/*
 * 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.solvers;

import org.apache.commons.math.ConvergenceException;
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 a modified version of the
 * <a href="http://mathworld.wolfram.com/SecantMethod.html">secant method</a>
 * for approximating a zero of a real univariate function.
 * <p>
 * The algorithm is modified to maintain bracketing of a root by successive
 * approximations. Because of forced bracketing, convergence may be slower than
 * the unrestricted secant algorithm. However, this implementation should in
 * general outperform the
 * <a href="http://mathworld.wolfram.com/MethodofFalsePosition.html"> regula
 * falsi method.</a>
 * </p>
 * <p>
 * The function is assumed to be continuous but not necessarily smooth.
 * </p>
 * 
 * @version $Revision$ $Date$
 */
public class SecantSolver extends UnivariateRealSolverImpl {

	/**
	 * Construct a solver for the given function.
	 * 
	 * @param f
	 *            function to solve.
	 * @deprecated as of 2.0 the function to solve is passed as an argument to
	 *             the {@link #solve(UnivariateRealFunction, double, double)} or
	 *             {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)}
	 *             method.
	 */
	@Deprecated
	public SecantSolver(UnivariateRealFunction f) {
		super(f, 100, 1E-6);
	}

	/**
	 * Construct a solver.
	 */
	public SecantSolver() {
		super(100, 1E-6);
	}

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

	/** {@inheritDoc} */
	@Deprecated
	public double solve(final double min, final double max, final double initial)
			throws ConvergenceException, FunctionEvaluationException {
		return solve(f, min, max, initial);
	}

	/**
	 * Find a zero in the given interval.
	 * 
	 * @param f
	 *            the function to solve
	 * @param min
	 *            the lower bound for the interval
	 * @param max
	 *            the upper bound for the interval
	 * @param initial
	 *            the start value to use (ignored)
	 * @return the value where the function is zero
	 * @throws MaxIterationsExceededException
	 *             if the maximum iteration count is exceeded
	 * @throws FunctionEvaluationException
	 *             if an error occurs evaluating the function
	 * @throws IllegalArgumentException
	 *             if min is not less than max or the signs of the values of the
	 *             function at the endpoints are not opposites
	 */
	public double solve(final UnivariateRealFunction f, final double min, final double max, final double initial)
			throws MaxIterationsExceededException, FunctionEvaluationException {
		return solve(f, min, max);
	}

	/**
	 * Find a zero in the given interval.
	 * 
	 * @param f
	 *            the function to solve
	 * @param min
	 *            the lower bound for the interval.
	 * @param max
	 *            the upper bound for the interval.
	 * @return the value where the function is zero
	 * @throws MaxIterationsExceededException
	 *             if the maximum iteration count is exceeded
	 * @throws FunctionEvaluationException
	 *             if an error occurs evaluating the function
	 * @throws IllegalArgumentException
	 *             if min is not less than max or the signs of the values of the
	 *             function at the endpoints are not opposites
	 */
	public double solve(final UnivariateRealFunction f, final double min, final double max)
			throws MaxIterationsExceededException, FunctionEvaluationException {

		clearResult();
		verifyInterval(min, max);

		// Index 0 is the old approximation for the root.
		// Index 1 is the last calculated approximation for the root.
		// Index 2 is a bracket for the root with respect to x0.
		// OldDelta is the length of the bracketing interval of the last
		// iteration.
		double x0 = min;
		double x1 = max;
		double y0 = f.value(x0);
		double y1 = f.value(x1);

		// Verify bracketing
		if (y0 * y1 >= 0) {
			throw MathRuntimeException
					.createIllegalArgumentException("function values at endpoints do not have different signs, "
							+ "endpoints: [{0}, {1}], values: [{2}, {3}]", min, max, y0, y1);
		}

		double x2 = x0;
		double y2 = y0;
		double oldDelta = x2 - x1;
		int i = 0;
		while (i < maximalIterationCount) {
			if (Math.abs(y2) < Math.abs(y1)) {
				x0 = x1;
				x1 = x2;
				x2 = x0;
				y0 = y1;
				y1 = y2;
				y2 = y0;
			}
			if (Math.abs(y1) <= functionValueAccuracy) {
				setResult(x1, i);
				return result;
			}
			if (Math.abs(oldDelta) < Math.max(relativeAccuracy * Math.abs(x1), absoluteAccuracy)) {
				setResult(x1, i);
				return result;
			}
			double delta;
			if (Math.abs(y1) > Math.abs(y0)) {
				// Function value increased in last iteration. Force bisection.
				delta = 0.5 * oldDelta;
			} else {
				delta = (x0 - x1) / (1 - y0 / y1);
				if (delta / oldDelta > 1) {
					// New approximation falls outside bracket.
					// Fall back to bisection.
					delta = 0.5 * oldDelta;
				}
			}
			x0 = x1;
			y0 = y1;
			x1 = x1 + delta;
			y1 = f.value(x1);
			if ((y1 > 0) == (y2 > 0)) {
				// New bracket is (x0,x1).
				x2 = x0;
				y2 = y0;
			}
			oldDelta = x2 - x1;
			i++;
		}
		throw new MaxIterationsExceededException(maximalIterationCount);
	}

}
