Incompatibility with SymTridiagonal matrices from LinearAlgebra

[ajalexei]

The last line of the following code:

using LinearAlgebra, FixedSizeArrays

T = Float64;
N = 100;

H=SymTridiagonal(FixedSizeVector{T}(undef, N), FixedSizeVector{T}(undef, N-1));

H'-H

causes an error:

ERROR: ArgumentError: diagonal vectors needed to be convertible to same type
Stacktrace:
 [1] (SymTridiagonal{Float64, V} where V<:AbstractVector{Float64})(dv::FixedSizeArray{Float64, 1, Memory{Float64}}, ev::Vector{Float64})
  @ LinearAlgebra ~/.julia/juliaup/julia-1.11.6+0.aarch64.linux.gnu/share/julia/stdlib/v1.11/LinearAlgebra/src/tridiag.jl:75
 [2] SymTridiagonal(d::FixedSizeArray{Float64, 1, Memory{Float64}}, e::Vector{Float64})
   @ LinearAlgebra ~/.julia/juliaup/julia-1.11.6+0.aarch64.linux.gnu/share/julia/stdlib/v1.11/LinearAlgebra/src/tridiag.jl:79
 [3] -(A::SymTridiagonal{Float64, FixedSizeArray{Float64, 1, Memory{Float64}}}, B::SymTridiagonal{Float64, FixedSizeArray{Float64, 1, Memory{Float64}}})
   @ LinearAlgebra ~/.julia/juliaup/julia-1.11.6+0.aarch64.linux.gnu/share/julia/stdlib/v1.11/LinearAlgebra/src/tridiag.jl:216
 [4] top-level scope
   @ REPL[60]:1

Confirmed for FixedSizeVectors version 1.0.1, official Julia release 1.11.6, macos 15.6 (arm64) and Linux (WSL/arm64)

[giordano]

The real issue is that the the difference between two views is a Vector, instead of a FixedSizeVector:

julia> using FixedSizeArrays

julia> v = FixedSizeVectorDefault{Float64}(undef, 3)
3-element FixedSizeArray{Float64, 1, Memory{Float64}}:
 2.3454965676e-314
 2.2471037736e-314
 2.3454965676e-314

julia> @view(v[1:2]) - @view(v[1:2])
2-element Vector{Float64}:
 0.0
 0.0

[ajalexei]

Thanks, I guess, this then is an issue with Julia, rather than with FixedSizeVectors.

[giordano]

Since the this entirely relies on the internals of the broadcast mechanism (functions Base.Broadcast.broadcasted and Base.Broadcast.materialize are involved, they're both non-public), I'd say this is a bug in Julia, not this package.

[giordano]

Do we need to define a broadcast style also for views?

[giordano]

Looks like that's enough: #147 (comment).

[giordano]

Now that the fix is in v1.1.0, a quick benchmark:

julia> using BenchmarkTools, FixedSizeArrays, LinearAlgebra, Random

julia> T = Float64;

julia> N = 4;

julia> H = SymTridiagonal(FixedSizeVector{T}(undef, N), FixedSizeVector{T}(undef, N-1));

julia> rand!(H.dv);

julia> rand!(H.ev);

julia> Hv = SymTridiagonal{Float64, Vector{Float64}}(H);

julia> @benchmark $(H)' - $(H)
BenchmarkTools.Trial: 10000 samples with 996 evaluations per sample.
 Range (min … max):  25.811 ns …   9.085 μs  ┊ GC (min … max):  0.00% … 99.48%
 Time  (median):     27.276 ns               ┊ GC (median):     0.00%
 Time  (mean ± σ):   33.518 ns ± 155.192 ns  ┊ GC (mean ± σ):  14.29% ±  3.41%

      ▂██▃▁                    ▁
  ▃▃▃▇█████▅▃▂▂▁▁▁▁▁▁▁▁▁▁▂▃▃▂▄▇█▅▂▂▁▁▁▁▁▁▁▁▂▂▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▂
  25.8 ns         Histogram: frequency by time         37.3 ns <

 Memory estimate: 112 bytes, allocs estimate: 2.

julia> @benchmark $(Hv)' - $(Hv)
BenchmarkTools.Trial: 10000 samples with 995 evaluations per sample.
 Range (min … max):  30.276 ns …  12.120 μs  ┊ GC (min … max):  0.00% … 99.49%
 Time  (median):     32.621 ns               ┊ GC (median):     0.00%
 Time  (mean ± σ):   43.336 ns ± 239.258 ns  ┊ GC (mean ± σ):  20.83% ±  4.07%

      ▁█▇▅▃
  ▁▃▅▆█████▆▄▂▂▂▂▂▁▁▁▁▁▂▂▂▅▃▂▃▂▂▂▂▂▂▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▂
  30.3 ns         Histogram: frequency by time         48.8 ns <

 Memory estimate: 176 bytes, allocs estimate: 4.

julia> versioninfo()
Julia Version 1.13.0-DEV.940
Commit 8ba3b11f9b* (2025-08-01 07:41 UTC)
Platform Info:
  OS: macOS (arm64-apple-darwin24.5.0)
  CPU: 8 × Apple M1
  WORD_SIZE: 64
  LLVM: libLLVM-20.1.2 (ORCJIT, apple-m1)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 4 virtual cores)