       Re: Counting number of numbers in a large list between two valus

• To: mathgroup at smc.vnet.net
• Subject: [mg114513] Re: Counting number of numbers in a large list between two valus
• From: "Carl K. Woll" <carlw at wolfram.com>
• Date: Mon, 6 Dec 2010 06:13:05 -0500 (EST)

```
On 12/5/2010 8:57 PM, Lyle wrote:
> Dear Listers,
>
> I have a large (5-20million) one dimensional list of real numbers and
> I want to count the number of entries in the list that lie between 2
> specific values (x1, x2). I need to run the function for a number of
> different ranges.
>
> ie. number of list entries (l), where x1<= l<= x2
>
> I've tried:
>
> tallydata[{x1_, x2_}] := Count[data, x_ /; x1<= x<= x2]
>
> that takes about 3-4 seconds
>
> and
>
> tallydata[{x1_, x2_}] := Length[Select[data, x1<= #<= x2&]]
>
> which takes a little bit longer.
>
> The best I've managed is (this last one might be off by 1 or 2 but
> this doesn't really matter to me):
>
> sorteddata = Sort[data];
> nf = Nearest[sorteddata];
> tallyrange[{x1_, x2_}] :=
>   First[Position[sorteddata, First[nf[x2]]]] -
>    First[Position[sorteddata, First[nf[x1]]]]
>
> which takes between 1 and 2 seconds but I was hoping there might be a
> faster way to do this?
>
> Any help would be great!
>
> Thanks,
> Lyle Gordon
>
> Northwestern University
>

Here's one possibility:

data = RandomReal[1, 10^7];

In:= Total@Unitize@Clip[data, {.2, .3}, {0, 0}] // Timing

Out= {0.14, 1000695}

Carl Woll
Wolfram Research

```

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