Thread: Linear Equation Solver

I am trying to port a mathematics library that I made in Python a few years ago to C++. It is not as hard as I had expected it to be, however, I am having trouble converting my Linear Equation Solver into C++. This is because it uses Complex numbers as well as the 'eval' function (it is amazingly only three lines of code). Can anyone give me any pointers on how I should convert this kind of thing into C++? I am just not sure as to the best way to tackle this problem in C++.
Thanks for any advice that you can give me.

This is the python code, it makes use of eval() and Complex (imaginary numbers).

Code:

def solve(eq,var='x'):
    eq1 = eq.replace("=","-(") + ")"
    c = eval(eq1,{var:1j})
    return -c.real/c.imag

>>> solve("x - 2*x + 5*x - 46*(235-24) = x + 2")
3236.0

I do not think that something along the same lines as the python one can be done using C++.

You'll have to specify in non-python specific language what is meant by "a dictionary containing one item as a complex number" and how "eval" works with it. While the mapping of that into C++ probably won't be trivial (eg a "dictionary" is not a basic concept in the C++ language so you'll have to implement all operations on dictionaries in a library, possibly in a class library, so you can use them in one-liners like you can in python).

The problem with mapping "high level" functions from languages like python (or perl, or ...) is that you have to implement a whole lot of helper code to make those functions work in C++. It's certainly possible to do that, if difficult.

You might want to do a hunt for clones of matlab or maple. They are proprietary interpreted languages for doing numerical work and symbolic logic respectively. Both would require a parser that can work with expressions. There are some free clones available, some (I understand) with source code in C/C++. The source for such a parser might give you a useful starting point.

A dictionary is like a hash map, or an array where they keys are strings rather than integers. The eval statement is the nasty one as it is a high level thing. It evaluates and compiles a piece of code (e.g. 5 + 6 /8 * 2) and returns the result. The second parameter is for passing in variables. Here is how the python function works.

Here's how I think it works
Code:
eq1 = eq.replace("=","-(") + ")"

Ok, that's easy. If you have x-2 = 2*x this line returns x-2 -(2*x).
If you would do the calculation by hand, you would end up with something like a*x + b, where the x is the solution. Well, this line
Code:
c = eval(eq1,{var:1j})

does something similar. It sets x to 1j and evaluates the expression:
Code:
x - 2 - 2*x # now set x to 1j
1j - 2 - 2*1j # gives
2 - 1j

Now, 2 - 1j is not really a complex number, where j would be sqrt(-1), but j here is our x, the solution. All we have to do now is to calculate j.
Code:
a + bj
bj = -a
j = (-a)/b