[Numpy-discussion] New DTypes: Are scalars a central concept in NumPy or not?

[josef.pktd at gmail.com]

On Sat, Feb 22, 2020 at 9:34 AM <josef.pktd at gmail.com> wrote:

> not having a hashable tuple conversion would be a strong limitation
>
> a = tuple(np.arange(5))
> versus
> a = tuple([np.array(i) for i in range(5)])
> {a:5}
>

also there is the question of which scalar

.item() versus [()]

This was used in the old times in scipy.stats, and I just saw
https://github.com/scipy/scipy/pull/11165#issuecomment-589952838

aside:
AFAIR, I use 0-dim arrays also to ensure that I have a numpy dtype and not,
e.g. some equivalent python type

Josef


>
> Josef
>
> On Sat, Feb 22, 2020 at 9:28 AM Evgeni Burovski <
> evgeny.burovskiy at gmail.com> wrote:
>
>> Hi Sebastian,
>>
>> Just to clarify the difference:
>>
>> >>> x = np.float64(42)
>> >>> y = np.array(42, dtype=float)
>>
>> Here `x` is a scalar and `y` is a 0D array, correct?
>> If that's the case, not having the former would be very confusing for
>> users (at least, that would be very confusing to me, FWIW).
>>
>> If anything, I think it'd be cleaner to not have the latter, and only
>> have either scalars or 1D arrays (i.e., N-D arrays with N>=1), but it
>> is probably way too late to even think about it anyway.
>>
>> Cheers,
>>
>> Evgeni
>>
>> On Sat, Feb 22, 2020 at 4:37 AM Sebastian Berg
>> <sebastian at sipsolutions.net> wrote:
>> >
>> > Hi all,
>> >
>> > When we create new datatypes, we have the option to make new choices
>> > for the new datatypes [0] (not the existing ones).
>> >
>> > The question is: Should every NumPy datatype have a scalar associated
>> > and should operations like indexing return a scalar or a 0-D array?
>> >
>> > This is in my opinion a complex, almost philosophical, question, and we
>> > do not have to settle anything for a long time. But, if we do not
>> > decide a direction before we have many new datatypes the decision will
>> > make itself...
>> > So happy about any ideas, even if its just a gut feeling :).
>> >
>> > There are various points. I would like to mostly ignore the technical
>> > ones, but I am listing them anyway here:
>> >
>> >   * Scalars are faster (although that can be optimized likely)
>> >
>> >   * Scalars have a lower memory footprint
>> >
>> >   * The current implementation incurs a technical debt in NumPy.
>> >     (I do not think that is a general issue, though. We could
>> >     automatically create scalars for each new datatype probably.)
>> >
>> > Advantages of having no scalars:
>> >
>> >   * No need to keep track of scalars to preserve them in ufuncs, or
>> >     libraries using `np.asarray`, do they need `np.asarray_or_scalar`?
>> >     (or decide they return always arrays, although ufuncs may not)
>> >
>> >   * Seems simpler in many ways, you always know the output will be an
>> >     array if it has to do with NumPy.
>> >
>> > Advantages of having scalars:
>> >
>> >   * Scalars are immutable and we are used to them from Python.
>> >     A 0-D array cannot be used as a dictionary key consistently [1].
>> >
>> >     I.e. without scalars as first class citizen `dict[arr1d[0]]`
>> >     cannot work, `dict[arr1d[0].item()]` may (if `.item()` is defined,
>> >     and e.g. `dict[arr1d[0].frozen()]` could make a copy to work. [2]
>> >
>> >   * Object arrays as we have them now make sense, `arr1d[0]` can
>> >     reasonably return a Python object. I.e. arrays feel more like
>> >     container if you can take elements out easily.
>> >
>> > Could go both ways:
>> >
>> >   * Scalar math `scalar = arr1d[0]; scalar += 1` modifies the array
>> >     without scalars. With scalars `arr1d[0, ...]` clarifies the
>> >     meaning. (In principle it is good to never use `arr2d[0]` to
>> >     get a 1D slice, probably more-so if scalars exist.)
>> >
>> > Note: array-scalars (the current NumPy scalars) are not useful in my
>> > opinion [3]. A scalar should not be indexed or have a shape. I do not
>> > believe in scalars pretending to be arrays.
>> >
>> > I personally tend towards liking scalars.  If Python was a language
>> > where the array (array-programming) concept was ingrained into the
>> > language itself, I would lean the other way. But users are used to
>> > scalars, and they "put" scalars into arrays. Array objects are in some
>> > ways strange in Python, and I feel not having scalars detaches them
>> > further.
>> >
>> > Having scalars, however also means we should preserve them. I feel in
>> > principle that is actually fairly straight forward. E.g. for ufuncs:
>> >
>> >    * np.add(scalar, scalar) -> scalar
>> >    * np.add.reduce(arr, axis=None) -> scalar
>> >    * np.add.reduce(arr, axis=1) -> array (even if arr is 1d)
>> >    * np.add.reduce(scalar, axis=()) -> array
>> >
>> > Of course libraries that do `np.asarray` would/could basically chose to
>> > not preserve scalars: Their signature is defined as taking strictly
>> > array input.
>> >
>> > Cheers,
>> >
>> > Sebastian
>> >
>> >
>> > [0] At best this can be a vision to decide which way they may evolve.
>> >
>> > [1] E.g. PyTorch uses `hash(tensor) == id(tensor)` which is arguably
>> > strange. E.g. Quantity defines hash correctly, but does not fully
>> > ensure immutability for 0-D Quantities. Ensuring immutability in a
>> > world where "views" are a central concept requires a write-only copy.
>> >
>> > [2] Arguably `.item()` would always return a scalar, but it would be a
>> > second class citizen. (Although if it returns a scalar, at least we
>> > already have a scalar implementation.)
>> >
>> > [3] They are necessary due to technical debt for NumPy datatypes
>> > though.
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