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<?php
/*=======================================================================
// File: JPGRAPH_REGSTAT.PHP
// Description: Regression and statistical analysis helper classes
// Created: 2002-12-01
// Author: Johan Persson (johanp@aditus.nu)
// Ver: $Id: jpgraph_regstat.php 21 2005-05-30 20:35:34Z ljp $
//
// Copyright (c) Aditus Consulting. 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
var $xdata,$ydata; // Data vectors
var $y2; // 2:nd derivate of ydata
var $n=0;
function Spline($xdata,$ydata) {
$this->y2 = array();
$this->xdata = $xdata;
$this->ydata = $ydata;
$n = count($ydata);
$this->n = $n;
// 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::Raise('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::Raise('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
?>
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