diff --git a/9_reduced_DOF/time_integrator.py b/9_reduced_DOF/time_integrator.py
index 29f423b..e94ce1b 100644
--- a/9_reduced_DOF/time_integrator.py
+++ b/9_reduced_DOF/time_integrator.py
@@ -56,6 +56,7 @@ def IP_hess(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, h):
     H = sparse.coo_matrix((IJV[2], (IJV[0], IJV[1])), shape=(len(x) * 2, len(x) * 2)).tocsr()
     return H
 
+# ANCHOR: search_dir
 def search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, is_DBC, reduced_basis, h):
     projected_hess = IP_hess(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, h)
     reshaped_grad = IP_grad(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, h).reshape(len(x) * 2, 1)
@@ -68,4 +69,5 @@ def search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area,
             reshaped_grad[i * 2] = reshaped_grad[i * 2 + 1] = 0.0
     reduced_hess = reduced_basis.T.dot(projected_hess.dot(reduced_basis)) # applying chain rule
     reduced_grad = reduced_basis.T.dot(reshaped_grad) # applying chain rule
-    return (reduced_basis.dot(spsolve(reduced_hess, -reduced_grad))).reshape(len(x), 2) # transform to full space after the solve
\ No newline at end of file
+    return (reduced_basis.dot(spsolve(reduced_hess, -reduced_grad))).reshape(len(x), 2) # transform to full space after the solve
+# ANCHOR_END: search_dir
\ No newline at end of file
diff --git a/9_reduced_DOF/utils.py b/9_reduced_DOF/utils.py
index 7cc69d4..0259442 100644
--- a/9_reduced_DOF/utils.py
+++ b/9_reduced_DOF/utils.py
@@ -50,6 +50,7 @@ def compute_abd_anchor_basis(x):
             basis[i * 2 + d][d * 3 + 2] = anchors[i][1]
     return basis
 
+# ANCHOR: compute_reduced_basis
 def compute_reduced_basis(x, e, vol, IB, mu_lame, lam, method, order):
     if method == 0: # full basis, no reduction
         basis = np.zeros((len(x) * 2, len(x) * 2))
@@ -99,4 +100,5 @@ def compute_reduced_basis(x, e, vol, IB, mu_lame, lam, method, order):
         IJV = NeoHookeanEnergy.hess(x, e, vol, IB, mu_lame, lam, project_PSD=False)
         H = sparse.coo_matrix((IJV[2], (IJV[0], IJV[1])), shape=(len(x) * 2, len(x) * 2)).tocsr()
         eigenvalues, eigenvectors = eigsh(H, k=order, which='SM') # get 'order' eigenvectors with smallest eigenvalues 
-        return eigenvectors
\ No newline at end of file
+        return eigenvectors
+# ANCHOR_END: compute_reduced_basis
\ No newline at end of file