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Unalias off-diagonals in Tridiagonal constructor #51763

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merged 6 commits into from
Dec 5, 2023
Merged

Unalias off-diagonals in Tridiagonal constructor #51763

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e2575fc
Unalias off-diagonals in Tridiagonal constructor
jishnub Oct 18, 2023
1ef603e
Update lu! test from #35197
jishnub Oct 18, 2023
8e37444
remove aliasing check
dkarrasch Oct 19, 2023
8a09229
also remove in lu!
dkarrasch Oct 19, 2023
daa2306
relax egality check to equality check
dkarrasch Oct 20, 2023
7b5c411
Add comment about unaliasing
jishnub Nov 7, 2023
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3 changes: 0 additions & 3 deletions stdlib/LinearAlgebra/src/lu.jl
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Expand Up @@ -520,9 +520,6 @@ end

# Initialize variables
info = 0
if dl === du
throw(ArgumentError("off-diagonals must not alias"))
end
fill!(du2, 0)

@inbounds begin
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11 changes: 6 additions & 5 deletions stdlib/LinearAlgebra/src/tridiag.jl
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Expand Up @@ -472,13 +472,13 @@ struct Tridiagonal{T,V<:AbstractVector{T}} <: AbstractMatrix{T}
"lengths of subdiagonal, diagonal and superdiagonal: ",
"($(length(dl)), $(length(d)), $(length(du)))")))
end
new{T,V}(dl, d, du)
new{T,V}(dl, d, Base.unalias(dl, du))
end
# constructor used in lu!
function Tridiagonal{T,V}(dl, d, du, du2) where {T,V<:AbstractVector{T}}
require_one_based_indexing(dl, d, du, du2)
# length checks?
new{T,V}(dl, d, du, du2)
new{T,V}(dl, d, Base.unalias(dl, du), du2)
end
end

Expand All @@ -491,6 +491,10 @@ solvers, but may be converted into a regular matrix with
[`convert(Array, _)`](@ref) (or `Array(_)` for short).
The lengths of `dl` and `du` must be one less than the length of `d`.

!!! note
The subdiagonal `dl` and the superdiagonal `du` must not be aliased to each other.
If aliasing is detected, the constructor will use a copy of `du` as its argument.

# Examples
```jldoctest
julia> dl = [1, 2, 3];
Expand Down Expand Up @@ -912,9 +916,6 @@ function ldiv!(A::Tridiagonal, B::AbstractVecOrMat)
dl = A.dl
d = A.d
du = A.du
if dl === du
throw(ArgumentError("off-diagonals of `A` must not alias"))
end

@inbounds begin
for i in 1:n-1
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4 changes: 3 additions & 1 deletion stdlib/LinearAlgebra/test/lu.jl
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Expand Up @@ -97,7 +97,9 @@ dimg = randn(n)/2
dlu = convert.(eltya, [1, 1])
dia = convert.(eltya, [-2, -2, -2])
tri = Tridiagonal(dlu, dia, dlu)
@test_throws ArgumentError lu!(tri)
L = lu(tri)
@test lu!(tri) == L
@test UpperTriangular(tri) == L.U
end
end
@testset for eltyb in (Float32, Float64, ComplexF32, ComplexF64, Int)
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10 changes: 9 additions & 1 deletion stdlib/LinearAlgebra/test/tridiag.jl
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Expand Up @@ -82,7 +82,7 @@ end
@test TT == Matrix(TT)
@test TT.dl === y
@test TT.d === x
@test TT.du === y
@test TT.du == y
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Should we document which off-diagonal is aliased to the argument of the constructor and which one may be just a copy?

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I feel we should document that the off diagonals shouldn't be aliased, and leave the de-aliasing as an implementation detail.

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Hello, as a Julia beginner and new user, I feel I might prefer to have a warning here along with the unaliasing if I alias dl and du (and not an error as earlier). The reason is that, in Julia, I always expect matrix assignments and calls to reuse the same memory. Silent unaliasing of dl and du would be (from my point of view) unexpected behaviour.

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I've added a comment to the docstring explaining that du is copied if aliasing is detected.

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Thank you very much, @jishnub. I'm not sure if it makes sense, in my comment above, I was actually referring to a runtime warning that would seem most correct to me as a beginner.

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I think runtime warnings may ruin performance. Moreover, we have the hint in the documentation, so it's not exactly "silent".

@test typeof(TT)(TT) === TT
end
ST = SymTridiagonal{elty}([1,2,3,4], [1,2,3])
Expand Down Expand Up @@ -521,6 +521,14 @@ end
@test Tridiagonal(4:5, 1:3, 1:2) == [1 1 0; 4 2 2; 0 5 3]
end

@testset "Prevent off-diagonal aliasing in Tridiagonal" begin
e = ones(4)
f = e[1:end-1]
T = Tridiagonal(f, 2e, f)
T ./= 10
@test all(==(0.1), f)
end

@testset "Issue #26994 (and the empty case)" begin
T = SymTridiagonal([1.0],[3.0])
x = ones(1)
Expand Down