[Tut] Python Math Domain Error (How to Fix This Stupid Bug)

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Python Math Domain Error (How to Fix This Stupid Bug)

You may encounter a special

Code:

ValueError

when working with Python’s

Code:

math

module.

Code:

ValueError: math domain error

Python raises this error when you try to do something that is not mathematically possible or mathematically defined.

To understand this error, have a look at the definition of the domain:

“The domain of a function is the complete set of possible values of the independent variable. Roughly speaking, the domain is the set of all possible (input) x-values which result in a valid (output) y-value.” (source)

The domain of a function is the set of all possible input values. If Python throws the

Code:

ValueError: math domain error

, you’ve passed an undefined input into the

Code:

math

function. Fix the error by passing a valid input for which the function is able to calculate a numerical output.

Here are a few examples:

Python Math Domain Error Sqrt

The math domain error appears if you pass a negative argument into the

Code:

math.sqrt()

function. It’s mathematically impossible to calculate the square root of a negative number without using complex numbers. Python doesn’t get that and throws a

Code:

ValueError: math domain error

.



Here’s a minimal example:

Code:

from math import sqrt print(sqrt(-1)) ''' Traceback (most recent call last): File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 2, in <module> print(sqrt(-1)) ValueError: math domain error '''

You can fix the math domain error by using the

Code:

cmath

package that allows the creation of complex numbers:

Code:

from cmath import sqrt print(sqrt(-1)) # 1j

Python Math Domain Error Log

The

Code:

math domain error

for the

Code:

math.log()

function appears if you pass a zero value into it—the logarithm is not defined for value 0.



Here’s the code on an input value outside the domain of the logarithm function:

Code:

from math import log print(log(0))

The output is the math domain error:

Code:

Traceback (most recent call last): File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 3, in <module> print(log(0)) ValueError: math domain error

You can fix this error by passing a valid input value into the

Code:

math.log()

function:

Code:

from math import log print(log(0.000001)) # -13.815510557964274

This error can sometimes appear if you pass a very small number into it—Python’s float type cannot express all numbers. To pass a value “close to 0”, use the

Code:

Decimal

module with higher precision, or pass a very small input argument such as:

Code:

math.log(sys.float_info.min)

Python Math Domain Error Acos

The

Code:

math domain error

for the

Code:

math.acos()

function appears if you pass a value into it for which it is not defined—arccos is only defined for values between -1 and 1.



Here’s the wrong code:

Code:

import math print(math.acos(2))

The output is the math domain error:

Code:

Traceback (most recent call last): File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 3, in <module> print(math.acos(2)) ValueError: math domain error

You can fix this error by passing a valid input value between [-1,1] into the

Code:

math.acos()

function:

Code:

import math print(math.acos(0.5)) # 1.0471975511965979

Python Math Domain Error Asin

The

Code:

math domain error

for the

Code:

math.asin()

function appears if you pass a value into it for which it is not defined—arcsin is only defined for values between -1 and 1.



Here’s the erroneous code:

Code:

import math print(math.asin(2))

The output is the math domain error:

Code:

Traceback (most recent call last): File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 3, in <module> print(math.asin(2)) ValueError: math domain error

You can fix this error by passing a valid input value between [-1,1] into the

Code:

math.asin()

function:

Code:

import math print(math.asin(0.5)) # 0.5235987755982989

Python Math Domain Error Pow

The

Code:

math domain error

for the

Code:

math.pow(a,b)

function to calculate a**b appears if you pass a negative base value into it and try to calculate a negative power of it. The reason it is not defined is that any negative number to the power of 0.5 would be the square number—and thus, a complex number. But complex numbers are not defined by default in Python!

Code:

import math print(math.pow(-2, 0.5))

The output is the math domain error:

Code:

Traceback (most recent call last): File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 3, in <module> print(math.pow(-2, 0.5)) ValueError: math domain error

If you need a complex number, ab must be rewritten into eb ln a. For example:

Code:

import cmath print(cmath.exp(0.5 * cmath.log(-2))) # (8.659560562354932e-17+1.414213562373095j)

You see, it’s a complex number!

NumPy Math Domain Error — np.log(x)

Code:

import numpy as np import matplotlib.pyplot as plt # Plotting y = log(x) fig, ax = plt.subplots() ax.set(xlim=(-5, 20), ylim=(-4, 4), title='log(x)', ylabel='y', xlabel='x') x = np.linspace(-10, 20, num=1000) y = np.log(x) plt.plot(x, y)

This is the graph of

Code:

log(x)

. Don’t worry if you don’t understand the code, what’s more important is the following point. You can see that log(x) tends to negative infinity as x tends to 0. Thus, it is mathematically meaningless to calculate the log of a negative number. If you try to do so, Python raises a math domain error.

Code:

>>> math.log(-10) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: math domain error

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