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;
        }

    }

}