HuasoFoundries/jpgraph

<?php

/**
 * JPGraph v4.0.3
 */

namespace Amenadiel\JpGraph\Util;

/**
 * File:        JPGRAPH_REGSTAT.PHP
 * // Description: Regression and statistical analysis helper classes
 * // Created:     2002-12-01
 * // Ver:         $Id: jpgraph_regstat.php 1131 2009-03-11 20:08:24Z ljp $
 * //
 * // Copyright (c) Asial Corporation. All rights reserved.
 */

/**
 * @class Spline
 * // Create a new data array from an existing data array but with more points.
 * // The new points are interpolated using a cubic spline algorithm
 */
class Spline
{
    // 3:rd degree polynom approximation

    private $xdata;
    private $ydata; // Data vectors
    private $y2; // 2:nd derivate of ydata
    private $n = 0;

    public function __construct($xdata, $ydata)
    {
        $this->y2    = [];
        $this->xdata = $xdata;
        $this->ydata = $ydata;

        $n       = safe_count($ydata);
        $this->n = $n;
        if ($this->n !== safe_count($xdata)) {
            JpGraphError::RaiseL(19001);
            //('Spline: Number of X and Y coordinates must be the same');
        }

        // Natural spline 2:derivate == 0 at endpoints
        $this->y2[0]      = 0.0;
        $this->y2[$n - 1] = 0.0;
        $delta[0]         = 0.0;

        // Calculate 2:nd derivate
        for ($i = 1; $i < $n - 1; ++$i) {
            $d = ($xdata[$i + 1] - $xdata[$i - 1]);
            if ($d == 0) {
                JpGraphError::RaiseL(19002);
                //('Invalid input data for spline. Two or more consecutive input X-values are equal. Each input X-value must differ since from a mathematical point of view it must be a one-to-one mapping, i.e. each X-value must correspond to exactly one Y-value.');
            }
            $s            = ($xdata[$i] - $xdata[$i - 1]) / $d;
            $p            = $s * $this->y2[$i - 1] + 2.0;
            $this->y2[$i] = ($s - 1.0) / $p;
            $delta[$i]    = ($ydata[$i + 1] - $ydata[$i]) / ($xdata[$i + 1] - $xdata[$i]) -
                ($ydata[$i] - $ydata[$i - 1]) / ($xdata[$i] - $xdata[$i - 1]);
            $delta[$i] = (6.0 * $delta[$i] / ($xdata[$i + 1] - $xdata[$i - 1]) - $s * $delta[$i - 1]) / $p;
        }

        // Backward substitution
        for ($j = $n - 2; $j >= 0; --$j) {
            $this->y2[$j] = $this->y2[$j] * $this->y2[$j + 1] + $delta[$j];
        }
    }

    // Return the two new data vectors
    public function Get($num = 50)
    {
        $n       = $this->n;
        $step    = ($this->xdata[$n - 1] - $this->xdata[0]) / ($num - 1);
        $xnew    = [];
        $ynew    = [];
        $xnew[0] = $this->xdata[0];
        $ynew[0] = $this->ydata[0];
        for ($j = 1; $j < $num; ++$j) {
            $xnew[$j] = $xnew[0] + $j * $step;
            $ynew[$j] = $this->Interpolate($xnew[$j]);
        }

        return [$xnew, $ynew];
    }

    // Return a single interpolated Y-value from an x value
    public function Interpolate($xpoint)
    {
        $max = $this->n - 1;
        $min = 0;

        // Binary search to find interval
        while ($max - $min > 1) {
            $k = ($max + $min) / 2;
            if ($this->xdata[$k] > $xpoint) {
                $max = $k;
            } else {
                $min = $k;
            }
        }

        // Each interval is interpolated by a 3:degree polynom function
        $h = $this->xdata[$max] - $this->xdata[$min];

        if ($h == 0) {
            JpGraphError::RaiseL(19002);
            //('Invalid input data for spline. Two or more consecutive input X-values are equal. Each input X-value must differ since from a mathematical point of view it must be a one-to-one mapping, i.e. each X-value must correspond to exactly one Y-value.');
        }

        $a = ($this->xdata[$max] - $xpoint) / $h;
        $b = ($xpoint - $this->xdata[$min]) / $h;

        return $a * $this->ydata[$min] + $b * $this->ydata[$max] +
            (($a * $a * $a - $a) * $this->y2[$min] + ($b * $b * $b - $b) * $this->y2[$max]) * ($h * $h) / 6.0;
    }
}

// EOF