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 * 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
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package org.apache.commons.math3.analysis.solvers;

import org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.exception.TooManyEvaluationsException;

Implements 
Newton's Method for finding zeros of real univariate functions.

The function should be continuous but not necessarily smooth.
Deprecated:
as of 3.1, replaced by NewtonRaphsonSolver/**
 * 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>
 *
 * @deprecated as of 3.1, replaced by {@link NewtonRaphsonSolver}
 */
@Deprecated
public class NewtonSolver extends AbstractDifferentiableUnivariateSolver {
    
Default absolute accuracy. /** Default absolute accuracy. */
    private static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6;

    
Construct a solver.
/**
     * Construct a solver.
     */
    public NewtonSolver() {
        this(DEFAULT_ABSOLUTE_ACCURACY);
    }
    
Construct a solver.
Params:
absoluteAccuracy – Absolute accuracy./**
     * Construct a solver.
     *
     * @param absoluteAccuracy Absolute accuracy.
     */
    public NewtonSolver(double absoluteAccuracy) {
        super(absoluteAccuracy);
    }

    
Find a zero near the midpoint of min and max. 
Params:
f – Function to solve.
min – Lower bound for the interval.
max – Upper bound for the interval.
maxEval – Maximum number of evaluations.
Throws:
TooManyEvaluationsException – 
if the maximum evaluation count is exceeded.
NumberIsTooLargeException –  if min >= max.
Returns:
the value where the function is zero./**
     * Find a zero near the midpoint of {@code min} and {@code max}.
     *
     * @param f Function to solve.
     * @param min Lower bound for the interval.
     * @param max Upper bound for the interval.
     * @param maxEval Maximum number of evaluations.
     * @return the value where the function is zero.
     * @throws org.apache.commons.math3.exception.TooManyEvaluationsException
     * if the maximum evaluation count is exceeded.
     * @throws org.apache.commons.math3.exception.NumberIsTooLargeException
     * if {@code min >= max}.
     */
    @Override
    public double solve(int maxEval, final DifferentiableUnivariateFunction f,
                        final double min, final double max)
        throws TooManyEvaluationsException {
        return super.solve(maxEval, f, UnivariateSolverUtils.midpoint(min, max));
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    @Override
    protected double doSolve()
        throws TooManyEvaluationsException {
        final double startValue = getStartValue();
        final double absoluteAccuracy = getAbsoluteAccuracy();

        double x0 = startValue;
        double x1;
        while (true) {
            x1 = x0 - (computeObjectiveValue(x0) / computeDerivativeObjectiveValue(x0));
            if (FastMath.abs(x1 - x0) <= absoluteAccuracy) {
                return x1;
            }

            x0 = x1;
        }
    }
}