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I know, the title may seem complicated. I have this list:

myList = { {1, 0},{2, 3},{4, 1} }

I want to sum all the sublists (element by element) to obtain this list:

sumList = {7,4}

Where the first element is 1+2+4 and the second is 0+3+1. How can i obtain this? In my project i won't know a priori neither the number of sublists nor the number of elements in the sublists. The only thing i know is that all the sublists have the same number of elements.

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2 Answers 2

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$\begingroup$ 
myList = {{1, 0}, {2, 3}, {4, 1}}
Plus @@ myList

Mathematica graphics

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  • 7
    $\begingroup$ Or Total[myList], which is the same thing. $\endgroup$
    – Roman
    Apr 28, 2019 at 18:59
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    $\begingroup$ Using Plus @@ myList unpacks myList, so for large packed arrays, using Total will be much faster. $\endgroup$
    – Carl Woll
    Apr 30, 2019 at 3:45
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An alternative is

Plus @@ # & /@ Transpose@myList

This is twice as slow for small lists like yours. For big lists it is more efficient:

biglist = RandomInteger[{0, 9}, {10000, 2}];

Plus @@ biglist // RepeatedTiming
Plus @@ # & /@ Transpose@biglist // RepeatedTiming

0.0068

0.0013

(Revised) Update

(see edits for history)

For lists containing more than ~14 (n = 2) sublists my method is quicker than Plus@@. However, as @Carl Woll points out, one must consider array unpacking with certain Mathematica functions.

(a good discussion of packed versus unpacked arrays can be found here)

sublistsum1 = 
 Transpose@
 Table[Module[{list, plist, tlist, totlist, ttotlist}, 
 list = RandomInteger[{0, 9}, {x, 2}];
 plist = RepeatedTiming[Plus @@ list][[1]];
 tlist = RepeatedTiming[Plus @@ # & /@ Transpose@list][[1]];
 totlist = RepeatedTiming[Total[list]][[1]];
 ttotlist = RepeatedTiming[Total[#] & /@ Transpose@list][[1]];

 {{x, plist}, {x, tlist}, {x, totlist}, {x, ttotlist}}], 
 {x, 2, 30, 2}
 ];

ListLinePlot[sublistsum1, PlotStyle -> {Red, Blue, Green, Orange}, 
 PlotLegends -> 
  {"Plus@@...", "Plus@@#&/@Transpose@...", 
   "Total...", "Total[#]&/@Transpose@..."}, 
 AxesLabel -> {"Number of sublists\n(of length 2)", "Speed (seconds)"}]

enter image description here

For the Plus-based methods as the sublists get longer the advantage of transposing the data diminishes.

Regardless, Total[..] is the fastest method.

sublistsum2 = 
 Transpose@
  Table[Module[{list, plist, tlist, totlist, ttotlist}, 
   list = RandomInteger[{0, 9}, {10000, x}];
   plist = RepeatedTiming[Plus @@ list][[1]];
   tlist = RepeatedTiming[Plus @@ # & /@ Transpose@list][[1]];
   totlist = RepeatedTiming[Total[list]][[1]];
   ttotlist = RepeatedTiming[Total[#] & /@ Transpose@list][[1]];
   {{x, plist}, {x, tlist}, {x, totlist}, {x, ttotlist}}], 
   {x, 10, 70, 10}];

  ListLinePlot[sublistsum2, PlotStyle -> {Red, Blue, Green, Orange}, 
   PlotLegends -> {"Plus@@...", 
                   "Plus@@#&/@Transpose@...", 
                   "Total...", 
                   "Total[#]&/@Transpose@..."}, 
   AxesLabel -> {"Length of sublists\n\[Times]10000", "Speed (seconds)"}]

enter image description here

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  • $\begingroup$ Very interesting, thank you! I'm new into Mathematica and i'm still trying to figure out the syntax. I will keep your answer for next projects, because i have to manage large amounts of data. $\endgroup$
    – alcor
    Apr 30, 2019 at 10:38
  • $\begingroup$ I'm glad it's useful. Functional manipulation of lists is one of the great joys of Mathematica. $\endgroup$
    – geordie
    Apr 30, 2019 at 12:14
  • $\begingroup$ I believe the y-axis should be labeled Time and not Speed. $\endgroup$
    – quoniam
    Aug 29 at 7:20

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