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Re: Using Select with arrays? (Relative newbie)

• To: mathgroup at smc.vnet.net
• Subject: [mg54245] Re: Using Select with arrays? (Relative newbie)
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Mon, 14 Feb 2005 21:50:37 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

>-----Original Message-----
>From: Hugo Mallinson [mailto:hfm21 at cam.ac.uk] 
To: mathgroup at smc.vnet.net
>Sent: Monday, February 14, 2005 4:17 AM
>To: mathgroup at smc.vnet.net
>Subject: [mg54245]  Using Select with arrays? (Relative newbie)
>
>The subject might not be entirely correct, but here is my problem:
>
>I have a list of 5-variable data points like
>
>data = {
>{1, 1, string1, c, d}
>{1, 2, string2, c, d}
>{1, 3, string3, c, d}
>{1, 4, string4, c, d}
>{2, 1, string1, c, d}
>{2, 2, string2, c, d}
>{3, 1, string3, c, d}
>{4, 1, string2, c, d}
>{4, 2, string4, c, d}
>}
>
>
>and I want to extract just the points that have 1 (or 2, etc) as their 
>first value. I think I should do something like
>
>Select[data, {1, _Integer, _String, _Integer, _Integer}]
>
>but that doesn't work.
>
>Having done that I need to find the maximum value of #2 for each 
>string, which I presumably do by the same method as above to extract 
>all string1 (or ...2) and then use Map[] and Max[]. I would do 
>this all 
>with For loops (revealing my lack of Mathematica chops :-) ) but I'd 
>really like to learn how to do this sort of extraction in a 
>Mathematica-y way. Any help would be greatly appreciated!
>
>Hugo
>
>

Hugo,

first check Length[data], if comes out as 1, then you had forgotten the
comma separators for the elements of your outer list.


If  you want to select certain elements (say cases) of your list, the
right command is Cases, not Select (check out with Help).

And, I recommend, don't be overly specific with a pattern if you need
not. So, as long as the symbols c, d haven't got integer values, your's
won't match. (And I don't recommend to substitute _Symbol for _Integer
here, then the pattern will not match if they _did_ get values.) This is
fine:

In[4]:= Cases[data, {1, __}]
Out[4]=
{{1, 1, "string1", c, d}, {1, 2, "string2", c, d}, 
 {1, 3, "string3", c, d}, {1, 4, "string4", c, d}}


For your second question, I propose (there are dozens of different
solutions)

In[5]:=
(# -> Max[Cases[data, {_, x_, #, __} :> x]] &) /@ Union[data[[All, 3]]]
Out[5]=
{"string1" -> 1, "string2" -> 2, "string3" -> 3, "string4" -> 4}




To explain:

In[7]:= data[[All, 3]]
Out[7]=
{"string1", "string2", "string3", "string4", "string1", "string2",
"string3", 
"string2", "string4"}

Just gives alle occurrences of your strings (3rd components) in proper
sequence.

In[8]:= Union[data[[All, 3]]]
Out[8]=
{"string1", "string2", "string3", "string4"}

Unifies and orders them.



Now

In[9]:= Cases[data, {_, x_, "string2", __}]
Out[9]=
{{1, 2, "string2", c, d}, {2, 2, "string2", c, d}, {4, 1, "string2", c,
d}}

gives all occurances with "string2", and 

In[10]:= Cases[data, {_, x_, "string2", __} :> x]
Out[10]=
{2, 2, 1}

just retains the corresponding values of the 2nd component (in same
order).



In[11]:= Max[Cases[data, {_, x_, "string2", __} :> x]]
Out[11]= 2

gives the Maximum of those.

To do that for all values of the string we map this over the set of the
strings:

In[12]:=
Max[Cases[data, {_, x_, #, __} :> x]] & /@ Union[data[[All, 3]]]
Out[12]=
{1, 2, 3, 4}


Now which result corresponds to which string? If you have control of
your bookkeeping (compare with Out[8]) you know, but it's better to be
explicit, and show the associations:

In[14]:=
{Max[Cases[data, {_, x_, #, __} :> x]], #} & /@ Union[data[[All, 3]]]
Out[14]=
{{1, "string1"}, {2, "string2"}, {3, "string3"}, {4, "string4"}}

or visually more pleasing as rules, as I did in Out[5].


--
Hartmut Wolf