| /* |
| * 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/TrapezoidalRule.html"> |
| * Trapezoidal Rule</a> for integration of real univariate functions. For |
| * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X, |
| * chapter 3. |
| * <p> |
| * The function should be integrable.</p> |
| * |
| * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $ |
| * @since 1.2 |
| */ |
| public class TrapezoidIntegrator extends UnivariateRealIntegratorImpl { |
| |
| /** Intermediate result. */ |
| private double s; |
| |
| /** |
| * 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 TrapezoidIntegrator(UnivariateRealFunction f) { |
| super(f, 64); |
| } |
| |
| /** |
| * Construct an integrator. |
| */ |
| public TrapezoidIntegrator() { |
| super(64); |
| } |
| |
| /** |
| * Compute the n-th stage integral of trapezoid rule. This function |
| * should only be called by API <code>integrate()</code> in the package. |
| * To save time it does not verify arguments - caller does. |
| * <p> |
| * The interval is divided equally into 2^n sections rather than an |
| * arbitrary m sections because this configuration can best utilize the |
| * alrealy computed values.</p> |
| * |
| * @param f the integrand function |
| * @param min the lower bound for the interval |
| * @param max the upper bound for the interval |
| * @param n the stage of 1/2 refinement, n = 0 is no refinement |
| * @return the value of n-th stage integral |
| * @throws FunctionEvaluationException if an error occurs evaluating the function |
| */ |
| double stage(final UnivariateRealFunction f, |
| final double min, final double max, final int n) |
| throws FunctionEvaluationException { |
| |
| if (n == 0) { |
| s = 0.5 * (max - min) * (f.value(min) + f.value(max)); |
| return s; |
| } else { |
| final long np = 1L << (n-1); // number of new points in this stage |
| double sum = 0; |
| final double spacing = (max - min) / np; // spacing between adjacent new points |
| double x = min + 0.5 * spacing; // the first new point |
| for (long i = 0; i < np; i++) { |
| sum += f.value(x); |
| x += spacing; |
| } |
| // add the new sum to previously calculated result |
| s = 0.5 * (s + sum * spacing); |
| return s; |
| } |
| } |
| |
| /** {@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 { |
| |
| clearResult(); |
| verifyInterval(min, max); |
| verifyIterationCount(); |
| |
| double oldt = stage(f, min, max, 0); |
| for (int i = 1; i <= maximalIterationCount; ++i) { |
| final double t = stage(f, min, max, i); |
| if (i >= minimalIterationCount) { |
| final double delta = FastMath.abs(t - oldt); |
| final double rLimit = |
| relativeAccuracy * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5; |
| if ((delta <= rLimit) || (delta <= absoluteAccuracy)) { |
| setResult(t, i); |
| return result; |
| } |
| } |
| oldt = t; |
| } |
| throw new MaxIterationsExceededException(maximalIterationCount); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected void verifyIterationCount() throws IllegalArgumentException { |
| super.verifyIterationCount(); |
| // at most 64 bisection refinements |
| if (maximalIterationCount > 64) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.INVALID_ITERATIONS_LIMITS, |
| 0, 64); |
| } |
| } |
| } |