I have defined a mathematical function with np.sqrt(a positive number) in it. It returns me RuntimeWarning.
After I simplify it to a very simple mathematical function that anyone can solve manually, it still return me the error. Below is the simplified function:
import numpy as np
n=30
def f0(x,k):
bot = 9.37 * 10**(-4) * k**(0.25)
x_0 = 2*bot
#print(x_0)
E_c = 4730 * np.sqrt(k)
#print(E_c)
r = E_c/(E_c - k/bot)
#print(r)
top = x/(1+(x/x_0)**n)**(1/n)
return (top/bot)**r
a = f0(-0.001,36)
It returns:
RuntimeWarning: invalid value encountered in double_scalars
And a is nan
It works well if the input x >= 0, or I remove np.sqrt() to the result of the square root of the number inside the np.sqrt().
What's reason of that.
I have noticed the type of np.sqrt is a bit different to another number. Is this the reason?
Your issue is not with the numpy square root. The value you are trying to return to a, involves raising a negative number to a non-integer power. This is mathematically undefined.
The mathematical operation, although I am quite sure python uses a different numerical approximation, is:
x = 5
r = 1.234
x**r # 7.2866680501380845
import math
math.exp(r*math.log(x)) # 7.286668050138084
Now imagine what happens if r is negative: you try to take the natural logarithm of a negative number. This will result in a NaN. Depending on the function used, you will be presented with a range of errors.
The solution is to enforce the quantity top/bot to be positive.