Re: SameTest in Union
- To: mathgroup at smc.vnet.net
- Subject: [mg61117] Re: SameTest in Union
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Tue, 11 Oct 2005 03:20:09 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <did38g$qht$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Jack Goldberg wrote:
> Hi Folks,
>
> I know there is a simple answer to this question but the help index
> idoes not help!
>
> I have a list, something like this:
>
> lst = {1.1101, 1.11095, 1.11076, 1.09, 2.3523, 2.352. 2.35211}
>
> I want to remove from the list those entries which are near each
> other but not identical, leaving only one representative for each of
> these numbers. One approach is to use Union with the option
> SameTest->???. Here the same test might be that the difference
> between entries is less than, say 10^(-2). But I can't seem to get
> SameTest to work. So, what I want is
>
> Union[ lst, SameTest- > ?]
>
> so that the union returns
>
> {1.1101, 2.35211}
>
> Here, I chose 2 representatives. Any other choice is OK; say,
>
> {1.11095, 2.352}
>
> is also satisfactory.
>
> There may be other ways to do this, but I thought of Union first.
> Perhaps, Cases or Select might be better. Any help is appreciated.
>
> Jack
>
Hi Jack,
One way of doing this is to use a pure function for *SameTest* that
compares absolute differences between each pair of values and returns
*True* whenever differences are less than, say, 10^(-2). Also, note that
I have corrected the syntax of your list for the last two numbers were
not separated by a comma but were concatenated by a dot.
In[1]:=
lst = {1.1101, 1.11095, 1.11076, 1.09, 2.3523, 2.352, 2.35211}
Out[1]=
{1.1101, 1.11095, 1.11076, 1.09, 2.3523, 2.352, 2.35211}
In[2]:=
Union[lst, SameTest -> (Abs[#2 - #1] < 10^(-2) & )]
Out[2]=
{1.09, 1.1101, 2.352}
Best regards,
/J.M.