Skip to main content

Performance: Collapsing repeated contiguous rows & cols from a matrix


In this answer I needed to remove contiguous zero-valued cols and rows from a matrix, leaving only two of them in place, no matter what the original number was.


I made up this code:


m = RandomVariate[BinomialDistribution[1, 10^-3], {400, 400}]; 
rule = {h__, {0 ..}, w : {0 ..}, {0 ..}, t__} -> {h, w, w, t};

mClean = Transpose[Transpose[m //. rule] //. rule];
Dimensions@mClean

But it is way too slow.
I'm pretty sure this code can be enhanced. Any better ideas?



Answer



Linked lists - based solution


The real reason for the slowdown seems to be the same as usual for ReplaceRepeated - multiple copying of large arrays. I can offer a solution which would still be rule-based, but uses linked lists to avoid the mentioned slowdown. Here are auxiliary functions:


zeroVectorQ[x_] := VectorQ[x, IntegerQ] && Total[Unitize[x]] == 0;


toLinkedList[l_List] := Fold[ll[#2, #1] &, ll[], Reverse[l]]

ClearAll[rzvecs];
rzvecs[mat_List] :=  rzvecs[ll[First@#, ll[]], Last@#] &@toLinkedList[mat];

rzvecs[accum_, rest : (ll[] | ll[_, ll[_, ll[]]])] := 
   List @@ Flatten[ll[accum, rest], Infinity, ll];

rzvecs[accum_, ll[head_?zeroVectorQ, ll[_?zeroVectorQ, tail : ll[_?zeroVectorQ, Except[ll[]]]]]] :=
   rzvecs[accum, ll[head, tail]];


rzvecs[accum_, ll[head_?zeroVectorQ, ll[_?zeroVectorQ, tail_]]] :=
   rzvecs[ll[ll[accum, head], head], tail];

rzvecs[accum_, ll[head_, tail_]] := rzvecs[ll[accum, head], tail];

Now the main function:


removeZeroVectors[mat_] := Nest[Transpose[rzvecs[#]] &, mat, 2]

Benchmarks



Now the benchmarks:


m = RandomVariate[BinomialDistribution[1, 10^-3], {600, 600}];
(res = removeZeroVectors[m]); // AbsoluteTiming
(res1 = Transpose[Transpose[m //. rule] //. rule]); // AbsoluteTiming
res == res1

(*
    {0.046875, Null}
    {3.715820, Null}
    True

*)

Remarks


I have been promoting the uses of linked lists for some time now. In my opinion, in Mathematica they allow one to stay of the higher level of abstraction while achieving very decent (for the top-level code) performance. They also allow one to avoid many non-obvious performance-tuning tricks which take time to come up with, and even more time to understand for others. The algorithms expressed with linked lists are usually rather straight-forward and can be directly read off from the code.


Comments

Post a Comment

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...
Post a Comment
Read more