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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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