Given a closed-form function f(x,y,z), what is the most efficient way to fill up a 3D ndarray arr[z][y][x] with the values of f(x,y,z)?
For example, if I wanted a 3D ndarray arr[z][y][x] with each element taking the value max((x+1)/(y+1), (y+1)/(z+1)), is there any better way to do so than iterating over the array element by element?
You can do this with ogrid:
# Shape of the desired array
m, n, p = 3, 4, 5
# Indexers in each dimension
x, y, z = np.ogrid[:m, :n, :p]
# Broadcasting in action with your function
print(np.maximum((x+1)/(y+1), (y+1)/(z+1)))
yields
[[[1. 1. 1. 1. 1. ]
[2. 1. 0.66666667 0.5 0.5 ]
[3. 1.5 1. 0.75 0.6 ]
[4. 2. 1.33333333 1. 0.8 ]]
[[2. 2. 2. 2. 2. ]
[2. 1. 1. 1. 1. ]
[3. 1.5 1. 0.75 0.66666667]
[4. 2. 1.33333333 1. 0.8 ]]
[[3. 3. 3. 3. 3. ]
[2. 1.5 1.5 1.5 1.5 ]
[3. 1.5 1. 1. 1. ]
[4. 2. 1.33333333 1. 0.8 ]]]
arr[x,y,z]. Ideally the indices will be arrays or slices. What kinds of values can your function take? Just scalars, or arrays? In other words can you only set individual elements at a time, or can you set blocks or ranges?ogridarrays. Maybe even try to creat them from scratch. It'll be a good learning step.