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Re: Reposted, Reformatted Re: "mapping" functions over lists, again!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96337] Re: Reposted, Reformatted Re: "mapping" functions over lists, again!
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 12 Feb 2009 06:32:50 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <gmu8ik$geb$1@smc.vnet.net>

In article <gmu8ik$geb$1 at smc.vnet.net>,
 "Paul Ellsmore" <paul.ellsmore at nanion.co.uk> wrote:

> This is a repost of an earlier post, as there were problems with the email
> formatting for some people. I have composed this one in Notepad, and cut and
> pasted to Outlook. Hope it works better.

You should try to copy and past Mathematica expressions in InputForm[], 
for it is way more readable and far less prone to misinterpretation 
(especially when your email/newsgroup client adds spurious equal sings 
and/or other unwanted characters or character conversions).

To use the _InputForm_ when copying an expression from a Mathematica 
notebook to an email client: select the cell(s) you want to include in 
your email, then within the *Cell* menu select either *Convert To* or 
*Display As* and choose *InputForm*. Finally, copy and paste as usual.
 
> Thanks to all who have already given me some advice, but I still haven't
> quite got it yet!
> 
>  My data is in the form:
> 
> shortTestdata = {{{40., 28.06776 + 1.208548*I}, {43.094, 28.05721 +
> 1.298519*I}, {46.428, 28.05527 + 1.400228*I}, {50.019, 28.05509 +
> 1.508759*I},
>     {53.888, 28.05729 + 1.624517*I}, {58.057, 28.05651 + 1.75026*I}}, {{40.,
> 7.42169 + 0.2198589*I}, {43.094, 7.408397 + 0.2343525*I},
>     {46.428, 7.403769 + 0.2521353*I}, {50.019, 7.401313 + 0.2715986*I},
> {53.888, 7.400478 + 0.2920617*I}, {58.057, 7.39994 + 0.3145005*I}},
>    {{40., 1685.526 + 0.04809976*I}, {43.094, 1694.691 - 0.09133625*I},
> {46.428, 1698.265 - 0.02731824*I}, {50.019, 1699.761 - 0.0491538*I},
>     {53.888, 1700.523 - 0.2179222*I}, {58.057, 1701.162 - 0.2423136*I}},
> {{40., 1808.702 - 0.006286621*I}, {43.094, 1808.524 - 0.1140757*I},
>     {46.428, 1808.534 - 0.02445889*I}, {50.019, 1808.443 - 0.1061664*I},
> {53.888, 1808.481 - 0.1762974*I}, {58.057, 1808.631 - 0.2894506*I}}}
> 
> This is a list of lists, the lowest level lists containing pairs of {real,
> complex}. The individual lists are not all the same length, and the total
> number of lists can vary, and I need to preserve the list structure.

[snip]

I suggest to use the replacement operator "/." (w/o the quotation marks) 
to apply the transformation rule. In doing so, the structure of the 
original list will be preserved. Therfore, rather than Cases[] or Map[], 
you could use

    shortTestdata /. {r_Real, c_Complex} :> {r, Re[c]}

For instance, here is a complete example applied to your data:

In[1]:= shortTestdata = {{{40., 28.06776 + 1.208548*I}, {43.094, 
     28.05721 + 1.298519*I}, {46.428, 28.05527 + 1.400228*I}, {50.019,
      28.05509 + 1.508759*I}, {53.888, 
     28.05729 + 1.624517*I}, {58.057, 28.05651 + 1.75026*I}}, {{40., 
     7.42169 + 0.2198589*I}, {43.094, 
     7.408397 + 0.2343525*I}, {46.428, 
     7.403769 + 0.2521353*I}, {50.019, 
     7.401313 + 0.2715986*I}, {53.888, 
     7.400478 + 0.2920617*I}, {58.057, 7.39994 + 0.3145005*I}}, {{40.,
      1685.526 + 0.04809976*I}, {43.094, 
     1694.691 - 0.09133625*I}, {46.428, 
     1698.265 - 0.02731824*I}, {50.019, 
     1699.761 - 0.0491538*I}, {53.888, 
     1700.523 - 0.2179222*I}, {58.057, 
     1701.162 - 0.2423136*I}}, {{40., 
     1808.702 - 0.006286621*I}, {43.094, 
     1808.524 - 0.1140757*I}, {46.428, 
     1808.534 - 0.02445889*I}, {50.019, 
     1808.443 - 0.1061664*I}, {53.888, 
     1808.481 - 0.1762974*I}, {58.057, 1808.631 - 0.2894506*I}}};

In[2]:= Dimensions[shortTestdata]

Out[2]= {4, 6, 2}

In[3]:= lst = shortTestdata /. {r_Real, c_Complex} :> {r, Re[c]}

Out[3]= {{{40., 28.0678}, {43.094, 28.0572}, {46.428, 
   28.0553}, {50.019, 28.0551}, {53.888, 28.0573}, {58.057, 
   28.0565}}, {{40., 7.42169}, {43.094, 7.4084}, {46.428, 
   7.40377}, {50.019, 7.40131}, {53.888, 7.40048}, {58.057, 
   7.39994}}, {{40., 1685.53}, {43.094, 1694.69}, {46.428, 
   1698.27}, {50.019, 1699.76}, {53.888, 1700.52}, {58.057, 
   1701.16}}, {{40., 1808.7}, {43.094, 1808.52}, {46.428, 
   1808.53}, {50.019, 1808.44}, {53.888, 1808.48}, {58.057, 
   1808.63}}}

In[4]:= Dimensions[lst]

Out[4]= {4, 6, 2}

HTH,
--Jean-Marc


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