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Re: Suggestions for translating a Do[] loop ...


David Annetts wrote:
> Hi,
>
> Given that a, b & r are lists of the same length, can anyone suggest a
> translation of the following Do[] loop to something functional?  It looks
> like an ideal application for Fold, but for me, the loop going backwards is
> really obscuring things.
>
> The loop is
>
> 	Do[
>     		r[[j]] = a[[j]] * (b[[j]] + r[[j + 1]]) / (1 + b[[j]] * r[[j
> + 1]]),
>     		{j, Length@a - 1, 1, -1}
>     		];
>
> with r[[Length@a]] = 0.
>
> Many thanks,
>
> Dave.

A "functional" solution :

In[1]:=
a = Table[Random[],{5}];
b = Table[Random[],{5}];
aa[i_] := a[[i]];
bb[i_] := b[[i]];
rr[Length[a]] = 0;
rr[j_] := rr[j] = aa[j] * (bb[j] + rr[j + 1]) /
	(1 + bb[j] * rr[j + 1]);
r = Reverse@Table[rr[j],{j,Length[a],1,-1}]

Out[1]=
{0.147028,0.184133,0.077559,0.519274,0}


hth

v.a.


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