Question

I have the following Nested table

 (myinputmatrix = Table[Nest[function, myinputmatrix[[i]][[j]], 
 myinputmatrix[[i]][[j]][[2]][[2]] + 
  myinputmatrix[[i]][[j]][[3]][[2]]], {i, 
 Dimensions[myinputmatrix][[1]]}, {j, 
 Dimensions[myinputmatrix][[2]]}]) // TableForm

fq[k_?NumericQ] := Count[RandomReal[{0, 1}, k], x_ /; x < .1]

 function[x_List] :=  ReplacePart[
 x, {{2, 1} -> x[[2]][[1]] - #1, 

{2, 2} -> x[[2]][[2]] + #1,

{3, 1} -> x[[3]][[1]] - #2, {3, 2} -> 
   x[[3]][[2]] + #2}] &[fq[x[[2]][[1]]], fq[x[[2]][[1]]]];

My problem is that I want to add only the #1 in the bold part above, but not only the new one, I want it to add all #1 for the n times (Nest function times]

If I try the function

 function[x_List] :=  ReplacePart[
 x, {{2, 1} -> x[[2]][[1]] - #1, {2, 2} ->   #1,
  {3, 1} -> x[[3]][[1]] - #2, {3, 2} ->  #2}] &[fq[x[[2]][[1]]],
 fq[x[[2]][[1]]]];

I am having as a result the last value of fq[k]. I thought of replacing that part in my table with 0 but is not going to work since I am using it in my nested list, also I thought of substricting that part from my initial table but I am not sure which way is the best to do it and if the way I am thinking is the correct one. Can anyone help me?

Answer 1

If I may restate the problem and hopefully clarify the question for myself. At each iteration in the Nest, you want to add not the current (random) output from fq, but the cumulation of the current and all past values of it. But because the random output depends at each iteration on the input matrix, you need to calculate both the random number and the current value of the matrix in the same iteration.
If that hadn’t been true you could use Fold.

Restating fq as Sasha suggested EDIT with some type checking to avoid problems with incorrect input:

fq[k_Integer?Positive]:=RandomVariate[BinomialDistribution[k,.1]]

You might want to add some other error checking code. Something like this, depending on your requirements, might do.

fq[0]:= 0;
fq[k_Real?Positive]:=RandomVariate[BinomialDistribution[Round[k],.1]]

You need function to take the random numbers as parameters. EDIT 1 and 2 I have changed the syntax of this function to use the parameters explicitly instead of the original question’s anonymous function within a function. This should avoid some syntax errors. Also note that I have used “NumericQ” rather than “Real” as the type for the rv1 and rv2 parameters, because they can be integers at the start of the Nest iteration.

function[x_List, rv1_?NumericQ, rv2_?NumericQ] :=  ReplacePart[
 x, {{2, 1} -> x[[2]][[1]] - rv1, {2, 2} ->   rv1,
 {3, 1} -> x[[3]][[1]] - rv2, {3, 2} ->  rv2}]

And then pass the current random number as a local constant using With to a Nest function that works on a list containing your matrix and the cumulation of the random variates. I have used myoutputmatrix because I really don’t like the idea of rewriting existing expressions all the time. That’s just me. Now, the one other thing is that you need to set n, the number of iterates. I’ve set it to 5 but you can make this a parameter in a function if you want (see below).

(myoutputmatrix = Table[ First[Nest[With[{rv=fq[#1[[1]][[2]][[1]] ]}, 
{function[#1[[1]],rv, rv+#1[[2]] ],rv+#1[[2]] }]&, 
 { myinputmatrix[[i]][[j]], 0 }, 5]],
 {i,  Dimensions[myinputmatrix][[1]]}, {j, 
 Dimensions[myinputmatrix][[2]]}]) // TableForm

The First is there because in the end you only want the matrix, not the cumulation of the random variates.

outputmatrix[input_List, n_Integer?Positive] /; 
  Length[Dimensions[input]] == 4 := 
  Table[First[
   Nest[With[{rv = fq[#1[[1]][[2]][[1]]]}, {function[#1[[1]], rv, 
    rv + #1[[2]]], rv + #1[[2]]}] &, {input[[i]][[j]], 0}, n]],
    {i, Dimensions[input][[1]]}, {j, Dimensions[input][[2]]}]

outputmatrix[myinputmatrix, 10] // TableForm

EDIT I have checked this now and it runs, but note that you can get negative numbers in the output, which is not what you want, I don’t think.