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Re: Using Map or Thread over selected parts of nested lists

  • To: mathgroup at smc.vnet.net
  • Subject: [mg95924] Re: Using Map or Thread over selected parts of nested lists
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 29 Jan 2009 06:01:41 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <glpfhn$knq$1@smc.vnet.net>

In article <glpfhn$knq$1 at smc.vnet.net>,
 "Paul Ellsmore" <paul.ellsmore at nanion.co.uk> wrote:

[snip]

> 1)      My GUI allows the user to select some data files to work with. I use
> the code:
> 
> source = SystemDialogInput[FileOpen]
> 
> This returns the full path for each file selected by the user - very
> convenient and user-friendly. My problem is that "source" is returned as a
> string (ie an atom) if one file is selected, but a nested list if multiple
> files are selected. I have similar instances in many parts of my program
> where the user might be working with one list of data or multiple lists, and
> I think the same issue will arise. So I would like to know if there is a way
> of forcing (in this case) "source" to be returned as a nestedlist type, even
> if the length of that list is one?

One possible way is as follows:

In[1]:= source = Flatten[{SystemDialogInput["FileOpen"]}]

Out[1]= {"/Users/jeanmarc/Documents/DCP_1175.JPG"}

In[2]:= source = Flatten[{SystemDialogInput["FileOpen"]}]

Out[2]= {"/Users/jeanmarc/Documents/DCP_1176.JPG", \
"/Users/jeanmarc/Documents/DCP_1178.JPG"}


> 2)      I have data in the format:
> 
> List1={{header,header},{header,header},{header,header},{frequency1,
> complexnumber1},{frequency2, complexnumber2},{frequency3, complexnumber4}.}
> 
> On very many occasions I want to deal with :
> 
> List2={{frequency1, realpart1},{frequency2, realpart2},{frequency3,
> realpart4}.}
> 
> Or some other trivial transform of complexnumbern. I have been through the
> VirtualBook, and Documentation centre, and tried various forms of Map and
> Thread, but I cannot find a way of "mapping" or "threading" a function like
> Re[expr] over one element of part of a list, as in:
>
> List2={{frequency1, Re[complexnumber1]},{frequency2,
> Re[complexnumber2]},{frequency3, Re[complexnumber4]}.}
> 
> If someone could give me a pointer to the correct syntax, I would be very
> grateful.
> 
> At present, I am getting the results I want by using Ifs and Do loops, to
> deconstruct and reconstruct my lists, but I feel that is the wrong way to
> approach things - I want to use Mathematica's strengths, not force it to use
> a C type approach, just because that's what I am comfortable with.
> 
> Any suggestions gratefully received,

Here is a Mathematica way of doing it:

    Cases[list1, {r_Real, c_Complex} :> {r, Re[c]}]

For instance,

In[1]:= list1 = {{header, header}, {header, header}, {header, 
   header}, {RandomReal[], RandomComplex[]}, {RandomReal[], 
   RandomComplex[]}, {RandomReal[], RandomComplex[]}, {RandomReal[], 
   RandomComplex[]}}

Out[1]= {{header, header}, {header, header}, {header, 
  header}, {0.675675, 0.225041+ 0.928453 I}, {0.667356, 
  0.820341+ 0.0827457 I}, {0.171542, 0.619974+ 0.143676 I}, {0.4259, 
  0.346343+ 0.190333 I}}

In[2]:= Cases[list1, {r_Real, c_Complex} :> {r, Re[c]}]

Out[2]= {{0.675675, 0.225041}, {0.667356, 0.820341}, {0.171542, 
  0.619974}, {0.4259, 0.346343}}

Regards,
--Jean-Marc


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