# There is an analog of numpy.reduceat in Julia?

**URL:** <https://discourse.julialang.org/t/there-is-an-analog-of-numpy-reduceat-in-julia/70187>\
**Category:** New to Julia\
**Tags:** question, python\
**Created:** [October 22, 2021, 2:36am UTC](https://discourse.julialang.org/t/there-is-an-analog-of-numpy-reduceat-in-julia/70187 "2021-10-22T02:36:15Z")\
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**Author:** ![jishnub](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jishnub/32/33620_2.png) [@jishnub](https://discourse.julialang.org/u/jishnub)\
**Post date:** [October 22, 2021, 6:56am UTC](https://discourse.julialang.org/t/there-is-an-analog-of-numpy-reduceat-in-julia/70187/4 "2021-10-22T06:56:11Z")

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Looking at a few examples, I have figured out a way to do this for square matrices

Python examples:

```python
In [28]: n = 4; Z = np.reshape(np.arange(n**2), (n, n));

In [29]: k = 2;

In [30]: np.add.reduceat(np.add.reduceat(Z, np.arange(0, Z.shape[0], k), axis=0),np.arange(0, Z.shape[1], k), axis=1)
Out[30]: 
array([[10, 18],
       [42, 50]])

In [31]: k = 3;

In [32]: np.add.reduceat(np.add.reduceat(Z, np.arange(0, Z.shape[0], k), axis=0),np.arange(0, Z.shape[1], k), axis=1)
Out[32]: 
array([[45, 21],
       [39, 15]])

In [33]: n = 5; Z = np.reshape(np.arange(n**2), (n, n));

In [34]: k = 2;

In [35]: np.add.reduceat(np.add.reduceat(Z, np.arange(0, Z.shape[0], k), axis=0),np.arange(0, Z.shape[1], k), axis=1)
Out[35]: 
array([[12, 20, 13],
       [52, 60, 33],
       [41, 45, 24]])

In [36]: k = 3;

In [37]: np.add.reduceat(np.add.reduceat(Z, np.arange(0, Z.shape[0], k), axis=0),np.arange(0, Z.shape[1], k), axis=1)
Out[37]: 
array([[54, 51],
       [111, 84]])

```

In julia:

```julia
julia> function addreduceat(Z, k)
           inds = Iterators.partition(axes(Z,1), k)
           [sum(@view Z[CartesianIndices((I,J))]) for I in inds, J in inds]
       end
addreduceat (generic function with 2 methods)

julia> n = 4; Z = collect(reshape(0:n^2-1, n, n)');

julia> addreduceat(Z, 2)
2×2 Matrix{Int64}:
 10 18
 42 50

julia> addreduceat(Z, 3)
2×2 Matrix{Int64}:
 45 21
 39 15

julia> n = 5; Z = collect(reshape(0:n^2-1, n, n)');

julia> addreduceat(Z, 2)
3×3 Matrix{Int64}:
 12 20 13
 52 60 33
 41 45 24

julia> addreduceat(Z, 3)
2×2 Matrix{Int64}:
  54 51
 111 84

```

Interestingly, here are the execution times:

```python
In [38]: %timeit np.add.reduceat(np.add.reduceat(Z, np.arange(0, Z.shape[0], k), axis=0),np.arange(0, Z.shape[1], k), axis=1)
7.04 µs ± 102 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)

```

```julia
julia> @btime addreduceat($Z, 3);
  243.859 ns (1 allocation: 112 bytes)

```

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