How to convert a Matrix into a Vector of Vectors?

Question

I have the following matrix A = [1.00 2.00; 3.00 4.00] and I need to convert it into a vector of Vectors as follows:

A1 = [1.00; 3.00] A2 = [2.00; 4.00]

Any ideas?

Bathysphere

Do you want a vector of vectors or separate objects for each vector? Your text indicators the former, your code illustration indicates the latter. – Adjunct

Also, can you give context on why you would need this? In almost every case I can think of, you'd be better just referencing the columns while they are still in your matrix or at most, creating separate views of them with sub(), e.g. B = sub(A, 1:size(A,2),1). – Adjunct

Answer 1

tl;dr
This can be very elegantly created with a list comprehension:

A = [A[:,i] for i in 1:size(A,2)]

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Explanation:

This essentially converts A from something that would be indexed as A[1,2] to something that would be indexed as A[2][1], which is what you asked.

Here I'm assigning directly back to A, which seems to me what you had in mind. But, only do this if the code is unambiguous! It's generally not a good idea to have same-named variables that represent different things at different points in the code.

NOTE: if this reversal of row / column order in the indexing isn't the order you had in mind, and you'd prefer A[1,2] to be indexed as A[1][2], then perform your list comprehension 'per row' instead, i.e.

A = [A[i,:] for i in 1:size(A,1)]

Khufu

Answer 2

It's even simpler.

eachcol is all you need. It's an abstract vector.

A=eachcol(A)

Now A[1] is [1.00; 3.00], and A[2] is [2.00; 4.00].

With this approach, there are no memory allocations. Everything is based on views.

Gianina

Answer 3

Another option is B = [eachcol(A)...]. This returns an variable with type Vector{SubArray} which might be fine depending on what you want to do. To get a Vector{Vector{Float64}} try,

B = Vector{eltype(A)}[eachcol(A)...]

Jasso

Answer 4

It would be much better simply to use slices of your matrix i.e. instead of A1 use A[:,1] and instead of A2 use A[:,2]

If you really need them to be "seperate" objections you could try creating a cell array like so:

myfirstcell = cell(size(A,2)) for i in 1:size(A,2) myfirstcell[i] = A[:,i] end

See http://docs.julialang.org/en/release-0.4/stdlib/arrays/#Base.cell

(Cell arrays allow several different types of object to be stored in the same array)

Extortionate

You could at least have an Array of Arrays explicitly, without needing to use cell A_vec = Array{Array{eltype(A),1}, size(A,2)} – Adjunct

Agreed, the accepted answer is still much better though! – Extortionate