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 * @since 1.2
036 */
037public class TrapezoidIntegrator extends BaseAbstractUnivariateIntegrator {
038
039    /** Maximum number of iterations for trapezoid. */
040    public static final int TRAPEZOID_MAX_ITERATIONS_COUNT = 64;
041
042    /** Intermediate result. */
043    private double s;
044
045    /**
046     * Build a trapezoid integrator with given accuracies and iterations counts.
047     * @param relativeAccuracy relative accuracy of the result
048     * @param absoluteAccuracy absolute accuracy of the result
049     * @param minimalIterationCount minimum number of iterations
050     * @param maximalIterationCount maximum number of iterations
051     * (must be less than or equal to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
052     * @exception NotStrictlyPositiveException if minimal number of iterations
053     * is not strictly positive
054     * @exception NumberIsTooSmallException if maximal number of iterations
055     * is lesser than or equal to the minimal number of iterations
056     * @exception NumberIsTooLargeException if maximal number of iterations
057     * is greater than {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
058     */
059    public TrapezoidIntegrator(final double relativeAccuracy,
060                               final double absoluteAccuracy,
061                               final int minimalIterationCount,
062                               final int maximalIterationCount)
063        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
064        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
065        if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
066            throw new NumberIsTooLargeException(maximalIterationCount,
067                                                TRAPEZOID_MAX_ITERATIONS_COUNT, false);
068        }
069    }
070
071    /**
072     * Build a trapezoid integrator with given iteration counts.
073     * @param minimalIterationCount minimum number of iterations
074     * @param maximalIterationCount maximum number of iterations
075     * (must be less than or equal to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
076     * @exception NotStrictlyPositiveException if minimal number of iterations
077     * is not strictly positive
078     * @exception NumberIsTooSmallException if maximal number of iterations
079     * is lesser than or equal to the minimal number of iterations
080     * @exception NumberIsTooLargeException if maximal number of iterations
081     * is greater than {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
082     */
083    public TrapezoidIntegrator(final int minimalIterationCount,
084                               final int maximalIterationCount)
085        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
086        super(minimalIterationCount, maximalIterationCount);
087        if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
088            throw new NumberIsTooLargeException(maximalIterationCount,
089                                                TRAPEZOID_MAX_ITERATIONS_COUNT, false);
090        }
091    }
092
093    /**
094     * Construct a trapezoid integrator with default settings.
095     * (max iteration count set to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT})
096     */
097    public TrapezoidIntegrator() {
098        super(DEFAULT_MIN_ITERATIONS_COUNT, TRAPEZOID_MAX_ITERATIONS_COUNT);
099    }
100
101    /**
102     * Compute the n-th stage integral of trapezoid rule. This function
103     * should only be called by API <code>integrate()</code> in the package.
104     * To save time it does not verify arguments - caller does.
105     * <p>
106     * The interval is divided equally into 2^n sections rather than an
107     * arbitrary m sections because this configuration can best utilize the
108     * already computed values.</p>
109     *
110     * @param baseIntegrator integrator holding integration parameters
111     * @param n the stage of 1/2 refinement, n = 0 is no refinement
112     * @return the value of n-th stage integral
113     * @throws TooManyEvaluationsException if the maximal number of evaluations
114     * is exceeded.
115     */
116    double stage(final BaseAbstractUnivariateIntegrator baseIntegrator, final int n)
117        throws TooManyEvaluationsException {
118
119        if (n == 0) {
120            final double max = baseIntegrator.getMax();
121            final double min = baseIntegrator.getMin();
122            s = 0.5 * (max - min) *
123                      (baseIntegrator.computeObjectiveValue(min) +
124                       baseIntegrator.computeObjectiveValue(max));
125            return s;
126        } else {
127            final long np = 1L << (n-1);           // number of new points in this stage
128            double sum = 0;
129            final double max = baseIntegrator.getMax();
130            final double min = baseIntegrator.getMin();
131            // spacing between adjacent new points
132            final double spacing = (max - min) / np;
133            double x = min + 0.5 * spacing;    // the first new point
134            for (long i = 0; i < np; i++) {
135                sum += baseIntegrator.computeObjectiveValue(x);
136                x += spacing;
137            }
138            // add the new sum to previously calculated result
139            s = 0.5 * (s + sum * spacing);
140            return s;
141        }
142    }
143
144    /** {@inheritDoc} */
145    @Override
146    protected double doIntegrate()
147        throws MathIllegalArgumentException, TooManyEvaluationsException, MaxCountExceededException {
148
149        double oldt = stage(this, 0);
150        incrementCount();
151        while (true) {
152            final int i = getIterations();
153            final double t = stage(this, i);
154            if (i >= getMinimalIterationCount()) {
155                final double delta = FastMath.abs(t - oldt);
156                final double rLimit =
157                    getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5;
158                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
159                    return t;
160                }
161            }
162            oldt = t;
163            incrementCount();
164        }
165
166    }
167
168}