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Commons Math example source code file (SecantSolver.java)
The Commons Math SecantSolver.java 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, * 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 * 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> * The function is assumed to be continuous but not necessarily smooth.</p> * * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $ */ 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); } } Other Commons Math examples (source code examples)Here is a short list of links related to this Commons Math SecantSolver.java source code file: |
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