Add support for almost banded matrix

Author: avik-pal

Project.toml

@@ -1,7 +1,7 @@
 name = "LinearSolve"
 uuid = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 authors = ["SciML"]
-version = "2.19.0"
+version = "2.20.0"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
@@ -34,6 +34,7 @@ BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 BlockDiagonals = "0a1fb500-61f7-11e9-3c65-f5ef3456f9f0"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+FastAlmostBandedMatrices = "9d29842c-ecb8-4973-b1e9-a27b1157504e"
 HYPRE = "b5ffcf37-a2bd-41ab-a3da-4bd9bc8ad771"
 IterativeSolvers = "42fd0dbc-a981-5370-80f2-aaf504508153"
 KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
@@ -54,6 +55,7 @@ LinearSolveKrylovKitExt = "KrylovKit"
 LinearSolveMetalExt = "Metal"
 LinearSolvePardisoExt = "Pardiso"
 LinearSolveRecursiveArrayToolsExt = "RecursiveArrayTools"
+LinearSolveFastAlmostBandedMatricesExt = ["FastAlmostBandedMatrices"]
 
 [compat]
 ArrayInterface = "7.4.11"
@@ -92,6 +94,7 @@ julia = "1.9"
 BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 BlockDiagonals = "0a1fb500-61f7-11e9-3c65-f5ef3456f9f0"
 Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+FastAlmostBandedMatrices = "9d29842c-ecb8-4973-b1e9-a27b1157504e"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 HYPRE = "b5ffcf37-a2bd-41ab-a3da-4bd9bc8ad771"

ext/LinearSolveFastAlmostBandedMatricesExt.jl

@@ -0,0 +1,33 @@
+module LinearSolveFastAlmostBandedMatricesExt
+
+using FastAlmostBandedMatrices, LinearAlgebra, LinearSolve
+import LinearSolve: defaultalg,
+    do_factorization, init_cacheval, DefaultLinearSolver, DefaultAlgorithmChoice
+
+function defaultalg(A::AlmostBandedMatrix, b, oa::OperatorAssumptions)
+    if oa.issq
+        return DefaultLinearSolver(DefaultAlgorithmChoice.DirectLdiv!)
+    else
+        return DefaultLinearSolver(DefaultAlgorithmChoice.QRFactorization)
+    end
+end
+
+# For BandedMatrix
+for alg in (:SVDFactorization, :MKLLUFactorization, :DiagonalFactorization,
+    :SparspakFactorization, :KLUFactorization, :UMFPACKFactorization,
+    :GenericLUFactorization, :RFLUFactorization, :BunchKaufmanFactorization,
+    :CHOLMODFactorization, :NormalCholeskyFactorization, :LDLtFactorization,
+    :AppleAccelerateLUFactorization, :CholeskyFactorization, :LUFactorization)
+    @eval begin
+        function init_cacheval(::$(alg), ::AlmostBandedMatrix, b, u, Pl, Pr, maxiters::Int,
+                abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
+            return nothing
+        end
+    end
+end
+
+function do_factorization(alg::QRFactorization, A::AlmostBandedMatrix, b, u)
+    return alg.inplace ? qr!(A) : qr(A)
+end
+
+end