# Column iterator

**URL:** <https://discourse.julialang.org/t/column-iterator/14967>\
**Category:** General Usage\
**Created:** [September 14, 2018, 5:18pm UTC](https://discourse.julialang.org/t/column-iterator/14967 "2018-09-14T17:18:33Z")\
**Posts on this page:** 9\
**Page:** 1

<div class="post-metadata">

**Author:** ![mschauer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mschauer/32/13946_2.png) [@mschauer](https://discourse.julialang.org/u/mschauer)\
**Post date:** [September 14, 2018, 5:18pm UTC](https://discourse.julialang.org/t/column-iterator/14967/1 "2018-09-14T17:18:33Z")

</div>

I’d like to define a plain iterator over the columns of a matrix in style of julienned arrays. If I take the state to be

```julia
struct Slice{T} <: AbstractVector{T}
    a::Matrix{T}
    idx::Int
end

```

what do I have to define of `size, length, getindex, setindex!, axes`  
to obtain a performant broadcast as below

```julia
a = rand(2, 1000)
x = rand(2)

y = Slice(a, 1) # a[:, 1]
y .= x

```

I’d like to avoid `view`s and leverage that columns are contiguous.

---

<div class="post-metadata">

**Author:** ![bramtayl](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bramtayl/32/3614_2.png) [@bramtayl](https://discourse.julialang.org/u/bramtayl)\
**Post date:** [September 14, 2018, 6:39pm UTC](https://discourse.julialang.org/t/column-iterator/14967/2 "2018-09-14T18:39:08Z")

</div>

Whats the problem with views? Are they allocating? Are you trying to call mutate in place functions?

---

<div class="post-metadata">

**Author:** ![mschauer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mschauer/32/13946_2.png) [@mschauer](https://discourse.julialang.org/u/mschauer)\
**Post date:** [September 14, 2018, 7:05pm UTC](https://discourse.julialang.org/t/column-iterator/14967/3 "2018-09-14T19:05:07Z")

</div>

Yeah, views are allocating and have overhead as they solve a considerably more difficult problem.

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<div class="post-metadata">

**Author:** ![mschauer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mschauer/32/13946_2.png) [@mschauer](https://discourse.julialang.org/u/mschauer)\
**Post date:** [September 14, 2018, 7:16pm UTC](https://discourse.julialang.org/t/column-iterator/14967/4 "2018-09-14T19:16:32Z")

</div>

To be sure, I benchmarked and it appears that creating the `view` is not a problem, the costs are stemming from broadcasting:

```julia
yy = rand(2, 10000)
y = rand(2)
using BenchmarkTools
function f5(yy, x) 
    for i in 1:size(yy, 2)
        y = Slice1(yy, i)
        for k in eachindex(x)
            @inbounds y[k] = x[k]
        end
    end
end
function f6(yy, x) 
    for i in 1:size(yy, 2)
        y = view(yy, :, i)
        for k in eachindex(x)
            @inbounds y[k] = x[k]
        end
    end
end

@btime f5($yy, $y)
@btime f6($yy, $y)
  25.072 μs (0 allocations: 0 bytes)
  27.160 μs (0 allocations: 0 bytes)

```

with

```julia

struct Slice1{T} <: AbstractVector{T}
    S::Matrix{T}
    idx::Int
    sz::Base.OneTo{Int}
end
@inline function Slice1(A::TA, i::Int) where {TA<:AbstractArray{T,2}} where {T} 
    Slice1(A, i, Base.OneTo(size(A)[1]) )
end

@inline size(S::Slice1) = (length(S.sz),)
@inline axes(S::Slice1) = (S.sz,)

@inline Base.IndexStyle(::Type{<:Slice1}) = IndexLinear()
@inline function setindex!(S::Slice1, x, k)
    @boundscheck checkbounds(S.S, k, S.idx)
    @inbounds S.S[k, S.idx] = x
end

```

---

<div class="post-metadata">

**Author:** ![mschauer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mschauer/32/13946_2.png) [@mschauer](https://discourse.julialang.org/u/mschauer)\
**Post date:** [September 14, 2018, 7:46pm UTC](https://discourse.julialang.org/t/column-iterator/14967/5 "2018-09-14T19:46:21Z")

</div>

Compare with

```julia

function f7(yy, x) 
    for i in 1:size(yy, 2)
        y = view(yy, :, i)
        @inbounds y .= x
    end
end

@btime f7($yy, $y)

```

```julia
 169.822 μs (10000 allocations: 468.75 KiB)

```

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<div class="post-metadata">

**Author:** ![raminammour](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/raminammour/32/13572_2.png) [@raminammour](https://discourse.julialang.org/u/raminammour)\
**Post date:** [September 14, 2018, 9:38pm UTC](https://discourse.julialang.org/t/column-iterator/14967/6 "2018-09-14T21:38:33Z")

</div>

I think broadcast is not strictly the problem. It acts like a function barrier and does not inline, therefore forcing the allocations of views. You can define the inner loop as a separate function and inline/noinline it to check.

Also, your benchmarking is probably skewed by copying two numbers a 1000 times. If these numbers are representative of the application, fine. If not, you will discover that, while the allocations don’t disappear, the performance is almost the same on a 200x1000 example.

Cheers!

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<div class="post-metadata">

**Author:** ![mschauer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mschauer/32/13946_2.png) [@mschauer](https://discourse.julialang.org/u/mschauer)\
**Post date:** [September 15, 2018, 5:41am UTC](https://discourse.julialang.org/t/column-iterator/14967/7 "2018-09-15T05:41:17Z")

</div>

You are right, the allocation because of the function barrier is a problem. The benchmark is representative of the application (low-dim ODEs). I don’t understand why though, the view is just an immutable struct with two fields… what has to be allocated there?

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<div class="post-metadata">

**Author:** ![bramtayl](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bramtayl/32/3614_2.png) [@bramtayl](https://discourse.julialang.org/u/bramtayl)\
**Post date:** [September 15, 2018, 2:42pm UTC](https://discourse.julialang.org/t/column-iterator/14967/8 "2018-09-15T14:42:19Z")

</div>

My philosophy on this is just wait for Base to catch up. I’m sure eventually they’ll be able to figure out a way to get rid of the views allocations.

---

<div class="post-metadata">

**Author:** ![raminammour](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/raminammour/32/13572_2.png) [@raminammour](https://discourse.julialang.org/u/raminammour)\
**Post date:** [September 17, 2018, 3:07pm UTC](https://discourse.julialang.org/t/column-iterator/14967/9 "2018-09-17T15:07:58Z")

</div>

I think the real difference is in one case the views are completely optimized out (the inlined case), in the other they are not. I had to unfortunately go back to `v0.6` to see `@code_warntype` which marks ` y <optimized out>`  
( I find the output in `0.7` illegible).