I have list of pure functions (All functions are InterpolatingFunction) i.e
{{a, b}, {c, d}, {e, f}, ...} and I would like to end up with
{ (a[#]/b[#])&, (c[#]/d[#])&,(e[#]/f[#])&,...} the closest I have got is to do
(Divide @@ Through[#[x]]) & /@ {{a, b}, {c, d}, {e, f}} {a[x]/b[x], c[x]/d[x], e[x]/f[x]}
but these are not pure functions.
This perhaps:
Function[{a, b}, a[#]/b[#] &] @@@ {{a, b}, {c, d}, {e, f}} (* Out: {a[#1]/b[#1] &, c[#1]/d[#1] &, e[#1]/f[#1] &} *) Mr.Wizard's way of writing it (see comment) looks like this in the frontend:
({x, y} \[Function] x[#]/y[#] &) @@@ {{a, b}, {c, d}, {e, f}} $\endgroup$ \[Function] before! I added an image to the answer so everyone can see how it looks there. $\endgroup$ You can almost always turn to replacement patterns when you need to transform expressions:
Cases[ {{a, b}, {c, d}, {e, f}}, {x_, y_} :> (x[#]/y[#] &) ] {a[#1]/b[#1] &, c[#1]/d[#1] &, e[#1]/f[#1] &}
Cases defaults to levelspec {1} so this is safer than using /..
Also:
With[{a = #1, b = #2}, a[#]/b[#] &] & @@@ {{a, b}, {c, d}, {e, f}} or
x[#]/y[#] & /. {x -> #1, y -> #2} & @@@ {{a, b}, {c, d}, {e, f}} (* {a[#1]/b[#1] &, c[#1]/d[#1] &, e[#1]/f[#1] &} *) 