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<?php
/*=======================================================================
// File: JPGRAPH_REGSTAT.PHP
// Description: Regression and statistical analysis helper classes
// Created: 2002-12-01
// Ver: $Id: jpgraph_regstat.php 1131 2009-03-11 20:08:24Z 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
private $xdata,$ydata; // Data vectors
private $y2; // 2:nd derivate of ydata
private $n=0;
function __construct($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://local.wasp.uwa.edu.au/~pbourke/geometry/bezier/index2.html
*/
private $datax = array();
private $datay = array();
private $n=0;
function __construct($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;
}
/**
* Return a set of data points that specifies the bezier curve with $steps points
* @param $steps Number of new points to return
* @return array($datax, $datay)
*/
function Get($steps) {
$datax = array();
$datay = array();
for ($i = 0; $i < $steps; $i++) {
list($datumx, $datumy) = $this->GetPoint((double) $i / (double) $steps);
$datax[$i] = $datumx;
$datay[$i] = $datumy;
}
$datax[] = end($this->datax);
$datay[] = end($this->datay);
return array($datax, $datay);
}
/**
* Return one point on the bezier curve. $mu is the position on the curve where $mu is in the
* range 0 $mu < 1 where 0 is tha start point and 1 is the end point. Note that every newly computed
* point depends on all the existing points
*
* @param $mu Position on the bezier curve
* @return array($x, $y)
*/
function GetPoint($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
?>
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