@rayyamhk/complex
Advanced tools
Readme
A lightweight and easy-to-use library for you to manipulate complex numbers
npm install --save @rayyamhk/complex
const Complex = require('@rayyamhk/complex');
const num1 = new Complex(3, 4); // 3 + 4i
const num2 = new Complex(-2); // -2 + 0i
const sum = Complex.add(num1, num2);
console.log(sum.toString()); // '1 + 4i'
npm install
npm run build
It creates a production version in /build
npm install
npm run test
It runs all tests in /lib/tests
@param { Number } re - Real part of the complex number
@param { Number } im - Imaginary part of the complex number
@return { Complex } Returns an instance of Complex
Note that the second argument, i.e. im, is optional.
new Complex(); // Complex.NaN
new Complex(3); // 3 + 0i
new Complex(Infinity); // Complex.NaN
new Complex('3'); // Complex.NaN
new Complex(3, 4); // 3 + 4i
new Complex(3, Infinity); // Complex.NaN
It represents NaN in this library. It is equivalent to new Complex(NaN).
It is important to know that this library doesn't introduce the concept of Complex Infinity, all Infinity in this library
are represented by Complex.NaN.
const num = new Complex(3, 4);
const quot = Complex.divide(num, Complex.ZERO); // Complex.NaN
It is equivalent to new Complex(1)
It is equivalent to new Complex(0)
It is equivalent to new Complex(Math.PI)
It is equivalent to new Complex(Math.E)
It represents the value of 5e-16, which is the smallest number considered as non-zero in this library. In the other words, any number less than Complex.EPSILON
is considered as 0. Note that Complex.EPSILON is js Number instead of instance of Complex.
@return { Number } - Returns the real part of the complex number
new Complex(3, 4).getReal(); // 3
new Complex(0, 1).getReal(); // 0
@return { Number } - Returns the imaginary part of the complex number
new Complex(3, 4).getImaginary(); // 4
Complex.ZERO.getImaginary(); // 0
@return { Number } - Returns the modulus of the complex number
Note that the modulus of the complex number is the length of the vector representing the complex number on complex plane.
new Complex(3, 4).getModulus(); // 5
Complex.ZERO.getModulus(); // 0
@return { Number } - Returns the argument of the complex number from the interval [0, 2π)
Note that the argument of the complex number is the angle between positive real-axis and the vector representing the complex number on complex plane.
new Complex(3, 3).getArgument(); // π/4
Complex.ZERO.getArgument(); // undefined
@return { String } - Returns the stringified complex number
new Complex(3, 4).toString(); // '3 + 4i'
new Complex(3.1415).toString(); // '3.1415'
Complex.NaN.toString(); // 'NaN'
@param { Complex } num
@return { Boolean } - Returns true if it is considered as NaN
It determines whether the given complex number is considered as NaN or not.
Complex.isNaN(new Complex(3)); // false
Complex.isNaN(new Complex(3, 4)); // false
Complex.isNaN(new Complex(Infinity)); // true
Complex.isNaN(Complex.NaN); // true
@param { Complex } num1
@param { Complex } num2
@param { Integer } [ digit = 15 ] - Number of significant digits
@return { Boolean } - Returns true if two complex numbers are considered as identical
It determines whether two complex numbers are considered as identical.
The optional argument digit limits the number of digits to check after the decimal point.
The test criterion is Math.abs(x - y) < 1 / (10 ** digit * 2). For default value 15, it should be 5e-16.
That means if the difference of two numbers is less than 5e-16, they are considered as same value.
const num1 = new Complex(3, 4);
const num2 = new Complex(3 + 4e-16, 4);
const num3 = new Complex(3 + 4e-16, 4 + 6e-16);
Complex.isEqual(num1, num2); // true as the diff of real parts is less than 5e-16
Complex.isEqual(num1, num3); // false as the diff of imaginary parts is greater than 5e-16
Complex.isEqual(Complex.NaN, new Complex(1 / 0)); // true as both are considered as NaN
@param { Complex } num1 - Complex number on the left of the operator
@param { Complex } num2 - Complex number on the right of the operator
@return { Complex } - Returns Sum | Difference | Product | Quotient of two numbers
Note that for Complex.divide, if the denominator, i.e. num2, is considered as 0, it returns Complex.NaN.
const num1 = new Complex(3, 4);
const num2 = new Complex(-1, 2);
Complex.add(num1, num2); // 2 + 6i
Complex.subtract(num1, num2); // 4 + 2i
Complex.multiply(num1, num2); // -11 + 2i
Complex.divide(num1, num2); // 1 - 2i
Complex.divide(num1, Complex.ZERO); // Complex.NaN
@param { Complex } num
@return { Complex } - Returns the complex conjugate
Note that if the complex number is represented by a + bi, its complex conjugate is given by a - bi.
Complex.conjugate(new Complex(3, 4)); // 3 - 4i
Complex.conjugate(new Complex(3, -4)); // 3 + 4i
Complex.conjugate(new Complex(-3, 4)); // -3 - 4i
Complex.conjugate(new Complex(3)); // 3 - 0i
Complex.conjugate(Complex.NaN); // Complex.NaN
@param { Complex } num
@return { Complex } - Returns the inverse
Complex.inverse(new Complex(3, 4)); // 3 / 25 - 4i / 25
Complex.inverse(Complex.ZERO); // Complex.NaN
@param { Complex } base
@param { Complex | Number } exponent
@return { Complex } - Returns the result of the exponentiation
The exponent can be either js Number or instance of Complex.
You can find the k-th root of complex number by setting the exponent to 1 / k. But you should know that it only returns one out of k possible solutions.
Complex.pow(z, 2); // z to the power of 2
Complex.pow(z, 1.234); // z to the power of 1.234
Complex.pow(z, 0); // Complex.ONE
Complex.pow(z, -2); // 1 divided by z to the power of 2
Complex.pow(z, 1 / 4); // one of the 4-th root of z
@param { Complex } num
@return { Complex } - Returns e to the power of num
Complex.exp(Complex.ZERO); // Complex.ONE
Complex.exp(new Complex(3, 4)); // -13.128783... - 15.200784463...i
@param { Complex } num
@return { Complex } - Returns the result after taking natural log
It calculates the natural log of the complex number.
Note that the complex log is a multivalued function, but this function only returns the principal value by restricting the imaginary part to the interval [0, 2π).
Complex.log(Complex.E); // Complex.ONE
Complex.log(Complex.ZERO); // Complex.NaN
@param { Complex } num
@return { Complex } - Returns the result of the trigo functions
It calculates the value of sin, cos, tan, csc, sec, cot of the complex number.
Note that if the argument is out of its domain, it returns Complex.NaN
Complex.sin(num); // Domain: entire complex plane C
Complex.cos(num); // Domain: entire complex plane C
Complex.tan(num); // Domain: entire complex plane C except the set { (2k+1)*π/2 : k is any integer }
Complex.tan(new Complex(Math.PI / 2)); // Complex.NaN
Complex.csc(num); // Domain: entire complex plane C except the set { kπ : k is any integer }
Complex.csc(Complex.ZERO); // Complex.NaN
Complex.sec(num); // Domain: entire complex plane C except the set { (2k+1)*π/2 : k is any integer }
Complex.sec(new Complex(Math.PI / 2)); // Complex.NaN
Complex.cot(num); // Domain: entire complex plane C except the set { kπ/2 : k is any integer }
Complex.cot(Complex.PI); // Complex.NaN
@param { Complex } num
@return { Complex } - Returns the result of the inverse trigo functions
It calculates the value of arcsin, arccos, arctan, arccsc, arcsec, arccot of the complex number.
Note that if the argument is out of its domain, it returns Complex.NaN
Complex.asin(num); // Domain: entire complex plane C
Complex.acos(num); // Domain: entire complex plane C
Complex.atan(num); // Domain: entire complex plane C except the set { i, -i }
Complex.acsc(num); // Domain: entire complex plane C except the set { 0 }
Complex.asec(num); // Domain: entire complex plane C except the set { 0 }
Complex.acot(num); // Domain: entire complex plane C except the set { i, -i , 0 }
You are welcome to contribute by:
Copyright (C) 2020 Ray Yam
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
FAQs
A lightweight and easy-to-use library for you to manipulate complex numbers
The npm package @rayyamhk/complex receives a total of 389 weekly downloads. As such, @rayyamhk/complex popularity was classified as not popular.
We found that @rayyamhk/complex demonstrated a not healthy version release cadence and project activity because the last version was released a year ago. It has 1 open source maintainer collaborating on the project.
Did you know?
Socket for GitHub automatically highlights issues in each pull request and monitors the health of all your open source dependencies. Discover the contents of your packages and block harmful activity before you install or update your dependencies.
Product
Streamline your login process and enhance security by enabling Single Sign-On (SSO) on the Socket platform, now available for all customers on the Enterprise plan, supporting 20+ identity providers.
Security News
Tea.xyz, a crypto project aimed at rewarding open source contributions, is once again facing backlash due to an influx of spam packages flooding public package registries.
Security News
As cyber threats become more autonomous, AI-powered defenses are crucial for businesses to stay ahead of attackers who can exploit software vulnerabilities at scale.