Author: luc
Date: Mon Jun 3 09:04:40 2013
New Revision: 1488914
URL: http://svn.apache.org/r1488914
Log:
Added midpoint integration method.
Patch contributed by Oleksandr Kornieiev.
JIRA: MATH-967
Added:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/integration/MidPointIntegrator.java
(with props)
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/analysis/integration/MidPointIntegratorTest.java
(with props)
Modified:
commons/proper/math/trunk/pom.xml
commons/proper/math/trunk/src/changes/changes.xml
Modified: commons/proper/math/trunk/pom.xml
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/pom.xml?rev=1488914&r1=1488913&r2=1488914&view=diff
==============================================================================
--- commons/proper/math/trunk/pom.xml (original)
+++ commons/proper/math/trunk/pom.xml Mon Jun 3 09:04:40 2013
@@ -217,6 +217,9 @@
<name>Eugene Kirpichov</name>
</contributor>
<contributor>
+ <name>Oleksandr Kornieiev</name>
+ </contributor>
+ <contributor>
<name>Piotr Kochanski</name>
</contributor>
<contributor>
Modified: commons/proper/math/trunk/src/changes/changes.xml
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/changes/changes.xml?rev=1488914&r1=1488913&r2=1488914&view=diff
==============================================================================
--- commons/proper/math/trunk/src/changes/changes.xml (original)
+++ commons/proper/math/trunk/src/changes/changes.xml Mon Jun 3 09:04:40 2013
@@ -51,6 +51,9 @@ If the output is not quite correct, chec
</properties>
<body>
<release version="x.y" date="TBD" description="TBD">
+ <action dev="luc" type="add" issue="MATH-967" due-to="Oleksandr
Kornieiev">
+ Added midpoint integration method.
+ </action>
<action dev="luc" type="fix" issue="MATH-988" due-to="Andreas Huber">
Fixed NullPointerException in 2D and 3D sub-line intersections.
</action>
Added:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/integration/MidPointIntegrator.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/integration/MidPointIntegrator.java?rev=1488914&view=auto
==============================================================================
---
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/integration/MidPointIntegrator.java
(added)
+++
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/integration/MidPointIntegrator.java
Mon Jun 3 09:04:40 2013
@@ -0,0 +1,165 @@
+/*
+ * 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.math3.analysis.integration;
+
+import org.apache.commons.math3.exception.MathIllegalArgumentException;
+import org.apache.commons.math3.exception.MaxCountExceededException;
+import org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import org.apache.commons.math3.exception.NumberIsTooLargeException;
+import org.apache.commons.math3.exception.NumberIsTooSmallException;
+import org.apache.commons.math3.exception.TooManyEvaluationsException;
+import org.apache.commons.math3.util.FastMath;
+
+/**
+ * Implements the <a href="http://en.wikipedia.org/wiki/Midpoint_method";>
+ * Midpoint Rule</a> for integration of real univariate functions. For
+ * reference, see <b>Numerical Mathematics</b>, ISBN 0387989595,
+ * chapter 9.2.
+ * <p>
+ * The function should be integrable.</p>
+ *
+ * @version $Id$
+ * @since 3.3
+ */
+public class MidPointIntegrator extends BaseAbstractUnivariateIntegrator {
+
+ /** Maximum number of iterations for midpoint. */
+ public static final int MIDPOINT_MAX_ITERATIONS_COUNT = 64;
+
+ /** Intermediate result. */
+ private double s;
+
+ /**
+ * Build a midpoint integrator with given accuracies and iterations counts.
+ * @param relativeAccuracy relative accuracy of the result
+ * @param absoluteAccuracy absolute accuracy of the result
+ * @param minimalIterationCount minimum number of iterations
+ * @param maximalIterationCount maximum number of iterations
+ * (must be less than or equal to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
+ * @exception NotStrictlyPositiveException if minimal number of iterations
+ * is not strictly positive
+ * @exception NumberIsTooSmallException if maximal number of iterations
+ * is lesser than or equal to the minimal number of iterations
+ * @exception NumberIsTooLargeException if maximal number of iterations
+ * is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
+ */
+ public MidPointIntegrator(final double relativeAccuracy,
+ final double absoluteAccuracy,
+ final int minimalIterationCount,
+ final int maximalIterationCount)
+ throws NotStrictlyPositiveException, NumberIsTooSmallException,
NumberIsTooLargeException {
+ super(relativeAccuracy, absoluteAccuracy, minimalIterationCount,
maximalIterationCount);
+ if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
+ throw new NumberIsTooLargeException(maximalIterationCount,
+ MIDPOINT_MAX_ITERATIONS_COUNT,
false);
+ }
+ }
+
+ /**
+ * Build a midpoint integrator with given iteration counts.
+ * @param minimalIterationCount minimum number of iterations
+ * @param maximalIterationCount maximum number of iterations
+ * (must be less than or equal to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
+ * @exception NotStrictlyPositiveException if minimal number of iterations
+ * is not strictly positive
+ * @exception NumberIsTooSmallException if maximal number of iterations
+ * is lesser than or equal to the minimal number of iterations
+ * @exception NumberIsTooLargeException if maximal number of iterations
+ * is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
+ */
+ public MidPointIntegrator(final int minimalIterationCount,
+ final int maximalIterationCount)
+ throws NotStrictlyPositiveException, NumberIsTooSmallException,
NumberIsTooLargeException {
+ super(minimalIterationCount, maximalIterationCount);
+ if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
+ throw new NumberIsTooLargeException(maximalIterationCount,
+ MIDPOINT_MAX_ITERATIONS_COUNT,
false);
+ }
+ }
+
+ /**
+ * Construct a midpoint integrator with default settings.
+ * (max iteration count set to {@link #MIDPOINT_MAX_ITERATIONS_COUNT})
+ */
+ public MidPointIntegrator() {
+ super(DEFAULT_MIN_ITERATIONS_COUNT, MIDPOINT_MAX_ITERATIONS_COUNT);
+ }
+
+ /**
+ * Compute the n-th stage integral of midpoint rule.
+ * This function should only be called by API <code>integrate()</code> in
the package.
+ * To save time it does not verify arguments - caller does.
+ * <p>
+ * The interval is divided equally into 2^n sections rather than an
+ * arbitrary m sections because this configuration can best utilize the
+ * already computed values.</p>
+ *
+ * @param n the stage of 1/2 refinement, n = 0 is no refinement
+ * @return the value of n-th stage integral
+ * @throws TooManyEvaluationsException if the maximal number of evaluations
+ * is exceeded.
+ */
+ private double stage(final int n)
+ throws TooManyEvaluationsException {
+
+ final double max = getMax();
+ final double min = getMin();
+
+ if (n == 0) {
+ final double midPoint = 0.5 * (max - min);
+ s = (max - min) * computeObjectiveValue(midPoint);
+ return s;
+ } else {
+ final long np = 1L << (n - 1); // number of new points
in this stage
+ double sum = 0;
+ // spacing between adjacent new points
+ final double spacing = (max - min) / np;
+ double x = min + 0.5 * spacing; // the first new point
+ for (long i = 0; i < np; i++) {
+ sum += computeObjectiveValue(x);
+ x += spacing;
+ }
+ // add the new sum to previously calculated result
+ s = 0.5 * (s + sum * spacing);
+ return s;
+ }
+ }
+
+ /** {@inheritDoc} */
+ protected double doIntegrate()
+ throws MathIllegalArgumentException, TooManyEvaluationsException,
MaxCountExceededException {
+
+ double oldt = stage(0);
+ iterations.incrementCount();
+ while (true) {
+ final int i = iterations.getCount();
+ final double t = stage(i);
+ if (i >= getMinimalIterationCount()) {
+ final double delta = FastMath.abs(t - oldt);
+ final double rLimit =
+ getRelativeAccuracy() * (FastMath.abs(oldt) +
FastMath.abs(t)) * 0.5;
+ if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
+ return t;
+ }
+ }
+ oldt = t;
+ iterations.incrementCount();
+ }
+
+ }
+
+}
Propchange:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/integration/MidPointIntegrator.java
------------------------------------------------------------------------------
svn:eol-style = native
Propchange:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/integration/MidPointIntegrator.java
------------------------------------------------------------------------------
svn:keywords = "Author Date Id Revision"
Added:
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/analysis/integration/MidPointIntegratorTest.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/analysis/integration/MidPointIntegratorTest.java?rev=1488914&view=auto
==============================================================================
---
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/analysis/integration/MidPointIntegratorTest.java
(added)
+++
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/analysis/integration/MidPointIntegratorTest.java
Mon Jun 3 09:04:40 2013
@@ -0,0 +1,132 @@
+/*
+ * 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.math3.analysis.integration;
+
+import org.apache.commons.math3.analysis.QuinticFunction;
+import org.apache.commons.math3.analysis.UnivariateFunction;
+import org.apache.commons.math3.analysis.function.Sin;
+import org.apache.commons.math3.exception.NumberIsTooLargeException;
+import org.apache.commons.math3.exception.NumberIsTooSmallException;
+import org.apache.commons.math3.util.FastMath;
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * Test case for midpoint integrator.
+ * <p>
+ * Test runs show that for a default relative accuracy of 1E-6, it generally
+ * takes 10 to 15 iterations for the integral to converge.
+ *
+ * @version $Id: MidPointIntegratorTest.java 1374632 2012-08-18 18:11:11Z luc $
+ */
+public final class MidPointIntegratorTest {
+
+ /**
+ * Test of integrator for the sine function.
+ */
+ @Test
+ public void testSinFunction() {
+ UnivariateFunction f = new Sin();
+ UnivariateIntegrator integrator = new MidPointIntegrator();
+
+ double min = 0;
+ double max = FastMath.PI;
+ double expected = 2;
+ double tolerance = FastMath.abs(expected *
integrator.getRelativeAccuracy());
+ double result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
+ Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
+ Assert.assertTrue(integrator.getIterations() <
MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
+ Assert.assertEquals(expected, result, tolerance);
+
+ min = -FastMath.PI/3;
+ max = 0;
+ expected = -0.5;
+ tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
+ result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
+ Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
+ Assert.assertTrue(integrator.getIterations() <
MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
+ Assert.assertEquals(expected, result, tolerance);
+
+ }
+
+ /**
+ * Test of integrator for the quintic function.
+ */
+ @Test
+ public void testQuinticFunction() {
+ UnivariateFunction f = new QuinticFunction();
+ UnivariateIntegrator integrator = new MidPointIntegrator();
+
+ double min = 0;
+ double max = 1;
+ double expected = -1.0 / 48;
+ double tolerance = FastMath.abs(expected *
integrator.getRelativeAccuracy());
+ double result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
+ Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
+ Assert.assertTrue(integrator.getIterations() <
MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
+ Assert.assertEquals(expected, result, tolerance);
+
+ min = 0;
+ max = 0.5;
+ expected = 11.0 / 768;
+ tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
+ result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
+ Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
+ Assert.assertTrue(integrator.getIterations() <
MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
+ Assert.assertEquals(expected, result, tolerance);
+
+ min = -1;
+ max = 4;
+ expected = 2048 / 3.0 - 78 + 1.0 / 48;
+ tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
+ result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
+ Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
+ Assert.assertTrue(integrator.getIterations() <
MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
+ Assert.assertEquals(expected, result, tolerance);
+
+ }
+
+ /**
+ * Test of parameters for the integrator.
+ */
+ @Test
+ public void testParameters() {
+ UnivariateFunction f = new Sin();
+
+ try {
+ // bad interval
+ new MidPointIntegrator().integrate(1000, f, 1, -1);
+ Assert.fail("Expecting NumberIsTooLargeException - bad interval");
+ } catch (NumberIsTooLargeException ex) {
+ // expected
+ }
+ try {
+ // bad iteration limits
+ new MidPointIntegrator(5, 4);
+ Assert.fail("Expecting NumberIsTooSmallException - bad iteration
limits");
+ } catch (NumberIsTooSmallException ex) {
+ // expected
+ }
+ try {
+ // bad iteration limits
+ new MidPointIntegrator(10, 99);
+ Assert.fail("Expecting NumberIsTooLargeException - bad iteration
limits");
+ } catch (NumberIsTooLargeException ex) {
+ // expected
+ }
+ }
+}
Propchange:
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/analysis/integration/MidPointIntegratorTest.java
------------------------------------------------------------------------------
svn:eol-style = native
Propchange:
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/analysis/integration/MidPointIntegratorTest.java
------------------------------------------------------------------------------
svn:keywords = "Author Date Id Revision"
