Defining Monad Function?

v=: ((1 2);(3 4);(0 5);<(2 1))
d =: (1,0.5,1,0.25);(0.5,1,0.75,0.25);(1,0.75,1,0);(0.75,0.25,0,1)
force=:(v ((0{>"0 v);])@{~ ] i.4) ,"1 0 <"0>(0{d)
force=:(v ((1{>"0 v);])@{~ ] i.4) ,"1 0 <"0>(1{d)
force=:(v ((2{>"0 v);])@{~ ] i.4) ,"1 0 <"0>(2{d)
force=:(v ((3{>"0 v);])@{~ ] i.4) ,"1 0 <"0>(3{d)
force=:(v ((4{>"0 v);])@{~ ] i.4) ,"1 0 <"0>(4{d)
force=:(v ((y{>"0 v);])@{~ ] i.4) ,"1 0 <"0>(y{d)

Given v and d, 1st column of force gives us (n+1)th vector from v.

2nd column of force gives us each vector from v.

3rd column of force gives us a constant between 2 vectors.

That is, (1 2);(1 2) will have 1 on 3rd column of force, but (1 2);(3 4) might not. I want to make a monad function which gives us

force=:(v ((1{>"0 v);])@{~ ] i.4) ,"1 0 <"0>(1{d)

if we type force_constant 1

or force=:(v ((2{>"0 v);])@{~ ] i.4) ,"1 0 <"0>(2{d)

if we type force_constant 2

Could someone help?

Solution

You wrote most of it yourself already. Just take your final version of force, the one you wrote using y, and wrap it in an explicit definition:

    v =:  ((1 2);(3 4);(0 5);<(2 1))
    d =:  (1,0.5,1,0.25);(0.5,1,0.75,0.25);(1,0.75,1,0);(0.75,0.25,0,1)

   force_constant =: monad def '(v ((y{>"0 v);])@{~ ] i.4) ,"1 0 <"0>(y{d)'

   force_constant 1
+---+---+----+
|3 4|1 2|0.5 |
+---+---+----+
|3 4|3 4|1   |
+---+---+----+
|3 4|0 5|0.75|
+---+---+----+
|3 4|2 1|0.25|
+---+---+----+

   force_constant 2
+---+---+----+
|0 5|1 2|1   |
+---+---+----+
|0 5|3 4|0.75|
+---+---+----+
|0 5|0 5|1   |
+---+---+----+
|0 5|2 1|0   |
+---+---+----+

Now, this formulation depends on the nouns v and d being globally defined. You might consider changing that so force_constant or related verbs take these arrays as inputs. The simplest method would be change the monads to dyads, and let v and d come in as the left argument, x¹.

¹_{But we can keep it simple for now. If you want more feedback on your code, feel free to post it over on http://codereview.stackexchange.com/.}