[Numpy-discussion] ndarray.T2 for 2D transpose

[Todd]

On Wed, Apr 6, 2016 at 5:20 PM, Nathaniel Smith <njs at pobox.com> wrote:

> On Wed, Apr 6, 2016 at 10:43 AM, Todd <toddrjen at gmail.com> wrote:
> >
> > My intention was to make linear algebra operations easier in numpy.  With
> > the @ operator available, it is now very easy to do basic linear algebra
> on
> > arrays without needing the matrix class.  But getting an array into a
> state
> > where you can use the @ operator effectively is currently pretty verbose
> and
> > confusing.  I was trying to find a way to make the @ operator more
> useful.
>
> Can you elaborate on what you're doing that you find verbose and
> confusing, maybe paste an example? I've never had any trouble like
> this doing linear algebra with @ or dot (which have similar semantics
> for 1d arrays), which is probably just because I've had different use
> cases, but it's much easier to talk about these things with a concrete
> example in front of us to put everyone on the same page.
>
>
Let's say you want to do a simple matrix multiplication example.  You
create two example arrays like so:

   a = np.arange(20)
   b = np.arange(10, 50, 10)

Now you want to do

    a.T @ b

First you need to turn a into a 2D array.  I can think of 10 ways to do
this off the top of my head, and there may be more:

    1a) a[:, None]
    1b) a[None]
    1c) a[None, :]
    2a) a.shape = (1, -1)
    2b) a.shape = (-1, 1)
    3a) a.reshape(1, -1)
    3b) a.reshape(-1, 1)
    4a) np.reshape(a, (1, -1))
    4b) np.reshape(a, (-1, 1))
    5) np.atleast_2d(a)

5 is pretty clear, and will work fine with any number of dimensions, but is
also long to type out when trying to do a simple example.  The different
variants of 1, 2, 3, and 4, however, will only work with 1D arrays (making
them less useful for functions), are not immediately obvious to me what the
result will be (I always need to try it to make sure the result is what I
expect), and are easy to get mixed up in my opinion.  They also require
people keep a mental list of lots of ways to do what should be a very
simple task.

Basically, my argument here is the same as the argument from pep465 for the
inclusion of the @ operator:
https://www.python.org/dev/peps/pep-0465/#transparent-syntax-is-especially-crucial-for-non-expert-programmers

"A large proportion of scientific code is written by people who are experts
in their domain, but are not experts in programming. And there are many
university courses run each year with titles like "Data analysis for social
scientists" which assume no programming background, and teach some
combination of mathematical techniques, introduction to programming, and
the use of programming to implement these mathematical techniques, all
within a 10-15 week period. These courses are more and more often being
taught in Python rather than special-purpose languages like R or Matlab.
For these kinds of users, whose programming knowledge is fragile, the
existence of a transparent mapping between formulas and code often means
the difference between succeeding and failing to write that code at all."
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