Broadcasting a function to a 3D array Python

Question

I tried understanding numpy broadcasting with 3d arrays but I think the OP there is asking something slightly different.

I have a 3D numpy array like so -

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

The shape of this array is (2,2,2). I want to apply a function to each 1x2 array in this 3D matrix like so -

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]

As you can see, I want to apply my function to each 1x2 array and replace it with the return value of my function. The output is a 3D array with the same dimensions. Is there a way to broadcast this function to each 1x2 array in my original 3D array? Currently I am using loops which becomes very slow as the 3D array increases in dimensions.

Currently I am doing this -

#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

And the returned 3D array is -

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

 [[ 7.81024968  0.87605805]
  [10.63014581  0.85196633]]]

Karl Knechtel · Accepted Answer · 2020-05-11 21:27:28Z

2

One way is to slice the arrays to extract the I and Q values, perform the computations using normal broadcasting, and then stick the values back together:

>>> 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]]])

answered May 11, 2020 at 21:27

Karl Knechtel

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Paddy Harrison · Accepted Answer · 2020-05-11 21:30:09Z

2

It can be done using arrays:

# 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]]])

edited May 11, 2020 at 21:30

answered May 11, 2020 at 21:24

Paddy Harrison

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Comments

Hammad Ahmed · Accepted Answer · 2020-07-04 19:01:57Z

0

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]]]

answered Jul 4, 2020 at 19:01

Hammad Ahmed

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