immutable-complex

    3.0.6 • Public • Published

    Immutable-Complex

    This is a fork of the original Complex library of Arian Stolwijk. Thanks for the initial work!

    It changes one fundamental thing and some details:

    Fundamental Change

    The Complex Objects are now immutable, in the sense that when applying mathematical operations on an instance of Complex doesn't change its value, but it returns a new instance with the new value. I need this for my math.

    Consequently, the finalize method was removed.

    Changes in Details

    • I changed the name of the imaginary part from "im" to "imag", because it is more verbose and because it reminds me of the API for complex numbers in Python.

    • I added an operator like API as aliases for existing functions. You can access them via the brackets c['='](d) New aliases are:

      • ** => pow
      • * => multiply
      • / => divide
      • + => add
      • - => subtract
      • = => equals

      Used like this:

    var c = new Complex(1,1);
     
    c.add === c['+']; // true
     
    // thus:
    var cc = c['+'](c)
      , cc2 = c.add(c)
      ;
    cc['='](cc2); // true
     

    About:

    Complex is a additional Type to deal with Complex Numbers in JavaScript. It provides several methods to add, multiply numbers as well as calculate the magnitude and angle in the complex plane.

    Screenshot

    Node

    You can get this package with NPM:

    npm install ComplexImmutable
    
    var Complex = require('Complex');
    console.log(new Complex(3, 4).abs()); // 5

    Browser

    Complex can be built for the browser with wrapup or other tools that can generate browser JS from Node packages.

    Testing

    Testing is done with Mocha and Expect.js:

    # install dependencies
    npm install
    # run the tests in node
    ./node_modules/.bin/mocha test/Complex.js
    

    or testing in the browser:

    # install dependencies
    npm install
    # run a small node server
    node ./test/server.js
    # run tests
    google-chrome http://localhost:3000
    

    API Documentation

    Complex constructor:

    var z = new Complex(real, imag);

    Arguments:

    1. real (number) the real part of the number
    2. imag (number) the imaginary part of the number

    Function: Complex.from

    A in line function like Number.from.

    var z = Complex.from(real[, imag]);

    Arguments:

    1. real (number) the real part of the number
    2. imag (number, optional) the imaginary part of the number

    Or

    1. real (string) a string representation of the number, for example 1+4i

    Examples:

    var z = Complex.from(2, 4);
    var z = Complex.from(5);
    var z = Complex.from('2+5i');

    Function: Complex.fromPolar

    Creates a complex instance from a polar representation: r*e^(phi*i) = r (cos(phi) + i sin(phi))

    var z = Complex.fromPolar(r, phi);

    Arguments:

    1. r (number) the radius/magnitude of the number
    2. phi (number) the angle/phase of the number

    Constant: Complex.i

    A instance of the imaginary unit i

    var i = Complex.i;

    Constant: Complex.one

    A instance for the real number 1

    var one = Complex.one;

    Method: fromRect

    Sets the real and imaginary properties a and b from a + bi

    myComplex.fromRect(real, imag);

    Arguments:

    1. real (number) the real part of the number
    2. imag (number) the imaginary part of the number

    Method: fromPolar

    Sets the a and b in a + bi from a polar representation.

    myComplex.fromPolar(r, phi);

    Arguments:

    1. r (number) the radius/magnitude of the number
    2. phi (number) the angle/phase of the number

    Method: toPrecision

    Sets the precision of the numbers. Similar to Number.prototype.toPrecision. Useful befor printing the number with the toString method.

    myComplex.toPrecision(k);

    Arguments:

    1. k (number) An integer specifying the number of significant digits

    Method: toFixed

    Formats a number using fixed-point notation. Similar to Number.prototype.toFixed. Useful before printing the number with the toString method.

    myComplex.toFixed(k);

    Arguments:

    1. k (number) The number of digits to appear after the decimal point; this may be a value between 0 and 20, inclusive, and implementations may optionally support a larger range of values. If this argument is omitted, it is treated as 0

    Method: magnitude

    Calculates the magnitude of the complex number

    myComplex.magnitude();

    Alias:

    • abs

    Method: angle

    Calculates the angle with respect to the real axis, in radians.

    myComplex.angle();

    Aliases

    • arg
    • phase

    Method: conjugate

    Calculates the conjugate of the complex number (multiplies the imaginary part with -1)

    myComplex.conjugate();

    Method: negate

    Negates the number (multiplies both the real and imaginary part with -1)

    myComplex.negate();

    Method: multiply

    Multiplies the number with a real or complex number

    myComplex.multiply(z);

    Arguments:

    1. z (number, complex) the number to multiply with

    Alias:

    • mult

    Method: divide

    Divides the number by a real or complex number

    myComplex.divide(z);

    Arguments:

    1. z (number, complex) the number to divide by

    Alias:

    • div
    • /

    Method: add

    Adds a real or complex number

    myComplex.add(z);

    Arguments:

    1. z (number, complex) the number to add

    Alias:

    Method: subtract

    Subtracts a real or complex number

    myComplex.subtract(z);

    Arguments:

    1. z (number, complex) the number to subtract

    Alias:

    • sub

    Method: pow

    Returns the base to the exponent

    myComplex.pow(z);

    Arguments:

    1. z (number, complex) the exponent

    Alias:

    • **

    Method: sqrt

    Returns the square root

    myComplex.sqrt();

    Method: log

    Returns the natural logarithm (base E)

    myComplex.log([k]);

    Arguments:

    1. k (number) the actual answer has a multiplicity (ln(z) = ln|z| + arg(z)) where arg(z) can return the same for different angles (every 2*pi), with this argument you can define which answer is required

    Method: exp

    Calculates the e^z where the base is E and the exponential the complex number.

    myComplex.exp();

    Method: sin

    Calculates the sine of the complex number

    myComplex.sin();

    Method: cos

    Calculates the cosine of the complex number

    myComplex.cos();

    Method: tan

    Calculates the tangent of the complex number

    myComplex.tan();

    Method: sinh

    Calculates the hyperbolic sine of the complex number

    myComplex.sinh();

    Method: cosh

    Calculates the hyperbolic cosine of the complex number

    myComplex.cosh();

    Method: tanh

    Calculates the hyperbolic tangent of the complex number

    myComplex.tanh();

    Method: clone

    Returns a new Complex instance with the same real and imaginary properties

    myComplex.clone();

    Method: toString

    Returns a string representation of the complex number

    myComplex.toString();

    Examples:

    new Complex(1, 2).toString(); // 1+2i
    new Complex(0, 1).toString(); // i
    new Complex(4, 0).toString(); // 4
    new Complex(1, 1).toString(); // 1+i
    'my Complex Number is: ' + (new Complex(3, 5)); // 'my Complex Number is: 3+5i

    Method: Equals

    Checks if the real and imaginary components are equal to the passed in compelex components.

    myComplex.equals(z);

    Arguments:

    1. z (number, complex) the complex number to compare with

    Alias:

    • =

    Examples:

    new Complex(1, 4).equals(new Complex(1, 4)); // true
    new Complex(1, 4).equals(new Complex(1, 3)); // false

    MIT License

    Copyright (c) 2014 Arian Stolwijk, Lasse Fister

    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.

    Install

    npm i immutable-complex

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    1

    Version

    3.0.6

    License

    none

    Last publish

    Collaborators

    • graphicore