I have to make a program using Euler’s method for the “ball in a spring” model

```
from pylab import*
from math import*
m=0.1
Lo=1
tt=30
k=200
t=20
g=9.81
dt=0.01
n=int((ceil(t/dt)))
km=k/m
r0=[-5,5*sqrt(3)]
v0=[-5,5*sqrt(3)]
a=zeros((n,2))
r=zeros((n,2))
v=zeros((n,2))
t=zeros((n,2))
r[1,:]=r0
v[1,:]=v0
for i in range(n-1):
rr=dot(r[i,:],r[i,:])**0.5
a=-g+km*cos(tt)*(rr-L0)*r[i,:]/rr
v[i+1,:]=v[i,:]+a*dt
r[i+1,:]=r[i,:]+v[i+1,:]*dt
t[i+1]=t[i]+dt
#print norm(r[i,:])
plot(r[:,0],r[:,1])
xlim(-100,100)
ylim(-100,100)
xlabel('x [m]')
ylabel('y [m]')
show()
```

I keep getting this error:

```
a=-g+km*cos(tt)*(rr-L0)*r[i,:]/rr
RuntimeWarning: invalid value encountered in divide
```

I can’t figure it out, what is wrong with the code?

### 4 Answers

I think your code is trying to “divide by zero” or “divide by NaN”. If you are aware of that and don’t want it to bother you, then you can try:

```
import numpy as np
np.seterr(divide='ignore', invalid='ignore')
```

For more details see:

Python indexing starts at 0 (rather than 1), so your assignment “r[1,:] = r0” defines the **second** (i.e. index 1) element of r and leaves the first (index 0) element as a pair of zeros. The first value of i in your for loop is 0, so rr gets the square root of the dot product of the first entry in r with itself (which is 0), and the division by rr in the subsequent line throws the error.

To prevent division by zero you could pre-initialize the output ‘out’ where the div0 error happens, eg `np.where`

does not cut it since the complete line is evaluated regardless of condition.

example with pre-initialization:

```
a = np.arange(10).reshape(2,5)
a[1,3] = 0
print(a) #[[0 1 2 3 4], [5 6 7 0 9]]
a[0]/a[1] # errors at 3/0
out = np.ones( (5) ) #preinit
np.divide(a[0],a[1], out=out, where=a[1]!=0) #only divide nonzeros else 1
```

You are dividing by `rr`

which may be 0.0. Check if `rr`

is zero and do something reasonable other than using it in the denominator.