/*
 * 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.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 
Simpson's Rule for integration of real univariate functions. For
reference, see Introduction to Numerical Analysis, ISBN 038795452X,
chapter 3.

This implementation employs the basic trapezoid rule to calculate Simpson's
rule.
Since:
1.2/**
 * Implements <a href="http://mathworld.wolfram.com/SimpsonsRule.html">
 * Simpson's Rule</a> for integration of real univariate functions. For
 * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
 * chapter 3.
 * <p>
 * This implementation employs the basic trapezoid rule to calculate Simpson's
 * rule.</p>
 *
 * @since 1.2
 */
public class SimpsonIntegrator extends BaseAbstractUnivariateIntegrator {

    
Maximal number of iterations for Simpson. /** Maximal number of iterations for Simpson. */
    public static final int SIMPSON_MAX_ITERATIONS_COUNT = 64;

    
Build a Simpson integrator with given accuracies and iterations counts.
Params:
relativeAccuracy – relative accuracy of the result
absoluteAccuracy – absolute accuracy of the result
minimalIterationCount – minimum number of iterations
maximalIterationCount – maximum number of iterations (must be less than or equal to SIMPSON_MAX_ITERATIONS_COUNT)
Throws:
NotStrictlyPositiveException – if minimal number of iterations
is not strictly positive
NumberIsTooSmallException – if maximal number of iterations
is lesser than or equal to the minimal number of iterations
NumberIsTooLargeException – if maximal number of iterations is greater than SIMPSON_MAX_ITERATIONS_COUNT/**
     * Build a Simpson 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 #SIMPSON_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 #SIMPSON_MAX_ITERATIONS_COUNT}
     */
    public SimpsonIntegrator(final double relativeAccuracy,
                             final double absoluteAccuracy,
                             final int minimalIterationCount,
                             final int maximalIterationCount)
        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
        if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
            throw new NumberIsTooLargeException(maximalIterationCount,
                                                SIMPSON_MAX_ITERATIONS_COUNT, false);
        }
    }

    
Build a Simpson integrator with given iteration counts.
Params:
minimalIterationCount – minimum number of iterations
maximalIterationCount – maximum number of iterations (must be less than or equal to SIMPSON_MAX_ITERATIONS_COUNT)
Throws:
NotStrictlyPositiveException – if minimal number of iterations
is not strictly positive
NumberIsTooSmallException – if maximal number of iterations
is lesser than or equal to the minimal number of iterations
NumberIsTooLargeException – if maximal number of iterations is greater than SIMPSON_MAX_ITERATIONS_COUNT/**
     * Build a Simpson 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 #SIMPSON_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 #SIMPSON_MAX_ITERATIONS_COUNT}
     */
    public SimpsonIntegrator(final int minimalIterationCount,
                             final int maximalIterationCount)
        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
        super(minimalIterationCount, maximalIterationCount);
        if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
            throw new NumberIsTooLargeException(maximalIterationCount,
                                                SIMPSON_MAX_ITERATIONS_COUNT, false);
        }
    }

    
Construct an integrator with default settings. (max iteration count set to SIMPSON_MAX_ITERATIONS_COUNT) /**
     * Construct an integrator with default settings.
     * (max iteration count set to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
     */
    public SimpsonIntegrator() {
        super(DEFAULT_MIN_ITERATIONS_COUNT, SIMPSON_MAX_ITERATIONS_COUNT);
    }

    
{@inheritDoc} /** {@inheritDoc} */
    @Override
    protected double doIntegrate()
        throws TooManyEvaluationsException, MaxCountExceededException {

        TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
        if (getMinimalIterationCount() == 1) {
            return (4 * qtrap.stage(this, 1) - qtrap.stage(this, 0)) / 3.0;
        }

        // Simpson's rule requires at least two trapezoid stages.
        double olds = 0;
        double oldt = qtrap.stage(this, 0);
        while (true) {
            final double t = qtrap.stage(this, getIterations());
            incrementCount();
            final double s = (4 * t - oldt) / 3.0;
            if (getIterations() >= getMinimalIterationCount()) {
                final double delta = FastMath.abs(s - olds);
                final double rLimit =
                    getRelativeAccuracy() * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
                    return s;
                }
            }
            olds = s;
            oldt = t;
        }

    }

}