I am teaching mysef a little about `numpy`

and I have dusted off some of my old undergraduate texts to use for examples. So, I wrote a function *without* `numpy`

to calculate the deflection in a cantilever beam due to a single point load at any point. Pretty straight forward, except that the deflection equation changes depending on what side of the point force you are on, so I will split the beam into two ranges, calculate the deflection values at each interval in the ranges and append the result to a list. Here's the code.

```
def deflection(l, P, a, E, I):
"""
Calculate the deflection of a cantilever beam due to a simple point load.
Calculates the deflection at equal one inch intervals along the beam and
returns the deflection as a list along with the the length range.
Parameters
----------
l : float
beam length (in)
P : float
Point Force (lbs)
a : float
distance from fixed end to force (in)
E : float
modulus of elasticity (psi)
I : float
moment of inertia (in**4)
Returns
-------
list
x : distance along beam (in)
list of floats
y : deflection of beam (in)
Raises
------
ValueError
If a < 0 or a > l (denoting force location is off the beam)
"""
if (a < 0) or (a > l):
raise ValueError('force location is off beam')
x1 = range(0, a)
x2 = range(a, l + 1)
deflects = []
for x in x1:
y = (3 * a - x) * (P * x**2) / (6 * E * I)
deflects.append(y)
for x in x2:
y = (3 * x - a) * (P * a**2) / (6 * E * I)
deflects.append(y)
return list(x1) + list(x2), deflects
```

Now I want to do the same thing using numpy, so I wrote the following function:

```
def np_deflection(l, P, a, E, I):
"""To Do. Write me."""
if (a < 0) or (a > l):
raise ValueError('force location is off beam')
x1 = np.arange(0, a)
x2 = np.arange(a, l + 1)
y1 = (3 * a - x1) * (P * x1**2) / (6 * E * I)
y2 = (3 * x2 - a) * (P * a**2) / (6 * E * I)
return np.hstack([x1, x2]), np.hstack([y1, y2])
```

Here's the issue, at some point in the calculations, the value of y1 changes sign. Here's an example.

```
if __name__ == '__main__':
import matplotlib.pyplot as plt
l, P, a, E, I = 120, 1200, 100, 30000000, 926
x, y = deflection(l, P, a, E, I)
print(max(y))
np_x, np_y = np_deflection(l, P, a, E, I)
print(max(np_y))
plt.subplot(2, 1, 1)
plt.plot(x, y, 'b.-')
plt.xlabel('dist from fixed end (in)')
plt.ylabel('using a range/list')
plt.subplot(2, 1, 2)
plt.plot(np_x, np_y, 'r.-')
plt.xlabel('dist from fixed end (in)')
plt.ylabel('using numpy range')
plt.show()
```

If you run the plot, you'll see that at point `x = 93`

which is in `x1`

, there is a dislocation in the curve where the value seems to change sign.

Can anyone explain a) what is happening? and b) what I did wrong?