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Add cholesky overload for tracer matrices #322

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adrhill merged 1 commit into from
Jun 24, 2026
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Add cholesky overload for tracer matrices #322

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4 changes: 4 additions & 0 deletions CHANGELOG.md
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Original file line number Diff line number Diff line change
@@ -1,5 +1,8 @@
# SparseConnectivityTracer.jl

## Unreleased
* ![Feature][badge-feature] Add support for `cholesky` ([#322])

## Version `v1.2.1`
* ![Bugfix][badge-bugfix] Fix `NaNMath.pow` method ambiguity ([#292])

Expand Down Expand Up @@ -166,6 +169,7 @@ This release is only breaking for users who touched unexported internals.
[badge-maintenance]: https://img.shields.io/badge/maintenance-gray.svg
[badge-docs]: https://img.shields.io/badge/docs-orange.svg

[#322]: https://github.com/adrhill/SparseConnectivityTracer.jl/pull/322
[#292]: https://github.com/adrhill/SparseConnectivityTracer.jl/pull/292
[#290]: https://github.com/adrhill/SparseConnectivityTracer.jl/pull/290
[#289]: https://github.com/adrhill/SparseConnectivityTracer.jl/pull/289
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25 changes: 25 additions & 0 deletions src/overloads/arrays.jl
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Expand Up @@ -72,6 +72,31 @@ function LinearAlgebra.eigen(
return LinearAlgebra.Eigen(values, vectors)
end

## Cholesky
# A generic `cholesky` compares matrix entries (pivoting / positive-definiteness), which on tracers
# return a tracer rather than a `Bool`. Like `eigen`, return a conservative all-depends factor.
function LinearAlgebra.cholesky(
A::AbstractMatrix{T},
::LinearAlgebra.NoPivot = LinearAlgebra.NoPivot();
check::Bool = true,
) where {T <: AbstractTracer}
LinearAlgebra.checksquare(A)
n = size(A, 1)
t = second_order_or(A)
return LinearAlgebra.Cholesky(Fill(t, n, n), 'U', 0)

@adrhill adrhill Jun 23, 2026

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For future reference (either here or a comment in the code):
What are the extra arguments to Cholesky?

@devmotion devmotion Jun 23, 2026 •
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The first argument is the upper or lower-triangular factor, the second argument indicates whether it's the upper ('U') or lower ('L') triangular factor, and the third argument is the BLAS info code (0 indicates success).

end
function LinearAlgebra.cholesky(
A::AbstractMatrix{T},
::LinearAlgebra.RowMaximum;
tol::Real = 0.0,
check::Bool = true,
) where {T <: AbstractTracer}
LinearAlgebra.checksquare(A)
n = size(A, 1)
t = second_order_or(A)
return LinearAlgebra.CholeskyPivoted(Fill(t, n, n), 'U', 1:n, n, tol, 0)

@adrhill adrhill Jun 23, 2026

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For future reference (either here or a comment in the code):
What are the extra arguments to CholeskyPivoted?

@devmotion devmotion Jun 23, 2026

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The first two arguments and the last argument are the same as for Cholesky (factor, type of factor and BLAS info code), the third argument is the pivoting, and the fourth argument the rank.

end

## Inverse
function Base.inv(A::StridedMatrix{T}) where {T <: AbstractTracer}
LinearAlgebra.checksquare(A)
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16 changes: 16 additions & 0 deletions test/test_arrays.jl
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Expand Up @@ -12,6 +12,7 @@ using Test
using LinearAlgebra: Symmetric, Diagonal, diagind
using LinearAlgebra: det, logdet, logabsdet, norm, opnorm
using LinearAlgebra: eigen, eigmax, eigmin
using LinearAlgebra: cholesky, NoPivot, RowMaximum
using LinearAlgebra: inv, pinv, dot
using SparseArrays: sparse, spdiagm

Expand Down Expand Up @@ -697,6 +698,21 @@ end
@test all(t -> sameidx(t, s_out), vectors)
end

@testset "Cholesky" begin
t1 = idx2tracer([1, 3, 4])
t2 = idx2tracer([2, 4])
t3 = idx2tracer([8, 9])
t4 = idx2tracer([8, 9])
A = [t1 t2; t3 t4]
s_out = idx2set([1, 2, 3, 4, 8, 9])
@testset "$pivot" for pivot in (NoPivot(), RowMaximum())
factors = cholesky(A, pivot).factors
@test size(factors) == (2, 2)
@test all(t -> sameidx(t, s_out), factors)
end
@test all(t -> sameidx(t, s_out), cholesky(A).factors)
end

@testset "SparseMatrixCSC construction" begin
t1 = idx2tracer(1)
t2 = idx2tracer(2)
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