# ValueError: math domain error

I was just testing an example from Numerical Methods in Engineering with Python.

from numpy import zeros, array
from math import sin, log
from newtonRaphson2 import *

def f(x):
f = zeros(len(x))
f[0] = sin(x[0]) + x[1]**2 + log(x[2]) - 7.0
f[1] = 3.0*x[0] + 2.0**x[1] - x[2]**3 + 1.0
f[2] = x[0] + x[1] + x[2] -5.0
return f

x = array([1.0, 1.0, 1.0])
print newtonRaphson2(f,x)

When I run it, it shows the following error:

File "example NR2method.py", line 8, in f
f[0] = sin(x[0]) + x[1]**2 + log(x[2]) - 7.0
ValueError: math domain error

I have narrowed it down to the log as when I remove log and add a different function, it works. I assume it is because of some sort of interference with the base, I can’t figure out how. Can anyone suggest a solution?

Your code is doing a log of a number that is less than or equal to zero. That’s mathematically undefined, so Python’s log function raises an exception. Here’s an example:

>>> from math import log
>>> log(-1)
Traceback (most recent call last):
File "<pyshell#59>", line 1, in <module>
log(-1)
ValueError: math domain error

Without knowing what your newtonRaphson2 function does, I’m not sure I can guess where the invalid x[2] value is coming from, but hopefully this will lead you on the right track.

You may also use math.log1p.

According to the official documentation :

math.log1p(x)

Return the natural logarithm of 1+x (base e). The result is calculated in a way which is accurate for x near zero.

You may convert back to the original value using math.expm1 which returns e raised to the power x, minus 1.

You are trying to do a logarithm of something that is not positive.

Logarithms figure out the base after being given a number and the power it was raised to. log(0) means that something raised to the power of 2 is 0. An exponent can never result in 0*, which means that log(0) has no answer, thus throwing the math domain error

*Note: 0^0 can result in 0, but can also result in 1 at the same time. This problem is heavily argued over.

you are getting math domain error for either one of the reason : either you are trying to use a negative number inside log function or a zero value.