Get a list of values from a 3D numpy array using a list of 3-component indices (4D array)

Question

I've looked through many different answers for indexing 2D and 3D arrays and I can't quite find a simple solution to my problem. I have a 3D array and have a list of 3-component indices (ix, iy, iz). I would like a list of values from the array, where each value is chosen using the one of the 3-component indices.

I've been able to solve the problem by flattening the array with reshape() and np.apply_along axis, but this seems inelegant, especially since I need to define a function to convert the 3-component indices to 1-component indices.

import numpy as np
data = np.arange(125).reshape(5,5,5)
indices = np.array(((0, 0, 0), (4, 4, 4), (0, 0, 4)), dtype=int)

# For-loop implementation
values = []
for i in indices:
    values.append(data[i[0], i[1], i[2]])
print(values)


# My inelegant numpy implementation
def three_to_one(index3d,dim):
    return index3d[0]*dim[1]*dim[2] + index3d[1]*dim[2] + index3d[2]

indices_1d = np.apply_along_axis(three_to_one, 1, indices, data.shape)
data_flat = data.reshape(-1)
values = data_flat[indices_1d]
print(values)

Answer 1

You can do this by transposing indices and using tuple() to interpret each column of indices as an index into data.

>>> data[tuple(indices.T)]
array([  0, 124,   4])

Answer 2

Starting with Python-3.11, this works:

data[*indices.T]

In older python versions, this is equivalent:

data[tuple(indices.T)]

The trick is that you can give one sequence per dimension, comma-separated or as a tuple (not a list!). You see this in use with np.nonzero

data = np.random.random((4, 5, 6))
above = data[np.nonzero(a > 0.75)]