简单的减法会导致不同阵列形状的广播问题

Question

我尝试使用描述 numpy 广播的 link 来解决我的问题，但无济于事。如何减去以下 numpy 数组：

X = np.array([[[1,2,3,4],[1,2,3,4],[1,2,3,4]],
              [[4,3,2,1],[4,3,2,1],[4,3,2,1]]])
X_mean = np.average(X_, axis=1)

当我执行 X - X_mean 时，它指出：

ValueError: operands could not be broadcast together with shapes (2,3,4) (2,4)

但是 X[0] - X_mean[0] 给出了正确的输出：

array([[ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.]])

Answer 1

您需要保持尺寸对齐才能 broadcasting 发生。你有 -

In [4]: whos
Variable   Type       Data/Info
-------------------------------
X          ndarray    2x3x4: 24 elems, type `int64`, 192 bytes
X_mean     ndarray    2x4: 8 elems, type `float64`, 64 bytes

X_mean

Axis-0 已经与 X 的 axis-0 对齐，所以一切都很好。

X_mean

Axis-1 与 X 的 axis-2 对齐，所以放在 X_mean 的新轴中有 None/np.newaxis 以便 axis-1 可以推回到 axis-2.

让我们验证形状对齐 -

In [7]: X_mean3D = X_mean[:,None,:] In [8]: whos Variable Type Data/Info ------------------------------- X ndarray 2x3x4: 24 elems, type `int64`, 192 bytes X_mean ndarray 2x4: 8 elems, type `float64`, 64 bytes X_mean3D ndarray 2x1x4: 8 elems, type `float64`, 64 bytes

然后，执行将引入广播的减法-

In [5]: X - X_mean[:,None,:] Out[5]: array([[[ 0., 0., 0., 0.], [ 0., 0., 0., 0.], [ 0., 0., 0., 0.]], [[ 0., 0., 0., 0.], [ 0., 0., 0., 0.], [ 0., 0., 0., 0.]]])

Answer 2

作为补充：根据Numpy Broadcasting Rules，

When operating on two arrays, NumPy compares their shapes element-wise. It starts with the trailing dimensions, and works its way forward. Two dimensions are compatible when

they are equal

one of them is 1

所以最好的办法是以在轴 0 上取平均值的方式来塑造数据。

你的情况：

Y=np.rollaxis(X,1) # reshape (3,2,4)

Y-Y.mean(0)现在直接

array([[[ 0.,  0.,  0.,  0.],
        [ 0.,  0.,  0.,  0.]],

       [[ 0.,  0.,  0.,  0.],
        [ 0.,  0.,  0.,  0.]],

       [[ 0.,  0.,  0.,  0.],
        [ 0.,  0.,  0.,  0.]]])

简单的减法会导致不同阵列形状的广播问题

Simple subtraction causes a broadcasting issue for different array shapes

python

arrays

numpy

array-broadcasting