FieldMidPointIntegrator.java
/*
* 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
*
* https://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.
*/
/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus.analysis.integration;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.Field;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.exception.MathIllegalStateException;
import org.hipparchus.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>
* @param <T> Type of the field elements.
* @since 2.0
*/
public class FieldMidPointIntegrator<T extends CalculusFieldElement<T>> extends BaseAbstractFieldUnivariateIntegrator<T> {
/** 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 field field to which function argument and value belong
* @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 MathIllegalArgumentException if minimal number of iterations
* is not strictly positive
* @exception MathIllegalArgumentException if maximal number of iterations
* is lesser than or equal to the minimal number of iterations
* @exception MathIllegalArgumentException if maximal number of iterations
* is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
*/
public FieldMidPointIntegrator(final Field<T> field,
final double relativeAccuracy,
final double absoluteAccuracy,
final int minimalIterationCount,
final int maximalIterationCount)
throws MathIllegalArgumentException {
super(field, relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
maximalIterationCount, MIDPOINT_MAX_ITERATIONS_COUNT);
}
}
/**
* Build a midpoint integrator with given iteration counts.
* @param field field to which function argument and value belong
* @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 MathIllegalArgumentException if minimal number of iterations
* is not strictly positive
* @exception MathIllegalArgumentException if maximal number of iterations
* is lesser than or equal to the minimal number of iterations
* @exception MathIllegalArgumentException if maximal number of iterations
* is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
*/
public FieldMidPointIntegrator(final Field<T> field,
final int minimalIterationCount,
final int maximalIterationCount)
throws MathIllegalArgumentException {
super(field, minimalIterationCount, maximalIterationCount);
if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
maximalIterationCount, MIDPOINT_MAX_ITERATIONS_COUNT);
}
}
/**
* Construct a midpoint integrator with default settings.
* @param field field to which function argument and value belong
* (max iteration count set to {@link #MIDPOINT_MAX_ITERATIONS_COUNT})
*/
public FieldMidPointIntegrator(final Field<T> field) {
super(field, 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 MathIllegalStateException if the maximal number of evaluations
* is exceeded.
*/
private T stage(final int n,
T previousStageResult,
T min,
T diffMaxMin)
throws MathIllegalStateException {
// number of new points in this stage
final long np = 1L << (n - 1);
T sum = getField().getZero();
// spacing between adjacent new points
final T spacing = diffMaxMin.divide(np);
// the first new point
T x = min.add(spacing.multiply(0.5));
for (long i = 0; i < np; i++) {
sum = sum.add(computeObjectiveValue(x));
x = x.add(spacing);
}
// add the new sum to previously calculated result
return previousStageResult.add(sum.multiply(spacing)).multiply(0.5);
}
/** {@inheritDoc} */
@Override
protected T doIntegrate()
throws MathIllegalArgumentException, MathIllegalStateException {
final T min = getMin();
final T diff = getMax().subtract(min);
final T midPoint = min.add(diff.multiply(0.5));
T oldt = diff.multiply(computeObjectiveValue(midPoint));
while (true) {
iterations.increment();
final int i = iterations.getCount();
final T t = stage(i, oldt, min, diff);
if (i >= getMinimalIterationCount()) {
final double delta = FastMath.abs(t.subtract(oldt)).getReal();
final double rLimit = FastMath.abs(oldt).add(FastMath.abs(t)).multiply(0.5 * getRelativeAccuracy()).getReal();
if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
return t;
}
}
oldt = t;
}
}
}