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<?php /* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4 foldmethod=marker: / // {{{ Header /* * Driver file contains Math_Numerical_RootFinding_Bisection class to provide * Newton-Raphson 2 method root finding calculation. * * PHP versions 4 and 5 * * LICENSE: * * BSD License * * Copyright (c) 2004-2006 Firman Wandayandi * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above * copyright notice, this list of conditions and the following * disclaimer in the documentation and/or other materials provided * with the distribution. * 3. Neither the name of Firman Wandayandi nor the names of * contributors may be used to endorse or promote products derived * from this software without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE * POSSIBILITY OF SUCH DAMAGE. * * @category Math * @package Math_Numerical_RootFinding * @subpackage Methods * @author Firman Wandayandi <firman@php.net> * @copyright Copyright (c) 2004-2006 Firman Wandayandi * @license http://www.opensource.org/licenses/bsd-license.php * BSD License * @version CVS: $Id: NewtonRaphson2.php,v 1.1 2006/01/30 18:42:00 firman Exp $ / // }}} // {{{ Dependencies /* * Load Math_Numerical_RootFinding_Common as base class. / require_once 'Math/Numerical/RootFinding/Common.php'; // }}} // {{{ Class: Math_Numerical_RootFinding_NewtonRaphson2 /* * Newton-Raphson 2 method class. * * @category Math * @package Math_Numerical_RootFinding * @subpackage Methods * @author Firman Wandayandi <firman@php.net> * @copyright Copyright (c) 2004-2006 Firman Wandayandi * @license http://www.opensource.org/licenses/bsd-license.php * BSD License * @version Release: 1.0.0 / class Math_Numerical_RootFinding_NewtonRaphson2 extends Math_Numerical_RootFinding_Common { // {{{ Constructor /* * Constructor. * * @param array $options (optional) Options. * * @access public * @see Math_Numerical_RootFinding_Common::Math_Numerical_RootFinding_Common() / function Math_Numerical_RootFinding_NewtonRaphson2($options = null) { parent::Math_Numerical_RootFinding_Common($options); } // }}} // {{{ infoCompute() /* * Print out parameters description for compute() function. * * @access public / function infoCompute() { print "<h2>False Position::compute()</h2>\n" . "<em>float</em> \| <em>PEAR_Error</em> " . "<strong>compute</strong>(<u>\$fxFunction</u>, " . "<u>\$dfx1Function</u>, <u>\$dfx2Function</u>, " . "<u>\$xR</u>)<br />\n" . "<h3>Description</h3>\n" . "<em>callback</em> <u>\$fxFunction</u> Callback f(x) equation " . "function or object/method tuple.<br>\n" . "<em>callback</em> <u>\$dfx1Function</u> Callback f'(x) " . "equation function or object/method tuple.<br>\n" . "<em>callback</em> <u>\$dfx2Function</u> Callback f''(x) " . "equation function or object/method tuple.<br>\n" . "<em>float</em> <u>\$xR</u> Initial guess.<br>\n"; } // }}} // {{{ compute() /* * Newton-Raphson method for calculate double root (twin root). * * @param callback $fxFunction Callback f(x) equation function or * object/method tuple. * @param callback $dfx1Function Callback f'(x) equation function or * object/method tuple. * @param callback $dfx2Function Callback f''(x) equation function or * object/method tuple. * @param float $xR Initial guess. * * @return float\|PEAR_Error Root value on success or PEAR_Error on failure. * @access public * @see Math_Numerical_RootFinding_Common::validateEqFunction() * @see Math_Numerical_RootFinding_Common::getEqResult() * @see Math_Numerical_RootFinding_Common::isDivergentRow() * @see Math_Numerical_RootFinding_Newtonraphson::compute() / function compute($fxFunction, $dfx1Function, $dfx2Function, $xR) { // Validate f(x) equation function. $err = Math_Numerical_RootFinding_Common::validateEqFunction($fxFunction); if (PEAR::isError($err)) { return $err; } // Validate f'(x) equation function. $err = Math_Numerical_RootFinding_Common::validateEqFunction($dfx1Function); if (PEAR::isError($err)) { return $err; } // Validate f''(x) equation function. $err = Math_Numerical_RootFinding_Common::validateEqFunction($dfx2Function); if (PEAR::isError($err)) { return $err; } // Sets maximum iteration and tolerance from options. $maxIteration = $this->options['max_iteration']; $errTolerance = $this->options['err_tolerance']; // Sets variable for saving errors during iteration, for divergent // detection. $epsErrors = array(); for ($i = 1; $i < $maxIteration; $i++) { // Calculate f(x[i]), where: x[i] = $xR. $fxR = Math_Numerical_RootFinding_Common::getEqResult($fxFunction, $xR); // Calculate f'(x[i]), where: x[i] = $xR. $d1xR = Math_Numerical_RootFinding_Common::getEqResult($dfx1Function, $xR); // Calculate f''(x[i]), where: x[i] = $xR. $d2xR = Math_Numerical_RootFinding_Common::getEqResult($dfx2Function, $xR); // Avoid division by zero. if (pow($d1xR, 2) - ($fxR $d2xR) == 0) { return PEAR::raiseError('Iteration skipped, division by zero'); } // Newton-Raphson's formula. $xN = $xR - (($fxR * $d1xR) / (pow($d1xR, 2) - ($fxR * $d2xR))); // xR is the root. if ($xN == 0) { $this->root = $xR; break; } // Compute error. $this->epsError = abs(($xN - $xR) / $xN); $epsErrors[] = $this->epsError; // Detect for divergent rows. if ($this->isDivergentRows($epsErrors) && $this->options['divergent_skip']) { return PEAR::raiseError('Iteration skipped, divergent rows detected'); break; } // Check for error tolerance, if lower than or equal with // $errTolerance it is the root. if ($this->epsError <= $errTolerance) { $this->root = $xR; break; } // Switch x[i+1] -> x[i], where: x[i] = $xR and x[i+1] = $xN. $xR = $xN; } $this->iterationCount = $i; return $this->root; } // }}} } // }}} /* * Local variables: * mode: php * tab-width: 4 * c-basic-offset: 4 * c-hanging-comment-ender-p: nil * End: */ ?>

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