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I currently have a two lists. The first list contains independent variables $x$, and the second list contains dependent variables in the form of $\{\{f[1][x]\},\{f[2][x]\},...,\{f[n][x]\}\}$.

I want to combine them in the form $$\{\{\{x1,f[1][x1]\},\{x2,f[1][x2]\},...,\{xn,f[1][xn]\}\},\{\{x1,f[2][x1]\},\{x2,f[2][x2]\},...,\{xn,f[2][xn]\}\},...,\{\{x1,f[n][x1]\},\{x2,f[n][x2]\},...,\{xn,f[n][xn]\}\}\}$$ ...an easy format for ListPlot.

For some example data:

a = Range[10];
b = a^2;
c = (a + 1/2)^2;
fa = {b,c};

Now one can easily do this with Table:

Table[{a[[j]], fa[[i, j]]}, {i, Length[fa]}, {j, Length[c]}]

but knowing Mathematica's many functions I thought there might be an easier way. I tried this as well:

Transpose@MapThread[Tuples@{{#1}, #2} &, {a, Transpose@fa}]

but with the multiple Transpose calls, I figured there would be a slight performance hit. And there was (2.854 vs 3.261 seconds for vectors with 1MM elements on my machine).

Is there an easier and more efficient way to combine these lists?

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So in your notation, f[1][x1] really means f[[1,1]] and not SubValues? –  rm -rf Nov 28 '12 at 20:33
@rm-rf, Nah, it just means f[1] is a data vector that corresponds to the x-values. f[2] is another data vector not related to f[1]. Etc. Feel free to suggest another notation. –  kale Nov 28 '12 at 20:38
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1 Answer 1

up vote 6 down vote accepted
Thread[{a, #}] & /@ fa


Inner[List, a, #, List] & /@ fa
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Yep. I love how I come up with Transpose@MapThread[Tuples@{{#1}, #2} &, {a, Transpose@fa}] but not Thread[{a,#}]&/@fa. Sigh. In any regards, the Thread method is 7.5x faster and the Inner method is 12x faster than the MapThread I suggested. Thanks! –  kale Nov 28 '12 at 23:29
@kale could you say how fast is Array in your setup? –  au700 Nov 29 '12 at 1:26
@au700, You'll have to elaborate. Not sure I see a way to use Array to solve the problem... –  kale Nov 29 '12 at 2:34
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