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Re: Grouping {x,y z} data set

  • To: mathgroup at smc.vnet.net
  • Subject: [mg99615] Re: Grouping {x,y z} data set
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Sat, 9 May 2009 03:21:53 -0400 (EDT)

On 5/8/09 at 12:18 AM, graser at gmail.com (graser) wrote:

>I have arbitrary data set.

>For example,

>Data={{x_1,y_1,z_1},{x_2,y_2,z_1},{x_1, y_2, z_3},........{x_n, y_m,
>z_L}}

I assume this is *not* what you actually entered into
Mathematica. If it was, entering data literally as x_1 will
definitely be a problem

>I tried to group this data set depending on z value.

>I mean I try to select all x, y values with same z value.

In version 7, this is easily done using GatherBy. For example,

In[3]:= data =
   ArrayFlatten@{{RandomReal[1, {10, 2}],
      Transpose@{RandomInteger[1, {10}]}}};

In[4]:= GatherBy[data, Last]

Out[4]= {{{0.654913, 0.942989, 1}, {0.899263, 0.0620125,
    1}, {0.872745, 0.876903, 1}, {0.99796, 0.425091, 1}, {0.399351,
    0.169411, 1}, {0.435277, 0.683664, 1}}, {{0.857486, 0.913224,
    0}, {0.951074, 0.237923, 0}, {0.528556, 0.0531316, 0}, {0.796729,
    0.942358, 0}}}

In earlier versions of Mathematica this can be achieve using
Split after ordering the data appropriately

Split[data[[Ordering[Last/@data]]],Last#1==Last#2&]

will group the data according to the last value in each row.
Note, while this will group the data in a manner equivalent to
GatherBy, the end result will typically have a different order.




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