|
1
|
|
|
<?php |
|
2
|
|
|
|
|
3
|
|
|
/** |
|
4
|
|
|
* JPGraph v4.0.3 |
|
5
|
|
|
*/ |
|
6
|
|
|
|
|
7
|
|
|
namespace Amenadiel\JpGraph\Util; |
|
8
|
|
|
|
|
9
|
|
|
/** |
|
10
|
|
|
* File: JPGRAPH_REGSTAT.PHP |
|
11
|
|
|
* // Description: Regression and statistical analysis helper classes |
|
12
|
|
|
* // Created: 2002-12-01 |
|
13
|
|
|
* // Ver: $Id: jpgraph_regstat.php 1131 2009-03-11 20:08:24Z ljp $ |
|
14
|
|
|
* // |
|
15
|
|
|
* // Copyright (c) Asial Corporation. All rights reserved. |
|
16
|
|
|
*/ |
|
17
|
|
|
|
|
18
|
|
|
/** |
|
19
|
|
|
* @class Spline |
|
20
|
|
|
* // Create a new data array from an existing data array but with more points. |
|
21
|
|
|
* // The new points are interpolated using a cubic spline algorithm |
|
22
|
|
|
*/ |
|
23
|
|
|
class Spline |
|
24
|
|
|
{ |
|
25
|
|
|
// 3:rd degree polynom approximation |
|
26
|
|
|
|
|
27
|
|
|
private $xdata; |
|
28
|
|
|
private $ydata; // Data vectors |
|
29
|
|
|
private $y2; // 2:nd derivate of ydata |
|
30
|
|
|
private $n = 0; |
|
31
|
|
|
|
|
32
|
|
|
public function __construct($xdata, $ydata) |
|
33
|
|
|
{ |
|
34
|
|
|
$this->y2 = []; |
|
35
|
|
|
$this->xdata = $xdata; |
|
36
|
|
|
$this->ydata = $ydata; |
|
37
|
|
|
|
|
38
|
|
|
$n = safe_count($ydata); |
|
39
|
|
|
$this->n = $n; |
|
40
|
|
|
if ($this->n !== safe_count($xdata)) { |
|
41
|
|
|
JpGraphError::RaiseL(19001); |
|
42
|
|
|
//('Spline: Number of X and Y coordinates must be the same'); |
|
43
|
|
|
} |
|
44
|
|
|
|
|
45
|
|
|
// Natural spline 2:derivate == 0 at endpoints |
|
46
|
|
|
$this->y2[0] = 0.0; |
|
47
|
|
|
$this->y2[$n - 1] = 0.0; |
|
48
|
|
|
$delta[0] = 0.0; |
|
|
|
|
|
|
49
|
|
|
|
|
50
|
|
|
// Calculate 2:nd derivate |
|
51
|
|
|
for ($i = 1; $i < $n - 1; ++$i) { |
|
52
|
|
|
$d = ($xdata[$i + 1] - $xdata[$i - 1]); |
|
53
|
|
|
if ($d == 0) { |
|
54
|
|
|
JpGraphError::RaiseL(19002); |
|
55
|
|
|
//('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.'); |
|
56
|
|
|
} |
|
57
|
|
|
$s = ($xdata[$i] - $xdata[$i - 1]) / $d; |
|
58
|
|
|
$p = $s * $this->y2[$i - 1] + 2.0; |
|
59
|
|
|
$this->y2[$i] = ($s - 1.0) / $p; |
|
60
|
|
|
$delta[$i] = ($ydata[$i + 1] - $ydata[$i]) / ($xdata[$i + 1] - $xdata[$i]) - |
|
61
|
|
|
($ydata[$i] - $ydata[$i - 1]) / ($xdata[$i] - $xdata[$i - 1]); |
|
62
|
|
|
$delta[$i] = (6.0 * $delta[$i] / ($xdata[$i + 1] - $xdata[$i - 1]) - $s * $delta[$i - 1]) / $p; |
|
63
|
|
|
} |
|
64
|
|
|
|
|
65
|
|
|
// Backward substitution |
|
66
|
|
|
for ($j = $n - 2; $j >= 0; --$j) { |
|
67
|
|
|
$this->y2[$j] = $this->y2[$j] * $this->y2[$j + 1] + $delta[$j]; |
|
68
|
|
|
} |
|
69
|
|
|
} |
|
70
|
|
|
|
|
71
|
|
|
// Return the two new data vectors |
|
72
|
|
|
public function Get($num = 50) |
|
73
|
|
|
{ |
|
74
|
|
|
$n = $this->n; |
|
75
|
|
|
$step = ($this->xdata[$n - 1] - $this->xdata[0]) / ($num - 1); |
|
76
|
|
|
$xnew = []; |
|
77
|
|
|
$ynew = []; |
|
78
|
|
|
$xnew[0] = $this->xdata[0]; |
|
79
|
|
|
$ynew[0] = $this->ydata[0]; |
|
80
|
|
|
for ($j = 1; $j < $num; ++$j) { |
|
81
|
|
|
$xnew[$j] = $xnew[0] + $j * $step; |
|
82
|
|
|
$ynew[$j] = $this->Interpolate($xnew[$j]); |
|
83
|
|
|
} |
|
84
|
|
|
|
|
85
|
|
|
return [$xnew, $ynew]; |
|
86
|
|
|
} |
|
87
|
|
|
|
|
88
|
|
|
// Return a single interpolated Y-value from an x value |
|
89
|
|
|
public function Interpolate($xpoint) |
|
90
|
|
|
{ |
|
91
|
|
|
$max = $this->n - 1; |
|
92
|
|
|
$min = 0; |
|
93
|
|
|
|
|
94
|
|
|
// Binary search to find interval |
|
95
|
|
|
while ($max - $min > 1) { |
|
96
|
|
|
$k = ($max + $min) / 2; |
|
97
|
|
|
if ($this->xdata[$k] > $xpoint) { |
|
98
|
|
|
$max = $k; |
|
99
|
|
|
} else { |
|
100
|
|
|
$min = $k; |
|
101
|
|
|
} |
|
102
|
|
|
} |
|
103
|
|
|
|
|
104
|
|
|
// Each interval is interpolated by a 3:degree polynom function |
|
105
|
|
|
$h = $this->xdata[$max] - $this->xdata[$min]; |
|
106
|
|
|
|
|
107
|
|
|
if ($h == 0) { |
|
108
|
|
|
JpGraphError::RaiseL(19002); |
|
109
|
|
|
//('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.'); |
|
110
|
|
|
} |
|
111
|
|
|
|
|
112
|
|
|
$a = ($this->xdata[$max] - $xpoint) / $h; |
|
113
|
|
|
$b = ($xpoint - $this->xdata[$min]) / $h; |
|
114
|
|
|
|
|
115
|
|
|
return $a * $this->ydata[$min] + $b * $this->ydata[$max] + |
|
116
|
|
|
(($a * $a * $a - $a) * $this->y2[$min] + ($b * $b * $b - $b) * $this->y2[$max]) * ($h * $h) / 6.0; |
|
117
|
|
|
} |
|
118
|
|
|
} |
|
119
|
|
|
|
|
120
|
|
|
// EOF |
|
121
|
|
|
|
HuasoFoundries /
jpgraph
Loading history...