Skip to main content

functions - Strange behaviour of Internal`InheritedBlock


I was going to post an answer for fast way to replace all zeros in the matrix. I was even quite happy because timings were the same order of magnitude as others.


The idea was to overwrite Identity:


Internal`InheritedBlock[{Identity}, Unprotect[Identity]; Identity[0] = 1; 

   Map[Identity, {{2, 0}, {Pi, 9}}, {2}]]


{{2, 1}, {Pi, 9}}


But I've checked that for bigger matrices the result is not even close to the expected one:


Internal`InheritedBlock[{Identity}, Unprotect[Identity]; Identity[0] = 1; 

   m = RandomInteger[1, {100, 2}]; 
   Map[Identity, m, {2}] ~ Shallow ~ {5, 2}]


{{0, 1}, {1, 0}, <<98>>}



It seem it breaks at size of the array of about $90$ positions:


 test = Internal`InheritedBlock[{Identity}, Unprotect[Identity]; Identity[0] = 1;

         Apply[
          Boole[Map[Identity, RandomInteger[1, {##}], {2}] == ConstantArray[1, {##}]
               ]&,                     
          Array[List, {35, 35}],
          {2}]];

Show[MatrixPlot[test, DataReversed -> True, Mesh -> All],

     ContourPlot[x y == 90, {x, 1, 35}, {y, 1, 35}]
     , BaseStyle -> {Thickness@.01, 18}]

enter image description here



I hope I haven't missed anything obvious. Any ideas?



Answer



I think this is related to my own question Block attributes of Equal though the circumstance is different. As already stated in the comments:



I can only speculate, I guess that the compiler sees Identity and assumes it knows how that behaves, not looking for changed definition. – ssch Oct 24 '13 at 21:37



Map auto-compiles, basically applying Compile to your mapped function. Of course, Compile uses its own versions for compilable functions, so whatever top-level definitions you have made won't fire. – Leonid Shifrin Oct 24 '13 at 21:56



Whether it be by auto-compilation or by special optimization for Packed Arrays, one must accept that top-level definitions and attributes may not be used in some cases.


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

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

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