1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 | <?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 ?> |