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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

?>