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Diffstat (limited to 'html/jpgraph/jpgraph_regstat.php')
| -rw-r--r-- | html/jpgraph/jpgraph_regstat.php | 215 |
1 files changed, 215 insertions, 0 deletions
diff --git a/html/jpgraph/jpgraph_regstat.php b/html/jpgraph/jpgraph_regstat.php new file mode 100644 index 0000000..0f6c96b --- /dev/null +++ b/html/jpgraph/jpgraph_regstat.php @@ -0,0 +1,215 @@ +<?php +/*======================================================================= + // 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 $xdata,$ydata; // Data vectors + private $y2; // 2:nd derivate of ydata + private $n=0; + + function __construct($xdata,$ydata) { + $this->y2 = array(); + $this->xdata = $xdata; + $this->ydata = $ydata; + + $n = count($ydata); + $this->n = $n; + if( $this->n !== count($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 + function Get($num=50) { + $n = $this->n ; + $step = ($this->xdata[$n-1]-$this->xdata[0]) / ($num-1); + $xnew=array(); + $ynew=array(); + $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[$j]); + } + return array($xnew,$ynew); + } + + // Return a single interpolated Y-value from an x value + function Interpolate($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; + } +} + +//------------------------------------------------------------------------ +// CLASS Bezier +// Create a new data array from a number of control points +//------------------------------------------------------------------------ +class Bezier { + /** + * @author Thomas Despoix, openXtrem company + * @license released under QPL + * @abstract Bezier interoplated point generation, + * computed from control points data sets, based on Paul Bourke algorithm : + * http://local.wasp.uwa.edu.au/~pbourke/geometry/bezier/index2.html + */ + private $datax = array(); + private $datay = array(); + private $n=0; + + function __construct($datax, $datay, $attraction_factor = 1) { + // Adding control point multiple time will raise their attraction power over the curve + $this->n = count($datax); + if( $this->n !== count($datay) ) { + JpGraphError::RaiseL(19003); + //('Bezier: Number of X and Y coordinates must be the same'); + } + $idx=0; + foreach($datax as $datumx) { + for ($i = 0; $i < $attraction_factor; $i++) { + $this->datax[$idx++] = $datumx; + } + } + $idx=0; + foreach($datay as $datumy) { + for ($i = 0; $i < $attraction_factor; $i++) { + $this->datay[$idx++] = $datumy; + } + } + $this->n *= $attraction_factor; + } + + /** + * Return a set of data points that specifies the bezier curve with $steps points + * @param $steps Number of new points to return + * @return array($datax, $datay) + */ + function Get($steps) { + $datax = array(); + $datay = array(); + for ($i = 0; $i < $steps; $i++) { + list($datumx, $datumy) = $this->GetPoint((double) $i / (double) $steps); + $datax[$i] = $datumx; + $datay[$i] = $datumy; + } + + $datax[] = end($this->datax); + $datay[] = end($this->datay); + + return array($datax, $datay); + } + + /** + * Return one point on the bezier curve. $mu is the position on the curve where $mu is in the + * range 0 $mu < 1 where 0 is tha start point and 1 is the end point. Note that every newly computed + * point depends on all the existing points + * + * @param $mu Position on the bezier curve + * @return array($x, $y) + */ + function GetPoint($mu) { + $n = $this->n - 1; + $k = 0; + $kn = 0; + $nn = 0; + $nkn = 0; + $blend = 0.0; + $newx = 0.0; + $newy = 0.0; + + $muk = 1.0; + $munk = (double) pow(1-$mu,(double) $n); + + for ($k = 0; $k <= $n; $k++) { + $nn = $n; + $kn = $k; + $nkn = $n - $k; + $blend = $muk * $munk; + $muk *= $mu; + $munk /= (1-$mu); + while ($nn >= 1) { + $blend *= $nn; + $nn--; + if ($kn > 1) { + $blend /= (double) $kn; + $kn--; + } + if ($nkn > 1) { + $blend /= (double) $nkn; + $nkn--; + } + } + $newx += $this->datax[$k] * $blend; + $newy += $this->datay[$k] * $blend; + } + + return array($newx, $newy); + } +} + +// EOF +?> |