Numpy: Index 3D array with index of last axis stored in 2D array

Question

I have a ndarray of shape(z,y,x) containing values. I am trying to index this array with another ndarray of shape(y,x) th

Answer 1

With readability, np.choose definitely looks great.

If performance is of essence, you can calculate the linear indices and then use np.take or use a flattened version with .ravel() and extract those specific elements from val_arr. The implementation would look something like this -

def linidx_take(val_arr,z_indices):

    # Get number of columns and rows in values array
     _,nC,nR = val_arr.shape

     # Get linear indices and thus extract elements with np.take
    idx = nC*nR*z_indices + nR*np.arange(nR)[:,None] + np.arange(nC)
    return np.take(val_arr,idx) # Or val_arr.ravel()[idx]

Runtime tests and verify results -

Ogrid based solution from here is made into a generic version for these tests, like so :

In [182]: def ogrid_based(val_arr,z_indices):
     ...:   v_shp = val_arr.shape
     ...:   y,x = np.ogrid[0:v_shp[1], 0:v_shp[2]]
     ...:   return val_arr[z_indices, y, x]
     ...: 

Case #1: Smaller datasize

In [183]: val_arr = np.random.rand(30,30,30)
     ...: z_indices = np.random.randint(0,30,(30,30))
     ...: 

In [184]: np.allclose(z_indices.choose(val_arr),ogrid_based(val_arr,z_indices))
Out[184]: True

In [185]: np.allclose(z_indices.choose(val_arr),linidx_take(val_arr,z_indices))
Out[185]: True

In [187]: %timeit z_indices.choose(val_arr)
1000 loops, best of 3: 230 µs per loop

In [188]: %timeit ogrid_based(val_arr,z_indices)
10000 loops, best of 3: 54.1 µs per loop

In [189]: %timeit linidx_take(val_arr,z_indices)
10000 loops, best of 3: 30.3 µs per loop

Case #2: Bigger datasize

In [191]: val_arr = np.random.rand(300,300,300)
     ...: z_indices = np.random.randint(0,300,(300,300))
     ...: 

In [192]: z_indices.choose(val_arr) # Seems like there is some limitation here with bigger arrays.
Traceback (most recent call last):

  File "", line 1, in 
    z_indices.choose(val_arr)

ValueError: Need between 2 and (32) array objects (inclusive).


In [194]: np.allclose(linidx_take(val_arr,z_indices),ogrid_based(val_arr,z_indices))
Out[194]: True

In [195]: %timeit ogrid_based(val_arr,z_indices)
100 loops, best of 3: 3.67 ms per loop

In [196]: %timeit linidx_take(val_arr,z_indices)
100 loops, best of 3: 2.04 ms per loop