[Numpy-discussion] Use-case for np.choose
josef.pktd@gmai...
josef.pktd@gmai...
Sun Nov 8 21:50:43 CST 2009
On Sun, Nov 8, 2009 at 10:40 PM, Anne Archibald
<peridot.faceted@gmail.com> wrote:
> As Josef said, this is not correct. I think the key point of confusion is this:
>
> Do not pass choose two arrays.
>
> Pass it one array and a *list* of arrays. The fact that choices can be
> an array is a quirk we can't change, but you should think of the
> second argument as a list of arrays, possibly of different shapes.
>
> np.choose(np.ones((2,1,1)), [ np.ones((1,3,1)), np.ones((1,1,5)) ] )
>
> Here the first argument is an array of choices. The second argument is
> a *list* - if you cast it to an array you'll get an error or nonsense
> - of arrays to choose from. The broadcasting ensures the first
> argument and *each element of the list* are the same shape.
> The only
> constraint on the number of arrays in the list is that it be larger
> than the largest value in a.
and it's possible to get around this constraint with the mode argument.
Josef
>
> If you try to make the second argument into a single array, for one
> thing you are throwing away useful generality by forcing each choice
> to be the same shape (and real shape, not zero-strided fake shape),
> and for another the broadcasting becomes very hard to understand.
>
> Anne
>
>
> 2009/11/8 David Goldsmith <d.l.goldsmith@gmail.com>:
>> OK, now I'm trying to wrap my brain around broadcasting in choose when both
>> `a` *and* `choices` need to be (non-trivially) broadcast in order to arrive
>> at a common shape, e.g.:
>>
>>>>> c=np.arange(4).reshape((2,1,2)) # shape is (2,1,2)
>>>>> a=np.eye(2, dtype=int) # shape is (2,2)
>>>>> np.choose(a,c)
>> array([[2, 1],
>> [0, 3]])
>>
>> (Unfortunately, the implementation is in C, so I can't easily insert print
>> statements to see intermediate results.)
>>
>> First, let me confirm that the above is indeed an example of what I think it
>> is, i.e., both `a` and `choices` are broadcast in order for this to work,
>> correct? (And if incorrect, how is one broadcast to the shape of the
>> other?) Second, both are broadcast to shape (2,2,2), correct? But how,
>> precisely, i.e., does c become
>>
>> [[[0, 1], [2, 3]], [[[0, 1], [0, 1]],
>> [[0, 1], [2, 3]]] or [[2, 3], [2, 3]]]
>>
>> and same question for a? Then, once a is broadcast to a (2,2,2) shape,
>> precisely how does it "pick and choose" from c to create a (2,2) result?
>> For example, suppose a is broadcast to:
>>
>> [[[1, 0], [0, 1]],
>> [[1, 0], [0, 1]]]
>>
>> (as indicated above, I'm uncertain at this point if this is indeed what a is
>> broadcast to); how does this create the (2,2) result obtained above?
>> (Obviously this depends in part on precisely how c is broadcast, I do
>> recognize that much.)
>>
>> Finally, a seemingly relevant comment in the C source is:
>>
>> /* Broadcast all arrays to each other, index array at the end.*/
>>
>> This would appear to confirm that "co-broadcasting" is performed if
>> necessary, but what does the "index array at the end" phrase mean?
>>
>> Thanks for your continued patience and tutelage.
>>
>> DG
>>
>> On Sun, Nov 8, 2009 at 5:36 AM, <josef.pktd@gmail.com> wrote:
>>>
>>> On Sun, Nov 8, 2009 at 5:00 AM, David Goldsmith <d.l.goldsmith@gmail.com>
>>> wrote:
>>> > On Sun, Nov 8, 2009 at 12:57 AM, Anne Archibald
>>> > <peridot.faceted@gmail.com>
>>> > wrote:
>>> >>
>>> >> 2009/11/8 David Goldsmith <d.l.goldsmith@gmail.com>:
>>> >> > On Sat, Nov 7, 2009 at 11:59 PM, Anne Archibald
>>> >> > <peridot.faceted@gmail.com>
>>> >> > wrote:
>>> >> >>
>>> >> >> 2009/11/7 David Goldsmith <d.l.goldsmith@gmail.com>:
>>> >> >> > So in essence, at least as it presently functions, the shape of
>>> >> >> > 'a'
>>> >> >> > *defines* what the individual choices are within 'choices`, and if
>>> >> >> > 'choices'
>>> >> >> > can't be parsed into an integer number of such individual choices,
>>> >> >> > that's
>>> >> >> > when an exception is raised?
>>> >> >>
>>> >> >> Um, I don't think so.
>>> >> >>
>>> >> >> Think of it this way: you provide np.choose with a selector array,
>>> >> >> a,
>>> >> >> and a list (not array!) [c0, c1, ..., cM] of choices. You construct
>>> >> >> an
>>> >> >> output array, say r, the same shape as a (no matter how many
>>> >> >> dimensions it has).
>>> >> >
>>> >> > Except that I haven't yet seen a working example with 'a' greater
>>> >> > than
>>> >> > 1-D,
>>> >> > Josef's last two examples notwithstanding; or is that what you're
>>> >> > saying
>>> >> > is
>>> >> > the bug.
>>> >>
>>> >> There's nothing magic about A being one-dimensional.
>>> >>
>>> >> C = np.random.randn(2,3,5)
>>> >> A = (C>-1).astype(int) + (C>0).astype(int) + (C>1).astype(int)
>>> >>
>>> >> R = np.choose(A, (-1, -C, C, 1))
>>> >
>>> > OK, now I get it: np.choose(A[0,:,:], (-1,-C,C,-1)) and
>>> > np.choose(A[0,:,0].reshape((3,1)), (-1,-C,C,1)), e.g., also work, but
>>> > np.choose(A[0,:,0], (-1,-C,C,-1)) doesn't - what's necessary for
>>> > choose's
>>> > arguments is that both can be broadcast to a common shape (as you state
>>> > below), but choose won't reshape the arguments for you to make this
>>> > possible, you have to do so yourself first, if necessary. That does
>>> > appear
>>> > to be what's happening now; but do we want choose to be smarter than
>>> > that
>>> > (e.g., for np.choose(A[0,:,0], (-1,-C,C,-1)) to work, so that the user
>>> > doesn't need to include the .reshape((3,1)))?
>>>
>>> No, I don't think we want to be that smart.
>>>
>>> If standard broadcasting rules apply, as I think they do, then I wouldn't
>>> want
>>> any special newaxis or reshapes done automatically. It will be confusing,
>>> the function wouldn't know what to do if there are, e.g., as many rows as
>>> columns, and this looks like a big source of errors.
>>> Standard broadcasting is pretty nice (once I got the hang of it), and
>>> adding
>>> a lot of np.newaxis (or some reshapes) to the code is only a small price
>>> to pay.
>>>
>>> Josef
>>>
>>>
>>>
>>> >
>>> > DG
>>> >
>>> >>
>>> >> Requv = np.minimum(np.abs(C),1)
>>> >>
>>> >> or:
>>> >>
>>> >> def wedge(*functions):
>>> >> """Return a function whose value is the minimum of those of
>>> >> functions"""
>>> >> def wedgef(X):
>>> >> fXs = [f(X) for f in functions]
>>> >> A = np.argmin(fXs, axis=0)
>>> >> return np.choose(A,fXs)
>>> >> return wedgef
>>> >>
>>> >> so e.g. np.abs is -wedge(lambda X: X, lambda X: -X)
>>> >>
>>> >> This works no matter what shape of X the user supplies - so a wedged
>>> >> function can be somewhat ufunclike - by making A the same shape.
>>> >>
>>> >> >> The (i0, i1, ..., iN) element of the output array
>>> >> >> is obtained by looking at the (i0, i1, ..., iN) element of a, which
>>> >> >> should be an integer no larger than M; say j. Then r[i0, i1, ...,
>>> >> >> iN]
>>> >> >> = cj[i0, i1, ..., iN]. That is, each element of the selector array
>>> >> >> determines which of the choice arrays to pull the corresponding
>>> >> >> element from.
>>> >> >
>>> >> > That's pretty clear (thanks for doing my work for me). ;-), Yet, see
>>> >> > above.
>>> >> >
>>> >> >> For example, suppose that you are processing an array C, and have
>>> >> >> constructed a selector array A the same shape as C in which a value
>>> >> >> is
>>> >> >> 0, 1, or 2 depending on whether the C value is too small, okay, or
>>> >> >> too
>>> >> >> big respectively. Then you might do something like:
>>> >> >>
>>> >> >> C = np.choose(A, [-inf, C, inf])
>>> >> >>
>>> >> >> This is something you might want to do no matter what shape A and C
>>> >> >> have. It's important not to require that the choices be an array of
>>> >> >> choices, because they often have quite different shapes (here, two
>>> >> >> are
>>> >> >> scalars) and it would be wasteful to broadcast them up to the same
>>> >> >> shape as C, just to stack them.
>>> >> >
>>> >> > OK, that's a pretty generic use-case, thanks; let me see if I
>>> >> > understand
>>> >> > it
>>> >> > correctly: A is some how created independently with a 0 everywhere C
>>> >> > is
>>> >> > too
>>> >> > small, a 1 everywhere C is OK, and a 2 everywhere C is too big; then
>>> >> > np.choose(A, [-inf, C, inf]) creates an array that is -inf everywhere
>>> >> > C
>>> >> > is
>>> >> > too small, inf everywhere C is too large, and C otherwise (and since
>>> >> > -inf
>>> >> > and inf are scalars, this implies broadcasting of these is taking
>>> >> > place).
>>> >> > This is what you're asserting *should* be the behavior. So, unless
>>> >> > there is
>>> >> > disagreement about this (you yourself said the opposite viewpoint
>>> >> > might
>>> >> > rationally be held) np.choose definitely presently has a bug, namely,
>>> >> > the
>>> >> > index array can't be of arbitrary shape.
>>> >>
>>> >> There seems to be some disagreement between versions, but both Josef
>>> >> and I find that the index array *can* be arbitrary shape. In numpy
>>> >> 1.2.1 I find that all the choose items must be the same shape as it,
>>> >> which I think is a bug.
>>> >>
>>> >> What I suggested might be okay was if the index array was not
>>> >> broadcasted, so that the outputs always had exactly the same shape as
>>> >> the index array. But upon reflection it's useful to be able to use a
>>> >> 1-d array to select rows from a set of matrices, so I now think that
>>> >> all of A and the elements of choose should be broadcast to the same
>>> >> shape. This seems to be what Josef observes in his version of numpy,
>>> >> so maybe there's nothing to do.
>>> >>
>>> >> Anne
>>> >>
>>> >> > DG
>>> >> >
>>> >> >>
>>> >> >> Anne
>>> >> >> _______________________________________________
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>>> >> >
>>> >> >
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