On Mon, Oct 29, 2018 at 9:49 PM Eric Wieser <wieser.eric+numpy@gmail.com> wrote:

The latter - changing the behavior of multiplication breaks the principle.

But this is not the main reason for deprecating matrix - almost all of the problems I’ve seen have been caused by the way that matrices behave when sliced. The way that

`m[i][j]`

and`m[i,j]`

are different is just one example of this, the fact that they must be 2d is another.Matrices behaving differently on multiplication isn’t super different in my mind to how string arrays fail to multiply at all.

Eric

It's certainly fine for arithmetic to work differently on an element-wise basis or even to error. But np.matrix changes the shape of results from various ndarray operations (e.g., both multiplication and indexing), which is more than any dtype can do.

The Liskov substitution principle (LSP) suggests that the set of reasonable ndarray subclasses are exactly those that could also in principle correspond to a new dtype. Of np.ndarray subclasses in wide-spread use, I think only the various "array with units" types come close satisfying this criteria. They only fall short insofar as they present a misleading dtype (without unit information).

The main problem with subclassing for numpy.ndarray is that it guarantees too much: a large set of operations/methods along with a specific memory layout exposed as part of its public API. Worse, ndarray itself is a little quirky (e.g., with indexing, and its handling of scalars vs. 0d arrays). In practice, it's basically impossible to layer on complex behavior with these exact semantics, so only extremely minimal ndarray subclasses don't violate LSP.

Once we have more easily extended dtypes, I suspect most of the good use cases for subclassing will have gone away.