How do I check if any element in a list is positive?

As a simple example of what I would like to do, suppose I have a list a of all real numbers. I would like to perform a simple check to see if some element of a is positive. Of course, I could do this with a simple loop, but I feel as if Mathematica would have a more efficient way of doing this, in the spirit of functional programming. Is there, or do I just have to do this with a clumsy loop:

test=False; For[counter=1;counter<=Length[a];counter++;If[a[[counter]]>0,test=True;];];

Answer

If I understand you correctly, simply test if the maximum value in the list is Positive:

Positive @ Max @ a

Speed comparison with other methods that were posted:

timeAvg = 
  Function[func,
    Do[If[# > 0.3, Return[#/5^i]] & @@ Timing@Do[func, {5^i}], {i, 0, 15}],
    HoldFirst];

a = RandomInteger[{-1*^7, 2}, 1*^7];


MemberQ[a, _?Positive] // timeAvg

Total@UnitStep[-a] =!= Length@a // timeAvg

Positive@Max@a // timeAvg

0.593

0.0624

0.01148

---

Early-exit methods

Although very fast, especially with packed lists, the method above does scan the entire list with no possibility for an early exit when a positive elements occurs near the front of the list. In that case a test that does not scan the entire list may be faster, such as the one that R.M posted. Exploring such methods I propose this:

! VectorQ[a, NonPositive]

Unlike MemberQ, VectorQ does not unpack a packed list.

Timings compared to MemberQ and Max, first with an early positive appearance:

SeedRandom[1]
a = RandomReal[{-1*^7, 1000}, 1*^7];


Positive @ Max @ a        // timeAvg
! VectorQ[a, NonPositive] // timeAvg
MemberQ[a, _?Positive]    // timeAvg

0.008736

0.00013984


0.2528

(Most of the MemberQ time is spent unpacking the list.)

Then no positive appearance (full scan):

a = RandomInteger[{-1*^7, 0}, 1*^7];

Positive @ Max @ a        // timeAvg
! VectorQ[a, NonPositive] // timeAvg
MemberQ[a, _?Positive]    // timeAvg

0.01148

1.544

2.528

Finally a mid-range appearance of a positive value in an unpacked list:

a = RandomReal[{-50, 0}, 1*^7];
a[[5*^6]] = 1;


Positive @ Max @ a        // timeAvg
! VectorQ[a, NonPositive] // timeAvg
MemberQ[a, _?Positive]    // timeAvg

0.212

0.702


1.045