<?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 1.2 2003/03/08 11:29:21 aditus 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?>