source: trunk/client/modules/Elezioni/grafici/jpgraph_regstat.php@ 73

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1<?php
2/*=======================================================================
3// File: JPGRAPH_REGSTAT.PHP
4// Description: Regression and statistical analysis helper classes
5// Created: 2002-12-01
6// Ver: $Id: jpgraph_regstat.php 781 2006-10-08 08:07:47Z ljp $
7//
8// Copyright (c) Aditus Consulting. All rights reserved.
9//========================================================================
10*/
11
12//------------------------------------------------------------------------
13// CLASS Spline
14// Create a new data array from an existing data array but with more points.
15// The new points are interpolated using a cubic spline algorithm
16//------------------------------------------------------------------------
17class Spline {
18 // 3:rd degree polynom approximation
19
20 private $xdata,$ydata; // Data vectors
21 private $y2; // 2:nd derivate of ydata
22 private $n=0;
23
24 function Spline($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 }
61
62 // Return the two new data vectors
63 function Get($num=50) {
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,$ynew);
75 }
76
77 // Return a single interpolated Y-value from an x value
78 function Interpolate($xpoint) {
79
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 }
106}
107
108//------------------------------------------------------------------------
109// CLASS Bezier
110// Create a new data array from a number of control points
111//------------------------------------------------------------------------
112class Bezier {
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://astronomy.swin.edu.au/~pbourke/curves/bezier/
119 */
120 private $datax = array();
121 private $datay = array();
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 *= $attraction_factor;
144 }
145
146 function Get($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, $datay);
159 }
160
161 function GetPoint($mu) {
162 $n = $this->n - 1;
163 $k = 0;
164 $kn = 0;
165 $nn = 0;
166 $nkn = 0;
167 $blend = 0.0;
168 $newx = 0.0;
169 $newy = 0.0;
170
171 $muk = 1.0;
172 $munk = (double) pow(1-$mu,(double) $n);
173
174 for ($k = 0; $k <= $n; $k++) {
175 $nn = $n;
176 $kn = $k;
177 $nkn = $n - $k;
178 $blend = $muk * $munk;
179 $muk *= $mu;
180 $munk /= (1-$mu);
181 while ($nn >= 1) {
182 $blend *= $nn;
183 $nn--;
184 if ($kn > 1) {
185 $blend /= (double) $kn;
186 $kn--;
187 }
188 if ($nkn > 1) {
189 $blend /= (double) $nkn;
190 $nkn--;
191 }
192 }
193 $newx += $this->datax[$k] * $blend;
194 $newy += $this->datay[$k] * $blend;
195 }
196
197 return array($newx, $newy);
198 }
199}
200
201// EOF
202?>
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