eachrow, eachcol, and reshape missing

[mgkurtz]

I personally prefer a functional programming style. Thus I am missing some functions to deal with matrices. Notably missing are eachrow, eachcol, and reshape. We could copy the first two from Base as

Base.eachrow(a::MatrixElem) = (view(a, i, :) for i in axes(a, 1))
Base.eachcol(a::MatrixElem) = (view(a, :, i) for i in axes(a, 2))

As view returns 1×n respectively m×1-matrices (instead of Vectors like it does for Matrix) the resulting eachrow and eachcol will accordingly also be somewhat inconsistent to their behavior for Matrix, but consistent with all other functions dealing with MatrixElem.

Reshaping with shared data would need support from the appropriate MatElem implementations. A flat copying reshape instead would be possible using the existing matrix interface. Just create a similar matrix with new size and fill in the values from the old matrix.

[fieker]

On Tue, May 30, 2023 at 06:52:45AM -0700, Markus Kurtz wrote: I personally prefer a functional programming style. Thus I am missing some functions to deal with matrices. Notably missing are `eachrow`, `eachcol`, and `reshape`. We could copy the first two from Base as ```julia Base.eachrow(a::MatrixElem) = (view(a, i, :) for i in axes(a, 1)) Base.eachcol(a::MatrixElem) = (view(a, :, i) for i in axes(a, 2)) ```

We can't - well with limited efficiency. Before we do this, can we possibly come together (Wednesday?) to see what that goal here is? - we cannot support all of julia efficiently - and I don't know if we should try to support the interface if performance is poor.

As `view` returns 1×n respectively m×1-matrices (instead of `Vector`s like it does for `Matrix`) the resulting `eachrow` and `eachcol` will accordingly also be somewhat inconsistent to their behavior for `Matrix`, but consistent with all other functions dealing with `MatrixElem`.

- see above: some of the problems.

Reshaping with shared data would need support from the appropriate `MatElem` implementations. A flat copying `reshape` instead would be possible using the existing matrix interface. Just create a `similar` matrix with new size and fill in the values from the old matrix.

- see above: some reshape can sometimes be done efficiently, but not all due to different storage - copying breaks some of the reshape promise: - it is slow - it incurs a big admin overhead (garbage collector) - it does not change the original elements/ matrices What is the goal here? what operations do we need/ want?

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[mgkurtz]

Sure, I can come along Thursday or Friday. A usage example for eachrow and reshape would be the task to LLL-reduce a Vector of matrices:

lll(a::Vector{ZZMatrix}) = isempty(a) ? a : frommatrix(lll(asmatrix(a)), size(a[1])...)

asmatrix(v::Vector{T}) :: T where T <: MatElem = reduce(vcat, reshape.(v, 1, :))

frommatrix(a::T, r::Int, c::Int) :: Vector{T} where T <: MatElem = [reshape(x, r, c) for x in eachrow(a)]

[fieker]

On Wed, May 31, 2023 at 06:35:09AM -0700, Markus Kurtz wrote: Sure, I can come along Thursday or Friday. A usage example for `eachrow` and `reshape` would be the task to LLL-reduce a `Vector` of matrices: ```julia lll(a::Vector{ZZMatrix}) = isempty(a) ? a : frommatrix(lll(asmatrix(a)), size(a[1])...) asmatrix(v::Vector{T}) :: T where T <: MatElem = reduce(vcat, reshape.(v, 1, :)) frommatrix(a::T, r::Int, c::Int) :: Vector{T} where T <: MatElem = [reshape(x, r, c) for x in eachrow(a)] ```

elegant: yes, full marks efficient: only if you're lucky... reshape could be done efficient iff the matrix if a plain vanilla Nemo matrix, ie. - no swapped rows - no view in this case we can do, similar to a view, a constant cost reshape - with shared data (so no need for frommatrix) However, the reshape to vector will be row-major, not col-major in this example, with the current technology, asmatrix copies everything twice - once in reshape - once in vcat frommatrix as well: - eachrow (might be lucky and use view) - reshape the less-elegant version is much faster... If we want useful, efficient, row-operations, then I don't think eachrow is (can be) the solution... Thinking (r)ref: you want to swap rows (currently for free) add multiple of one row to another to do this via rowslices, I'd have to check carefully if the slices refer to the same matrix in "all" operations. What is the advantage over swap_rows or add_scaled_row or similar?

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[fieker]

On Wed, May 31, 2023 at 06:35:09AM -0700, Markus Kurtz wrote: Sure, I can come along Thursday or Friday. A usage example for `eachrow` and `reshape` would be the task to LLL-reduce a `Vector` of matrices: ```julia lll(a::Vector{ZZMatrix}) = isempty(a) ? a : frommatrix(lll(asmatrix(a)), size(a[1])...) asmatrix(v::Vector{T}) :: T where T <: MatElem = reduce(vcat, reshape.(v, 1, :)) frommatrix(a::T, r::Int, c::Int) :: Vector{T} where T <: MatElem = [reshape(x, r, c) for x in eachrow(a)] ```

for (formerly) fmpz_mat ``` function Base.reshape(x::ZZMatrix, r::Int, c::Int) @Assert nrows(x) * ncols(x) == r*c @Assert r == 1 b = ZZMatrix() b.view_parent = x ccall((:fmpz_mat_window_init, libflint), Nothing, (Ref{ZZMatrix}, Ref{ZZMatrix}, Int, Int, Int, Int), b, x, 0, 0, r, c) finalizer(_fmpz_mat_window_clear_fn, b) return b end ``` julia> m = ZZ[1 2; 3 4] [1 2] [3 4] ulia> r = reshape(m, 1, 4) [1 2 3 4] julia> m[1,1] = 17 17 julia> r [17 2 3 4] julia> r[1,3] = -9 -9 julia> m [17 2] [-9 4] Note - this can only work for r==1 (using window_init) - it is row major - I think this would work similarly with all Nemo matrices, however AA (Generic) would be col-major