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pythonnumpymultidimensional-array
DeLorean88
DeLorean88

Reputation: 657

creating numpy array with coordinates of vertices of N-dimensional cube

What could be an efficient way of creating numpy array containing the coordinates of vertices of the N-dimensional cube centered at origin of coordinates, given the dimension N.

For example, for N=1 it should return np.array([[1],[-1]])

For N=2 it should return np.array([[1,1],[1,-1],[-1,1],[-1,-1]])

For N=3: np.array([[1,1,1],[1,1,-1],[1,-1,1],[1,-1,-1],[-1,1,1],[-1,1,-1],[-1,-1,1],[-1,-1,-1]])

Upvotes: 3

Views: 2583

Answers (3)

Warren Weckesser
Warren Weckesser

Reputation: 114976

Here's another method: 2*((np.arange(2**N)[:,None] & (1 << np.arange(N))) > 0) - 1

In [25]: N = 1

In [26]: 2*((np.arange(2**N)[:,None] & (1 << np.arange(N))) > 0) - 1
Out[26]: 
array([[-1],
       [ 1]])

In [27]: N = 2

In [28]: 2*((np.arange(2**N)[:,None] & (1 << np.arange(N))) > 0) - 1
Out[28]: 
array([[-1, -1],
       [ 1, -1],
       [-1,  1],
       [ 1,  1]])

In [29]: N = 3

In [30]: 2*((np.arange(2**N)[:,None] & (1 << np.arange(N))) > 0) - 1
Out[30]: 
array([[-1, -1, -1],
       [ 1, -1, -1],
       [-1,  1, -1],
       [ 1,  1, -1],
       [-1, -1,  1],
       [ 1, -1,  1],
       [-1,  1,  1],
       [ 1,  1,  1]])

What it does:

  • Create an array of integers from 0 to 2**N-1.
  • Convert the integers to binary (e.g. 3 becomes [1, 1, 0]).
  • Multiply the binary array by 2 and subtract 1 to convert from 0 and 1 to -1 and 1.

Numpy broadcasting is used to vectorize the operations.

Upvotes: 2

kevinkayaks
kevinkayaks

Reputation: 2726

Here is a pure numpy implementation involving meshgrid and stack. It's a little contrived-- would welcome input to make it better. 

pts = np.stack(([-1,1],)*N,0)
vertices = (np.array(np.meshgrid(*pts)).T).reshape(2**N,N)
vertices

N=3 returns 

array([[-1, -1, -1],
       [-1,  1, -1],
       [ 1, -1, -1],
       [ 1,  1, -1],
       [-1, -1,  1],
       [-1,  1,  1],
       [ 1, -1,  1],
       [ 1,  1,  1]])

N=1 returns 

array([[-1],
       [ 1]])

Upvotes: 2

Chris Mueller
Chris Mueller

Reputation: 6700

You can use product from itertools

from itertools import product

def vertices(N): 
    return list(product((1, -1), repeat=N))

print(vertices(1))
# [(1,), (-1,)]

print(vertices(2))
# [(1, 1), (1, -1), (-1, 1), (-1, -1)]

print(vertices(3))
# [(1, 1, 1), (1, 1, -1), (1, -1, 1), (1, -1, -1), (-1, 1, 1), (-1, 1, -1), (-1, -1, 1), (-1, -1, -1)]

Upvotes: 5

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