       Re: Segregating the elements of a list based on given lower and upper

• To: mathgroup at smc.vnet.net
• Subject: [mg77281] Re: Segregating the elements of a list based on given lower and upper
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 6 Jun 2007 07:12:20 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <f43hin\$342\$1@smc.vnet.net>

```R.G wrote:
> Hi Mathgroup members,
>
> Say, I have a list with the following elements:
>
> A={6.32553, 7.09956, 8.56784, 16.1871, 15.3989, 17.2285, 7.40711, \
> 14.8876, 19.9068, 10.0834}
>
> and I have the following list with each {xvalue, yvalue}={lower bound,
> upper bound}:
>  B={{0, 7}, {8, 10}, {11, 12}, {13, 15}, {16, 18}}
>
> How can I segregate values in A according to lower bound and upper
> bound from B and find the number number of occurrence ?For example:
> {0,7}={6.32553}, thus the number of occurrence is 1.
> {8, 10}={7.09956,7.40711,8.56784}, the number of occurrence is 3.

Here, I believe you meant the number of occurrences is 1 since only
8.56784 belongs to the interval.

> {11,12}=None, the number of occurrence is 0.
>
> The code should be able work for any number Length[A] and Length[B].
> Thank you,
> R.G

Assuming I have correctly understood what you want, you could use
interval arithmetic as in the following expressions:

In:=
lst = {6.32553, 7.09956, 8.56784, 16.1871, 15.3989, 17.2285, 7.40711,
14.8876, 19.9068, 10.0834};

bounds = {{0, 7}, {8, 10}, {11, 12}, {13, 15}, {16, 18}};

intervals = Interval /@ bounds;

Total[Transpose[(Boole[IntervalMemberQ[#1, lst]] & ) /@ intervals]]

Total[Transpose[Outer[Boole[IntervalMemberQ[#1, #2]] & , intervals,
lst]]]

Out= {1, 1, 0, 1, 2}

Out= {1, 1, 0, 1, 2}

Regards,
Jean-Marc

```

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