Make a function of a list of expressions

Question

I have a family of functions, each of which takes a long time to build the expression. Once the functional form is determined, however, calculations are very fast. So I want to build a table of functions programatically. Something like:

exprList = Table[buildExpr[a, b, x], {a, 1, 5}, {b, 1, 100}]
exprFunc[a_, b_, x_] := Evaluate[exprList[[a, b]]]

However, the above throws a Part error, saying I can't use a and b in Part in a function. I've tried various other things from related questions on the internet, but still no luck.

Answer 1

You can use:

exprFunc[a_, b_, x_] = Indexed[exprList, {a, b}];

Then:

exprFunc[1, 5, z]

buildExpr[1, 5, z]

Answer 2

There is more than one way to do things in Mathematica. A simple example code

buildExpr[a_, b_, v_] := a + b v;
ClearAll[x]; (* clears values associated with 'x' *)
exprList = Table[buildExpr[a, b, x], {a, 3}, {b, 3}];
exprFunc[a_, b_, v_] := Block[{x = v}, exprList[[a, b]]];
exprFunc[1, 2, u] == 1 + 2 u

returns True. The initial problem you encountered was the Evaluate[exprList[[a, b]]] which was being evaluated in defining the exprFunc but a and b were not defined yet. You want to avoid using Evaluate and use Block instead to give a local value of the variable x which will be used by the expressions in exprList. The documentation for Evaluate shows that it is only needed for some special cases to override Holds.