I am seeking a vectorized form of the following computation:

```
import numpy as np
D = 100
N = 1000
K = 10
X = np.random.uniform(0, 1, (K, N))
T = np.random.uniform(0, 1000, (D, N))
out = np.zeros((D, K))
for i in range(D):
for j in range(K):
out[i, j] = np.prod(X[j, :] ** T[i, :])
```

There are einsum-style things I’ve tried, but the presence of the np.prod is throwing me off a bit.

EDIT: Reduced size of matrices.

### >Solution :

I’m trying to make the broadcasting as explicit as possible – the `None`

introduces an additional dummy dimension of size 1:

```
out = np.prod(X[None, :, :] ** T[:, None, :], axis=2)
```

It is easy to see how it works if we recall the shapes: `X.shape = (K, N)`

, `T.shape = (D, N)`

and `out.shape = (D, K)`

. With the dummy dimension we basically take something of `(1, K, N)`

to the power of `(D, 1, N)`

which results in `(D, K, N)`

. Finally if we reduce via product over the last dimension we get our desired output of `(D, K)`

.