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jBasics is a collection of useful utility classes for Java. This includes helper for XML, mathematic functions, restful web services helper, pattern oriented programming interfaces and more. Currently Java7 and up is supported. Version 1.0 will required at leaset Java8.
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/*
 * Copyright (c) 2009-2015
 * 	IT-Consulting Stephan Schloepke (http://www.schloepke.de/)
 * 	klemm software consulting Mirko Klemm (http://www.klemm-scs.com/)
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */
package org.jbasics.math.approximation;

import java.math.BigDecimal;
import java.math.MathContext;

import org.jbasics.checker.ContractCheck;
import org.jbasics.math.BigDecimalMathLibrary;
import org.jbasics.math.MathFunction;
import org.jbasics.math.MathFunctionHelper;
import org.jbasics.math.NumberConverter;
import org.jbasics.math.exception.NoConvergenceException;
import org.jbasics.types.tuples.Range;
import org.jbasics.utilities.DataUtilities;

public class BiSectionApproximation implements Approximation {
	private final MathFunction function;
	private final int maxIterations;
	private final BigDecimal accuracy;
	private final boolean iterateCloseWithoutConvergence;

	public BiSectionApproximation(final MathFunction function) {
		this(function, 100);
	}

	public BiSectionApproximation(final MathFunction function, final int maxIterations) {
		this(function, maxIterations, 300, false);
	}

	public BiSectionApproximation(final MathFunction function, final int maxIterations, final int accuracy,
								  final boolean iterateCloseWithoutConvergence) {
		this.function = ContractCheck.mustNotBeNull(function, "function"); //$NON-NLS-1$
		this.maxIterations = Math.max(10, Math.min(2000, maxIterations));
		this.accuracy = BigDecimal.ONE.scaleByPowerOfTen(-Math.abs(accuracy));
		this.iterateCloseWithoutConvergence = iterateCloseWithoutConvergence;
	}

	@SuppressWarnings("null")
	@Override
	public ApproximatedResult approximate(final MathContext mcIn, final BigDecimal c, final Range range) {
		final MathContext mc = DataUtilities.coalesce(mcIn, MathContext.DECIMAL64);
		BigDecimal x1 = range == null ? BigDecimal.ONE.negate() : DataUtilities.coalesce(range.from(), BigDecimal.ONE.negate());
		BigDecimal x2 = range == null ? BigDecimal.ONE : DataUtilities.coalesce(range.to(), BigDecimal.ONE);
		if (x1.compareTo(x2) == 0) {
			x2 = x1.add(x1.ulp());
		}
		BigDecimal m = BigDecimalMathLibrary.CONSTANT_TWO;
		BigDecimal f1, f2;
		int i = this.maxIterations;
		BigDecimal x1Old = null, x2Old = null;
		do {
			x1 = MathFunctionHelper.fitToBoundaries(this.function, x1);
			x2 = MathFunctionHelper.fitToBoundaries(this.function, x2);
			f1 = NumberConverter.toBigDecimal(this.function.calculate(mc, x1)).subtract(c);
			f2 = NumberConverter.toBigDecimal(this.function.calculate(mc, x2)).subtract(c);
			if (f1.signum() == 0) {
				return new ApproximatedResult(this.maxIterations - i + 1, x1, x1, x2);
			} else if (f2.signum() == 0) {
				return new ApproximatedResult(this.maxIterations - i + 1, x2, x1, x2);
			} else if (f1.signum() == f2.signum()) {
				x1Old = x1;
				x1 = x1.subtract(m, mc);
				x2Old = x2;
				x2 = x2.add(m, mc);
			} else {
				break;
			}
			m = m.multiply(BigDecimalMathLibrary.CONSTANT_TWO, mc);
		} while (--i > 1);
		if (x1Old != null) {
			if (x1.signum() != x1Old.signum()) {
				x2 = x1Old;
			} else {
				x1 = x2Old;
			}
		}
		BigDecimal x3;
		do {
			x3 = MathFunctionHelper.fitToBoundaries(this.function, x1.add(x2.subtract(x1, mc).divide(BigDecimalMathLibrary.CONSTANT_TWO)));
			try {
				final BigDecimal f3 = NumberConverter.toBigDecimal(this.function.calculate(mc, x3)).subtract(c);
				if (f3.signum() == 0) {
					break;
				} else if (f3.signum() == f1.signum()) {
					x1 = x3;
					f1 = f3;
				} else {
					x2 = x3;
					f2 = f3;
				}
			} catch (final NumberFormatException e) {
				if (this.iterateCloseWithoutConvergence) {
					break;
				} else {
					throw new NoConvergenceException("Could not continue iteration due to exception in the function call"); //$NON-NLS-1$
				}
			}
		} while (--i > 0 && x3.compareTo(this.accuracy) > 0);
		if (i > 0 || this.iterateCloseWithoutConvergence) {
			return new ApproximatedResult(this.maxIterations - i, x3, x1, x2);
		} else {
			throw new NoConvergenceException("BiSection approximation does not terminate within the maximum iterations (" + this.maxIterations //$NON-NLS-1$
					+ ")"); //$NON-NLS-1$
		}
	}
}