Counting negative values in list

Question

I would like to count the negative values of a list.

My approach was Count[data, -_] which doesn't work.

How can I tell Mathematica to count all numbers with a negative sign?

Answer 1

I assume that you have numeric values. A much more efficient way would be

-Total[UnitStep[data] - 1]]

or

Total[1-UnitStep[data]]

Note: While the second notation is certainly a bit more compact, it is about 35% slower than the double-minus notation. I have no idea why. On my system, it takes on average 0.22 sec vs 0.30 sec.

Compare timings between the faster UnitStep version and the pattern matching approach:

data = RandomReal[{-10, 10}, 10^7];

Timing[-Total[UnitStep[data] - 1]]
(* ==> {0.222, 5001715} *)

Timing[Count[data, _?Negative]]
(* ==> {6.734, 5001715} *)

Answer 2

Use _?Negative:

list = RandomInteger[{-9, 9}, 30]

Count[list, _?Negative]

---

Your pattern will match an object with an explicit negative sign:

Count[{a, -b, c, a, -a, a, -b}, -_]

3

You could combine the patterns to match either:

Count[{-1, -2, 3, 4, -a, b, -c}, -_ | _?Negative]

4

---

Since this has become a speed competition (which is fine by me), rather than the beginner's question I took it to be, here is my own variation, using Tr for fast packed array summing:

neg = Length@# - Tr@UnitStep@# &;

Timings:

SetAttributes[timeAvg, HoldFirst]

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

list = RandomInteger[1*^7 {-1, 1}, 1*^8];

-Total[UnitStep[list] - 1] // timeAvg

Length[list] - Total[UnitStep[list]] // timeAvg

neg @ list // timeAvg

0.592

0.234

0.1278

Answer 3

For numeric values, the following:

Length[data] - Total[UnitStep[data]] 

is 50% faster than Thomas' solution.

Update: An even faster approach will be to compile to C, as shown in the following function f:

ClearAll[f];
f = Compile[{{vector, _Real, 1}, {bound, _Real}},
      Module[{t = 0, i = 1, len = Length[vector]}, 
        For[i = 1, i <= len, i++, t += Boole[vector[[i]] < bound]]; t], 
      CompilationTarget -> "C", "RuntimeOptions" -> "Speed"]

Using the timeAvg function, as defined in Mr. Wizard's answer, we have:

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

data = RandomReal[{-10, 10}, 10^7];

{-Total[UnitStep[data] - 1] // timeAvg,
 Length[data] - Total[UnitStep[data]] // timeAvg,
 Length[data] - Tr[UnitStep[data]] // timeAvg,
 f[data, 0.] // timeAvg}

(* ==> {0.105993, 0.0431972, 0.0422639, 0.0141324} *)

Note that the function f defined above will work for any upper bound, and not just 0. And would be significantly faster (at least in my machine) than the corresponding Length[data]- Tr[UnitStep[data - bound]] approach when bound is not zero.

For the dangers with the use of "RuntimeOptions"->"Speed", see the Mathematica help: RuntimeOptions.

Answer 4

Lots of nice answers. Here's another, but I'm afraid it's quite slow.

Total[Select[data, # < 0 &]]

Though this totals all the negative numbers. To count them you could do:

-Total[Sign[Select[data, # < 0 &]]]

Then I got to thinking, "how would I program this in Matlab?"

 Total[1 - Sign[data]]/2

Answer 5

This seems competitive in terms of speed:

Total@Clip[list, {0, 0}, {1, 0}]

Testing:

SetAttributes[timeAvg, HoldFirst]
$HistoryLength = 0;
timeAvg[func_] := 
 Do[If[# > 0.3, Return[#/5^i]] & @@ Timing@Do[func, {5^i}], {i, 0, 15}]
neg = Length@# - Tr@UnitStep@# &;
list = RandomReal[1*^7 {-1, 1}, 1*^7];

Total@Clip[list, {0, 0}, {1, 0}] // timeAvg
-Total[UnitStep[list] - 1] // timeAvg
Length[list] - Total[UnitStep[list]] // timeAvg
neg@list // timeAvg

(* 0.1594, 0.375, 0.1812, 0.197 *)