How to force Manipulate to use preserve control settings over successive evaluations

Question

I have this Manipulate:

Manipulate[Plot[Sin[a x], {x, 0, 2 Pi}], {a, 0, 3}]

Now, I realize I had mistyped the expression and it's actually x^2 instead. I go back and fix it, but when I evaluate the cell again, the value of a reverts to default/zero.

I've tried multiple things from various Q&A: adding SaveDefinitions -> True, saving parameter to a global variable within the Manipulate block, using bookmarks, but none of them achieved the effect of having the Manipulate start up with a previously-set control value.

Interesting, I find that saving the parameter to a global variable, and then initialize the parameter with the same global variable solves the problem, i.e., Manipulate can remember the manipulated parameter from a previous run. If I add the option SaveDefinitions -> True, the value is also saved between sessions.

Below is an example: a remains at the same value even when the expression in Manipulate was changed and the cell was evaluated.

I went to the chat room to ask people if doing this is OK. I was told that I should not do this. What kind of potential issues would I have with this method? And if it's bad, is there another method to achieve the same result, i.e., preventing Manipulate from resetting control values after each evaluation?

Answer 1

Why don't you use a lokal variable?

Define a local variable first, then do your plot:

In[1]:= startingA = 0;

In[2]:= Manipulate[
           startingA = a;
           Plot[Sin[a x^2], {x, 0, 2 Pi}]
           , {{a, startingA}, 0, 3}]

(Note: The vaiable has NOT to be in the same evaluation cell as Manipulate[]!)

The first time a starts at the defined value zero (it could be any number inside the given range).

Change a:

Now you can change the function in the Plot and eveluate Manipulate[] again. a start at your last a/startingA:

Manipulate[
 startingA = a;
 Plot[Sin[a x], {x, 0, 2 Pi}]
 , {{a, startingA}, 0, 3}]

Animated GIF with the complete process:

Giving the Range in Manipulate as

{{a, startingA}, 0, 3}

says Manipulate should change the value "a" in the range between 0 and 3 with the starting value "startingA". One could give the range also as

{{a, startingA}, 0, 3, 1}

In this case "1" defines the stepsize.