Q:

Faster median in very large numpy arrays

I have a very large numpy array with the dimension of (4000, 6000, 15).
I now want the median for each stack, i.e. along the third dimension. Current code works, but is curiously slow, the median for a single stack [0,0,:] (15 values) takes at least half a second or so to complete.
height = 4000
width = 6000
N = 15

poolmedian = np.zeros((height,width,3))
RGBmedian = np.zeros((height,width,N), dtype=float)    

for n in range(0,height):
    for m in range(0,width):
                poolmedian[n,m,0] = np.median(RGBmedian[n,m,:])

A:

You'll want to vectorize the median computation as much as possible. Every time you call a numpy function, you take a hit going back and forth between the C and Python layer. Do as much in the C layer as possible:
import numpy as np
height = 40
width = 60
N = 15

np.random.seed(1)
poolmedian = np.zeros((height,width,3))
RGBmedian = np.random.random((height,width,N))

def original():
    for n in range(0,height):
        for m in range(0,width):
            poolmedian[n,m,0] = np.median(RGBmedian[n,m,:])
    return poolmedian

def vectorized():
    # Note: np.median is only called ONCE, not n*m times.
    poolmedian[:, :, 0] = np.median(RGBmedian, axis=-1)
    return poolmedian

orig = original()
vec = vectorized()

np.testing.assert_array_equal(orig, vec)

You can see that the values are the same since the assert passes (although it's not clear why you need 3 dims in poolmedian). I put the above code in a file called test.py and am using IPython for it's convenient %timeit. I also toned down the size a bit just so it runs faster, but you should get similar savings on your large data. The vectorized version is about 100x faster:
In [1]: from test import original, vectorized

In [2]: %timeit original()
69.1 ms ± 394 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

In [3]: %timeit vectorized()
618 µs ± 4.1 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

In general, you want to use numpys broadcasting rules and call a function as few times as possible. Calling functions in a loop is almost always a no-no if you're looking for performant numpy code.
Addendum:
I've added the following function to test.py, since there is another answer, I want to make it clear that it's faster to call a fully vectorized version (i.e. no loops), and also modified to code to use dims 4000 by 6000:
import numpy as np
height = 4000
width = 6000
N = 15

...

def fordy():
    for n in range(0,height):
        for m in range(0,width):
            array = RGBmedian[n,m,:]
            array.sort()
            poolmedian[n, m, 0] = (array[6] + array[7])/2
    return poolmedian

and if we load all of this into IPython, we get:
In [1]: from test import original, fordy, vectorized

In [2]: %timeit original()
6.87 s ± 72.6 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [3]: %timeit fordy()
262 ms ± 737 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [4]: %timeit vectorized()
18.4 ms ± 149 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

HTH.

