apply_over_axes() applies the function sequentially to each specified axis, and it preserves the original dimensionality by keeping singleton dimensions for the axes it operates on - numpy.apply_over_axes

For your scenario you can try np.sum() with a tuple of axes

c_simplified = b.sum(axis=(1,2))
print(c_simplified.shape)

In a Picture

import numpy as np
b = np.random.randint(6, size=(100, 101, 102))

result_sum = b.sum(axis=(1, 2))  

result_max = b.max(axis=(1, 2)) 

result_mean = b.mean(axis=(1, 2))

output#

Sum shape: (100,)
Max shape: (100,)
Mean shape: (100,)

Edit 1:

f: Specifies the axis along which np.sum operates. Without it, the function cannot correctly sum over the intended axis.

axes parameter in np.apply_over_axes: Specifies the axes over which the function f should be applied iteratively, reducing them to size 1.

The axis parameter in your function f is necessary because np.sum needs to know which axis to operate on. Without it, the function call will fail, as np.sum defaults to summing over all axes if axis isn't specified, which conflicts with the iterative application of np.apply_over_axes

More can be found at - https://numpy.org/doc/stable/reference/generated/numpy.apply_over_axes.html

Summing Over Axes 1 and 2

import numpy as np

def custom_sum(array, axes):
 
    axes = tuple(axes)
    return np.sum(array, axis=axes)

b = np.random.randint(6, size=(100, 101, 102))
c = custom_sum(b, axes=(1, 2))
print(c.shape)  

output

(100,)

Second Largest Element Over Axes 1 and 2

you can reshape the array, sort along the flattened axes

axes = tuple(axes)
flattened = np.reshape(array, (-1,) + array.shape[len(axes):])
sorted_array = np.sort(flattened, axis=1)
print(sorted_array[:, -2])