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Posted to commits@commons.apache.org by er...@apache.org on 2017/05/14 23:16:29 UTC
[1/2] [math] MATH-1416: Depend on "Commons Numbers" (module
"commons-numbers-gamma").
Repository: commons-math
Updated Branches:
refs/heads/master 44ab25696 -> b81be1fea
MATH-1416: Depend on "Commons Numbers" (module "commons-numbers-gamma").
Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/7f747082
Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/7f747082
Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/7f747082
Branch: refs/heads/master
Commit: 7f74708201c2ab9f5d1f83c7052487116b8f7114
Parents: 44ab256
Author: Gilles <er...@apache.org>
Authored: Mon May 15 01:15:09 2017 +0200
Committer: Gilles <er...@apache.org>
Committed: Mon May 15 01:15:09 2017 +0200
----------------------------------------------------------------------
.../commons/math4/distribution/LevyDistribution.java | 7 ++++---
.../commons/math4/distribution/LogNormalDistribution.java | 7 ++++---
.../commons/math4/distribution/NormalDistribution.java | 10 ++++++----
3 files changed, 14 insertions(+), 10 deletions(-)
----------------------------------------------------------------------
http://git-wip-us.apache.org/repos/asf/commons-math/blob/7f747082/src/main/java/org/apache/commons/math4/distribution/LevyDistribution.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/distribution/LevyDistribution.java b/src/main/java/org/apache/commons/math4/distribution/LevyDistribution.java
index 1986cac..5f99f8e 100644
--- a/src/main/java/org/apache/commons/math4/distribution/LevyDistribution.java
+++ b/src/main/java/org/apache/commons/math4/distribution/LevyDistribution.java
@@ -17,7 +17,8 @@
package org.apache.commons.math4.distribution;
import org.apache.commons.math4.exception.OutOfRangeException;
-import org.apache.commons.math4.special.Erf;
+import org.apache.commons.numbers.gamma.Erfc;
+import org.apache.commons.numbers.gamma.InverseErfc;
import org.apache.commons.math4.util.FastMath;
/**
@@ -105,7 +106,7 @@ public class LevyDistribution extends AbstractRealDistribution {
if (x < mu) {
return Double.NaN;
}
- return Erf.erfc(FastMath.sqrt(halfC / (x - mu)));
+ return Erfc.value(FastMath.sqrt(halfC / (x - mu)));
}
/** {@inheritDoc} */
@@ -114,7 +115,7 @@ public class LevyDistribution extends AbstractRealDistribution {
if (p < 0.0 || p > 1.0) {
throw new OutOfRangeException(p, 0, 1);
}
- final double t = Erf.erfcInv(p);
+ final double t = InverseErfc.value(p);
return mu + halfC / (t * t);
}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/7f747082/src/main/java/org/apache/commons/math4/distribution/LogNormalDistribution.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/distribution/LogNormalDistribution.java b/src/main/java/org/apache/commons/math4/distribution/LogNormalDistribution.java
index b5d4bf0..3025417 100644
--- a/src/main/java/org/apache/commons/math4/distribution/LogNormalDistribution.java
+++ b/src/main/java/org/apache/commons/math4/distribution/LogNormalDistribution.java
@@ -20,7 +20,8 @@ package org.apache.commons.math4.distribution;
import org.apache.commons.math4.exception.NotStrictlyPositiveException;
import org.apache.commons.math4.exception.NumberIsTooLargeException;
import org.apache.commons.math4.exception.util.LocalizedFormats;
-import org.apache.commons.math4.special.Erf;
+import org.apache.commons.numbers.gamma.Erf;
+import org.apache.commons.numbers.gamma.ErfDifference;
import org.apache.commons.math4.util.FastMath;
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.rng.sampling.distribution.ContinuousSampler;
@@ -200,7 +201,7 @@ public class LogNormalDistribution extends AbstractRealDistribution {
if (FastMath.abs(dev) > 40 * shape) {
return dev < 0 ? 0.0d : 1.0d;
}
- return 0.5 + 0.5 * Erf.erf(dev / (shape * SQRT2));
+ return 0.5 + 0.5 * Erf.value(dev / (shape * SQRT2));
}
/** {@inheritDoc} */
@@ -218,7 +219,7 @@ public class LogNormalDistribution extends AbstractRealDistribution {
final double denom = shape * SQRT2;
final double v0 = (FastMath.log(x0) - scale) / denom;
final double v1 = (FastMath.log(x1) - scale) / denom;
- return 0.5 * Erf.erf(v0, v1);
+ return 0.5 * ErfDifference.value(v0, v1);
}
/** {@inheritDoc} */
http://git-wip-us.apache.org/repos/asf/commons-math/blob/7f747082/src/main/java/org/apache/commons/math4/distribution/NormalDistribution.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/distribution/NormalDistribution.java b/src/main/java/org/apache/commons/math4/distribution/NormalDistribution.java
index da4c65c..76c41a3 100644
--- a/src/main/java/org/apache/commons/math4/distribution/NormalDistribution.java
+++ b/src/main/java/org/apache/commons/math4/distribution/NormalDistribution.java
@@ -21,7 +21,9 @@ import org.apache.commons.math4.exception.NotStrictlyPositiveException;
import org.apache.commons.math4.exception.NumberIsTooLargeException;
import org.apache.commons.math4.exception.OutOfRangeException;
import org.apache.commons.math4.exception.util.LocalizedFormats;
-import org.apache.commons.math4.special.Erf;
+import org.apache.commons.numbers.gamma.Erfc;
+import org.apache.commons.numbers.gamma.InverseErf;
+import org.apache.commons.numbers.gamma.ErfDifference;
import org.apache.commons.math4.util.FastMath;
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.rng.sampling.distribution.ContinuousSampler;
@@ -142,7 +144,7 @@ public class NormalDistribution extends AbstractRealDistribution {
if (FastMath.abs(dev) > 40 * standardDeviation) {
return dev < 0 ? 0.0d : 1.0d;
}
- return 0.5 * Erf.erfc(-dev / (standardDeviation * SQRT2));
+ return 0.5 * Erfc.value(-dev / (standardDeviation * SQRT2));
}
/** {@inheritDoc}
@@ -153,7 +155,7 @@ public class NormalDistribution extends AbstractRealDistribution {
if (p < 0.0 || p > 1.0) {
throw new OutOfRangeException(p, 0, 1);
}
- return mean + standardDeviation * SQRT2 * Erf.erfInv(2 * p - 1);
+ return mean + standardDeviation * SQRT2 * InverseErf.value(2 * p - 1);
}
/** {@inheritDoc} */
@@ -168,7 +170,7 @@ public class NormalDistribution extends AbstractRealDistribution {
final double denom = standardDeviation * SQRT2;
final double v0 = (x0 - mean) / denom;
final double v1 = (x1 - mean) / denom;
- return 0.5 * Erf.erf(v0, v1);
+ return 0.5 * ErfDifference.value(v0, v1);
}
/** {@inheritDoc} */
[2/2] [math] MATH-1416: Delete functionality now in "Commons Numbers".
Posted by er...@apache.org.
MATH-1416: Delete functionality now in "Commons Numbers".
Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/b81be1fe
Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/b81be1fe
Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/b81be1fe
Branch: refs/heads/master
Commit: b81be1fea344c07c3024011066f0c8bb8865cc65
Parents: 7f74708
Author: Gilles <er...@apache.org>
Authored: Mon May 15 01:15:47 2017 +0200
Committer: Gilles <er...@apache.org>
Committed: Mon May 15 01:15:47 2017 +0200
----------------------------------------------------------------------
.../org/apache/commons/math4/special/Erf.java | 243 -----------------
.../apache/commons/math4/special/ErfTest.java | 261 -------------------
2 files changed, 504 deletions(-)
----------------------------------------------------------------------
http://git-wip-us.apache.org/repos/asf/commons-math/blob/b81be1fe/src/main/java/org/apache/commons/math4/special/Erf.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/special/Erf.java b/src/main/java/org/apache/commons/math4/special/Erf.java
deleted file mode 100644
index 47d6ed4..0000000
--- a/src/main/java/org/apache/commons/math4/special/Erf.java
+++ /dev/null
@@ -1,243 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one or more
- * contributor license agreements. See the NOTICE file distributed with
- * this work for additional information regarding copyright ownership.
- * The ASF licenses this file to You under the Apache License, Version 2.0
- * (the "License"); you may not use this file except in compliance with
- * the License. You may obtain a copy of the License at
- *
- * http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-package org.apache.commons.math4.special;
-
-import org.apache.commons.math4.util.FastMath;
-import org.apache.commons.numbers.gamma.RegularizedGamma;
-
-/**
- * This is a utility class that provides computation methods related to the
- * error functions.
- */
-public class Erf {
-
- /**
- * The number {@code X_CRIT} is used by {@link #erf(double, double)} internally.
- * This number solves {@code erf(x)=0.5} within 1ulp.
- * More precisely, the current implementations of
- * {@link #erf(double)} and {@link #erfc(double)} satisfy:<br>
- * {@code erf(X_CRIT) < 0.5},<br>
- * {@code erf(Math.nextUp(X_CRIT) > 0.5},<br>
- * {@code erfc(X_CRIT) = 0.5}, and<br>
- * {@code erfc(Math.nextUp(X_CRIT) < 0.5}
- */
- private static final double X_CRIT = 0.4769362762044697;
-
- /**
- * Default constructor. Prohibit instantiation.
- */
- private Erf() {}
-
- /**
- * Returns the error function.
- *
- * <p>erf(x) = 2/√π <sub>0</sub>∫<sup>x</sup> e<sup>-t<span style="position: relative; top: -.5em">2</span></sup>dt </p>
- *
- * <p>This implementation computes erf(x) using the
- * {@link RegularizedGamma.P.value(double, double, double, int) regularized gamma function},
- * following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3)</p>
- *
- * <p>The value returned is always between -1 and 1 (inclusive).
- * If {@code abs(x) > 40}, then {@code erf(x)} is indistinguishable from
- * either 1 or -1 as a double, so the appropriate extreme value is returned.
- * </p>
- *
- * @param x the value.
- * @return the error function erf(x)
- * @throws org.apache.commons.math4.exception.MaxCountExceededException
- * if the algorithm fails to converge.
- * @see RegularizedGamma.P#value(double, double, double, int)
- */
- public static double erf(double x) {
- if (FastMath.abs(x) > 40) {
- return x > 0 ? 1 : -1;
- }
- final double ret = RegularizedGamma.P.value(0.5, x * x, 1.0e-15, 10000);
- return x < 0 ? -ret : ret;
- }
-
- /**
- * Returns the complementary error function.
- *
- * <p>erfc(x) = 2/√π <sub>x</sub>∫<sup>∞</sup> e<sup>-t<span style="position: relative; top: -.5em">2</span></sup>dt
- * <br>
- * = 1 - {@link #erf(double) erf(x)} </p>
- *
- * <p>This implementation computes erfc(x) using the
- * {@link RegularizedGamma.Q#value(double, double, double, int) regularized gamma function},
- * following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3).</p>
- *
- * <p>The value returned is always between 0 and 2 (inclusive).
- * If {@code abs(x) > 40}, then {@code erf(x)} is indistinguishable from
- * either 0 or 2 as a double, so the appropriate extreme value is returned.
- * </p>
- *
- * @param x the value
- * @return the complementary error function erfc(x)
- * @throws org.apache.commons.math4.exception.MaxCountExceededException
- * if the algorithm fails to converge.
- * @see RegularizedGamma.Q#value(double, double, double, int)
- * @since 2.2
- */
- public static double erfc(double x) {
- if (FastMath.abs(x) > 40) {
- return x > 0 ? 0 : 2;
- }
- final double ret = RegularizedGamma.Q.value(0.5, x * x, 1.0e-15, 10000);
- return x < 0 ? 2 - ret : ret;
- }
-
- /**
- * Returns the difference between erf(x1) and erf(x2).
- *
- * The implementation uses either erf(double) or erfc(double)
- * depending on which provides the most precise result.
- *
- * @param x1 the first value
- * @param x2 the second value
- * @return erf(x2) - erf(x1)
- */
- public static double erf(double x1, double x2) {
- if(x1 > x2) {
- return -erf(x2, x1);
- }
-
- return
- x1 < -X_CRIT ?
- x2 < 0.0 ?
- erfc(-x2) - erfc(-x1) :
- erf(x2) - erf(x1) :
- x2 > X_CRIT && x1 > 0.0 ?
- 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 -= 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);
- }
-
-}
-
http://git-wip-us.apache.org/repos/asf/commons-math/blob/b81be1fe/src/test/java/org/apache/commons/math4/special/ErfTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/special/ErfTest.java b/src/test/java/org/apache/commons/math4/special/ErfTest.java
deleted file mode 100644
index 3bd9bf0..0000000
--- a/src/test/java/org/apache/commons/math4/special/ErfTest.java
+++ /dev/null
@@ -1,261 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one or more
- * contributor license agreements. See the NOTICE file distributed with
- * this work for additional information regarding copyright ownership.
- * The ASF licenses this file to You under the Apache License, Version 2.0
- * (the "License"); you may not use this file except in compliance with
- * the License. You may obtain a copy of the License at
- *
- * http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-
-package org.apache.commons.math4.special;
-
-import org.apache.commons.math4.TestUtils;
-import org.apache.commons.math4.special.Erf;
-import org.apache.commons.math4.util.FastMath;
-import org.junit.Test;
-import org.junit.Assert;
-
-/**
- */
-public class ErfTest {
- @Test
- public void testErf0() {
- double actual = Erf.erf(0.0);
- double expected = 0.0;
- Assert.assertEquals(expected, actual, 1.0e-15);
- Assert.assertEquals(1 - expected, Erf.erfc(0.0), 1.0e-15);
- }
-
- @Test
- public void testErf1960() {
- double x = 1.960 / FastMath.sqrt(2.0);
- double actual = Erf.erf(x);
- double expected = 0.95;
- Assert.assertEquals(expected, actual, 1.0e-5);
- Assert.assertEquals(1 - actual, Erf.erfc(x), 1.0e-15);
-
- actual = Erf.erf(-x);
- expected = -expected;
- Assert.assertEquals(expected, actual, 1.0e-5);
- Assert.assertEquals(1 - actual, Erf.erfc(-x), 1.0e-15);
- }
-
- @Test
- public void testErf2576() {
- double x = 2.576 / FastMath.sqrt(2.0);
- double actual = Erf.erf(x);
- double expected = 0.99;
- Assert.assertEquals(expected, actual, 1.0e-5);
- Assert.assertEquals(1 - actual, Erf.erfc(x), 1e-15);
-
- actual = Erf.erf(-x);
- expected = -expected;
- Assert.assertEquals(expected, actual, 1.0e-5);
- Assert.assertEquals(1 - actual, Erf.erfc(-x), 1.0e-15);
- }
-
- @Test
- public void testErf2807() {
- double x = 2.807 / FastMath.sqrt(2.0);
- double actual = Erf.erf(x);
- double expected = 0.995;
- Assert.assertEquals(expected, actual, 1.0e-5);
- Assert.assertEquals(1 - actual, Erf.erfc(x), 1.0e-15);
-
- actual = Erf.erf(-x);
- expected = -expected;
- Assert.assertEquals(expected, actual, 1.0e-5);
- Assert.assertEquals(1 - actual, Erf.erfc(-x), 1.0e-15);
- }
-
- @Test
- public void testErf3291() {
- double x = 3.291 / FastMath.sqrt(2.0);
- double actual = Erf.erf(x);
- double expected = 0.999;
- Assert.assertEquals(expected, actual, 1.0e-5);
- Assert.assertEquals(1 - expected, Erf.erfc(x), 1.0e-5);
-
- actual = Erf.erf(-x);
- expected = -expected;
- Assert.assertEquals(expected, actual, 1.0e-5);
- Assert.assertEquals(1 - expected, Erf.erfc(-x), 1.0e-5);
- }
-
- /**
- * MATH-301, MATH-456
- */
- @Test
- public void testLargeValues() {
- for (int i = 1; i < 200; i*=10) {
- double result = Erf.erf(i);
- Assert.assertFalse(Double.isNaN(result));
- Assert.assertTrue(result > 0 && result <= 1);
- result = Erf.erf(-i);
- Assert.assertFalse(Double.isNaN(result));
- Assert.assertTrue(result >= -1 && result < 0);
- result = Erf.erfc(i);
- Assert.assertFalse(Double.isNaN(result));
- Assert.assertTrue(result >= 0 && result < 1);
- result = Erf.erfc(-i);
- Assert.assertFalse(Double.isNaN(result));
- Assert.assertTrue(result >= 1 && result <= 2);
- }
- Assert.assertEquals(-1, Erf.erf(Double.NEGATIVE_INFINITY), 0);
- Assert.assertEquals(1, Erf.erf(Double.POSITIVE_INFINITY), 0);
- Assert.assertEquals(2, Erf.erfc(Double.NEGATIVE_INFINITY), 0);
- Assert.assertEquals(0, Erf.erfc(Double.POSITIVE_INFINITY), 0);
- }
-
- /**
- * Compare Erf.erf against reference values computed using GCC 4.2.1 (Apple OSX packaged version)
- * erfl (extended precision erf).
- */
- @Test
- public void testErfGnu() {
- final double tol = 1E-15;
- final double[] gnuValues = new double[] {-1, -1, -1, -1, -1,
- -1, -1, -1, -0.99999999999999997848,
- -0.99999999999999264217, -0.99999999999846254017, -0.99999999980338395581, -0.99999998458274209971,
- -0.9999992569016276586, -0.99997790950300141459, -0.99959304798255504108, -0.99532226501895273415,
- -0.96610514647531072711, -0.84270079294971486948, -0.52049987781304653809, 0,
- 0.52049987781304653809, 0.84270079294971486948, 0.96610514647531072711, 0.99532226501895273415,
- 0.99959304798255504108, 0.99997790950300141459, 0.9999992569016276586, 0.99999998458274209971,
- 0.99999999980338395581, 0.99999999999846254017, 0.99999999999999264217, 0.99999999999999997848,
- 1, 1, 1, 1,
- 1, 1, 1, 1};
- double x = -10d;
- for (int i = 0; i < 41; i++) {
- Assert.assertEquals(gnuValues[i], Erf.erf(x), tol);
- x += 0.5d;
- }
- }
-
- /**
- * Compare Erf.erfc against reference values computed using GCC 4.2.1 (Apple OSX packaged version)
- * erfcl (extended precision erfc).
- */
- @Test
- public void testErfcGnu() {
- final double tol = 1E-15;
- final double[] gnuValues = new double[] { 2, 2, 2, 2, 2,
- 2, 2, 2, 1.9999999999999999785,
- 1.9999999999999926422, 1.9999999999984625402, 1.9999999998033839558, 1.9999999845827420998,
- 1.9999992569016276586, 1.9999779095030014146, 1.9995930479825550411, 1.9953222650189527342,
- 1.9661051464753107271, 1.8427007929497148695, 1.5204998778130465381, 1,
- 0.47950012218695346194, 0.15729920705028513051, 0.033894853524689272893, 0.0046777349810472658333,
- 0.00040695201744495893941, 2.2090496998585441366E-05, 7.4309837234141274516E-07, 1.5417257900280018858E-08,
- 1.966160441542887477E-10, 1.5374597944280348501E-12, 7.3578479179743980661E-15, 2.1519736712498913103E-17,
- 3.8421483271206474691E-20, 4.1838256077794144006E-23, 2.7766493860305691016E-26, 1.1224297172982927079E-29,
- 2.7623240713337714448E-33, 4.1370317465138102353E-37, 3.7692144856548799402E-41, 2.0884875837625447567E-45};
- double x = -10d;
- for (int i = 0; i < 41; i++) {
- Assert.assertEquals(gnuValues[i], Erf.erfc(x), tol);
- x += 0.5d;
- }
- }
-
- /**
- * Tests erfc against reference data computed using Maple reported in Marsaglia, G,,
- * "Evaluating the Normal Distribution," Journal of Statistical Software, July, 2004.
- * http//www.jstatsoft.org/v11/a05/paper
- */
- @Test
- public void testErfcMaple() {
- double[][] ref = new double[][]
- {{0.1, 4.60172162722971e-01},
- {1.2, 1.15069670221708e-01},
- {2.3, 1.07241100216758e-02},
- {3.4, 3.36929265676881e-04},
- {4.5, 3.39767312473006e-06},
- {5.6, 1.07175902583109e-08},
- {6.7, 1.04209769879652e-11},
- {7.8, 3.09535877195870e-15},
- {8.9, 2.79233437493966e-19},
- {10.0, 7.61985302416053e-24},
- {11.1, 6.27219439321703e-29},
- {12.2, 1.55411978638959e-34},
- {13.3, 1.15734162836904e-40},
- {14.4, 2.58717592540226e-47},
- {15.5, 1.73446079179387e-54},
- {16.6, 3.48454651995041e-62}
- };
- for (int i = 0; i < 15; i++) {
- final double result = 0.5*Erf.erfc(ref[i][0]/FastMath.sqrt(2));
- Assert.assertEquals(ref[i][1], result, 1E-15);
- TestUtils.assertRelativelyEquals(ref[i][1], result, 1E-13);
- }
- }
-
- /**
- * Test the implementation of Erf.erf(double, double) for consistency with results
- * obtained from Erf.erf(double) and Erf.erfc(double).
- */
- @Test
- public void testTwoArgumentErf() {
- double[] xi = new double[]{-2.0, -1.0, -0.9, -0.1, 0.0, 0.1, 0.9, 1.0, 2.0};
- for(double x1 : xi) {
- for(double x2 : xi) {
- double a = Erf.erf(x1, x2);
- double b = Erf.erf(x2) - Erf.erf(x1);
- double c = Erf.erfc(x1) - Erf.erfc(x2);
- Assert.assertEquals(a, b, 1E-15);
- Assert.assertEquals(a, c, 1E-15);
- }
- }
- }
-
- @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);
- }
- }
-}