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

/**
 * Implements <a href="http://mathworld.wolfram.com/NewtonsMethod.html">
 * Newton's Method</a> for finding zeros of real univariate functions.
 * <p>
 * The function should be continuous but not necessarily smooth.
 * </p>
 *
 * @version $Revision$ $Date$
 */
public class NewtonSolver 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 NewtonSolver(DifferentiableUnivariateRealFunction f) {
		super(f, 100, 1E-6);
	}

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

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

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

	/**
	 * Find a zero near the midpoint of <code>min</code> and <code>max</code>.
	 * 
	 * @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 or derivative
	 * @throws IllegalArgumentException
	 *             if min is not less than max
	 */
	public double solve(final UnivariateRealFunction f, final double min, final double max)
			throws MaxIterationsExceededException, FunctionEvaluationException {
		return solve(f, min, max, UnivariateRealSolverUtils.midpoint(min, max));
	}

	/**
	 * Find a zero near the value <code>startValue</code>.
	 * 
	 * @param f
	 *            the function to solve
	 * @param min
	 *            the lower bound for the interval (ignored).
	 * @param max
	 *            the upper bound for the interval (ignored).
	 * @param startValue
	 *            the start value to use.
	 * @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 or derivative
	 * @throws IllegalArgumentException
	 *             if startValue is not between min and max or if function is
	 *             not a {@link DifferentiableUnivariateRealFunction} instance
	 */
	public double solve(final UnivariateRealFunction f, final double min, final double max, final double startValue)
			throws MaxIterationsExceededException, FunctionEvaluationException {

		try {

			final UnivariateRealFunction derivative = ((DifferentiableUnivariateRealFunction) f).derivative();
			clearResult();
			verifySequence(min, startValue, max);

			double x0 = startValue;
			double x1;

			int i = 0;
			while (i < maximalIterationCount) {

				x1 = x0 - (f.value(x0) / derivative.value(x0));
				if (Math.abs(x1 - x0) <= absoluteAccuracy) {
					setResult(x1, i);
					return x1;
				}

				x0 = x1;
				++i;
			}

			throw new MaxIterationsExceededException(maximalIterationCount);
		} catch (ClassCastException cce) {
			throw MathRuntimeException.createIllegalArgumentException("function is not differentiable");
		}
	}

}
