I have a long list (vector) of matrices. They are size 3xn where n is typically 1 < n < 7. My long list typically varies between 100K and 1 million. My task is to reduce this list using a rather complicated and expensive equivalence relation (reduction factor is about 100x to 1000x, depending on the case).

My current solution, to identifying the unique matrices, is basically an N^2 search but with as many early loop exits as I can invent. As I accumulate unique matrices, I’m storing them (via `append`

) in an *initially* empty vector. `@time`

tells me that 85% of my time is spent in garbage collection. Presumably it’s expensive to append because of frequent reallocations and copying.

Also, I couldn’t figure out how to initialize an empty vector of matrices `{Matrix{Float64}}`

so my initial vector is of type `Any`

. Maybe that is also trouble?

How would I initialize an empty vector of `{Matrix{Float64}}`

? So that I can `append!`

or `push!`

matrices to it?

Here are some attempts:

```
julia> testList = Vector{Matrix{Float64}}
Vector{Matrix{Float64}} (alias for Array{Array{Float64, 2}, 1})
julia> testm
3×3 Matrix{Float64}:
-0.5 0.0 0.0
0.0 0.0 0.5
0.5 0.0 0.5
julia> append!(testList,testm)
ERROR: MethodError: no method matching append!(::Type{Vector{Matrix{Float64}}}, ::Matrix{Float64})
Closest candidates are:
append!(::DataStructures.MutableLinkedList, ::Any...) at ~/.julia/packages/DataStructures/59MD0/src/mutable_list.jl:160
append!(::StructArrays.StructVector, ::Any) at ~/.julia/packages/StructArrays/wbEEd/src/tables.jl:27
append!(::Plots.Series, ::Any...) at ~/.julia/packages/Plots/Ra8fG/src/utils.jl:790
...
Stacktrace:
[1] top-level scope
@ REPL[276]:1
julia> push!(testList,testm)
ERROR: MethodError: no method matching push!(::Type{Vector{Matrix{Float64}}}, ::Matrix{Float64})
Closest candidates are:
push!(::Any, ::Any, ::Any) at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/base/abstractarray.jl:2970
push!(::Any, ::Any, ::Any, ::Any...) at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/base/abstractarray.jl:2971
push!(::VSCodeServer.JSON.Parser.PushVector, ::Any) at ~/.vscode/extensions/julialang.language-julia-1.6.28/scripts/packages/JSON/src/pushvector.jl:20
...
Stacktrace:
[1] top-level scope
@ REPL[277]:1
julia> testList = Vector{Matrix{Float64}}[]
Vector{Matrix{Float64}}[]
julia> push!(testList,testm)
ERROR: MethodError: no method matching Vector{Matrix{Float64}}(::Matrix{Float64})
Closest candidates are:
Array{T, N}(::AbstractArray{S, N}) where {T, N, S} at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/base/array.jl:563
Vector{T}() where T at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/base/boot.jl:476
Array{T, N}(::StaticArraysCore.SizedArray{S, T, N, M, TData} where {M, TData<:AbstractArray{T, M}}) where {T, S, N} at ~/.julia/packages/StaticArrays/8Dz3j/src/SizedArray.jl:66
```