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Java example source code file (SecantSolver.java)

This example Java source code file (SecantSolver.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

abstractunivariatesolver, default_absolute_accuracy, nobracketingexception, override, secantsolver, toomanyevaluationsexception

The SecantSolver.java Java example source code

 * 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,
 * See the License for the specific language governing permissions and
 * limitations under the License.

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

import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;

 * Implements the <em>Secant method for root-finding (approximating a
 * zero of a univariate real function). The solution that is maintained is
 * not bracketed, and as such convergence is not guaranteed.
 * <p>Implementation based on the following article: M. Dowell and P. Jarratt,
 * <em>A modified regula falsi method for computing the root of an
 * equation</em>, BIT Numerical Mathematics, volume 11, number 2,
 * pages 168-174, Springer, 1971.</p>
 * <p>Note that since release 3.0 this class implements the actual
 * <em>Secant algorithm, and not a modified one. As such, the 3.0 version
 * is not backwards compatible with previous versions. To use an algorithm
 * similar to the pre-3.0 releases, use the
 * {@link IllinoisSolver <em>Illinois} algorithm or the
 * {@link PegasusSolver <em>Pegasus} algorithm.

* */ public class SecantSolver extends AbstractUnivariateSolver { /** Default absolute accuracy. */ protected static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6; /** Construct a solver with default accuracy (1e-6). */ public SecantSolver() { super(DEFAULT_ABSOLUTE_ACCURACY); } /** * Construct a solver. * * @param absoluteAccuracy absolute accuracy */ public SecantSolver(final double absoluteAccuracy) { super(absoluteAccuracy); } /** * Construct a solver. * * @param relativeAccuracy relative accuracy * @param absoluteAccuracy absolute accuracy */ public SecantSolver(final double relativeAccuracy, final double absoluteAccuracy) { super(relativeAccuracy, absoluteAccuracy); } /** {@inheritDoc} */ @Override protected final double doSolve() throws TooManyEvaluationsException, NoBracketingException { // Get initial solution double x0 = getMin(); double x1 = getMax(); double f0 = computeObjectiveValue(x0); double f1 = computeObjectiveValue(x1); // If one of the bounds is the exact root, return it. Since these are // not under-approximations or over-approximations, we can return them // regardless of the allowed solutions. if (f0 == 0.0) { return x0; } if (f1 == 0.0) { return x1; } // Verify bracketing of initial solution. verifyBracketing(x0, x1); // Get accuracies. final double ftol = getFunctionValueAccuracy(); final double atol = getAbsoluteAccuracy(); final double rtol = getRelativeAccuracy(); // Keep finding better approximations. while (true) { // Calculate the next approximation. final double x = x1 - ((f1 * (x1 - x0)) / (f1 - f0)); final double fx = computeObjectiveValue(x); // If the new approximation is the exact root, return it. Since // this is not an under-approximation or an over-approximation, // we can return it regardless of the allowed solutions. if (fx == 0.0) { return x; } // Update the bounds with the new approximation. x0 = x1; f0 = f1; x1 = x; f1 = fx; // If the function value of the last approximation is too small, // given the function value accuracy, then we can't get closer to // the root than we already are. if (FastMath.abs(f1) <= ftol) { return x1; } // If the current interval is within the given accuracies, we // are satisfied with the current approximation. if (FastMath.abs(x1 - x0) < FastMath.max(rtol * FastMath.abs(x1), atol)) { return x1; } } } }

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