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     */
017    package org.apache.commons.math.analysis.integration;
018    
019    import org.apache.commons.math.FunctionEvaluationException;
020    import org.apache.commons.math.MathRuntimeException;
021    import org.apache.commons.math.MaxIterationsExceededException;
022    import org.apache.commons.math.analysis.UnivariateRealFunction;
023    import org.apache.commons.math.exception.util.LocalizedFormats;
024    import org.apache.commons.math.util.FastMath;
025    
026    /**
027     * Implements the <a href="http://mathworld.wolfram.com/TrapezoidalRule.html">
028     * Trapezoidal Rule</a> for integration of real univariate functions. For
029     * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
030     * chapter 3.
031     * <p>
032     * The function should be integrable.</p>
033     *
034     * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 f??vr. 2011) $
035     * @since 1.2
036     */
037    public class TrapezoidIntegrator extends UnivariateRealIntegratorImpl {
038    
039        /** Intermediate result. */
040        private double s;
041    
042        /**
043         * Construct an integrator for the given function.
044         *
045         * @param f function to integrate
046         * @deprecated as of 2.0 the integrand function is passed as an argument
047         * to the {@link #integrate(UnivariateRealFunction, double, double)}method.
048         */
049        @Deprecated
050        public TrapezoidIntegrator(UnivariateRealFunction f) {
051            super(f, 64);
052        }
053    
054        /**
055         * Construct an integrator.
056         */
057        public TrapezoidIntegrator() {
058            super(64);
059        }
060    
061        /**
062         * Compute the n-th stage integral of trapezoid rule. This function
063         * should only be called by API <code>integrate()</code> in the package.
064         * To save time it does not verify arguments - caller does.
065         * <p>
066         * The interval is divided equally into 2^n sections rather than an
067         * arbitrary m sections because this configuration can best utilize the
068         * alrealy computed values.</p>
069         *
070         * @param f the integrand function
071         * @param min the lower bound for the interval
072         * @param max the upper bound for the interval
073         * @param n the stage of 1/2 refinement, n = 0 is no refinement
074         * @return the value of n-th stage integral
075         * @throws FunctionEvaluationException if an error occurs evaluating the function
076         */
077        double stage(final UnivariateRealFunction f,
078                     final double min, final double max, final int n)
079            throws FunctionEvaluationException {
080    
081            if (n == 0) {
082                s = 0.5 * (max - min) * (f.value(min) + f.value(max));
083                return s;
084            } else {
085                final long np = 1L << (n-1);           // number of new points in this stage
086                double sum = 0;
087                final double spacing = (max - min) / np; // spacing between adjacent new points
088                double x = min + 0.5 * spacing;    // the first new point
089                for (long i = 0; i < np; i++) {
090                    sum += f.value(x);
091                    x += spacing;
092                }
093                // add the new sum to previously calculated result
094                s = 0.5 * (s + sum * spacing);
095                return s;
096            }
097        }
098    
099        /** {@inheritDoc} */
100        @Deprecated
101        public double integrate(final double min, final double max)
102            throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
103            return integrate(f, min, max);
104        }
105    
106        /** {@inheritDoc} */
107        public double integrate(final UnivariateRealFunction f, final double min, final double max)
108            throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
109    
110            clearResult();
111            verifyInterval(min, max);
112            verifyIterationCount();
113    
114            double oldt = stage(f, min, max, 0);
115            for (int i = 1; i <= maximalIterationCount; ++i) {
116                final double t = stage(f, min, max, i);
117                if (i >= minimalIterationCount) {
118                    final double delta = FastMath.abs(t - oldt);
119                    final double rLimit =
120                        relativeAccuracy * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5;
121                    if ((delta <= rLimit) || (delta <= absoluteAccuracy)) {
122                        setResult(t, i);
123                        return result;
124                    }
125                }
126                oldt = t;
127            }
128            throw new MaxIterationsExceededException(maximalIterationCount);
129        }
130    
131        /** {@inheritDoc} */
132        @Override
133        protected void verifyIterationCount() throws IllegalArgumentException {
134            super.verifyIterationCount();
135            // at most 64 bisection refinements
136            if (maximalIterationCount > 64) {
137                throw MathRuntimeException.createIllegalArgumentException(
138                        LocalizedFormats.INVALID_ITERATIONS_LIMITS,
139                        0, 64);
140            }
141        }
142    }