diff --git a/lib/ODEProblemLibrary/src/ODEProblemLibrary.jl b/lib/ODEProblemLibrary/src/ODEProblemLibrary.jl
index cc671e2..6a9e2fd 100644
--- a/lib/ODEProblemLibrary/src/ODEProblemLibrary.jl
+++ b/lib/ODEProblemLibrary/src/ODEProblemLibrary.jl
@@ -1,7 +1,8 @@
 module ODEProblemLibrary
 
 using DiffEqBase: DiffEqBase, ODEFunction, ODEProblem
-using LinearAlgebra: LinearAlgebra, Diagonal, I, SymTridiagonal, diagind, ldiv!, mul!, rmul!
+using LinearAlgebra: LinearAlgebra, Diagonal, I, SymTridiagonal, diagind, ldiv!, lmul!, mul!,
+    rmul!
 using Random: Random
 
 Random.seed!(100)
diff --git a/lib/ODEProblemLibrary/src/filament_prob.jl b/lib/ODEProblemLibrary/src/filament_prob.jl
index 04bd2fd..60bb243 100644
--- a/lib/ODEProblemLibrary/src/filament_prob.jl
+++ b/lib/ODEProblemLibrary/src/filament_prob.jl
@@ -227,13 +227,13 @@ function projection!(f::FilamentCache)
     mul!(J_JT, J, J')
     LDLt_inplace!(J_JT_LDLT, J_JT)
     ldiv!(P0, J_JT_LDLT, J)
-    mul!(P', P0, J)
+    mul!(P, P0', J)
     subtract_from_identity!(P)
     return nothing
 end
 
 function subtract_from_identity!(A)
-    rmul!(-1, A)
+    lmul!(-1, A)
     @inbounds for i in 1:size(A, 1)
         A[i, i] += 1
     end
diff --git a/lib/ODEProblemLibrary/test/filament.jl b/lib/ODEProblemLibrary/test/filament.jl
new file mode 100644
index 0000000..0801021
--- /dev/null
+++ b/lib/ODEProblemLibrary/test/filament.jl
@@ -0,0 +1,34 @@
+using ODEProblemLibrary, LinearAlgebra, Test
+
+# The right hand side is dr = P(r) * (A * r + F(t)), where P projects onto the
+# tangent space of the inextensibility constraints, so every squared segment
+# length must have zero rate of change for any state and any time.
+function max_segment_rate(prob, N, u, t)
+    du = similar(u)
+    prob.f(du, u, prob.p, t)
+    R, dR = reshape(u, 3, N + 1), reshape(du, 3, N + 1)
+    rate = maximum(
+        abs(2 * dot(R[:, i + 1] - R[:, i], dR[:, i + 1] - dR[:, i])) for i in 1:N
+    )
+    return rate / max(1.0, maximum(abs, du)), du
+end
+
+@testset "prob_ode_filament" begin
+    prob = prob_ode_filament
+    N = length(prob.u0) ÷ 3 - 1
+    @test length(prob.u0) == 3 * (N + 1)
+
+    for (u, t) in (
+            (copy(prob.u0), 0.0),
+            (copy(prob.u0), 0.013),
+            (prob.u0 .+ 0.01 .* sinpi.(range(0, 2, length = length(prob.u0))), 0.013),
+        )
+        rate, du = max_segment_rate(prob, N, u, t)
+        @test all(isfinite, du)
+        @test rate < 1.0e-10
+    end
+
+    J = zeros(length(prob.u0), length(prob.u0))
+    prob.f.jac(J, prob.u0, prob.p, 0.0)
+    @test all(isfinite, J)
+end
diff --git a/lib/ODEProblemLibrary/test/runtests.jl b/lib/ODEProblemLibrary/test/runtests.jl
index 8b9c556..e28caec 100644
--- a/lib/ODEProblemLibrary/test/runtests.jl
+++ b/lib/ODEProblemLibrary/test/runtests.jl
@@ -15,6 +15,7 @@ if TEST_GROUP == "Core" || TEST_GROUP == "All"
     @time @testset "Load Tests" begin
         @test ODEProblemLibrary isa Module
     end
+    @time @safetestset "Filament" include("filament.jl")
 end
 
 # Quality assurance: no undefined exports, stale dependencies, etc.