Nikhil - 4 months ago 31

Python Question

I have the following numpy arrays:

`arr_1 = [[1,2],[3,4],[5,6]] # 3 X 2`

arr_2 = [[0.5,0.6],[0.7,0.8],[0.9,1.0],[1.1,1.2],[1.3,1.4]] # 5 X 2

`arr_1`

`3 X 2`

`arr_2`

`5 X 2`

Now without looping, I want to element-wise multiply arr_1 and arr_2 so that I apply a sliding window technique (window size 3) to arr_2.

`Example:`

Multiplication 1: np.multiply(arr_1,arr_2[:3,:])

Multiplication 2: np.multiply(arr_1,arr_2[1:4,:])

Multiplication 3: np.multiply(arr_1,arr_2[2:5,:])

I want to do this in some sort of a matrix multiplication form to make it faster than my current solution which is of the form:

`for i in (2):`

np.multiply(arr_1,arr_2[i:i+3,:])

So if the number of rows in arr_2 are large (of the order of tens of thousands), this solution doesn't really scale very well.

Any help would be much appreciated.

Answer

We can use `NumPy broadcasting`

to create those sliding windowed indices in a vectorized manner. Then, we can simply index into `arr_2`

with those to create a `3D`

array and perform element-wise multiplication with `2D`

array `arr_1`

, which in turn will bring on `broadcasting`

again.

So, we would have a vectorized implementation like so -

```
W = arr_1.shape[0] # Window size
idx = np.arange(arr_2.shape[0]-W+1)[:,None] + np.arange(W)
out = arr_1*arr_2[idx]
```

Runtime test and verify results -

```
In [143]: # Input arrays
...: arr_1 = np.random.rand(3,2)
...: arr_2 = np.random.rand(10000,2)
...:
...: def org_app(arr_1,arr_2):
...: W = arr_1.shape[0] # Window size
...: L = arr_2.shape[0]-W+1
...: out = np.empty((L,W,arr_1.shape[1]))
...: for i in range(L):
...: out[i] = np.multiply(arr_1,arr_2[i:i+W,:])
...: return out
...:
...: def vectorized_app(arr_1,arr_2):
...: W = arr_1.shape[0] # Window size
...: idx = np.arange(arr_2.shape[0]-W+1)[:,None] + np.arange(W)
...: return arr_1*arr_2[idx]
...:
In [144]: np.allclose(org_app(arr_1,arr_2),vectorized_app(arr_1,arr_2))
Out[144]: True
In [145]: %timeit org_app(arr_1,arr_2)
10 loops, best of 3: 47.3 ms per loop
In [146]: %timeit vectorized_app(arr_1,arr_2)
1000 loops, best of 3: 1.21 ms per loop
```