Iterating over an array
The goal
Questions to David Rotermund
This is an optional topic!
numpy.apply_along_axis
numpy.apply_along_axis(func1d, axis, arr, *args, **kwargs)
Apply a function to 1-D slices along the given axis.
Execute func1d(a, *args, **kwargs) where func1d operates on 1-D arrays and a is a 1-D slice of arr along axis.
This is equivalent to (but faster than) the following use of ndindex and s_, which sets each of ii, jj, and kk to a tuple of indices:
Ni, Nk = a.shape[:axis], a.shape[axis+1:]
for ii in ndindex(Ni):
for kk in ndindex(Nk):
f = func1d(arr[ii + s_[:,] + kk])
Nj = f.shape
for jj in ndindex(Nj):
out[ii + jj + kk] = f[jj]
Equivalently, eliminating the inner loop, this can be expressed as:
Ni, Nk = a.shape[:axis], a.shape[axis+1:]
for ii in ndindex(Ni):
for kk in ndindex(Nk):
out[ii + s_[...,] + kk] = func1d(arr[ii + s_[:,] + kk])
Example
import numpy as np
def function_1d(input):
print(f"input shape: {input.shape}, input: {input}")
return input + input.shape[0]
a = np.arange(1, 13).reshape(3, 4)
print(a)
print(a.shape) # -> (3, 4)
print()
print("******")
b = np.apply_along_axis(function_1d, axis=0, arr=a)
print("******")
print()
print(b)
print(b.shape) # -> (3, 4)
print()
print("++++++")
b = np.apply_along_axis(function_1d, axis=1, arr=a)
print("++++++")
print()
print(b)
print(b.shape) # -> (3, 4)
Output:
[[ 1 2 3 4]
[ 5 6 7 8]
[ 9 10 11 12]]
******
input shape: (3,), input: [1 5 9]
input shape: (3,), input: [ 2 6 10]
input shape: (3,), input: [ 3 7 11]
input shape: (3,), input: [ 4 8 12]
******
[[ 4 5 6 7]
[ 8 9 10 11]
[12 13 14 15]]
++++++
input shape: (4,), input: [1 2 3 4]
input shape: (4,), input: [5 6 7 8]
input shape: (4,), input: [ 9 10 11 12]
++++++
[[ 5 6 7 8]
[ 9 10 11 12]
[13 14 15 16]]
The output dimension is allowed to change:
import numpy as np
def function_1d(input):
print(f"input shape: {input.shape}, input: {input}")
return [input.sum() + input.mean()]
a = np.arange(1, 13).reshape(3, 4)
print(a)
print(a.shape) # -> (3, 4)
print()
print("******")
b = np.apply_along_axis(function_1d, axis=0, arr=a)
print("******")
print()
print(b)
print(b.shape) # -> (1, 4)
print()
print("++++++")
b = np.apply_along_axis(function_1d, axis=1, arr=a)
print("++++++")
print()
print(b)
print(b.shape) # -> (3, 1)
Output:
[[ 1 2 3 4]
[ 5 6 7 8]
[ 9 10 11 12]]
******
input shape: (3,), input: [1 5 9]
input shape: (3,), input: [ 2 6 10]
input shape: (3,), input: [ 3 7 11]
input shape: (3,), input: [ 4 8 12]
******
[[20. 24. 28. 32.]]
++++++
input shape: (4,), input: [1 2 3 4]
input shape: (4,), input: [5 6 7 8]
input shape: (4,), input: [ 9 10 11 12]
++++++
[[12.5]
[32.5]
[52.5]]
We can do the same for more then 2d ndarrays:
import numpy as np
def function_1d(input):
print(f"input shape: {input.shape}, input: {input}")
return [input.sum() + input.mean()]
a = np.arange(1, 25).reshape(3, 4, 2)
print(a)
print(a.shape) # -> (3, 4, 2)
print()
print("******")
b = np.apply_along_axis(function_1d, axis=0, arr=a)
print("******")
print()
print(b)
print(b.shape) # -> (1, 4, 2)
Output:
[[[ 1 2]
[ 3 4]
[ 5 6]
[ 7 8]]
[[ 9 10]
[11 12]
[13 14]
[15 16]]
[[17 18]
[19 20]
[21 22]
[23 24]]]
******
input shape: (3,), input: [ 1 9 17]
input shape: (3,), input: [ 2 10 18]
input shape: (3,), input: [ 3 11 19]
input shape: (3,), input: [ 4 12 20]
input shape: (3,), input: [ 5 13 21]
input shape: (3,), input: [ 6 14 22]
input shape: (3,), input: [ 7 15 23]
input shape: (3,), input: [ 8 16 24]
******
[[[36. 40.]
[44. 48.]
[52. 56.]
[60. 64.]]]
The source code is Open Source and can be found on GitHub.