Getting ValueError: math domain error in Python

Question

I wrote a short Python code to compute the Discrete Fourier Transform of a signal. Here is the code.

#import packages
from numpy import *
import math
import cmath

def computedft(x):
#function to calculate the dft of a signal
#Inputs : x(t) time domain signal
#output : K Fourier coff magnitudes

        N=len(x)
        #Caluclate omeag for DFT
        omega=2* math.pi /N
        for k in range(N):
        #outer loop is for each Fourier Coff
                sum=0
                for i in range(N):
                        sum=sum+x[i]*exp(- math.sqrt(-1)*k*omega*i)
                X[k]=sum
        return X

Then I went to ipython and gave these commands

In [1]: x=[9,6,7,8,9,-4,-8,-1]

In [2]: import computedft

In [3]: computedft.computedft(x)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)

~/Documents/<ipython console> in <module>()

~/Documents/computedft.py in computedft(x)
     16                 sum=0
     17                 for i in range(N):
---> 18                         sum=sum+x[i]*exp(- math.sqrt(-1)*k*omega*i)
     19                 X[k]=sum
     20         return X

ValueError: math domain error

I dont understand why I am getting this error. I have included the cmath package, so thus it should be able to multiply complex numbers. But why doesnt it work?

You could replace "math.sqrt(-1)" with "1j"

smots-18
– smots-18

2023-08-22 09:37:37 +00:00
Commented Aug 22, 2023 at 9:37 — smots-18
– smots-18, Commented Aug 22, 2023 at 9:37

zhangxaochen · Accepted Answer · 2014-01-26 15:34:15Z

2

use cmath instead of math:

In [123]: math.sqrt(-1)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-123-5234f21f3b4d> in <module>()
----> 1 math.sqrt(-1)

ValueError: math domain error

In [124]: import cmath

In [125]: cmath.sqrt(-1)
Out[125]: 1j

answered Jan 26, 2014 at 15:34

zhangxaochen

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3 Comments

user76170 Over a year ago

ok, I got it, so if we import cmath package then we dont need to import math package separately, I have another doubt: when I make changes to the code I m using vim editor then I run in ipython import computedft and then run the python file, it doesnt get updated and still shows the error before I made the change. If I quit ipython and restart it, then it compiles the new code. Why does this happen?

zhangxaochen Over a year ago

once you've imported a package (e.g. computedft), it's cached in dictionary sys.modules, next time you import it, it's omitted. So you need to restart ipython kernel, or reload(computedft) ;)

smots-18 Over a year ago

You could just use "1j" as it is an (imaginary) literal [imaginary meaning imaginary number]

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