Skip to main content

Differentiation inside package




I am trying to put all my functions in a single package and some of them do not work because of differentiation. Suppose I have the following package


BeginPackage["Diff`"] 
Diff[yy_]:=Module[{cc},cc=D[yy,x[1]];cc];
End[]
EndPackage[]

And suppose I do the following


<Diff[x[1]^2]


I expect to get 2x[1], but I get 0, what is going on? Probably I am missing something very simple. And yes I need variables in the form x[1],x[2],..., not x,y,z. Interestingly everything works perfectly fine if I do it without packaging:


Diff[yy_]:=Module[{cc},cc=D[yy,x[1]];cc];
Diff[x[1]^2]

The last operation gives 2x[1].



Answer



If you define Diff in a private context, like


BeginPackage["Diff`"]
Diff::usage = ""
Begin["`Private`"]

Diff[yy_] := Module[{cc}, cc = D[yy, x[1]]; cc];
End[]
EndPackage[]

then you will get


<< Diff`

Diff[x[1]^2]
(* 0 *)


That's because the x referred to in the package is in the Diff`Private` context:


Definition@Diff // InputForm
(* Diff[Diff`Private`yy_] := Module[{Diff`Private`cc},
Diff`Private`cc = D[Diff`Private`yy, Diff`Private`x[1]]; Diff`Private`cc] *)

and so it's not the same x that you are calling Diff with, which is in the Global context:


Context[x]
(* "Global`" *)

To solve this, you can declare the x in your package to be in the Diff` context like so:



BeginPackage["Diff`"]
Diff::usage = ""
x::usage = ""
Begin["`Private`"]
Diff[yy_] := Module[{cc}, cc = D[yy, x[1]]; cc];
End[]
EndPackage[]

Since Diff` is put on the $ContextPath by EndPackage, when you refer to x after loading the package, it is translated to Diff`x, which matches the definition in the package (Make sure you restart the kernel first, if you're following along):


<< Diff`


Diff[x[1]^2]
(* 2 x[1] *)

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...

plotting - Magnifying Glass on a Plot

Although there is a trick in TEX magnifying glass but I want to know is there any function to magnifying glass on a plot with Mathematica ? For example for a function as Sin[x] and at x=Pi/6 Below, this is just a picture desired from the cited site. the image got huge unfortunately I don't know how can I change the size of an image here! Answer Insetting a magnified part of the original Plot A) by adding a new Plot of the specified range xPos = Pi/6; range = 0.2; f = Sin; xyMinMax = {{xPos - range, xPos + range}, {f[xPos] - range*GoldenRatio^-1, f[xPos] + range*GoldenRatio^-1}}; Plot[f[x], {x, 0, 5}, Epilog -> {Transparent, EdgeForm[Thick], Rectangle[Sequence @@ Transpose[xyMinMax]], Inset[Plot[f[x], {x, xPos - range, xPos + range}, Frame -> True, Axes -> False, PlotRange -> xyMinMax, ImageSize -> 270], {4., 0.5}]}, ImageSize -> 700] B) by adding a new Plot within a Circle mf = RegionMember[Disk[{xPos, f[xPos]}, {range, range/GoldenRatio}]] Show...