如何在将值四分之一的同时将矩阵的维度加倍？

Question

我想实现这个：

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])

从数学上讲，它们不是相同的矩阵。但我想你知道我想做什么。我想将矩阵的维度加倍。但是因此我想通过为四个相应的单元格取四分之一来保留初始矩阵 a 中的信息。

有人知道如何在 numpy 中高效地执行此操作吗？

Answer 1

您可以在两个轴上使用两个重复函数，然后进行简单的除法：

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]])

Answer 2

这是 np.broadcast_to 的一个，它利用 broadcasting 来避免两个复制阶段或平铺以获得性能优势 -

# "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)

样品运行 -

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]])

大型数组的运行时测试 -

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

具有 (2 x 2) 扩展的更大数组 -

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

如何在将值四分之一的同时将矩阵的维度加倍？

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

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