How do you control evaluation when using apply?

[Brentt]

Why does this work

In[0]: = jacobianFunction[func_, vars_List] := Module[{f},
f = Function[Evaluate[vars], Evaluate[D[func, {vars}]]];
f
];
jacobianFunction[{Sin[x y], Cos[x + y]}, {x, y}] @@ {10, 2}

out[0]:= {{2 Cos[20], 10 Cos[20]}, {-Sin[12], -Sin[12]}}

But this does not (the goal is to make the function take a point as an
argument)


In[0]: = jacobianFunction[func_, vars_List] := Module[{f},
f = Evaluate[Function[Evaluate[vars], Evaluate[D[func, {vars}]]]];
f@@ # &
];
jacobianFunction[{Sin[x y], Cos[x + y]}, {x, y}][{10, 2}]



I can't get f@@ # & to evaluate properly (I've tried wrapping it in
ReleaseHold and evaluate statements, nothing seems to get it to evaluate.

I know I can just rewrite the function to take the point but I'm just
curious why it won't work.

[Roland Franzius]

Do your evaluation during function body contruction and replace the
Function-head after evaluation

jacobianFunction[func_, vars_List] :=
Module[ {function},
( function[ {vars}, D[func, {vars} ] /.function->Function )]


or apply the Function head to a List construct

jacobianFunction[func_, vars_List] :=
Function@@ { {vars}, D[func, {vars} ] }

More easy define a function generator once for all

MakeFunction = (Set@@{#1,Function@@{##2}}&);

MakeFunction[Subscript[f,1],{x,y},D[f[x,y],x]];

Subscript[f,1]

Function[{x, y}, Derivative[1, 0][f][x, y]]

--

Roland Franzius