This is an automated email from the ASF dual-hosted git repository.
erans pushed a commit to branch master
in repository https://gitbox.apache.org/repos/asf/commons-numbers.git
commit 151ea6bbbd9ecbaf5948213adfda77977cae8400
Author: Gilles Sadowski <gil...@harfang.homelinux.org>
AuthorDate: Tue Jun 4 03:53:43 2019 +0200
NUMBERS-112: Implement Brent's algorithm for finding the zero of a function.
New maven module created.
Code copied and adapted from "Commons Statistics" (where it was ported from
"Commons Math").
---
commons-numbers-rootfinder/LICENSE.txt | 201 ++++++++++++++++
commons-numbers-rootfinder/NOTICE.txt | 5 +
commons-numbers-rootfinder/README.md | 98 ++++++++
commons-numbers-rootfinder/pom.xml | 52 ++++
.../commons/numbers/rootfinder/BrentSolver.java | 239 ++++++++++++++++++
.../numbers/rootfinder/SolverException.java | 55 +++++
.../commons/numbers/rootfinder/package-info.java | 20 ++
.../src/site/resources/profile.jacoco | 17 ++
commons-numbers-rootfinder/src/site/site.xml | 35 +++
commons-numbers-rootfinder/src/site/xdoc/index.xml | 40 ++++
.../numbers/rootfinder/BrentSolverTest.java | 266 +++++++++++++++++++++
.../numbers/rootfinder/MonitoredFunction.java | 52 ++++
.../numbers/rootfinder/QuinticFunction.java | 29 +++
.../org/apache/commons/numbers/rootfinder/Sin.java | 29 +++
pom.xml | 1 +
15 files changed, 1139 insertions(+)
diff --git a/commons-numbers-rootfinder/LICENSE.txt
b/commons-numbers-rootfinder/LICENSE.txt
new file mode 100644
index 0000000..261eeb9
--- /dev/null
+++ b/commons-numbers-rootfinder/LICENSE.txt
@@ -0,0 +1,201 @@
+ Apache License
+ Version 2.0, January 2004
+ http://www.apache.org/licenses/
+
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+ 7. Disclaimer of Warranty. Unless required by applicable law or
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diff --git a/commons-numbers-rootfinder/NOTICE.txt
b/commons-numbers-rootfinder/NOTICE.txt
new file mode 100644
index 0000000..b4ce061
--- /dev/null
+++ b/commons-numbers-rootfinder/NOTICE.txt
@@ -0,0 +1,5 @@
+Apache Commons Numbers
+Copyright 2001-2019 The Apache Software Foundation
+
+This product includes software developed at
+The Apache Software Foundation (http://www.apache.org/).
diff --git a/commons-numbers-rootfinder/README.md
b/commons-numbers-rootfinder/README.md
new file mode 100644
index 0000000..aa902d6
--- /dev/null
+++ b/commons-numbers-rootfinder/README.md
@@ -0,0 +1,98 @@
+<!---
+ 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.
+-->
+<!---
+ +======================================================================+
+ |**** ****|
+ |**** THIS FILE IS GENERATED BY THE COMMONS BUILD PLUGIN ****|
+ |**** DO NOT EDIT DIRECTLY ****|
+ |**** ****|
+ +======================================================================+
+ | TEMPLATE FILE: readme-md-template.md |
+ | commons-build-plugin/trunk/src/main/resources/commons-xdoc-templates |
+ +======================================================================+
+ | |
+ | 1) Re-generate using: mvn commons:readme-md |
+ | |
+ | 2) Set the following properties in the component's pom: |
+ | - commons.componentid (required, alphabetic, lower case) |
+ | - commons.release.version (required) |
+ | |
+ | 3) Example Properties |
+ | |
+ | <properties> |
+ | <commons.componentid>math</commons.componentid> |
+ | <commons.release.version>1.2</commons.release.version> |
+ | </properties> |
+ | |
+ +======================================================================+
+--->
+Apache Commons Numbers Root Finder
+===================
+
+Root finding utilities.
+
+Documentation
+-------------
+
+More information can be found on the
[homepage](https://commons.apache.org/proper/commons-numbers).
+The
[JavaDoc](https://commons.apache.org/proper/commons-numbers/javadocs/api-release)
can be browsed.
+Questions related to the usage of Apache Commons Numbers Root Finder should be
posted to the [user mailing list][ml].
+
+Where can I get the latest release?
+-----------------------------------
+You can download source and binaries from our [download
page](https://commons.apache.org/proper/commons-numbers/download_numbers.cgi).
+
+Alternatively you can pull it from the central Maven repositories:
+
+```xml
+<dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-rootfinder</artifactId>
+ <version>1.0</version>
+</dependency>
+```
+
+Contributing
+------------
+
+We accept PRs via github. The [developer mailing list][ml] is the main channel
of communication for contributors.
+There are some guidelines which will make applying PRs easier for us:
++ No tabs! Please use spaces for indentation.
++ Respect the code style.
++ Create minimal diffs - disable on save actions like reformat source code or
organize imports. If you feel the source code should be reformatted create a
separate PR for this change.
++ Provide JUnit tests for your changes and make sure your changes don't break
any existing tests by running ```mvn clean test```.
+
+If you plan to contribute on a regular basis, please consider filing a
[contributor license agreement](https://www.apache.org/licenses/#clas).
+You can learn more about contributing via GitHub in our [contribution
guidelines](CONTRIBUTING.md).
+
+License
+-------
+Code is under the [Apache Licence
v2](https://www.apache.org/licenses/LICENSE-2.0.txt).
+
+Donations
+---------
+You like Apache Commons Numbers Root Finder? Then [donate back to the
ASF](https://www.apache.org/foundation/contributing.html) to support the
development.
+
+Additional Resources
+--------------------
+
++ [Apache Commons Homepage](https://commons.apache.org/)
++ [Apache Bugtracker (JIRA)](https://issues.apache.org/jira/)
++ [Apache Commons Twitter Account](https://twitter.com/ApacheCommons)
++ #apachecommons IRC channel on freenode.org
+
+[ml]:https://commons.apache.org/mail-lists.html
diff --git a/commons-numbers-rootfinder/pom.xml
b/commons-numbers-rootfinder/pom.xml
new file mode 100644
index 0000000..90465c8
--- /dev/null
+++ b/commons-numbers-rootfinder/pom.xml
@@ -0,0 +1,52 @@
+<?xml version="1.0"?>
+<!--
+ 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.
+-->
+<project xsi:schemaLocation="http://maven.apache.org/POM/4.0.0
http://maven.apache.org/xsd/maven-4.0.0.xsd";
+ xmlns="http://maven.apache.org/POM/4.0.0";
+ xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance";>
+ <modelVersion>4.0.0</modelVersion>
+
+ <parent>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-parent</artifactId>
+ <version>1.0-SNAPSHOT</version>
+ </parent>
+
+ <artifactId>commons-numbers-root-finder</artifactId>
+ <name>Apache Commons Numbers Root Finder</name>
+
+ <description>Root finding utilities.</description>
+
+ <properties>
+ <!-- The Java Module System Name -->
+
<commons.module.name>org.apache.commons.numbers.rootfinder</commons.module.name>
+ <!-- This value must reflect the current name of the base package. -->
+
<commons.osgi.symbolicName>org.apache.commons.numbers.rootfinder</commons.osgi.symbolicName>
+ <!-- OSGi -->
+
<commons.osgi.export>org.apache.commons.numbers.rootfinder</commons.osgi.export>
+ <!-- Workaround to avoid duplicating config files. -->
+ <numbers.parent.dir>${basedir}/..</numbers.parent.dir>
+ </properties>
+
+ <dependencies>
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-core</artifactId>
+ </dependency>
+ </dependencies>
+
+</project>
diff --git
a/commons-numbers-rootfinder/src/main/java/org/apache/commons/numbers/rootfinder/BrentSolver.java
b/commons-numbers-rootfinder/src/main/java/org/apache/commons/numbers/rootfinder/BrentSolver.java
new file mode 100644
index 0000000..493985f
--- /dev/null
+++
b/commons-numbers-rootfinder/src/main/java/org/apache/commons/numbers/rootfinder/BrentSolver.java
@@ -0,0 +1,239 @@
+/*
+ * 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.rootfinder;
+
+import java.util.function.DoubleUnaryOperator;
+import org.apache.commons.numbers.core.Precision;
+
+/**
+ * This class implements the <a
href="http://mathworld.wolfram.com/BrentsMethod.html";>
+ * Brent algorithm</a> for finding zeros of real univariate functions.
+ * The function should be continuous but not necessarily smooth.
+ * The {@code solve} method returns a zero {@code x} of the function {@code f}
+ * in the given interval {@code [a, b]} to within a tolerance
+ * {@code 2 eps abs(x) + t} where {@code eps} is the relative accuracy and
+ * {@code t} is the absolute accuracy.
+ * <p>The given interval must bracket the root.</p>
+ * <p>
+ * The reference implementation is given in chapter 4 of
+ * <blockquote>
+ * <b>Algorithms for Minimization Without Derivatives</b>,
+ * <em>Richard P. Brent</em>,
+ * Dover, 2002
+ * </blockquote>
+ */
+public class BrentSolver {
+ /** Relative accuracy. */
+ private final double relativeAccuracy;
+ /** Absolutee accuracy. */
+ private final double absoluteAccuracy;
+ /** Function accuracy. */
+ private final double functionValueAccuracy;
+
+ /**
+ * Construct a solver.
+ *
+ * @param relativeAccuracy Relative accuracy.
+ * @param absoluteAccuracy Absolute accuracy.
+ * @param functionValueAccuracy Function value accuracy.
+ */
+ public BrentSolver(double relativeAccuracy,
+ double absoluteAccuracy,
+ double functionValueAccuracy) {
+ this.relativeAccuracy = relativeAccuracy;
+ this.absoluteAccuracy = absoluteAccuracy;
+ this.functionValueAccuracy = functionValueAccuracy;
+ }
+
+ /**
+ * Search the function's zero within the given interval.
+ *
+ * @param func Function to solve.
+ * @param min Lower bound.
+ * @param max Upper bound.
+ * @return the root.
+ */
+ public double findRoot(DoubleUnaryOperator func,
+ double min,
+ double max) {
+ return findRoot(func, min, 0.5 * (min + max), max);
+ }
+
+ /**
+ * Search the function's zero within the given interval,
+ * starting from the given estimate.
+ *
+ * @param func Function to solve.
+ * @param min Lower bound.
+ * @param initial Initial guess.
+ * @param max Upper bound.
+ * @return the root.
+ */
+ public double findRoot(DoubleUnaryOperator func,
+ double min,
+ double initial,
+ double max) {
+ if (min > max) {
+ throw new SolverException(SolverException.TOO_LARGE, min, max);
+ }
+ if (initial < min ||
+ initial > max) {
+ throw new SolverException(SolverException.OUT_OF_RANGE, initial,
min, max);
+ }
+
+ // Return the initial guess if it is good enough.
+ final double yInitial = func.applyAsDouble(initial);
+ if (Math.abs(yInitial) <= functionValueAccuracy) {
+ return initial;
+ }
+
+ // Return the first endpoint if it is good enough.
+ final double yMin = func.applyAsDouble(min);
+ if (Math.abs(yMin) <= functionValueAccuracy) {
+ return min;
+ }
+
+ // Reduce interval if min and initial bracket the root.
+ if (yInitial * yMin < 0) {
+ return brent(func, min, initial, yMin, yInitial);
+ }
+
+ // Return the second endpoint if it is good enough.
+ final double yMax = func.applyAsDouble(max);
+ if (Math.abs(yMax) <= functionValueAccuracy) {
+ return max;
+ }
+
+ // Reduce interval if initial and max bracket the root.
+ if (yInitial * yMax < 0) {
+ return brent(func, initial, max, yInitial, yMax);
+ }
+
+ throw new SolverException(SolverException.BRACKETING, min, yMin, max,
yMax);
+ }
+
+ /**
+ * Search for a zero inside the provided interval.
+ * This implementation is based on the algorithm described at page 58 of
+ * the book
+ * <blockquote>
+ * <b>Algorithms for Minimization Without Derivatives</b>,
+ * <i>Richard P. Brent</i>,
+ * Dover 0-486-41998-3
+ * </blockquote>
+ *
+ * @param func Function to solve.
+ * @param lo Lower bound of the search interval.
+ * @param hi Higher bound of the search interval.
+ * @param fLo Function value at the lower bound of the search interval.
+ * @param fHi Function value at the higher bound of the search interval.
+ * @return the value where the function is zero.
+ */
+ private double brent(DoubleUnaryOperator func,
+ double lo, double hi,
+ double fLo, double fHi) {
+ double a = lo;
+ double fa = fLo;
+ double b = hi;
+ double fb = fHi;
+ double c = a;
+ double fc = fa;
+ double d = b - a;
+ double e = d;
+
+ final double t = absoluteAccuracy;
+ final double eps = relativeAccuracy;
+
+ while (true) {
+ if (Math.abs(fc) < Math.abs(fb)) {
+ a = b;
+ b = c;
+ c = a;
+ fa = fb;
+ fb = fc;
+ fc = fa;
+ }
+
+ final double tol = 2 * eps * Math.abs(b) + t;
+ final double m = 0.5 * (c - b);
+
+ if (Math.abs(m) <= tol ||
+ Precision.equals(fb, 0)) {
+ return b;
+ }
+ if (Math.abs(e) < tol ||
+ Math.abs(fa) <= Math.abs(fb)) {
+ // Force bisection.
+ d = m;
+ e = d;
+ } else {
+ double s = fb / fa;
+ double p;
+ double q;
+ // The equality test (a == c) is intentional,
+ // it is part of the original Brent's method and
+ // it should NOT be replaced by proximity test.
+ if (a == c) {
+ // Linear interpolation.
+ p = 2 * m * s;
+ q = 1 - s;
+ } else {
+ // Inverse quadratic interpolation.
+ q = fa / fc;
+ final double r = fb / fc;
+ p = s * (2 * m * q * (q - r) - (b - a) * (r - 1));
+ q = (q - 1) * (r - 1) * (s - 1);
+ }
+ if (p > 0) {
+ q = -q;
+ } else {
+ p = -p;
+ }
+ s = e;
+ e = d;
+ if (p >= 1.5 * m * q - Math.abs(tol * q) ||
+ p >= Math.abs(0.5 * s * q)) {
+ // Inverse quadratic interpolation gives a value
+ // in the wrong direction, or progress is slow.
+ // Fall back to bisection.
+ d = m;
+ e = d;
+ } else {
+ d = p / q;
+ }
+ }
+ a = b;
+ fa = fb;
+
+ if (Math.abs(d) > tol) {
+ b += d;
+ } else if (m > 0) {
+ b += tol;
+ } else {
+ b -= tol;
+ }
+ fb = func.applyAsDouble(b);
+ if ((fb > 0 && fc > 0) ||
+ (fb <= 0 && fc <= 0)) {
+ c = a;
+ fc = fa;
+ d = b - a;
+ e = d;
+ }
+ }
+ }
+}
diff --git
a/commons-numbers-rootfinder/src/main/java/org/apache/commons/numbers/rootfinder/SolverException.java
b/commons-numbers-rootfinder/src/main/java/org/apache/commons/numbers/rootfinder/SolverException.java
new file mode 100644
index 0000000..c35f2fe
--- /dev/null
+++
b/commons-numbers-rootfinder/src/main/java/org/apache/commons/numbers/rootfinder/SolverException.java
@@ -0,0 +1,55 @@
+/*
+ * 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.rootfinder;
+
+import java.text.MessageFormat;
+
+/**
+ * Package private exception class with constants for frequently used messages.
+ */
+class SolverException extends IllegalArgumentException {
+ /** Error message for "too large" condition. */
+ static final String TOO_LARGE = "{0} > {1}";
+ /** Error message for "out of range" condition. */
+ static final String OUT_OF_RANGE = "{0} is out of range [{1}, {2}]";
+ /** Error message for "failed bracketing" condition. */
+ static final String BRACKETING = "No bracketing: f({0})={1}, f({2})={3}";
+
+ /** Serializable version identifier. */
+ private static final long serialVersionUID = 20190602L;
+
+ /** Arguments for formatting the message. */
+ private final Object[] formatArguments;
+
+ /**
+ * Create an exception where the message is constructed by applying
+ * the {@code format()} method from {@code java.text.MessageFormat}.
+ *
+ * @param message the exception message with replaceable parameters
+ * @param formatArguments the arguments for formatting the message
+ */
+ SolverException(String message, Object... formatArguments) {
+ super(message);
+ this.formatArguments = formatArguments;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public String getMessage() {
+ return MessageFormat.format(super.getMessage(), formatArguments);
+ }
+}
diff --git
a/commons-numbers-rootfinder/src/main/java/org/apache/commons/numbers/rootfinder/package-info.java
b/commons-numbers-rootfinder/src/main/java/org/apache/commons/numbers/rootfinder/package-info.java
new file mode 100644
index 0000000..5fb3a3a
--- /dev/null
+++
b/commons-numbers-rootfinder/src/main/java/org/apache/commons/numbers/rootfinder/package-info.java
@@ -0,0 +1,20 @@
+/*
+ * 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.
+ */
+/**
+ * Root finding utilities.
+ */
+package org.apache.commons.numbers.rootfinder;
diff --git a/commons-numbers-rootfinder/src/site/resources/profile.jacoco
b/commons-numbers-rootfinder/src/site/resources/profile.jacoco
new file mode 100644
index 0000000..a12755f
--- /dev/null
+++ b/commons-numbers-rootfinder/src/site/resources/profile.jacoco
@@ -0,0 +1,17 @@
+# 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.
+# -----------------------------------------------------------------------------
+#
+# Empty file used to automatically trigger JaCoCo profile from commons parent
pom
diff --git a/commons-numbers-rootfinder/src/site/site.xml
b/commons-numbers-rootfinder/src/site/site.xml
new file mode 100644
index 0000000..454d015
--- /dev/null
+++ b/commons-numbers-rootfinder/src/site/site.xml
@@ -0,0 +1,35 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<!--
+ 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.
+-->
+<project name="Numbers">
+ <bannerRight>
+ <name>Apache Commons Numbers</name>
+ <src>/images/commons_numbers.small.png</src>
+ <href>/index.html</href>
+ </bannerRight>
+
+ <body>
+ <menu name="Numbers Root Finder">
+ <item name="Overview" href="index.html"/>
+ <item name="Latest API docs (development)"
+ href="apidocs/index.html"/>
+ <!--item name="Javadoc (1.0 release)"
+
href="http://commons.apache.org/rng/commons-numbers-rootfinder/javadocs/api-1.0/index.html"/-->
+ </menu>
+
+ </body>
+</project>
diff --git a/commons-numbers-rootfinder/src/site/xdoc/index.xml
b/commons-numbers-rootfinder/src/site/xdoc/index.xml
new file mode 100644
index 0000000..8979130
--- /dev/null
+++ b/commons-numbers-rootfinder/src/site/xdoc/index.xml
@@ -0,0 +1,40 @@
+<?xml version="1.0"?>
+
+<!--
+ 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.
+ -->
+
+<document>
+
+ <properties>
+ <title>Commons Numbers Root Finder</title>
+ </properties>
+
+ <body>
+
+ <section name="Apache Commons Numbers: Number types" href="summary">
+ <p>
+ Commons Numbers provides utilities such as complex numbers and
fractions.
+ </p>
+
+ <p>
+ The "rootfinder" module contains utilities for finding the zero of a
function.
+ </p>
+ </section>
+
+ </body>
+
+</document>
diff --git
a/commons-numbers-rootfinder/src/test/java/org/apache/commons/numbers/rootfinder/BrentSolverTest.java
b/commons-numbers-rootfinder/src/test/java/org/apache/commons/numbers/rootfinder/BrentSolverTest.java
new file mode 100644
index 0000000..b414f6a
--- /dev/null
+++
b/commons-numbers-rootfinder/src/test/java/org/apache/commons/numbers/rootfinder/BrentSolverTest.java
@@ -0,0 +1,266 @@
+/*
+ * 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.rootfinder;
+
+import java.util.function.DoubleUnaryOperator;
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * Test cases for the {@link BrentSolver} class.
+ */
+public class BrentSolverTest {
+ private static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6;
+ private static final double DEFAULT_RELATIVE_ACCURACY = 1e-14;
+ private static final double DEFAULT_FUNCTION_ACCURACY = 1e-15;
+
+ @Test
+ public void testSinZero() {
+ // The sinus function is behaved well around the root at pi. The second
+ // order derivative is zero, which means linar approximating methods
will
+ // still converge quadratically.
+ final DoubleUnaryOperator func = new Sin();
+ final BrentSolver solver = new BrentSolver(DEFAULT_ABSOLUTE_ACCURACY,
+ DEFAULT_RELATIVE_ACCURACY,
+ DEFAULT_FUNCTION_ACCURACY);
+
+ double result;
+ MonitoredFunction f;
+
+ // Somewhat benign interval. The function is monotonous.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 3, 4);
+ Assert.assertEquals(result, Math.PI, DEFAULT_ABSOLUTE_ACCURACY);
+ Assert.assertTrue(f.getCallsCount() <= 7);
+
+ // Larger and somewhat less benign interval. The function is grows
first.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 1, 4);
+ Assert.assertEquals(result, Math.PI, DEFAULT_ABSOLUTE_ACCURACY);
+ Assert.assertTrue(f.getCallsCount() <= 8);
+ }
+
+ @Test
+ public void testQuinticZero() {
+ // The quintic function has zeros at 0, +-0.5 and +-1.
+ // Around the root of 0 the function is well behaved, with a second
derivative
+ // of zero a 0.
+ // The other roots are less well to find, in particular the root at 1,
because
+ // the function grows fast for x>1.
+ // The function has extrema (first derivative is zero) at 0.27195613
and 0.82221643,
+ // intervals containing these values are harder for the solvers.
+ final DoubleUnaryOperator func = new QuinticFunction();
+ final BrentSolver solver = new BrentSolver(DEFAULT_ABSOLUTE_ACCURACY,
+ DEFAULT_RELATIVE_ACCURACY,
+ DEFAULT_FUNCTION_ACCURACY);
+
+ double result;
+ MonitoredFunction f;
+
+ // Symmetric bracket around 0. Test whether solvers can handle hitting
+ // the root in the first iteration.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, -0.2, 0.2);
+ Assert.assertEquals(result, 0, DEFAULT_ABSOLUTE_ACCURACY);
+ Assert.assertTrue(f.getCallsCount() <= 3);
+
+ // 1 iterations on i586 JDK 1.4.1.
+ // Asymmetric bracket around 0. Contains extremum.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, -0.1, 0.3);
+ Assert.assertEquals(result, 0, DEFAULT_ABSOLUTE_ACCURACY);
+ // 5 iterations on i586 JDK 1.4.1.
+ Assert.assertTrue(f.getCallsCount() <= 7);
+
+ // Large bracket around 0. Contains two extrema.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, -0.3, 0.45);
+ Assert.assertEquals(result, 0, DEFAULT_ABSOLUTE_ACCURACY);
+ // 6 iterations on i586 JDK 1.4.1.
+ Assert.assertTrue(f.getCallsCount() <= 8);
+
+ // Benign bracket around 0.5, function is monotonous.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 0.3, 0.7);
+ Assert.assertEquals(0.5, result, DEFAULT_ABSOLUTE_ACCURACY);
+ // 6 iterations on i586 JDK 1.4.1.
+ Assert.assertTrue(f.getCallsCount() <= 9);
+
+ // Less benign bracket around 0.5, contains one extremum.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 0.2, 0.6);
+ Assert.assertEquals(0.5, result, DEFAULT_ABSOLUTE_ACCURACY);
+ Assert.assertTrue(f.getCallsCount() <= 10);
+
+ // Large, less benign bracket around 0.5, contains both extrema.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 0.05, 0.95);
+ Assert.assertEquals(0.5, result, DEFAULT_ABSOLUTE_ACCURACY);
+ Assert.assertTrue(f.getCallsCount() <= 11);
+
+ // Relatively benign bracket around 1, function is monotonous. Fast
growth for x>1
+ // is still a problem.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 0.85, 1.25);
+ Assert.assertEquals(1.0, result, DEFAULT_ABSOLUTE_ACCURACY);
+ Assert.assertTrue(f.getCallsCount() <= 11);
+
+ // Less benign bracket around 1 with extremum.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 0.8, 1.2);
+ Assert.assertEquals(1.0, result, DEFAULT_ABSOLUTE_ACCURACY);
+ Assert.assertTrue(f.getCallsCount() <= 11);
+
+ // Large bracket around 1. Monotonous.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 0.85, 1.75);
+ Assert.assertEquals(1.0, result, DEFAULT_ABSOLUTE_ACCURACY);
+ Assert.assertTrue(f.getCallsCount() <= 13);
+
+ // Large bracket around 1. Interval contains extremum.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 0.55, 1.45);
+ Assert.assertEquals(1.0, result, DEFAULT_ABSOLUTE_ACCURACY);
+ Assert.assertTrue(f.getCallsCount() <= 10);
+ }
+
+ @Test
+ public void testTooManyCalls() {
+ final DoubleUnaryOperator func = new QuinticFunction();
+ final BrentSolver solver = new BrentSolver(DEFAULT_ABSOLUTE_ACCURACY,
+ DEFAULT_RELATIVE_ACCURACY,
+ DEFAULT_FUNCTION_ACCURACY);
+
+ double result;
+ MonitoredFunction f;
+
+ // Very large bracket around 1 for testing fast growth behaviour.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 0.85, 5);
+ Assert.assertEquals(1.0, result, DEFAULT_ABSOLUTE_ACCURACY);
+ Assert.assertTrue(f.getCallsCount() <= 15);
+
+ try {
+ f = new MonitoredFunction(func, 10);
+ result = solver.findRoot(f, 0.85, 5);
+ Assert.fail("Expected too many calls condition");
+ } catch (IllegalStateException ex) {
+ // Expected.
+ // Ensure expected error condition.
+ Assert.assertFalse(ex.getMessage().indexOf("too many calls") ==
-1);
+ }
+ }
+
+ @Test
+ public void testRootEndpoints() {
+ final DoubleUnaryOperator f = new Sin();
+ final BrentSolver solver = new BrentSolver(DEFAULT_ABSOLUTE_ACCURACY,
+ DEFAULT_RELATIVE_ACCURACY,
+ DEFAULT_FUNCTION_ACCURACY);
+
+ // Endpoint is root.
+ double result = solver.findRoot(f, Math.PI, 4);
+ Assert.assertEquals(Math.PI, result, DEFAULT_ABSOLUTE_ACCURACY);
+
+ result = solver.findRoot(f, 3, Math.PI);
+ Assert.assertEquals(Math.PI, result, DEFAULT_ABSOLUTE_ACCURACY);
+
+ result = solver.findRoot(f, Math.PI, 3.5, 4);
+ Assert.assertEquals(Math.PI, result, DEFAULT_ABSOLUTE_ACCURACY);
+
+ result = solver.findRoot(f, 3, 3.07, Math.PI);
+ Assert.assertEquals(Math.PI, result, DEFAULT_ABSOLUTE_ACCURACY);
+ }
+
+ @Test
+ public void testBadEndpoints() {
+ final DoubleUnaryOperator f = new Sin();
+ final BrentSolver solver = new BrentSolver(DEFAULT_ABSOLUTE_ACCURACY,
+ DEFAULT_RELATIVE_ACCURACY,
+ DEFAULT_FUNCTION_ACCURACY);
+ try { // Bad interval.
+ solver.findRoot(f, 1, -1);
+ Assert.fail("Expecting bad interval condition");
+ } catch (SolverException ex) {
+ // Ensure expected error condition.
+ Assert.assertFalse(ex.getMessage().indexOf(" > ") == -1);
+ }
+ try { // No bracketing.
+ solver.findRoot(f, 1, 1.5);
+ Assert.fail("Expecting non-bracketing condition");
+ } catch (SolverException ex) {
+ // Ensure expected error condition.
+ Assert.assertFalse(ex.getMessage().indexOf("No bracketing") == -1);
+ }
+ try { // No bracketing.
+ solver.findRoot(f, 1, 1.2, 1.5);
+ Assert.fail("Expecting non-bracketing condition");
+ } catch (SolverException ex) {
+ // Ensure expected error condition.
+ Assert.assertFalse(ex.getMessage().indexOf("No bracketing") == -1);
+ }
+ }
+
+ @Test
+ public void testBadInitialGuess() {
+ final DoubleUnaryOperator func = new QuinticFunction();
+ final BrentSolver solver = new BrentSolver(DEFAULT_ABSOLUTE_ACCURACY,
+ DEFAULT_RELATIVE_ACCURACY,
+ DEFAULT_FUNCTION_ACCURACY);
+
+ try {
+ // Invalid guess (it *is* a root, but outside of the range).
+ double result = solver.findRoot(func, 0.0, 7.0, 0.6);
+ Assert.fail("an out of range condition was expected");
+ } catch (SolverException ex) {
+ // Ensure expected error condition.
+ Assert.assertFalse(ex.getMessage().indexOf("out of range") == -1);
+ }
+ }
+
+ @Test
+ public void testInitialGuess() {
+ final DoubleUnaryOperator func = new QuinticFunction();
+ final BrentSolver solver = new BrentSolver(DEFAULT_ABSOLUTE_ACCURACY,
+ DEFAULT_RELATIVE_ACCURACY,
+ DEFAULT_FUNCTION_ACCURACY);
+ double result;
+ MonitoredFunction f;
+
+ // No guess.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 0.6, 7.0);
+ Assert.assertEquals(1.0, result, DEFAULT_ABSOLUTE_ACCURACY);
+ final int referenceCallsCount = f.getCallsCount();
+ Assert.assertTrue(referenceCallsCount >= 13);
+
+ // Bad guess.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 0.6, 0.61, 7.0);
+ Assert.assertEquals(1.0, result, DEFAULT_ABSOLUTE_ACCURACY);
+ Assert.assertTrue(f.getCallsCount() > referenceCallsCount);
+
+ // Good guess.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 0.6, 0.9999990001, 7.0);
+ Assert.assertEquals(1.0, result, DEFAULT_ABSOLUTE_ACCURACY);
+ Assert.assertTrue(f.getCallsCount() < referenceCallsCount);
+
+ // Perfect guess.
+ f = new MonitoredFunction(func);
+ result = solver.findRoot(f, 0.6, 1.0, 7.0);
+ Assert.assertEquals(1.0, result, DEFAULT_ABSOLUTE_ACCURACY);
+ Assert.assertEquals(1, f.getCallsCount());
+ }
+}
diff --git
a/commons-numbers-rootfinder/src/test/java/org/apache/commons/numbers/rootfinder/MonitoredFunction.java
b/commons-numbers-rootfinder/src/test/java/org/apache/commons/numbers/rootfinder/MonitoredFunction.java
new file mode 100644
index 0000000..04c4e03
--- /dev/null
+++
b/commons-numbers-rootfinder/src/test/java/org/apache/commons/numbers/rootfinder/MonitoredFunction.java
@@ -0,0 +1,52 @@
+/*
+ * 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.rootfinder;
+
+import java.util.function.DoubleUnaryOperator;
+
+/**
+ * Wrapper class for counting functions calls.
+ */
+class MonitoredFunction implements DoubleUnaryOperator {
+ final int maxCount;
+ private int callsCount;
+ private final DoubleUnaryOperator f;
+
+ public MonitoredFunction(DoubleUnaryOperator f) {
+ this(f, Integer.MAX_VALUE);
+ }
+
+ public MonitoredFunction(DoubleUnaryOperator f,
+ int maxCount) {
+ callsCount = 0;
+ this.f = f;
+ this.maxCount = maxCount;
+ }
+
+ public int getCallsCount() {
+ return callsCount;
+ }
+
+ @Override
+ public double applyAsDouble(double x) {
+ if (++callsCount > maxCount) {
+ throw new IllegalStateException(callsCount + " > " + maxCount +
+ ": too many calls");
+ }
+ return f.applyAsDouble(x);
+ }
+}
diff --git
a/commons-numbers-rootfinder/src/test/java/org/apache/commons/numbers/rootfinder/QuinticFunction.java
b/commons-numbers-rootfinder/src/test/java/org/apache/commons/numbers/rootfinder/QuinticFunction.java
new file mode 100644
index 0000000..4385cf3
--- /dev/null
+++
b/commons-numbers-rootfinder/src/test/java/org/apache/commons/numbers/rootfinder/QuinticFunction.java
@@ -0,0 +1,29 @@
+/*
+ * 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.rootfinder;
+
+import java.util.function.DoubleUnaryOperator;
+
+/**
+ * Auxiliary class for testing solvers.
+ */
+class QuinticFunction implements DoubleUnaryOperator {
+ @Override
+ public double applyAsDouble(double x) {
+ return (x - 1) * (x - 0.5) * x * (x + 0.5) * (x + 1);
+ }
+}
diff --git
a/commons-numbers-rootfinder/src/test/java/org/apache/commons/numbers/rootfinder/Sin.java
b/commons-numbers-rootfinder/src/test/java/org/apache/commons/numbers/rootfinder/Sin.java
new file mode 100644
index 0000000..e569c05
--- /dev/null
+++
b/commons-numbers-rootfinder/src/test/java/org/apache/commons/numbers/rootfinder/Sin.java
@@ -0,0 +1,29 @@
+/*
+ * 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.rootfinder;
+
+import java.util.function.DoubleUnaryOperator;
+
+/**
+ * Auxiliary class for testing solvers.
+ */
+class Sin implements DoubleUnaryOperator {
+ @Override
+ public double applyAsDouble(double x) {
+ return Math.sin(x);
+ }
+}
diff --git a/pom.xml b/pom.xml
index b3d5dff..c22e030 100644
--- a/pom.xml
+++ b/pom.xml
@@ -628,6 +628,7 @@
<module>commons-numbers-combinatorics</module>
<module>commons-numbers-arrays</module>
<module>commons-numbers-field</module>
+ <module>commons-numbers-rootfinder</module>
</modules>
</project>
