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

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}]

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1....