From a4ce8de6616429a427850b6634a5c5d43d69e83d Mon Sep 17 00:00:00 2001
From: Qingyu Qu <2283984853@qq.com>
Date: Fri, 25 Apr 2025 17:15:57 +0800
Subject: [PATCH] Default to QR with BandedMatrix{BigFloat}

---
 ext/LinearSolveBandedMatricesExt.jl | 10 ++++++++--
 test/adjoint.jl                     |  4 ++--
 test/banded.jl                      |  6 ++++++
 test/defaults_loading.jl            |  2 +-
 4 files changed, 17 insertions(+), 5 deletions(-)

diff --git a/ext/LinearSolveBandedMatricesExt.jl b/ext/LinearSolveBandedMatricesExt.jl
index 3941b0864..deb85e25a 100644
--- a/ext/LinearSolveBandedMatricesExt.jl
+++ b/ext/LinearSolveBandedMatricesExt.jl
@@ -16,6 +16,11 @@ function defaultalg(A::BandedMatrix, b, oa::OperatorAssumptions{Bool})
     end
 end
 
+function defaultalg(
+        A::BandedMatrix{T}, b, oa::OperatorAssumptions{Bool}) where {T <: BigFloat}
+    return DefaultLinearSolver(DefaultAlgorithmChoice.QRFactorization)
+end
+
 function defaultalg(A::Symmetric{<:Number, <:BandedMatrix}, b, ::OperatorAssumptions{Bool})
     return DefaultLinearSolver(DefaultAlgorithmChoice.CholeskyFactorization)
 end
@@ -42,8 +47,9 @@ for alg in (:SVDFactorization, :MKLLUFactorization, :DiagonalFactorization,
     end
 end
 
-function init_cacheval(::LUFactorization, A::BandedMatrix, b, u, Pl, Pr, maxiters::Int,
-        abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
+function init_cacheval(::LUFactorization, A::BandedMatrix{T}, b, u, Pl, Pr, maxiters::Int,
+        abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions) where {T}
+    (T <: BigFloat) && return qr(similar(A, 0, 0))
     return lu(similar(A, 0, 0))
 end
 
diff --git a/test/adjoint.jl b/test/adjoint.jl
index b31c447e8..8fd9e163c 100644
--- a/test/adjoint.jl
+++ b/test/adjoint.jl
@@ -45,8 +45,8 @@ db12 = ForwardDiff.gradient(x -> f(eltype(x).(A), x), copy(b1))
 @test db1 ≈ db12
 
 # Test complex numbers
-A = rand(n, n) + 1im*rand(n, n);
-b1 = rand(n) + 1im*rand(n);
+A = rand(n, n) + 1im * rand(n, n);
+b1 = rand(n) + 1im * rand(n);
 
 function f3(A, b1, b2; alg = KrylovJL_GMRES())
     prob = LinearProblem(A, b1)
diff --git a/test/banded.jl b/test/banded.jl
index 89c104966..0c61905eb 100644
--- a/test/banded.jl
+++ b/test/banded.jl
@@ -52,3 +52,9 @@ A = AlmostBandedMatrix(BandedMatrix(fill(2.0, n + 2, n), (1, 1)), fill(3.0, 2, n
 A[band(0)] .+= 1:n
 
 @test_nowarn solve(LinearProblem(A, b))
+
+# Workaround for no lu from BandedMatrices
+A = BandedMatrix{BigFloat}(ones(3, 3), (0, 0))
+b = BigFloat[1, 2, 3]
+prob = LinearProblem(A, b)
+@test_nowarn solve(prob)
diff --git a/test/defaults_loading.jl b/test/defaults_loading.jl
index a7b456f41..a7c54f934 100644
--- a/test/defaults_loading.jl
+++ b/test/defaults_loading.jl
@@ -31,4 +31,4 @@ prob = LinearProblem(mat, rhs)
 
 using Sparspak
 sol = solve(prob).u
-@test sol isa Vector{BigFloat}
\ No newline at end of file
+@test sol isa Vector{BigFloat}