Altering values in Manipulate with dynamically generated controls

Question

I have a Manipulate whose controls are generated based on a parameter in a containing Manipulate:

Manipulate[
 With[{f = Table[c[i], {i, n}], 
   controls = Sequence @@ Table[{{c[i], 0}, -1, 1}, {i, n}]}, 
  Manipulate[f, controls, 
   Button["Random", Do[c[i] = RandomReal[{-1, 1}], {i, n}]]]], {n, {3, 4, 5}}]

When I hit the "Random" button, to assign a random set of values to the parameters in the inner manipulate, chaos ensues, e.g.: "Manipulate argument {{-0.975768,0},-1,1} does not have the correct form for a variable specification." If I change the above slightly, for example:

Manipulate[
 With[{f = Table[c[i], {i, n}], 
   controls = Sequence @@ Table[{{c[i], 0}, -1, 1}, {i, n}]}, 
  Manipulate[f, controls, 
   Button["Random", c[1] = RandomReal[{-1, 1}]]]], {n, {3, 4, 5}}]

I don't get similar errors (and c[1] gets randomly assigned a value as expected). I can't wrap my head around what's going on... what's the relevant difference between these two examples? How can I assign to a parameter as in the second example but using a loop as in the first?

Edit: Turns out I also have additional controls beyond the c[i], whose position should be maintained through the randomization of the c[i]. For example, using belisarius' technique resets r here:

Manipulate[
 With[{f = Table[c[i], {i, n}], 
   controls = Sequence @@ Table[{{c[i], s[i]}, -1, 1}, {i, n}]}, 
  Manipulate[Append[f, r], controls, {{r, 0}, -1, 1}, 
   Button["Random", Do[s[i] = RandomReal[{-1, 1}], {i, n}]]]],
    {n, {3, 4, 5}}, Initialization -> {s@_ := 0}]

Assigning directly to e.g. c[1] as in the second example above does what I want:

Manipulate[
 With[{f = Table[c[i], {i, n}], 
   controls = Sequence @@ Table[{{c[i], 0}, -1, 1}, {i, n}]}, 
  Manipulate[Append[f, r], controls, {{r, 0}, -1, 1}, 
   Button["Random", Do[c[1] = RandomReal[{-1, 1}], {i, n}]]]], {n, {3, 4, 5}}]

What's different about assigning directly to c[1] as opposed to assigning to c[i] with i == 1?

Answer 1

You need to randomize the control initial value, not the name of the symbol associated to the control.
Perhaps this is what you want:

Manipulate[
 With[{f = Table[c[i], {i, n}], controls = Sequence @@ Table[{{c[i], s[i]}, -1, 1}, {i, n}]},
  Manipulate[f,
   controls,
   Button["Random", Do[s[i] = RandomReal[{-1, 1}], {i, n}]]]],
 {n, {3, 4, 5}}, Initialization -> {s@_ := 0}]

Answer 2

Here's the solution I ended up going with:

Manipulate[
 With[{f = Table[c[i], {i, n}], 
   controls = Sequence @@ Table[{{c[i], 0}, -1, 1}, {i, n}], 
   randomize = Hold@CompoundExpression @@ 
    Table[Hold[c[i] = RandomReal[{-1, 1}]] /. i -> j, {j, n}]}, 
  Manipulate[Append[f, r], controls, {{r, 0}, -1, 1}, 
   Button["Random", ReleaseHold[randomize]]]], {n, {3, 4, 5}}]

Basically, the c[i] only get replaced by Manipulate with their localized versions if they appear exactly as c[1], c[2], etc., at the time the Manipulate is first evaluated. Later evaluation of c[i] with i == 1 for instance evaluates to the global c[1], not the one local to Manipulate. Thus, the trick is to generate the CompoundExpression that should execute on the button press outside of the Manipulate, with all of the c[1], c[2], etc. already in place, and put it inside the Manipulate using With. The Hold/ReleaseHold ensure that the CompoundExpression and assignments evaluate only at the appropriate time (when the button gets pressed).

Answer 3

Your question puzzled me for a long time. Let us have a look at your first question:

Manipulate[
  With[{f = Table[c[i], {i, n}], controls = Sequence @@ Table[{{c[i], 0}, -1, 1}, {i, n}]}, 
    Manipulate[f, controls, Button["Random", Do[c[i] = RandomReal[{-1, 1}], {i, n}]]]],
 {n, {3, 4, 5}}]

Why does it not work? You have a sliders that assign to c[1], c[2], etc, you have a button that assigns to c[1], c[2], etc, but the combination does not work. As usual with this sort of things, as soon as you understand it, it turns out to be simple. When you evalute the above command, the outer Manipulate will show the inner Manipulate for n=3. So there are controls for c[1], c[2] and c[3]. Also the button must be created. In the second argument there is a c[i], not being one of the control variables. The function Button does not evaluate the second argument, so this expression c[i] will be Global. Therefore, when we use the button, assignments will be done to Global`c[1], Global`c[2] and Global`c[3] instead of the localized control variables.

Hence, to make it work, we have to take care that the symbol c does not turn up in the button. That can be done:

Manipulate[
  With[{f = Table[c[i], {i, n}], controls = Sequence @@ Table[{{c[i], 0}, -1, 1}, {i, n}]}, 
    Manipulate[f, controls, Button["Random", f = RandomReal[{-1, 1}, {n}]]]],
  {n, {3, 4, 5}}]

On posting this answer, I saw that your solution for your extended problem (I did not see you edit before) follows more or less the same lines. I think this is a little bit shorter:

Manipulate[
  With[{f = Table[c[i], {i, n}], controls = Sequence @@ Table[{{c[i], 0}, -1, 1}, {i, n}]}, 
    Manipulate[Append[f, r], controls, {{r, 0}, -1, 1},
      Button["Random", f = andomReal[{-1, 1}, {n}]]]],
  {n, {3, 4, 5}}]