Two index-summation loop

New to Julia
1

Hi everyone.

I am trying to program the following summation into Julia:

y_i = c_i + \sum_{r=1}^{i-1} b_r*y_{i-r}

So for example, in the following toy numerical example:

using DataFrames
test = DataFrame(months = 0:3, y = 0
test[!,:y] = convert.(Float64,test[!,:y])
c_test = [0,1,1.1,1.2]
b_test = [0,2,2.1,2.2]

the correct code would spit out the following column-vector (working out can be provided if required):

y' = [0,1,3.1,9.5,29.01]

I tried different ways of using forloops but got nowhere with them. I know the following lines are completely wrong but I don’t know where to even begin to fix it

for i in 2:nrow(test)
    for r in 2:nrow(test)
        test[i,2] = c_test[i,1] + sum(b_test[r,1]*test[i-r,2])
    end
end

Any help would be really appreciated, tysm!

2

I think your “correct result” is wrong

julia> for i in eachindex(y)
           second_term = 0.0
           for r=1:i-1
               second_term += b_test[r] * y[i-r]
           end
           y[i] = c_test[i] + second_term
       end

julia> y
4-element Vector{Float64}:
 0.0
 1.0
 1.1
 3.2
1 Like
3

It seems the expression you want is:
y_i = c_i + \sum_{r=1}^{i-1} b_r*y_{i-r+1}

i.e. y_{i-r+1} instead of y_{i-r} . Implementing that gives the result you expect.

julia> test= DataFrame(months = 0:3, y = 0.0)
4×2 DataFrame
 Row │ months  y       
     │ Int64   Float64 
─────┼─────────────────
   1 │      0      0.0
   2 │      1      0.0
   3 │      2      0.0
   4 │      3      0.0

julia> for i in 1:nrow(test)
         test.y[i] = c_test[i]
         for r in 1:i - 1
           test.y[i] += b_test[r] * test.y[i - r + 1]
         end
       end

julia> test
4×2 DataFrame
 Row │ months  y       
     │ Int64   Float64 
─────┼─────────────────
   1 │      0      0.0
   2 │      1      1.0
   3 │      2      3.1
   4 │      3      9.5
1 Like