" >
+        Implementations for inverse error function and inverse complementary
+        error functions have been added.
+      </action>
       <action dev="luc" type="fix" issue="MATH-580" >
         Extended ranges for FastMath performance tests.
       </action>

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/special/Erf.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/special/Erf.java?rev=1456905&r1=1456904&r2=1456905&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/special/Erf.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/special/Erf.java Fri
Mar 15 11:37:35 2013
@@ -126,5 +126,119 @@ public class Erf {
                 erfc(x1) - erfc(x2) :
                 erf(x2) - erf(x1);
     }
+
+    /**
+     * Returns the inverse erf.
+     * <p>
+     * This implementation is described in the paper:
+     * <a href="http://people.maths.ox.ac.uk/gilesm/files/gems_erfinv.pdf">Approximating
+     * the erfinv function</a> by Mike Giles, Oxford-Man Institute of Quantitative
Finance,
+     * which was published in GPU Computing Gems, volume 2, 2010.
+     * The source code is available <a href="http://gpucomputing.net/?q=node/1828">here</a>.
+     * </p>
+     * @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);
+    }
+
 }
 

Modified: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/special/ErfTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/special/ErfTest.java?rev=1456905&r1=1456904&r2=1456905&view=diff
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/special/ErfTest.java
(original)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/special/ErfTest.java
Fri Mar 15 11:37:35 2013
@@ -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);
+        }
+    }
 }



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