Revert "refactor: use Symbolics.semilinear_form for LinearProblem codegen"

This reverts commit 2aba391.

Author: AayushSabharwal

src/systems/codegen.jl

@@ -1150,15 +1150,35 @@ Return matrix `A` and vector `b` such that the system `sys` can be represented a
 - `sparse`: return a sparse `A`.
 """
 function calculate_A_b(sys::System; sparse = false)
-    rhss = [-eq.rhs for eq in full_equations(sys)]
+    rhss = [eq.rhs for eq in full_equations(sys)]
     dvs = unknowns(sys)
 
-    A, b = semilinear_form(rhss, dvs)
-    if !sparse
-        A = collect(A)
+    A = Matrix{Any}(undef, length(rhss), length(dvs))
+    b = Vector{Any}(undef, length(rhss))
+    for (i, rhs) in enumerate(rhss)
+        # mtkcompile makes this `0 ~ rhs` which typically ends up giving
+        # unknowns negative coefficients. If given the equations `A * x ~ b`
+        # it will simplify to `0 ~ b - A * x`. Thus this negation usually leads
+        # to more comprehensible user API.
+        resid = -rhs
+        for (j, var) in enumerate(dvs)
+            p, q, islinear = Symbolics.linear_expansion(resid, var)
+            if !islinear
+                throw(ArgumentError("System is not linear. Equation $((0 ~ rhs)) is not linear in unknown $var."))
+            end
+            A[i, j] = p
+            resid = q
+        end
+        # negate beucause `resid` is the residual on the LHS
+        b[i] = -resid
+    end
+
+    @assert all(Base.Fix1(isassigned, A), eachindex(A))
+    @assert all(Base.Fix1(isassigned, A), eachindex(b))
+
+    if sparse
+        A = SparseArrays.sparse(A)
     end
-    A = unwrap.(A)
-    b = unwrap.(-b)
     return A, b
 end