# Can't get sortperm to return the sorting order of columns of a matrix

**URL:** <https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081>\
**Category:** General Usage\
**Tags:** question, sort, sortperm\
**Created:** [July 12, 2022, 4:20am UTC](https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081 "2022-07-12T04:20:09Z")\
**Posts on this page:** 12\
**Page:** 1

<div class="post-metadata">

**Author:** ![Gus\_Hart](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gus_hart/32/6987_2.png) [@Gus\_Hart](https://discourse.julialang.org/u/Gus_Hart)\
**Post date:** [July 12, 2022, 4:20am UTC](https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081/1 "2022-07-12T04:20:09Z")

</div>

I’m sorting the columns of each matrix in long vector of matrices (having the matrix columns in a canonical order makes it easy to identify approximately equal matrices). Here’s a minimal working example:

```julia
julia> t
3×2 transpose(::Matrix{Float64}) with eltype Float64:
 0.0 -0.5
 0.0 -0.5
 0.0 0.0

julia> sort(t,dims=2)
3×2 Matrix{Float64}:
 -0.5 0.0
 -0.5 0.0
  0.0 0.0

```

There are functions associated with each column of each matrix as well, and I need to permute these polynomials in the same way when the columns are sorted. But `sortperm` does not accept the same arguments that `sort` does. It seems the `dims` keyword is unsupported.

```julia
julia> sortperm(t,dims=2)
ERROR: MethodError: no method matching sortperm(::Transpose{Float64, Matrix{Float64}}; dims=2)
Closest candidates are:
  sortperm(::AbstractUnitRange) at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/base/range.jl:1309 got unsupported keyword argument "dims"
  sortperm(::AbstractRange) at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/base/range.jl:1310 got unsupported keyword argument "dims"
  sortperm(::StaticArrays.StaticVector; alg, lt, by, rev, order) at ~/.julia/packages/StaticArrays/58yy1/src/sort.jl:26 got unsupported keyword argument "dims"
  ...
Stacktrace:
 [1] top-level scope
   @ REPL[1417]:1

```

Am I missing something? Anyone have ideas for a simple workaround?

I would assume (naively?) that `sort` and `sortperm` are the same function under the hood and just return different parts of the sort results (sorted items vs. order of sort). EDIT: for the first time ever, I looked at the source code in `Base`. It seems that `sortperm` and `sort` are separate functions…still, I really need a work around for this…

```julia
julia> versioninfo()
Julia Version 1.7.1
Commit ac5cc99908 (2021-12-22 19:35 UTC)
Platform Info:
  OS: macOS (x86_64-apple-darwin19.5.0)
  CPU: Apple M1 Pro

```

---

<div class="post-metadata">

**Author:** ![mkitti](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mkitti/32/12459_2.png) [@mkitti](https://discourse.julialang.org/u/mkitti)\
**Post date:** [July 12, 2022, 5:40am UTC](https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081/2 "2022-07-12T05:40:51Z")

</div>

`sortperm` is a generalized method for a 1-D sort. What we need to do then is obtain either an array of rows or an array of columns to sort over.

There are functions `eachrow`, `eachcol`, and `eachslice` that are generators. To turn these into arrays we need to `collect` them.

```julia
julia> A = rand(5, 5)
5×5 Matrix{Float64}:
 0.212887 0.505692 0.656134 0.23317 0.607276
 0.535299 0.36777 0.595655 0.168758 0.225478
 0.934146 0.98104 0.556343 0.473143 0.836663
 0.216165 0.253191 0.854917 0.165115 0.44384
 0.339784 0.940717 0.35101 0.169418 0.271189

julia> rowsperm = sortperm(collect(eachslice(A; dims = 1)))
5-element Vector{Int64}:
 1
 4
 5
 2
 3

julia> colsperm = sortperm(collect(eachslice(A; dims = 2)))
5-element Vector{Int64}:
 1
 4
 2
 5
 3

julia> @view A[rowsperm,:]
5×5 view(::Matrix{Float64}, [1, 4, 5, 2, 3], :) with eltype Float64:
 0.212887 0.505692 0.656134 0.23317 0.607276
 0.216165 0.253191 0.854917 0.165115 0.44384
 0.339784 0.940717 0.35101 0.169418 0.271189
 0.535299 0.36777 0.595655 0.168758 0.225478
 0.934146 0.98104 0.556343 0.473143 0.836663

julia> @view A[:,colsperm]
5×5 view(::Matrix{Float64}, :, [1, 4, 2, 5, 3]) with eltype Float64:
 0.212887 0.23317 0.505692 0.607276 0.656134
 0.535299 0.168758 0.36777 0.225478 0.595655
 0.934146 0.473143 0.98104 0.836663 0.556343
 0.216165 0.165115 0.253191 0.44384 0.854917
 0.339784 0.169418 0.940717 0.271189 0.35101

```

---

<div class="post-metadata">

**Author:** ![mkitti](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mkitti/32/12459_2.png) [@mkitti](https://discourse.julialang.org/u/mkitti)\
**Post date:** [July 12, 2022, 5:48am UTC](https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081/3 "2022-07-12T05:48:49Z")

</div>

Also see [Sortperm for matrix sorting in Julia lang - Stack Overflow](https://stackoverflow.com/questions/68344823/sortperm-for-matrix-sorting-in-julia-lang)

---

<div class="post-metadata">

**Author:** ![mkitti](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mkitti/32/12459_2.png) [@mkitti](https://discourse.julialang.org/u/mkitti)\
**Post date:** [July 12, 2022, 6:06am UTC](https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081/4 "2022-07-12T06:06:50Z")

</div>

If you are wondering why `sortperm` does not have a `dims` parameter, the answer is that Julia will have a `dims` parameter in Julia version 1.9 since @pjentsch0 just implemented it:

[https://github.com/JuliaLang/julia/pull/45211](https://github.com/JuliaLang/julia/pull/45211)

It looks like `sortslicesperm` is on the way also due to the efforts of **[jgonzalez49](https://github.com/jgonzalez49)**

[https://github.com/JuliaLang/julia/pull/45787](https://github.com/JuliaLang/julia/pull/45787)

---

<div class="post-metadata">

**Author:** ![Gus\_Hart](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gus_hart/32/6987_2.png) [@Gus\_Hart](https://discourse.julialang.org/u/Gus_Hart)\
**Post date:** [July 12, 2022, 3:12pm UTC](https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081/5 "2022-07-12T15:12:27Z")

</div>

I modified the example you referenced ([https://stackoverflow.com/questions/68344823/sortperm-for-matrix-sorting-in-julia-lang](https://stackoverflow.com/questions/68344823/sortperm-for-matrix-sorting-in-julia-lang) so that the permutations would be non-trivial for a sort over columns and so that multiple components of the vectors would be needed to break ties. Your solution was just what I needed. Thanks.

```julia
julia> B =
       [ 2 4 4 4 5 ;
         1 2 2 3 5 ;
         1 2 3 3 3 ;
         1 2 2 5 6 ;
         1 3 4 4 4 ; ]|>transpose
5×5 transpose(::Matrix{Int64}) with eltype Int64:
 2 1 1 1 1
 4 2 2 2 3
 4 2 3 2 4
 4 3 3 5 4
 5 5 3 6 4

julia> sortperm(collect(eachslice(B,dims=2)))
5-element Vector{Int64}:
 2
 4
 3
 5
 1

```

---

<div class="post-metadata">

**Author:** ![Gus\_Hart](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gus_hart/32/6987_2.png) [@Gus\_Hart](https://discourse.julialang.org/u/Gus_Hart)\
**Post date:** [July 13, 2022, 5:35am UTC](https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081/6 "2022-07-13T05:35:02Z")

</div>

Something I didn’t understand at first—a fundamental misunderstanding—`sort(t,dims=2)` does not preserve the columns necessarily. It sorts the columns of each row _separately_. What I really wanted was to sort the entire columns (preserving their contents).

```julia
julia> t
3×2 Matrix{Float64}:
 0.5 0.5
 0.5 0.0
 0.0 0.5

julia> sort(t,dims=2) # Doesn't preserve the columns
3×2 Matrix{Float64}:
 0.5 0.5
 0.0 0.5
 0.0 0.5

julia> sort(collect(eachslice(t,dims=2))) # Does preserve the columns
2-element Vector{SubArray{Float64, 1, Matrix{Float64}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}}:
 [0.5, 0.0, 0.5]
 [0.5, 0.5, 0.0]

```

---

<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:** [July 13, 2022, 6:15am UTC](https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081/7 "2022-07-13T06:15:23Z")

</div>

Have you looked at `sortslices()`?

```julia
julia> sortslices(t, dims=2)
3×2 Matrix{Float64}:
 0.5 0.5
 0.0 0.5
 0.5 0.0

```

---

<div class="post-metadata">

**Author:** ![Gus\_Hart](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gus_hart/32/6987_2.png) [@Gus\_Hart](https://discourse.julialang.org/u/Gus_Hart)\
**Post date:** [July 15, 2022, 3:43pm UTC](https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081/8 "2022-07-15T15:43:27Z")

</div>

Super helpful! Thanks. I wasn’t aware of `sortslices`. That makes my sorting syntax simpler (though I still need the `sortperm` too but @mkitti shared above that a perm version is coming).

---

<div class="post-metadata">

**Author:** ![mkitti](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mkitti/32/12459_2.png) [@mkitti](https://discourse.julialang.org/u/mkitti)\
**Post date:** [July 15, 2022, 11:17pm UTC](https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081/9 "2022-07-15T23:17:37Z")

</div>

Per @Lilith , perhaps it is not coming:

[https://github.com/JuliaLang/julia/issues/9258#issuecomment-1183294739](https://github.com/JuliaLang/julia/issues/9258#issuecomment-1183294739)

---

<div class="post-metadata">

**Author:** ![Lilith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lilith/32/27492_2.png) [@Lilith](https://discourse.julialang.org/u/Lilith)\
**Post date:** [July 16, 2022, 11:11am UTC](https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081/10 "2022-07-16T11:11:47Z")

</div>

We don’t need `sortslicesperm` because we already have `eachslice` and `sortperm`, which @Gus_Hart put together to achieve the same result above:

> [@Gus\_Hart](#):
>
> ```julia
> julia> sortperm(collect(eachslice(B,dims=2)))
> 
> ```

As of 1.9.0, `collect` is unnecessary here because the result of `eachslice` is already indexable:

```julia
julia> @btime sortperm(eachslice(B,dims=2))
  316.099 ns (5 allocations: 176 bytes)
5-element Vector{Int64}:
 2
 4
 3
 5
 1

julia> @btime sortperm(collect(eachslice(B,dims=2)))
  522.126 ns (6 allocations: 432 bytes)
5-element Vector{Int64}:
 2
 4
 3
 5
 1

```

---

<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:** [July 16, 2022, 11:15am UTC](https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081/11 "2022-07-16T11:15:47Z")

</div>

> [@Lilith](#):
>
> `collect` is unnecessary here because `sortperm` does not mutate its input

It seems to be necessary at least with Julia 1.7.3. Which version are you using?

---

<div class="post-metadata">

**Author:** ![Lilith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lilith/32/27492_2.png) [@Lilith](https://discourse.julialang.org/u/Lilith)\
**Post date:** [July 16, 2022, 11:27am UTC](https://discourse.julialang.org/t/cant-get-sortperm-to-return-the-sorting-order-of-columns-of-a-matrix/84081/12 "2022-07-16T11:27:38Z")

</div>

Good catch! I’m on 1.9.0-DEV.925. I imagine that `collect` became unnecessary after [add Slices array type for eachslice/eachrow/eachcol by simonbyrne · Pull Request #32310 · JuliaLang/julia · GitHub](https://github.com/JuliaLang/julia/pull/32310), which would make 1.9.0-DEV the cutoff. I edited my previous post to reflect that.