From 73ec36f3d8d73b9636c9403954ec6a55b028efe6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?David=20M=C3=BCller-Widmann?=
 <devmotion@users.noreply.github.com>
Date: Wed, 7 Oct 2026 09:35:53 +0200
Subject: [PATCH] Add cheap lu_instance/qr_instance for FixedSizeArrays

Previously `lu_instance` and `qr_instance` fell back to a full
factorization for `FixedSizeMatrix`. The new `FixedSizeArraysExt`
factorizes an empty `similar(A, 0, 0)` instead, which matches the
factorization types for all eltypes (including BigFloat) and pivot modes.

Fixes #510

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 Project.toml              |  6 +++++-
 ext/FixedSizeArraysExt.jl | 15 +++++++++++++++
 test/fixedsizearrays.jl   | 17 +++++++++++++++++
 test/runtests.jl          |  1 +
 4 files changed, 38 insertions(+), 1 deletion(-)
 create mode 100644 ext/FixedSizeArraysExt.jl
 create mode 100644 test/fixedsizearrays.jl

diff --git a/Project.toml b/Project.toml
index 78f60758..2475ad87 100644
--- a/Project.toml
+++ b/Project.toml
@@ -15,6 +15,7 @@ CUDSS = "45b445bb-4962-46a0-9369-b4df9d0f772e"
 ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
+FixedSizeArrays = "3821ddf9-e5b5-40d5-8e25-6813ab96b5e2"
 GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
 Metal = "dde4c033-4e86-420c-a63e-0dd931031962"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
@@ -38,6 +39,7 @@ ArrayInterfaceReverseDiffExt = "ReverseDiff"
 ArrayInterfaceSparseArraysExt = "SparseArrays"
 ArrayInterfaceStaticArraysCoreExt = "StaticArraysCore"
 ArrayInterfaceTrackerExt = "Tracker"
+FixedSizeArraysExt = "FixedSizeArrays"
 
 [compat]
 AMDGPU = "2"
@@ -51,6 +53,7 @@ ChainRulesCore = "1"
 ChainRulesTestUtils = "1"
 ComponentArrays = "0.4.1 - 0"
 FillArrays = "1"
+FixedSizeArrays = "1"
 GPUArraysCore = "0.1, 0.2"
 JLArrays = "0.3"
 LinearAlgebra = "1.10"
@@ -70,6 +73,7 @@ ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
 ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
 ComponentArrays = "b0b7db55-cfe3-40fc-9ded-d10e2dbeff66"
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
+FixedSizeArrays = "3821ddf9-e5b5-40d5-8e25-6813ab96b5e2"
 GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
 JLArrays = "27aeb0d3-9eb9-45fb-866b-73c2ecf80fcb"
 JuliaFormatter = "98e50ef6-434e-11e9-1051-2b60c6c9e899"
@@ -86,4 +90,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 
 [targets]
-test = ["SafeTestsets", "Pkg", "Test", "Aqua", "Random", "SparseArrays", "SuiteSparse", "BandedMatrices", "BlockBandedMatrices", "GPUArraysCore", "JLArrays", "StaticArrays", "Tracker", "ReverseDiff", "ChainRules", "FillArrays", "ComponentArrays", "ChainRulesTestUtils"]
+test = ["SafeTestsets", "Pkg", "Test", "Aqua", "Random", "SparseArrays", "SuiteSparse", "BandedMatrices", "BlockBandedMatrices", "GPUArraysCore", "JLArrays", "StaticArrays", "Tracker", "ReverseDiff", "ChainRules", "FillArrays", "FixedSizeArrays", "ComponentArrays", "ChainRulesTestUtils"]
diff --git a/ext/FixedSizeArraysExt.jl b/ext/FixedSizeArraysExt.jl
new file mode 100644
index 00000000..b0415326
--- /dev/null
+++ b/ext/FixedSizeArraysExt.jl
@@ -0,0 +1,15 @@
+module FixedSizeArraysExt
+
+using ArrayInterface: ArrayInterface
+using FixedSizeArrays: FixedSizeMatrix
+using LinearAlgebra: lu, qr
+
+# Factorizing an empty matrix is cheap and yields exactly the factorization type
+# of `A` (pivot vector types differ across eltypes, e.g. for BigFloat).
+ArrayInterface.lu_instance(A::FixedSizeMatrix) = lu(similar(A, 0, 0), check = false)
+
+function ArrayInterface.qr_instance(A::FixedSizeMatrix, pivot = ArrayInterface.DEFAULT_CHOLESKY_PIVOT)
+    return qr(similar(A, 0, 0), pivot)
+end
+
+end
diff --git a/test/fixedsizearrays.jl b/test/fixedsizearrays.jl
new file mode 100644
index 00000000..c20bf737
--- /dev/null
+++ b/test/fixedsizearrays.jl
@@ -0,0 +1,17 @@
+using ArrayInterface, FixedSizeArrays, LinearAlgebra, Test
+
+@testset "$T" for T in (Float64, Float32, ComplexF64, Int, BigFloat)
+    F = FixedSizeMatrix{T}(T.(rand(1:5, 4, 4)) + 10I)
+
+    luF = ArrayInterface.lu_instance(F)
+    @test luF isa typeof(lu(F, check = false))
+    @test size(luF.factors) == (0, 0)
+
+    qrF = ArrayInterface.qr_instance(F)
+    @test qrF isa typeof(qr(F))
+    @test size(qrF.factors) == (0, 0)
+
+    qrpF = ArrayInterface.qr_instance(F, ColumnNorm())
+    @test qrpF isa typeof(qr(F, ColumnNorm()))
+    @test size(qrpF.factors) == (0, 0)
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index c312622a..0b563c62 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -17,6 +17,7 @@ end
         @time @safetestset "StaticArrays" begin include("staticarrays.jl") end
         @time @safetestset "ChainRules" begin include("chainrules.jl") end
         @time @safetestset "FillArrays" begin include("fillarrays.jl") end
+        @time @safetestset "FixedSizeArrays" begin include("fixedsizearrays.jl") end
     end
 
     if GROUP == "GPU"