Revert error throwing to return nothing for default algorithm support

The init_cacheval methods need to return nothing when concretization
is not supported, so that the default algorithm selection can fall
back to other methods like Krylov solvers.

Author: claude

ext/LinearSolveSparseArraysExt.jl

@@ -4,7 +4,7 @@ using LinearSolve: LinearSolve, BLASELTYPES, pattern_changed, ArrayInterface,
                    @get_cacheval, CHOLMODFactorization, GenericFactorization,
                    GenericLUFactorization,
                    KLUFactorization, LUFactorization, NormalCholeskyFactorization,
-                   OperatorAssumptions, LinearVerbosity, RequiresConcreteMatrixError,
+                   OperatorAssumptions, LinearVerbosity,
                    QRFactorization, RFLUFactorization, UMFPACKFactorization, solve
 using SciMLOperators: AbstractSciMLOperator, has_concretization
 using ArrayInterface: ArrayInterface
@@ -284,7 +284,7 @@ function LinearSolve.init_cacheval(
         return LinearSolve.init_cacheval(alg, convert(AbstractMatrix, A), b, u, Pl, Pr,
             maxiters, abstol, reltol, verbose, assumptions)
     else
-        throw(RequiresConcreteMatrixError("KLUFactorization"))
+        nothing
     end
 end
 
@@ -296,7 +296,7 @@ function LinearSolve.init_cacheval(
         return LinearSolve.init_cacheval(alg, convert(AbstractMatrix, A), b, u, Pl, Pr,
             maxiters, abstol, reltol, verbose, assumptions)
     else
-        throw(RequiresConcreteMatrixError("UMFPACKFactorization"))
+        nothing
     end
 end
 
@@ -308,7 +308,7 @@ function LinearSolve.init_cacheval(
         return LinearSolve.init_cacheval(alg, convert(AbstractMatrix, A), b, u, Pl, Pr,
             maxiters, abstol, reltol, verbose, assumptions)
     else
-        throw(RequiresConcreteMatrixError("LUFactorization"))
+        nothing
     end
 end
 
@@ -320,7 +320,7 @@ function LinearSolve.init_cacheval(
         return LinearSolve.init_cacheval(alg, convert(AbstractMatrix, A), b, u, Pl, Pr,
             maxiters, abstol, reltol, verbose, assumptions)
     else
-        throw(RequiresConcreteMatrixError("CHOLMODFactorization"))
+        nothing
     end
 end
 
@@ -332,7 +332,7 @@ function LinearSolve.init_cacheval(
         return LinearSolve.init_cacheval(alg, convert(AbstractMatrix, A), b, u, Pl, Pr,
             maxiters, abstol, reltol, verbose, assumptions)
     else
-        throw(RequiresConcreteMatrixError("GenericFactorization"))
+        nothing
     end
 end
 
@@ -344,7 +344,7 @@ function LinearSolve.init_cacheval(
         return LinearSolve.init_cacheval(alg, convert(AbstractMatrix, A), b, u, Pl, Pr,
             maxiters, abstol, reltol, verbose, assumptions)
     else
-        throw(RequiresConcreteMatrixError("GenericLUFactorization"))
+        nothing
     end
 end
 
@@ -356,7 +356,7 @@ function LinearSolve.init_cacheval(
         return LinearSolve.init_cacheval(alg, convert(AbstractMatrix, A), b, u, Pl, Pr,
             maxiters, abstol, reltol, verbose, assumptions)
     else
-        throw(RequiresConcreteMatrixError("QRFactorization"))
+        nothing
     end
 end
 
@@ -368,7 +368,7 @@ function LinearSolve.init_cacheval(
         return LinearSolve.init_cacheval(alg, convert(AbstractMatrix, A), b, u, Pl, Pr,
             maxiters, abstol, reltol, verbose, assumptions)
     else
-        throw(RequiresConcreteMatrixError("NormalCholeskyFactorization"))
+        nothing
     end
 end
 

src/LinearSolve.jl

@@ -230,30 +230,6 @@ for integrating custom algorithms or simple solve strategies.
 """
 abstract type AbstractSolveFunction <: SciMLLinearSolveAlgorithm end
 
-# Errors
-
-"""
-    RequiresConcreteMatrixError(alg::String)
-
-Error thrown when a factorization algorithm that requires a concrete matrix
-receives an operator that does not support concretization (i.e., `has_concretization(A)` returns `false`).
-
-## Example
-
-```julia
-throw(RequiresConcreteMatrixError("KLUFactorization"))
-```
-
-This error suggests using a Krylov method instead, which can work with abstract operators.
-"""
-struct RequiresConcreteMatrixError <: Exception
-    alg::String
-end
-
-function Base.showerror(io::IO, e::RequiresConcreteMatrixError)
-    print(io, "$(e.alg) requires a concrete matrix. The provided operator does not support concretization. Use a Krylov method instead.")
-end
-
 # Traits
 
 """
@@ -543,8 +519,6 @@ export MetalOffload32MixedLUFactorization
 
 export OperatorAssumptions, OperatorCondition
 
-export RequiresConcreteMatrixError
-
 export LinearSolveAdjoint
 
 export LinearVerbosity