# Listplot imaginary part of complex numbers

I have the following list

w={{0.01,99 +0.00001414 I},{0.15,6.6370108 +0.003144129 I},{0.25,3.9515722 +0.00854493297 I},{6,0.10041 +0.28132187 I}}


and I want to ListPlot the imaginary part but with the command Im[w] I get the list

{{0,0.00001414},{0,0.00314413},{0,0.00854493},{0,0.281322}}


This way I basically lose the x axis values 0.01, 0.15, 0.25 and 6. How can I get in a list the imaginary part and the x axis values? (With Re[w] I can get the real part right, the 0.01, 0.15 etc don't change)

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ListPlot[Im[Flatten@w]] Given the range you may wish to use ListLogPlot – ubpdqn Aug 31 '14 at 11:21
@ubpdqn Thanks but I need a function to give me this: {{0.01,0.00001414},{0.15,0.00314413},{0.25,0.00854493},{6,0.281322}} not {0,0.00001414,0,0.00314413,0,0.00854493,0,0.281322}. – epl Aug 31 '14 at 11:31
@EvPi apologies I misread your data...ListPlot[{#1, Im@#2} & @@@ w] Same comment wrt log – ubpdqn Aug 31 '14 at 11:34

Almost a dozen alternatives with timings:

ClearAll[f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11];
f1[w_] := w /. {a_, Complex[_, b_]} :> {a, b};
f2[w_] := {#, Im@#2} & @@@ w; (* my favorite ... credit: ubpdqn *)
f3[w_] := w /. Complex[_, b_] :> b;
f4[w_] := MapAt[Im, w, {{All, -1}}];
f5[w_] := Module[{s = Im /@ w}, s[[All, 1]] = w[[All, 1]]; s];
f6[w_] := Module[{s = w}, s[[All, -1]] = Im /@ w[[All, -1]]; s];
f7[w_] := Transpose@{First /@ w, Im /@ Last /@ w};
f8[w_] := Transpose@{w[[All, 1]], Im /@ w[[All, -1]]};
f9[w_] := Through@{First, Composition[Im, Last]}@# & /@ w;
f10[w_] := Transpose@{First /@ w, Composition[Im, Last] /@ w};
f11[w_] := Replace[w, {x_, complex_} :> {x, Im@complex}, {1}];

f1@w
(* {{0.01, 0.00001414},{0.15, 0.003144129},{0.25, 0.00854493297},{6, 0.28132187}}*)

functions = {f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11};
results = (Through@functions@w);
Equal @@ results
(* True *)


Timings:

testdata1 = Transpose[{RandomReal[100, 10000], RandomComplex[100, 10000]}];
testdata2 = Transpose[{RandomReal[100, 100000], RandomComplex[100, 100000]}];
testdata3 = Transpose[{RandomReal[100, 1000000], RandomComplex[100, 1000000]}];


Using Mr.Wizard's timeAvg function:

SetAttributes[timeAvg, HoldFirst]
timeAvg[func_]:= Do[If[#>0.3, Return[#/5^i]] &@@ AbsoluteTiming@Do[func,{5^i}], {i, 0, 15}]

TableForm[{#, timeAvg[#@testdata1;]} & /@ functions]


results = Through@functions@testdata1;
Equal @@ results
(* True *)

TableForm[{#, timeAvg[#@testdata2;]} & /@ functions]


results = Through@functions@testdata2;
Equal @@ results
(* True *)

TableForm[{#, timeAvg[#@testdata3;]} & /@ functions]


results = Through@functions@testdata3;
Equal @@ results
(* True *)

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thanks for wonderful exploration...I've never been good at efficient...and like terse...a great illustration of variety of approaches and terse!= efficient... – ubpdqn Sep 1 '14 at 0:18
w =
{
{0.01, 99 + 0.00001414 I},
{0.15, 6.6370108 + 0.003144129 I},
{0.25, 3.9515722 + 0.00854493297 I},
{6, 0.10041 + 0.28132187 I}
};

res = Replace[w, {x_, complex_} :> {x, Im @ complex}, {1}]

{{0.01, 0.00001414}, {0.15, 0.00314413}, {0.25, 0.00854493}, {6, 0.281322}}

ListLogPlot[res, PlotTheme -> "Detailed"]


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+1 neat and like the plot theme – ubpdqn Aug 31 '14 at 11:52
I would use Replace instead of ReplaceAll, and also using Complex is brittle; what if the list contains complex numbers of the form r Exp[I theta]? – Teake Nutma Aug 31 '14 at 17:30
@TeakeNutma Why don't you publish an optimized answer? I would be the first to upvote. I tried Replace` but to no avail :) – eldo Aug 31 '14 at 17:49
If I would post an answer it'd be @ubpdqn's, so I won't :). If you want, I could update your answer with my suggestions. – Teake Nutma Aug 31 '14 at 18:06
@TeakeNutma Yes, please update. – eldo Aug 31 '14 at 18:22