python - I am getting a warning <RuntimeWarning: invalid value encountered in sqrt>

Question

I am trying to run a quadratic equation in python. However, it keeps on giving me a warning

RuntimeWarning: invalid value encountered in sqrt

Here's my code:

import numpy as np


a = 0.75 + (1.25 - 0.75)*np.random.randn(10000)
print(a)
b = 8 + (12 - 8)*np.random.randn(10000)
print(b)
c = -12 + 2*np.random.randn(10000)
print(c)
x0 = (-b - np.sqrt(b**2 - (4*a*c)))/(2 * a)
print(x0)

Answer 1

This is not 100% Python related. You can't calculate the square root of a negative number (when dealing with real numbers that is).

You didn't take any precautions for when b**2 - (4*a*c) is a negative number.

>>> import numpy as np
>>>
>>> np.sqrt(4)
2.0
>>> np.sqrt(-4)
__main__:1: RuntimeWarning: invalid value encountered in sqrt
nan

Let's test if you have negative values:

>>> import numpy as np
>>> 
>>> a = 0.75 + (1.25 - 0.75) * np.random.randn(10000)
>>> b = 8 + (12 - 8) * np.random.randn(10000)
>>> c = -12 + 2 * np.random.randn(10000)
>>> 
>>> z = b ** 2 - (4 * a * c)
>>> print len([_ for _ in z if _ < 0])
71