forked from mberktas/javascript-algorithms
-
Notifications
You must be signed in to change notification settings - Fork 0
/
ComplexNumber.js
160 lines (138 loc) · 3.94 KB
/
ComplexNumber.js
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
import radianToDegree from '../radian/radianToDegree';
export default class ComplexNumber {
/**
* z = re + im * i
* z = radius * e^(i * phase)
*
* @param {number} [re]
* @param {number} [im]
*/
constructor({ re = 0, im = 0 } = {}) {
this.re = re;
this.im = im;
}
/**
* @param {ComplexNumber|number} addend
* @return {ComplexNumber}
*/
add(addend) {
// Make sure we're dealing with complex number.
const complexAddend = this.toComplexNumber(addend);
return new ComplexNumber({
re: this.re + complexAddend.re,
im: this.im + complexAddend.im,
});
}
/**
* @param {ComplexNumber|number} subtrahend
* @return {ComplexNumber}
*/
subtract(subtrahend) {
// Make sure we're dealing with complex number.
const complexSubtrahend = this.toComplexNumber(subtrahend);
return new ComplexNumber({
re: this.re - complexSubtrahend.re,
im: this.im - complexSubtrahend.im,
});
}
/**
* @param {ComplexNumber|number} multiplicand
* @return {ComplexNumber}
*/
multiply(multiplicand) {
// Make sure we're dealing with complex number.
const complexMultiplicand = this.toComplexNumber(multiplicand);
return new ComplexNumber({
re: this.re * complexMultiplicand.re - this.im * complexMultiplicand.im,
im: this.re * complexMultiplicand.im + this.im * complexMultiplicand.re,
});
}
/**
* @param {ComplexNumber|number} divider
* @return {ComplexNumber}
*/
divide(divider) {
// Make sure we're dealing with complex number.
const complexDivider = this.toComplexNumber(divider);
// Get divider conjugate.
const dividerConjugate = this.conjugate(complexDivider);
// Multiply dividend by divider's conjugate.
const finalDivident = this.multiply(dividerConjugate);
// Calculating final divider using formula (a + bi)(a − bi) = a^2 + b^2
const finalDivider = (complexDivider.re ** 2) + (complexDivider.im ** 2);
return new ComplexNumber({
re: finalDivident.re / finalDivider,
im: finalDivident.im / finalDivider,
});
}
/**
* @param {ComplexNumber|number} number
*/
conjugate(number) {
// Make sure we're dealing with complex number.
const complexNumber = this.toComplexNumber(number);
return new ComplexNumber({
re: complexNumber.re,
im: -1 * complexNumber.im,
});
}
/**
* @return {number}
*/
getRadius() {
return Math.sqrt((this.re ** 2) + (this.im ** 2));
}
/**
* @param {boolean} [inRadians]
* @return {number}
*/
getPhase(inRadians = true) {
let phase = Math.atan(Math.abs(this.im) / Math.abs(this.re));
if (this.re < 0 && this.im > 0) {
phase = Math.PI - phase;
} else if (this.re < 0 && this.im < 0) {
phase = -(Math.PI - phase);
} else if (this.re > 0 && this.im < 0) {
phase = -phase;
} else if (this.re === 0 && this.im > 0) {
phase = Math.PI / 2;
} else if (this.re === 0 && this.im < 0) {
phase = -Math.PI / 2;
} else if (this.re < 0 && this.im === 0) {
phase = Math.PI;
} else if (this.re > 0 && this.im === 0) {
phase = 0;
} else if (this.re === 0 && this.im === 0) {
// More correctly would be to set 'indeterminate'.
// But just for simplicity reasons let's set zero.
phase = 0;
}
if (!inRadians) {
phase = radianToDegree(phase);
}
return phase;
}
/**
* @param {boolean} [inRadians]
* @return {{radius: number, phase: number}}
*/
getPolarForm(inRadians = true) {
return {
radius: this.getRadius(),
phase: this.getPhase(inRadians),
};
}
/**
* Convert real numbers to complex number.
* In case if complex number is provided then lefts it as is.
*
* @param {ComplexNumber|number} number
* @return {ComplexNumber}
*/
toComplexNumber(number) {
if (number instanceof ComplexNumber) {
return number;
}
return new ComplexNumber({ re: number });
}
}