Defining multiple functions

Question

I have a matrix with 4 elements that I want to turn into functions without explicitely defininig all the functions "by hand":

matrix={{(6. u2 - 3 v2 + 0.3 u2 x11 + 0.1 v2 x11)/(
  3 u2 + 1. v2), (-15. + 1.5 u2 x12 + 0.5 v2 x12)/(-3. u2 - v2)}, {(
  5. u2 v2 + 3.6 u2 x21 + 1.2 v2 x21)/(
  3 u2 + 1. v2), (-9. u2 + 2 v2 - 1.8 u2 x22 - 0.6 v2 x22)/(
  3 u2 + 1. v2)}}

in other words, in order to define a function for each element I have to manually specify the functions:

eq1[u1_,u2_, v1_,v2_, x11_,x12_,x21_,x22_] := matrix[[1,1]];
eq2[u1_,u2_, v1_,v2_, x11_,x12_,x21_,x22_] := matrix[[1,2]];
eq3[u1_,u2_, v1_,v2_, x11_,x12_,x21_,x22_] := matrix[[2,1]];
eq4[u1_,u2_, v1_,v2_, x11_,x12_,x21_,x22_] := matrix[[2,2]];

(Although the arguments do not all appear in the RHS, they might in different scenarios, so I chose to specify all arguments).

I tried:

Table[eq[i, j][u1_,u2_, v1_,v2_, x11_,x12_,x21_,x22_] := matrix[[i, j]], {i, 2}, {j, 2}]

but that does not seem to work. Or at least I don't get how to access eq now:

eq[1, 1]

does not work. Any help appreciated.

Answer 1

matrix = {{(6. u2 - 3 v2 + 0.3 u2 x11 + 0.1 v2 x11)/(3 u2 + 1. v2),
    (-15. + 1.5 u2 x12 + 0.5 v2 x12)/(-3. u2 - v2)},
   {(5. u2 v2 + 3.6 u2 x21 + 1.2 v2 x21)/(3 u2 + 1. v2),
    (-9. u2 + 2 v2 - 1.8 u2 x22 - 0.6 v2 x22)/(3 u2 + 1. v2)}};

Table[eq[i, j][u1_, u2_, v1_, v2_, x11_, x12_, x21_, x22_] := 
  Evaluate[matrix[[i, j]]], {i, 2}, {j, 2}];

?eq

(definitions displayed)

Evaluation examples

eq[1, 1][1, 2, 3, 4, 5, 6, 7, 8]

0.5

Table[eq[i, j][1, 2, 3, 4, 5, 6, 7, 8], {i, 2}, {j, 2}]

{{0.5, -1.5}, {12.4, -5.8}}