Caution, spoilers ahead!
Interesting case!
Indeed some data might have helped.
I recognized (+/ .*)&(% +/&.:*:) as the dot product between normalised
vectors, because I recently needed it as cosine similarity between
histograms of token frequencies between paragraphs of text for roughly
comparing their topics.
It is clear from the code it's not meant to be applied on matrices (where
rows have instances and columns have variables) because then it would have
required a transpose around the matrix product to ensure the matrices are
normalised along the same axis). So I think it's meant for vectors.
The rest I figured out from some tests:
mis=: 0j_180p_1*^.@(j.-.&.*:)@(+/ .*)&(% +/&.:*:)
1 1 mis 0 1
45
2 2 mis 0 1
45
1 0 mis 0 1
90
_1 0 mis 0 1
90
So I'd say it is the unsigned angle in degrees between two vectors. I have
to say the complex phrasing after the cosine distance, both in the
mathematical as in the common sense, baffled me a bit...
I would simplify using arccos:
simp=: (180p_1 * _2 o. (+/ .*)&(% +/&.:*:))
It seems this would be off only by some rounding errors on my test:
test=: 100 3?.@$0
(mis"1/~ -: simp"1/~) test NB. equal?
0
+/,(mis"1/~ = simp"1/~) test NB. # of correct
9964
+/-.,(mis"1/~ = simp"1/~) test NB. # of wrong
36
w=: ($#:I.@,) (mis"1/~ ~:simp"1/~)test NB. coords of wrong pairs in test
$w{test
36 2 3
>./ | +. (mis/"2 - simp/"2) w{test NB. max deviation of real and
imaginary parts
1.23179e_13 6.36111e_15
This can likely be simplified more if it's meant to work only on 2D vectors.
I guess this one is a good reminder that having a concise language doesn't
mean one has to forgo writing sensible comments.
Jan-Pieter
On Wed, 16 Aug 2023, 13:34 Raul Miller, <[email protected]> wrote:
> Given a J expression:
> 0j_180p_1*^.@(j.-.&.*:)@(+/ .*)&(% +/&.:*:)
>
> (1) Describe its purpose, and
>
> (2) Use that to simplify the expression.
>
> Here, the biggest hurdle is extracting the purpose from even a short
> bit of code. I'm not sure that extracting purpose from code is
> particularly viable in the general case. (Though having example
> arguments would be a tremendous help.) Once that's done, the rest is
> much easier.
>
> --
> Raul
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