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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,v 1.1 2004/06/15 10:13:19 jpm Exp $ |
// |
// License: This code is released under QPL |
// Copyright (C) 2002 Johan Persson |
//======================================================================== |
*/ |
|
//------------------------------------------------------------------------ |
// 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 |
?> |