Manipulate: Display Slider Value in Custom Format

Question

I am plotting two functions using 'Manipulate' and I am trying to change the way the values of certain adjustable parameters are being displayed. Here is a photo of the plot so I can refer to the exact variable names: Briefly put, the plot will depend on two variables and when I display their value, I would like to display the slider value times some number (because I need it in multiples of a certain quantity).

Specifically in connection to the photo: you can see how the E_G variable (named 'g' in the Manipulate sequence) is very small ... here I would like it to be displayed in multiples of a constant kk (already defined, as you can see) times the current value of the t-variable.

The specific case aside, I guess there is a general way to manipulate the way a slider variable is displayed, I just have not found anything yet. I would really appreciate your help with that!

Answer 1

The easiest way is probably to simply rescale the slider limits and variable: Let's say you want to control x between 0 and 2, but show 10*x. You would do the following:

Manipulate[
 Row@{"Value of x: ", x10/10},
 {{x10, 1, "10·x"}, 0, 10}
 ]

The above approach effectively delegates the transformation of the variable to the user: Every time you want to use x, you have to write x10/10. If you want a more user friendly (but more complicated internally) solution, you can take advantage of custom Manipulate controls and the second argument of Dynamic

First, we define a custom slider function:

iTransformedSlider[func_][Dynamic@var_, lims_ : {0, 1}] :=
 Manipulator[
  Dynamic[func@var, (var = InverseFunction[func][#]) &],
  func /@ lims
  ]
transformedSlider[func_] := iTransformedSlider[func][##] &

The iTransformedSlider trick is necessary since Manipulate only accepts expressions with explicit head Function. As for how it works: We construct a Manipulator using the arguments passed to us (var and lims), but the apply the transformation function func where appropriate. This means: Scaling the displayed value and the limits using func, and applying the inverse of func when setting var. We can then use it simply as:

Manipulate[
 Row@{"Value of x: ", x},
 {{x, 1, "10·x"}, 0, 1, transformedSlider[10 # &]}
 ]