将函数广播到 3D 数组 Python

Question

我试着理解但我认为 OP 的要求略有不同。

我有一个像这样的 3D numpy 数组 -

IQ = np.array([
    [[1,2],
    [3,4]],
    [[5,6],
    [7,8]]
], dtype = 'float64')

这个数组的形状是(2,2,2)。我想像这样对这个 3D 矩阵中的每个 1x2 数组应用一个函数 -

def func(IQ):
   I = IQ[0]
   Q = IQ[1]
   amp = np.power((np.power(I,2) + np.power(Q, 2)),1/2)
   phase = math.atan(Q/I)
   return [amp, phase]

如您所见，我想将我的函数应用于每个 1x2 数组，并将其替换为我函数的 return 值。输出是具有相同维度的 3D 数组。有没有办法将这个函数广播到我原来的 3D 数组中的每个 1x2 数组？目前我正在使用循环，随着 3D 数组维度的增加，循环变得非常慢。

目前我正在做这个-

#IQ is defined from above

for i in range(IQ.shape[0]):
    for j in range(IQ.shape[1]):
        I = IQ[i,j,0]
        Q = IQ[i,j,1]
        amp = np.power((np.power(I,2) + np.power(Q, 2)),1/2)
        phase = math.atan(Q/I)
        IQ[i,j,0] = amp
        IQ[i,j,1] = phase

returned 3D 数组是 -

 [[[ 2.23606798  1.10714872]
  [ 5.          0.92729522]]

 [[ 7.81024968  0.87605805]
  [10.63014581  0.85196633]]]

Answer 1

可以用数组来完成：

# sort of sum of squares along axis 2, ie (IQ[..., 0]**2 + IQ[..., 1]**2 + ...)**0.5
amp = np.sqrt(np.square(IQ).sum(axis=2))
amp
>>> array([[ 2.23606798,  5.        ],
           [ 7.81024968, 10.63014581]])

# and phase is arctan for each component in each matrix
phase = np.arctan2(IQ[..., 1], IQ[..., 0])
phase 
>>> array([[1.10714872, 0.92729522],
           [0.87605805, 0.85196633]])

# then combine the arrays to 3d
np.stack([amp, phase], axis=2)
>>> array([[[ 2.23606798,  1.10714872],
            [ 5.        ,  0.92729522]],

           [[ 7.81024968,  0.87605805],
            [10.63014581,  0.85196633]]])

Answer 2

一种方法是对数组进行切片以提取 I 和 Q 值，使用普通广播执行计算，然后将值重新组合在一起：

>>> Is, Qs = IQ[...,0], IQ[...,1]
>>> np.stack(((Is**2 + Qs**2) ** 0.5, np.arctan2(Qs, Is)), axis=-1)
array([[[ 2.23606798,  1.10714872],
        [ 5.        ,  0.92729522]],

       [[ 7.81024968,  0.87605805],
        [10.63014581,  0.85196633]]])

Answer 3

I = IQ[..., 0]
Q = IQ[..., 1]

amp   = np.linalg.norm(IQ, axis= 2)
phase = np.arctan(Q/I)

IQ[..., 0] = amp
IQ[..., 1] = phase

IQ

>> [[[ 2.23606798,  1.10714872],
     [ 5.        ,  0.92729522]],

    [[ 7.81024968,  0.87605805],
     [10.63014581,  0.85196633]]]

将函数广播到 3D 数组 Python

Broadcasting a function to a 3D array Python

python

arrays

numpy

broadcast

multidimensional-array