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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 org.jbasics.checker.ContractCheck;
import org.jbasics.math.BigDecimalMathLibrary;
import org.jbasics.math.BoundedMathFunction;
import org.jbasics.math.MathFunction;
import org.jbasics.math.NumberConverter;
import org.jbasics.utilities.DataUtilities;

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

/**
 * Calculate the derivation of a function by using a numerical approximation. The calculation is made with a {@link
 * MathContext} more precise than the one given in order achieve a precise result within the given {@link MathContext}.
 * However since it is a numerical approach calculating the derivation it is not guaranteed to be precise. But it is a
 * very good approximation of the derivation.
 */
public class DerivateNumericalApproximation implements BoundedMathFunction {
	private final MathFunction function;
	private final BigDecimal lowerBoundary;
	private final BigDecimal upperBoundary;

	/**
	 * Create the numerical derivation function for the given {@link MathFunction}. If the {@link MathContext}
	 * implements {@link BoundedMathFunction} the boundaries of the function will hold as well for the derivation of the
	 * function.
	 *
	 * @param function The function to derive (must NOT be null)
	 */
	public DerivateNumericalApproximation(final MathFunction function) {
		this.function = ContractCheck.mustNotBeNull(function, "function"); //$NON-NLS-1$
		if (function instanceof BoundedMathFunction) {
			this.lowerBoundary = NumberConverter.toBigDecimal(((BoundedMathFunction) function).lowerBoundery());
			this.upperBoundary = NumberConverter.toBigDecimal(((BoundedMathFunction) function).upperBoundery());
		} else {
			this.lowerBoundary = null;
			this.upperBoundary = null;
		}
	}

	public DerivateNumericalApproximation(final MathFunction function, final BigDecimal lowerBoundary, final BigDecimal upperBoundary) {
		this.function = ContractCheck.mustNotBeNull(function, "function"); //$NON-NLS-1$
		this.lowerBoundary = lowerBoundary;
		this.upperBoundary = upperBoundary;
	}

	@Override
	public BigDecimal calculate(final Number x) {
		return calculate(null, x);
	}

	@Override
	public BigDecimal calculate(final MathContext mcInput, final Number xNum) {
		final MathContext mcIn = DataUtilities.coalesce(MathFunction.DEFAULT_MATH_CONTEXT);
		final BigDecimal x = NumberConverter.toBigDecimal(xNum);
		if (x.signum() == 0) {
			// In case of a zero X value we only use a forward difference of the precision
			// to avoid problems with a negative x value in case the function cannot handle
			// it. A better way maybe is to check if the function can handle negative values
			// by checking it's boundary?
			final BigDecimal x2 = BigDecimal.ONE.scaleByPowerOfTen(-mcIn.getPrecision());
			final BigDecimal x1 = this.lowerBoundary != null && this.lowerBoundary.compareTo(BigDecimal.ZERO) < 0 ? x2.negate() : x;
			final MathContext mc = new MathContext(mcIn.getPrecision() + 10, RoundingMode.HALF_EVEN);
			return NumberConverter.toBigDecimal(this.function.calculate(mc, x1))
					.subtract(NumberConverter.toBigDecimal(this.function.calculate(mc, x2)), mc).divide(x1.subtract(x2, mc), mc);
		} else {
			final BigDecimal min = BigDecimal.ONE.add(BigDecimal.ONE.scaleByPowerOfTen(-mcIn.getPrecision()));
			final MathContext mc = new MathContext(mcIn.getPrecision() + 10, RoundingMode.HALF_EVEN);
			final BigDecimal x1 = x.multiply(min);
			final BigDecimal x2 = x.multiply(BigDecimalMathLibrary.CONSTANT_TWO).subtract(x1);
			final BigDecimal f1 = NumberConverter.toBigDecimal(this.function.calculate(mc, x1));
			final BigDecimal f2 = NumberConverter.toBigDecimal(this.function.calculate(mc, x2));
			final BigDecimal fDiff = f1.subtract(f2, mc);
			final BigDecimal xDiff = x1.subtract(x2, mc);
			return fDiff.divide(xDiff, mc);
		}
	}

	@Override
	public double calculate(final double x) {
		return calculate(MathContext.DECIMAL64, BigDecimal.valueOf(x)).doubleValue();
	}

	@Override
	public BigDecimal lowerBoundery() {
		return this.lowerBoundary;
	}

	@Override
	public BigDecimal upperBoundery() {
		return this.upperBoundary;
	}
}