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)
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
If you're hoping to do complex analysis (working with imaginary numbers as defined by sqrt(-1)) you can import cmath and use cmath.sqrt(-1) instead of numpy.sqrt(-1).
For example, when I'm calculating the refractive index of materials from permittivity and permeability (by definition, j is involved), I'll write functions in python as such:
def n(f):
y = cmath.sqrt(mu1f(f) - j*mu2f(f)) * (e1f(f) - j*e2f(f))
return y.real
Where e1f etc. are previously defined interpolating functions, all of which are a function of incident frequency f. The y resultant is, in it of itself, a complex value, the complex index of refraction, but I'm oftentimes only interested in the real portion (the refractive index) so that is what is returned.
Hope this helps
