For loop and predefined functions

Question

I tried to write a function which is basically given by a for loop and some predefined functions. I checked already that all of the predefined functions are working, but somehow my for loop does not stop. I was trying to add up these elements ProbNeu1*ProbNeu1 where in every step there is some new element from this function RuTable. Here is my code:

AvProb6[rho_, Nu_, Nstat_, list1_, list2_] := 
  Module[{val, valn, RU1, value}, 
   val = 0;
   For[n = 1, n <= Nstat, n++,
    RU1 = RUTable[Nu];
    valn = ProbNeu1[rho, RU1, list1]*ProbNeu1[rho, RU1, list2];
    val = val + valn;
    ];
   value = (val/Nstat);
    Return[value]
   ];

Is there someone who finds a problem with what I did here?

Answer 1

If I understand what you are doing, you should be able to re-define your function to make use of vector operations, which are more natural in MMA than loops:

ClearAll[AvProb6]
AvProb6[rho_, Nu_, Nstat_, list1_, list2_] :=
 Mean@
  Map[
    ProbNeu1[rho, #, list1] ProbNeu1[rho, #, list2] &,
    Table[RUTable[Nu], Nstat]
  ]

Here:

• Table[RUTable[Nu], Nstat] produces a list of matrices of length Nstat using your RUTable function;
• On each item of that list, it applies ProbNeu1[rho, oneMatrixFormTheList, list1], then ProbNeu1[rho, oneMatrixFormTheList, list2], and takes the product of the two results, forming a new list of these products;
• In your original code, you were accumulating these values then dividing by the length of the list, i.e. taking the arithmetic mean; since we already have the whole list, here we directly calculate the mean value using Mean instead.

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Here are a few reasons why you should consider avoiding the For loop in MMA.