FieldTrapezoidIntegrator.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://mathworld.wolfram.com/TrapezoidalRule.html">
* Trapezoid 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>
* @param <T> Type of the field elements.
* @since 2.0
*/
public class FieldTrapezoidIntegrator<T extends CalculusFieldElement<T>> extends BaseAbstractFieldUnivariateIntegrator<T> {
/** Maximum number of iterations for trapezoid. */
public static final int TRAPEZOID_MAX_ITERATIONS_COUNT = 64;
/** Intermediate result. */
private T s;
/**
* Build a trapezoid 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 #TRAPEZOID_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 #TRAPEZOID_MAX_ITERATIONS_COUNT}
*/
public FieldTrapezoidIntegrator(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 > TRAPEZOID_MAX_ITERATIONS_COUNT) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
maximalIterationCount, TRAPEZOID_MAX_ITERATIONS_COUNT);
}
}
/**
* Build a trapezoid 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 #TRAPEZOID_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 #TRAPEZOID_MAX_ITERATIONS_COUNT}
*/
public FieldTrapezoidIntegrator(final Field<T> field,
final int minimalIterationCount,
final int maximalIterationCount)
throws MathIllegalArgumentException {
super(field, minimalIterationCount, maximalIterationCount);
if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
maximalIterationCount, TRAPEZOID_MAX_ITERATIONS_COUNT);
}
}
/**
* Construct a trapezoid integrator with default settings.
* @param field field to which function argument and value belong
* (max iteration count set to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT})
*/
public FieldTrapezoidIntegrator(final Field<T> field) {
super(field, 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 <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 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 MathIllegalStateException if the maximal number of evaluations
* is exceeded.
*/
T stage(final BaseAbstractFieldUnivariateIntegrator<T> baseIntegrator, final int n)
throws MathIllegalStateException {
if (n == 0) {
final T max = baseIntegrator.getMax();
final T min = baseIntegrator.getMin();
s = max.subtract(min).multiply(0.5).
multiply(baseIntegrator.computeObjectiveValue(min).
add(baseIntegrator.computeObjectiveValue(max)));
return s;
} else {
final long np = 1L << (n-1); // number of new points in this stage
T sum = getField().getZero();
final T max = baseIntegrator.getMax();
final T min = baseIntegrator.getMin();
// spacing between adjacent new points
final T spacing = max.subtract(min).divide(np);
T x = min.add(spacing.multiply(0.5)); // the first new point
for (long i = 0; i < np; i++) {
sum = sum.add(baseIntegrator.computeObjectiveValue(x));
x = x.add(spacing);
}
// add the new sum to previously calculated result
s = s.add(sum.multiply(spacing)).multiply(0.5);
return s;
}
}
/** {@inheritDoc} */
@Override
protected T doIntegrate()
throws MathIllegalArgumentException, MathIllegalStateException {
T oldt = stage(this, 0);
iterations.increment();
while (true) {
final int i = iterations.getCount();
final T t = stage(this, i);
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;
iterations.increment();
}
}
}