FieldRombergIntegrator.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;
- import org.hipparchus.util.MathArrays;
- /**
- * Implements the <a href="http://mathworld.wolfram.com/RombergIntegration.html">
- * Romberg Algorithm</a> for integration of real univariate functions. For
- * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
- * chapter 3.
- * <p>
- * Romberg integration employs k successive refinements of the trapezoid
- * rule to remove error terms less than order O(N^(-2k)). Simpson's rule
- * is a special case of k = 2.</p>
- * @param <T> Type of the field elements.
- * @since 2.0
- */
- public class FieldRombergIntegrator<T extends CalculusFieldElement<T>> extends BaseAbstractFieldUnivariateIntegrator<T> {
- /** Maximal number of iterations for Romberg. */
- public static final int ROMBERG_MAX_ITERATIONS_COUNT = 32;
- /**
- * Build a Romberg 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 #ROMBERG_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 #ROMBERG_MAX_ITERATIONS_COUNT}
- */
- public FieldRombergIntegrator(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 > ROMBERG_MAX_ITERATIONS_COUNT) {
- throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
- maximalIterationCount, ROMBERG_MAX_ITERATIONS_COUNT);
- }
- }
- /**
- * Build a Romberg 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 #ROMBERG_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 #ROMBERG_MAX_ITERATIONS_COUNT}
- */
- public FieldRombergIntegrator(final Field<T> field,
- final int minimalIterationCount,
- final int maximalIterationCount)
- throws MathIllegalArgumentException {
- super(field, minimalIterationCount, maximalIterationCount);
- if (maximalIterationCount > ROMBERG_MAX_ITERATIONS_COUNT) {
- throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
- maximalIterationCount, ROMBERG_MAX_ITERATIONS_COUNT);
- }
- }
- /**
- * Construct a Romberg integrator with default settings
- * @param field field to which function argument and value belong
- * (max iteration count set to {@link #ROMBERG_MAX_ITERATIONS_COUNT})
- */
- public FieldRombergIntegrator(final Field<T> field) {
- super(field, DEFAULT_MIN_ITERATIONS_COUNT, ROMBERG_MAX_ITERATIONS_COUNT);
- }
- /** {@inheritDoc} */
- @Override
- protected T doIntegrate()
- throws MathIllegalStateException {
- final int m = iterations.getMaximalCount() + 1;
- T[] previousRow = MathArrays.buildArray(getField(), m);
- T[] currentRow = MathArrays.buildArray(getField(), m);
- FieldTrapezoidIntegrator<T> qtrap = new FieldTrapezoidIntegrator<>(getField());
- currentRow[0] = qtrap.stage(this, 0);
- iterations.increment();
- T olds = currentRow[0];
- while (true) {
- final int i = iterations.getCount();
- // switch rows
- final T[] tmpRow = previousRow;
- previousRow = currentRow;
- currentRow = tmpRow;
- currentRow[0] = qtrap.stage(this, i);
- iterations.increment();
- for (int j = 1; j <= i; j++) {
- // Richardson extrapolation coefficient
- final double r = (1L << (2 * j)) - 1;
- final T tIJm1 = currentRow[j - 1];
- currentRow[j] = tIJm1.add(tIJm1.subtract(previousRow[j - 1]).divide(r));
- }
- final T s = currentRow[i];
- if (i >= getMinimalIterationCount()) {
- final double delta = FastMath.abs(s.subtract(olds)).getReal();
- final double rLimit = FastMath.abs(olds).add(FastMath.abs(s)).multiply(0.5 * getRelativeAccuracy()).getReal();
- if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
- return s;
- }
- }
- olds = s;
- }
- }
- }