/*
 * 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.math.analysis.integration;

import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.MaxIterationsExceededException;
import org.apache.commons.math.analysis.UnivariateRealFunction;

/**
 * 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>
 * 
 * @version $Revision$ $Date$
 * @since 1.2
 */
public class RombergIntegrator extends UnivariateRealIntegratorImpl {

	/**
	 * Construct an integrator for the given function.
	 * 
	 * @param f
	 *            function to integrate
	 * @deprecated as of 2.0 the integrand function is passed as an argument to
	 *             the
	 *             {@link #integrate(UnivariateRealFunction, double, double)}method.
	 */
	@Deprecated
	public RombergIntegrator(UnivariateRealFunction f) {
		super(f, 32);
	}

	/**
	 * Construct an integrator.
	 */
	public RombergIntegrator() {
		super(32);
	}

	/** {@inheritDoc} */
	@Deprecated
	public double integrate(final double min, final double max)
			throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
		return integrate(f, min, max);
	}

	/** {@inheritDoc} */
	public double integrate(final UnivariateRealFunction f, final double min, final double max)
			throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {

		int i = 1, j, m = maximalIterationCount + 1;
		// Array structure here can be improved for better space
		// efficiency because only the lower triangle is used.
		double r, t[][] = new double[m][m], s, olds;

		clearResult();
		verifyInterval(min, max);
		verifyIterationCount();

		TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
		t[0][0] = qtrap.stage(f, min, max, 0);
		olds = t[0][0];
		while (i <= maximalIterationCount) {
			t[i][0] = qtrap.stage(f, min, max, i);
			for (j = 1; j <= i; j++) {
				// Richardson extrapolation coefficient
				r = (1L << (2 * j)) - 1;
				t[i][j] = t[i][j - 1] + (t[i][j - 1] - t[i - 1][j - 1]) / r;
			}
			s = t[i][i];
			if (i >= minimalIterationCount) {
				final double delta = Math.abs(s - olds);
				final double rLimit = relativeAccuracy * (Math.abs(olds) + Math.abs(s)) * 0.5;
				if ((delta <= rLimit) || (delta <= absoluteAccuracy)) {
					setResult(s, i);
					return result;
				}
			}
			olds = s;
			i++;
		}
		throw new MaxIterationsExceededException(maximalIterationCount);
	}

	/** {@inheritDoc} */
	@Override
	protected void verifyIterationCount() throws IllegalArgumentException {
		super.verifyIterationCount();
		// at most 32 bisection refinements due to higher order divider
		if (maximalIterationCount > 32) {
			throw MathRuntimeException.createIllegalArgumentException("invalid iteration limits: min={0}, max={1}", 0,
					32);
		}
	}
}
