Vectorised Operations

It’s well known that vectorised operations should be preferred in numpy/pandas for reasons of performance. A less common reason is that it actually makes the code easier to read. For a simple example imagine that you are doing a multivariate linear regression to transform an $n$ dimensional input to an $m$ dimensional output. The model takes the form $y = Bx$ where $B$ is an $(n \times m)$ matrix. Now imagine you have $k$ pairs of $(x, y)$ data, and the $k$ inputs are collected in an iterable data structure $X$. The naive way to gather model predictions is to code up a single prediction and then loop over all data:

# Single observation.
y = x @ B

# All observations.
Y = np.array([x @ B for x in X])

Everybody will tell you this is bad because you are using slow loops, and they’re right. But consider an alternative reason why the vectorised version would be better. If $X$ is a $(k \times n)$ array holding your input data, you can simply write

# All observations.
Y = X @ B

and you will notice that apart from capitalisation the form of this equation is identical to the prediction for a single observation. In other words, if your arrays have the right shape, then you can almost forget that you are operating on all your data at once and use a mental model of manipulating a single observation. The vectorised version is so clear and saves the reader having to go and examine the contents of a loop or comprehension.