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plotting - 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)



Answer



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]

enter image description here


results = Through@functions@testdata1;
Equal @@ results

(* True *)

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

enter image description here


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

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


enter image description here


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

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