# How to CartesianIndex array comprehension?

**URL:** <https://discourse.julialang.org/t/how-to-cartesianindex-array-comprehension/53308>\
**Category:** New to Julia\
**Tags:** question\
**Created:** [January 13, 2021, 10:14pm UTC](https://discourse.julialang.org/t/how-to-cartesianindex-array-comprehension/53308 "2021-01-13T22:14:39Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![Impressium](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/impressium/32/19575_2.png) [@Impressium](https://discourse.julialang.org/u/Impressium)\
**Post date:** [January 13, 2021, 10:14pm UTC](https://discourse.julialang.org/t/how-to-cartesianindex-array-comprehension/53308/1 "2021-01-13T22:14:39Z")

</div>

Hey community 😃

```julia
julia> CartesianIndex(1,1) .+ [CartesianIndex(i,i) for i in 1:10]      
ERROR: iteration is deliberately unsupported for CartesianIndex. Use `I` rather than `I...`, or use `Tuple(I)...`
Stacktrace:
 [1] error(::String) at .\error.jl:33
 [2] iterate(::CartesianIndex{2}) at .\multidimensional.jl:164
 [3] copyto!(::Array{Int64,1}, ::CartesianIndex{2}) at .\abstractarray.jl:721
 [4] _collect(::UnitRange{Int64}, ::CartesianIndex{2}, ::Base.HasEltype, ::Base.HasLength) at .\array.jl:609
 [5] collect(::CartesianIndex{2}) at .\array.jl:603
 [6] broadcastable(::CartesianIndex{2}) at .\broadcast.jl:665
 [7] broadcasted(::Function, ::CartesianIndex{2}, ::Array{CartesianIndex{2},1}) at .\broadcast.jl:1235
 [8] top-level scope at REPL[5]:1

```

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<div class="post-metadata">

**Author:** ![tim.holy](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tim.holy/32/52_2.png) [@tim.holy](https://discourse.julialang.org/u/tim.holy)\
**Post date:** [January 13, 2021, 10:27pm UTC](https://discourse.julialang.org/t/how-to-cartesianindex-array-comprehension/53308/2 "2021-01-13T22:27:21Z")

</div>

`(CartesianIndex(1,1),) .+ [CartesianIndex(i,i) for i in 1:10]`

Wrapping it in a tuple indicates the first argument is to be broadcast. This is arguably a case where defensive programming gets in the way. If we were confident that no one would try to broadcast over the “elements” of a `CartesianIndex` we could make what you tried work.

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<div class="post-metadata">

**Author:** ![BLI](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bli/32/37206_2.png) [@BLI](https://discourse.julialang.org/u/BLI)\
**Post date:** [January 13, 2021, 10:37pm UTC](https://discourse.julialang.org/t/how-to-cartesianindex-array-comprehension/53308/3 "2021-01-13T22:37:05Z")

</div>

> [@Impressium](#):
>
> `CartesianIndex(1,1) .+ [CartesianIndex(i,i) for i in 1:10] `

Why not replace it with:

```julia
[CartesianIndex(1,1) + CartesianIndex(i,i) for i in 1:10]

```

E.g.,

```julia
julia> v = reshape(1:121,11,11)
11×11 reshape(::UnitRange{Int64}, 11, 11) with eltype Int64:
  1 12 23 34 45 56 67 78 89 100 111
  2 13 24 35 46 57 68 79 90 101 112
  3 14 25 36 47 58 69 80 91 102 113
  4 15 26 37 48 59 70 81 92 103 114
  5 16 27 38 49 60 71 82 93 104 115
  6 17 28 39 50 61 72 83 94 105 116
  7 18 29 40 51 62 73 84 95 106 117
  8 19 30 41 52 63 74 85 96 107 118
  9 20 31 42 53 64 75 86 97 108 119
 10 21 32 43 54 65 76 87 98 109 120
 11 22 33 44 55 66 77 88 99 110 121

julia> v[[CartesianIndex(1,1)+CartesianIndex(i,i) for i in 1:10]]
10-element Array{Int64,1}:
  13
  25
  37
  49
  61
  73
  85
  97
 109
 121

```

…if that is what you want.

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<div class="post-metadata">

**Author:** ![Impressium](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/impressium/32/19575_2.png) [@Impressium](https://discourse.julialang.org/u/Impressium)\
**Post date:** [January 13, 2021, 10:39pm UTC](https://discourse.julialang.org/t/how-to-cartesianindex-array-comprehension/53308/4 "2021-01-13T22:39:21Z")

</div>

Oh I understand. It’s not clear what to do…

```julia
julia> [each for each in CartesianIndex(1,1)]
ERROR: iteration is deliberately unsupported for CartesianIndex. Use `I` rather than `I...`, or use `Tuple(I)...`
Stacktrace:
 [1] error(::String) at .\error.jl:33
 [2] iterate(::CartesianIndex{2}) at .\multidimensional.jl:164
 [3] iterate at .\generator.jl:44 [inlined]
 [4] collect(::Base.Generator{CartesianIndex{2},typeof(identity)}) at .\array.jl:665
 [5] top-level scope at REPL[13]:1

julia> iterate(CartesianIndex(1,1))
ERROR: iteration is deliberately unsupported for CartesianIndex. Use `I` rather than `I...`, or use `Tuple(I)...`
Stacktrace:
 [1] error(::String) at .\error.jl:33
 [2] iterate(::CartesianIndex{2}) at .\multidimensional.jl:164
 [3] top-level scope at REPL[14]:1

julia> for each in CartesianIndex(1,1) println(each) end
ERROR: iteration is deliberately unsupported for CartesianIndex. Use `I` rather than `I...`, or use `Tuple(I)...`
Stacktrace:
 [1] error(::String) at .\error.jl:33
 [2] iterate(::CartesianIndex{2}) at .\multidimensional.jl:164
 [3] top-level scope at .\REPL[15]:1

```

---

<div class="post-metadata">

**Author:** ![tim.holy](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tim.holy/32/52_2.png) [@tim.holy](https://discourse.julialang.org/u/tim.holy)\
**Post date:** [January 13, 2021, 10:45pm UTC](https://discourse.julialang.org/t/how-to-cartesianindex-array-comprehension/53308/5 "2021-01-13T22:45:16Z")

</div>

Right. The bottom line is we want people to use `CartesianIndex` like a scalar; `A[3, 4]` should be identical in every respect with `A[CartesianIndex(3, 4)]`. That imposes certain rules with respect to broadcasting, including the fact that you can’t iterate over `(3, 4)` as if it’s a list. But what we don’t (yet) do is _trust_ that people won’t try to iterate over those entries, so we look for that and try to throw a helpful error. However, in your case, that attempt to be helpful actually got in the way of the perfectly well-justified idea you had in the beginning.