How to double the dimension of a matrix while quartering the values?

Question

I want to achieve this:

a = np.array ([[1, 2],
               [2, 1]])

b = np.array ([[0.25, 0.25, 0.5, 0.5],
               [0.25, 0.25, 0.5, 0.5],
               [0.5, 0.5, 0.25, 0.25],
               [0.5, 0.5, 0.25, 0.25])

Mathematically they r not the same matrices. But i think you get the idea what i want to do. I want to double the dimension of a matrix. But therefore i want to keep the information from the initial matrix a by take the quarter for the four corresponding cells.

Does some1 knows how to do this efficiently in numpy?

score 3 · Answer 1 · answered Dec 04 '18 at 07:26

You can use two repeat functions over both axis and then a simple division:

In [8]: np.repeat(np.repeat(a, 2, 1), 2, 0)/4
Out[8]: 
array([[0.25, 0.25, 0.5 , 0.5 ],
       [0.25, 0.25, 0.5 , 0.5 ],
       [0.5 , 0.5 , 0.25, 0.25],
       [0.5 , 0.5 , 0.25, 0.25]])

Divakar · Accepted Answer · 2018-12-04T08:38:19.010

Here's one with np.broadcast_to that leverages broadcasting to avoid two stages of replications or tiling for performance benefits by doing it one -

# "Expand" array a by Height, H and Width, W
def expand_blockavg(a, H, W): 
    m,n = a.shape
    return np.broadcast_to((a/float(H*W))[:,None,:,None],(m,H,n,W)).reshape(m*H,-1)

Sample runs -

In [93]: a
Out[93]: 
array([[1, 2],
       [2, 1]])

In [94]: expand_blockavg(a, H=2, W=2)
Out[94]: 
array([[0.25, 0.25, 0.5 , 0.5 ],
       [0.25, 0.25, 0.5 , 0.5 ],
       [0.5 , 0.5 , 0.25, 0.25],
       [0.5 , 0.5 , 0.25, 0.25]])

In [95]: expand_blockavg(a, H=2, W=3)
Out[95]: 
array([[0.17, 0.17, 0.17, 0.33, 0.33, 0.33],
       [0.17, 0.17, 0.17, 0.33, 0.33, 0.33],
       [0.33, 0.33, 0.33, 0.17, 0.17, 0.17],
       [0.33, 0.33, 0.33, 0.17, 0.17, 0.17]])

Runtime test on a large array -

In [2]: a = np.random.rand(200,200)

# Expand by (2 x 2)
# @Kasrâmvd's soln
In [85]: %timeit np.repeat(np.repeat(a, 2, 1), 2, 0)/4
1000 loops, best of 3: 492 µs per loop

In [86]: %timeit expand_blockavg(a, H=2, W=2)
1000 loops, best of 3: 382 µs per loop

# Expand by (20 x 20)
# @Kasrâmvd's soln
In [5]: %timeit np.repeat(np.repeat(a, 20, 1), 20, 0)/400
10 loops, best of 3: 32 ms per loop

In [6]: %timeit expand_blockavg(a, H=20, W=20)
10 loops, best of 3: 20.1 ms per loop

Larger array with (2 x 2) expansion -

In [87]: a = np.random.rand(2000,2000)

# @Kasrâmvd's soln
In [88]: %timeit np.repeat(np.repeat(a, 2, 1), 2, 0)/4
10 loops, best of 3: 70.2 ms per loop

In [89]: %timeit expand_blockavg(a, H=2, W=2)
10 loops, best of 3: 51.6 ms per loop

Just wo, thank you very much Divakar. You saved me a lot of time with your solution. It works really well with large arrays :) — Marcel H., Dec 04 '18 at 08:27

How to double the dimension of a matrix while quartering the values?

2 Answers2