<?php 
/*=======================================================================
// File:	JPGRAPH_REGSTAT.PHP
// Description: Regression and statistical analysis helper classes
// Created: 	2002-12-01
// Author:	Johan Persson (johanp@aditus.nu)
// Ver:		$Id$
//
// 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;
	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://astronomy.swin.edu.au/~pbourke/curves/bezier/
 */
    var $datax = array();
    var $datay = array();
    var $n=0;
 
    function Bezier($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;
    }

    function Get($steps) {
	$datax = array();
	$datay = array();
	for ($i = 0; $i < $steps; $i++) {
	    list($datumx, $datumy) = $this->GetPoint((double) $i / (double) $steps);       
	    $datax[] = $datumx;
	    $datay[] = $datumy;
	}
   
	$datax[] = end($this->datax);
	$datay[] = end($this->datay);
   
	return array($datax, $datay);
    }
 
    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
?>