Array of checkboxes in Manipulate

Question

I try to produce an example where I can mark check boxes corresponding to 10 integer variables which can be 1 or 0 and the result should be the total of marked variables.

As an example for three variables I did the following:

Manipulate[n1 + n2 + n3, {n1, {1, 0}}, {n2, {1, 0}}, {n3, {1, 0}}]

Question 1: How can the check boxes be aligned in a row?

Question 2: How can a certain number of check boxes (e.g. 10) be created at once?

Question 3: If I have a more complicated code how can I find out if a check box is marked and then do something depending on it?

Answer 1

With[{n = 10},
 Manipulate[
  Length[x],
  {{x, {}, ""},
   Table[m -> Subscript["n", m], {m, n}],
   ControlType -> CheckboxBar,
   Appearance -> ("Horizontal" -> {Automatic, 5})}]]

Answer 2

We can use Bob Hanlon's answer as the basis for figuring out how to answer your 3rd question.

With[{n = 10},
  Manipulate[Row[{"checked: ", Length[boxes], "  values: ", boxes}],
    {{boxes, {}, ""},
     Table[m -> Subscript["n", m], {m, n}],
     ControlType -> CheckboxBar,
     Appearance -> ("Horizontal" -> {Automatic, 5})}]]

This tells us that boxes is a list of the checked boxes, not sorted, but maintained in the order in which they were checked. There are many way to use this information. I will discuss a couple of them, both depending on the function MapAt.

If you want the same action to applied to all the checked items, a direct application of MapAt will do. The following will highlight any grid item in red when the corresponding checkbox is checked.

With[{n = 10},
  Manipulate[
    Grid[
      TakeDrop[
        MapAt[Style[#, Red] &, items[[All, 2]], {#} & /@ boxes],
        Quotient[n, 2]],
      Dividers -> All],
    {{items, Table[m -> Subscript["n", m], {m, n}]}, None},
    {{boxes, {}, ""}, items,
     ControlType -> CheckboxBar,
     Appearance -> ("Horizontal" -> {Automatic, 5})}]]

A more general way would be create an association of actions. Using such an association requires a little deeper understanding of Mathematica, but isn't too hard. My example is somewhat contrived; it is a grid which shows the power of 2 for those powers indicated by a checked box.

With[{n = 10},
  DynamicModule[{actions},
    actions = AssociationThread[Range[n], Function /@ Table[#^i, {i, n}]];
    Manipulate[
      Grid[
        {{"Powers of 2", SpanFromLeft}} ~ Join ~
          TakeDrop[
            (Composition @@ (MapAt[actions[#], #] & /@ boxes)) @ ConstantArray[2, n],
            Quotient[n, 2]],
        Dividers -> All],
      {{items, Table[m -> "2"^m, {m, n}]}, None},
      {{boxes, {}, ""}, items,
       ControlType -> CheckboxBar,
       Appearance -> ("Horizontal" -> {Automatic, 5})}]]]

Answer 3

Here's an alternative that lets you choose the number of checkboxes with the slider:

g[n_] := TogglerBar[Dynamic[x], Range[n]]
Manipulate[If[x == {2}, x = 100]; Row[{g[n], x}], {n, 1, 10, 1}]

I've added the If to show one way to use the boxes to change things -- in this case, whenever the second button (alone) is pressed, x displays 100, otherwise it just displays a vector of numbers corresponding to the checked boxes.