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Vectorized cs231n Beautifully with numpy

I started to work on cs231n assigments recently.

Probably just as everyone who first take a crack at these assigments, the vectorization parts of them are crazily frustrating but engaging.

So here I make a memo on manipulating ND-arrays. But it is better to also look up document for details on how to play with these methods.

  1. np.*
    1. choose
  2. np.random.*
    1. choice
  3. Clever usage of methods
    1. np.arange(N*M).reshape((N, M))
  4. Index tricks
    1. change value of the labeled elements
  5. Broadcasting
    1. add an (N,) vector to every column/row of an (N,M)/(M,N) matrix.
    2. calculate difference between every element of two same size vectors

np.*

Roughly speaking, np.* is the functions part of numpy. Accordingly, np.ndarray.* is the methods part, which is the simpler paraphrases of their counterpart functions.

choose

Used to pick out the score of the label class of a not-yet-classified sample.

for label(N) and scores(N, C)

np.choose(label, scores.T)

will choose the scores of labels(N). Transpose is needed as the label are treated as row vector here.

a slightly confusing paraphrase is

label.choose(scores.T)

It should sounds like “use label to choose on scores”.

np.random.*

choice

Used to generate samples.

Generate num random numbers from 0 ~ N-1 by

np.random.choice(N, num)

and generate samples from array using

np.random.choice(arr, num)

Also check out for non-uniform and no-replacement sampling.

Clever usage of methods

np.arange(N*M).reshape((N, M))

More generally, when you want to create a (N, M) 2D-array, probably for playing in ipython, you can create an (N * M,) 1D-array and reshape it immediately.

As an aside, arange is quite simple to play with, as entrices are not only distinct, but when you play with it, you can easily calculate the result by heart.

if the case requires a matrix without order, np.random.choice(choice_list, N\*M).reshape((N, M)) may do the job.

Index tricks

I referred to clever manipulation of matrix of the form matrix[...] as index tricks.

change value of the labeled elements

I want to do

np.choose(label, scores.T) -= scores.max(1)

for scores(N, C). It is made possible by

scores[np.arange(N), label] -= scores.max(1)

because the above line picks every labeled element from the scores, the left will be degenerated to a 1D-array, whose shape coincides with that of the right.

Broadcasting

Great guide here.

Scenarios for broadcasting comes out everywhere.

add an (N,) vector to every column/row of an (N,M)/(M,N) matrix.

for (N, M) matrix

vec.reshape((N, 1)) + mat

calculate difference between every element of two same size vectors

vec1.reshape((N, 1)) - vec2.reshape((1, N))

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