# Designating the axes for broadcasting

**URL:** <https://discourse.julialang.org/t/designating-the-axes-for-broadcasting/29203>\
**Category:** General Usage\
**Tags:** question\
**Created:** [September 26, 2019, 4:32pm UTC](https://discourse.julialang.org/t/designating-the-axes-for-broadcasting/29203 "2019-09-26T16:32:41Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![crinders](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/crinders/32/8434_2.png) [@crinders](https://discourse.julialang.org/u/crinders)\
**Post date:** [September 26, 2019, 4:32pm UTC](https://discourse.julialang.org/t/designating-the-axes-for-broadcasting/29203/1 "2019-09-26T16:32:41Z")

</div>

I can’t find a way to designate the axes over which to broadcast. I looked at broadcast.jl and combine\_axes and I can’t make heads or tails of it.

I just want to do

```julia
julia> T = randn((3,2,4))
3×2×4 Array{Float64,3}:
[:, :, 1] =
 -1.58198 -1.85354 
  3.75281 0.346631
 -1.58355 -1.78938 

[:, :, 2] =
 -0.995975 -0.590384
 -0.702673 1.73817 
 -1.20793 -1.09226 

[:, :, 3] =
 -0.621339 -1.13472 
  0.671315 -0.81942 
 -0.243524 0.337465

[:, :, 4] =
  1.14836 1.50395 
 -2.23298 -0.819601
  1.19123 0.335359
julia> T2 = randn((3,4))
3×4 Array{Float64,2}:
 -0.88205 0.191643 -0.0997018 -0.720557
  1.01956 0.519003 -1.52737 0.507286
  0.262649 -0.541134 -0.789812 -0.488137

julia> T.*T2
ERROR: DimensionMismatch("arrays could not be broadcast to a common size")
Stacktrace:
 [1] _bcs1 at ./broadcast.jl:438 [inlined]
 [2] _bcs at ./broadcast.jl:432 [inlined] (repeats 2 times)
 [3] broadcast_shape at ./broadcast.jl:426 [inlined]
 [4] combine_axes at ./broadcast.jl:421 [inlined]
 [5] instantiate at ./broadcast.jl:255 [inlined]
 [6] materialize(::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{3},Nothing,typeof(*),Tuple{Array{Float64,3},Array{Float64,2}}}) at ./broadcast.jl:753
 [7] top-level scope at none:0

```

I was hoping there was a simple syntax akin to  
`broadcast(*,T,T2,dims=(1,3))`  
I could use permutedims, but that pushes my memory and the actual tensors are considerably larger.

How do I designate dimensions?

---

<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:** [September 26, 2019, 4:42pm UTC](https://discourse.julialang.org/t/designating-the-axes-for-broadcasting/29203/2 "2019-09-26T16:42:57Z")

</div>

Here’s one way:

```julia
julia> T3 = T .* reshape(T2, 3,1,4);

julia> size(T3)
(3, 2, 4)

```

You can also do this, at the cost of copying `T2`:

```julia
julia> T4 = T .* T2[:,[CartesianIndex()],:];

julia> T4 == T3
true

```

Here’s another way, the function `orient` just does the same reshape, but is smart enough to copy instead if say `T2::Transpose` which will be very slow once reshaped:

```julia
julia> using TensorCast

julia> T3 == @cast T5[c,b,d] := T[c,b,d] * T2[c,d]
true

julia> @pretty @cast T5[c,b,d] := T[c,b,d] * T2[c,d]
begin
    local penguin = orient(T2, (:, *, :))
    T5 = @ __dot__ (T * penguin)
end

```

One more:

```julia
julia> T6 = PermutedDimsArray(T, (1,3,2)) .* T2;

julia> size(T6)
(3, 4, 2)

```

---

<div class="post-metadata">

**Author:** ![crinders](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/crinders/32/8434_2.png) [@crinders](https://discourse.julialang.org/u/crinders)\
**Post date:** [September 26, 2019, 5:11pm UTC](https://discourse.julialang.org/t/designating-the-axes-for-broadcasting/29203/3 "2019-09-26T17:11:00Z")

</div>

The `PermutedDimsArray` does the trick for me. Thanks!