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A question about pattern-matching

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63728] A question about pattern-matching
  • From: gardyloo <gardyloo at mail.wsu.edu>
  • Date: Thu, 12 Jan 2006 03:22:37 -0500 (EST)
  • References: <djcgcs$6du$1@smc.vnet.net> <200510230946.FAA10826@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com
Hi,  all.

   I am trying to extract certain parts of a dataset, while retaining 
some of the overall structure. I decided to do it using pattern-matching
and replacements, but have run into some problems.

First, a small subset of the data:

testList = {{-90, {{60493, 0.061}, {62493, 0.15881}, {64493.5, 

            0.559}}}, {-88, {{62493, 0.151}, {64493., 0.61617}, {65993.4, 

            0.171}, {68993.10, 0.06}}}, {-86, {{62493.75, 0.14}, {64493.55, 

            0.61440}, {65993., 0.18}, {67993, 0.0}, {68993.100, 0.06448}}}};


The data consists of lists of the form  { integer, {  ordered pair1,
ordered pair2, ... } }, and my goal is to extract the second number in
each of the ordered pairs, while retaining the lists' overall structure.
So, for example, from testList, I'd want something like
      { { 0.061, 0.15881, 0.559}, {0.151, 0.61617, 0.171, 0.06}, {0.14,
0.61440, 0.18,  0.0, 0.06448}}
returned.

I've tried several patterns, with variously named bits, and only some of
them make sense to me (and none of them, yet, return what I really
want). Can someone explain them to me?

I'd expect this one to return the list of lists of ordered pairs. It
returns the full testList:

testList /. {{(z_)?NumberQ, x:{{_Real, _Real}...}} -> x}


On the other hand, this one returns only the lists of ordered pairs:

testList /. {{(z_)?NumberQ, x:{{_, _}...}} -> x}

I thought that one was free to "type" the parts of the pattern to
return. I also thought that naming the parts rather freely was allowed.
The first three of the following return what I would expect, but the
last one, in naming the first of the ordered pairs' elements, returns
the testList apparently unchanged:

In[54]:=

testList /. {{z_, {x:{_, _}...}} -> z}

testList /. {{z_, {x:{_, _}...}} -> x}

testList /. {{z_, x:{{_, _}...}} -> x}

testList /. {{z_, {x:{a_, _}...}} -> x}

Out[54]=

{-90, -88, -86}

Out[55]=

{{60493, 0.061}, {62493, 0.15881}, {64493.5, 0.559}, {62493, 0.151}, {64493., 0.61617}, 

  {65993.4, 0.171}, {68993.1, 0.06}, {62493.75, 0.14}, {64493.55, 0.6144}, {65993., 0.18}, 

  {67993, 0.}, {68993.1, 0.06448}}

Out[56]=

{{{60493, 0.061}, {62493, 0.15881}, {64493.5, 0.559}}, {{62493, 0.151}, {64493., 0.61617}, 

   {65993.4, 0.171}, {68993.1, 0.06}}, {{62493.75, 0.14}, {64493.55, 0.6144}, {65993., 0.18}, 

   {67993, 0.}, {68993.1, 0.06448}}}

Out[57]=

{{-90, {{60493, 0.061}, {62493, 0.15881}, {64493.5, 0.559}}}, 

  {-88, {{62493, 0.151}, {64493., 0.61617}, {65993.4, 0.171}, {68993.1, 0.06}}}, 

  {-86, {{62493.75, 0.14}, {64493.55, 0.6144}, {65993., 0.18}, {67993, 0.}, 

    {68993.1, 0.06448}}}}


    Although a solution would help me a lot, I really would like to know
what I'm missing in applying these replacement rules.

                Thanks!
                        Curtis O.
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