Skip to content

lfex/complex

Folders and files

NameName
Last commit message
Last commit date

Latest commit

 

History

76 Commits
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Repository files navigation

complex

Build Status LFE Versions Erlang Versions Tags Downloads

LFE support for numbers both real and imagined

Complex project logo

Table of Contents

Introduction

This library provides complex number data types (LFE records for rectangular and polar complex numbers) as well as many mathematical operations which support the complex data type. For a full list of functions in the API,see the bottom of this README file.

Installation

Just add it to your rebar.config deps:

{deps, [
    {complex, {git, "https://github.com/lfex/complex.git", {branch, "master"}}}
  ]}.

At this point, the complex library will be avialable in your project's dependencies.

Usage

Creating Complex Numbers

Create some new complex numbers using the standard rectangular coordinates:

lfe> (set z1 (complex:new 4 -2))
#(complex 4 -2)
lfe> (set z2 (complex:new 4 2))
#(complex 4 2)

Create complex numbers using polar coordinates:

lfe> (set z3 (complex:new-polar 4 (* -0.5 (math:pi))))
#(complex-polar 4 -1.5707963267948966)
lfe> (set z4 (complex:new-polar 4 (* 0.5 (math:pi))))
#(complex-polar 4 1.5707963267948966)

Creating from Strings

You can also create a new complex number using a string value:

lfe> (complex:new "4-2i")
#(complex 4 -2)
lfe> (complex:new "4+2i")
#(complex 4 2)

There are rules for using complex strings, though:

  • there can be no spaces in the complex string
  • you must always include the real part, even if the value is zero: (complex:new "0+2i")
  • the imaginary part must always include the number, even if the component value is 1: (complex:new "2+1i")

Optional usage:

  • if the imaginary component is zero, you may leave it off: (complex:new "2")
  • you may use i, j, I, or J to indicate the imaginary part: (complex:new "-4+2j")
  • you may use floating point values: (complex:new "1.2-3.4i")
  • you may use scientific notation: (complex:new "1.2e3-4.5e-6i")

Creating from Atoms

Using the same rules, you may use atoms to create a new complex number:

lfe> (complex:new '4-2i)
#(complex 4 -2)
lfe> (complex:new '4.3+2.1i)
#(complex 4.3 2.1)
lfe> (complex:new '4.3e10-2.1e-20j)
#(complex 4.3e10 -2.1e-20)

However, do keep in mind that the use of atoms to create complex numbers should not be done automatically in large numbers, or you run the risk of exhuasting the Erlang atom table and thus crashing your VM.

Convenience Functions

For the rest of the usage, we'll just slurp so that the calls are easier to type:

lfe> (slurp "src/complex.lfe")
#(ok complex)

Printing Complex Numbers

Print the numbers we previously defined:

lfe> (format z1)
4-2i
ok
lfe> (format z2)
4+2i
ok
lfe> (format z3)
0-4.0i
ok
lfe> (format z4)
0+4.0i
ok

Note that format/1 will convert a polar coordinate to rectangular; thus the last two above.

Common Numbers

lfe> (one)
#(complex 1 0)
lfe> (two)
#(complex 2 0)
lfe> (i)
#(complex 0 1)
lfe> (pi)
#(complex 3.141592653589793 0)
lfe> (e)
#(complex 2.718281828459045 0)
lfe> (-pi/2)
#(complex -1.5707963267948966 0)

Math

Arithmatic

lfe> (add (complex 4 2) (i))
#(complex 4 3)
lfe> (sub (complex 4 2) (i))
#(complex 4 1)
lfe> (mult (complex 4 2) (i))
#(complex -2 4)
lfe> (div (complex 4 2) (i))
#(complex 2.0 -4.0)

Note that complex/2 is an alias for new/2; it just looks nicer when not using the module name.

Operations

lfe> (conj z2)
#(complex 4 -2)
lfe> (eq z1 z2)
false
lfe> (eq z1 (conj z2))
true
lfe> (inv z1)
#(complex 0.2 0.1)
lfe> (inv z2)
#(complex 0.2 -0.1)
lfe> (modulus z1)
4.47213595499958
lfe> (modulus z1 #(complex))
#(complex 4.47213595499958 0)
lfe> (modulus (complex-polar 4 (math:pi)))
4
lfe> (arg (complex-polar 4 (math:pi)))
3.141592653589793
lfe> (sqrt (-one))
#(complex 0.0 1.0)
ok
lfe> (eq (sqrt (-one)) (i))
true

Powers

Using exponents to demonstrate the cyclic values of the powers of i:

lfe> (format (pow (i) 0))
1+0i
ok
lfe> (format (pow (i) 1))
0+1i
ok
lfe> (format (pow (i) 2))
-1+0i
ok
lfe> (format (pow (i) 3))
0-1i
ok
lfe> (format (pow (i) 4))
1+0i
ok

Negative powers are supported:

lfe> (pow (pi) -2)
#(complex 0.10132118364233778 0.0)
lfe> (pow (two) -4)
#(complex 0.0625 0.0)

As are fractional powers (roots):

lfe> (pow 16 (/ 1 2))
#(complex 4.0 0)
lfe> (pow 16 (/ 1 4))
#(complex 2.0 0)
lfe> (pow 16 (/ 1 8))
#(complex 1.4142135623730951 0)

See the unit tests for a greater number of examples.

API

The list of functions currently supported by the complex library are as follows:

complex:-2pi/0
complex:->atom/1
complex:->str/1
complex:-i/0
complex:-i/2/0
complex:-one/0
complex:-pi/0
complex:-pi/2/0
complex:-two/0
complex:2pi/0
complex:abs/1
complex:abs/2
complex:acos/1
complex:acosh/1
complex:acot/1
complex:acoth/1
complex:acsc/1
complex:acsch/1
complex:add/2
complex:angle/1
complex:arg/1
complex:arg/2
complex:asec/1
complex:asech/1
complex:asin/1
complex:asinh/1
complex:atan/1
complex:atanh/1
complex:atom->/1
complex:complex/2
complex:complex-polar/2
complex:complex-polar?/1
complex:complex?/1
complex:conj/1
complex:cos/1
complex:cosh/1
complex:cot/1
complex:coth/1
complex:csc/1
complex:csch/1
complex:distance/1
complex:div/2
complex:e/0
complex:eeq/2
complex:eq/2
complex:eq/3
complex:exp/1
complex:i/0
complex:i/2/0
complex:img/1
complex:inv/1
complex:ln/1
complex:modsq/1
complex:modulus/1
complex:modulus/2
complex:mult/2
complex:neg/1
complex:new/0
complex:new/1
complex:new/2
complex:new-polar/0
complex:new-polar/1
complex:new-polar/2
complex:one/0
complex:phase/1
complex:phi/1
complex:pi/0
complex:pi/2/0
complex:polar->rect/1
complex:polar->rect/2
complex:pow/2
complex:print/1
complex:r/1
complex:real/1
complex:rect->polar/1
complex:sec/1
complex:sech/1
complex:sign/1
complex:sin/1
complex:sinh/1
complex:sqrt/1
complex:str->/1
complex:sub/2
complex:tan/1
complex:tanh/1
complex:two/0

License

Apache Version 2 License

Copyright © 2015-2020, Duncan McGreggor oubiwann@gmail.com