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

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

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

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