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Function composition using common argument
Hi,
Newbie question I guess. To simplify, say I have 2 functions f1 & f2:
q) f1: {1-x%y} q) f2: {mavg[x;y]} /This is voluntarywhich actually in this case, have a common argument when a composition <g> is applied, eg. :
q) a: til 10 q) g: f1 . (f2 . (3;a); a) 0n 0.5 0.5 0.3333333 0.25 0.2 0.1666667 0.1428571 0.125 0.1111111
I can’t figure a compact/elegant way to specify <g> without repeating twice argument <a>.
A wrapper function can obviously do the job, though complexity grows with the number of compositions. So the question is basically: Is there an iterative (or other) way to pass an identical argument to any number of multivalent functions composed successively?
Thx
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3 Replies
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You can do this using iteration over a list of the functions to apply.
q){z .(y;x)}[a]/[3;(f2;f1)] 0n 0.5 0.5 0.3333333 0.25 0.2 0.1666667 0.1428571 0.125 0.1111111Adding another function:
q)f3:+ q){z .(y;x)}[a]/[3;(f2;f1;f3)] 0n 1.5 2.5 3.333333 4.25 5.2 6.166667 7.142857 8.125 9.111111 -
Q doesnt really offer built-in combinators as liberally as its ancestor language APL does. An elegant way to compose the projections off1andf2? You can lose the parensq)c: f1[;a] f2[;a]@ q)c 3 0n 0.5 0.5 0.3333333 0.25 0.2 0.1666667 0.1428571 0.125 0.1111111
Of course, if you have to do this often, you can write your own combinator. Call itcrfor curry right:q)cr:{x[;y]} q)c:('[;])over(f1;f2)cr:a / Compose over (f1[;a];f2[;a]) q)c 3 0n 0.5 0.5 0.3333333 0.25 0.2 0.1666667 0.1428571 0.125 0.1111111Compose over a list of functions as many as you need. -
Many thanks to you both for your inputs, very useful illustrations of projection/iteration/composition functionalities.
The function approaches work well in their current incarnation, with the small caveat (at least from my understanding) that functions to be composed must have the same rank. Relatively easy to implement argument condition handling should allow for a more generic multivalent case. Again, thank you,
Best,
JP
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