Functions for outputting the rows and columns of a matrix

Question

I often want to iterate either row-wise or column-wise though a matrix in Julia, so I've created a pair of functions to help:

function cols(x::Matrix)
    function _it()
        for ii in 1:size(x,2)
            produce(x[:,ii])
        end
    end
    Task(_it)
end

function rows(x::Matrix)
    function _it()
        for ii in 1:size(x,1)
            produce(x[ii,:])
        end
    end
    Task(_it)
end

Example of use:

AA = [1 2 3; 1 2 3]

println("Columns are:")
for ii in cols(AA)
    println(ii)
end
println("\nRows are:")
for ii in rows(AA)
    println(ii)
end

Outputs:

Columns are:
[1,1]
[2,2]
[3,3]

Rows are:
[1 2 3]
[1 2 3]

---

Possible issues:

• It seems like this could be one function, that just takes the dimension as a parameter.
• This might confound the JIT, which would mean losing out out a bunch of speed. (The Julia JIT can normally vectorize for loops).
• I feel like there should be a inbuild function for this, but the closest I know of is mapslice.

Answer 1

I think the most performant solution here would be to create an iterator:

julia> immutable EachRow{T<:AbstractMatrix}
           A::T
       end
       Base.start(::EachRow) = 1
       Base.next(itr::EachRow, s) = (itr.A[s,:], s+1)
       Base.done(itr::EachRow, s) = s > size(itr.A,1)
done (generic function with 48 methods)

julia> AA = [1 2 3; 1 2 3]
       for ii in EachRow(AA)
         println(ii)
       end
[1 2 3]
[1 2 3]

EachCol would be coded similarly.

---

This is advantageous over your task-based iterator design because Julia is not able to infer the return types from anonymous tasks. This means that within your loop, the iteration variable ii is typed as Any, so the compiler isn't able to emit efficient type-specific code. The custom iterator is type-stable, so that means that Julia knows that the iteration variable is always going to be an array, allowing it to compile specific and optimized instructions.

To answer a few of your questions: We could similarly make an EachDim iterator which also stored the dimension parameter, but this is a little trickier to write in a type-stable manner. Since indexing into columns returns a 1-dimensional column vector and indexing rows returns a 2-dimensional row vector, simply using an integer argument 1 or 2 to specify which dimension would result in a type-instability. We'd need to ensure that the dimension information is stored in the type-domain. One way to do this would be to use a parametric type… but doing this nicely requires the call-overloading feature from the development 0.4 version.

Also note that Julia's JIT doesn't "vectorize" for loops in the way you're using the word. It can be thought of more as a just-barely-ahead-of-time compiler that compiles specialized machine code for each function based upon the types of the arguments. This is why type-stability is so important; when Julia can infer the types precisely the compiled code is typically very similar to what you'd get from equivalent C code.