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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 java.math.RoundingMode;

import org.jbasics.checker.ContractCheck;
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 RegulaFalsiApproximation implements Approximation {
	private final MathFunction function;
	private final boolean extendedVersion;
	private final int maxIterations;

	public RegulaFalsiApproximation(final MathFunction function, final boolean extendedVersion) {
		this(function, extendedVersion, 100);
	}

	public RegulaFalsiApproximation(final MathFunction function, final boolean extendedVersion, final int maxIterations) {
		this.function = ContractCheck.mustNotBeNull(function, "function"); //$NON-NLS-1$
		this.extendedVersion = extendedVersion;
		this.maxIterations = Math.min(5000, Math.max(10, maxIterations));
	}

	@Override
	public ApproximatedResult approximate(final MathContext mcIn, final BigDecimal c, final Range range) {
		BigDecimal xMin, xMax;
		xMin = BigDecimal.ZERO;
		xMax = BigDecimal.TEN;
		if (range != null) {
			if (range.from() != null) {
				xMin = range.from();
				if (range.to() == null) {
					xMax = xMin.add(xMax);
				} else {
					xMax = range.to();
				}
			} else if (range.to() != null) {
				xMin = range.to().subtract(xMax);
				xMax = range.to();
			}
		}
		final MathContext mc = DataUtilities.coalesce(mcIn, MathContext.DECIMAL64);
		final BigDecimal epsilon = BigDecimal.ONE.scaleByPowerOfTen(1 - mc.getPrecision());
		if (this.extendedVersion) {
			return findZeroExtended(mc, c, xMin, xMax, epsilon);
		} else {
			return findZeroStandard(mc, c, xMin, xMax, epsilon);
		}
	}

	private ApproximatedResult findZeroExtended(final MathContext mcIn, final BigDecimal fx, final BigDecimal xMin, final BigDecimal xMax,
												final BigDecimal epsilon) {
		final MathContext mc = new MathContext(mcIn.getPrecision() + 5, RoundingMode.HALF_EVEN);
		BigDecimal x1 = xMin;
		BigDecimal x2 = xMax;
		BigDecimal f1 = NumberConverter.toBigDecimal(this.function.calculate(mc, x1)).subtract(fx, mc);
		BigDecimal f2 = NumberConverter.toBigDecimal(this.function.calculate(mc, x2)).subtract(fx, mc);
		BigDecimal z, fz;
		for (int i = this.maxIterations; i > 0; i--) {
			final BigDecimal temp = f2.subtract(f1);
			if (temp.signum() == 0) {
				throw new NoConvergenceException("Near zero derivation at x=" + x1); //$NON-NLS-1$
			}
			z = MathFunctionHelper.fitToBoundaries(this.function, x1.subtract(x2.subtract(x1).divide(temp, mc).multiply(f1, mc)));
			fz = NumberConverter.toBigDecimal(this.function.calculate(mc, z)).subtract(fx, mc);
			if (f1.signum() == fz.signum()) {
				f1 = f1.multiply(f2.divide(f2.add(fz), mc));
				x2 = z;
				f2 = fz;
			} else {
				x1 = x2;
				f1 = f2;
				x2 = z;
				f2 = fz;
			}
			if (x2.subtract(x1).abs().compareTo(epsilon) <= 0 || fz.abs().compareTo(epsilon) <= 0) {
				return new ApproximatedResult(this.maxIterations - i - 1, z.round(mcIn), x1.round(mcIn), x2.round(mcIn));
			}
		}
		throw new NoConvergenceException("Approximation search does not converge within the maximum iterations"); //$NON-NLS-1$
	}

	private ApproximatedResult findZeroStandard(final MathContext mcIn, final BigDecimal fx, final BigDecimal xMin, final BigDecimal xMax,
												final BigDecimal epsilon) {
		final MathContext mc = new MathContext(mcIn.getPrecision() + 5, RoundingMode.HALF_EVEN);
		BigDecimal x1 = xMin;
		BigDecimal x2 = xMax;
		BigDecimal f1 = NumberConverter.toBigDecimal(this.function.calculate(mc, x1)).subtract(fx, mc);
		BigDecimal f2 = NumberConverter.toBigDecimal(this.function.calculate(mc, x2)).subtract(fx, mc);
		BigDecimal z, fz;
		for (int i = this.maxIterations; i > 0; i--) {
			z = MathFunctionHelper.fitToBoundaries(this.function,
					x1.subtract(x2.subtract(x1, mc).divide(f2.subtract(f1, mc), mc).multiply(f1, mc), mc));
			fz = NumberConverter.toBigDecimal(this.function.calculate(mc, z)).subtract(fx, mc);
			if (f1.signum() == fz.signum()) {
				x1 = z;
				f1 = fz;
			} else {
				x2 = z;
				f2 = fz;
			}
			if (x2.subtract(x1).abs().compareTo(epsilon) <= 0 || fz.abs().compareTo(epsilon) <= 0) {
				return new ApproximatedResult(this.maxIterations - i - 1, z.round(mcIn), x1.round(mcIn), x2.round(mcIn));
			}
		}
		throw new NoConvergenceException("Approximation search does not converge within the maximum iterations"); //$NON-NLS-1$
	}
}