Fix type inference issue in LinearCache initialization with LinearVerbosity

This commit resolves a type stability issue in the `init` function where
the compiler could not infer a concrete type for the `LinearVerbosity`
parameter in `LinearCache`, causing `@inferred` tests to fail.

Changes:
- Added `Base.@constprop :aggressive` to `__init` function to enable
  aggressive constant propagation for better type inference
- Refactored verbose parameter processing into type-stable helper methods
  `_process_verbose` that use method dispatch
- Made `LinearVerbosity(Standard())` constructor explicit with concrete
  argument types instead of calling `LinearVerbosity()`
- Added `@inline` annotation to preset constructor for better optimization

The fix ensures that when `verbose=true` (the default), the compiler can
determine the concrete `LinearVerbosity` type at compile time, eliminating
the type instability that caused the test failure.

Fixes the CI error:
```
return type LinearCache{..., LinearVerbosity{...}, ...} does not match
inferred return type LinearCache{..., _A<:LinearVerbosity, ...}
```

All tests pass with this change.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

Author: ChrisRackauckas

src/common.jl

@@ -232,6 +232,28 @@ default_alias_b(::AbstractSparseFactorization, ::Any, ::Any) = true
 
 DEFAULT_PRECS(A, p) = IdentityOperator(size(A)[1]), IdentityOperator(size(A)[2])
 
+# Helper functions for type-stable verbose conversion
+@inline function _process_verbose(verbose::Bool)
+    # Type-stable processing of boolean verbose parameter
+    if verbose
+        verbose_spec = LinearVerbosity(SciMLLogging.Standard())
+        init_cache_verb = verbose
+    else
+        verbose_spec = LinearVerbosity(SciMLLogging.None())
+        init_cache_verb = verbose
+    end
+    return verbose_spec, init_cache_verb
+end
+
+@inline function _process_verbose(verbose::SciMLLogging.AbstractVerbosityPreset)
+    verbose_spec = LinearVerbosity(verbose)
+    return verbose_spec, verbose_spec
+end
+
+@inline function _process_verbose(verbose::LinearVerbosity)
+    return verbose, verbose
+end
+
 """
     __init_u0_from_Ab(A, b)
 
@@ -261,7 +283,7 @@ function SciMLBase.init(prob::LinearProblem, alg::SciMLLinearSolveAlgorithm, arg
     __init(prob, alg, args...; kwargs...)
 end
 
-function __init(prob::LinearProblem, alg::SciMLLinearSolveAlgorithm,
+Base.@constprop :aggressive function __init(prob::LinearProblem, alg::SciMLLinearSolveAlgorithm,
         args...;
         alias = LinearAliasSpecifier(),
         abstol = default_tol(real(eltype(prob.b))),
@@ -324,22 +346,9 @@ function __init(prob::LinearProblem, alg::SciMLLinearSolveAlgorithm,
         copy(A)
     end
 
-    if verbose isa Bool
-        # @warn "Using `true` or `false` for `verbose` is being deprecated. Please use a `LinearVerbosity` type to specify verbosity settings.
-        # For details see the verbosity section of the common solver options documentation page."
-        init_cache_verb = verbose
-        if verbose 
-            verbose_spec = LinearVerbosity()
-        else
-            verbose_spec = LinearVerbosity(SciMLLogging.None())
-        end
-    elseif verbose isa SciMLLogging.AbstractVerbosityPreset
-        verbose_spec = LinearVerbosity(verbose)
-        init_cache_verb = verbose_spec
-    else
-        verbose_spec = verbose
-        init_cache_verb = verbose_spec
-    end
+    # @warn "Using `true` or `false` for `verbose` is being deprecated. Please use a `LinearVerbosity` type to specify verbosity settings.
+    # For details see the verbosity section of the common solver options documentation page."
+    verbose_spec, init_cache_verb = _process_verbose(verbose)
 
     b = if issparsematrix(b) && !(A isa Diagonal)
         Array(b) # the solution to a linear solve will always be dense!

src/verbosity.jl

@@ -159,7 +159,7 @@ end
 # Constructor for verbosity presets following the hierarchical levels:
 # None < Minimal < Standard < Detailed < All
 # Each level includes all messages from levels below it plus additional ones
-function LinearVerbosity(verbose::AbstractVerbosityPreset)
+@inline function LinearVerbosity(verbose::AbstractVerbosityPreset)
     if verbose isa Minimal
         # Minimal: Only fatal errors and critical warnings (BLAS errors/invalid args)
         LinearVerbosity(
@@ -182,7 +182,23 @@ function LinearVerbosity(verbose::AbstractVerbosityPreset)
         )
     elseif verbose isa Standard
         # Standard: Everything from Minimal + non-fatal warnings
-        LinearVerbosity()
+        LinearVerbosity(
+            Silent(),
+            Silent(),
+            Silent(),
+            Silent(),
+            CustomLevel(1), # WARN_LEVEL in KrylovKit.jl
+            Silent(),
+            InfoLevel(),
+            Silent(),
+            ErrorLevel(),
+            ErrorLevel(),
+            Silent(),
+            Silent(),
+            Silent(),
+            WarnLevel(),
+            WarnLevel(),
+            WarnLevel())
     elseif verbose isa Detailed
         # Detailed: Everything from Standard + debugging/solver behavior
         LinearVerbosity(