001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.math3.analysis.integration;
018
019import org.apache.commons.math3.exception.MathIllegalArgumentException;
020import org.apache.commons.math3.exception.MaxCountExceededException;
021import org.apache.commons.math3.exception.NotStrictlyPositiveException;
022import org.apache.commons.math3.exception.NumberIsTooLargeException;
023import org.apache.commons.math3.exception.NumberIsTooSmallException;
024import org.apache.commons.math3.exception.TooManyEvaluationsException;
025import org.apache.commons.math3.util.FastMath;
026
027/**
028 * Implements the <a href="http://mathworld.wolfram.com/TrapezoidalRule.html">
029 * Trapezoid Rule</a> for integration of real univariate functions. For
030 * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
031 * chapter 3.
032 * <p>
033 * The function should be integrable.</p>
034 *
035 * @version $Id: TrapezoidIntegrator.java 1455194 2013-03-11 15:45:54Z luc $
036 * @since 1.2
037 */
038public class TrapezoidIntegrator extends BaseAbstractUnivariateIntegrator {
039
040    /** Maximum number of iterations for trapezoid. */
041    public static final int TRAPEZOID_MAX_ITERATIONS_COUNT = 64;
042
043    /** Intermediate result. */
044    private double s;
045
046    /**
047     * Build a trapezoid integrator with given accuracies and iterations counts.
048     * @param relativeAccuracy relative accuracy of the result
049     * @param absoluteAccuracy absolute accuracy of the result
050     * @param minimalIterationCount minimum number of iterations
051     * @param maximalIterationCount maximum number of iterations
052     * (must be less than or equal to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
053     * @exception NotStrictlyPositiveException if minimal number of iterations
054     * is not strictly positive
055     * @exception NumberIsTooSmallException if maximal number of iterations
056     * is lesser than or equal to the minimal number of iterations
057     * @exception NumberIsTooLargeException if maximal number of iterations
058     * is greater than {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
059     */
060    public TrapezoidIntegrator(final double relativeAccuracy,
061                               final double absoluteAccuracy,
062                               final int minimalIterationCount,
063                               final int maximalIterationCount)
064        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
065        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
066        if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
067            throw new NumberIsTooLargeException(maximalIterationCount,
068                                                TRAPEZOID_MAX_ITERATIONS_COUNT, false);
069        }
070    }
071
072    /**
073     * Build a trapezoid integrator with given iteration counts.
074     * @param minimalIterationCount minimum number of iterations
075     * @param maximalIterationCount maximum number of iterations
076     * (must be less than or equal to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
077     * @exception NotStrictlyPositiveException if minimal number of iterations
078     * is not strictly positive
079     * @exception NumberIsTooSmallException if maximal number of iterations
080     * is lesser than or equal to the minimal number of iterations
081     * @exception NumberIsTooLargeException if maximal number of iterations
082     * is greater than {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
083     */
084    public TrapezoidIntegrator(final int minimalIterationCount,
085                               final int maximalIterationCount)
086        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
087        super(minimalIterationCount, maximalIterationCount);
088        if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
089            throw new NumberIsTooLargeException(maximalIterationCount,
090                                                TRAPEZOID_MAX_ITERATIONS_COUNT, false);
091        }
092    }
093
094    /**
095     * Construct a trapezoid integrator with default settings.
096     * (max iteration count set to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT})
097     */
098    public TrapezoidIntegrator() {
099        super(DEFAULT_MIN_ITERATIONS_COUNT, TRAPEZOID_MAX_ITERATIONS_COUNT);
100    }
101
102    /**
103     * Compute the n-th stage integral of trapezoid rule. This function
104     * should only be called by API <code>integrate()</code> in the package.
105     * To save time it does not verify arguments - caller does.
106     * <p>
107     * The interval is divided equally into 2^n sections rather than an
108     * arbitrary m sections because this configuration can best utilize the
109     * already computed values.</p>
110     *
111     * @param baseIntegrator integrator holding integration parameters
112     * @param n the stage of 1/2 refinement, n = 0 is no refinement
113     * @return the value of n-th stage integral
114     * @throws TooManyEvaluationsException if the maximal number of evaluations
115     * is exceeded.
116     */
117    double stage(final BaseAbstractUnivariateIntegrator baseIntegrator, final int n)
118        throws TooManyEvaluationsException {
119
120        if (n == 0) {
121            final double max = baseIntegrator.getMax();
122            final double min = baseIntegrator.getMin();
123            s = 0.5 * (max - min) *
124                      (baseIntegrator.computeObjectiveValue(min) +
125                       baseIntegrator.computeObjectiveValue(max));
126            return s;
127        } else {
128            final long np = 1L << (n-1);           // number of new points in this stage
129            double sum = 0;
130            final double max = baseIntegrator.getMax();
131            final double min = baseIntegrator.getMin();
132            // spacing between adjacent new points
133            final double spacing = (max - min) / np;
134            double x = min + 0.5 * spacing;    // the first new point
135            for (long i = 0; i < np; i++) {
136                sum += baseIntegrator.computeObjectiveValue(x);
137                x += spacing;
138            }
139            // add the new sum to previously calculated result
140            s = 0.5 * (s + sum * spacing);
141            return s;
142        }
143    }
144
145    /** {@inheritDoc} */
146    @Override
147    protected double doIntegrate()
148        throws MathIllegalArgumentException, TooManyEvaluationsException, MaxCountExceededException {
149
150        double oldt = stage(this, 0);
151        iterations.incrementCount();
152        while (true) {
153            final int i = iterations.getCount();
154            final double t = stage(this, i);
155            if (i >= getMinimalIterationCount()) {
156                final double delta = FastMath.abs(t - oldt);
157                final double rLimit =
158                    getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5;
159                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
160                    return t;
161                }
162            }
163            oldt = t;
164            iterations.incrementCount();
165        }
166
167    }
168
169}