Flattening a nested matrix

[Stu]

The first example, where you tessellate the 4×6 array, is exactly what I wanted. Since in my case the original array and the tessellated array will always have identical contents, I don't have to worry about padding.

The solution is more complicated than I initially thought it would be, which is why I ask the experts on this forum.

[Stu]

This function does exactly what I wanted; however, can the definition be modified so that it doesn't depend on ⎕ML?

[Veli-Matti]

The tessellate code's not []ML dependent, so it should work fine when using in the APL2 friendly environment, too (just leave the []ML part off).

<offtopic>
I personally detest seeing something like r c <- .. - it should _always_ be with parens: (r c) <-.. *sigh*
</offtopic>

-Veli-Matti

[Stu]

I think the problem is that in some APL's monadic "↑" doesn't denote Mix. ⎕ML←0 guarantees that it does in Dyalog. Is there a way to simulate monadic "↑" that doesn't depend on Migration Level?

[DanB|Dyalog]

Monadic UP-arrow (↑) means Mix in ⎕ML 0 or 1.
1 is the default in Dyalog today.
If your application only contains utilities written by Dyalog you shouldn't have to worry about setting ⎕ML before using Mix.
OTOH if you think there could be ANYTHING changing ⎕ML you should account for that and e.g. use

Code: Select all

Mix←{⎕ML←1 ⋄ ↑⍵}


Unfortunately, there is no simple way around it.

⊃ is similar. It means (monadic) First or (dyadic) Pick. You can't get around the ⎕ML problem with First but you can work around some cases with Pick. I personally use 1⊃V instead of ⊃V if I know that ⎕ML may change, that V is a vector with at least one element and that ⎕IO is 1 (or I can use ⎕IO⊃V).
Like this, if ⎕ML is changed underfoot, the expression will still work.

[Phil Last]

      mix←↑⍤0
      mix←⊃⍤0

are both identical to

      mix←{⎕ML←0 ⋄ ↑⍵}

It works because both ↑ and ⊃ merely disclose scalars in any migration level. f⍤0 applies f to the scalars in its argument. The required mix operation is being done as a tidy-up after the fact.

Not guaranteed to be quicker although I'm sure it could be made to be as quick.

[Phil Last]

Similarly

      first←⊃⍬∘⍴
      first←↑⍬∘⍴

are both identical to

      first←{⎕ML←0 ⋄ ⊃⍵}

in any migration level and for the same reason that mix on a scalar is equivalent to first as there is an empty frame to be catenated to the single cell shape. Again, whichever of ↑ and ⊃ is mix takes marginally longer as it has the overhead of preparing the frame even though it is empty.