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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) Asial Corporation. 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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