# Operation on transpose sparse array is slow
**URL:** https://discourse.julialang.org/t/operation-on-transpose-sparse-array-is-slow/114330
**Category:** Performance
**Created:** [May 15, 2024, 11:18pm UTC](https://discourse.julialang.org/t/operation-on-transpose-sparse-array-is-slow/114330 "2024-05-15T23:18:26Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@tiZ](https://discourse.julialang.org/u/tiZ)
#### Post date: [May 15, 2024, 11:18pm UTC](https://discourse.julialang.org/t/operation-on-transpose-sparse-array-is-slow/114330/1 "2024-05-15T23:18:26Z")
Hi Friends, I am searching for a better solution for speed up my script, my script accept a sparse matrix as input, (some time the sparse matrix is sample X features, and sometimes it is features X sample), I have to transpose it to make sure sample is always on column.
But I found that some operation on transpose sparse matrix will be much slow, so I wonder could it have a better solution?
```julia
X = read_mtx("file path")
# 232320×32840 SparseMatrixCSC{Float32, Int64}
# sample x feature
idx_1 = rand(Bool, 232320) # condition select by sample
idx_2 = rand(Bool, 32840) # condition select by features
@time mean(X[idx_1,idx_2])
# 3.291982 seconds (18 allocations: 1.532 GiB, 3.49% gc time)
```
But if I index on the transpose it will much slow, actually I wait a looong time but it is still running…
```Julia
Y = X'
# 32840×232320 LinearAlgebra.Adjoint{Float32, SparseMatrixCSC{Float32, Int64}}
# now it is feature x sample
@time mean(Y[idx_2,idx_1])
# looooooooog time waiting and no return...
```
of course I can use view:
```julia
@time @views mean(X[idx_1,idx_2]);
# 30.983588 seconds (10 allocations: 1.264 MiB)
@time @views mean(Y[idx_2,idx_1])
# looooooooog time waiting and no return...
```
I have no idea how to improve it, and I would greatly appreciate any advice!
Thank you!!!
---
### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [May 15, 2024, 11:50pm UTC](https://discourse.julialang.org/t/operation-on-transpose-sparse-array-is-slow/114330/2 "2024-05-15T23:50:13Z")
Transposing a sparse matrix with `Y = X'` doesn’t actually copy any data, it wraps it with a special [`Adjoint` type](https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#LinearAlgebra.Adjoint) that gives a (conjugate-)transposed view of the underlying `X` matrix.
`Adjoint` views of sparse matrices have several optimized methods, e.g. `Y * vector` is fast, but not all of the optimized methods for sparse matrices are implemented for the `Adjoint` wrapper. In particular, “logical indexing” with a vector of booleans has a [fast implementation](https://github.com/JuliaSparse/SparseArrays.jl/blob/a09f90b43105229e42ac687ab4e3f6cf50deed8c/src/sparsematrix.jl#L3166-L3175) for sparse matrices, but not for `Adjoint` wrappers thereof, and in consequence the corresponding operation on `Y` falls back to the generic method for dense matrices, which is very slow because it does not exploit sparsity.
Three possible workarounds:
1. Set `Y = SparseMatrixCSC(X')` — this makes an explicit sparse-matrix copy of the `Adjoint` wrapper, which uses up some extra memory but then subsequent operations will be fast.
2. Re-organize your code so that you do your calculations directly on the un-transposed matrix `X`
3. Define the missing specialized methods for `Adjoint` wrappers of sparse matrices. (This is [“type piracy”](https://docs.julialang.org/en/v1/manual/style-guide/#Avoid-type-piracy) but may be a reasonable stopgap measure in the short run.)
For example, your code above should become fast again if we define:
```julia
using LinearAlgebra, SparseArrays
Base.getindex(A::Adjoint{<:Any,<:SparseArrays.AbstractSparseMatrixCSC}, I::AbstractVector{Bool}, J::AbstractVector{Bool}) = parent(A)[findall(J),findall(I)]'
```
If someone wants to volunteer to make a PR to [SparseArrays.jl](https://github.com/JuliaSparse/SparseArrays.jl) with this and similar enhancements, that would be great. See also [getindex is very slow for adjoints of sparse arrays · Issue #36 · JuliaSparse/SparseArrays.jl · GitHub](https://github.com/JuliaSparse/SparseArrays.jl/issues/36) and [Strange performance with Adjoint structures](https://discourse.julialang.org/t/strange-performance-with-adjoint-structures/13397)