Using array indexing to apply 2D array function on 3D array

Question

I wrote a function that takes in one set of randomized cartesian coordinates and returns the subset that remains within some spatial domain. To illustrate:

grid = np.ones((5,5))
grid = np.lib.pad(grid, ((10,10), (10,10)), 'constant')

>> np.shape(grid)
(25, 25)

random_pts = np.random.random(size=(100, 2)) * len(grid)

def inside(input):
     idx = np.floor(input).astype(np.int)
     mask = grid[idx[:,0], idx[:,1]] == 1
     return input[mask]

>> inside(random_pts)
array([[ 10.59441506,  11.37998288],
       [ 10.39124766,  13.27615815],
       [ 12.28225713,  10.6970708 ],
       [ 13.78351949,  12.9933591 ]])

But now I want the ability to simultaneously generate n sets of random_pts and keep n corresponding subsets that satisfy the same functional condition. So, if n=3,

random_pts = np.random.random(size=(3, 100, 2)) * len(grid)

Without resorting to for loop, how could I index my variables such that inside(random_pts) returns something like

array([[[ 17.73323523,   9.81956681],
        [ 10.97074592,   2.19671642],
        [ 21.12081044,  12.80412997]],

       [[ 11.41995519,   2.60974757]],

       [[  9.89827156,   9.74580059],
        [ 17.35840479,   7.76972241]]])

It's functional but not very practical; the extra array operations leads to slower performance when the function needs to get called iteratively. I was hoping there's a more direct way to slicing the input that could achieve the same result. — neither-nor
– neither-nor, Commented Jul 14, 2015 at 19:31
So, for the posted data in the question, you were looking to have three separate arrays, right? For getting such separate arrays, np.split is the best known method, but it is slow, because there is a splitting-into-many-arrays operation. I would think that to be the slowest part here. If you are okay with non-split output, out_cat_array in the posted solution could be the output for you. — Divakar
– Divakar, Commented Jul 15, 2015 at 4:34

Divakar · Accepted Answer · 2015-07-12 06:49:43Z

One approach -

def inside3d(input):
    # Get idx in 3D
    idx3d = np.floor(input).astype(np.int)

    # Create a similar mask as witrh 2D case, but in 3D now
    mask3d = grid[idx3d[:,:,0], idx3d[:,:,1]]==1

    # Count of mask matches for each index in 0th dim    
    counts = np.sum(mask3d,axis=1)

    # Index into input to get masked matches across all elements in 0th dim
    out_cat_array = input.reshape(-1,2)[mask3d.ravel()]

    # Split the rows based on the counts, as the final output
    return np.split(out_cat_array,counts.cumsum()[:-1])

Verify results -

Create 3D random input:

In [91]: random_pts3d = np.random.random(size=(3, 100, 2)) * len(grid)

With inside3d:

In [92]: inside3d(random_pts3d)
Out[92]: 
[array([[ 10.71196268,  12.9875877 ],
        [ 10.29700184,  10.00506662],
        [ 13.80111411,  14.80514828],
        [ 12.55070282,  14.63155383]]), array([[ 10.42636137,  12.45736944],
        [ 11.26682474,  13.01632751],
        [ 13.23550598,  10.99431284],
        [ 14.86871413,  14.19079225],
        [ 10.61103434,  14.95970597]]), array([[ 13.67395756,  10.17229061],
        [ 10.01518846,  14.95480515],
        [ 12.18167251,  12.62880968],
        [ 11.27861513,  14.45609646],
        [ 10.895685  ,  13.35214678],
        [ 13.42690335,  13.67224414]])]

With inside:

In [93]: inside(random_pts3d[0])
Out[93]: 
array([[ 10.71196268,  12.9875877 ],
       [ 10.29700184,  10.00506662],
       [ 13.80111411,  14.80514828],
       [ 12.55070282,  14.63155383]])

In [94]: inside(random_pts3d[1])
Out[94]: 
array([[ 10.42636137,  12.45736944],
       [ 11.26682474,  13.01632751],
       [ 13.23550598,  10.99431284],
       [ 14.86871413,  14.19079225],
       [ 10.61103434,  14.95970597]])

In [95]: inside(random_pts3d[2])
Out[95]: 
array([[ 13.67395756,  10.17229061],
       [ 10.01518846,  14.95480515],
       [ 12.18167251,  12.62880968],
       [ 11.27861513,  14.45609646],
       [ 10.895685  ,  13.35214678],
       [ 13.42690335,  13.67224414]])

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