# Tullio with pre-computed index broadcasting

**URL:** https://discourse.julialang.org/t/tullio-with-pre-computed-index-broadcasting/97345
**Category:** General Usage
**Tags:** question, indexing, tullio
**Created:** [April 11, 2023, 1:33pm UTC](https://discourse.julialang.org/t/tullio-with-pre-computed-index-broadcasting/97345 "2023-04-11T13:33:00Z")
**Posts on this page:** 3
**Page:** 1

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### Author: ![ovt](https://avatars.discourse-cdn.com/v4/letter/o/87869e/32.png) [@ovt](https://discourse.julialang.org/u/ovt)
#### Post date: [April 11, 2023, 1:33pm UTC](https://discourse.julialang.org/t/tullio-with-pre-computed-index-broadcasting/97345/1 "2023-04-11T13:33:01Z")

</div>

It’s my first time with Tullio, so my problem may look very basic. Here is a minimal example that provides the error `"expected integers!"` :

```julia
using Tullio

m,r = 5,5
rr = div(r*(r-1),2)
A = rand(m,rr)
B = rand(m,r)
C = similar(B)

jbar = Vector{Vector{Int}}(undef,r)
jtild = Vector{Vector{Int}}(undef,r)
for j in 1:r
    jbar[j] = vcat(1:j-1,j+1:r)
    jtild[j] = vcat([(k-1)*r-div(k*(k+1),2)+j for k in 1:j-1],[(j-1)*r-div(j*(j-1),2)+k for k = 1:(r-j)])
end

@tullio C[i,j] = dot(A[i,jtild[j]],B[i,jbar[j]])

```

I then replaced the `@tullio` line with `@tullio C[i,j] = A[i,jtild[j][k]]*B[i,jbar[j][k]]` but I have the error `UndefVarError: j not defined`.

edit:  
The following code works, but I don’t understand why the previous one wouldn’t.

```julia
using Tullio

m,r = 5,5
rr = div(r*(r-1),2)
A = rand(m,rr)
B = rand(m,r)
C = similar(B)

jbar = Matrix{Int}(undef,r-1,r)
jtild = Matrix{Int}(undef,r-1,r)
for j in 1:r
    jbar[:,j] = vcat(1:j-1,j+1:r)
    jtild[:,j] = vcat([(k-1)*r-div(k*(k+1),2)+j for k in 1:j-1],[(j-1)*r-div(j*(j-1),2)+k for k = 1:(r-j)])
end

@tullio C[i,j] = A[i,jtild[k,j]]*B[i,jbar[k,j]]

```

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<div class="post-metadata">

### Author: ![mcabbott](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mcabbott/32/6603_2.png) [@mcabbott](https://discourse.julialang.org/u/mcabbott)
#### Post date: [April 11, 2023, 1:50pm UTC](https://discourse.julialang.org/t/tullio-with-pre-computed-index-broadcasting/97345/2 "2023-04-11T13:50:52Z")

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The first one indexes A using not a number but an array of numbers, to make an array. Such things sometimes work by accident but aren’t the goal, and will sometimes be very inefficient. In particular, the code trying to check that all indices within `jtild` are in-bounds for `A` fails; it understands arrays if integers but not arrays of arrays.

The second one, with `A[i,jtild[j][k]]`, also fails in the bounds-checking code. But this time because the macro writes a literal `tild[j]` outside of a loop over `j`. It notices the `[k]` but is insufficiently recursive. That’s more clearly a bug, but not sure how easy it’ll be to fix.

The third one with `A[i,jtild[k,j]]` is much easier for Tullio to understand, as it only has arrays of numbers, and only one level of indexing.

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<div class="post-metadata">

### Author: ![ovt](https://avatars.discourse-cdn.com/v4/letter/o/87869e/32.png) [@ovt](https://discourse.julialang.org/u/ovt)
#### Post date: [April 11, 2023, 1:58pm UTC](https://discourse.julialang.org/t/tullio-with-pre-computed-index-broadcasting/97345/3 "2023-04-11T13:58:12Z")

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Thank you !