I have this code.
n_nodes = len(data_x)
X = np.zeros((n_nodes, n_nodes))
for i in range(n_nodes):
for j in range(n_nodes):
X[i, j] = data_x[i] ** j
I want to do the same task with no loops used at all. How can I do that with NumPy functions?
I'd suggest
data_x[:,None]**np.arange(n_nodes)
A check
In [17]: data_x = np.array((3,5,7,4,6))
...: n_nodes = len(data_x)
...: X = np.zeros((n_nodes, n_nodes))
...:
...: for i in range(n_nodes):
...: for j in range(n_nodes):
...: X[i, j] = data_x[i] ** j
...: print(X)
...: print('-----------')
...: print(data_x[:,None]**np.arange(n_nodes))
[[1.000e+00 3.000e+00 9.000e+00 2.700e+01 8.100e+01]
[1.000e+00 5.000e+00 2.500e+01 1.250e+02 6.250e+02]
[1.000e+00 7.000e+00 4.900e+01 3.430e+02 2.401e+03]
[1.000e+00 4.000e+00 1.600e+01 6.400e+01 2.560e+02]
[1.000e+00 6.000e+00 3.600e+01 2.160e+02 1.296e+03]]
-----------
[[ 1 3 9 27 81]
[ 1 5 25 125 625]
[ 1 7 49 343 2401]
[ 1 4 16 64 256]
[ 1 6 36 216 1296]]
Some timing
In [18]: %timeit data_x[:,None]**np.arange(n_nodes)
2.18 µs ± 7.49 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)
In [19]: %%timeit
...: for i in range(n_nodes):
...: for j in range(n_nodes):
...: X[i, j] = data_x[i] ** j
10.9 µs ± 107 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)
You can do this in one step with numpy.power.outer:
np.power.outer(data_x, np.arange(len(data_x)))
numpy.power manual page.
numpy.ufunc.outer ;)
np.power is a ufunc that takes 2 arguments. This category of functions has methods like outer. However, it's usually just as easy to use broadcasting as done in the accepted answer.If data_x is big, you will be faster using only numpy functions.
You can first repeat the input array and then use np.power with a vector giving the powers. This should be calculated fully vectorised in comparison to the already given list comprehension version.
x = np.arange(10)
X = x[:,np.newaxis].repeat(x.size,axis=1)
X = np.power(X,np.arange(x.size))
If data_x is already a numpy array, you can use it directly, if not you would need to do
x = np.array(data_x)
broadcasting you don't need to use repeat. Simply make x a (10,1) array.