YBerman - 6 months ago 21

Python Question

I need to randomly pick an n-dimensional vector with length 1. My best idea is to pick a random point in the sphere an normalize it:

`import random`

def point(n):

sq = 0

v = []

while len(v) < n:

x = 1 - 2*random.random()

v.append(x)

sq = sq + x*x

if sq > 1:

sq = 0

v = []

l = sq**(0.5)

return [x / l for x in v]

The only problem is the volume of an n-ball gets smaller as the dimension goes up, so using a uniform distribution from

`random.random`

Answer

According to Muller, M. E. "A Note on a Method for Generating Points Uniformly on N-Dimensional Spheres" you would need to create a vector of n gaussian random variables and divide by its length:

```
import random
import math
def randnsphere(n):
v = [random.gauss(0, 1) for i in range(0, n)]
inv_len = 1.0 / math.sqrt(sum(coord * coord for coord in v))
return [coord * inv_len for coord in v]
```

As stated by @Bakuriu in the comments, using `numpy.random`

can offer you a performance advantage when working with larger vectors.