c++ Regex for reading Complex Numbers

Question

I'm trying to write a regular expression to match the input of complex number in the following forms: (With a,b real number, and i/I imaginay unit)

a

a+bi

a-bi

+bi

-bi

a+i

ai

i

-i

Of course in all numbers I want to be able to also read exponential form (eg: 1.23e+45-67.89e-1256i). I've come up with this:

   regex aplusbi ("(([\\+-]?[\\d]+([\\.][\\d]+)?)?([eE][\\+-]?[\\d]+)?)?(([\\+-])?(([\\d]+?([\\.][\\d]+)?)?([eE]?[\\+-]?[\\d]+)?)?[iI])?")

It gets most of them correct, however when I input +bi or -bi or simply bi the b part goes into the real one, and it also recognises this number as correct:

12.418.546i

getting 12.41 into the real part and 8.546 into the imaginary one. How could I correct it? I'm kind of new to C++ and regexes so any kind of help would be appreciated, thanks!

Answer 1

Since you have like real/imaginary clusters, you'd have to introduce 2 assertions
to control it.

Raw: ^(?=[iI.\\d+-])([+-]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+-]?\\d+)?(?![iI.\\d]))?([+-]?(?:(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+-]?\\d+)?)?[iI])?$

Stringed: "^(?=[iI.\\\\d+-])([+-]?(?:\\\\d+(?:\\\\.\\\\d*)?|\\\\.\\\\d+)(?:[eE][+-]?\\\\d+)?(?![iI.\\\\d]))?([+-]?(?:(?:\\\\d+(?:\\\\.\\\\d*)?|\\\\.\\\\d+)(?:[eE][+-]?\\\\d+)?)?[iI])?$"

https://regex101.com/r/0JMEZ8/1

Readable version

 ^ 
 (?= [iI.\d+-] )               # Assertion that keeps it from matching empty string
 (                             # (1 start), Real
      [+-]? 
      (?:
           \d+ 
           (?: \. \d* )?
        |  \. \d+ 
      )
      (?: [eE] [+-]? \d+ )?
      (?! [iI.\d] )            # Assertion that separates real/imaginary
 )?                            # (1 end)
 (                             # (2 start), Imaginary
      [+-]? 
      (?:
           (?:
                \d+ 
                (?: \. \d* )?
             |  \. \d+ 
           )
           (?: [eE] [+-]? \d+ )?
      )?
      [iI] 
 )?                            # (2 end)
 $

Answer 2

Regex: ^(?:(?<real>\\d+(?:(?:\\.\\d+)?(?:e[+\\-]\\d+)?)?)?(?:[+\\-]))?(?<imaginary>\\d+(?:(?:\\.\\d+)?(?:e[+\\-]\\d+)?)?)?[iI]$

Demo

Answer 3

So the above was a good start, but I needed some improvements. For instance, Matlab writes out complex numbers in .csv files in the form -0.0232877540359511+-0.00509035792974122i, which could not read because of the leading sign. I also wanted to handle the case where the exponent character is E instead of e, and the exponent has no sign (default positive) so here is a small adjustment to properly handle these additional cases:

^(?:(?<real>[+\-]?\d+(?:(?:\.\d+)?(?:[eE][+\-]?\d+)?)?)?(?:[+\-]))?(?<imaginary>[+\-]?\d+(?:(?:\.\d+)?(?:[eE]?[+\-]\d+)?)?)?[iI]$