# A question on broadcasting fft for vectors of matrices

**URL:** <https://discourse.julialang.org/t/a-question-on-broadcasting-fft-for-vectors-of-matrices/76806>\
**Category:** Numerics\
**Tags:** question, arrays, broadcasting\
**Created:** [February 20, 2022, 3:55pm UTC](https://discourse.julialang.org/t/a-question-on-broadcasting-fft-for-vectors-of-matrices/76806 "2022-02-20T15:55:26Z")\
**Posts on this page:** 10\
**Page:** 1

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**Author:** ![andreasvarga](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/andreasvarga/32/11634_2.png) [@andreasvarga](https://discourse.julialang.org/u/andreasvarga)\
**Post date:** [February 20, 2022, 3:55pm UTC](https://discourse.julialang.org/t/a-question-on-broadcasting-fft-for-vectors-of-matrices/76806/1 "2022-02-20T15:55:26Z")

</div>

In the following I am creating a 3-vector of 2x2 matrices M:

`M = [rand(2,2) for i in 1:3]`

Is it any easy compact way to extract/view (e.g., for the purpose of broadcasting), say, the vector of [1,1] elements of the three matrices ?

My solution was to build a 3d matrix and use view:

`view(reshape(hcat(M...),2,2,3),1,1,:)`

but I am afraid this is quite inefficient for large matrices.

This problem I encountered trying to apply the `fft` elementwise to each vector of corresponding entries, but

```julia

fft.(M)

```

produces the wrong result. I wonder actually what?

Many thanks in advance for any help.

---

<div class="post-metadata">

**Author:** ![nilshg](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/nilshg/32/2283_2.png) [@nilshg](https://discourse.julialang.org/u/nilshg)\
**Post date:** [February 20, 2022, 4:03pm UTC](https://discourse.julialang.org/t/a-question-on-broadcasting-fft-for-vectors-of-matrices/76806/2 "2022-02-20T16:03:41Z")

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Not sure whether maybe your MWE is too simple but:

```julia
julia> M = [rand(2,2) for i in 1:3]
3-element Vector{Matrix{Float64}}:
 [0.798300477803938 0.7394167094533922; 0.020090132086653556 0.8809955596136937]
 [0.486959574050713 0.9602589802986382; 0.18396003854515464 0.8687833148070098]
 [0.5894287539978448 0.9398716351164952; 0.8376087279393974 0.23575124677607961]

julia> view(reshape(hcat(M...),2,2,3),1,1,:)
3-element view(::Array{Float64, 3}, 1, 1, :) with eltype Float64:
 0.798300477803938
 0.486959574050713
 0.5894287539978448

julia> first.(M)
3-element Vector{Float64}:
 0.798300477803938
 0.486959574050713
 0.5894287539978448

```

---

<div class="post-metadata">

**Author:** ![rafael.guerra](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rafael.guerra/32/216610_2.png) [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)\
**Post date:** [February 20, 2022, 4:29pm UTC](https://discourse.julialang.org/t/a-question-on-broadcasting-fft-for-vectors-of-matrices/76806/3 "2022-02-20T16:29:23Z")

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Please check if this transformation suits you:

```julia
M = [rand(2,2) for i in 1:3]

using TensorCast
@cast T[i,j][k] := M[k][i,j] # := returns a view

using FFTW
fft.(T)

```

> **Result**
>
> ```julia
> julia> fft.(T)
> 2×2 Matrix{Vector{ComplexF64}}:
> [0.676581+0.0im, 0.266587+0.162225im, 0.266587-0.162225im] … [1.30509+0.0im, 0.728171-0.156387im, 0.728171+0.156387im]
> [1.45385+0.0im, -0.3766+0.38125im, -0.3766-0.38125im] [2.19093+0.0im, 0.018722-0.186763im, 0.018722+0.186763im]
> 
> ```

---

<div class="post-metadata">

**Author:** ![DNF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dnf/32/10191_2.png) [@DNF](https://discourse.julialang.org/u/DNF)\
**Post date:** [February 20, 2022, 5:22pm UTC](https://discourse.julialang.org/t/a-question-on-broadcasting-fft-for-vectors-of-matrices/76806/5 "2022-02-20T17:22:27Z")

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Isn’t this just

```julia
getindex.(M, 1)

```

? (basically the same as `first.(M)`)

For more general indices

```julia
getindex.(M, CartesianIndex(1,1))

```

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<div class="post-metadata">

**Author:** ![andreasvarga](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/andreasvarga/32/11634_2.png) [@andreasvarga](https://discourse.julialang.org/u/andreasvarga)\
**Post date:** [February 20, 2022, 6:02pm UTC](https://discourse.julialang.org/t/a-question-on-broadcasting-fft-for-vectors-of-matrices/76806/6 "2022-02-20T18:02:46Z")

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Actually I have to make similar selections for all entries. Thanks for the nice solution.

---

<div class="post-metadata">

**Author:** ![andreasvarga](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/andreasvarga/32/11634_2.png) [@andreasvarga](https://discourse.julialang.org/u/andreasvarga)\
**Post date:** [February 20, 2022, 6:28pm UTC](https://discourse.julialang.org/t/a-question-on-broadcasting-fft-for-vectors-of-matrices/76806/7 "2022-02-20T18:28:47Z")

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Many thanks for this idea. And yes,

`getindex.(M,i,j)`

does exactly what I needed for any indices.

However, on Julia1 1.7.1, the following fails (not sure I can understand the reason)

```julia
 getindex.(M, CartesianIndex(1,1))
ERROR: iteration is deliberately unsupported for CartesianIndex. Use `I` rather than `I...`, or use `Tuple(I)...`

```

---

<div class="post-metadata">

**Author:** ![andreasvarga](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/andreasvarga/32/11634_2.png) [@andreasvarga](https://discourse.julialang.org/u/andreasvarga)\
**Post date:** [February 20, 2022, 6:33pm UTC](https://discourse.julialang.org/t/a-question-on-broadcasting-fft-for-vectors-of-matrices/76806/8 "2022-02-20T18:33:37Z")

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I will check if this is faster than cycling over all indices with  
`getindex.(M,i,j)`. Many thanks.

---

<div class="post-metadata">

**Author:** ![rafael.guerra](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rafael.guerra/32/216610_2.png) [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)\
**Post date:** [February 20, 2022, 6:36pm UTC](https://discourse.julialang.org/t/a-question-on-broadcasting-fft-for-vectors-of-matrices/76806/9 "2022-02-20T18:36:40Z")

</div>

The original question was about how to broadcast `fft()` on a vector of matrices though, you may wanna change the post title accordingly.

---

<div class="post-metadata">

**Author:** ![rafael.guerra](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rafael.guerra/32/216610_2.png) [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)\
**Post date:** [February 20, 2022, 6:44pm UTC](https://discourse.julialang.org/t/a-question-on-broadcasting-fft-for-vectors-of-matrices/76806/10 "2022-02-20T18:44:59Z")

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> [@andreasvarga](#):
>
> `getindex.(M, CartesianIndex(1,1))`

Try this:

```julia
getindex.(M, (CartesianIndex(1,1),))

```

_ **NB:** _  
_And my comment on changing the title of the OP to match what was needed is that it seems to be about how to access a subset of a vector of matrices as specified by some indices, and not so much about broadcasting_ `fft()`.

---

<div class="post-metadata">

**Author:** ![DNF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dnf/32/10191_2.png) [@DNF](https://discourse.julialang.org/u/DNF)\
**Post date:** [February 20, 2022, 7:36pm UTC](https://discourse.julialang.org/t/a-question-on-broadcasting-fft-for-vectors-of-matrices/76806/11 "2022-02-20T19:36:18Z")

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> [@andreasvarga](#):
>
> `ERROR: iteration is deliberately unsupported for CartesianIndex.`

That is surprising. Not that one cannot iterate, I knew that, but expected it to therefore to be treated as a scalar.