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/RombergIntegration.html">
028     * Romberg Algorithm</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     * Romberg integration employs k successive refinements of the trapezoid
033     * rule to remove error terms less than order O(N^(-2k)). Simpson's rule
034     * is a special case of k = 2.</p>
035     *
036     * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 f??vr. 2011) $
037     * @since 1.2
038     */
039    public class RombergIntegrator extends UnivariateRealIntegratorImpl {
040    
041        /**
042         * Construct an integrator for the given function.
043         *
044         * @param f function to integrate
045         * @deprecated as of 2.0 the integrand function is passed as an argument
046         * to the {@link #integrate(UnivariateRealFunction, double, double)}method.
047         */
048        @Deprecated
049        public RombergIntegrator(UnivariateRealFunction f) {
050            super(f, 32);
051        }
052    
053        /**
054         * Construct an integrator.
055         */
056        public RombergIntegrator() {
057            super(32);
058        }
059    
060        /** {@inheritDoc} */
061        @Deprecated
062        public double integrate(final double min, final double max)
063            throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
064            return integrate(f, min, max);
065        }
066    
067        /** {@inheritDoc} */
068        public double integrate(final UnivariateRealFunction f, final double min, final double max)
069            throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
070    
071            final int m = maximalIterationCount + 1;
072            double previousRow[] = new double[m];
073            double currentRow[]  = new double[m];
074    
075            clearResult();
076            verifyInterval(min, max);
077            verifyIterationCount();
078    
079            TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
080            currentRow[0] = qtrap.stage(f, min, max, 0);
081            double olds = currentRow[0];
082            for (int i = 1; i <= maximalIterationCount; ++i) {
083    
084                // switch rows
085                final double[] tmpRow = previousRow;
086                previousRow = currentRow;
087                currentRow = tmpRow;
088    
089                currentRow[0] = qtrap.stage(f, min, max, i);
090                for (int j = 1; j <= i; j++) {
091                    // Richardson extrapolation coefficient
092                    final double r = (1L << (2 * j)) - 1;
093                    final double tIJm1 = currentRow[j - 1];
094                    currentRow[j] = tIJm1 + (tIJm1 - previousRow[j - 1]) / r;
095                }
096                final double s = currentRow[i];
097                if (i >= minimalIterationCount) {
098                    final double delta  = FastMath.abs(s - olds);
099                    final double rLimit = relativeAccuracy * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
100                    if ((delta <= rLimit) || (delta <= absoluteAccuracy)) {
101                        setResult(s, i);
102                        return result;
103                    }
104                }
105                olds = s;
106            }
107            throw new MaxIterationsExceededException(maximalIterationCount);
108        }
109    
110        /** {@inheritDoc} */
111        @Override
112        protected void verifyIterationCount() throws IllegalArgumentException {
113            super.verifyIterationCount();
114            // at most 32 bisection refinements due to higher order divider
115            if (maximalIterationCount > 32) {
116                throw MathRuntimeException.createIllegalArgumentException(
117                        LocalizedFormats.INVALID_ITERATIONS_LIMITS,
118                        0, 32);
119            }
120        }
121    }