# Constructing a table from a constraint on another table

I have a 1000X6 table, where in each row the first three columns are dependent on the second three. I then make smaller tables of 1000X2 from these first three columns and basically ListPlot the τ s. Here's the code:

FullTab1 = Table[{Subscript[τ, extra], Subscript[τ, mix1],
Subscript[τ, mix2], u, Subscript[ϕ, 1], Subscript[ϕ, 2]}
/. {Subscript[ϕ, 2] -> Subscript[ϕ, 1] - u^2/(8 Subscript[ϕ, 1]^2)}
/. {Subscript[ϕ, 1] -> (RandomReal[{0.5, 1}])*Exp[I*RandomReal[{0, 2*Pi}]],
u -> (RandomReal[{0.001, .1}])*Exp[I*RandomReal[{0, 2*Pi}]]}, {i, 1, 1000}]

Smtabext = Table[{Re[FullTab1[[i, 1]]], Im[FullTab1[[i, 1]]]}, {i, 1, 1000}]
Smtabmix1 = Table[{Re[FullTab1[[i, 2]]], Im[FullTab1[[i, 2]]]}, {i, 1, 1000}]
Smtabmix2 = Table[{Re[FullTab1[[i, 3]]], Im[FullTab1[[i, 3]]]}, {i, 1, 1000}]

ListPlot[Smtabext]
ListPlot[Smtabmix1]
ListPlot[Smtabmix2]


So here's the question. The values of the first column of FullTab1, i.e. Subscript[τ, extra] , should all have imaginary part equal to 1, but not all of them do. I'm only interested in the rows that do satisfy the Im[#1]=1 condition. I would like to make my 'Smtab' s only consistent of these rows. Any insight on how this could be done?

I have tried If, For, Select, Do, and a few other commands but I'm not sure if I'm using them right. Any help would be appreciated.

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• As written the first column of FullTab1 contains only the symbol, Subscript[\[Tau], extra], and no complex numbers, because no values have been assigned to Subscript[\[Tau], extra]. – bbgodfrey Feb 26 '15 at 0:34
• the [Tau] 's are complicated functions based on [Phi]s and u. and they give numerical values. – AM_ Feb 26 '15 at 0:36

SeedRandom[0]
FullTab1 = RandomComplex[{0 I + 0, 2 I + 2}, {20, 3}];  (* example data *)

sel = Select[FullTab1, Im[First[#]] > 0.9 &];
lgt = Length @ sel;

{ext, mx1, mx2} = Transpose[{Re@sel, Im@sel}, {3, 2, 1}];

ListPlot[ext]
ListPlot[mx1]
ListPlot[mx2]


I found my desired answer. In case anyone needs something similar, I'm posting my code here. If anyone cares to clean it up that would be great because I don't know most shortcut tricks. Here it is:

lgt = Length[Select[FullTab1, Im[First[#]] > 0.9 &][[All, 1]]]

ext = Table[{Re[Select[FullTab1, Im[First[#]] > 0.9 &][[j, 1]]],
Im[Select[FullTab1, Im[First[#]] > 0.9 &][[j, 1]]]}, {j, lgt}]
mx1 = Table[{Re[Select[FullTab1, Im[First[#]] > 0.9 &][[j, 2]]],
Im[Select[FullTab1, Im[First[#]] > 0.9 &][[j, 2]]]}, {j, lgt}]
mx2 = Table[{Re[Select[FullTab1, Im[First[#]] > 0.9 &][[j, 3]]],
Im[Select[FullTab1, Im[First[#]] > 0.9 &][[j, 3]]]}, {j, lgt}]

ListPlot[ext]
ListPlot[mx1]
ListPlot[mx2]


This only plots the 648 out of 1000 entries of FullTab1 , were the imaginary part of First[#1] is 1. (for some reason ==1 was not working, but since I knew the values were either 1 or 0.5, writing >0.9 works for me.)

Good luck!