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Commons Math example source code file (TrapezoidIntegrator.java)

This example Commons Math source code file (TrapezoidIntegrator.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Java - Commons Math tags/keywords

deprecated, functionevaluationexception, functionevaluationexception, illegalargumentexception, illegalargumentexception, maxiterationsexceededexception, maxiterationsexceededexception, override, trapezoidintegrator, trapezoidintegrator, univariaterealfunction, univariaterealintegratorimpl

The Commons Math TrapezoidIntegrator.java source code

/*
 * 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;

/**
 * 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, ISBN 038795452X,
 * chapter 3.
 * <p>
 * The function should be integrable.</p>
 *
 * @version $Revision: 825919 $ $Date: 2009-10-16 10:51:55 -0400 (Fri, 16 Oct 2009) $
 * @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() 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 = Math.abs(t - oldt);
                final double rLimit =
                    relativeAccuracy * (Math.abs(oldt) + Math.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(
                    "invalid iteration limits: min={0}, max={1}",
                    0, 64);
        }
    }
}

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