The standard way to bin a large array to a smaller one by averaging is to reshape it into a higher dimension and then take the means over the appropriate new axes. The following function does this, assuming that each dimension of the new shape is a factor of the corresponding dimension in the old one.

def rebin(arr, new_shape): shape = (new_shape[0], arr.shape[0] // new_shape[0], new_shape[1], arr.shape[1] // new_shape[1]) return arr.reshape(shape).mean(-1).mean(1)

To see how this works, consider reshaping a $4 \times 6$ array to become $2 \times 3$:

In [x]: arr = np.arange(24).reshape((4,6)) In [x]: arr Out[x]: array([[ 0, 1, 2, 3, 4, 5], [ 6, 7, 8, 9, 10, 11], [12, 13, 14, 15, 16, 17], [18, 19, 20, 21, 22, 23]])

We reshape from `(4, 6)`

to `(2, 4//2, 3, 6//3) = (2, 2, 3, 2)`

:

In [x]: arr.reshape(2, 4//2, 3, 6//3) Out[x]: array([[[[ 0, 1], [ 2, 3], [ 4, 5]], [[ 6, 7], [ 8, 9], [10, 11]]], [[[12, 13], [14, 15], [16, 17]], [[18, 19], [20, 21], [22, 23]]]])

This has grouped entries so that each row has become a $3 \times 2$ subarray and these subarrays are arranged as entries in the first $2 \times 2$ dimensions of the new 4D array. Now consider averaging over the last dimension (indexed with `-1`

):

In [x]: arr.reshape(2, 2, 3, 2).mean(-1) Out[x]: array([[[ 0.5, 2.5, 4.5], [ 6.5, 8.5, 10.5]], [[ 12.5, 14.5, 16.5], [ 18.5, 20.5, 22.5]]])

This has averaged entries along each row to leave an array of shape `(2,2,3)`

(for example, the first entry is the average of 0 and 1, which is 0.5). Now, averaging over the second dimension of this array (indexed with `1`

) corresponding to columns of the original array:

In [x]: arr.reshape(2, 2, 3, 2).mean(-1).mean(1) Out[x]: array([[ 3.5, 5.5, 7.5], [ 15.5, 17.5, 19.5]])

This is the $2\times 3$ binned array that we wanted.

Here is an illustration of the technique, based on USGS elevation data for the vicinity of Mt Ranier, which can be obtained from their download service.

import os from osgeo import gdal import numpy as np import matplotlib.pyplot as plt from matplotlib import cm from mpl_toolkits.mplot3d import Axes3D imgdir = '/Users/christian/temp/mt-ranier' # Mt Ranier spans two IMG files in the USGS data set. imgnameW = 'ned19_n47x00_w122x00_wa_mounttrainier_2008' imgnameE = 'ned19_n47x00_w121x75_wa_mounttrainier_2008' def get_elev_arr(imgname): """Read in the elevation data as a NumPy array.""" imgfile = os.path.join(imgdir, imgname, imgname+'.img') print(imgfile) geo = gdal.Open(imgfile) arr = geo.ReadAsArray() # invalid or missing data is indicated by a large negative value, so # replace these entries with NaN. arr[arr<0] = np.nan return arr # stack the East and West arrays next to each other to give elevation across # the entire area. elev = np.hstack((get_elev_arr(imgnameW), get_elev_arr(imgnameE))) # The latitude and longitude bouhnds of the elevation array N, S = 47.000185185185195, 46.749814814814826 E, W = -121.49981481481484, -122.00018518518522 # The centre of the mountain clat, clong = 46.88, -121.70 # Extract the region in a square centred on the Mt Ranier Ny, Nx = elev.shape icx, icy = int((N-clat)/(N-S) * Nx), int((W-clong)/(W-E) * Ny) Dpx = 3200 ix1, iy1, ix2, iy2 = icx-Dpx, icy-Dpx, icx+Dpx, icy+Dpx nx, ny = ix2-ix1, iy2-iy1 elev = elev[iy1:iy2,ix1:ix2] def rebin(arr, new_shape): """Rebin 2D array arr to shape new_shape by averaging.""" shape = (new_shape[0], arr.shape[0] // new_shape[0], new_shape[1], arr.shape[1] // new_shape[1]) return arr.reshape(shape).mean(-1).mean(1) # Create four surface subplots with different binnings fig, axes = plt.subplots(nrows=2, ncols=2, subplot_kw={'projection': '3d'}) binfacs = (640, 256, 64, 32) for i, binfac in enumerate(binfacs): ax = axes[i // 2, i % 2] bnx, bny = nx//binfac, ny//binfac X, Y = np.linspace(1,bnx,bnx), np.linspace(1,bny,bny) X, Y = np.meshgrid(Y, X) binned_elev = rebin(elev, (bny, bnx)) ax.plot_surface(X, Y, binned_elev, rstride=4, cstride=4, linewidth=0.1, antialiased=True, cmap=cm.plasma) cset = ax.contourf(X, Y, binned_elev, zdir='z', offset=0, cmap=cm.inferno) ax.set_axis_off() ax.dist=12 plt.savefig('ranier-rebinned.png') plt.show()

## Comments

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## Steve Boege 1 year, 6 months ago

Thanks for the clear, detailed explanation!

Link | Reply## lost_mitten 10 months, 1 week ago

It is about 1.5 times more efficient to use .mean(axis=(-1,1)) instead of .mean(-1).mean(1)

Link | ReplyAlso setting appropriate dtype will spare some of time, cause default is float64 - .mean(axis=(-1,1), dtype=np.uint16)

## christian 10 months, 1 week ago

Hi @lost_mitten,

Link | ReplyI don't see any time difference on my system between the two averaging methods. In IPython, for example, compare

%timeit np.random.random(240000).reshape((20,20,30,20)).mean(-1).mean(1)

and

%timeit np.random.random(240000).reshape((20,20,30,20)).mean(axis=(-1,1))

You could use uint16 but I guess you risk losing some resolution from the integer division.

If issues of speed and memory are critically important for your application, you should perhaps consider whether Python is the right language to use.

## lost_mitten 10 months, 1 week ago

You're also timing array creation - it takes up most the time.

Link | Replya = np.random.randint(2, size=(9000,9000))

%timeit a.reshape((3000,3,3000,3)).mean(axis=(-1,1))

%timeit a.reshape((3000,3,3000,3)).mean(-1).mean(1)

532 ms ± 8.15 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

757 ms ± 15.5 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

## christian 10 months, 1 week ago

Interesting. The main difference seems to be though that my test array is more nearly square than yours, e.g. reshaping yours to (150,60,150,60) makes the two approaches much more similar in timings.

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