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

*To*: mathgroup at smc.vnet.net*Subject*: [mg96287] Reposted, Reformatted Re: "mapping" functions over lists, again!*From*: "Paul Ellsmore" <paul.ellsmore at nanion.co.uk>*Date*: Wed, 11 Feb 2009 05:17:28 -0500 (EST)

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. 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. I want to "map" functions across all the lists, to convert the data = pairs to {real, f(real,complex)}. One suggestion was to use a Rule in Cases: Cases[shortTestdata, {r_Real, c_Complex} :> {r, Re[c]}], but when = applied to the data above it Flattens my list structure: In: realpart = Cases[shortTestdata, {r_Real, c_Complex} :> {r, Re[c]}, = 2] Out: {{40., 28.06776}, {43.094, 28.05721}, {46.428, 28.05527}, {50.019, 28.05509}, {53.888, 28.05729}, {58.057, 28.05651}, {40., 7.42169}, = {43.094, 7.408397}, {46.428, 7.403769}, {50.019, 7.401313}, {53.888, 7.400478}, {58.057, 7.39994}, {40., 1685.526}, {43.094, 1694.691}, {46.428, 1698.265}, = {50.019, 1699.761}, {53.888, 1700.523}, {58.057, 1701.162}, {40., 1808.702}, {43.094, 1808.524}, {46.428, 1808.534}, {50.019, 1808.443}, {53.888, 1808.481}, {58.057, 1808.631}} I can ressurect the list structure by checking the length of every list = in the data, and using these lengths in a Partition statement, but I'd = rather not lose the list structure in the first place. Is there a way to do = that? I am sure I could use Map in some way: realpart=Map[fxn, shortTestdata,2] but I have no real idea how to set up fxn to do what I want. I have = tried: In: Map[Cases[#_,{r_Real,c_Complex}->{r,Re[c]}&,shortTestdata,2] but I = get a list of empty lists out: Out:{{},{},{},{}} Another suggestion was to use First[#], Last[#], so: In: realpart=Map[{First[#],Re[Last[#]]}&,shortTestdata,2] but this = takes first and last of the level 2 list: Out: {{{40., 28.06776}, {58.057, 28.05651}}, {{40., 7.42169}, {58.057, 7.39994}}, {{40., 1685.526}, {58.057, 1701.162}}, {{40., 1808.702}, = {58.057, 1808.631}}} If I Map at level 3 I get an error message. Why doesn't this work? = Surely at Level 3, each element is a list of length 2, so First would be the real = and Last would be the complex? My basic problem is that I don't know how to structure a fxn to be = Mapped over my lists, so that it applies different transformations to each = element of my data pairs. So I think the most succinct way of expressing my problem is, what form = does fxn take if I want to Map it across my lists of {real,complex} so that = it returns {fxn1[real],fxn2[complex]} or even {real,fxn[complex]}? Apologies if this is either a trivial question, or a nonsense question. Ultimately, I think I can make Cases and Partition work for me, but I = feel sure there is a more elegant way, if only I understood the Mathematica syntax better. Thanks again, Cheers, Paul. Dr. Paul A. Ellsmore Nanion Limited Oxford Centre for Innovation Mill Street Oxford United Kingdom OX2 0JX Tel: +44 (0) 1865 811175 Fax: +44 (0) 1865 248594

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