Changeset 265 for trunk/client/modules/Elezioni/grafici/jpgraph_regstat.php
- Timestamp:
- Apr 13, 2019, 8:05:15 PM (5 years ago)
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- 1 edited
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trunk/client/modules/Elezioni/grafici/jpgraph_regstat.php
r2 r265 1 <?php 1 <?php 2 2 /*======================================================================= 3 // File:JPGRAPH_REGSTAT.PHP4 // Description: Regression and statistical analysis helper classes5 // Created:2002-12-016 // Ver: $Id: jpgraph_regstat.php 781 2006-10-08 08:07:47Z ljp $7 //8 // Copyright (c) Aditus Consulting. All rights reserved.9 //========================================================================10 */3 // File: JPGRAPH_REGSTAT.PHP 4 // Description: Regression and statistical analysis helper classes 5 // Created: 2002-12-01 6 // Ver: $Id: jpgraph_regstat.php 1131 2009-03-11 20:08:24Z ljp $ 7 // 8 // Copyright (c) Asial Corporation. All rights reserved. 9 //======================================================================== 10 */ 11 11 12 12 //------------------------------------------------------------------------ … … 19 19 20 20 private $xdata,$ydata; // Data vectors 21 private $y2; // 2:nd derivate of ydata21 private $y2; // 2:nd derivate of ydata 22 22 private $n=0; 23 23 24 function Spline($xdata,$ydata) {25 26 27 28 29 30 31 32 33 //('Spline: Number of X and Y coordinates must be the same');34 35 36 37 38 39 40 41 42 43 44 45 46 //('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.');47 48 49 50 51 $delta[$i] = ($ydata[$i+1]-$ydata[$i])/($xdata[$i+1]-$xdata[$i]) - 52 53 54 55 56 57 58 59 24 function __construct($xdata,$ydata) { 25 $this->y2 = array(); 26 $this->xdata = $xdata; 27 $this->ydata = $ydata; 28 29 $n = count($ydata); 30 $this->n = $n; 31 if( $this->n !== count($xdata) ) { 32 JpGraphError::RaiseL(19001); 33 //('Spline: Number of X and Y coordinates must be the same'); 34 } 35 36 // Natural spline 2:derivate == 0 at endpoints 37 $this->y2[0] = 0.0; 38 $this->y2[$n-1] = 0.0; 39 $delta[0] = 0.0; 40 41 // Calculate 2:nd derivate 42 for($i=1; $i < $n-1; ++$i) { 43 $d = ($xdata[$i+1]-$xdata[$i-1]); 44 if( $d == 0 ) { 45 JpGraphError::RaiseL(19002); 46 //('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.'); 47 } 48 $s = ($xdata[$i]-$xdata[$i-1])/$d; 49 $p = $s*$this->y2[$i-1]+2.0; 50 $this->y2[$i] = ($s-1.0)/$p; 51 $delta[$i] = ($ydata[$i+1]-$ydata[$i])/($xdata[$i+1]-$xdata[$i]) - 52 ($ydata[$i]-$ydata[$i-1])/($xdata[$i]-$xdata[$i-1]); 53 $delta[$i] = (6.0*$delta[$i]/($xdata[$i+1]-$xdata[$i-1])-$s*$delta[$i-1])/$p; 54 } 55 56 // Backward substitution 57 for( $j=$n-2; $j >= 0; --$j ) { 58 $this->y2[$j] = $this->y2[$j]*$this->y2[$j+1] + $delta[$j]; 59 } 60 60 } 61 61 62 62 // Return the two new data vectors 63 63 function Get($num=50) { 64 65 66 67 68 69 70 71 72 73 74 64 $n = $this->n ; 65 $step = ($this->xdata[$n-1]-$this->xdata[0]) / ($num-1); 66 $xnew=array(); 67 $ynew=array(); 68 $xnew[0] = $this->xdata[0]; 69 $ynew[0] = $this->ydata[0]; 70 for( $j=1; $j < $num; ++$j ) { 71 $xnew[$j] = $xnew[0]+$j*$step; 72 $ynew[$j] = $this->Interpolate($xnew[$j]); 73 } 74 return array($xnew,$ynew); 75 75 } 76 76 … … 78 78 function Interpolate($xpoint) { 79 79 80 81 82 83 84 85 86 if( $this->xdata[$k] > $xpoint ) 87 88 else 89 90 } 91 92 93 94 95 96 97 //('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.');98 99 100 101 102 103 104 80 $max = $this->n-1; 81 $min = 0; 82 83 // Binary search to find interval 84 while( $max-$min > 1 ) { 85 $k = ($max+$min) / 2; 86 if( $this->xdata[$k] > $xpoint ) 87 $max=$k; 88 else 89 $min=$k; 90 } 91 92 // Each interval is interpolated by a 3:degree polynom function 93 $h = $this->xdata[$max]-$this->xdata[$min]; 94 95 if( $h == 0 ) { 96 JpGraphError::RaiseL(19002); 97 //('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.'); 98 } 99 100 101 $a = ($this->xdata[$max]-$xpoint)/$h; 102 $b = ($xpoint-$this->xdata[$min])/$h; 103 return $a*$this->ydata[$min]+$b*$this->ydata[$max]+ 104 (($a*$a*$a-$a)*$this->y2[$min]+($b*$b*$b-$b)*$this->y2[$max])*($h*$h)/6.0; 105 105 } 106 106 } … … 111 111 //------------------------------------------------------------------------ 112 112 class Bezier { 113 /**114 * @author Thomas Despoix, openXtrem company115 * @license released under QPL116 * @abstract Bezier interoplated point generation,117 * computed from control points data sets, based on Paul Bourke algorithm :118 * http://astronomy.swin.edu.au/~pbourke/curves/bezier/119 */113 /** 114 * @author Thomas Despoix, openXtrem company 115 * @license released under QPL 116 * @abstract Bezier interoplated point generation, 117 * computed from control points data sets, based on Paul Bourke algorithm : 118 * http://local.wasp.uwa.edu.au/~pbourke/geometry/bezier/index2.html 119 */ 120 120 private $datax = array(); 121 121 private $datay = array(); 122 122 private $n=0; 123 124 function Bezier($datax, $datay, $attraction_factor = 1) { 125 // Adding control point multiple time will raise their attraction power over the curve 126 $this->n = count($datax); 127 if( $this->n !== count($datay) ) { 128 JpGraphError::RaiseL(19003); 129 //('Bezier: Number of X and Y coordinates must be the same'); 130 } 131 $idx=0; 132 foreach($datax as $datumx) { 133 for ($i = 0; $i < $attraction_factor; $i++) { 134 $this->datax[$idx++] = $datumx; 135 } 136 } 137 $idx=0; 138 foreach($datay as $datumy) { 139 for ($i = 0; $i < $attraction_factor; $i++) { 140 $this->datay[$idx++] = $datumy; 141 } 142 } 143 $this->n *= $attraction_factor; 144 } 145 123 124 function __construct($datax, $datay, $attraction_factor = 1) { 125 // Adding control point multiple time will raise their attraction power over the curve 126 $this->n = count($datax); 127 if( $this->n !== count($datay) ) { 128 JpGraphError::RaiseL(19003); 129 //('Bezier: Number of X and Y coordinates must be the same'); 130 } 131 $idx=0; 132 foreach($datax as $datumx) { 133 for ($i = 0; $i < $attraction_factor; $i++) { 134 $this->datax[$idx++] = $datumx; 135 } 136 } 137 $idx=0; 138 foreach($datay as $datumy) { 139 for ($i = 0; $i < $attraction_factor; $i++) { 140 $this->datay[$idx++] = $datumy; 141 } 142 } 143 $this->n *= $attraction_factor; 144 } 145 146 /** 147 * Return a set of data points that specifies the bezier curve with $steps points 148 * @param $steps Number of new points to return 149 * @return array($datax, $datay) 150 */ 146 151 function Get($steps) { 147 $datax = array(); 148 $datay = array(); 149 for ($i = 0; $i < $steps; $i++) { 150 list($datumx, $datumy) = $this->GetPoint((double) $i / (double) $steps); 151 $datax[] = $datumx; 152 $datay[] = $datumy; 153 } 154 155 $datax[] = end($this->datax); 156 $datay[] = end($this->datay); 157 158 return array($datax, $datay); 159 } 160 152 $datax = array(); 153 $datay = array(); 154 for ($i = 0; $i < $steps; $i++) { 155 list($datumx, $datumy) = $this->GetPoint((double) $i / (double) $steps); 156 $datax[$i] = $datumx; 157 $datay[$i] = $datumy; 158 } 159 160 $datax[] = end($this->datax); 161 $datay[] = end($this->datay); 162 163 return array($datax, $datay); 164 } 165 166 /** 167 * Return one point on the bezier curve. $mu is the position on the curve where $mu is in the 168 * range 0 $mu < 1 where 0 is tha start point and 1 is the end point. Note that every newly computed 169 * point depends on all the existing points 170 * 171 * @param $mu Position on the bezier curve 172 * @return array($x, $y) 173 */ 161 174 function GetPoint($mu) { 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 175 $n = $this->n - 1; 176 $k = 0; 177 $kn = 0; 178 $nn = 0; 179 $nkn = 0; 180 $blend = 0.0; 181 $newx = 0.0; 182 $newy = 0.0; 183 184 $muk = 1.0; 185 $munk = (double) pow(1-$mu,(double) $n); 186 187 for ($k = 0; $k <= $n; $k++) { 188 $nn = $n; 189 $kn = $k; 190 $nkn = $n - $k; 191 $blend = $muk * $munk; 192 $muk *= $mu; 193 $munk /= (1-$mu); 194 while ($nn >= 1) { 195 $blend *= $nn; 196 $nn--; 197 if ($kn > 1) { 198 $blend /= (double) $kn; 199 $kn--; 200 } 201 if ($nkn > 1) { 202 $blend /= (double) $nkn; 203 $nkn--; 204 } 205 } 206 $newx += $this->datax[$k] * $blend; 207 $newy += $this->datay[$k] * $blend; 208 } 209 210 return array($newx, $newy); 198 211 } 199 212 }
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