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


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)
b = 8 + (12 - 8)*np.random.randn(10000)
c = -12 + 2*np.random.randn(10000)
x0 = (-b - np.sqrt(b**2 - (4*a*c)))/(2 * a)
Asked By: Maroof G



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)
>>> np.sqrt(-4)
__main__:1: RuntimeWarning: invalid value encountered in sqrt

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])
Answered By: DeepSpace

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

Answered By: Michael Green

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 e.g.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
Infinity np.inf np.inf
Negative infinity -np.inf nan ⚠️
NaN np.nan nan
Answered By: iacob

I would like to add an insight along with the above answers.
The cmath function always returns complex numbers but if you want a unified treatment of complex and float object I would recommend using numpy.lib.scimath.

Note: The sqrt() function in this is slower that that of the versions from cmath and math module but it has flexibility to return a complex object in the case of a negative argument and a float object otherwise

Answered By: jick jack