I am getting a warning <RuntimeWarning: invalid value encountered in sqrt>
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 sqrtnanLet'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
Square roots are not defined for strictly negative real numbers, and numpy will produce nan for negative inputs of "real" dtype int, float, and it's two special values -np.inf and nan.
However, square roots are defined for all complex dtype:
| dtype | example x | np.sqrt(x) | RuntimeWarning |
|---|---|---|---|
| Positive float | 1. | 1. | |
| Positive int | 1 | 1 | |
| Positive complex | 1+0J | 1 | |
| Negative float | -1. | nan | ⚠️ |
| Negative int | -1 | nan | ⚠️ |
| Negative complex | -1+0j | 1j | |
np.inf | np.inf | ||
-np.inf | nan | ⚠️ | |
np.nan | nan |
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.realWhere 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