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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* 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
* Trapezoid Rule for integration of real univariate functions. For
* reference, see Introduction to Numerical Analysis, ISBN 038795452X,
* chapter 3.
*
* The function should be integrable.
*
* @since 1.2
*/
public class TrapezoidIntegrator extends BaseAbstractUnivariateIntegrator {
/** Maximum number of iterations for trapezoid. */
public static final int TRAPEZOID_MAX_ITERATIONS_COUNT = 64;
/** Intermediate result. */
private double s;
/**
* Build a trapezoid 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 #TRAPEZOID_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 #TRAPEZOID_MAX_ITERATIONS_COUNT}
*/
public TrapezoidIntegrator(final double relativeAccuracy,
final double absoluteAccuracy,
final int minimalIterationCount,
final int maximalIterationCount)
throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
throw new NumberIsTooLargeException(maximalIterationCount,
TRAPEZOID_MAX_ITERATIONS_COUNT, false);
}
}
/**
* Build a trapezoid 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 #TRAPEZOID_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 #TRAPEZOID_MAX_ITERATIONS_COUNT}
*/
public TrapezoidIntegrator(final int minimalIterationCount,
final int maximalIterationCount)
throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
super(minimalIterationCount, maximalIterationCount);
if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
throw new NumberIsTooLargeException(maximalIterationCount,
TRAPEZOID_MAX_ITERATIONS_COUNT, false);
}
}
/**
* Construct a trapezoid integrator with default settings.
* (max iteration count set to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT})
*/
public TrapezoidIntegrator() {
super(DEFAULT_MIN_ITERATIONS_COUNT, TRAPEZOID_MAX_ITERATIONS_COUNT);
}
/**
* Compute the n-th stage integral of trapezoid rule. This function
* should only be called by API integrate() in the package.
* To save time it does not verify arguments - caller does.
*
* 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.
*
* @param baseIntegrator integrator holding integration parameters
* @param n the stage of 1/2 refinement, n = 0 is no refinement
* @return the value of n-th stage integral
* @throws TooManyEvaluationsException if the maximal number of evaluations
* is exceeded.
*/
double stage(final BaseAbstractUnivariateIntegrator baseIntegrator, final int n)
throws TooManyEvaluationsException {
if (n == 0) {
final double max = baseIntegrator.getMax();
final double min = baseIntegrator.getMin();
s = 0.5 * (max - min) *
(baseIntegrator.computeObjectiveValue(min) +
baseIntegrator.computeObjectiveValue(max));
return s;
} else {
final long np = 1L << (n-1); // number of new points in this stage
double sum = 0;
final double max = baseIntegrator.getMax();
final double min = baseIntegrator.getMin();
// spacing between adjacent new points
final double spacing = (max - min) / np;
double x = min + 0.5 * spacing; // the first new point
for (long i = 0; i < np; i++) {
sum += baseIntegrator.computeObjectiveValue(x);
x += spacing;
}
// add the new sum to previously calculated result
s = 0.5 * (s + sum * spacing);
return s;
}
}
/** {@inheritDoc} */
@Override
protected double doIntegrate()
throws MathIllegalArgumentException, TooManyEvaluationsException, MaxCountExceededException {
double oldt = stage(this, 0);
incrementCount();
while (true) {
final int i = getIterations();
final double t = stage(this, i);
if (i >= getMinimalIterationCount()) {
final double delta = FastMath.abs(t - oldt);
final double rLimit =
getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5;
if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
return t;
}
}
oldt = t;
incrementCount();
}
}
}