Consider :
dist = Parallelize[
Table[RandomVariate[NormalDistribution[]], {100000}]];
How could I create a recursive function such that :
Subscript[d, 1] = dist[[1]]
Subscript[d, 2] = .95 Subscript[d, 1] + dist[[2]]
Subscript[d, 3] = .95 Subscript[d, 2] + dist[[3]]
And do this till Subscript[d, 100000]
Thank You.
It is surprisingly the first time I run into this.
Consider this:
dist = RandomVariate[NormalDistribution[], {100000}];
dist2 = Rest@FoldList[0.95 # + #2 &, 0, dist];
Subscript[d, x_] := dist2[[x]]
I don't normally use Subscript this way; I don't know what may break doing this. If you describe more of your problem, I may have an alternate suggestion.
d[x_] or func[d, x_] rather than attaching a definition to Subscript.
(Parallel)Table.RandomVariate? This is not in version 7. In version 8, is it faster than RandomReal?How about using something like
In[1]:= dist = ParallelTable[RandomVariate[NormalDistribution[]], {100000}];//Timing
Out[1]= {0.15601, Null}
In[2]:= folded = FoldList[.95 #1 + #2 &, First@dist, Rest@dist]; // Timing
Out[2]= {0.056003, Null}
which you can compare to
In[3]:= Subscript[d, 1] = dist[[1]];
Do[Subscript[d, n] = 0.95 Subscript[d, n - 1] + dist[[n]],
{n, 2, Length@dist}] // Timing
Out[3]= {1.09607, Null}
In[4]:= Table[Subscript[d, n], {n, 1, Length@dist}] === folded
Out[4]= True
Do loop I give does implement something like what the OP originally had in mind. (If it wasn't early Sunday morning, then I might have been quicker and beaten you!)
dist[[i]]be0.05*dist[[i]]? (If not, I'm curious as to the application for this.)