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

• To: mathgroup at smc.vnet.net
• Subject: [mg96343] Re: Reposted, Reformatted Re: "mapping" functions over lists, again!
• From: dh <dh at metrohm.com>
• Date: Thu, 12 Feb 2009 06:33:56 -0500 (EST)
• References: <gmu8ik\$geb\$1@smc.vnet.net>

```
Hi Paul,

assume you have some function fun of 2 variables (e.g.fun[r_,c]=r+ Im[c]

) then we can map this by:

Map[{#[[1]], fun @@ #} &, shortTestdata, {2}]

hope this helps, Daniel

Paul Ellsmore 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.

>

> 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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