Question

Functions that work on both scalars and arrays are known as ufuncs. For arrays, ufuncs apply the function in an element-wise fashion. Use of ufuncs is an esssential aspect of vectorization and typically much more computtionally efficient than using an explicit loop over each element.

xs = np.linspace(0, 2*np.pi, 100)
ys = np.sin(xs) # np.sin is a universal function
plt.plot(xs, ys);

# operators also perform elementwise operations by default

xs = np.arange(10)
print xs
print -xs
print xs+xs
print xs*xs
print xs**3
print xs < 5

[0 1 2 3 4 5 6 7 8 9]
[ 0 -1 -2 -3 -4 -5 -6 -7 -8 -9]
[ 0  2  4  6  8 10 12 14 16 18]
[ 0  1  4  9 16 25 36 49 64 81]
[  0   1   8  27  64 125 216 343 512 729]
[ True  True  True  True  True False False False False False]