MapThread multiple functions onto multiple lists

Question

I'm trying to learn the functional style which seems to prevail in Mathematica. I'm having trouble accomplishing the following:

Let's say I have multiple lists of arbitrary data (using two lists here to keep it simple):

a = {1,2,3,4,5,6}
b = {1,1,2,2,3,3}

I also have multiple arbitrary functions (again using two to keep it simple) which all take the same inputs in the same order, but use them to generate different outputs:

f = Function[{u,v},{{u^2,u*v},{-u*v,v^2}}]
g = Function[{u,v},{{u^2,1},{-1,v^2}}]

I understand how to build lists of results, threading over lists a,b, with MapThread:

fOut = MapThread[f,{a,b}]
gOut = MapThread[g,{a,b}]

However, because in reality there are dozens of functions (f,g,etc.) and dozens of lists of data (a,b,etc.), I end up with dozens of MapThread commands, each with the same long list of arguments, creating a wall of text that is far from elegant-looking. So I tried to merge it into a single MapThread command, which didn't work:

{fOut,gOut} = MapThread[{f,g},{a,b}]

Is there a way to MapThread many functions onto many lists of data (assuming each function expects the data in the same order)? If possible, I would like to avoid creating new variables because the functions are intended to be compiled, and I think it would create redundant data.

Answer 1

It is not entirely clear to me what your larger problem looks like. If you have the same set of lists each time and merely want to MapThread a series of functions across them you can use a simple construct such as:

a = {1, 2, 3, 4, 5, 6};
b = {1, 1, 2, 2, 3, 3};

MapThread[#, {a, b}] & /@ {f, g}

{{f[1, 1], f[2, 1], f[3, 2], f[4, 2], f[5, 3], f[6, 3]},
 {g[1, 1], g[2, 1], g[3, 2], g[4, 2], g[5, 3], g[6, 3]}}

If you have a more involved operation in mind please describe it in greater detail.