How can I use Compile to implement recurrence?

Question

I am trying to make the code for the following recurrence. Here wjoin[[i]] is used for calling values from a data set and a is a parameter.

• How can I perform the following recurrence using Compile?
• How can I store the previous values of gg[i] to calculate gg[i + 1]?

I wrote the following code. But it is not working.

gg[1] = a - wjoin[[1]]
gg[2] = (a)*gg[1] - wjoin[[2]])
gg = Compile[{{r1, _Integer}}, 1/(a)*((1 + a )*gg[r1] - wjoin[[r1]])];
gg[3]

Answer 1

Maybe this way?

getgg = Compile[{{a, _Real}, {w, _Real, 1}},
   Block[{g},
    g = Table[0., {Length[w]}];
    g[[1]] = a - w[[1]];
    g[[2]] = a g[[1]] - w[[2]];
    Do[
     g[[i]] = ((1. + a) g[[i - 1]] - w[[i]])/a,
     {i, 3, Length[w]}
     ];
    g
    ],
   CompilationTarget -> "C"
   ];

And then

a = RandomReal[{0, 1}];
w = RandomReal[{0, 1}, 10000];
gg = getgg[a, w];