Matrices in Julia - Sorting and Sort Permutations - sorting

Question

How can matrices be sorted in Julia.
Let's define a matrix:
a = [1 1 1;
1 3 1;
1 2 2;
1 2 1]
I'm looking for several things here:
Sort by multiple Columns
So, you can sort the matrix by all columns from left to right with
sortslices(a, dims = 1)
4×3 Array{Int64,2}:
1 1 1
1 2 1
1 2 2
1 3 1
Sort by particular Column Order
But what if want to sort by the 3rd then the 2nd and then the 1st column? Expected output:
4×3 Array{Int64,2}:
1 1 1
1 2 1
1 3 1
1 2 2
Sort permutation
Let's assume I had a Vector
b = ["a", "d", "c", "b"]
and I would like to sort its elements by the sort permutation of the matrix' columns. As seen above sortslices() let's me sort the matrix so I get the rows in the order [1,4,3,2]. How can I get this vector to sort b to
4-element Array{String,1}:
"a"
"b"
"c"
"d"
I know there are other similar questions, but they seem either address other issues or they seem to be outdated (e.g. Julia: Sort Matrix by column 2 then 3).

Answer 1

It isn't ideal to ask multiple questions within a single post. It makes searching for questions much harder.
Anyway, here we go:
Sort by multiple Columns
julia> a = [1 1 1;
1 3 1;
1 2 2;
1 2 1]
4×3 Matrix{Int64}:
1 1 1
1 3 1
1 2 2
1 2 1
julia> sortslices(a, dims = 1, by=x->(x[1], x[2], x[3]))
4×3 Matrix{Int64}:
1 1 1
1 2 1
1 2 2
1 3 1
Sort by particular Column Order
julia> a = [1 1 1;
1 3 1;
1 2 2;
1 2 1]
4×3 Matrix{Int64}:
1 1 1
1 3 1
1 2 2
1 2 1
julia> sortslices(a, dims = 1, by=x->(x[3], x[2], x[1]))
4×3 Matrix{Int64}:
1 1 1
1 2 1
1 3 1
1 2 2
Sort permutation
julia> b = ["a", "d", "c", "b"]
4-element Vector{String}:
"a"
"d"
"c"
"b"
julia> sortperm(b)
4-element Vector{Int64}:
1
4
3
2
julia> b[sortperm(b)]
4-element Vector{String}:
"a"
"b"
"c"
"d"

Answer 2

Building on #mcabbot's comment, I think that by clause is unnecessary. This suffices: p = sortperm(collect(eachrow(a))).
Whether this is the most performant solution, I don't know.