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I have this Manipulate:

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

Sin[a x]

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.

Mathematica graphics

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.

Mathematica graphics

Mathematica graphics

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?

share|improve this question
@seismatica For a simple Manipulate like this one I find your approach rather clever. – eldo Jun 25 '14 at 12:50
up vote 2 down vote accepted

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).

enter image description here

Change a:

enter image description here

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

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

enter image description here

Animated GIF with the complete process: enter image description here

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.

share|improve this answer
Could you help me understand what {{a,startingA},0,2} is supposed to me? Is this the same thing as initializing a with startingA. I've never seen a range written like this before. – seismatica Jun 26 '14 at 2:20
@seismatica It says Manipulate[] to change a between 0 and 2 starting at startingA. With initializing it first to zero, to first startpoint for a is zero. With startingA=a; in Manipulate[] you're saving your current a to startingA in every step. (And startingA is stored outside Manipulate[].) So next time you evaluate Manipulate[] again, startingA has still the "old value of a" and will start at this point with changing a. ... I may should edit this in my answer. – Phab Jun 26 '14 at 6:39
Thank you so much for your explanation and effort to clarify your answer. This fix is working well for me. BTW how did you make that gif? – seismatica Jun 26 '14 at 17:36
@seismatica Making animated GIFs is easy using LICEcap (link). – Phab Jun 27 '14 at 6:50
you rock! ugh 15 char! – seismatica Jun 27 '14 at 7:27

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