/*
* 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.math3.analysis.integration;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.apache.commons.math3.util.FastMath;
/**
* Implements the <a href="http://en.wikipedia.org/wiki/Midpoint_method">
* Midpoint Rule</a> for integration of real univariate functions. For
* reference, see <b>Numerical Mathematics</b>, ISBN 0387989595,
* chapter 9.2.
* <p>
* The function should be integrable.</p>
*
* @since 3.3
*/
public class MidPointIntegrator extends BaseAbstractUnivariateIntegrator {
/** Maximum number of iterations for midpoint. */
public static final int MIDPOINT_MAX_ITERATIONS_COUNT = 64;
/**
* Build a midpoint integrator with given accuracies and iterations counts.
* @param relativeAccuracy relative accuracy of the result
* @param absoluteAccuracy absolute accuracy of the result
* @param minimalIterationCount minimum number of iterations
* @param maximalIterationCount maximum number of iterations
* (must be less than or equal to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
* @exception NotStrictlyPositiveException if minimal number of iterations
* is not strictly positive
* @exception NumberIsTooSmallException if maximal number of iterations
* is lesser than or equal to the minimal number of iterations
* @exception NumberIsTooLargeException if maximal number of iterations
* is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
*/
public MidPointIntegrator(final double relativeAccuracy,
final double absoluteAccuracy,
final int minimalIterationCount,
final int maximalIterationCount)
throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
throw new NumberIsTooLargeException(maximalIterationCount,
MIDPOINT_MAX_ITERATIONS_COUNT, false);
}
}
/**
* Build a midpoint integrator with given iteration counts.
* @param minimalIterationCount minimum number of iterations
* @param maximalIterationCount maximum number of iterations
* (must be less than or equal to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
* @exception NotStrictlyPositiveException if minimal number of iterations
* is not strictly positive
* @exception NumberIsTooSmallException if maximal number of iterations
* is lesser than or equal to the minimal number of iterations
* @exception NumberIsTooLargeException if maximal number of iterations
* is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
*/
public MidPointIntegrator(final int minimalIterationCount,
final int maximalIterationCount)
throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
super(minimalIterationCount, maximalIterationCount);
if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
throw new NumberIsTooLargeException(maximalIterationCount,
MIDPOINT_MAX_ITERATIONS_COUNT, false);
}
}
/**
* Construct a midpoint integrator with default settings.
* (max iteration count set to {@link #MIDPOINT_MAX_ITERATIONS_COUNT})
*/
public MidPointIntegrator() {
super(DEFAULT_MIN_ITERATIONS_COUNT, MIDPOINT_MAX_ITERATIONS_COUNT);
}
/**
* Compute the n-th stage integral of midpoint 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
* already computed values.</p>
*
* @param n the stage of 1/2 refinement. Must be larger than 0.
* @param previousStageResult Result from the previous call to the
* {@code stage} method.
* @param min Lower bound of the integration interval.
* @param diffMaxMin Difference between the lower bound and upper bound
* of the integration interval.
* @return the value of n-th stage integral
* @throws TooManyEvaluationsException if the maximal number of evaluations
* is exceeded.
*/
private double stage(final int n,
double previousStageResult,
double min,
double diffMaxMin)
throws TooManyEvaluationsException {
// number of new points in this stage
final long np = 1L << (n - 1);
double sum = 0;
// spacing between adjacent new points
final double spacing = diffMaxMin / np;
// the first new point
double x = min + 0.5 * spacing;
for (long i = 0; i < np; i++) {
sum += computeObjectiveValue(x);
x += spacing;
}
// add the new sum to previously calculated result
return 0.5 * (previousStageResult + sum * spacing);
}
/** {@inheritDoc} */
@Override
protected double doIntegrate()
throws MathIllegalArgumentException, TooManyEvaluationsException, MaxCountExceededException {
final double min = getMin();
final double diff = getMax() - min;
final double midPoint = min + 0.5 * diff;
double oldt = diff * computeObjectiveValue(midPoint);
while (true) {
incrementCount();
final int i = getIterations();
final double t = stage(i, oldt, min, diff);
if (i >= getMinimalIterationCount()) {
final double delta = Math.abs(t - oldt);
final double rLimit =
getRelativeAccuracy() * (Math.abs(oldt) + Math.abs(t)) * 0.5;
if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
return t;
}
}
oldt = t;
}
}
}