5.4 KiB
Complex.js - ℂ in JavaSript
Complex.js is a well tested JavaScript library to work with complex number arithmetic in JavaScript. It implements every elementary complex number manipulation function and the API is intentionally similar to Fraction.js. Furthermore, it's the basis of Polynomial.js and Math.js.
Example
var Complex = require('complex.js');
var c = new Complex("99.3+8i");
c.mul({re: 3, im: 9}).div(4.9).sub(3, 2);
Parser
Any function (see below) as well as the constructor of the Complex class parses its input like this.
You can pass either Objects, Doubles or Strings.
Objects
new Complex({re: real, im: imaginary});
new Complex({arg: angle, abs: radius});
new Complex({phi: angle, r: radius});
Doubles
new Complex(55.4);
Strings
new Complex("123.45");
new Complex("15+3i");
new Complex("i");
Two arguments
new Complex(3, 2); // 3+2i
Functions
Complex sign()
Returns the complex sign, defined as the complex number normalized by it's absolute value
Complex add(n)
Adds another complex number
Complex sub(n)
Subtracts another complex number
Complex mul(n)
Multiplies the number with another complex number
Complex div(n)
Divides the number by another complex number
Complex pow(exp)
Returns the number raised to the complex exponent
Complex sqrt()
Returns the complex square root of the number
Complex exp(n)
Returns e^n with complex exponent n.
Complex log()
Returns the natural logarithm (base E) of the actual complex number
double abs()
Calculates the magnitude of the complex number
double arg()
Calculates the angle of the complex number
Complex inverse()
Calculates the multiplicative inverse of the complex number (1 / z)
Complex conjugate()
Calculates the conjugate of the complex number (multiplies the imaginary part with -1)
Complex neg()
Negates the number (multiplies both the real and imaginary part with -1) in order to get the additive inverse
Complex floor([places=0])
Floors the complex number parts towards zero
Complex ceil([places=0])
Ceils the complex number parts off zero
Complex round([places=0])
Rounds the complex number parts
boolean equals(n)
Checks if both numbers are exactly the same
boolean isNaN()
Checks if the given number is not a number
Complex clone()
Returns a new Complex instance with the same real and imaginary properties
Array toVector()
Returns a Vector of the actual complex number with two components
String toString()
Returns a string representation of the actual number. As of v1.9.0 the output is a bit more human readable
new Complex(1, 2).toString(); // 1 + 2i
new Complex(0, 1).toString(); // i
new Complex(9, 0).toString(); // 9
new Complex(1, 1).toString(); // 1 + i
double valueOf()
Returns the real part of the number if imaginary part is zero. Otherwise null
Trigonometric functions
The following trigonometric functions are defined on Complex.js:
| Trig | Arcus | Hyperbolic | Arcus-Hyperbolic |
|---|---|---|---|
| sin() | asin() | sinh() | asinh() |
| cos() | acos() | cosh() | acosh() |
| tan() | atan() | tanh() | atanh() |
| cot() | acot() | coth() | acoth() |
| sec() | asec() | sech() | asech() |
| csc() | acsc() | csch() | acsch() |
Constants
Complex.ZERO
A complex zero instance
Complex.ONE
A complex one instance
Complex.I
An imaginary number i instance
Complex.PI
A complex PI instance
Complex.E
A complex euler number instance
Complex.EPSILON
A small epsilon value used for equal() comparison in order to circumvent double inprecision.
Installation
Installing complex.js is as easy as cloning this repo or use one of the following commands:
bower install complex.js
or
npm install complex.js
Using Complex.js with the browser
<script src="complex.js"></script>
<script>
console.log(Complex("4+3i"));
</script>
Using Complex.js with require.js
<script src="require.js"></script>
<script>
requirejs(['complex.js'],
function(Complex) {
console.log(Complex("4+3i"));
});
</script>
Coding Style
As every library I publish, complex.js is also built to be as small as possible after compressing it with Google Closure Compiler in advanced mode. Thus the coding style orientates a little on maxing-out the compression rate. Please make sure you keep this style if you plan to extend the library.
Testing
If you plan to enhance the library, make sure you add test cases and all the previous tests are passing. You can test the library with
npm test
Copyright and licensing
Copyright (c) 2015, Robert Eisele (robert@xarg.org) Dual licensed under the MIT or GPL Version 2 licenses.