Thanks Raul. I'm pleased you asked. Originally, I couldn't see what you were trying to demonstrate. It's now morning here, and having slept, I think I can see your point.
You're right. Sorry. My sentence wasn't entirely correct. You did assign (and demonstrate) x =: 1 0 1$0 which indeed lacks any atoms. I think I see my critical mistake. The x arguments in (1), (2), (3), (4) have ranks 3, 3, 2, 1. My hasty application of (erroneous) intuition has brought me unstuck: 0 atoms does not necessarily imply rank 0. I'll have make a poster "rank = #$" and hang it on my wall. On Sat, Feb 6, 2016 at 12:27 AM, Raul Miller <[email protected]> wrote: > Why do you say "Your x arguments all have atoms so, I'm sorry, I can't > see their significance."? > > What is different between the x values in my email message and the x > values you originally specified? > > Thanks, > > -- > Raul > > > On Fri, Feb 5, 2016 at 5:42 AM, Matthew Baulch <[email protected]> > wrote: > > The 'x $ y' dyad, like you say, has rank 1 for x and _ for y. Examples > > (1)-(3) have rank 0 arguments for x. The x arguments are arrays with > > non-empty shape but no atoms in these cases. Your x arguments all have > > atoms so, I'm sorry, I can't see their significance. My x arguments have > > shapes containing only non-negative integers (as you mentioned), although > > some are zero. I'm not sure what you mean by: > > > > "So your first example is not even going to get to the reshape part of > the > > operation. Your frame, which will hold your results, is empty." > > > > I understand and agree that the frame of the left argument is empty. That > > doesn't surprise or concern me. What I don't understand are the reasons > for > > the result shapes in (1)-(3), and why the result for (3) has an atom. > > > > All verbs (that I can think of) with an argument of rank >= 1 are defined > > also for arguments of rank 0. For instance, 'i. y', 'x # y' (x has rank > > 1), and so on. Of course, there are very many verbs having arguments of > > infinite rank too. Therefore, I don't see it as remarkable to apply a > rank > > 0 array as an argument to a verb with rank > 0. > > > > Your comment > > > > "the dictionary definitions for verbs mostly only deal with arguments > which > > fit within the dictionary defined rank for the verb" > > > > was enlightening and made me think. Is it simply that the case that most > > verb definitions don't cover the case of rank 0 arguments with no atoms? > > Perhaps my question relates to an undefined part of J? > > > > On Fri, Feb 5, 2016 at 7:27 PM, Raul Miller <[email protected]> > wrote: > > > >> I'm going to go with the original vocab definition, because that's how > >> I understand reshape. > >> > >> But also keep in mind that the left rank of reshape is 1. A shape is a > >> (usually quite short) list of non-negative integers. This is something > >> that we all have to go through - remembering that the dictionary > >> definitions for verbs mostly only deal with arguments which fit within > >> the dictionary defined rank for the verb. That's good enough for most > >> purposes, when you need to concern yourself with rank it's the same > >> rules for all verbs (except for the actual numeric values being > >> different on some verbs). > >> > >> Perhaps http://www.jsoftware.com/help/dictionary/dictb.htm would be > >> worth reviewing? > >> > >> Anyways, to see what that means for your reshape examples, consider > this: > >> > >> <"1 x=: 1 0 1 $ 0 > >> > >> (that's an empty result - no boxes.) > >> > >> $<"1 x=: 1 0 1 $ 0 > >> 1 0 > >> > >> (that's what your frame looks like, for this example.) > >> > >> So your first example is not even going to get to the reshape part of > >> the operation. Your frame, which will hold your results, is empty. > >> > >> In your first example, x is empty, so you'll be using an array of > >> fills (which are zeros) for the test run of reshape. So you actually > >> do get a final dimension here - the last dimension is 1, and although > >> x is empty, the interpreter uses that 1 to decide how many zeros it's > >> going to use. > >> > >> Your second and third examples have the same issue - you're not doing > >> a single reshape but a collection of reshapes. But in those examples > >> your last dimension of x is zero. So when the interpreter does its > >> test run on the verb to see what kinds of results it's getting instead > >> of doing: > >> > >> (,0) $ 1 2 3 > >> > >> like it was in the first example, it is instead doing > >> > >> '' $ 1 2 3 > >> 1 > >> > >> In other words there trial result doesn't have a shape, so you get one > >> less dimension in your result than you had in x. > >> > >> As for your last example: > >> > >> <"1 x=: 1 $ 0 > >> +-+ > >> |0| > >> +-+ > >> $ <"1 x=: 1 $ 0 > >> > >> ...so your final example does do the reshaping, but you are reshaping > >> with an empty shape, so you still get an empty result. > >> > >> Does this make sense? > >> > >> Thanks, > >> > >> -- > >> Raul > >> > >> On Fri, Feb 5, 2016 at 3:06 AM, Matthew Baulch <[email protected]> > >> wrote: > >> > Original vocab says: > >> > "The shape of x$y is x,siy where siy is the shape of an item of y." > >> > > >> > NuVoc says (for x $ y): > >> > "If y is an atom or a list, the shape of the result is x", and "the > shape > >> > of [the result of x$y] is always x,}.$y". > >> > > >> > Let y =: 1 2 3 for all that follows. > >> > > >> > (1) > >> > x =: 1 0 1 $ 0 > >> > x$y has no atoms, shape 1 0 0 > >> > (2) > >> > x =: 1 0 0 $ 0 > >> > x$y has no atoms, shape 1 0 > >> > (3) > >> > x =: 1 0 $ 0 > >> > x$y has a single atom: 1, and shape 1 > >> > (4) > >> > x =: 1 $ 0 > >> > x$y has no atoms, shape 0 > >> > > >> > Examples (1)-(3) appear to violate the definitions. Only example (4) > >> > agrees. Can anyone shed some light on this? (3) strikes me as > >> particularly > >> > strange. I'm sure I must have missed something. > >> > > >> > My head is spinning! > >> > ---------------------------------------------------------------------- > >> > For information about J forums see > http://www.jsoftware.com/forums.htm > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
