Create a dynamically updating function

Questions
,
1

I am attempted to create a function with will be dynamically update when I input the initial parameters in the InputField space, but it doesn’t work, I misunderstand something here:

InputField[Dynamic[n]]

Dynamic@If[NumberQ[n],
  
  A = Table[c, {i, 3 n} ];
  
  
  Grid[{Table[With[{i = i}, InputField[Dynamic[A[[i]]]]], {i, 3 n}]}]]

Dynamic@If[NumberQ[n],
   f[t_] := 
    Sum[A[[3 i - 2]] PDF[NormalDistribution[A[[3 i - 1]], A[[3 i]]], 
       t], {i, n}]
   ];

Then I execute f[2] and get nothing. Any ideas?

2

Both SetDelayed and Sum have the attribute HoldAll, also the n in your Sum is localized in the Sum and is not the n that you are changing globally --so you need to get your n into the definition via a Pure function.

I believe that the following works:

Dynamic@If[NumberQ[n], Function[nn,
    f[t_] := 
     Sum[A[[3 i - 2]] PDF[NormalDistribution[A[[3 i - 1]], A[[3 i]]], 
        t], {i, nn}]
    ][n]
  ]
3

What is c?
Assuming you want n and c numeric I cooked up something simple:

DynamicModule[{n = 2, c = 1},
 Column[{
   nin@Dynamic[n],
   
   Dynamic[If[NumberQ[n], A = Table[c, {i, 3 n}];
     Grid[{Table[With[{i = i}, nin[Dynamic[A[[i]]]]], {i, 3 n}]}]],
    
    If[NumberQ[n],
     With[{n = n},
      f[t_] := 
       Sum[A[[3 i - 2]] PDF[
          NormalDistribution[A[[3 i - 1]], A[[3 i]]], t], {i, n}]]]]}],
 Initialization :> (nin = InputField[#, Number, FieldSize -> 2] &)]
4

Thanks for explanation. No i see the problem. I am not sure Sum has attribute Hold: this code seems to work:

Dynamic@If[NumberQ[n],
  
  A = Table[c, {i, 3 n} ];
 
  Grid[{Table[With[{i = i}, InputField[Dynamic[A[[i]]]]], {i, 3 n}]}]]
    
Dynamic@(f = 
   Sum[A[[3 i - 2]] PDF[NormalDistribution[A[[3 i - 1]], A[[3 i]]], 
      t], {i, n}])
    
Dynamic@Plot[f, {t, 0, 10}]

I used c just a sumbol to declare a matrix. Is there a better way?

5

In[1]:= Attributes[Sum]

Out[1]= {HoldAll, Protected, ReadProtected}
6

I am a little confuse: “With” does or does not override the “Hold” attribute? Because this code below doesn’t work:

Clear[f, fn, c, n, t];
InputField[Dynamic[n]]

Dynamic@If[NumberQ[n],
  
  A = Table[c, {i, 3 n} ];
  
      Grid[{Table[ With[{i = i},  InputField[Dynamic[A[[i]]], FieldSize -> Tiny]], {i, 3 n}]}]]
    
Dynamic@If[NumberQ[n], 
   With[{n = n},   fn[t_] :=  Sum[A[[3 i - 2]] PDF[NormalDistribution[A[[3 i - 1]], A[[3 i]]], 
        t], {i, 3 n}]]];

Dynamic@Plot[fn[t], {t, -10, 10}]
7

Why is it that when put semicolon after your code, it doesn’t subsequently execute the Dynamic@Plot[f[t], {t, -10, 10}] command? What is special about the semicolon?

Another problem seems to be that when I use the function:

Dynamic@(If[NumberQ[n],    f[t_]: = Sum[A[[3 i - 2]] PDF[NormalDistribution[A[[3 i - 1]], A[[3 i]]], t], {i, n}]])

the machine is getting close to freezing, while this version:

Dynamic@(If[NumberQ[n],    f = Sum[A[[3 i - 2]] PDF[NormalDistribution[A[[3 i - 1]], A[[3 i]]], t], {i, n}]])

doesn’t do that.
Thanks.