Skip to main content

evaluation - How to return the unevaluated variable names from a list of variables which have been declared


I feel like this should have a simple answer but I haven't found anything that works. The toy example of what I want is as follows:


testx = 1;
testy = 2;
testlist = {testx, testy};


And I'm looking for a function that I could use on testlist (f[testlist]) that will return {testx, testy} in their unevaluated symbols or strings.


I've tried OwnValues, Values, Variables, Information, and various others along with their permutations. My intuition says that some combination of pure functions could do what I want, but I'm still very unsure of how to use most of them.


Edit*


Some context for this problem: I am procedurally defining a function (for example):


func = Sum[ToExpression["a"<>ToString[i]],{i, 1, large_number}]

Separately I generate a list of the variable names which occur in the defintion, like shown above, except in this case it would appear as


varsList = {a1, a2, ... , a}

And I wish to be able to procedurally select the string or undeclared variable symbol from varsList for use in manipulate.



Edit 2*


I'm doing a terrible job asking this question. What I'm attempting to do is use the answer provided here, which allows for manually adjusting parameters within manipulate and then using those manually determined values as starting values for a fit, finally feeding the best-fit values back into the current values for the parameters and allowing for subsequent manual control.


Except in my case, the function must have variable number of parameters. I already procedurally generate my function (as above). But am stuck on how to generate the Sequence of parameters inside manipulate, as well as how to call the symbols for resetting their values to those of the best-fit results. That is the ultimate goal and apparently my previous attempts are not possible.


Final Edit*


I've improved the manipulate functionality shown here to also include procedural generation of a function with variable number of parameters.


To do so required applying Hold to the function and its variables, but this alone was not enough because any attempt to redefine the variables on the LHS of an equation was met with simply trying to define a number as another number. The solution was then to construct the line of code I wanted to run entirely as a string, then Evaluate[ToExpression[[]] it. Code below should run as is, the 4 in testplotfit[] may be changed to any positive integer between 1 and 10 currently, determined by the internal clear command. I truly do wonder why there is no better, or at least more well-known, way to procedurally redefine previously assigned variables.


data = Table[{x, 
8 x^3 - 7 x^2 - 10 x + 1 + RandomReal[{-5, 5}]}, {x, -2, 2, 0.1}];



function[terms_] :=
Sum[ToExpression["a" <> ToString[i]]*x^(i - 1), {i, terms}];
functiontemp[terms_] :=
Sum[ToExpression["b" <> ToString[i]]*x^(i - 1), {i, terms}];

testplotfit[terms_] := DynamicModule[{(*sol, solString*)},
ClearAll[Evaluate[Sequence @@ Table["a" <> ToString[i], {i, 10}]]];
funcString = TextString[function[terms]];
vars =
Thread[Hold@Evaluate[DeleteCases[Variables[function[terms]], x]]];

varsString = ToString[vars[[All, 1]]];
tempvars =
Table[ToExpression["b" <> ToString[i]], {i, Length[vars]}];
solString = ConstantArray["blank", terms];

Manipulate[
If[computeFlag == True,
Evaluate[
sol =
FindFit[data, functiontemp[terms],

Table[{tempvars[[i]], ReleaseHold[vars[[i]]]}, {i,
Length[vars]}], x];
];
Evaluate[
ToExpression[
varsString <> " = " <>(*ToString[solString]*)
ToString[tempvars /. sol]]];
computeFlag = False;
];


Column[
{Dynamic[Button["Compute", computeFlag = True]],
Show[
Plot[#, {x, -2, 2}, PlotStyle -> Black],
ListPlot[data, PlotStyle -> Red],
ImageSize -> 300,
PlotRange -> {{-2.05, 2.05}, All}]}
]

(*;sol*),


{{computeFlag, False}, ControlType -> None},
Evaluate[
Sequence @@
Table[{{i, 1}, -10, 10, Appearance -> "Open"}, {i,
vars[[All, 1]]}]],
LocalizeVariables -> False
] &@function[terms] (*end of Manipulate*)
];


testplotfit[4]

Answer



Why not use 'Hold' ?



testx = 1; testy = 2; testlist = Hold@{testx, testy}
Hold[{testx, testy}]
Thread[%]
{Hold[testx], Hold[testy]}



For the variable names, I would use :




Names["a*"]
{"a1", "a2", "a3", "a4"}



which gives a list of variable names as strings. Those can be turned into variables by



ToExpression



Comments

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...

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...

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-...