Repository: commons-numbers Updated Branches: refs/heads/master 61d27bd9e -> 4de442f68
NUMBERS-39: "Erf" family of functions. Project: http://git-wip-us.apache.org/repos/asf/commons-numbers/repo Commit: http://git-wip-us.apache.org/repos/asf/commons-numbers/commit/4de442f6 Tree: http://git-wip-us.apache.org/repos/asf/commons-numbers/tree/4de442f6 Diff: http://git-wip-us.apache.org/repos/asf/commons-numbers/diff/4de442f6 Branch: refs/heads/master Commit: 4de442f68f7debc828e202e3b89e2e4d0de1e4d8 Parents: 61d27bd Author: Gilles Sadowski <gil...@harfang.homelinux.org> Authored: Mon May 15 00:51:33 2017 +0200 Committer: Gilles Sadowski <gil...@harfang.homelinux.org> Committed: Mon May 15 00:51:33 2017 +0200 ---------------------------------------------------------------------- .../org/apache/commons/numbers/gamma/Erf.java | 50 +++++++ .../commons/numbers/gamma/ErfDifference.java | 65 +++++++++ .../org/apache/commons/numbers/gamma/Erfc.java | 53 +++++++ .../commons/numbers/gamma/InverseErf.java | 124 ++++++++++++++++ .../commons/numbers/gamma/InverseErfc.java | 39 ++++++ .../numbers/gamma/ErfDifferenceTest.java | 43 ++++++ .../apache/commons/numbers/gamma/ErfTest.java | 140 +++++++++++++++++++ .../apache/commons/numbers/gamma/ErfcTest.java | 85 +++++++++++ .../commons/numbers/gamma/InverseErfTest.java | 48 +++++++ .../commons/numbers/gamma/InverseErfcTest.java | 48 +++++++ 10 files changed, 695 insertions(+) ---------------------------------------------------------------------- http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/4de442f6/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erf.java ---------------------------------------------------------------------- diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erf.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erf.java new file mode 100644 index 0000000..7892219 --- /dev/null +++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erf.java @@ -0,0 +1,50 @@ +/* + * 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.numbers.gamma; + +/** + * <a href="http://mathworld.wolfram.com/Erf.html";>Error function</a>. + */ +public class Erf { + /** + * <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 returned value is always between -1 and 1 (inclusive). + * If {@code abs(x) > 40}, then {@code Erf.value(x)} is indistinguishable from + * either 1 or -1 at {@code double} precision, so the appropriate extreme value + * is returned. + * </p> + * + * @param x the value. + * @return the error function. + * @throws ArithmeticException if the algorithm fails to converge. + * + * @see RegularizedGamma.P#value(double, double, double, int) + */ + public static double value(double x) { + if (Math.abs(x) > 40) { + return x > 0 ? 1 : -1; + } + final double ret = RegularizedGamma.P.value(0.5, x * x, 1e-15, 10000); + return x < 0 ? -ret : ret; + } +} http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/4de442f6/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/ErfDifference.java ---------------------------------------------------------------------- diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/ErfDifference.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/ErfDifference.java new file mode 100644 index 0000000..31e1f59 --- /dev/null +++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/ErfDifference.java @@ -0,0 +1,65 @@ +/* + * 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.numbers.gamma; + +/** + * Computes the difference between {@link Erf error function values}. + */ +public class ErfDifference { + /** + * This number solves {@code erf(x) = 0.5} within 1 ulp. + * More precisely, the current implementations of + * {@link Erf#value(double)} and {@link Erfc#value(double)} satisfy: + * <ul> + * <li>{@code Erf.value(X_CRIT) < 0.5},</li> + * <li>{@code Erf.value(Math.nextUp(X_CRIT) > 0.5},</li> + * <li>{@code Erfc.value(X_CRIT) = 0.5}, and</li> + * <li>{@code Erfc.value(Math.nextUp(X_CRIT) < 0.5}</li> + * </ul> + */ + private static final double X_CRIT = 0.4769362762044697; + + /** + * The implementation uses either {@link Erf} or {@link Erfc}, + * depending on which provides the most precise result. + * + * @param x1 First value. + * @param x2 Second value. + * @return {@link Erf#value(double) Erf.value(x2) - Erf.value(x1)}. + */ + public static double value(double x1, + double x2) { + if (x1 > x2) { + return -value(x2, x1); + } else { + if (x1 < -X_CRIT) { + if (x2 < 0) { + return Erfc.value(-x2) - Erfc.value(-x1); + } else { + return Erf.value(x2) - Erf.value(x1); + } + } else { + if (x2 > X_CRIT && + x1 > 0) { + return Erfc.value(x1) - Erfc.value(x2); + } else { + return Erf.value(x2) - Erf.value(x1); + } + } + } + } +} http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/4de442f6/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erfc.java ---------------------------------------------------------------------- diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erfc.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erfc.java new file mode 100644 index 0000000..674f582 --- /dev/null +++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erfc.java @@ -0,0 +1,53 @@ +/* + * 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.numbers.gamma; + +/** + * <a href="http://mathworld.wolfram.com/Erfc.html";>Complementary error function</a>. + */ +public class Erfc { + /** + * <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 at {@code double} precision, so the appropriate extreme + * value is returned. + * </p> + * + * @param x Value. + * @return the complementary error function. + * @throws ArithmeticExceptionException if the algorithm fails to converge. + * + * @see RegularizedGamma.Q#value(double, double, double, int) + */ + public static double value(double x) { + if (Math.abs(x) > 40) { + return x > 0 ? 0 : 2; + } + final double ret = RegularizedGamma.Q.value(0.5, x * x, 1e-15, 10000); + return x < 0 ? + 2 - ret : + ret; + } +} + http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/4de442f6/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/InverseErf.java ---------------------------------------------------------------------- diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/InverseErf.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/InverseErf.java new file mode 100644 index 0000000..b149fa5 --- /dev/null +++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/InverseErf.java @@ -0,0 +1,124 @@ +/* + * 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.numbers.gamma; + +/** + * Inverse of the <a href="http://mathworld.wolfram.com/Erf.html";>error function</a>. + * <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> + */ +public class InverseErf { + /** + * Returns the inverse error function. + * + * @param x Value. + * @return t such that {@code x =} {@link Erf#value(double) Erf.value(t)}. + */ + public static double value(final double x) { + // Beware that the logarithm argument must be + // commputed as (1 - x) * (1 + x), + // it must NOT be simplified as 1 - x * x as this + // would induce rounding errors near the boundaries +/-1 + double w = -Math.log((1 - x) * (1 + 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 = Math.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 = Math.sqrt(w) - 5; + 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; + } +} + http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/4de442f6/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/InverseErfc.java ---------------------------------------------------------------------- diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/InverseErfc.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/InverseErfc.java new file mode 100644 index 0000000..e1a4359 --- /dev/null +++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/InverseErfc.java @@ -0,0 +1,39 @@ +/* + * 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.numbers.gamma; + +/** + * Inverse of the <a href="http://mathworld.wolfram.com/Erfc.html";>complementary error function</a>. + * <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> + */ +public class InverseErfc { + /** + * Returns the inverse complementary error function. + * + * @param x Value. + * @return t such that {@code x =} {@link Erfc#value(double) Erfc.value(t)}. + */ + public static double value(double x) { + return InverseErf.value(1 - x); + } +} http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/4de442f6/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/ErfDifferenceTest.java ---------------------------------------------------------------------- diff --git a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/ErfDifferenceTest.java b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/ErfDifferenceTest.java new file mode 100644 index 0000000..8e9afad --- /dev/null +++ b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/ErfDifferenceTest.java @@ -0,0 +1,43 @@ +/* + * 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.numbers.gamma; + +import org.junit.Assert; +import org.junit.Test; + +/** + * Tests for {@link ErfDifference}. + */ +public class ErfDifferenceTest { + /** + * Test the implementation of ErfDifference.value(double, double) for consistency + * with results obtained from Erf.value(double) and Erfc.value(double). + */ + @Test + public void testTwoArgumentErf() { + final double[] xi = new double[] { -2, -1, -0.9, -0.1, 0, 0.1, 0.9, 1, 2 }; + for(double x1 : xi) { + for(double x2 : xi) { + double a = ErfDifference.value(x1, x2); + double b = Erf.value(x2) - Erf.value(x1); + double c = Erfc.value(x1) - Erfc.value(x2); + Assert.assertEquals(a, b, 1e-15); + Assert.assertEquals(a, c, 1e-15); + } + } + } +} http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/4de442f6/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/ErfTest.java ---------------------------------------------------------------------- diff --git a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/ErfTest.java b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/ErfTest.java new file mode 100644 index 0000000..11fff47 --- /dev/null +++ b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/ErfTest.java @@ -0,0 +1,140 @@ +/* + * 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.numbers.gamma; + +import org.junit.Assert; +import org.junit.Test; + +/** + * Tests for {@link Erf}. + */ +public class ErfTest { + @Test + public void testErf0() { + double actual = Erf.value(0); + double expected = 0; + Assert.assertEquals(expected, actual, 1e-15); + Assert.assertEquals(1 - expected, Erfc.value(0), 1e-15); + } + + @Test + public void testErf1960() { + double x = 1.960 / Math.sqrt(2); + double actual = Erf.value(x); + double expected = 0.95; + Assert.assertEquals(expected, actual, 1e-5); + Assert.assertEquals(1 - actual, Erfc.value(x), 1e-15); + + actual = Erf.value(-x); + expected = -expected; + Assert.assertEquals(expected, actual, 1e-5); + Assert.assertEquals(1 - actual, Erfc.value(-x), 1e-15); + } + + @Test + public void testErf2576() { + double x = 2.576 / Math.sqrt(2); + double actual = Erf.value(x); + double expected = 0.99; + Assert.assertEquals(expected, actual, 1e-5); + Assert.assertEquals(1 - actual, Erfc.value(x), 1e-15); + + actual = Erf.value(-x); + expected = -expected; + Assert.assertEquals(expected, actual, 1e-5); + Assert.assertEquals(1 - actual, Erfc.value(-x), 1e-15); + } + + @Test + public void testErf2807() { + double x = 2.807 / Math.sqrt(2); + double actual = Erf.value(x); + double expected = 0.995; + Assert.assertEquals(expected, actual, 1e-5); + Assert.assertEquals(1 - actual, Erfc.value(x), 1e-15); + + actual = Erf.value(-x); + expected = -expected; + Assert.assertEquals(expected, actual, 1e-5); + Assert.assertEquals(1 - actual, Erfc.value(-x), 1e-15); + } + + @Test + public void testErf3291() { + double x = 3.291 / Math.sqrt(2); + double actual = Erf.value(x); + double expected = 0.999; + Assert.assertEquals(expected, actual, 1e-5); + Assert.assertEquals(1 - expected, Erfc.value(x), 1e-5); + + actual = Erf.value(-x); + expected = -expected; + Assert.assertEquals(expected, actual, 1e-5); + Assert.assertEquals(1 - expected, Erfc.value(-x), 1e-5); + } + + /** + * MATH-301, MATH-456 + */ + @Test + public void testLargeValues() { + for (int i = 1; i < 200; i *= 10) { + double result = Erf.value(i); + Assert.assertFalse(Double.isNaN(result)); + Assert.assertTrue(result > 0 && result <= 1); + result = Erf.value(-i); + Assert.assertFalse(Double.isNaN(result)); + Assert.assertTrue(result >= -1 && result < 0); + result = Erfc.value(i); + Assert.assertFalse(Double.isNaN(result)); + Assert.assertTrue(result >= 0 && result < 1); + result = Erfc.value(-i); + Assert.assertFalse(Double.isNaN(result)); + Assert.assertTrue(result >= 1 && result <= 2); + } + Assert.assertEquals(-1, Erf.value(Double.NEGATIVE_INFINITY), 0); + Assert.assertEquals(1, Erf.value(Double.POSITIVE_INFINITY), 0); + Assert.assertEquals(2, Erfc.value(Double.NEGATIVE_INFINITY), 0); + Assert.assertEquals(0, Erfc.value(Double.POSITIVE_INFINITY), 0); + } + + /** + * Compare Erf.value 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 = -10; + for (int i = 0; i < 41; i++) { + Assert.assertEquals(gnuValues[i], Erf.value(x), tol); + x += 0.5d; + } + } +} http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/4de442f6/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/ErfcTest.java ---------------------------------------------------------------------- diff --git a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/ErfcTest.java b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/ErfcTest.java new file mode 100644 index 0000000..e68ee18 --- /dev/null +++ b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/ErfcTest.java @@ -0,0 +1,85 @@ +/* + * 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.numbers.gamma; + +import org.junit.Assert; +import org.junit.Test; + +/** + * Tests for {@link Erfc}. + */ +public class ErfcTest { + /** + * Compare 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 = -10; + for (int i = 0; i < 41; i++) { + Assert.assertEquals(gnuValues[i], Erfc.value(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 * Erfc.value(ref[i][0] / Math.sqrt(2)); + Assert.assertEquals(ref[i][1], result, 1e-15); + Assert.assertEquals(1, ref[i][1] / result, 1e-13); + } + } +} http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/4de442f6/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/InverseErfTest.java ---------------------------------------------------------------------- diff --git a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/InverseErfTest.java b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/InverseErfTest.java new file mode 100644 index 0000000..e22ee5e --- /dev/null +++ b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/InverseErfTest.java @@ -0,0 +1,48 @@ +/* + * 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.numbers.gamma; + +import org.junit.Assert; +import org.junit.Test; + +/** + * Tests for {@link InverseErf}. + */ +public class InverseErfTest { + @Test + public void testErfInvNaN() { + Assert.assertTrue(Double.isNaN(InverseErf.value(-1.001))); + Assert.assertTrue(Double.isNaN(InverseErf.value(+1.001))); + } + + @Test + public void testErfInvInfinite() { + Assert.assertTrue(Double.isInfinite(InverseErf.value(-1))); + Assert.assertTrue(InverseErf.value(-1) < 0); + Assert.assertTrue(Double.isInfinite(InverseErf.value(+1))); + Assert.assertTrue(InverseErf.value(+1) > 0); + } + + @Test + public void testErfInv() { + for (double x = -5.9; x < 5.9; x += 0.01) { + final double y = Erf.value(x); + final double dydx = 2 * Math.exp(-x * x) / Math.sqrt(Math.PI); + Assert.assertEquals(x, InverseErf.value(y), 1.0e-15 / dydx); + } + } +} http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/4de442f6/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/InverseErfcTest.java ---------------------------------------------------------------------- diff --git a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/InverseErfcTest.java b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/InverseErfcTest.java new file mode 100644 index 0000000..79c5c11 --- /dev/null +++ b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/InverseErfcTest.java @@ -0,0 +1,48 @@ +/* + * 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.numbers.gamma; + +import org.junit.Assert; +import org.junit.Test; + +/** + * Tests for {@link InverseErfc}. + */ +public class InverseErfcTest { + @Test + public void testErfcInvNaN() { + Assert.assertTrue(Double.isNaN(InverseErfc.value(-0.001))); + Assert.assertTrue(Double.isNaN(InverseErfc.value(+2.001))); + } + + @Test + public void testErfcInvInfinite() { + Assert.assertTrue(Double.isInfinite(InverseErfc.value(-0))); + Assert.assertTrue(InverseErfc.value( 0) > 0); + Assert.assertTrue(Double.isInfinite(InverseErfc.value(+2))); + Assert.assertTrue(InverseErfc.value(+2) < 0); + } + + @Test + public void testErfcInv() { + for (double x = -5.85; x < 5.9; x += 0.01) { + final double y = Erfc.value(x); + final double dydxAbs = 2 * Math.exp(-x * x) / Math.sqrt(Math.PI); + Assert.assertEquals(x, InverseErfc.value(y), 1.0e-15 / dydxAbs); + } + } +}
