Skip to main content

How can I tally continuous sequences in a list?


I have a stream of data like this:


0001100111100000111111001110000001111111111000000111000111110000...

(I can represent them as a list, like in {0,0,0,1,1,...}, I guess that's easier to work with.)


Now I want to count how many sequences of two "1"s, three "1"s, etc there are (the zeros lengths are not important, they're just separators), to show them in a histogram. I have no problems doing this procedural, but functional programming remains difficult for me. While I don't mind pausing for a cup of coffee (there's 4.8 million data points), I guess in functional programming this will be orders of magnitude faster. How do I do this with functional programming?


Note
"0011100" only counts as a sequence of length 3, the two sub-sequences of length 2 should not be taken into account.



Answer




If your data is in list form (conversion from string will swamp advantage), this should be quite a bit faster (5-50+X than existing answers, timings on the loungbook, so I'd expect 10+X faster for all on W/S):


tOnes = Module[{p = Append[Pick[Range@Length@#, #, 1], 0], sa},
    If[p === {0}, {},
     sa = SparseArray[Subtract[Rest@p, Most@p], Automatic, 1]["AdjacencyLists"];
     Tally[Differences[Prepend[sa, 0]]]]] &;

Comparable in speed, and arguably prettier:


tOnes2 = With[{d = Join[{0}, #, {0}]}, 
    Tally[Differences@DeleteDuplicates@Pick[Accumulate@d, d, 0]]] &;


Comparison:


(* make some data & string/digit equivalents for string/Mr.W solutions *)
data = RandomInteger[{0, 1}, 4000000];
strng = StringJoin[ToString /@ data];
mwdata = FromDigits[data];
ClearSystemCache[]

(* eldo *)
eldotim = 
  First@Timing[

    eldo = Tally@
       Select[StringLength /@ StringSplit[strng, "0"], # > 0 &];];

(* Mr. W *)
mwtim = First@
   Timing[mwr = 
      Tally[Length /@ Split[IntegerDigits@mwdata][[;; ;; 2]]];];

(* 2012rcampion *)
rctim = First@Timing[

    lengths = Cases[Split[data], l : {1, ___} :> Length[l]];
    tally = Tally[lengths];
    ];

(* kguler *)
kgtim = First@
   Timing[tally2 = Tally@StringLength@StringCases[strng, "1" ..];];

(* Me *)
me1tim = First@Timing[me = tOnes@data;];

me2tim = First@Timing[me2 = tOnes2@data;];

Transpose[{{"Mr.W", "eldo", "2012rcampion", "kguler", "Me1", "Me2"},
   {mwtim, eldotim, rctim, kgtim, me1tim, me2tim}}] // TableForm

(* Check *)
me == me2 == tally == eldo == tally2 == mwr

enter image description here


(* True *)



Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]
Post a Comment
Read more