fix(Rosenbrock): extract DAE fields into typed function for inference stability

The if mass_matrix === I branch in HybridExplicitImplicitRK alg_cache
caused type instability. Extract into _build_dae_fields with explicit
return type annotation to create a type stability barrier.

Fixes @inferred solve(prob, Tsit5DA()) failure.

Author: Harsh Singh

lib/OrdinaryDiffEqRosenbrock/src/rosenbrock_caches.jl

@@ -365,27 +365,11 @@ function alg_cache(
         verbose = verbose.linear_verbosity
     )
 
-    # Detect algebraic variables from mass matrix
-    mass_matrix = f.mass_matrix
-    if mass_matrix === I
-        diff_vars = collect(1:length(u))
-        alg_vars = Int[]
-        g_z = zeros(eltype(u), 0, 0)
-        g_y = zeros(eltype(u), 0, 0)
-        W_z = zeros(eltype(u), 0, 0)
-        linsolve_tmp_z = zeros(eltype(u), 0)
-        linsolve_z = nothing
-    else
-        n = length(u)
-        diff_vars = findall(i -> mass_matrix[i, i] != 0, 1:n)
-        alg_vars = findall(i -> mass_matrix[i, i] == 0, 1:n)
-        n_g = length(alg_vars)
-        n_f = length(diff_vars)
-        g_z = zeros(eltype(u), n_g, n_g)
-        g_y = zeros(eltype(u), n_g, n_f)
-        W_z = zeros(eltype(u), n_g, n_g)
-        linsolve_tmp_z = zeros(eltype(u), n_g)
-    end
+    # Detect algebraic variables from mass matrix and build DAE workspace.
+    # Wrapped in a function call to create a type stability barrier —
+    # the concrete cache type must not depend on the mass_matrix branch.
+    diff_vars, alg_vars, g_z, g_y, W_z, linsolve_tmp_z = _build_dae_fields(
+        f.mass_matrix, u)
 
     return HybridExplicitImplicitCache(
         u, uprev, dense, du, du1, du2, ks,
@@ -395,3 +379,21 @@ function alg_cache(
         diff_vars, alg_vars, g_z, g_y, W_z, linsolve_tmp_z
     )
 end
+
+function _build_dae_fields(
+        mass_matrix, u
+    )::Tuple{Vector{Int}, Vector{Int}, Matrix{eltype(u)}, Matrix{eltype(u)}, Matrix{eltype(u)}, Vector{eltype(u)}}
+    T = eltype(u)
+    n = length(u)
+    if mass_matrix === I
+        diff_vars = collect(1:n)
+        alg_vars = Int[]
+    else
+        diff_vars = findall(i -> mass_matrix[i, i] != 0, 1:n)
+        alg_vars = findall(i -> mass_matrix[i, i] == 0, 1:n)
+    end
+    n_g = length(alg_vars)
+    n_f = length(diff_vars)
+    return diff_vars, alg_vars, zeros(T, n_g, n_g), zeros(T, n_g, n_f),
+        zeros(T, n_g, n_g), zeros(T, n_g)
+end