<?php
/**
 * PHPExcel
 *
 * Copyright (c) 2006 - 2014 PHPExcel
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 *
 * @category   PHPExcel
 * @package    PHPExcel_Shared_Trend
 * @copyright  Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)
 * @license    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt	LGPL
 * @version    ##VERSION##, ##DATE##
 */
require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/trend/bestFitClass.php';
require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/Matrix.php';

/**
 * PHPExcel_Polynomial_Best_Fit
 *
 * @category   PHPExcel
 * @package    PHPExcel_Shared_Trend
 * @copyright  Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)
 */
class PHPExcel_Polynomial_Best_Fit extends PHPExcel_Best_Fit
{
    /**
     * Algorithm type to use for best-fit
     * (Name of this trend class)
     *
     * @var	string
     **/
    protected $_bestFitType = 'polynomial';

    /**
     * Polynomial order
     *
     * @protected
     * @var	int
     **/
    protected $_order = 0;

    /**
     * Return the order of this polynomial
     *
     * @return	 int
     **/
    public function getOrder()
    {
        return $this->_order;
    }

    //	function getOrder()

    /**
     * Return the Y-Value for a specified value of X
     *
     * @param	 float		$xValue			X-Value
     * @return	 float						Y-Value
     **/
    public function getValueOfYForX($xValue)
    {
        $retVal = $this->getIntersect();
        $slope = $this->getSlope();
        foreach ($slope as $key => $value) {
            if (0.0 != $value) {
                $retVal += $value * pow($xValue, $key + 1);
            }
        }

        return $retVal;
    }

    //	function getValueOfYForX()

    /**
     * Return the X-Value for a specified value of Y
     *
     * @param	 float		$yValue			Y-Value
     * @return	 float						X-Value
     **/
    public function getValueOfXForY($yValue)
    {
        return ($yValue - $this->getIntersect()) / $this->getSlope();
    }

    //	function getValueOfXForY()

    /**
     * Return the Equation of the best-fit line
     *
     * @param	 int		$dp		Number of places of decimal precision to display
     * @return	 string
     **/
    public function getEquation($dp = 0)
    {
        $slope = $this->getSlope($dp);
        $intersect = $this->getIntersect($dp);

        $equation = 'Y = ' . $intersect;
        foreach ($slope as $key => $value) {
            if (0.0 != $value) {
                $equation .= ' + ' . $value . ' * X';
                if ($key > 0) {
                    $equation .= '^' . ($key + 1);
                }
            }
        }

        return $equation;
    }

    //	function getEquation()

    /**
     * Return the Slope of the line
     *
     * @param	 int		$dp		Number of places of decimal precision to display
     * @return	 string
     **/
    public function getSlope($dp = 0)
    {
        if (0 != $dp) {
            $coefficients = [];
            foreach ($this->_slope as $coefficient) {
                $coefficients[] = round($coefficient, $dp);
            }

            return $coefficients;
        }

        return $this->_slope;
    }

    //	function getSlope()

    public function getCoefficients($dp = 0)
    {
        return array_merge([$this->getIntersect($dp)], $this->getSlope($dp));
    }

    //	function getCoefficients()

    /**
     * Execute the regression and calculate the goodness of fit for a set of X and Y data values
     *
     * @param	int			$order		Order of Polynomial for this regression
     * @param	float[]		$yValues	The set of Y-values for this regression
     * @param	float[]		$xValues	The set of X-values for this regression
     * @param	bool		$const
     */
    private function _polynomial_regression($order, $yValues, $xValues, $const)
    {
        // calculate sums
        $x_sum = array_sum($xValues);
        $y_sum = array_sum($yValues);
        $xx_sum = $xy_sum = 0;
        for ($i = 0; $i < $this->_valueCount; ++$i) {
            $xy_sum += $xValues[$i] * $yValues[$i];
            $xx_sum += $xValues[$i] * $xValues[$i];
            $yy_sum += $yValues[$i] * $yValues[$i];
        }
        /*
         *	This routine uses logic from the PHP port of polyfit version 0.1
         *	written by Michael Bommarito and Paul Meagher
         *
         *	The function fits a polynomial function of order $order through
         *	a series of x-y data points using least squares.
         *
         */
        for ($i = 0; $i < $this->_valueCount; ++$i) {
            for ($j = 0; $j <= $order; ++$j) {
                $A[$i][$j] = pow($xValues[$i], $j);
            }
        }
        for ($i = 0; $i < $this->_valueCount; ++$i) {
            $B[$i] = [$yValues[$i]];
        }
        $matrixA = new Matrix($A);
        $matrixB = new Matrix($B);
        $C = $matrixA->solve($matrixB);

        $coefficients = [];
        for ($i = 0; $i < $C->m; ++$i) {
            $r = $C->get($i, 0);
            if (abs($r) <= pow(10, -9)) {
                $r = 0;
            }
            $coefficients[] = $r;
        }

        $this->_intersect = array_shift($coefficients);
        $this->_slope = $coefficients;

        $this->_calculateGoodnessOfFit($x_sum, $y_sum, $xx_sum, $yy_sum, $xy_sum);
        foreach ($this->_xValues as $xKey => $xValue) {
            $this->_yBestFitValues[$xKey] = $this->getValueOfYForX($xValue);
        }
    }

    //	function _polynomial_regression()

    /**
     * Define the regression and calculate the goodness of fit for a set of X and Y data values
     *
     * @param	int			$order		Order of Polynomial for this regression
     * @param	float[]		$yValues	The set of Y-values for this regression
     * @param	float[]		$xValues	The set of X-values for this regression
     * @param	bool		$const
     */
    public function __construct($order, $yValues, $xValues = [], $const = true)
    {
        if (false !== parent::__construct($yValues, $xValues)) {
            if ($order < $this->_valueCount) {
                $this->_bestFitType .= '_' . $order;
                $this->_order = $order;
                $this->_polynomial_regression($order, $yValues, $xValues, $const);
                if (($this->getGoodnessOfFit() < 0.0) || ($this->getGoodnessOfFit() > 1.0)) {
                    $this->_error = true;
                }
            } else {
                $this->_error = true;
            }
        }
    }

    //	function __construct()
}	//	class polynomialBestFit
