Skip to main content

performance tuning - Fast function to do multiple rectangle region checks



Suppose I have a set of "rectangles" and a set of "points":


SeedRandom[5]
rects = RandomReal[10, {5, 2, 2}]
pts = RandomReal[10, {5, 2}]


{{{0.00790584, 0.650192}, {9.89555, 9.68768}}, {{2.00866, 8.19521}, {0.897634, 9.70701}}, {{2.2991, 6.12503}, {0.96816, 5.48855}}, {{1.32548, 2.32332}, {7.76135, 5.50949}}, {{0.586896, 9.60602}, {0.982487, 0.343521}}}


{{8.06562, 4.39186}, {1.42284, 0.27687}, {0.794711, 8.59505}, {2.42136, 8.42835}, {5.54556, 7.21645}}



I want to find out which points are members of their associated rectangles. One slow possibility is to use RegionMember:



MapThread[RegionMember[Rectangle@@#1, #2]&, {rects, pts}]


{True, RegionMember[ Rectangle[{2.00866, 8.19521}, {0.897634, 9.70701}], {1.42284, 0.27687}], RegionMember[ Rectangle[{2.2991, 6.12503}, {0.96816, 5.48855}], {0.794711, 8.59505}], False, RegionMember[ Rectangle[{0.586896, 9.60602}, {0.982487, 0.343521}], {5.54556, 7.21645}]}



This approach doesn't work because RegionMember needs the first Rectangle coordinate to be strictly smaller than the second Rectangle coordinate. It also unpacks the rects variable. I would like a function inRange that returns 1 if the point is in the rectangle, and 0 otherwise, and I want to avoid unpacking. For the above example:


inRange[rects, pts]

should return:


{1, 0, 0, 0, 0}


A compiled solution is acceptable, but I would prefer a version that works for both packed arrays and mixed data types.


An alternate version using vectors only is fine, e.g.:


inRange[x1, y1, x2, y2, x, y]

A 1D version would also be interesting, with intervals instead of rectangles. The simplest approach in that case would be to use IntervalMemberQ, but that would cause unpacking.




Comments

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-...

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...

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...