|
1
|
|
|
<?php |
|
2
|
|
|
|
|
3
|
|
|
namespace Hotrush\AngularSweep; |
|
4
|
|
|
|
|
5
|
|
|
class ComplexNumber |
|
6
|
|
|
{ |
|
7
|
|
|
/** |
|
8
|
|
|
* The real part of the complex number |
|
9
|
|
|
* |
|
10
|
|
|
* @var float |
|
11
|
|
|
* @access private |
|
12
|
|
|
*/ |
|
13
|
|
|
private $_real; |
|
14
|
|
|
/** |
|
15
|
|
|
* The imaginary part of the complex number |
|
16
|
|
|
* |
|
17
|
|
|
* @var float |
|
18
|
|
|
* @access private |
|
19
|
|
|
*/ |
|
20
|
|
|
private $_im; |
|
21
|
|
|
|
|
22
|
|
|
/** |
|
23
|
|
|
* Constructor for ComplexNumberPoint |
|
24
|
|
|
* |
|
25
|
|
|
* @param float $real Real part of the number |
|
26
|
|
|
* @param float $im Imaginary part of the number |
|
27
|
|
|
*/ |
|
28
|
|
|
public function __construct($real, $im) |
|
29
|
|
|
{ |
|
30
|
|
|
$this->_real = floatval($real); |
|
31
|
|
|
$this->_im = floatval($im); |
|
32
|
|
|
} |
|
33
|
|
|
|
|
34
|
|
|
/** |
|
35
|
|
|
* Simple string representation of the number. |
|
36
|
|
|
* |
|
37
|
|
|
* @return string |
|
38
|
|
|
*/ |
|
39
|
|
|
public function toString() |
|
40
|
|
|
{ |
|
41
|
|
|
$r = $this->getReal(); |
|
42
|
|
|
$i = $this->getIm(); |
|
43
|
|
|
$str = $r; |
|
44
|
|
|
$str .= ($i < 0) ? ' - ' : ' + '; |
|
45
|
|
|
$str .= abs($i) . 'i'; |
|
46
|
|
|
return $str; |
|
47
|
|
|
} |
|
48
|
|
|
|
|
49
|
|
|
/** |
|
50
|
|
|
* Returns the square of the magnitude of the number. |
|
51
|
|
|
* |
|
52
|
|
|
* @return float |
|
53
|
|
|
*/ |
|
54
|
|
|
public function abs2() |
|
55
|
|
|
{ |
|
56
|
|
|
return ($this->_real * $this->_real + $this->_im * $this->_im); |
|
57
|
|
|
} |
|
58
|
|
|
|
|
59
|
|
|
/** |
|
60
|
|
|
* Returns the magnitude (also referred as norm) of the number. |
|
61
|
|
|
* |
|
62
|
|
|
* @return float |
|
63
|
|
|
*/ |
|
64
|
|
|
public function abs() |
|
65
|
|
|
{ |
|
66
|
|
|
return sqrt($this->abs2()); |
|
67
|
|
|
} |
|
68
|
|
|
|
|
69
|
|
|
/** |
|
70
|
|
|
* Returns the argument of the complex number. |
|
71
|
|
|
* |
|
72
|
|
|
* @return float A floating point number on success |
|
73
|
|
|
* @throws \Exception |
|
74
|
|
|
*/ |
|
75
|
|
|
public function arg() |
|
76
|
|
|
{ |
|
77
|
|
|
$arg = atan2($this->_im, $this->_real); |
|
78
|
|
|
if (M_PI < $arg || $arg < -1 * M_PI) { |
|
79
|
|
|
throw new \Exception('Argument has an impossible value'); |
|
80
|
|
|
} else { |
|
81
|
|
|
return $arg; |
|
82
|
|
|
} |
|
83
|
|
|
} |
|
84
|
|
|
|
|
85
|
|
|
/** |
|
86
|
|
|
* Returns the angle (argument) associated with the complex number. |
|
87
|
|
|
* |
|
88
|
|
|
* @return mixed A float on success |
|
89
|
|
|
* @throws \Exception |
|
90
|
|
|
*/ |
|
91
|
|
|
public function angle() |
|
92
|
|
|
{ |
|
93
|
|
|
return $this->arg(); |
|
94
|
|
|
} |
|
95
|
|
|
|
|
96
|
|
|
/** |
|
97
|
|
|
* Returns the real part of the complex number. |
|
98
|
|
|
* |
|
99
|
|
|
* @return float |
|
100
|
|
|
*/ |
|
101
|
|
|
public function getReal() |
|
102
|
|
|
{ |
|
103
|
|
|
return $this->_real; |
|
104
|
|
|
} |
|
105
|
|
|
|
|
106
|
|
|
/** |
|
107
|
|
|
* Returns the imaginary part of the complex number. |
|
108
|
|
|
* @return float |
|
109
|
|
|
*/ |
|
110
|
|
|
public function getIm() |
|
111
|
|
|
{ |
|
112
|
|
|
return $this->_im; |
|
113
|
|
|
} |
|
114
|
|
|
|
|
115
|
|
|
/** |
|
116
|
|
|
* Subtract complex number. |
|
117
|
|
|
* |
|
118
|
|
|
* @param ComplexNumber $number |
|
119
|
|
|
* @return ComplexNumber |
|
120
|
|
|
*/ |
|
121
|
|
|
public function subtract(ComplexNumber $number) |
|
122
|
|
|
{ |
|
123
|
|
|
return new ComplexNumber( |
|
124
|
|
|
$this->getReal() - $number->getReal(), |
|
125
|
|
|
$this->getIm() - $number->getIm() |
|
126
|
|
|
); |
|
127
|
|
|
} |
|
128
|
|
|
} |