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<?php
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/**
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 * PHPExcel
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 *
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 * Copyright (c) 2006 - 2013 PHPExcel
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 *
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 * This library is free software; you can redistribute it and/or
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 * modify it under the terms of the GNU Lesser General Public
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 * License as published by the Free Software Foundation; either
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 * version 2.1 of the License, or (at your option) any later version.
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 *
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 * This library is distributed in the hope that it will be useful,
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 * but WITHOUT ANY WARRANTY; without even the implied warranty of
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 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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 * Lesser General Public License for more details.
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 *
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 * You should have received a copy of the GNU Lesser General Public
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 * License along with this library; if not, write to the Free Software
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 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
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 *
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 * @category   PHPExcel
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 * @package    PHPExcel_Shared_Trend
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 * @copyright  Copyright (c) 2006 - 2013 PHPExcel (http://www.codeplex.com/PHPExcel)
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 * @license    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt	LGPL
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 * @version    ##VERSION##, ##DATE##
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 */
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require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/trend/bestFitClass.php';
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require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/Matrix.php';
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/**
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 * PHPExcel_Polynomial_Best_Fit
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 *
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 * @category   PHPExcel
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 * @package    PHPExcel_Shared_Trend
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 * @copyright  Copyright (c) 2006 - 2013 PHPExcel (http://www.codeplex.com/PHPExcel)
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 */
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class PHPExcel_Polynomial_Best_Fit extends PHPExcel_Best_Fit
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{
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	/**
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	 * Algorithm type to use for best-fit
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	 * (Name of this trend class)
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	 *
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	 * @var	string
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	 **/
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	protected $_bestFitType		= 'polynomial';
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	/**
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	 * Polynomial order
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	 *
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	 * @protected
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	 * @var	int
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	 **/
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	protected $_order			= 0;
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	/**
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	 * Return the order of this polynomial
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	 *
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	 * @return	 int
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	 **/
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	public function getOrder() {
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		return $this->_order;
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	}	//	function getOrder()
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	/**
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	 * Return the Y-Value for a specified value of X
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	 *
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	 * @param	 float		$xValue			X-Value
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	 * @return	 float						Y-Value
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	 **/
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	public function getValueOfYForX($xValue) {
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		$retVal = $this->getIntersect();
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		$slope = $this->getSlope();
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		foreach($slope as $key => $value) {
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			if ($value != 0.0) {
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				$retVal += $value * pow($xValue, $key + 1);
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			}
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		}
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		return $retVal;
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	}	//	function getValueOfYForX()
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	/**
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	 * Return the X-Value for a specified value of Y
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	 *
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	 * @param	 float		$yValue			Y-Value
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	 * @return	 float						X-Value
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	 **/
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	public function getValueOfXForY($yValue) {
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		return ($yValue - $this->getIntersect()) / $this->getSlope();
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	}	//	function getValueOfXForY()
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	/**
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	 * Return the Equation of the best-fit line
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	 *
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	 * @param	 int		$dp		Number of places of decimal precision to display
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	 * @return	 string
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	 **/
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	public function getEquation($dp=0) {
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		$slope = $this->getSlope($dp);
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		$intersect = $this->getIntersect($dp);
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		$equation = 'Y = '.$intersect;
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		foreach($slope as $key => $value) {
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			if ($value != 0.0) {
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				$equation .= ' + '.$value.' * X';
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				if ($key > 0) {
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					$equation .= '^'.($key + 1);
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				}
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			}
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		}
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		return $equation;
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	}	//	function getEquation()
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	/**
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	 * Return the Slope of the line
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	 *
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	 * @param	 int		$dp		Number of places of decimal precision to display
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	 * @return	 string
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	 **/
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	public function getSlope($dp=0) {
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		if ($dp != 0) {
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			$coefficients = array();
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			foreach($this->_slope as $coefficient) {
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				$coefficients[] = round($coefficient,$dp);
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			}
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			return $coefficients;
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		}
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		return $this->_slope;
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	}	//	function getSlope()
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	public function getCoefficients($dp=0) {
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		return array_merge(array($this->getIntersect($dp)),$this->getSlope($dp));
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	}	//	function getCoefficients()
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	/**
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	 * Execute the regression and calculate the goodness of fit for a set of X and Y data values
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	 *
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	 * @param	int			$order		Order of Polynomial for this regression
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	 * @param	float[]		$yValues	The set of Y-values for this regression
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	 * @param	float[]		$xValues	The set of X-values for this regression
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	 * @param	boolean		$const
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	 */
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	private function _polynomial_regression($order, $yValues, $xValues, $const) {
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		// calculate sums
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		$x_sum = array_sum($xValues);
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		$y_sum = array_sum($yValues);
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		$xx_sum = $xy_sum = 0;
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		for($i = 0; $i < $this->_valueCount; ++$i) {
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			$xy_sum += $xValues[$i] * $yValues[$i];
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			$xx_sum += $xValues[$i] * $xValues[$i];
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			$yy_sum += $yValues[$i] * $yValues[$i];
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		}
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		/*
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		 *	This routine uses logic from the PHP port of polyfit version 0.1
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		 *	written by Michael Bommarito and Paul Meagher
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		 *
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		 *	The function fits a polynomial function of order $order through
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		 *	a series of x-y data points using least squares.
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		 *
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		 */
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		for ($i = 0; $i < $this->_valueCount; ++$i) {
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			for ($j = 0; $j <= $order; ++$j) {
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				$A[$i][$j] = pow($xValues[$i], $j);
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			}
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		}
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		for ($i=0; $i < $this->_valueCount; ++$i) {
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			$B[$i] = array($yValues[$i]);
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		}
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		$matrixA = new Matrix($A);
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		$matrixB = new Matrix($B);
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		$C = $matrixA->solve($matrixB);
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		$coefficients = array();
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		for($i = 0; $i < $C->m; ++$i) {
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			$r = $C->get($i, 0);
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			if (abs($r) <= pow(10, -9)) {
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				$r = 0;
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			}
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			$coefficients[] = $r;
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		}
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		$this->_intersect = array_shift($coefficients);
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		$this->_slope = $coefficients;
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		$this->_calculateGoodnessOfFit($x_sum,$y_sum,$xx_sum,$yy_sum,$xy_sum);
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		foreach($this->_xValues as $xKey => $xValue) {
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			$this->_yBestFitValues[$xKey] = $this->getValueOfYForX($xValue);
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		}
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	}	//	function _polynomial_regression()
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	/**
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	 * Define the regression and calculate the goodness of fit for a set of X and Y data values
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	 *
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	 * @param	int			$order		Order of Polynomial for this regression
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	 * @param	float[]		$yValues	The set of Y-values for this regression
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	 * @param	float[]		$xValues	The set of X-values for this regression
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	 * @param	boolean		$const
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	 */
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	function __construct($order, $yValues, $xValues=array(), $const=True) {
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		if (parent::__construct($yValues, $xValues) !== False) {
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			if ($order < $this->_valueCount) {
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				$this->_bestFitType .= '_'.$order;
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				$this->_order = $order;
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				$this->_polynomial_regression($order, $yValues, $xValues, $const);
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				if (($this->getGoodnessOfFit() < 0.0) || ($this->getGoodnessOfFit() > 1.0)) {
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					$this->_error = True;
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				}
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			} else {
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				$this->_error = True;
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			}
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		}
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	}	//	function __construct()
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}	//	class polynomialBestFit