Fix reinit! to use keyword argument for b

Changed reinit!(cache, b_new) to reinit!(cache; b = b_new)

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

Co-Authored-By: Claude <[email protected]>

Author: ChrisRackauckas

test/trim/linear_lu.jl

@@ -15,7 +15,7 @@ const cache = init(prob, alg)
 function solve_linear(x)
     # Create a new problem with a modified b vector
     b_new = [x, 2.0 * x]
-    reinit!(cache, b_new)
+    reinit!(cache; b = b_new)
     solve!(cache)
     return cache
 end

test/trim/linear_mkl.jl

@@ -15,7 +15,7 @@ const cache = init(prob, alg)
 function solve_linear(x)
     # Create a new problem with a modified b vector
     b_new = [x, 2.0 * x]
-    reinit!(cache, b_new)
+    reinit!(cache; b = b_new)
     solve!(cache)
     return cache
 end

test/trim/linear_rf.jl

@@ -16,7 +16,7 @@ const cache = init(prob, alg)
 function solve_linear(x)
     # Create a new problem with a modified b vector
     b_new = [x, 2.0 * x]
-    reinit!(cache, b_new)
+    reinit!(cache; b = b_new)
     solve!(cache)
     return cache
 end