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List: pear-cvs
Subject: [PEAR-CVS] cvs: pear /Math_Numerical_RootFinding/Math/Numerical/RootFinding FalsePosition.php FixedP
From: "Firman Wandayandi" <firman () php ! net>
Date: 2006-01-30 18:42:00
Message-ID: cvsfirman1138646520 () cvsserver
[Download RAW message or body]
firman Mon Jan 30 18:42:00 2006 UTC
Added files:
/pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding
FalsePosition.php
FixedPoint.php
NewtonRaphson.php
NewtonRaphson2.php
RalstonRabinowitz.php
Log:
Fix the coding standar
Pointing the constructor to Math_Numerical_RootFinding_Common::Math_Numerical_RootFinding_Common
Rename file names to the camel-case style
["firman-20060130184200.txt" (text/plain)]
http://cvs.php.net/viewcvs.cgi/pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/FalsePosition.php?view=markup&rev=1.1
Index: pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/FalsePosition.php
+++ pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/FalsePosition.php
<?php
/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4 foldmethod=marker: */
// {{{ Header
/**
* Driver file contains Math_Numerical_RootFinding_Bisection class to provide
* False Position/Regula Falsi 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: FalsePosition.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_FalsePosition
/**
* False Position/Regula Falsi 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: @package_version@
*/
class Math_Numerical_RootFinding_FalsePosition
extends Math_Numerical_RootFinding_Common
{
// {{{ Constructor
/**
* Constructor.
*
* @param array $options (optional) Options.
*
* @access public
* @see Math_Numerical_RootFinding_Common::Math_Numerical_RootFinding_Common()
*/
function Math_Numerical_RootFinding_FalsePosition($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>\$xL</u>, ".
"<u>\$xU</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>float</em> <u>\$xL</u> Lower guess.<br>\n" .
"<em>float</em> <u>\$xU</u> Upper guess.<br>\n";
}
// }}}
// {{{ compute()
/**
* False Position/Regula Falsi method.
*
* @param callback $fxFunction Callback f(x) equation function or
* object/method tuple.
* @param float $xL Lower guess.
* @param float $xU Upper guess.
*
* @return float|PEAR_Error root value on success or PEAR_Error on failure.
* @access public
* @see Math_Numerical_RootFinding_Common::validateEqFunction()
* @see Math_Numerical_RootFinding_Common::getEqResult()
* @see Math_Numerical_RootFinding_Bisection::compute()
*/
function compute($fxFunction, $xL, $xU)
{
// Validate f(x) equation function.
$err = Math_Numerical_RootFinding_Common::validateEqFunction($fxFunction);
if (PEAR::isError($err)) {
return $err;
}
// Sets maximum iteration and tolerance from options.
$maxIteration = $this->options['max_iteration'];
$errTolerance = $this->options['err_tolerance'];
// Calculate first approximation $xR (False Position's formula).
$fxL = Math_Numerical_RootFinding_Common::getEqResult($fxFunction, $xL);
$fxU = Math_Numerical_RootFinding_Common::getEqResult($fxFunction, $xU);
if ($fxL - $fxU == 0) {
return PEAR::raiseError('Iteration skipped, division by zero');
}
$xR = $xU - (($fxU * ($xL - $xU)) / ($fxL - $fxU));
// Sets variable for saving errors during iteration, for divergent
// detection.
$epsErrors = array();
for ($i = 0; $i < $maxIteration; $i++) {
// Calculate f(xr), where: xr = $xR
$fxR = Math_Numerical_RootFinding_Common::getEqResult($fxFunction, $xR);
if ($fxL * $fxR < 0) { // Root is at first subinterval.
$xU = $xR;
} elseif ($fxL * $fxR > 0) { // Root is at second subinterval.
$xL = $xR;
} elseif ($fxL * $fxR == 0) { // $xR is the exact root.
$this->root = $xR;
break;
}
// Avoid division by zero.
if ($fxL - $fxU == 0) {
return PEAR::raiseError('Iteration skipped, division by zero');
}
// Compute new approximation.
$xN = $xU - (($fxU * ($xL - $xU)) / ($fxL - $fxU));
// Compute approximation 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 = $xN;
break;
}
// Calculate f(xl), where xl = $xL.
$fxL = Math_Numerical_RootFinding_Common::getEqResult($fxFunction, $xL);
// Calculate f(xu), where xu = $xU.
$fxU = Math_Numerical_RootFinding_Common::getEqResult($fxFunction, $xU);
// Switch xn -> xr, where xn = $xN and xr = $xR.
$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:
*/
?>
http://cvs.php.net/viewcvs.cgi/pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/FixedPoint.php?view=markup&rev=1.1
Index: pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/FixedPoint.php
+++ pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/FixedPoint.php
<?php
/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4 foldmethod=marker: */
// {{{ Header
/**
* Driver file contains Math_Numerical_RootFinding_Bisection class to provide
* Fixed Point 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: FixedPoint.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_FixedPoint
/**
* Fixed Point 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: @package_version@
*/
class Math_Numerical_RootFinding_FixedPoint
extends Math_Numerical_RootFinding_Common
{
// {{{ Constructor
/**
* Constructor.
*
* @param array $options (optional) Options.
*
* @access public
* @see Math_Numerical_RootFinding_Common::Math_Numerical_RootFinding_Common()
*/
function Math_Numerical_RootFinding_FixedPoint($options = null)
{
parent::Math_Numerical_RootFinding_Common($options);
}
// }}}
// {{{ infoCompute()
/**
* Print out parameters description for compute() function.
*
* @access public
*/
function infoCompute()
{
print "<h2>Fixed Point::compute()</h2>\n" .
"<em>float</em> | <em>PEAR_Error</em> ".
"<strong>compute</strong>(<u>\$gxFunction</u>, <u>\$xR</u>)<br />\n" .
"<h3>Description</h3>\n" .
"<em>callback</em> <u>\$gxFunction</u> Callback g(x) " .
"equation (the modification of f(x), which g(x) = x) " .
"function or object/method tuple.<br>\n" .
"<em>float</em> <u>\$xR</u> Initial guess.<br>\n";
}
// }}}
// {{{ compute()
/**
* Fixed Point method.
*
* This method using g(x) (the modification of f(x), which g(x) = x).
*
* @param callback $gxFunction Callback g(x) equation function or
* object/method tuple.
* @param float $xR Initial guess.
*
* @return float|PEAR_Error root value on success or PEAR_Error on failure.
* @access public
* @see Math_Numerical_RootFinding_Common::validateEqFunction()
* @see Math_Numerical_RootFinding_Common::getEqResult()
* @see Math_Numerical_RootFinding_Common::isDivergentRow()
*/
function compute($gxFunction, $xR)
{
// Validate g(x) equation function.
$err = Math_Numerical_RootFinding_Common::validateEqFunction($gxFunction);
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 = 0; $i < $maxIteration; $i++) {
// Calculate g(x[i]), where x[i] = $xR (Fixed Point's formula).
$xN = Math_Numerical_RootFinding_Common::getEqResult($gxFunction, $xR);
// xR is the root.
if ($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:
*/
?>
http://cvs.php.net/viewcvs.cgi/pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/NewtonRaphson.php?view=markup&rev=1.1
Index: pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/NewtonRaphson.php
+++ pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/NewtonRaphson.php
<?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 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: NewtonRaphson.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_NewtonRaphson
/**
* Newton-Raphson 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: @package_version@
*/
class Math_Numerical_RootFinding_NewtonRaphson
extends Math_Numerical_RootFinding_Common
{
// {{{ Constructor
/**
* Constructor.
*
* @param array $options (optional) Options.
*
* @access public
* @see Math_Numerical_RootFinding_Common::Math_Numerical_RootFinding_Common()
*/
function Math_Numerical_RootFinding_NewtonRaphson($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>\$dfxFunction</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>\$dfxFunction</u> Callback f'(x) equation " .
"function or object/method tuple.<br>\n" .
"<em>float</em> <u>\$xR</u> Initial guess.<br>\n";
}
// }}}
// {{{ compute()
/**
* Netwon-Raphson method.
*
* @param callback $fxFunction Callback f(x) equation function or
* object/method tuple.
* @param callback $dfxFunction Callback f'(x) equation function or
* object/method tuple.
* @param float $xR Initial guess.
*
* @return float|PEAR_Error Root value on success or PEAR_Error on
* failure.
* @access public
* @see Math_Numerical_RootFinding_Common::validateEqFunction()
* @see Math_Numerical_RootFinding_Common::getEqResult()
* @see Math_Numerical_RootFinding_Common::isDivergentRow()
* @see Math_Numerical_RootFinding_Newtonraphson2::compute()
*/
function compute($fxFunction, $dfxFunction, $xR) {
// evaluate f(x) equation function before begin anything
$err = Math_Numerical_RootFinding_Common::validateEqFunction($fxFunction);
if (PEAR::isError($err)) {
return $err;
}
// evaluate df(x) equation function before begin anything
$err = Math_Numerical_RootFinding_Common::validateEqFunction($dfxFunction);
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.
$dxR = Math_Numerical_RootFinding_Common::getEqResult($dfxFunction, $xR);
// Avoid division by zero.
if ($dxR == 0) {
return PEAR::raiseError('Iteration skipped, division by zero');
}
// Newton-Raphson's formula.
$xN = $xR - ($fxR / $dxR);
// xR is the root.
if ($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:
*/
?>
http://cvs.php.net/viewcvs.cgi/pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/NewtonRaphson2.php?view=markup&rev=1.1
Index: pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/NewtonRaphson2.php
+++ pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/NewtonRaphson2.php
<?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: @package_version@
*/
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:
*/
?>
http://cvs.php.net/viewcvs.cgi/pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/RalstonRabinowitz.php?view=markup&rev=1.1
Index: pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/RalstonRabinowitz.php
+++ pear/Math_Numerical_RootFinding/Math/Numerical/RootFinding/RalstonRabinowitz.php
<?php
/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4 foldmethod=marker: */
// {{{ Header
/**
* Driver file contains Math_Numerical_RootFinding_Bisection class to provide
* Ralston and Rabinowitz 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: RalstonRabinowitz.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_RalstonRabinowitz
/**
* Ralston and Rabinowitz 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: @package_version@
*/
class Math_Numerical_RootFinding_RalstonRabinowitz
extends Math_Numerical_RootFinding_Common
{
// {{{ Constructor
/**
* Constructor.
*
* @param array $options (optional) Options.
*
* @access public
* @see Math_Numerical_RootFinding_Common::Math_Numerical_RootFinding_Common()
*/
function Math_Numerical_RootFinding_RalstonRabinowitz($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>\$dfxFunction</u>, <u>\$xR0</u>, " .
"<u>\$xR1</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>\$dfxFunction</u> Callback f'(x) " .
"equation function or object/method tuple.<br>\n" .
"<em>float</em> <u>\$xR0</u> First initial guess.<br>\n" .
"<em>float</em> <u>\$xR1</u> Second initial guess.<br>\n";
}
// }}}
// {{{ compute()
/**
* Ralston and Rabinowitz method for calculate double root (twin root).
*
* @param callback $fxFunction Callback f(x) equation function or
* object/method tuple.
* @param callback $dxFunction Callback f'(x) equation function or
* object/method tuple.
* @param float $xR0 First initial guess.
* @param float $xR1 Second initial guess.
*
* @return float|PEAR_Error Root value on success or PEAR_Error on failure.
* @access public
* @see Math_Numerical_RootFinding_Common::validateEqFunction()
* @see Math_Numerical_RootFinding_Common::getEqResult()
* @see Math_Numerical_RootFinding_Common::isDivergentRow()
* @see Math_Numerical_RootFinding_Secant::compute()
*/
function compute($fxFunction, $dxFunction, $xR0, $xR1)
{
// Validate f(x) equation function.
$err = Math_Numerical_RootFinding_Common::validateEqFunction($fxFunction);
if (PEAR::isError($err)) {
return $err;
}
// Validate f'(x) equation function.
$err = Math_Numerical_RootFinding_Common::validateEqFunction($dxFunction);
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-1]) and f'(x[1]), where: x[i-1] = $xR0.
$fxR0 = Math_Numerical_RootFinding_Common::getEqResult($fxFunction, \
$xR0);
$dxR0 = Math_Numerical_RootFinding_Common::getEqResult($dxFunction, \
$xR0);
// Calculate f(x[i]) and f'(x[1]), where: x[i] = $xR1.
$fxR1 = Math_Numerical_RootFinding_Common::getEqResult($fxFunction, \
$xR1);
$dxR1 = Math_Numerical_RootFinding_Common::getEqResult($dxFunction, \
$xR1);
// Calculate f(x[i-1]) / f'(x[i-1], where x[i-1] = $xR0.
$uxR0 = $fxR0 / $dxR0;
// Calculate f(x[i]) / f'(x[i]), where x[i] = $xR1;
$uxR1 = $fxR1 / $dxR1;
// Avoid division by zero.
if ($uxR0 - $uxR1 == 0) {
return PEAR::raiseError('Iteration skipped division by zero');
}
// Ralston and Rabinowitz's formula.
$xN = $xR1 - ($uxR1 * ($xR0 - $xR1) / ($uxR0 - $uxR1));
// xR is the root.
if ($xN == 0) {
$this->root = $xR;
break;
}
// Compute error.
$this->epsError = abs(($xN - $xR1) / $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 = $xR1;
break;
}
// Swicth the values for next iteration x[i] -> x[i-1] and
// x[i+1] -> x[i], where: x[i-1] = $xR0, x[i] = $xR1, and
// x[i+1] = $xN.
$xR0 = $xR1;
$xR1 = $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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