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
|
<?php
namespace PhpOffice\PhpSpreadsheet\Shared\Trend;
use PhpOffice\PhpSpreadsheet\Shared\JAMA\Matrix;
class PolynomialBestFit extends BestFit
{
/**
* Algorithm type to use for best-fit
* (Name of this Trend class).
*
* @var string
*/
protected $bestFitType = 'polynomial';
/**
* Polynomial order.
*
* @var int
*/
protected $order = 0;
/**
* Return the order of this polynomial.
*
* @return int
*/
public function getOrder()
{
return $this->order;
}
/**
* Return the Y-Value for a specified value of X.
*
* @param float $xValue X-Value
*
* @return float Y-Value
*/
public function getValueOfYForX($xValue)
{
$retVal = $this->getIntersect();
$slope = $this->getSlope();
foreach ($slope as $key => $value) {
if ($value != 0.0) {
$retVal += $value * $xValue ** ($key + 1);
}
}
return $retVal;
}
/**
* Return the X-Value for a specified value of Y.
*
* @param float $yValue Y-Value
*
* @return float X-Value
*/
public function getValueOfXForY($yValue)
{
return ($yValue - $this->getIntersect()) / $this->getSlope();
}
/**
* Return the Equation of the best-fit line.
*
* @param int $dp Number of places of decimal precision to display
*
* @return string
*/
public function getEquation($dp = 0)
{
$slope = $this->getSlope($dp);
$intersect = $this->getIntersect($dp);
$equation = 'Y = ' . $intersect;
foreach ($slope as $key => $value) {
if ($value != 0.0) {
$equation .= ' + ' . $value . ' * X';
if ($key > 0) {
$equation .= '^' . ($key + 1);
}
}
}
return $equation;
}
/**
* Return the Slope of the line.
*
* @param int $dp Number of places of decimal precision to display
*
* @return string
*/
public function getSlope($dp = 0)
{
if ($dp != 0) {
$coefficients = [];
foreach ($this->slope as $coefficient) {
$coefficients[] = round($coefficient, $dp);
}
return $coefficients;
}
return $this->slope;
}
public function getCoefficients($dp = 0)
{
return array_merge([$this->getIntersect($dp)], $this->getSlope($dp));
}
/**
* Execute the regression and calculate the goodness of fit for a set of X and Y data values.
*
* @param int $order Order of Polynomial for this regression
* @param float[] $yValues The set of Y-values for this regression
* @param float[] $xValues The set of X-values for this regression
*/
private function polynomialRegression($order, $yValues, $xValues): void
{
// calculate sums
$x_sum = array_sum($xValues);
$y_sum = array_sum($yValues);
$xx_sum = $xy_sum = $yy_sum = 0;
for ($i = 0; $i < $this->valueCount; ++$i) {
$xy_sum += $xValues[$i] * $yValues[$i];
$xx_sum += $xValues[$i] * $xValues[$i];
$yy_sum += $yValues[$i] * $yValues[$i];
}
/*
* This routine uses logic from the PHP port of polyfit version 0.1
* written by Michael Bommarito and Paul Meagher
*
* The function fits a polynomial function of order $order through
* a series of x-y data points using least squares.
*
*/
$A = [];
$B = [];
for ($i = 0; $i < $this->valueCount; ++$i) {
for ($j = 0; $j <= $order; ++$j) {
$A[$i][$j] = $xValues[$i] ** $j;
}
}
for ($i = 0; $i < $this->valueCount; ++$i) {
$B[$i] = [$yValues[$i]];
}
$matrixA = new Matrix($A);
$matrixB = new Matrix($B);
$C = $matrixA->solve($matrixB);
$coefficients = [];
for ($i = 0; $i < $C->getRowDimension(); ++$i) {
$r = $C->get($i, 0);
if (abs($r) <= 10 ** (-9)) {
$r = 0;
}
$coefficients[] = $r;
}
$this->intersect = array_shift($coefficients);
$this->slope = $coefficients;
$this->calculateGoodnessOfFit($x_sum, $y_sum, $xx_sum, $yy_sum, $xy_sum, 0, 0, 0);
foreach ($this->xValues as $xKey => $xValue) {
$this->yBestFitValues[$xKey] = $this->getValueOfYForX($xValue);
}
}
/**
* Define the regression and calculate the goodness of fit for a set of X and Y data values.
*
* @param int $order Order of Polynomial for this regression
* @param float[] $yValues The set of Y-values for this regression
* @param float[] $xValues The set of X-values for this regression
* @param bool $const
*/
public function __construct($order, $yValues, $xValues = [], $const = true)
{
parent::__construct($yValues, $xValues);
if (!$this->error) {
if ($order < $this->valueCount) {
$this->bestFitType .= '_' . $order;
$this->order = $order;
$this->polynomialRegression($order, $yValues, $xValues);
if (($this->getGoodnessOfFit() < 0.0) || ($this->getGoodnessOfFit() > 1.0)) {
$this->error = true;
}
} else {
$this->error = true;
}
}
}
}
|
