Order of evaluation in nested expression

Question

I am trying to make a function that works as follows: Integrate 1 for all t in the interval $ [0,1] $ such that the first element of function vstar is positive. vstar is a function that outputs a pair of real numbers. Unfortunately the test vstar[t, a1, a2, f1, f2, σ]][[1]] > 0 does not work as expected (this is waht I've tried):

D1[f1_, a1_, f2_, a2_,σ_] := NIntegrate [If[vstar[t, a1, a2, f1, f2,σ][[1]] > 0, 1, 0] f[t], {t, 0, tup}, AccuracyGoal -> 8];

The way it is, Mathematica tests if the first slot of vstar is greater than zero (that is $ t>0 $) rather than testing if the first part of the output of vstar is greater than zero. vstar is defined so that it evaluates only for numerical values. I think I need to evaluate the function vstar before the test is performed, I just don't know how to do it - could someone explain how?

p.s. For further reference, here's the code of vstar:

vstar[tt_?NumericQ, aa1_?NumericQ, aa2_?NumericQ, 
  ff1_?NumericQ, ff2_?NumericQ, σσ_?NumericQ] := 
 Module[{list}, 
  list = {objm, objs1, objs2}  /. {t -> tt, 
     a1 -> aa1, a2 -> aa2, f1 -> ff1, 
     f2 -> ff2, σ -> σσ}; 
  If[list[[1]] < 0 && list[[2]] < 0 && list[[3]] < 0, {0, 0},
   Which[Ordering[list , -1] == {1}, {v1, v2} /. vm, 
     Ordering[list , -1] == {2}, {v1 /. v1s, 0}, 
     Ordering[list, -1] == {3}, {0, 
      v2 /. v2s}]  /. {t ->tt, a1 -> aa1, 
     a2 -> aa2, f1 -> ff1, f2 -> ff2, σ -> σσ}]]

I edited your question but your code still has issues so I can't really help much more. At first sight, there are wrong square brackets inserted in your If clause so I suggest you edit the code to amend this (I have not touched your code other than formatting) and also provide the function vstar. May I also suggest you read the relevant section on formatting for future posts. — gpap, Sep 17 '13 at 11:26
Ok, so, this isn't much help now - it depends on other bits of code. The idea is to have a self-containted, minimally working example for people to test, without having to see part sof your code that are irrelevant to the problem. So, if the output of vstar always gives out a pair {a,b} where, say, 0<a,b<1, it will be easier to write vstar[args__]:=RandomReal[{0,1},{2,1}]. Also, the page about formatting that I linked tells you that a code block is formatted easily by selecting the code a pressing ctrl + K. I have done that now, but you should be able to do it yourself in the future — gpap, Sep 17 '13 at 12:04
Possible duplicate: Prevent Part[] from trying to extract parts of symbolic expressions — Mr.Wizard, Sep 18 '13 at 21:02

score 1 · Answer 1 · answered Sep 17 '13 at 12:06

What happens now since vstar only evaluates on numerical arguments Part sees the unevaluated form and extracts the first argument since it doesn't know any better:

vstar[t, a1, a2, f1, f2, s][[1]]
(* t *)

To get around this you can make a function that extracts the first part only on numerical input:

numericFirst[l_?(VectorQ[#, NumericQ] &)] := l[[1]]

numericFirst[vstar[t, a1, a2, f1, f2, s]]
(* vstar[t, a1, a2, f1, f2, s] *)

numericFirst[{0.1,0.2,0.3}]
(* 0.1 *)

Order of evaluation in nested expression

1 Answers1