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Re: Select only certain sublists matching criteria

• To: mathgroup at smc.vnet.net
• Subject: [mg110992] Re: Select only certain sublists matching criteria
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Fri, 16 Jul 2010 05:16:52 -0400 (EDT)

On 7/15/10 at 3:09 AM, chris at chrispoole.com (Chris Poole) wrote:

>I have a list like this: {{0, -4, 2.283}, {0.5, -4, 2.282}, {1, -4,
>2.280}, {1.5, -4, 2.276}, {2, -4, 2.271}, {2.5, -4, 2.264}, {3,
>-4, 2.255}, {3.5, -4,
>2.242}}

>I want to look at each list of 3 numbers, and keep only the lists
>where the third item in each list fits some criteria.

>I can do something like this: Select[{2, 15, 1, 16, 17}, Abs[3 - #]
>< 3 &]

Change # to #[[3]] and the selection criteria will be applied to
the 3rd element of each item in the list

>But it only works for flat lists.

>For example, I want only the lists where the third item is around
>2.25 +- 0.001. Something like that.

Here are a few ways to do what you want for the data above after
setting the tolerance to 0.01. I changed the tolerance since
there is nothing within 0.001 of 2.25 in your data

In[3]:= Select[data, Abs[#[[3]] - 2.25] < .01 &]

Out[3]= {{3, -4, 2.255}, {3.5, -4, 2.242}}

In[4]:= Select[data, Abs[Last@# - 2.25] < .01 &]

Out[4]= {{3, -4, 2.255}, {3.5, -4, 2.242}}

In[5]:= Cases[data, {_, _, _?(Abs[# - 2.25] < .01 &)}]

Out[5]= {{3, -4, 2.255}, {3.5, -4, 2.242}}

In[7]:= Pick[data, data[[All, 3]], _?(Abs[# - 2.25] < .01 &)]

Out[7]= {{3, -4, 2.255}, {3.5, -4, 2.242}}

This last approach is most useful when you already have the
element of each sublist you want as your selector in a separate
list. If this is not the case, then the overhead required to
create the second argument to Pick will make this method slower
than the others for long lists.