How to fix 'RuntimeWarning: divide by zero encountered in double_scalars'

Question

After doing for loop in my code, there is an error in one line:

RuntimeWarning: divide by zero encountered in double_scalars

and in another line two errors:

RuntimeWarning: divide by zero encountered in double_scalars

RuntimeWarning: invalid value encountered in arcsin

I found it might be problem with float values, but im not sure about it and im typing it here for looking yours help. :)

Here is the code:

T_max = 0.5 * v_PM(Me) * RTOD 
DT = (90 - T_max) - np.fix(90 - T_max) 
n = int(T_max * 2)

P = np.zeros((n+1))    
T = np.zeros((n+1))
M = np.zeros((n+1))
RR = np.zeros((n+1))
LR = np.zeros((n+1))
SL = np.zeros((n+1))

for m in range(n+1):
    T[m] = (DT + m) * DTOR
    func = lambda x: T[m] - v_PM(x) 
    M[m] = brentq(func, 1, Me+1) 
    M[0] = 0
    P[m] = TR * np.tan(T[m]) #X-AXIS POINTS
    P[0] = 0
    RR[m] = -TR / P[m]
    RR[0] = 0
    LR[m] = (np.tan(T[m] + np.arcsin(1 / M[m]))) 
    LR[0] = 0
    SL[m] = -RR[m] 
    SL[0] = 0 

I defined earlier (before loop) v_PM and it's equal

v_PM = lambda x : (A * np.arctan(np.sqrt(B * (x ** 2 - 1))) - np.arctan(np.sqrt(x ** 2 - 1)))

As i mentioned, error RuntimeWarning: divide by zero encountered in double_scalars refer to RR[m] = -TR / P[m]

and two errors RuntimeWarning: divide by zero encountered in double_scalars and

RuntimeWarning: invalid value encountered in arcsin refers to:

LR[m] = (np.tan(T[m] + np.arcsin(1 / M[m])))

I put there also P[0] = 0 and M[0] = 0 etc. because i want to have first element as 0.

I dont know if i can forget about this error and move on with my code or if it is some serious problem. Thanks for your help.

Solution

Those are not actual errors, but warnings. They are there because you are trying to divide something by zero.

Namely, you are setting M[0] = 0 and then dividing by M[0] (at first iteration, where m = 0) and same for P[0].

The question is, what do you want the first values to be?

Maybe a solution would be initialize the zero values as you wish (before the loop) and start the loop with m=1 (so using for m in range(1,n+1):). Is that what you needed?

However, the warning may still be there if at different iterations P[m] or M[m] will be zero.

T_max = 0.5 * v_PM(Me) * RTOD 
DT = (90 - T_max) - np.fix(90 - T_max) 
n = int(T_max * 2)

P = np.zeros((n+1))    
T = np.zeros((n+1))
M = np.zeros((n+1))
RR = np.zeros((n+1))
LR = np.zeros((n+1))
SL = np.zeros((n+1))

# initialize your values
M[0] = 0 # actually not needed
P[0] = 0 # actually not needed
RR[0] = 0 # actually not needed
LR[0] = 0 # actually not needed
SL[0] = 0 # actually not needed
T[m] = (DT) * DTOR

for m in range(1,n+1):
    T[m] = (DT + m) * DTOR
    #Mach from T[i] using T[i] = v_PM (FALSE POSITION)
    func = lambda x: T[m] - v_PM(x) 
    M[m] = brentq(func, 1, Me+1) 
    P[m] = TR * np.tan(T[m]) #X-AXIS POINTS

    #RR SLOPES
    RR[m] = -TR / P[m]

    #LR slopes
    LR[m] = (np.tan(T[m] + np.arcsin(1 / M[m]))) 
    SL[m] = -RR[m]