| /* |
| * 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.math.analysis.integration; |
| |
| import org.apache.commons.math.FunctionEvaluationException; |
| import org.apache.commons.math.MathRuntimeException; |
| import org.apache.commons.math.MaxIterationsExceededException; |
| import org.apache.commons.math.analysis.UnivariateRealFunction; |
| import org.apache.commons.math.exception.util.LocalizedFormats; |
| import org.apache.commons.math.util.FastMath; |
| |
| /** |
| * Implements the <a href="http://mathworld.wolfram.com/RombergIntegration.html"> |
| * Romberg Algorithm</a> for integration of real univariate functions. For |
| * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X, |
| * chapter 3. |
| * <p> |
| * Romberg integration employs k successive refinements of the trapezoid |
| * rule to remove error terms less than order O(N^(-2k)). Simpson's rule |
| * is a special case of k = 2.</p> |
| * |
| * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $ |
| * @since 1.2 |
| */ |
| public class RombergIntegrator extends UnivariateRealIntegratorImpl { |
| |
| /** |
| * Construct an integrator for the given function. |
| * |
| * @param f function to integrate |
| * @deprecated as of 2.0 the integrand function is passed as an argument |
| * to the {@link #integrate(UnivariateRealFunction, double, double)}method. |
| */ |
| @Deprecated |
| public RombergIntegrator(UnivariateRealFunction f) { |
| super(f, 32); |
| } |
| |
| /** |
| * Construct an integrator. |
| */ |
| public RombergIntegrator() { |
| super(32); |
| } |
| |
| /** {@inheritDoc} */ |
| @Deprecated |
| public double integrate(final double min, final double max) |
| throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException { |
| return integrate(f, min, max); |
| } |
| |
| /** {@inheritDoc} */ |
| public double integrate(final UnivariateRealFunction f, final double min, final double max) |
| throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException { |
| |
| final int m = maximalIterationCount + 1; |
| double previousRow[] = new double[m]; |
| double currentRow[] = new double[m]; |
| |
| clearResult(); |
| verifyInterval(min, max); |
| verifyIterationCount(); |
| |
| TrapezoidIntegrator qtrap = new TrapezoidIntegrator(); |
| currentRow[0] = qtrap.stage(f, min, max, 0); |
| double olds = currentRow[0]; |
| for (int i = 1; i <= maximalIterationCount; ++i) { |
| |
| // switch rows |
| final double[] tmpRow = previousRow; |
| previousRow = currentRow; |
| currentRow = tmpRow; |
| |
| currentRow[0] = qtrap.stage(f, min, max, i); |
| for (int j = 1; j <= i; j++) { |
| // Richardson extrapolation coefficient |
| final double r = (1L << (2 * j)) - 1; |
| final double tIJm1 = currentRow[j - 1]; |
| currentRow[j] = tIJm1 + (tIJm1 - previousRow[j - 1]) / r; |
| } |
| final double s = currentRow[i]; |
| if (i >= minimalIterationCount) { |
| final double delta = FastMath.abs(s - olds); |
| final double rLimit = relativeAccuracy * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5; |
| if ((delta <= rLimit) || (delta <= absoluteAccuracy)) { |
| setResult(s, i); |
| return result; |
| } |
| } |
| olds = s; |
| } |
| throw new MaxIterationsExceededException(maximalIterationCount); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected void verifyIterationCount() throws IllegalArgumentException { |
| super.verifyIterationCount(); |
| // at most 32 bisection refinements due to higher order divider |
| if (maximalIterationCount > 32) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.INVALID_ITERATIONS_LIMITS, |
| 0, 32); |
| } |
| } |
| } |