attempt to explain why broadcasting is bae
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|A starter example is centering a matrix|
|import numpy as np|
|X = np.random.normal(size=(3, 3)) # random 3 by 3 matrix|
|mu = X.mean(axis = 0) # array (vector) of column means|
|print("\nArray of column means")|
|# array effectively copied till vector matches matrix in size|
|print("\nBroadcast subtraction operation")|
|print(X - mu)|
|To do this in R you have to loop or use something like map/apply.|
|This lets you create kernel matrices in a fast and fairly readable way, for example.|
|import numpy as np|
|X = np.random.normal(size=(10, 5))|
|Y = np.random.normal(size=(2, 5))|
|sigma = 0.1|
|# calculate all pairwise distances between rows in X and Y|
|# (x - y)^2 = a^2 - 2 ab + b^2|
|dist_sq = np.square(X).sum(axis=1)[:, np.newaxis] - 2.0 * np.dot(X, Y.T) + np.square(Y).sum(axis=1)|
|# turn this into an RBF kernel (math might be off, but hopefully the point is clear)|
|rbf = np.exp(-np.sqrt(dist_sq) / (2 * sigma ** 2))|
|In R you have to hope someone vectorized the components of the operation that|
|you care about, copy an object along an appropriate dimension, or use|
|loops/applys/maps, which I think make the math harder to think about.|
Oct 18, 2017
Just discovered this, don't know how I hadn't seen your comment yet -- super cool!
FYI if you dig broadcasting, the whole point of
xtensor is to provide the same Numpy interface and broadcasting niceness from within Rcpp.
Ugh if only that played better with windows.
Jun 19, 2019
So this is how
rray came to be hmm
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I had way too much fun with this. I'm starting to appreciate broadcasting, so I took a stab at how you might solve these two specific problems with new functions that attempt to mimic basic broadcasting for subtraction and addition (%-% and %+%).
The first bit it me exploring what R does natively, then I create the functions, then test a few things!
I am completely aware the functions would need to be dramatically improved, but I think its kind of neat.
FYI - the most important bit is the Pairwise Distance chunk down at the bottom so you may want to just skip to that first.